├── docs ├── static │ ├── mapi │ │ ├── test.txt │ │ ├── TiO2_energy.txt │ │ ├── 24972.txt │ │ └── Fe2O3.txt │ └── js │ │ └── mathjax.js ├── CNAME ├── img │ ├── favicon.ico │ └── phase-diagram │ │ ├── Li-Fe-O_exp.png │ │ ├── Li-Fe-O_700K.png │ │ ├── Fe-P_calculated.png │ │ └── Li-Fe-O_calculated.png ├── user-guide │ ├── img │ │ ├── .DS_Store │ │ ├── nanoporous │ │ │ ├── MOF.png │ │ │ ├── XRD.png │ │ │ ├── Explorer.png │ │ │ └── Zeolite.png │ │ ├── battery │ │ │ └── battery_Muoscale.gif │ │ ├── pourbaix-app │ │ │ ├── Fe_pourbaix.png │ │ │ ├── FeCr_pourbaix.png │ │ │ ├── Fe_Lines_marked.png │ │ │ ├── Ion_ref_energy.png │ │ │ └── Fe2O3_stability_map.png │ │ ├── materials-explorer │ │ │ ├── by_ids.png │ │ │ ├── by_formula.png │ │ │ ├── by_mpquery.png │ │ │ ├── by_elements.png │ │ │ ├── by_structure.png │ │ │ └── by_elements_results.png │ │ ├── structure-predictor │ │ │ ├── convex-hull.png │ │ │ ├── ions-correlation.png │ │ │ ├── substitution-example.png │ │ │ └── substitution-flowchart.png │ │ ├── molecules-explorer │ │ │ └── free_energy_cycle.png │ │ ├── error-checking │ │ │ ├── Vol_change_hist_sep_23_2011.png │ │ │ ├── Vol_change_hist_sep_23_2011_fitted.png │ │ │ └── Vol_change_hist_sep_23_2011_fitted_cdf.png │ │ └── interface-reactions │ │ │ ├── plot_LiCoO2-Li3PS4_open_MP_release.png │ │ │ ├── plot_LiCoO2-Li3PS4_close_MP_release.png │ │ │ ├── table_LiCoO2-Li3PS4_close_MP_release.png │ │ │ └── table_LiCoO2-Li3PS4_open_MP_release.png │ ├── crystal-toolkit.md │ ├── share-your-story.md │ ├── xray-absorption-spectra.md │ ├── deprecations.md │ ├── molecular_terms.md │ ├── xas-matcher.md │ ├── materials-explorer.md │ ├── mpcomplete.md │ ├── developers-area.md │ ├── molecules-explorer.md │ ├── reaction-calculator.md │ ├── glossary-of-terms.md │ ├── rfb_dashboard.md │ ├── batteries-explorer.md │ ├── structure-similarity.md │ ├── structure-predictor.md │ ├── pourbaix-tool.md │ └── interface-reactions.md ├── methodology │ ├── img │ │ ├── calculations-manual │ │ │ ├── Gaps.png │ │ │ └── FormE_errors.png │ │ ├── piezoelectricity │ │ │ ├── Ortho_1.png │ │ │ ├── Cubic_pic1.png │ │ │ ├── Piezomain.png │ │ │ └── Piezo_wiki_fig.png │ │ ├── elasticity │ │ │ └── Data_figure_11_22.png │ │ ├── equations-of-state │ │ │ └── EOS_eqtable.png │ │ └── dielectricity │ │ │ └── Dielectric_benchmarking.png │ ├── static │ │ └── KtablesBinaries.txt │ ├── equations-of-state.md │ ├── phonons.md │ ├── electronic-structure.md │ ├── elasticity-prediction.md │ ├── gga-plus-u.md │ ├── piezoelectricity.md │ ├── dielectricity.md │ └── total-energies.md ├── index.md ├── contrib │ └── spec │ │ └── newsfeed.md ├── database-updates.md └── error-checking.md ├── .gitignore ├── requirements.txt ├── .github ├── dependabot.yml └── workflows │ └── test.yml ├── README.md ├── .pre-commit-config.yaml ├── .markdownlint.yaml ├── LICENSE └── mkdocs.yml /docs/static/mapi/test.txt: -------------------------------------------------------------------------------- 1 | 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package-ecosystem: "github-actions" 8 | directory: "/" 9 | schedule: 10 | interval: "weekly" 11 | -------------------------------------------------------------------------------- /docs/user-guide/crystal-toolkit.md: -------------------------------------------------------------------------------- 1 | # Crystal Toolkit 2 | 3 | **New for 2019!** Crystal Toolkit is receiving an update, stay tuned... 4 | 5 | Crystal Toolkit is an app that allows one to load, analyze, transformation crystal structures, and optionally submit them to our database using [MPComplete](mpcomplete.md). 6 | -------------------------------------------------------------------------------- /docs/static/js/mathjax.js: -------------------------------------------------------------------------------- 1 | window.MathJax = { 2 | tex: { 3 | //inlineMath: [["\\(", "\\)"]], 4 | //displayMath: [["\\[", "\\]"]], 5 | processEscapes: true, 6 | processEnvironments: true, 7 | }, 8 | options: { 9 | ignoreHtmlClass: ".*|", 10 | processHtmlClass: "arithmatex", 11 | }, 12 | }; 13 | 14 | document$.subscribe(() => { 15 | MathJax.typesetPromise(); 16 | }); 17 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Materials Project Documentation 2 | 3 | This repository holds an archive of an older version of the Materials Project documentation, generated 4 | using the mkdocs system. The Materials Project has since transitioned to a new documentation system 5 | using GitBook. Please read the current documentation here: [https://docs.materialsproject.org](https://docs.materialsproject.org). 6 | 7 | Thank you to everyone who contributed to this version of the documentation! 8 | -------------------------------------------------------------------------------- /.pre-commit-config.yaml: -------------------------------------------------------------------------------- 1 | repos: 2 | - repo: https://github.com/pre-commit/pre-commit-hooks 3 | rev: v2.3.0 4 | hooks: 5 | - id: check-yaml 6 | - id: end-of-file-fixer 7 | - id: trailing-whitespace 8 | - id: flake8 9 | - repo: https://github.com/ambv/black 10 | rev: 21.11b1 11 | hooks: 12 | - id: black 13 | - repo: https://github.com/pre-commit/mirrors-prettier 14 | rev: v2.5.0 15 | hooks: 16 | - id: prettier 17 | -------------------------------------------------------------------------------- /.markdownlint.yaml: -------------------------------------------------------------------------------- 1 | ############### 2 | # Rules by id # 3 | ############### 4 | MD004: false # Unordered list style 5 | MD007: 6 | indent: 2 # Unordered list indentation 7 | MD013: 8 | line_length: 400 # Line length 80 is far to short 9 | MD026: 10 | punctuation: ".,;:!。，；:" # List of not allowed 11 | MD029: false # Ordered list item prefix 12 | MD033: false # Allow inline HTML 13 | MD036: false # Emphasis used instead of a heading 14 | 15 | ################# 16 | # Rules by tags # 17 | ################# 18 | blank_lines: false # Error on blank lines 19 | -------------------------------------------------------------------------------- /docs/user-guide/share-your-story.md: -------------------------------------------------------------------------------- 1 | # Share Your Story 2 | 3 | Data from the Materials Project has been used by researchers all over the world. We keep track of papers that cite the Materials Project and its work at the following page: 4 | 5 | 6 | 7 | If you would like to see your paper added to that page, or if you'd like to share with us a story about how you use Materials Project, please let us know: 8 | 9 | feedback@materialsproject.org 10 | 11 | We are looking to feature user stories in future on the Materials Project website to showcase interesting work coming from the community. 12 | -------------------------------------------------------------------------------- /docs/index.md: -------------------------------------------------------------------------------- 1 | # Materials Project Documentation 2 | 3 | !!! warning 4 | Migration of content from our old wiki ([https://www.materialsproject.org/wiki](https://www.materialsproject.org/wiki)) is underway. Until this notice is removed, there might still be inconsistencies. 5 | 6 | This is a place for all documentation relating to the 7 | [Materials Project](https://materialsproject.org) (MP), encompassing: 8 | 9 | - Foundation: concepts in materials and computer science we use to structure 10 | and interpret our data sets 11 | - Methodology: how we generate and validate our computed data sets 12 | - User Guide: materials analysis and design using our data and tools 13 | - User Reference: Detailed help for using our website, 14 | application programming interface (API), and codebases. 15 | - Contribution: Developer guides and design specifications 16 | 17 | If you notice an error or omission, please post an [issue](https://github.com/materialsproject/docs/issues/new) or click a pencil icon 18 | (edit) on a page to suggest an 19 | edit to us. 20 | 21 | Thanks, 22 | Materials Project Team 23 | -------------------------------------------------------------------------------- /docs/user-guide/xray-absorption-spectra.md: -------------------------------------------------------------------------------- 1 | # X-Ray Absorption Spectra 2 | 3 | ## Methodology 4 | 5 | All the spectra (only K-edge XANES currently) were computed using the [FEFF](http://leonardo.phys.washington.edu/index-feffproject.html) code. For each structure, spectra were computed with each symmetrically unique site 6 | in the structure as the absorbing site. The workflow used for the calculations can be found in the open source comprehensive materials science 7 | workflow package, [Atomate](https://github.com/hackingmaterials/atomate) [^1] in the atomate.feff namespace. The package leverages [Pymatgen](https://github.com/materialsproject/pymatgen) and 8 | [Fireworks](https://github.com/materialsproject/fireworks) packages for the generation of the input/output files for the calculations and for the workflow 9 | execution management respectively. 10 | 11 | These results are intended to be semi-quantitative in that corrections, such as edge shifts and Debye-Waller damping, have not been included. 12 | 13 | ## Presentation of Spectra 14 | 15 | The computed absorption coefficient for an element in the given structure is set to the absorption coefficient averaged over all the sites in the structure with that element. 16 | 17 | See MP's database builder repository [Emmet](https://github.com/materialsproject/emmet) (emmet.feff.builders.xas module) for details. 18 | 19 | ## References 20 | 21 | [^1]: 10.1016/j.commatsci.2017.07.030 22 | -------------------------------------------------------------------------------- /docs/user-guide/deprecations.md: -------------------------------------------------------------------------------- 1 | # Deprecated Calculations 2 | 3 | The Materials Project has been performing calculations of materials since 2011. As computing power increases and the state-of-the-art in scientific computation advances, some of our older calculations no longer meet our current quality standards, or have had other technical issues associated with them. 4 | 5 | In 2019 we have decided to implement a formal deprecation process, whereby we can remove an older calculation and replace it with a newer one. In the process, we will hide this older calculation from our default search results, but in the interests of transparency all old calculations remain accessible via our programmatic API or via direct access on the website. 6 | 7 | Deprecations are not retractions. However, if a material only had a single deprecated task associated with it, that material will no longer have data associated with it on the website until the updated calculation is completed. We are running these calculations continuously, with the website database being updated around once a month. 8 | 9 | We will update this document with a full list of deprecated calculations ("task_ids") in due course, along with the reason for their deprecation. 10 | 11 | If you have any questions about the deprecation process, or if there's a material ID you're interested in that you can no longer find, [please ask us on our community forum](https://discuss.materialsproject.org) and we'd be happy to help. 12 | -------------------------------------------------------------------------------- /docs/static/mapi/TiO2_energy.txt: -------------------------------------------------------------------------------- 1 | { 2 | "created_at": "2012-08-30T03:09:51.273521", 3 | "version": { 4 | "pymatgen": "2.2.1dev", 5 | "db": "2012.07.09", 6 | "rest": "1.0" 7 | }, 8 | "valid_response": true, 9 | "copyright": "Copyright 2012, The Materials Project", 10 | "response": [ 11 | { 12 | "energy": -105.53538843, 13 | "material_id": 25434 14 | }, 15 | { 16 | "energy": -26.4601124, 17 | "material_id": 25433 18 | }, 19 | { 20 | "energy": -105.53596712, 21 | "material_id": 25263 22 | }, 23 | { 24 | "energy": -105.53608265, 25 | "material_id": 25262 26 | }, 27 | { 28 | "energy": -105.53571656, 29 | "material_id": 25334 30 | }, 31 | { 32 | "energy": -106.89659362, 33 | "material_id": 430 34 | }, 35 | { 36 | "energy": -106.96996255, 37 | "material_id": 9173 38 | }, 39 | { 40 | "energy": -214.88106624, 41 | "material_id": 1840 42 | }, 43 | { 44 | "energy": -107.30373862, 45 | "material_id": 1439 46 | }, 47 | { 48 | "energy": -53.61979397, 49 | "material_id": 2657 50 | }, 51 | { 52 | "energy": -53.80383122, 53 | "material_id": 390 54 | }, 55 | { 56 | "energy": -53.75637567, 57 | "material_id": 34688 58 | } 59 | ] 60 | } 61 | -------------------------------------------------------------------------------- /docs/static/mapi/24972.txt: -------------------------------------------------------------------------------- 1 | { 2 | "created_at": "2012-08-30T02:55:02.661695", 3 | "version": { 4 | "pymatgen": "2.2.1dev", 5 | "db": "2012.07.09", 6 | "rest": "1.0" 7 | }, 8 | "valid_response": true, 9 | "copyright": "Copyright 2012, The Materials Project", 10 | "response": [ 11 | { 12 | "formation_energy_per_atom": -1.8333796954440005, 13 | "elements": [ 14 | "O", 15 | "Fe" 16 | ], 17 | "band_gap": { 18 | "energy": 1.5422000000000002, 19 | "transition": "\\Gamma-(0.318,0.000,-0.318)", 20 | "direct": false 21 | }, 22 | "e_above_hull": 0.0, 23 | "nelements": 2, 24 | "pretty_formula": "Fe2O3", 25 | "energy": -66.62512425, 26 | "is_hubbard": true, 27 | "nsites": 10, 28 | "material_id": 24972, 29 | "unit_cell_formula": { 30 | "Fe": 4.0, 31 | "O": 6.0 32 | }, 33 | "volume": 106.26838837282664, 34 | "is_compatible": true, 35 | "hubbards": { 36 | "Fe": 5.3, 37 | "O": 0.0 38 | }, 39 | "icsd_id": 245851, 40 | "spacegroup": { 41 | "symbol": "R-3c", 42 | "number": 167, 43 | "point_group": "-3m", 44 | "source": "spglib", 45 | "crystal_system": "trigonal", 46 | "hall": "-P 3* 2n" 47 | }, 48 | "energy_per_atom": -6.662512425, 49 | "full_formula": "Fe4O6", 50 | "density": 4.990329676353726 51 | } 52 | ] 53 | } 54 | -------------------------------------------------------------------------------- /docs/user-guide/molecular_terms.md: -------------------------------------------------------------------------------- 1 | # Molecular Glossary of Terms 2 | 3 | ## Molecules Explorer 4 | 5 | ### Formula 6 | 7 | **IUPAC International Chemical Identifier(InChI)** is a textual identifier for chemical substances, designed to provide a standard and human-readable way to encode molecular information and to facilitate the search for such information in databases and on the web. For more info please refer to [InChI Wikipedia](https://en.wikipedia.org/wiki/International_Chemical_Identifier) 8 | 9 | **Simplified molecular-input line-entry system (SMILES)** is a specification in form of a line notation for describing the structure of chemical species using short ASCII strings. For more info please refer to [SMILES Wikipedia](https://en.wikipedia.org/wiki/Simplified_molecular-input_line-entry_system) 10 | 11 | ### Structure 12 | 13 | **Point group**: The symmetry of the molecular system in [Schoenflies notation](https://en.wikipedia.org/wiki/Schoenflies_notation) 14 | 15 | ### Chemistry 16 | 17 | **Charge**: Net charge of the system 18 | 19 | ### Energetics 20 | 21 | **Ionization Potential(IP)**: The energy required to oxidize a molecule. AKA **Ionization Energy (IE).** 22 | 23 | **Electron Affinity(EA)**: The energy required to reduce a molecule. 24 | 25 | The IP and EA are two important properties of an electrolyte component. For a salt or solvent, these properties can determine the electrochemical window, which limits the potential within which the battery can operate. For redox active molecules, the IP and EA quantities can be used to infer the oxidation/reduction potentials, which determine the operating voltage of a redox flow battery. 26 | 27 | ### References 28 | 29 | [The Electrolyte Genome project: A big data approach in battery materials discovery](https://www.sciencedirect.com/science/article/pii/S0927025615001512?via%3Dihub) 30 | -------------------------------------------------------------------------------- /.github/workflows/test.yml: -------------------------------------------------------------------------------- 1 | name: testing 2 | 3 | on: 4 | push: 5 | branches: 6 | - master 7 | pull_request: 8 | branches: 9 | - master 10 | 11 | jobs: 12 | lint: 13 | runs-on: ubuntu-latest 14 | 15 | steps: 16 | - uses: actions/checkout@v2 17 | 18 | - name: Lint Code Base 19 | uses: github/super-linter@v4 20 | env: 21 | VALIDATE_ALL_CODEBASE: false 22 | VALIDATE_MARKDOWN: true 23 | VALIDATE_YAML: true 24 | DEFAULT_BRANCH: master 25 | GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} 26 | 27 | test: 28 | runs-on: ubuntu-latest 29 | 30 | steps: 31 | - uses: actions/checkout@v2 32 | 33 | - uses: actions/setup-python@v2 34 | with: 35 | python-version: 3.8 36 | 37 | - name: Install dependencies 38 | run: | 39 | python -m pip install --upgrade pip 40 | pip install -r requirements.txt 41 | 42 | - name: Build 43 | run: mkdocs build 44 | 45 | merge-deps: 46 | needs: 47 | - test 48 | - lint 49 | runs-on: ubuntu-latest 50 | steps: 51 | - name: Merge me! 52 | uses: ridedott/merge-me-action@master 53 | with: 54 | GITHUB_LOGIN: dependabot[bot] 55 | GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} 56 | 57 | deploy: 58 | needs: 59 | - test 60 | runs-on: ubuntu-latest 61 | if: github.ref == 'refs/heads/master' 62 | steps: 63 | - uses: actions/checkout@v2 64 | 65 | - uses: actions/setup-python@v2 66 | with: 67 | python-version: 3.8 68 | 69 | - name: Install dependencies 70 | run: | 71 | python -m pip install --upgrade pip 72 | pip install -r requirements.txt 73 | 74 | - name: Build 75 | run: mkdocs build 76 | 77 | - name: Deploy 78 | uses: peaceiris/actions-gh-pages@v3.6.4 79 | with: 80 | github_token: ${{ secrets.GITHUB_TOKEN }} 81 | publish_dir: ./site 82 | -------------------------------------------------------------------------------- /docs/user-guide/xas-matcher.md: -------------------------------------------------------------------------------- 1 | # XAS Matcher 2 | 3 | ## Overview 4 | 5 | We have computed X-Ray Absorption (XAS) spectra for over half of the materials in our database, and this number is growing," 6 | In particular, we have computed XANES K-edge spectra using the FEFF code," 7 | Read more about our methodology for computing spectra [here](/user-guide/xray-absorption-spectra) and at the first reference below," 8 | We are also in the process of computing other kinds of spectra," 9 | This page focuses on use of our app for comparing computed x-ray absorption spectra and automatically matching our spectra against user-uploaded experimental spectra. 10 | 11 | Reference for database and validation: [^1] 12 | 13 | Reference for app: [^2] 14 | 15 | ## Using the App 16 | 17 | ### Comparing Spectra 18 | 19 | You first enter a chemical system to ensure we have spectra calculated," 20 | Then, the first few spectra by increasing energy above hull (a proxy for thermodynamic stability) are plotted, and you can toggle plotting of spectra via the results table," 21 | You can filter the table by e.g. chemical formula via the search box above the table, and you can change the sorting by clicking on column headers (shift-click to sort secondary to the primary sort). 22 | 23 | With an uploaded spectrum and after matching, the $P_{softmax}$ column is the softmax probability that the given material's spectrum matches the one uploaded according to the match ranking of a suite of metrics," 24 | More info in [How Matching Works](#how-matching-works). 25 | 26 | ### Uploading Spectra 27 | 28 | Spectra files should have two values per line, separated by a standard delimiter like a comma or tab character," 29 | Comment lines (beginning with a '#') are allowed and will be ignored by the parser," 30 | The first value on each line should be the energy in units of eV," 31 | The second value, the absorption coefficient of arbitrary units, will be max-value normalized for plotting and matching. 32 | 33 | ## How Matching Works 34 | 35 | Coming soon... 36 | 37 | ## Authors 38 | 39 | - Donny Winston 40 | - Chen Zheng 41 | 42 | ## References 43 | 44 | [^1]: https://doi.org/10.1038/sdata.2018.151 45 | [^2]: http://dx.doi.org/10.1038/s41524-018-0067-x 46 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Materials Project Documentation Copyright (c) 2018, The Regents of the University of 2 | California, through Lawrence Berkeley National Laboratory (subject 3 | to receipt of any required approvals from the U.S. Dept. of Energy). 4 | All rights reserved. 5 | 6 | Redistribution and use in source and binary forms, with or without 7 | modification, are permitted provided that the following conditions 8 | are met: 9 | 10 | (1) Redistributions of source code must retain the above copyright 11 | notice, this list of conditions and the following disclaimer. 12 | 13 | (2) Redistributions in binary form must reproduce the above 14 | copyright notice, this list of conditions and the following 15 | disclaimer in the documentation and/or other materials provided with 16 | the distribution. 17 | 18 | (3) Neither the name of the University of California, Lawrence 19 | Berkeley National Laboratory, U.S. Dept. of Energy nor the names of 20 | its contributors may be used to endorse or promote products derived 21 | from this software without specific prior written permission. 22 | 23 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 24 | "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 25 | LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS 26 | FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 27 | COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, 28 | INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, 29 | BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 30 | LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER 31 | CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 32 | LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN 33 | ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 34 | POSSIBILITY OF SUCH DAMAGE. 35 | 36 | You are under no obligation whatsoever to provide any bug fixes, 37 | patches, or upgrades to the features, functionality or performance 38 | of the source code ("Enhancements") to anyone; however, if you 39 | choose to make your Enhancements available either publicly, or 40 | directly to Lawrence Berkeley National Laboratory or its 41 | contributors, without imposing a separate written license agreement 42 | for such Enhancements, then you hereby grant the following license: 43 | a non-exclusive, royalty-free perpetual license to install, use, 44 | modify, prepare derivative works, incorporate into other computer 45 | software, distribute, and sublicense such enhancements or derivative 46 | works thereof, in binary and source code form. 47 | -------------------------------------------------------------------------------- /docs/user-guide/materials-explorer.md: -------------------------------------------------------------------------------- 1 | # Initial release of Materials Explorer 2 | 3 | In Materials Project we offer 5 options to explore materials: by elements, by formula, by IDs, by mpquery and by Structure. 4 | 5 | ## Key features 6 | 7 | ### By Elements 8 | 9 | The following example is to show you how to query the materials by assigning the elements in the materials. 10 | Let's say 11 | you want to find all the materials that contain Li, Al and O. 12 | In the search box, simply type `Li-Al-O` and search. 13 | You would see the following searching results. 14 | ![by_elements example](img/materials-explorer/by_elements.png) 15 | 16 | ![by_elements example_results](img/materials-explorer/by_elements_results.png) 17 | 18 | _Figure 1: Exploring materials that contain Li, Al and O._ 19 | 20 | ### By formula 21 | 22 | If you have a specific material in mind, you can also explore the materials by its formula. 23 | For example, 24 | to search all the LaAlO3, change the search option to `by Formula` and type `LaAlO3`. 25 | ![by_formula example](img/materials-explorer/by_formula.png) 26 | 27 | _Figure 2: Exploring all the LaAlO3 materials._ 28 | 29 | ### By IDs 30 | 31 | If you know the mp id of the material, you can search it by ID. 32 | You can also search multiple IDs 33 | at the same time. 34 | Change the search option to `by IDs` and type the mp IDs that you are looking 35 | for. 36 | ![by_ids example](img/materials-explorer/by_ids.png) 37 | 38 | _Figure 3: Exploring specific materials by their mp IDs._ 39 | 40 | ### By mpquery 41 | 42 | In addition to the previous three basic explore options, Materials Project also provides an advanced 43 | query option by mpquery, using Mongo-like language for flexible queries on the Materials Project 44 | database. 45 | This provides the possibility of queries which would otherwise not be possible using 46 | the other simpler REST forms. 47 | For example, to search all the iron oxides and manganese oxides, 48 | change the search option to `by mpquery` and type `{'elements':{'$in':['Fe', 'Mn'], '$all': ['O']}, 'nelements':2}`. 49 | ![by_mpquery example](img/materials-explorer/by_mpquery.png) 50 | 51 | _Figure 4: Exploring materials by using Mongo-like language for flexible queries._ 52 | 53 | ### By Structure 54 | 55 | Additionally, if you already have structure but need to know the materials properties, such as 56 | band gap and formation energy, from the Materials Project database, you can change the search option 57 | to `by Structure` and drag and drop your structure file in the grey box. 58 | ![by_structure example](img/materials-explorer/by_structure.png) 59 | 60 | _Figure 4: Exploring materials by using Mongo-like language for flexible queries._ 61 | -------------------------------------------------------------------------------- /docs/user-guide/mpcomplete.md: -------------------------------------------------------------------------------- 1 | # Help Us Expand Our Database 2 | 3 | ## What is MPComplete? 4 | 5 | MPComplete is a service we offer to the community, whereby users can submit crystal structures to us that are not already in our database, that we then add to our calculation queue to calculate lattice parameters, relaxed atomic geometries, and total energies. 6 | This helps us to complete our database. 7 | 8 | ## What Crystal Structures Are Appropriate 9 | 10 | Any bulk-like crystal structure can be submitted to the Materials Project using MPComplete. 11 | Please do not submit defects, surfaces, and the like, or organic compounds. 12 | 13 | Two-dimensional materials can be submitted but we do not currently converge the vacuum layer, so please make sure there is sufficient vacuum in the cell (typically at least greater than 10 Å). 14 | Layered materials can also be submitted but note that we do not currently use a van der Waals functional so inter-layer spacing will not be calculated accurately. 15 | 16 | ## Submitting Crystal Structures via the Website 17 | 18 | You can submit individual structures online using [Crystal Toolkit](crystal-toolkit.md) and using the 'Submit to MPComplete' button. 19 | Crystal structures can be imported by uploading a CIF file or similar and can be optionally transformed by substituting atomic species or similar before submission. 20 | Please make sure to enter any comments or references as appropriate so that we can properly attribute the source of the crystal structure. 21 | 22 | A one-minute video walkthrough of the process is available [here](https://www.youtube.com/watch?v=4c8MZdD0L3c). 23 | 24 | ## Submitting Crystal Structures in Bulk 25 | 26 | For bulk submission of structures it would be easier to use our _pymatgen_ Python code and API to submit structures. 27 | Please contact us for detailed instructions at feedback@materialsproject.org 28 | 29 | ## Monitoring the Status of Your Submissions 30 | 31 | On your [Dashboard](https://materialsproject.org/dashboard), under Submitted Structures, each structure entry has a status label that corresponds to the 'state' of a corresponding FireWorks workflow ([reference of FireWorks states](https://materialsproject.github.io/fireworks/reference.html/)). 32 | 33 | Common states include: 34 | 35 | - `READY`: calculations are ready to be performed for the submission, where the crystal structure has passed initial inspection, but the job has not started running. 36 | - `REJECTED`: calculations were not performed, and an explanation for why the crystal structure was rejected will be shown. 37 | - `RESERVED`: At least one calculation has been submitted to the queue to run. The queue is finite in size, so `READY` jobs do not necessarily become immediately `RESERVED`. 38 | - `RUNNING`: Calculations are running. Depending on your structure, this stage could take a while. 39 | - `COMPLETED`: The submission has been fully processed, and should result in a new material on our website in our next database release, provided it did not relax to a duplicate structure. 40 | -------------------------------------------------------------------------------- /docs/static/mapi/Fe2O3.txt: -------------------------------------------------------------------------------- 1 | { 2 | "created_at": "2012-08-30T02:55:49.139558", 3 | "version": { 4 | "pymatgen": "2.2.1dev", 5 | "db": "2012.07.09", 6 | "rest": "1.0" 7 | }, 8 | "valid_response": true, 9 | "copyright": "Copyright 2012, The Materials Project", 10 | "response": [ 11 | { 12 | "formation_energy_per_atom": -1.7873700829440011, 13 | "elements": [ 14 | "Fe", 15 | "O" 16 | ], 17 | "band_gap": null, 18 | "e_above_hull": 0.0460096124999998, 19 | "nelements": 2, 20 | "pretty_formula": "Fe2O3", 21 | "energy": -132.33005625, 22 | "is_hubbard": true, 23 | "nsites": 20, 24 | "material_id": 542309, 25 | "unit_cell_formula": { 26 | "Fe": 8.0, 27 | "O": 12.0 28 | }, 29 | "volume": 206.71354216115657, 30 | "is_compatible": true, 31 | "hubbards": { 32 | "Fe": 5.3, 33 | "O": 0.0 34 | }, 35 | "icsd_id": 96077, 36 | "spacegroup": { 37 | "symbol": "Pbna", 38 | "number": 60, 39 | "point_group": "mmm", 40 | "source": "spglib", 41 | "crystal_system": "orthorhombic", 42 | "hall": "-P 2ac 2b" 43 | }, 44 | "energy_per_atom": -6.6165028125, 45 | "full_formula": "Fe8O12", 46 | "density": 5.130910017900618 47 | }, 48 | { 49 | "formation_energy_per_atom": -1.8333796954440005, 50 | "elements": [ 51 | "O", 52 | "Fe" 53 | ], 54 | "band_gap": { 55 | "energy": 1.5422000000000002, 56 | "transition": "\\Gamma-(0.318,0.000,-0.318)", 57 | "direct": false 58 | }, 59 | "e_above_hull": 0.0, 60 | "nelements": 2, 61 | "pretty_formula": "Fe2O3", 62 | "energy": -66.62512425, 63 | "hubbards": { 64 | "Fe": 5.3, 65 | "O": 0.0 66 | }, 67 | "nsites": 10, 68 | "material_id": 24972, 69 | "unit_cell_formula": { 70 | "Fe": 4.0, 71 | "O": 6.0 72 | }, 73 | "volume": 106.26838837282664, 74 | "is_compatible": true, 75 | "is_hubbard": true, 76 | "icsd_id": 245851, 77 | "spacegroup": { 78 | "symbol": "R-3c", 79 | "number": 167, 80 | "point_group": "-3m", 81 | "source": "spglib", 82 | "crystal_system": "trigonal", 83 | "hall": "-P 3* 2n" 84 | }, 85 | "energy_per_atom": -6.662512425, 86 | "full_formula": "Fe4O6", 87 | "density": 4.990329676353726 88 | } 89 | ] 90 | } 91 | -------------------------------------------------------------------------------- /docs/user-guide/developers-area.md: -------------------------------------------------------------------------------- 1 | # Developer's Area 2 | 3 | ## Welcome 4 | 5 | Welcome to the Materials Project Developer's Area. 6 | This page describes how to develop your own applications using the data and software of the Materials Project. 7 | 8 | ## Programming language 9 | 10 | Although you can use any programming language to develop applications, we recommend the Python programming language (version 3.0 or newer). 11 | Python is the language of the Materials Project codebases, is widely used and supported by the scientific community, and allows for rapid development. 12 | If you choose not to use Python, we suggest a language with good JSON parsing support (JSON is the data exchange format of the Materials Project). 13 | In addition, we suggest a language that can easily make requests to web servers and fetch responses as JSON. 14 | 15 | ## Programming environment 16 | 17 | If you are programming in Python, we suggest using a Python IDE such as PyCharm (commercial) or Eclipse+PyDev (free). 18 | However, some people prefer to use a UNIX-style text editor such as vi or emacs. 19 | 20 | ## Getting and analyzing data using pymatgen 21 | 22 | The Materials Project provides an open-source Python code, pymatgen (Python Materials Genomics), that can be used to: 23 | 24 | - Access Materials Project data 25 | - Convert data between several file formats 26 | - Perform materials analyses 27 | - Set up calculations 28 | The pymatgen documentation provides many examples on how to perform common tasks. 29 | For example, this [gist](https://gist.github.com/shyuep/3570304) by Shyue Ping Ong demonstrates how to generate phase diagrams dynamically using Materials Project data, as well as check a new material's stability with respect to decomposition. 30 | 31 | To get started with pymatgen, we suggest you visit the [official pymatgen documentation](http://pymatgen.org/). 32 | 33 | ## Accessing Materials Project data from any program 34 | 35 | With the Materials API, you can get Materials Project data from any program that can perform a GET request to our server. 36 | To get started: 37 | 38 | 1. Generate an API key in your profile page. 39 | 40 | - Log into the Materials Project web site (top-right) 41 | - Click 'profile' (top-right) 42 | - In the section labeled 'API key', click 'regenerate key'. 43 | This is your API key (copy it). 44 | - Click 'Save Settings' (your API key will not work until this is done) 45 | 46 | 2. Make a GET request to a valid URL, for example: `https://www.materialsproject.org/rest/v1/materials/C/vasp/density?API_KEY=YOUR_API_KEY` 47 | 48 | - (make sure you replace the text YOUR_API_KEY with your Materials Project API key) 49 | - You should see a JSON-formatted response that includes the density of the material. 50 | A simple description of the Materials API [can be found here](http://www.materialsproject.org/open#) (click the 'Materials API' button). 51 | For more details, see our documentation on The Materials API. 52 | 53 | ## Automating calculations using FireWorks 54 | 55 | FireWorks is an open-source Python code developed by the Materials Project for automating calculations over supercomputing clusters. 56 | More information, including download links, is at 57 | -------------------------------------------------------------------------------- /mkdocs.yml: -------------------------------------------------------------------------------- 1 | site_name: "Materials Project Documentation" 2 | site_description: Documentation for The Materials Project, an open database of computed materials properties to accelerate materials discovery and design. 3 | copyright: Built by The Materials Project 4 | site_url: https://docs.materialsproject.org 5 | 6 | repo_name: "materialsproject/docs" 7 | repo_url: "https://github.com/materialsproject/docs" 8 | 9 | nav: 10 | - Home: "index.md" 11 | #- Foundation: "foundation.md" 12 | - Methodology: 13 | - "Total energies": "methodology/total-energies.md" 14 | - "Electronic structure": "methodology/electronic-structure.md" 15 | - "Pseudopotentials": "methodology/pseudopotentials.md" 16 | - "GGA+U": "methodology/gga-plus-u.md" 17 | - "Elasticity": "methodology/elasticity.md" 18 | - "Elasticity prediction": "methodology/elasticity-prediction.md" 19 | - "Piezoelectricity": "methodology/piezoelectricity.md" 20 | - "Dielectricity": "methodology/dielectricity.md" 21 | - "Equations of State": "methodology/equations-of-state.md" 22 | - "Phonons": "methodology/phonons.md" 23 | - "Volume Change Error": methodology/volume-change-error.md 24 | - User Reference: 25 | - "Crystal Toolkit": "user-guide/crystal-toolkit.md" 26 | - "Materials Explorer": "user-guide/materials-explorer.md" 27 | - "Battery Explorer": "user-guide/batteries-explorer.md" 28 | - "Molecules Explorer": "user-guide/molecules-explorer.md" 29 | - "Structure Predictor": "user-guide/structure-predictor.md" 30 | - "Pourbaix Diagram": "user-guide/pourbaix-tool.md" 31 | - "Phase Diagram": "user-guide/phase-diagram.md" 32 | - "XAS Spectra": user-guide/xray-absorption-spectra.md 33 | - "XAS Matcher": "user-guide/xas-matcher.md" 34 | - "Reaction Calculator": "user-guide/reaction-calculator.md" 35 | - "Glossary": "user-guide/glossary-of-terms.md" 36 | - "Materials API (MAPI)": "open-apis/the-materials-api.md" 37 | - "Nanoporous Explorer": "user-guide/nanoporous-explorer.md" 38 | - "Deprecations": "user-guide/deprecations.md" 39 | - "Developer Area": "user-guide/developers-area.md" 40 | - "Interface Reactions": user-guide/interface-reactions.md 41 | - "Molecular Terms": user-guide/molecular_terms.md 42 | - "MPComplete": user-guide/mpcomplete.md 43 | - "RFB Dashboard": user-guide/rfb_dashboard.md 44 | - "Share your story": user-guide/share-your-story.md 45 | - "Structure Similarity": user-guide/structure-similarity.md 46 | - Database Updates: "database-updates.md" 47 | - Contribution: 48 | - "Newsfeed": "contrib/spec/newsfeed.md" 49 | 50 | theme: 51 | name: "material" 52 | features: 53 | - navigation.instant 54 | - navigation.tracking 55 | - navigation.tabs 56 | - navigation.tabs.sticky 57 | - navigation.top 58 | - toc.integrate 59 | - search.suggest 60 | - search.highlight 61 | - search.share 62 | markdown_extensions: 63 | - admonition 64 | - footnotes 65 | - pymdownx.arithmatex: 66 | generic: true 67 | - pymdownx.inlinehilite 68 | - pymdownx.highlight 69 | - pymdownx.superfences 70 | - pymdownx.tabbed 71 | - pymdownx.caret 72 | - pymdownx.tilde 73 | - pymdownx.betterem: 74 | smart_enable: all 75 | - toc: 76 | permalink: true 77 | 78 | plugins: 79 | - search 80 | - bibtex: 81 | bib_dir: "refs" 82 | cite_style: "pandoc" 83 | 84 | extra_javascript: 85 | - static/js/mathjax.js 86 | - https://polyfill.io/v3/polyfill.min.js?features=es6 87 | - https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js 88 | -------------------------------------------------------------------------------- /docs/user-guide/molecules-explorer.md: -------------------------------------------------------------------------------- 1 | # Molecules Explorer 2 | 3 | ## Release Notes 4 | 5 | ### Recent changes 6 | 7 | #### Version 0.1 - July 16, 2016 8 | 9 | - Initial release of Molecules Explorer. 10 | 11 | ## Introduction 12 | 13 | The primary goal of the molecular explorer is to report the atomic structure of molecules, found using quantum chemistry computational methods. 14 | Further quantities of interest, including the electron affinity (EA) and ionization energies (IE), are also reported. 15 | 16 | ## Manual 17 | 18 | - [Molecular Glossary of Terms](/user-guide/molecular_terms) 19 | 20 | ## Calculations 21 | 22 | Atomic structures and quantities of interest were calculated using the Materials Project infrastructure with the quantum chemistry software Q-Chem at the backend. 23 | For small molecules, Q-Chem calculations were performed using the 6-31+G\* Pople bases[^1] and the hybrid-functional B3LYP[^2]. 24 | For molecules with more than 50 atoms, a hybrid procedure[^3] was used in which the geometry is optimized at a low level of theory and quantities of interest are still calculated at the B3LYP/6-31+G\* level as a single point calculation. 25 | 26 | ### Geometry Optimization 27 | 28 | An atomic structure is stable if its vibrational frequency spectrum contains no imaginary frequencies. 29 | Thus, the atomic structures were calculated using a dynamic workflow that performs successive calculations until a geometry with zero imaginary frequencies is obtained[^3]. 30 | 31 | ### Properties 32 | 33 | The electron affinity (EA) and ionization potential (IP) are given by 34 | $$EA = -\frac{\Delta G_{red}(sol)}{nF}$$ 35 | $$IP = -\frac{\Delta G_{ox}(sol)}{nF}$$ 36 | 37 | where F is the Faraday constant, and $\Delta G_{ox}(sol)$ and $\Delta G_{red}(sol)$ are the Gibbs free energy change of oxidation and reduction in the solution phase, respectively. 38 | 39 | ![Free energy cycle](img/molecules-explorer/free_energy_cycle.png) 40 | _Figure 2: Free energy cycle for computing the oxidation/reduction potential. R denotes the molecule of interest._ 41 | 42 | According to the thermodynamic cycle in Fig. 1, $\Delta G_{ox}(sol)$ and $\Delta G_{red}(sol)$ can be calculated from the Gibbs free energy change of gas phase: 43 | 44 | $$\Delta G_{ox}(sol)=\Delta G_{ox}(gas)+\Delta G_{solv}(R^+)-\Delta G_{solv}(R)$$ 45 | $$\Delta G_{red}(sol)=\Delta G_{red}(gas)+\Delta G_{solv}(R^-)-\Delta G_{solv}(R)$$ 46 | 47 | The reported IP/EA are the adiabatic IP/EA[^4], which optimizes the geometry at different charge states (cation, anion, neutral) to emphasize high-fidelity results. 48 | 49 | ## Database 50 | 51 | The database was generated from three sources: 52 | 53 | 1. Molecules computed via systematic substitution of the functional groups in a base molecule 54 | 2. Molecules from public databases such as SciFinder and Reaxys 55 | 3. Molecules submitted by collaborators 56 | 57 | As of May, 2019 about 22,000 molecules have been added to the database. 58 | 59 | ## Using the Computational Molecular Explorer 60 | 61 | In order to search the database for the molecule in question, four methods can be employed. 62 | 63 | 1. Elements : returns any entry that includes the queried elements 64 | 2. Formula : returns any entry that satisfies a permutation of the queried atoms (e.g. 65 | H2O1, H2O, HOH, OHH all return water) 66 | 3. InChi (The IUPAC International Chemical Identifier): uses “bond connectivity, 67 | tautomeric information, isotope information, stereochemistry, and electronic charge 68 | information.” (See [InChI 69 | Wikipedia](https://en.wikipedia.org/wiki/International_Chemical_Identifier)) This may 70 | be the most precise way of searching for a molecule but perhaps the most complicated. 71 | 4. Chem Doodle: allows drawing of the chemical structure to query for the database entry 72 | (currently not supported on Firefox) 73 | 74 | ## References 75 | 76 | [^1]: Ditchfield, R., Hehre, W.J. & Pople, J.A. J. Chem. Phys. 54, 724 (1971) 77 | [^2]: Becke, A.D. Phys. Rev. A. 38, 3098 (1988) 78 | [^3]: 79 | [^4]: S. P. Ong , G. Ceder , Electrochim. Acta , 55 , 3804 (2010) 80 | -------------------------------------------------------------------------------- /docs/contrib/spec/newsfeed.md: -------------------------------------------------------------------------------- 1 | # Newsfeed 2 | 3 | !!! info 4 | This page is a _design specification_ for a feature that was implemented and 5 | tested before release. 6 | 7 | The [MP website](//materialsproject.org) exposes a lot of data and tools. 8 | Sometimes, people are surprised to learn about data and tools that have been 9 | available on the site for months, especially if they have logged in and used the 10 | site recently. One way to keep returning users informed, seen on many websites, 11 | is a news feed. Such a feed consists of short entries, each with a date and 12 | summary of the news. 13 | 14 | Often, there is a subtle and unobtrusive visual cue for 15 | returning users to review recent news before continuing to use the site. In 16 | other cases, the recent news is presented in focus for the user to review and 17 | dismiss. Apart from viewing a feed while visiting its website, the feed may 18 | also be formatted as per e.g. the 19 | [RSS](https://validator.w3.org/feed/docs/rss2.html) or 20 | [Atom](https://validator.w3.org/feed/docs/atom.html) specifications to allow 21 | users to aggregate such news feeds from many websites of interest. 22 | 23 | ## Data entry 24 | 25 | To enter news feed items, one creates a Markdown file in the `newsfeed/data` 26 | directory with a name of the format `YYYY-MM-DD-entry-title.md`, where 27 | `YYYY-MM-DD` is a [ISO 8601](https://en.wikipedia.org/wiki/ISO_8601)-formatted 28 | date. The file itself will look something like 29 | 30 | ```markdown 31 | --- 32 | title: My feed item title 33 | --- 34 | 35 | This is a great piece of news. 36 | More info [here](https://materialsproject.org/newstuff). 37 | ``` 38 | 39 | This format is based on that used by the [Jekyll](https://jekyllrb.com/) static 40 | site framework -- a simple organization of news items into separate files. The 41 | first section of the file (delimited by `---` lines) is meta-data, aka "front 42 | matter", and will be pre-processed for relevant key-value pairs. The remainder 43 | of the file will be converted to HTML. This may be implemented in one pass, for 44 | example using the Python `markdown` package with it's built-in `"meta-data"` 45 | extension. 46 | 47 | The `title` is the only required piece of metadata. If the feed entry requires a 48 | significant change, then an `updated` metadata field and value (in `YYYY-MM-DD` 49 | format) should be added -- do not change the filename. If a change to the entry 50 | is insignificant, like fixing a typo, then you don't need to create or update an 51 | `updated` field. 52 | 53 | ## Data display 54 | 55 | The news feed is displayed in two places: on the static (not-signed-in) home 56 | page, and on the signed-in default app view. Both views are in centered, 57 | responsive two-column layouts near the top of their respective pages. For a 58 | signed-in user, there is up to three months of unseen news. For the static home 59 | page, the news fills the two columns -- this depends on the summary-lengths of 60 | the news items, but does not exceed ten items (five per column). Finally, the 61 | signed-in user view is dismissible with a click. 62 | 63 | Each feed item on display shows a date, a title, and a summary. The date is 64 | gathered from the item's filename or from its `updated` metadata field if 65 | given. The summary is the rendered HTML of the item file's Markdown body. Feed 66 | items are presented in reverse chronological order. 67 | 68 | ## Data management 69 | 70 | The last time a user has seen the news feed is stored in the `app_db`'s 71 | `newsfeed_views` collection, one document per user. The query 72 | 73 | ```python 74 | return_document = app_db.newsfeed_views.find_one_and_update( 75 | {"user": request.user.username}, 76 | {"$set": {"last_seen": datetime.utcnow()}, 77 | upsert=True) 78 | ``` 79 | 80 | will update a user's document (inserting a document if one doesn't exist) with 81 | the current time as the last-seen time, and return the old user document (or 82 | `None` if no document existed). The application can then determine which 83 | feed items to render to the user based on the last `"last_seen"` value. This 84 | example uses the Django `request` object to get a user's immutable `username`. 85 | The expression `request.user.is_authenticated` may be evaluated first in this 86 | case to determine which view is to be rendered. 87 | -------------------------------------------------------------------------------- /docs/database-updates.md: -------------------------------------------------------------------------------- 1 | # Database updates 2 | 3 | !!! warning 4 | Up-to-date release notes are now posted to 5 | [this thread](https://discuss.materialsproject.org/t/materials-project-database-release-log/1609) 6 | on our discussion forum. 7 | 8 | !!! info 9 | Confused about materials being "deprecated"? [More info here](/user-guide/deprecations). 10 | 11 | ## Current Database versions 12 | 13 | ### V2019.05 14 | 15 | - Introduced a new `deprecated` field to materials. By default the website and API only search for materials that are not deprecated: {"deprecated": false}. 16 | - Deprecated 15,000 and added 3,600 new materials. We will be recomputing the deprecated materials to fill these spaces back up. Some of these new relaxations may end up matching current materials, so the total number of materials is not guaranteed to be the same as in V2019.02. 17 | - Fixed an issue with sandboxes not properly building the whole hull. Previously, only the sandboxed chemical systems were being recalculated for energy_above_hull searches 18 | 19 | ### V2019.02 20 | 21 | - Added over 47,000 new materials from orderings of disordered ICSD as well as compounds from the Pauling File 22 | - Finalized enforcing symmetry on piezo tensors 23 | - Moved third order elastic data to elasticity_third_order so that people are not swamped by the mountain of information associated with it. 24 | 25 | ### V2018.12 26 | 27 | - Adjusted the mp-id naming scheme to fix “mvc” ids taking over old mp-ids. 28 | - Fixed piezoeletric max_direction to be a miller index rather than a unit vector. 29 | 30 | ### Version 2018.11, Release Date: 2018-11-01 31 | 32 | We've released a new revision of the Materials Project database as part of major overhaul of our software infrastructure 33 | to enable us to continue to build new properties and deliver them to you, the material science community, at an accelerating 34 | pace. This has also caused some growing pains as we fix bugs we created in building our new infrastructure from scratch. 35 | 36 | Many of our users have reported bugs and we are very grateful for that. We're making great strides in being as transparent 37 | as possible so everyone knows what is changing. As part of this we've settled on a monthly release schedule including an 38 | announcement that informs everyone on what has or has not changed. To kick this process off we have our current changes 39 | for the MP Database Release V2018.11. This will be updated on a monthly basis with what has changed. 40 | 41 | V2018.11 42 | 43 | - Changed the grouping of magnetic materials to aggregate all magnetic orderings of a given material into a single 44 | material-id, and report the lowest energy ordering 45 | - Fixed incorrect calculation and display of polycrystalline dielectric constants 46 | - Fixed labeling of all materials as high-pressure. Note we're parsing ICSD tags for this labeling so while some materials 47 | may not conventionally be considered high-pressure, a single matching ICSD entry can tag a material as such. We would love 48 | to hear comments on how we could better tag high-pressure materials 49 | - 5,849 new material ids. 50 | - 3,556 retiring/re-aggregated material ids 51 | 52 | ### Version 2.0.0, Release Date: 04/13/2016 53 | 54 | - Equivalent to old version "2014.04.18" 55 | - Use major.minor.patch versioning, inspired by [semantic versioning](https://semver.org/), but for data. Arbitrarily choose "2" as the initial major version. 56 | - When new data is added (typically nightly), db version remains the same 57 | - When new kinds of data are added, bump the patch (x.y.Z) version 58 | - When data organization (schema) changes, bump the minor (x.Y.z) version 59 | - When calculation methodology changes, bump the major (X.y.z) version 60 | 61 | ## Old databases 62 | 63 | Data from the earlier 'Materials Genome' web site, served prior to 10/10/2011, is no longer supported. 64 | 65 | ### Version 2014.04.18, Release Date: 04/18/2014 66 | 67 | - Version unchanged until 04/13/2016. Renamed to "2.0.0" for semantic versioning. 68 | 69 | ### Version 0.5.1, Release Date: 10/10/2011 70 | 71 | - Initial Materials Project Database 72 | 73 | ### Version 1.1, Release Date: 3/25/2011 74 | 75 | - Removed fitted adjustments to P,S,C,Br,H2 by default in the calculations. 76 | 77 | ### Version 1.0, Release Date: 2/28/2011 78 | 79 | - Root database (MIT database with ICSD only entries) 80 | -------------------------------------------------------------------------------- /docs/methodology/static/KtablesBinaries.txt: -------------------------------------------------------------------------------- 1 | Ag2O 2 | Ag2S 3 | AgBr 4 | AgCl 5 | AgF 6 | AgI 7 | Al2O3 8 | Al2S3 9 | AlBr3 10 | AlCl3 11 | AlF3 12 | AlI3 13 | AlN 14 | AlP 15 | As2O3 16 | As2O5 17 | As2S3 18 | AsI3 19 | AsS 20 | Au2O3 21 | Au2P3 22 | AuBr 23 | AuCl3 24 | AuI 25 | B2O3 26 | B2S3 27 | BN 28 | BP 29 | BaBr2 30 | BaCl2 31 | BaF2 32 | BaO 33 | BaO2 34 | BaS 35 | Be3N2 36 | BeBr2 37 | BeCl2 38 | BeF2 39 | BeI2 40 | BeO 41 | BeS 42 | Bi2O3 43 | Bi2S3 44 | BiBr3 45 | BiCl3 46 | BiF3 47 | BiI3 48 | Ca3N2 49 | CaBr2 50 | CaCl2 51 | CaF2 52 | CaO 53 | CaS 54 | CdBr2 55 | CdCl2 56 | CdF2 57 | CdI2 58 | CdO 59 | CdS 60 | Ce2O3 61 | Ce3S4 62 | CeBr3 63 | CeCl3 64 | CeN 65 | CeO2 66 | CeS 67 | Co3O4 68 | CoBr2 69 | CoCl2 70 | CoF2 71 | CoF3 72 | CoI2 73 | CoO 74 | CoP 75 | CoP3 76 | CoS2 77 | Cr2N 78 | Cr2O3 79 | CrBr2 80 | CrCl2 81 | CrCl3 82 | CrF2 83 | CrF3 84 | CrI2 85 | CrN 86 | CrO3 87 | CrS 88 | Cs2O 89 | CsBr 90 | CsCl 91 | CsF 92 | CsI 93 | CsO2 94 | Cu2O 95 | Cu2S 96 | Cu3P 97 | CuBr 98 | CuCl 99 | CuCl2 100 | CuF2 101 | CuI 102 | CuO 103 | CuS 104 | Dy2O3 105 | DyCl3 106 | Er2O3 107 | ErF3 108 | Eu2O3 109 | EuCl3 110 | EuF3 111 | EuN 112 | EuO 113 | EuS 114 | Fe2O3 115 | Fe2P 116 | Fe3O4 117 | Fe3P 118 | Fe4N 119 | 2-Feb 120 | FeCl2 121 | FeCl3 122 | FeF2 123 | FeS 124 | FeS2 125 | Ga2O3 126 | Ga2S3 127 | GaBr3 128 | GaCl3 129 | GaI3 130 | GaN 131 | GaP 132 | GaS 133 | Gd2O3 134 | GdBr3 135 | GdCl3 136 | GeO2 137 | GeP 138 | GeS 139 | GeS2 140 | HfCl4 141 | HfF4 142 | HfI4 143 | HfN 144 | HfO2 145 | HgBr 146 | HgBr2 147 | HgCl 148 | HgCl2 149 | HgF 150 | HgF2 151 | HgI 152 | HgI2 153 | HgO 154 | HgS 155 | Ho2O3 156 | HoF3 157 | In2O3 158 | In2S3 159 | InBr 160 | InBr3 161 | InCl 162 | InI 163 | InI3 164 | InN 165 | InP 166 | InS 167 | IrCl3 168 | IrO2 169 | IrS2 170 | K2O 171 | K2S 172 | KBr 173 | KCl 174 | KF 175 | KI 176 | La2O3 177 | La2S3 178 | LaBr3 179 | LaCl3 180 | LaF3 181 | LaI3 182 | LaN 183 | LaS 184 | Li2O 185 | Li2S 186 | Li3N 187 | LiBr 188 | LiCl 189 | LiF 190 | LiI 191 | Lu2O3 192 | Mg3N2 193 | MgBr2 194 | MgCl2 195 | MgF2 196 | MgI2 197 | MgO 198 | MgS 199 | Mn2O3 200 | Mn3O4 201 | MnBr2 202 | MnCl2 203 | MnF2 204 | MnO 205 | MnO2 206 | MnP 207 | MnS 208 | MnS2 209 | Mo2S3 210 | MoCl5 211 | MoF5 212 | MoO2 213 | MoO3 214 | MoS2 215 | Na2O 216 | Na2S 217 | NaBr 218 | NaCl 219 | NaF 220 | NaI 221 | Nb2O5 222 | NbBr5 223 | NbCl4 224 | NbCl5 225 | NbF5 226 | NbN 227 | NbO 228 | NbO2 229 | Nd2O3 230 | NdCl3 231 | NdF3 232 | Ni2P 233 | Ni3P 234 | Ni3S2 235 | NiBr2 236 | NiCl2 237 | NiF2 238 | NiI2 239 | NiO 240 | NiS 241 | OsO2 242 | OsO4 243 | OsS2 244 | Pb3O4 245 | PbBr2 246 | PbCl2 247 | PbF2 248 | PbI2 249 | PbO 250 | PbO2 251 | PbS 252 | Pd4S 253 | PdCl2 254 | PdI2 255 | PdO 256 | PdS 257 | PdS2 258 | Pr2O3 259 | PrCl3 260 | PrS 261 | PtCl4 262 | PtS 263 | PtS2 264 | PuN 265 | Rb2O 266 | Rb2S 267 | RbBr 268 | RbCl 269 | RbF 270 | RbI 271 | Re2O7 272 | ReCl3 273 | ReO2 274 | ReO3 275 | ReS2 276 | Rh2O3 277 | Rh2S3 278 | Rh3S4 279 | RhCl3 280 | RuCl3 281 | RuF5 282 | RuO2 283 | RuS2 284 | Sb2O3 285 | Sb2O5 286 | Sb2S3 287 | SbBr3 288 | SbCl3 289 | SbF3 290 | SbI3 291 | SbO2 292 | Sc2O3 293 | ScCl3 294 | ScF3 295 | ScN 296 | SeCl4 297 | SeO2 298 | Si3N4 299 | SiI4 300 | SiO2 301 | SiP 302 | SiS2 303 | Sm2O3 304 | SmCl2 305 | SmS 306 | Sn2S3 307 | SnBr2 308 | SnCl2 309 | SnI2 310 | SnI4 311 | SnO 312 | SnO2 313 | SnS 314 | SnS2 315 | SrBr2 316 | SrCl2 317 | SrF2 318 | SrI2 319 | SrO 320 | SrO2 321 | SrS 322 | Ta2N 323 | Ta2O5 324 | TaCl4 325 | TaCl5 326 | TaN 327 | TaS2 328 | Tb2O3 329 | TbCl3 330 | TbF3 331 | TbO2 332 | TeCl4 333 | TeO2 334 | Th2S3 335 | Th3N4 336 | ThBr4 337 | ThCl4 338 | ThF4 339 | ThI4 340 | ThN 341 | ThO2 342 | ThS 343 | ThS2 344 | Ti2O3 345 | Ti3O5 346 | TiBr2 347 | TiBr3 348 | TiBr4 349 | TiCl3 350 | TiF4 351 | TiI4 352 | TiN 353 | TiO 354 | TiO2 355 | TiS 356 | TiS2 357 | Tl2O 358 | Tl2O3 359 | Tl2S 360 | TlBr 361 | TlCl 362 | TlF 363 | TlI 364 | Tm2O3 365 | TmCl3 366 | U3O8 367 | UBr4 368 | UCl3 369 | UCl4 370 | UCl5 371 | UCl6 372 | UF3 373 | UF4 374 | UF5 375 | UF6 376 | UI4 377 | UN 378 | UO2 379 | UO3 380 | UP 381 | US 382 | US2 383 | V2O3 384 | V2O5 385 | VCl2 386 | VCl3 387 | VF4 388 | VN 389 | VO 390 | VO2 391 | WCl5 392 | WCl6 393 | WO2 394 | WO3 395 | WS2 396 | Y2O3 397 | YCl3 398 | YF3 399 | YN 400 | Zn3N2 401 | Zn3P2 402 | ZnBr2 403 | ZnCl2 404 | ZnF2 405 | ZnI2 406 | ZnO 407 | ZnP2 408 | ZnS 409 | ZrCl4 410 | ZrI4 411 | ZrN 412 | ZrO2 413 | ZrS2 414 | -------------------------------------------------------------------------------- /docs/user-guide/reaction-calculator.md: -------------------------------------------------------------------------------- 1 | # Reaction Calculator 2 | 3 | Welcome to the Reaction Calculator wiki! 4 | 5 | You will find in here all relevant information regarding the Reaction Calculator, including release notes, the manual, etc. 6 | 7 | ## Release Notes 8 | 9 | ### Version 0.3 - May 13, 2011 10 | 11 | - Ability to select a particular crystal structure for the reaction via structureid 12 | 13 | ### Version 0.2 - Mar 31, 2011 14 | 15 | - Ability to select between three different energy adjustment strategies via a slider 16 | 17 | ### Version 0.1 - Mar 6, 2011 18 | 19 | - Initial release 20 | 21 | ## Manual 22 | 23 | ### Overview 24 | 25 | The reaction calculator allows users to estimate tens of thousands solid-state reaction enthalpies from a database of density functional theory calculations. In addition, the reaction calculator reports known experimental enthalpies (at 298 K and 1 atm) where available. 26 | 27 | The reaction calculator's energies are generally a good estimate of room temperature formation enthalpies, although all calculations are performed at 0 K and 0 atm. More information regarding methods to perform the calculations and their accuracy can be found in the Calculations Manual. 28 | 29 | ### Using the Reaction Calculator 30 | 31 | To use the reaction calculator, the **reactants input** and **products input** fields must be completed. Other fields are optional. Multiple **advanced arguments** may be specified by comma-separating each argument. 32 | 33 | #### Specifying Reactants and Products 34 | 35 | Reactants and Products are specified via chemical formula in the free-form text fields. Chemical formulas must be "+"-separated. The coefficients of all compounds are automatically determined; there is no need for the user to balance the reaction. 36 | 37 | For each chemical formula, our database automatically selects the lowest energy compound at the specified composition (handling of gaseous and liquid elements is explained in the Calculations Manual). The crystal structure used for a particular reaction calculation may be examined by clicking the blue links in the reaction output. 38 | 39 | There are several ways of specifying the chemical formula (examples follow). In all cases, element names should have only the first letter capitalized. 40 | 41 | - **Reactants** - enter in this field a '+'-separated list of chemical formulas for the desired reactants. 42 | 1. Usage example: Li + O + P + Fe 43 | 2. Usage example: Li2O + Fe2O3 + P2O5 + O 44 | 3. Usage example: LiFePO4 45 | - **Products** - enter in this field a '+'-separated list of chemical formulas for the desired products (same format as 'Reactants') 46 | 47 | The reaction energy will always be normalized for the reaction shown in the output. 48 | 49 | #### Choosing a particular phase / crystal structure 50 | 51 | This feature will be supported in a future release of the reaction calculator. 52 | 53 | #### Reading the output 54 | 55 | The reaction calculator balances the reaction and displays the balanced reaction as the first line in the output. The next line gives the computed reaction energy. 56 | 57 | When a computational energy is available, the computed $\delta H_{calculated}$ of reaction indicates the overall reaction enthalpy of the reaction as written in the first line of the output. The $\delta H_f$ for each compound in the reaction lists formation energies from the elements. Clicking the compound displays its crystal structure. 58 | 59 | When an experimental energy is available, the computed $\delta H_{experimental}$ of reaction indicates the overall reaction enthalpy of the reaction. The $\delta H_f$ for each compound in the reaction lists formation enthalpies from the elements. The blue book graphic links to the source(s) of experimental information. 60 | 61 | When both computational and experimental data are available, a graphical chart displays the error for each compound in the calculation. 62 | 63 | ### Calculation Details / Estimating Errors 64 | 65 | The Calculations Manual provides details on our calculation methodology and provides information on the magnitude of errors that may be expected. 66 | 67 | ### Citation 68 | 69 | To cite the reaction calculator, please reference the following works: 70 | 71 | - Jain, A., Hautier, G., Moore, C. J., Ong, S. P., Fischer, C. C., Mueller, T., ... & Ceder, G. (2011). A high-throughput infrastructure for density functional theory calculations. Computational Materials Science, 50(8), 2295-2310. 72 | - Jain, A., Hautier, G., Ong, S. P., Moore, C. J., Fischer, C. C., Persson, K. A., & Ceder, G. (2011). Formation enthalpies by mixing GGA and GGA+ U calculations. Physical Review B, 84(4), 045115. 73 | 74 | ### Authors 75 | 76 | - Anubhav Jain 77 | - Shyue Ping Ong 78 | - Charles Moore 79 | -------------------------------------------------------------------------------- /docs/user-guide/glossary-of-terms.md: -------------------------------------------------------------------------------- 1 | # Glossary of Terms 2 | 3 | ## Materials Explorer 4 | 5 | ## Formula 6 | 7 | **Anonymous chemical formula:** 8 | The chemical formula with the element names anonymized to the letters A, B, C, etc. 9 | The order of the anonymized elements is from least atomic fraction to greatest atomic fraction, thus the coefficients are non-decreasing. 10 | For example, both $\ce{TiO2}$ and $\ce{Na2O}$ have an anonymous formula of $\ce{A1B2}$. 11 | 12 | ## Structure 13 | 14 | **Crystal system:** 15 | The crystal system is commonly referred to as 'lattice' for periodic crystals and describes the shape of the repeating cell. 16 | Examples include cubic, tetragonal, and monoclinic. 17 | Calculations that simulate non-periodic systems, for example molecules, will be assigned as 'noncrystalline'. 18 | 19 | **Number of sites in unit cell:** 20 | The number of atoms in the unit cell of the calculation. 21 | For supercell calculations, this quantity refers to the number of atoms in the full supercell. 22 | 23 | **Cell volume:** 24 | The volume, in cubic Angstroms, of the unit cell of the calculation. 25 | For supercell calculations, this quantity refers to the volume of the full supercell. 26 | 27 | **Density:** 28 | The calculated bulk crystalline density, in grams/cc. 29 | 30 | **Material id:** 31 | This number is used to uniquely identify a material in the database. 32 | 33 | ## Chemistry 34 | 35 | **Oxidation state:** 36 | The degree of oxidation of the element in the material for ionic compounds. 37 | 38 | **Coordination number:** 39 | The number of atoms to which the element in the material is bound. 40 | 41 | **Ordered only:** 42 | Refers to whether the initial crystal data was obtained explicitly from experimental data (true) or required converting fractional occupancies into integer occupancies though an ordering algorithm (false). 43 | 44 | ## Energetics 45 | 46 | **Formation energy:** 47 | Computed formation energy at 0K, 0atm using a reference state of zero for the pure elements. 48 | This quantity is often a good approximation for formation _enthalpy_ at ambient conditions. 49 | 50 | **Energy above hull:** 51 | The energy of decomposition of this material into the set of most stable materials at this chemical composition, in eV/atom. 52 | Stability is tested against all potential chemical combinations that result in the material's composition. 53 | For example, a $\ce{Co2O3}$ structure would be tested for decomposition against other $\ce{Co2O3}$ structures, against $\ce{Co}$ and $\ce{O2}$ mixtures, and against $\ce{CoO}$ and $\ce{O2}$ mixtures. 54 | 55 | A positive E above hull indicates that this material is unstable with respect to decomposition. 56 | A zero E above hull indicates that this is the most stable material at its composition. 57 | 58 | ## Mechanics 59 | 60 | **Elastic Tensor:** 61 | The elastic tensor $C$ describes the response of a crystalline material to mechanical stress. 62 | Specifically, it relates the stress tensor $S$ to the strain tensor $E$. 63 | 64 | **Bulk, Shear, and Young's Moduli:** 65 | The bulk modulus $K$ describes the response of a material to compression. 66 | The shear modulus $G$ describes the response of a material to shear stress. 67 | Young's modulus $E$ relates uniaxial strain to stress in the same direction. 68 | All three are scalars with units of pressure. 69 | 70 | For isotropic materials, these three moduli fully describe the linear elastic response, and are related to each other by the Poisson ratio $\nu$: $2G(1+\nu)=E=3K(1-2\nu)$. 71 | For anisotropic materials (most crystals), the full elastic tensor $C$ is required because the stress-strain ratio is dependent on the direction of the stress and strain. 72 | 73 | **Poisson Ratio:** 74 | The Poisson ratio $\nu$ is the negative of the ratio of transverse strain to axial strain under uniaxial stress. 75 | 76 | **Voigt-Reuss-Hill Average Bulk and Shear Moduli:** 77 | The Voigt-Reuss-Hill (VRH) moduli describe a polycrystalline material's approximate average responses to stress. 78 | See the [Elasticity calculations](/methodology/elasticity) page for details on how these moduli are constructed. 79 | 80 | ## Data Science and Machine/Statistical Learning 81 | 82 | **Cross validation**: 83 | Cross validation is a method for testing the accuracy of a machine learning model by setting aside part of the available data as a validation set, training the model on the remaining data, and comparing the predicted values for the validation set to the known values. 84 | [Cross Validation Wikipedia article]() 85 | 86 | **Gradient Boosting**: 87 | Gradient boosting is a machine learning method in which weak learner models are repeatedly fit to the residual (errors) of the existing model in order to improve it. 88 | [Gradient Boosting Wikipedia article](https://en.wikipedia.org/wiki/Gradient_boosting) 89 | 90 | **Local Polynomial Regression**: 91 | In local polynomial regression, polynomial curves are fit to subsets of the data in proximity to specific points. 92 | Predictions are made by combining these curves weighted by how close the test sample is to each local regression's center. 93 | [Local Regression Wikipedia article](https://en.wikipedia.org/wiki/Local_regression) 94 | 95 | ## Authors 96 | 97 | - Handong Ling 98 | - Oxana Andriuc 99 | -------------------------------------------------------------------------------- /docs/methodology/equations-of-state.md: -------------------------------------------------------------------------------- 1 | # Equations of State 2 | 3 | ## Introduction 4 | 5 | Thermodynamic equations of state (EOS) for crystalline solids describe 6 | material behaviors under changes in pressure, volume, entropy and 7 | temperature. Despite over a century of theoretical development and 8 | experimental testing of energy-volume (E-V) EOS for solids, there is 9 | still a lack of consensus with regard to which equation is optimal, as 10 | well as to what metrics are most appropriate for making this 11 | judgment. 12 | 13 | Calculation of EOS is automated using self-documenting workflows 14 | compiled in the atomate code base. Atomate couples pymatgen for materials 15 | analysis, custodian for just-in-time debugging of DFT codes, and 16 | Fireworks for workflow management. The EOS workflow begins with a 17 | structure optimization and subsequently calculates the energy of 18 | isotropic deformations including ionic relaxation with volumetric strain 19 | ranging from -15.7% to 15.7% (-5% to 5% linear strain) of the 20 | optimized structure. Density-functional-theory (DFT) calculations were 21 | performed as necessary using the projector augmented wave (PAW) method 22 | as implemented in the Vienna Ab Initio Simulation Package (VASP) within 23 | the Perdew-Burke-Enzerhof (PBE) Generalized Gradient Approximation (GGA) 24 | formulation of the exchange-correlation functional. A cut-off for the 25 | plane waves of 520 eV is used and a uniform k-point density of 26 | approximately 1,000 per reciprocal atom is employed. In addition, 27 | standard Materials Project Hubbard U corrections are used for a number 28 | of transition metal oxides, as documented and implemented in the 29 | pymatgen VASP input sets. We note that the computational and convergence 30 | parameters were chosen consistently with the settings used in the 31 | Materials Project to enable direct comparisons with the large set of 32 | available MP data. 33 | 34 | ## Fitted Equation Forms 35 | 36 | | **Equation** | **$\boldsymbol{E(\nu^\*)}$** | **$\boldsymbol{K(\nu = 1)}$** | **$\boldsymbol{K'(\nu = 1)}$** | **Ref** | 37 | | ----------------- | ------------------------------------------------------------------------------------------------------------------------------------------ | ----------------------------- | ------------------------------ | ------- | 38 | | Birch (Euler) | $E = E_o^{\*\*} + BV_o\Big(\big(\nu^{-\frac{2}{3}} - 1\big)^2 + \frac{C}{2}\big(\nu^{-\frac{2}{3}} - 1\big)^3\Big)$ | $\frac{8B}{9}$ | $C + 4$ | [^1] | 39 | | Birch (Lagrange) | $E = E_o + BV_oC - BV_o\nu^{\frac{2}{3}}\Big(\big(C - 2\big)\big(1 - \nu^{\frac{2}{3}}\big)^2 + C\big(1 - \nu^{\frac{2}{3}}\big) + C\Big)$ | $\frac{16B}{9}$ | $C - 2$ | [^1] | 40 | | Mie-Gruneisen | $E = E_o + \frac{BV_o}{C} - \frac{BV_o}{C - 1}\Big(\nu^{-\frac{1}{3}} - \frac{1}{C}\nu^{-\frac{C}{3}}\Big)$ | $\frac{B}{9}$ | $\frac{7 + C}{3}$ | [^2] | 41 | | Murnaghan | $E = E_o + \frac{BV_o}{(C + 1)}\Big(\frac{\nu^{-C} - 1}{C} + \nu - 1\Big)$ | $B$ | $C + 1$ | [^3] | 42 | | Pack-Evans-James | $E = E_o + \frac{BV_o}{C}\Big(\frac{1}{C}\big(e^{3C(1 - \nu^{\frac{1}{3}})} - 1\big) - 3\big(1 -\nu^{\frac{1}{3}}\big)\Big)$ | $B$ | $C + 1$ | [^4] | 43 | | Poirier-Tarantola | $E = E_o + BV_o\Big(ln(\nu)\Big)^2\Big(3 - C\big(ln(\nu)\big)\Big)$ | $6B$ | $C + 2$ | [^5] | 44 | | Tait | $E = E_o + \frac{BV_o}{C}\Big(\nu - 1 + \frac{1}{C}\big(e^{C(1 -\nu)} - 1\big)\Big)$ | $B$ | $C - 1$ | [^6] | 45 | | Vinet | $E = E_o + \frac{BV_o}{C^2}\Big(1 - \big(1 + C(\nu^{\frac{1}{3}} - 1)\big)e^{-C(\nu^{\frac{1}{3}} - 1)}\Big)$ | $\frac{B}{9}$ | $\frac{2}{3}C + 1$ | [^7] | 46 | 47 | $^\*$ $\nu = \frac{V}{V_o}$, where $V_o$ is the volume at zero pressure. 48 | 49 | $^{\*\*}$ $E_o = E(\nu = 1)$ 50 | 51 | ## Citation 52 | 53 | To cite the EOS data in the Materials Project, please reference the following work: 54 | 55 | Latimer, K., Dwaraknath, S., Mathew, K., Winston, D., Persson, K. A. 56 | Evaluation of thermodynamic equations of state across chemistry and structure in the materials project. 57 | _NPJ Computational Materials._ **4,** 1, 2057-3960 (2018). 58 | [DOI:10.1038/s41524-018-0091-x](https://doi.org/10.1038/s41524-018-0091-x) 59 | 60 | ## Authors 61 | 62 | 1. Katherine Latimer 63 | 2. Shyam Dwaraknath 64 | 3. Donny Winston 65 | 66 | ## References 67 | 68 | [^1]: 69 | Birch, F. Finite elastic strain of cubic crystals. _Physical 70 | Review._ **71,** 11, 809–824 (1947). 71 | 72 | [^2]: 73 | Roy, B. and Roy, S. B. Applicability of isothermal three-parameter 74 | equations of state of solids: A reappraisal. _Journal of Physics: 75 | Condensed Matter._ **17,** 39, 6193–6216 (2005). 76 | 77 | [^3]: 78 | Murnaghan, F. D. The compressibility of media under extreme pressures. 79 | _Proceedings of the National Academy of Sciences._ **30,** 80 | 244–247 (1944). 81 | 82 | [^4]: 83 | Pack, D., Evans, W., James, H. The Propagation of Shock Waves in Steel 84 | and Lead. _The Proceedings of the Physical Society._ 85 | **60,** 1–8 (1948). 86 | 87 | [^5]: 88 | Poirier,  J. P. and Tarantola, A. A logarithmic equation of state. 89 | _Physics of the Earth and Planetary Interiors._ **109,** 90 | 1-2, 1–8 (1998). 91 | 92 | [^6]: 93 | Dymond,  J. H. and Malhotra, R. The Tait equation: 100 years on. 94 | _International Journal of Thermophysics._ **9,** 6, 941–951 95 | (1988). 96 | 97 | [^7]: 98 | Vinet, P., Ferrante, J., Rose,  J. H., Smith,  J. R. Compressibility of 99 | solids. _Journal of Geophysical Research._ **92,** 100 | 9319–9325 (1987). 101 | -------------------------------------------------------------------------------- /docs/user-guide/rfb_dashboard.md: -------------------------------------------------------------------------------- 1 | # RFB Dashboard 2 | 3 | ## Overview 4 | 5 | Redox flow batteries (RFBs) provide a promising pathway towards low-cost grid-scale energy storage devices. 6 | The economic viability of non-aqueous and aqueous redox flow batteries (NAqRFBs and AqRFBs respectively) is highly dependent on electroactive materials, salt, and solvent choices.[^1] 7 | The interactive RFB Dashboard can be used to select redox active materials for use in nonaqueous and aqueous RFBs by displaying individual materials along with regions of economic viability defined by the target battery price and minimum redox active species concentration.[^2] 8 | In addition, the tool provides concentration targets for redox active materials achieving the target battery price. 9 | This tool can be used to analyze both experimentally demonstrated materials and simulated families of materials. 10 | Reference 2 describes the techno-economic model implemented in the present tool. 11 | The default values of all input parameters are assumed to be the median values presented in Ref. 1. 12 | 13 | ## Redox Active Material Design Space 14 | 15 | Redox active materials are defined using three electrochemical properties: molecular weight (g/mol e-), redox potential (V vs. Li/Li+), and active material concentration (mol actives/kg solvent). 16 | The molecular weight is defined as the molecular weight of redox active material normalized by the number of electrons transferred. 17 | The redox potential is defined as the average potential of electron transfer events that the material undergoes. 18 | 19 | The molecular weight and redox potential of a redox active molecule can be measured or simulated in less time and with more accuracy than active material solubility. 20 | Thus, the RFB Dashboard shows redox active materials on a two-dimensional materials-selection map, with axes of molecular weight and redox potential, while drawing concentration contours that achieves the target battery price. 21 | In the model each material is assumed to pair with a hypothetical counter-electrode material having a different potential than the material of interest, but common concentration and molecular weight. 22 | 23 | ## Using the RFB Dashboard 24 | 25 | ### Importing Data for Analysis 26 | 27 | #### Via Molecule Explorer 28 | 29 | Data can be imported into the tool via Molecule Explorer. 30 | By clicking on the "via Molecule Explorer" button on top of the RFB Dashboard, the Molecule Explorer would appear and materials with desired structures can be selected. 31 | Once a set of molecules is selected, click on the "Explore Solubility" button to import them into the RFB Dashboard for further analysis. 32 | For a visual tutorial on how to import data via Molecule Explorer, a [short video](https://www.youtube.com/watch?v=w5NHcwujX30) is available to demonstrate how the Molecule Explorer is used. 33 | 34 | #### Via CSV 35 | 36 | Data can be imported into the tool via a Comma Separated Values (CSV) file. 37 | The CSV file should be formatted in such a way that there is a header for the first row of the data sheet and the order of the data columns does not matter. 38 | However, the header names for each column has to have 'formula' for molecular formula, 'mw' for molecular weight, 'redpot' for reduction potential and 'oxpot' for oxidation potential. 39 | Once your CSV file is ready, it can be uploaded into the tool by clicking on the "via CSV" button on top of the tool to upload the file, and the data will then be displayed on the tool. 40 | 41 | ## Description of Input Parameters 42 | 43 | ### Target Battery Price 44 | 45 | The Target Battery Price is the maximum battery price for RFBs built using the redox active materials enclosed by the concentration contours. 46 | The battery price is a combination of reactor cost, electrolyte cost, balance-of-plant and addition-to-price costs. 47 | Battery price neglects the cost of power-conditioning equipment that is included in system price defined in Ref. 1. As a result, when calculating battery price balance-of-plant costs are reduced by $100/kW compared to that in Ref. 1 used to calculate system price($/kWh). 48 | 49 | ### Target Molality 50 | 51 | The Target Molality is the minimum concentration achieving the target battery price for redox active materials enclosed by the concentration contours. 52 | The molality is defined as a ratio of moles of redox active species to kilograms of solvent in mol/kg. 53 | 54 | ### Cost Parameters 55 | 56 | - Reactor Cost Per Unit Area ($/m2) 57 | - Salt Cost: cost per unit mass of supporting salt ($/kg) 58 | - Solvent Cost: cost per unit mass of solvent ($/kg) 59 | - Active Material Cost: cost per unit mass of active material ($/kg) 60 | - Additional Contribution to Price: accounts for depreciation, labor, overhead, and margin ($/kW) 61 | - Balance of Plant Cost: accounts for ancillary equipment costs ($/kW) 62 | 63 | ### Operating Conditions 64 | 65 | - System Discharge Time: battery discharge time (hours) 66 | - Depth of Discharge: allowable range of state-of-charge (-) 67 | - Discharge Voltage Efficiency: ratio of cell potential during cycling to the thermodynamically reversible open-circuit cell potential (-) 68 | - Round-trip Coulombic Efficiency: ratio of the charge released during the discharging step of a complete cycle relative to the charge stored during the charging step of a complete cycle. (-) 69 | - Discharge System Efficiency: accounts for losses in energy during discharge due to auxiliary equipment. (-) 70 | 71 | ### Electrochemical Parameters 72 | 73 | - Area-Specific Resistance: accounts for ohmic, kinetic, and mass-transfer resistance in the separator, electrodes, and electrolyte (Ω-cm2) 74 | - Stability Limits (Nonaqueous only): solvent window of stability beyond which breakdown occurs (V vs. Li/Li+) 75 | - Hypothetical Counter-Electrode Potential (Nonaqueous only): assumed hypothetical counter-electrode for full-cell analysis of single electrode materials. (V vs. Li/Li+) 76 | - pH (Aqueous only): sets the pH of the aqueous solution. 77 | Aqueous stability limits are determined by the oxygen and hydrogen evolution potentials, which depend on the pH of the solution. 78 | The hypothetical counter-electrode potentials are selected in order to be within the stability limits within a margin of the "Voltage Offset" parameter. (-) 79 | - Voltage Offset (Aqueous only): Hypothetical counter-electrodes, with which each molecule of interest is paired, are specified by an increment in voltage, called the Voltage Offset. 80 | For positive-electrode molecules of interest the potential of the counter-electrode exceeds the hydrogen evolution potential by the magnitude of the Voltage Offset, and for negative-electrode molecules of interest the potential of the counter-electrode is set below the oxygen evolution potential by the magnitude of the Voltage Offset. (V) 81 | 82 | ## References 83 | 84 | [^1]: 10.1039/c4ee02158d 85 | [^2]: 10.1016/j.jpowsour.2016.08.129 86 | -------------------------------------------------------------------------------- /docs/error-checking.md: -------------------------------------------------------------------------------- 1 | # Error Checking 2 | 3 | ## High-pressure phase detection manual 4 | 5 | So far, all computations in the materials project database have been ran assuming 0 pressure. However, sometimes 6 | experimental data refers to high-pressure phases. While the ICSD web site tags high-pressure phases, we could not 7 | technically retrieved this data. To detect high-pressure phase, we had instead to rely on an imperfect word detection 8 | in the journal title of the entry. Any entry with a journal title containing G[Pp]a, [kM]bar or [Pp]ressure will be 9 | considered as likely high-pressure phase and will be tagged with a warning accordingly. 10 | 11 | ## Unusual oxidation state detection manual 12 | 13 | Unusual oxidation states (e.g., +2 for Al) can be the indication of a problem with the experiment or lead to large errors 14 | in computations (e.g., when an oxidation state requires electrons in the core of the pseudopotential to participate in 15 | bonding). 16 | 17 | To tag the entries with less common oxidation states and warn the user about them, we performed statistics on all the 18 | unique entries in the ICSD. From this statistical analysis, we estimated the probability p(n|A) where n is an oxidation 19 | state and A is an element. For instance, we p(+2|Al) will be very low, as it is very rare to observe Al in a +2 state. 20 | 21 | We decided to tag any entry with oxidation states according to the ICSD with a probability lower than 10%. Please note that 22 | this affect only compounds with assigned oxidation states in the ICSD. 23 | 24 | ## Volume Change Error manual 25 | 26 | We have used the difference between the computed volume after DFT relaxation and the volume reported experimentally as an 27 | indicator of a problem with a computation or entry. The problem can come from the experimental side (for instance atomic 28 | positions wrongly assigned in the ICSD) or from the approximation used in DFT. 29 | 30 | Our analysis focused only on GGA (without U) results. Our strategy consist in first establishing a volume change distribution 31 | from our large data set. After establishing this distribution, outliers will be easily identified and tagged with a warning. 32 | 33 | ### Volume Change Distribution in GGA 34 | 35 | Our analysis focused on the GGA data in the database available on Friday September 23, 2011. In total, we considered 36 | 11579 entries. We report on volume changes by computing: 37 | $$ \Delta V=\frac{V*{GGA}-V*{exp}}{V*{exp}} $$ 38 | Where $$ V*{GGA} $$ is the unit cell volume obtained by GGA and $$ V\_{exp} $$ the experimental volume given by the ICSD 39 | 40 | #### The issue with high pressure phases 41 | 42 | If the data is right away used, we would observe a longer tail on the positive values. This data is from the high pressure 43 | phase. Indeed, while our computations have been performed at 0 atm, compounds characterized at high-pressure will show a 44 | lower experimental than computed volume. This is not per se an error but instead a discrepancy between the experimental and 45 | computational conditions. To mitigate, this issue we removed from this analysis any entry likely to refer to a high-pressure 46 | phase according to the methodology presented in [^1] 47 | 48 | #### The fitting of the distribution 49 | 50 | After exclusion of the possible high-pressure phases, we have 10768 points available to study the difference between 51 | experimental and computed volume. Figure 1 shows the histogram of volume difference. The distribution is symmetric but 52 | its median is positive (3.2%) indicating a tendency for GGA to overestimate the volume. This is in agreement with the 53 | know-how in the field established from previous studies on smaller set of compounds. 54 | 55 | We obtained a very good fit to the data by using the a t-location scale distribution.[^2] A normal distribution could not 56 | be fitted to this data because of the heavy tail observed. Using matlab and a maximum likelihood approach, we obtained 57 | maximum likelihood estimates as well as confidence intervals for the three parameters of the distribution. Figure 2 shows 58 | the good agreement between the raw data and the t-location scale probability density distribution. 59 | 60 | #### The tagging of the entries 61 | 62 | After fitting the distribution, it is possible to tag the entries outlying the distribution. We assigned a warning tag to 63 | any entry in our database with a volume error higher than the 95th percentile (situated at 9.6% volume change) and lower 64 | than the 5th percentile (situated at -3,2% volume change). Figure 3 shows these boundaries on the cumulative t-location 65 | scale distribution. 66 | 67 | In total, 959 entries have been assigned a warning. 68 | 69 | #### Some examples of outliers detected by the volume difference 70 | 71 | Here, we analyze some of the largest outliers found in our analysis. Through these examples, we illustrate what kind of 72 | errors can be observed. 73 | 74 | ##### YZn and YbZn 75 | 76 | Both compounds (task_id: 11577 and 179, icsd_id: 106232, 206226) show enormous volume differences: 370% and 350% ! Looking 77 | at the data present in the ICSD, we found that the paper reference mentioned CsCl structures, while the entry given by the 78 | ICSD is a fcc based alloy. The volume discrepancy comes therefore from an erroneous export of the experimental data in the 79 | paper to the ICSD. 80 | 81 | ##### Sn 82 | 83 | 55% volume difference task_id: 7162 and icsd_id: 52487. This entry refers to a high pressure structure our algorithm did 84 | not catch. It is not surprising to see the computed data reporting a much larger volume than the experimental obtained at 85 | high-pressure 86 | 87 | ##### TaMn2O3 88 | 89 | -27% volume difference task_id: 7521, icsd_id: 15995 The icsd indicates already that the experimental data is dubious. 90 | There is a warning on the ICSD web site: "Unusual difference between calculated and measured density". The oxidation state 91 | reported for Ta: +2 is extremely rare. 92 | 93 | ##### MoS2 94 | 95 | 18% volume difference task_id: 1434, icsd_id: 644257 This is most likely due to an inherent error from GGA. The MoS2 96 | structure is layered and van der Waals interactions between the S atoms are essential to the geometry of the structure 97 | (c lattice parameter especially). However, it is known that GGA does not model well VDW interactions. 98 | 99 | ### Citation 100 | 101 | To cite the Materials Project, please reference the following work: 102 | 103 | - A. Jain, G. Hautier, C. J. Moore, S. P. Ong, C. C. Fischer, T. Mueller, K. A. Persson, and G. Ceder, A high-throughput infrastructure for density functional theory calculations, Computational Materials Science, vol. 50, 2011, pp. 2295-2310. 104 | 105 | ### Authors 106 | 107 | 1. Geoffroy Hautier 108 | 2. Jordan Burns 109 | 110 | ## Bond length Change Error manual 111 | -------------------------------------------------------------------------------- /docs/user-guide/batteries-explorer.md: -------------------------------------------------------------------------------- 1 | # Battery Explorer Manual 2 | 3 | ## Introduction 4 | 5 | The Battery Explorer is a customized tool to search the Materials Project database for battery materials satisfying various critical criteria such as voltage, capacity, stability and energy density. 6 | 7 | Currently, this app contains more than 4,000 intercalation compounds and 16,000 conversion compounds with different types of working ions (such as Li, Mg, Zn, Al and more). 8 | These numbers will increase as new compounds are continuously added to the database, including many new structural predictions. 9 | 10 | ## Searching Using the Battery Explorer 11 | 12 | The battery explorer is designed to help battery scientists find electrode materials of interest. 13 | There are a number of search fields that can be used to filter all the battery material entries to customize the results returned. 14 | Every battery material entry compiles multiple material entries that represent a given battery electrode at different states of charge and the corresponding data analysis to predict useful battery properties such as voltage or change in volume. 15 | 16 | The search bar above the periodic table in the battery explorer app can be used to search for battery material entries based on the composition (either by typying into the search bar or clicking on the periodic table to specify elements), by Material ID, or by Battery ID. 17 | In the toolbar to the right of the periodic table, there are a number of additional criteria that can be used to filter the results: 18 | 19 | - Number of Elements (including the working ion) 20 | - Excluded Elements 21 | - Toggle select between Intercalation Compounds or Conversion Compounds 22 | - Type of Working Ion 23 | - Average Voltage in V with respect to the voltage of the pure metal for the corresponding working ion 24 | - Volumetric Capacity in Ah/L 25 | - Gravimetric Capacity (also known as Specific Capacity) in (mAh/g) 26 | 27 | At the bottom of the toolbar to the right of the periodic table, a number of advanced search options can be expanded: 28 | 29 | - Max Voltage Step in V 30 | - Max Volume Change in fractional units (for example 1 corresponds to 100% volume change) 31 | - Max Instability in eV/atom determined from the energy above hull metric (see glossary for more information) 32 | 33 | ## The Search Results Table 34 | 35 | The search results table presents the resulting battery material entries from your search. 36 | You can add or hide fields from the result table by clicking the "Show/ hide columns" button and filter the results based on these fields by clicking the arrow in the column of interest. 37 | There are also buttons to print or export the Search Results Table to save your results for future reference. 38 | 39 | To investigate an individual battery material entry, click on one of the rows in the Search Results Table. 40 | This will open a new page containing a detailed summary for that entry including links and additional information for each material entry associated with a given battery material entry and data analysis such as the predicted voltage profile, oxidative stability, volume change, etc. 41 | 42 | ## Viewing Details of a Battery Material 43 | 44 | Within a single battery material entry, each associated material entry is dedicated to one structural framework that represents a different state of charge or working ion intercalation level (e.g. $\ce{Mn2O4}$ spinel, $\ce{Li0.5Mn2O4}$ spinel, or $\ce{LiMn2O4}$ spinel). 45 | These entries have been grouped together into a single battery material entry by comparing the structure frameworks with the working ion(s) removed to match similar host lattices. 46 | The details view has many components and more detailed data analysis from these grouped entries (including interactive plots and features) which are described below. 47 | 48 | ### Voltage Curve 49 | 50 | The voltage curve graph displays the calculated equilibrium voltage versus state of charge. 51 | If voltage criteria were specified in the query, the line might be segmented into different colors. 52 | Try hovering over points on the voltage curve plot with your mouse for more details on that data point. 53 | 54 | ### O2 Evolution Curve 55 | 56 | One concern for battery electrode design is resistance to $\ce{O_2}$ release, as $\ce{O_2}$ release from an electrode can lead to thermal runaway which is a safety hazard. 57 | The $\ce{O_2}$ evolution diagram determines the equilibrium chemical potentials at which $\ce{O_2}$ release can be expected, and the amount of $\ce{O_2}$ released[^1][^2]. 58 | One way to read this chart is to look at the chemical potential at which $\ce{O_2}$ release begins (the first x-value for which the y-axis is greater than zero). 59 | Compounds for which O2 release begins at more negative muO2 are more stable with respect to $\ce{O_2}$ release. 60 | The $\mu_\ce{O_2}$ needed for release can be referenced against established battery compounds to get an idea of stability to $\ce{O_2}$ release. 61 | This plot is interactive so you can hover over a data point with your mouse for more detailed information. 62 | 63 | ### Structure Viewer 64 | 65 | For viewing convenience, there is a drop down list below the structure viewer window where you can select the structure of each material entries associated with a battery material entry. 66 | 67 | ### Overall Battery Material Properties 68 | 69 | The overall battery materials properties display aggregate or average properties derived from all states of charge (e.g. intercalation levels) for a given structural framework. 70 | Note that some intercalation levels presented in this section may be outside the desired range of voltage, stability, or safety. 71 | More details are given in the 'Voltage pair properties' section. 72 | 73 | ### Voltage Pair Properties 74 | 75 | This table displays calculated data for each voltage step along the voltage profile. 76 | In each row, the two material entries associated with a single voltage step and the corresponding properties (volume change, capacity, voltage, etc.) are displayed. 77 | Click on the composition of one of the materials listed to be directed to that material entry. 78 | 79 | ## Authors 80 | 81 | 1. Shyue Ping Ong 82 | 2. Anubhav Jain 83 | 3. Stefan Adams (diffusion data) 84 | 4. Eric Sivonxay 85 | 5. Jimmy Shen 86 | 6. Ann Rutt 87 | 88 | ## References 89 | 90 | [^1]: S. P. Ong, L. Wang, B. Kang, G. Ceder., The Li-Fe-P-O2 Phase Diagram from First Principles Calculations, Chemistry of Materials, vol. 20, Mar. 2008, pp. 1798-1807. [doi:10.1021/cm702327g](https://doi.org/10.1021/cm702327g) 91 | [^2]: S.P. Ong, A. Jain, G. Hautier, B. Kang, and G. Ceder, Thermal stabilities of delithiated olivine MPO4 (M=Fe, Mn) cathodes investigated using first principles calculations, Electrochemistry Communications, vol. 12, 2010, pp. 427-430. [doi:10.1016/j.elecom.2010.01.010](https://doi.org/10.1016/j.elecom.2010.01.010) 92 | [^3]: S. Adams, Solid State Ionics 177, 1625 (2006). 93 | [^4]: S. Adams, Acta Crystallogr. B, Struct. Sci. 57, 278 (2001). 94 | [^5]: S. Adams and R. Prasada Rao, Phys. Chem. Chem. Phys. 11, 3210 (2009). 95 | [^6]: S. Adams and R. P. Rao: High power Li ion battery materials by computational design; Phys. Status Solidi A 208, 1746–1753 (2011). [doi:10.1002/pssa.201001116](https://doi.org/10.1002/pssa.201001116) 96 | -------------------------------------------------------------------------------- /docs/methodology/phonons.md: -------------------------------------------------------------------------------- 1 | # Phonons 2 | 3 | ## Introduction 4 | 5 | A phonon is a collective excitation of a set of atoms in condensed 6 | matter. 7 | These excitations can be decomposed into different modes, each 8 | being associated with an energy that corresponds to the frequency of the 9 | vibration. 10 | The different energies associated with each vibrational mode 11 | constitute the phonon vibrational spectra (or phonon band structure). 12 | The vibrational spectra of materials play an important role in physical 13 | phenomena such as thermal conductivity, superconductivity, 14 | ferroelectricity and carrier thermalization. 15 | 16 | There are different methods to calculate the vibrational spectra from 17 | first-principles using the density functional theory formalism (DFT). 18 | It can be obtained from the Fourier transform of the trajectories of the 19 | atoms on a molecular dynamics run, from finite-differences of the total 20 | energy with respect to atomic displacements or directly from density 21 | functional perturbation theory (DFPT). 22 | The latter method is the one used 23 | in the calculations on the Materials project page. 24 | 25 | ## Formalism 26 | 27 | In the density functional perturbation theory formalism the derivatives 28 | of the total energy with respect to a perturbation are directly obtained 29 | from the self-consistency loop [^1] For a generic point **q** in the 30 | Brillouin zone the phonon frequencies $\omega\_{\mathbf{q},m}$ and 31 | eigenvectors $U_m(\mathbf{q}\kappa'\beta)$ are obtained by solving 32 | of the generalized eigenvalue problem 33 | 34 | $$ 35 | \sum_{\kappa'\beta}\widetilde{C}_{\kappa\alpha,\kappa'\beta}(\mathbf{q})U*m(\mathbf{q}\kappa'\beta) = M_{\kappa}\omega^2_{\mathbf{q},m}U_m(\mathbf{q}\kappa\alpha) 36 | $$ 37 | 38 | where $\kappa$ labels the atoms in the cell, $\alpha$ and 39 | $\beta$ are cartesian coordinates and 40 | $\widetilde{C}\_{\kappa\alpha,\kappa'\beta}(\mathbf{q})$ are the 41 | interatomic force constants in reciprocal space, which are related to 42 | the second derivatives of the energy with respect to atomic 43 | displacements. 44 | These values have been obtained by performing a Fourier 45 | interpolation of those calculated on a regular grid of **q**-points 46 | obtained with DFPT. 47 | 48 | ## Thermodynamic properties 49 | 50 | The vibrational density of states $g(\omega)$ is obtained from an 51 | integration over the full Brillouin zone 52 | 53 | $$ 54 | g(\omega) = \frac{1}{3nN}\sum_{\mathbf{q},m}\delta(\omega-\omega_{\mathbf{q},m}) 55 | $$ 56 | 57 | where $n$ is the number of atoms per unit cell and $N$ is the 58 | number of unit cells. 59 | The expressions for the Helmholtz free energy 60 | $\Delta F$, the phonon contribution to the internal energy 61 | $\Delta E\_{\text{ph}}$, the constant-volume specific heat $C_v$ 62 | and the entropy $S$ can be obtained in the harmonic approximation 63 | [^2] 64 | 65 | $$ 66 | \Delta F = 3nNk*BT\int_{0}^{\omega_L}\text{ln}\left(2\text{sinh}\frac{\hbar\omega}{2k_BT}\right)g(\omega)d\omega 67 | $$ 68 | 69 | $$ 70 | \Delta E_{\text{ph}} = 3nN\frac{\hbar}{2}\int_{0}^{\omega_L}\omega\text{coth}\left(\frac{\hbar\omega}{2k_BT}\right)g(\omega)d\omega 71 | $$ 72 | 73 | $$ 74 | C*v = 3nNk_B\int_{0}^{\omega_L}\left(\frac{\hbar\omega}{2k_BT}\right)^2\text{csch}^2\left(\frac{\hbar\omega}{2k_BT}\right)g(\omega)d\omega 75 | $$ 76 | 77 | $$ 78 | S = 3nNk*B\int_{0}^{\omega_L}\left(\frac{\hbar\omega}{2k_BT}\text{coth}\left(\frac{\hbar\omega}{2k_BT}\right) - \text{ln}\left(2\text{sinh}\frac{\hbar\omega}{2k_BT}\right)\right)g(\omega)d\omega 79 | $$ 80 | 81 | where $k_B$ is the Boltzmann constant and $\omega_L$ is the 82 | largest phonon frequency. 83 | 84 | ## Calculation details 85 | 86 | All the DFT and DFPT calculations are performed with the ABINIT software 87 | package [^3] [^4]. 88 | 89 | The PBEsol [^5] semilocal generalized gradient approximation 90 | exchange-correlation functional (XC) is used for the calculations. 91 | This 92 | functional is proven to provide accurate phonon frequencies compared to 93 | experimental data [^6]. 94 | The pseudopotentials are norm-conserving [^7] 95 | and taken from the pseudopotentials table Pseudo-dojo version 0.3 [^8]. 96 | 97 | The plane wave cutoff is chosen based on the hardest element for each 98 | compound, according to the values suggested in the Pseudo-dojo table. 99 | The Brillouin zone is sampled using equivalent **k**-point and 100 | **q**-point grids that respect the symmetries of the crystal with a 101 | density of approximately 1500 points per reciprocal atom and the 102 | **q**-point grid is always $\Gamma$-centered [^9]. 103 | 104 | All the structures are relaxed with strict convergence criteria, i.e. 105 | until all the forces on the atoms are below $10^{-6}$ Ha/Bohr and the 106 | stresses are below $10^{-4}$ Ha/Bohr$^3$. 107 | 108 | The primitive cells and the band structures are defined according to the 109 | conventions of Setyawan and Curtarolo [^10]. 110 | 111 | ## Citation 112 | 113 | Guido Petretto, Shyam Dwaraknath, Henrique P. C. Miranda, Donald 114 | Winston, Matteo Giantomassi, Michiel J. van Setten, Xavier Gonze, 115 | Kristin A. Persson, Geoffroy Hautier, Gian-Marco Rignanese, 116 | _High-throughput density functional perturbation theory phonons for 117 | inorganic materials_, **Scientific Data**, 5, 180065 (2018). 118 | [doi:10.1038/sdata.2018.65](https://doi.org/10.1038/sdata.2018.65) 119 | 120 | ## References 121 | 122 | [^1]: 123 | Gonze, X. & Lee, C. Dynamical matrices, Born effective charges, 124 | dielectric permittivity tensors, and interatomic force constants 125 | from density functional perturbation theory. Phys. Rev. B 55, 126 | 10355–10368 (1997) 127 | 128 | [^2]: 129 | C. Lee & X. Gonze, Ab initio calculation of the thermodynamic 130 | properties and atomic temperature factors of SiO2 α-quartz and 131 | stishovite. Phys. Rev. B 51, 8610 (1995) 132 | 133 | [^3]: 134 | Gonze, X. et al. First-principles computation of material 135 | properties: the Abinit software project. Computational Materials 136 | Science 25, 478 – 492 (2002) 137 | 138 | [^4]: 139 | Gonze, X. et al. ABINIT: First-principles approach to material and 140 | nanosystem properties. Computer Physics Communications 180, 2582 – 141 | 2615 (2009) 142 | 143 | [^5]: 144 | Perdew, J. P. et al. Restoring the density-gradient expansion for 145 | exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406 (2008) 146 | 147 | [^6]: 148 | He, L. et al. Accuracy of generalized gradient approximation 149 | functionals for density-functional perturbation theory calculations. 150 | Phys. Rev. B 89, 064305 (2014) 151 | 152 | [^7]: 153 | Hamann, D. R. Optimized norm-conserving Vanderbilt 154 | pseudopotentials. Phys. Rev. B 88, 085117 (2013) 155 | 156 | [^8]: 157 | van Setten, M., Giantomassi, M., Bousquet, E., Verstraete, M.J., 158 | Hamann, D.R., Gonze, X. & Rignanese, G.-M., et al. The PseudoDojo: 159 | Training and grading a 85 element optimized norm-conserving 160 | pseudopotential table (2018). Computer Physics Communications 226, 39. 161 | 162 | [^9]: 163 | Petretto, G., Gonze, X., Hautier, G. & Rignanese, G.-M. 164 | Convergence and pitfalls of density functional perturbation theory 165 | phonons calculations from a high-throughput perspective. 166 | Computational Materials Science 144, 331 – 337 (2018) 167 | 168 | [^10]: 169 | Setyawan, W. & Curtarolo, S. High-throughput electronic band 170 | structure calculations: Challenges and tools. Computational 171 | Materials Science 49, 299 – 312 (2010) 172 | -------------------------------------------------------------------------------- /docs/methodology/electronic-structure.md: -------------------------------------------------------------------------------- 1 | # Electronic Structure Calculations 2 | 3 | ## Band Structure and DOS computations details 4 | 5 | We used the relaxed structure from the total energy run to perform using 6 | the same GGA functional (and U if any) a DOS and band structure run. 7 | This data is available for many entries in 8 | the materials explorer. We ran first a static run with a uniform 9 | (Monkhorst Pack or $\Gamma$-centered for hexagonal systems) k-point grid. 10 | From this run the DOS and the charge density were extracted. The charge 11 | density was then used to perform a band structure computation for 12 | k-points along the symmetry lines of the Brillouin zone. The symmetry 13 | lines have been determined following the methodology from Curtarolo et 14 | al.[^1] using the aconvasp software. 15 | 16 | The band structure data is displayed with full lines for up spin and 17 | dashed lines for down spin. For insulators, the band gap is computed 18 | according to the band structure. The nature of the gap (direct or 19 | undirect) as well as the k-points involved in the band gap transition 20 | are displayed. The VBM and CBMs are displayed for insulators as well by 21 | red and white dots. The web site does not display the 10% highest bands 22 | as those higher energies bands tend to converge more slowly. 23 | 24 | The DOS indicates the full DOS by default but projections along atoms or 25 | orbitals are also available through a scroll down menu. Please note that 26 | the DOS data and band structure can be slightly different as the k-point 27 | grid is not the same. For instance, the k-point grid for the DOS might 28 | not include Gamma while the band structure does. 29 | 30 | ## Accuracy of Band Structures 31 | 32 | **Note**: _the term 'band gap' in this section generally refers to the 33 | fundamental gap, not the optical gap. The difference between these 34 | quantities is reported to be small in semiconductors but significant in 35 | insulators._ [^2] 36 | 37 | ![band gaps](/methodology/img/calculations-manual/Gaps.png) 38 | _Figure 1: Experimental versus computed band gaps for 39 | 237 compounds in an internal test. The computed gaps are underestimated 40 | by an average factor of 1.6, and the residual error even after 41 | accounting for this shift is significant (MAE of 0.6 eV). We thank M. 42 | Chan for her assistance in compiling this data._ 43 | 44 | Density functional theory is formulated to calculate ground state 45 | properties. Although the band structure involves excitations of 46 | electrons to unoccupied states, the Kohn-Sham energies used in solving 47 | the DFT equations are often interpreted to correspond to electron energy 48 | levels in the solid. 49 | 50 | The correspondence between the Kohm-Sham eigenvalues computed by DFT and 51 | true electron energies is theoretically valid only for the highest 52 | occupied electron state. The Kohn-Sham energy of this state matches the 53 | first ionization energy of the material, given an exact 54 | exchange-correlation functional. However, for other energies, there is 55 | no guarantee that Kohn-Sham eigenvalues will correspond to physical 56 | observables. 57 | 58 | Despite the lack of a rigorous theoretical basis, the DFT band structure 59 | does provide useful information. In general, band dispersions predicted 60 | by DFT are reported to match experimental observations; one small test 61 | of band dispersion accuracy found that errors ranged from 0.1 to about 62 | 0.4 eV.[^3] However, predicted band gaps are usually severely 63 | underestimated. Therefore, a common way to interpret DFT band structures 64 | is to apply a 'scissor' operation whereby the conduction bands are 65 | shifted in energy by a constant amount so that the band gap matches 66 | known experimental observations. 67 | 68 | ### Band gaps 69 | 70 | In general, band gaps computed with common exchange-correlation 71 | functionals such as the LDA and GGA are severely underestimated. 72 | Typically the disagreement is reported to be around 50% in the 73 | literature. Some internal testing by the Materials Project supports 74 | these statements; typically, we find that band gaps are underestimated 75 | by about 40% (Figure 1). We additionally find that several known 76 | insulators are predicted to be metallic. 77 | 78 | #### Origin of band gap error and improving accuracy 79 | 80 | The errors in DFT band gaps obtained from calculations can be attributed 81 | to two sources: 1. Approximations employed to the exchange correlation 82 | functional 2. A derivative discontinuity term, originating from the true 83 | density functional being discontinuous with the total number of 84 | electrons in the system. 85 | 86 | Of these contributions, (2) is generally regarded to be the larger and 87 | more important contribution to the error. It can be partly addressed by 88 | a variety of techniques such as the GW approximation but typically at 89 | high computational cost. 90 | 91 | Strategies to improve band gap prediction at moderate to low 92 | computational cost now been developed by several groups, including Chan 93 | and Ceder (delta-sol),[^4] Heyd et al. (hybrid functionals) [^5], and 94 | Setyawan et al. (empirical fits) [^6]. (These references also contain 95 | additional data regarding the accuracy of DFT band gaps.) The Materials 96 | Project may employ such methods in the future in order to more 97 | quantitatively predict band gaps. For the moment, computed band gaps 98 | should be interpreted with caution. 99 | 100 | ## Citation 101 | 102 | To cite the calculation methodology, please reference the following 103 | works: 104 | 105 | 1. A. Jain, G. Hautier, C. Moore, S.P. Ong, C.C. Fischer, T. 106 | Mueller, K.A. Persson, G. Ceder., A High-Throughput Infrastructure 107 | for Density Functional Theory Calculations, Computational Materials 108 | Science, vol. 50, 2011, pp. 2295-2310. 109 | [DOI:10.1016/j.commatsci.2011.02.023](https://dx.doi.org/10.1016/j.commatsci.2011.02.023) 110 | 2. A. Jain, G. Hautier, S.P. Ong, C. Moore, C.C. Fischer, K.A. 111 | Persson, G. Ceder, Accurate Formation Enthalpies by Mixing GGA and 112 | GGA+U calculations, Physical Review B, vol. 84, 2011, p. 045115. 113 | [DOI:10.1103/PhysRevB.84.045115](https://doi.org/10.1103/PhysRevB.84.045115) 114 | 115 | ## Authors 116 | 117 | 1. Anubhav Jain 118 | 2. Shyue Ping Ong 119 | 3. Geoffroy Hautier 120 | 4. Charles Moore 121 | 122 | ## References 123 | 124 | [^1]: 125 | Setyawan, W.; Curtarolo, S. Computational Materials Science 2010, 126 | 49, 299-312. 127 | 128 | [^2]: 129 | E.N. Brothers, A.F. Izmaylov, J.O. Normand, V. Barone, G.E. 130 | Scuseria, Accurate solid-state band gaps via screened hybrid 131 | electronic structure calculations., The Journal of Chemical Physics. 132 | 129 (2008) 133 | 134 | [^3]: 135 | R. Godby, M. Schluter, L.J. Sham, Self-energy operators and 136 | exchange-correlation potentials in semiconductors, Physical Review 137 | B. 37 (1988). 138 | 139 | [^4]: 140 | M. Chan, G. Ceder, Efficient Band Gap Predictions for Solids, 141 | Physical Review Letters 19 (2010) 142 | 143 | [^5]: 144 | J. Heyd, J.E. Peralta, G.E. Scuseria, R.L. Martin, Energy band 145 | gaps and lattice parameters evaluated with the 146 | Heyd-Scuseria-Ernzerhof screened hybrid functional, Journal of 147 | Chemical Physics 123 (2005) 148 | 149 | [^6]: 150 | W. Setyawan, R.M. Gaume, S. Lam, R. Feigelson, S. Curtarolo, 151 | High-throughput combinatorial database of electronic band structures 152 | for inorganic scintillator materials., ACS Combinatorial Science. 153 | (2011). 154 | -------------------------------------------------------------------------------- /docs/methodology/elasticity-prediction.md: -------------------------------------------------------------------------------- 1 | # Elasticity Predictions 2 | 3 | ## Introduction 4 | 5 | The Materials Project (MP) provides a growing collection of elastic constants calculated from first principles Density Functional Theory (DFT). 6 | Please see [Elasticity calculations](/methodology/elasticity) for details regarding the MP elasticity workflow [^1]. 7 | 8 | For compounds that have not yet been processed with the elasticity workflow, the MP offers statistical learning (SL) predictions of the Voigt-Reuss-Hill [^2] average bulk and shear moduli ($K_{VRH}$ and $G_{VRH}$, respectively). 9 | The SL models were trained with a diverse set of 1,940 k-nary compounds, using the $K_{VRH}$ and $G_{VRH}$ moduli calculated by the elasticity workflow. 10 | 11 | **IMPORTANT NOTE**: The SL predictions are generated by a local polynomial regression of several composition and structural descriptors (see Table 1) to available DFT-calculated elasticity data. 12 | They are not directly physics-based predictions and should not be viewed as having similar accuracy or precision to experimental or DFT data.See the SL paper [^3] and Table 2 for prediction accuracy details. 13 | In addition, the SL predictions are based on a fraction of currently available DFT elasticity data. 14 | More sophisticated SL models with larger datasets are an objective for future work. 15 | 16 | ## Formalism 17 | 18 | Ensemble statistical learning techniques construct a predictor from a collection or ensemble of weak learners. 19 | Each weak learner is either a single descriptor or a function of just a few descriptors, which limits the level of interaction between descriptors. 20 | Gradient boosting (GB) is a very flexible ensemble technique, which makes few assumptions regarding the form of the solution and iteratively builds a predictor from a series of weak learners while minimizing the residual of a loss function [^4]. 21 | GB implementations use regularization techniques to reduce the risk of over-fitting, which typically include limiting the level of interaction between descriptors, limiting the number of iterations per some risk criteria, and employing shrinkage [^4]. 22 | At each iteration, the weak learner that causes the greatest reduction in the loss function’s residual is selected and added to the model; however, when shrinkage is employed, each new term is attenuated by the learning rate. 23 | See the SL paper [^3] and references therein for details about the regression model. 24 | 25 | ## Descriptors 26 | 27 | The successful application of SL requires a set of descriptor candidates that sufficiently explain the diversity of the phenomenon being learned. 28 | We distinguish between composition and structural descriptors. 29 | Composition descriptors are calculated from elemental properties and only require knowledge of a compound’s composition. 30 | Structural descriptors require knowledge of a compound’s specific structure and are calculated using DFT. 31 | The descriptors used for the final learned model and their relative influence (RI) are presented in Table 1. 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |
ModelRankDescriptorUnderlying propertyRI (%)
K1log(V)volume per atom46.6
2μ1(Rn)row number24.5
3Eccohesive energy19.4
4μ-4(X)electronegativity9.5
G1Eccohesive energy37.0
2log(V)volume per atom35.9
3μ-3(Rn)row number13.8
4μ4(X)electronegativity13.3
91 | 92 | Table 1: Descriptor rank and relative influence (RI) for the models for $K$ and $G$. 93 | Composition descriptors are constructed as Hölder means $\mu_p(x)$ (power $p$, property $x$). 94 | This table and caption are from de Jong et al.'s SL paper [^3], which also provides details on Hölder means. 95 | 96 | ## Accuracy 97 | 98 | The accuracy of the model is summarized below. 99 | 100 | 101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 | 111 | 112 | 113 | 114 | 115 | 116 | 117 | 118 | 119 | 120 | 121 | 122 | 123 | 124 | 125 | 126 | 127 | 128 | 129 | 130 | 131 | 132 | 133 | 134 |
ModelIteration ThresholdPrediction RMSE (log(GPa))Percent of Predictions within Relative Error of
5%10%20%30%
K990.075033.158.487.394.5
G900.137813.628.853.073.0
135 | 136 | Table 2: Iteration threshold as determined by cross validation, prediction root mean squared error (RMSE), and percentage of predictions within 5, 10, 20, and 30 percent relative error for _K_ and _G_ models. 137 | This table and caption are from de Jong et al.'s SL paper [^3]. 138 | 139 | ## Citations 140 | 141 | To cite elastic constant predictions within the Materials Project, please reference the following works: 142 | 143 | 1. "de Jong M, Chen W, Notestine R, Persson K, Ceder G, Jain A, Asta M, 144 | and Gamst A (2016) A Statistical Learning Framework for Materials 145 | Science: Application to Elastic Moduli of k-nary Inorganic 146 | Polycrystalline Compounds, Scientific Reports 6: 34256." 147 | [doi:10.1038/srep34256](http://dx.doi.org/10.1038/srep34256) 148 | 2. "de Jong M, Chen W, Angsten T, Jain A, Notestine R, Gamst A, Sluiter 149 | M, Ande CK, van der Zwaag S, Plata JJ, Toher C, Curtarolo S, Ceder 150 | G, Persson KA, Asta M (2015) Charting the complete elastic 151 | properties of inorganic crystalline compounds. Scientific Data 2: 152 | 150009." 153 | [doi:10.1038/sdata.2015.9](http://dx.doi.org/10.1038/sdata.2015.9) 154 | 155 | ## Authors 156 | 157 | 1. Randy Notestine 158 | 2. Maarten de Jong 159 | 3. Kyle Bystrom 160 | 161 | ## References 162 | 163 | [^1]: de Jong M, Chen W, Angsten T, Jain A, Notestine R, Gamst A, Sluiter M, Ande CK, van der Zwaag S, Plata JJ, Toher C, Curtarolo S, Ceder G, Persson KA, Asta M (2015) Charting the complete elastic properties of inorganic crystalline compounds. Scientific Data 2: 150009. 164 | [^2]: Hill, R. The elastic behaviour of a crystalline aggregate. Proceedings of the Physical Society. Section A 65, 349 (1952). 165 | [^3]: de Jong M, Chen W, Notestine R, Persson K, Ceder G, Jain A, Asta M, and Gamst A (2016) A Statistical Learning Framework for Materials Science: Application to Elastic Moduli of k-nary Inorganic Polycrystalline Compounds, Scientific Reports 6: 34256. [doi:10.1038/srep34256](http://dx.doi.org/10.1038/srep34256) 166 | [^4]: Hastie, T., Tibshirani, R. & Friedman, J. The elements of statistical learning: data mining, inference, and prediction. (Springer, 2011), second edition. 167 | -------------------------------------------------------------------------------- /docs/methodology/gga-plus-u.md: -------------------------------------------------------------------------------- 1 | # GGA+U Calculations 2 | 3 | It is well-known that first principles calculations within the local 4 | density approximation (LDA) or generalized gradient approximation (GGA) 5 | lead to considerable error in calculated redox reaction energies of many 6 | transition metal compounds. This error arises from the self-interaction 7 | error in LDA and GGA, which is not canceled out in redox reactions where 8 | an electron is transferred between significantly different environments, 9 | such as between a metal and a transition metal or between a transition 10 | metal and oxygen or fluorine. Extensive discussion of this issue can be found in the 11 | following works.[^1][^2][^3][^4] 12 | 13 | In the Materials Project, we have calibrated U values for many 14 | transition metals of interest using the approach outlined in Wang et 15 | al.'s work[^5]. At the present moment, U values have only been calibrated for 16 | transition metal oxide systems. U values were calibrated for the following 17 | elements: Co, Cr, Fe, Mn, Mo, Ni, V and W. The choice of systems to which we 18 | apply U was largely determined by our experience and by systematic 19 | benchmarking. It is very likely that we will expand calibration of U 20 | values to more chemical systems in the future. 21 | 22 | In the Materials Project, for an oxide or fluoride material with a transition 23 | element listed previously, with the VASP input settings constructed according to 24 | the logic defined in [pymatgen](https://github.com/materialsproject/pymatgen/blob/master/pymatgen/io/vasp/MPRelaxSet.yaml). 25 | 26 | Note that for fluorides, the U value gets set to the one calibrated from the oxide system, although 27 | in principle our architecture allows different U values to be set for oxides and fluorides respectively. 28 | 29 | ## Calibration of U values 30 | 31 | The U values were obtained by fitting to experimental binary formation 32 | enthalpies as described in Wang et al.'s work. This method is simple yet 33 | accurately reproduces phase stabilities. A least squares method of 34 | obtaining the correct U value was used, as follows: 35 | 36 | 1. For each non-overlapping formation energy reaction considered, we 37 | find the region where the formation energy error passes zero. For 38 | the V-O system, this includes the following: 39 | - $\ce{2 V2O3 + O2 -> 4 VO2}$ 40 | - $\ce{4 VO2 + O2 -> 2 V2O5}$ 41 | 2. For each formation energy region identified, we fit the linear 42 | equation $\begin{align} \mbox{Error/redox} & = m U + c \end{align}$ to 43 | the final U range. In the case of V, we will have two sets of (m,c). 44 | 3. We find the U value that minimizes the sum of square Error / Redox. 45 | 4. In the case of V, we get a U value of 3.25. 46 | 47 | ## U values 48 | 49 | The full list of U values used is described in the table below. For 50 | oxides and fluorides containing any of the elements, only GGA+U calculations 51 | are performed. 52 | 53 | 54 | 55 | | Element | System | Fitting Reaction | Redox Couple | Calibrated U (eV) | Comments | 56 | | :------ | ------ | ---------------------------------------------------------------- | -------------------------------------------------------------- | ----------------- | ------------------------------------------------------------------------------------------------------------------------------------------ | 57 | | Co | Oxides | $\ce{6 CoO + O2 -> 2 Co3O4}$ | $\ce{Co^{2+} -> Co^{2.67+}}$ | 3.32 | | 58 | | Cr | Oxides | $\ce{2/3 Cr2O3 + O2 -> 4/3 CrO3}$ | $\ce{Cr^{3+} -> Cr^{6+}}$ | 3.7 | | 59 | | Fe | Oxides | $\ce{6 FeO + O2 -> 2 Fe3O4}$
$\ce{4 Fe3O4 + O2 -> 6 Fe2O3}$ | $\ce{Fe^{2+} -> Fe^{2.67+}}$
$\ce{Fe^{2.67+} -> Fe^{3+}}$ | 5.3 | | 60 | | Mn | Oxides | $\ce{6 MnO + O2 -> 2 Mn3O4}$
$\ce{Mn3O4 + O2 -> 3 MnO2}$ | $\ce{Mn^{2+} -> Mn^{2.67+}}$
$\ce{Mn^{2.67+} -> Mn^{4+}}$ | 3.9 | $\ce{Mn2O3}$ was explicitly excluded from calibration set due to the large number of atoms in its unit cell. | 61 | | Mo | Oxides | $\ce{2 MoO2 + O2 -> 2 MoO3}$ | $\ce{Mo^{4+} -> Mo^{6+}}$ | 4.38 | | 62 | | Ni | Oxides | $\ce{Li2O + 2NiO + 1/2 O2 -> 2LiNiO2}$ | $\ce{Ni^{2+} -> Ni^{3+}}$ | 6.2 | Binary formation energies are not readily available for Ni. The Ni U calibration was performed using a ternary oxide formation energy.[^5] | 63 | | V | Oxides | $\ce{2 V2O3 + O2 -> 4 VO2}$
$\ce{4 VO2 + O2 -> 2 V2O5}$ | $\ce{V^{3+} -> V^{4+}}$
$\ce{V^{4+} -> V^{5+}}$ | 3.25 | $\ce{VO}$ was explicitly excluded from calibration due to its known metallic nature. | 64 | | W | Oxides | $\ce{2 WO2 + O2 -> 2 WO3}$ | $\ce{W^{4+} -> W^{6+}}$ | 6.2 | | 65 | 66 | ## Caveats 67 | 68 | The U values are calibrated for phase stability analyses, and should be 69 | used with care if applied to obtain other properties such as band 70 | structures. Also, the U values depend on the pseudopotential used. Further, 71 | typically, U values should be site specific, however in our approach, U values were 72 | applied to all sites with an element listed above, and only to the d-orbitals. A discussion of the 73 | pseudopotentials used in the Materials Project can be 74 | found [here](/methodology/pseudopotentials). 75 | 76 | ## Authors 77 | 78 | 1. Shyue Ping Ong 79 | 80 | ## References 81 | 82 | [^1]: 83 | F. Zhou, M. Cococcioni, C. A. Marianetti, D. Morgan and G. Ceder. 84 | First-principles prediction of redox potentials in transition-metal 85 | compounds with LDA+U. Physical Review B, 2004, 70, 235121. 86 | 87 | 88 | [^2]: 89 | M. Cococcioni, S. de Gironcoli, Linear response approach to the 90 | calculation of the effective interaction parameters in the LDA+U 91 | method. Physical Review B, 2005, 71, 035105. 92 | 93 | 94 | [^3]: 95 | L. Wang, T. Maxisch, & G. Ceder. Oxidation energies of transition 96 | metal oxides within the GGA+U framework. Physical Review B. 2006, 97 | 73, 195107, 98 | 99 | [^4]: 100 | A. Jain, G. Hautier, S. P. Ong, C. Moore, C. Fischer, K. A. 101 | Persson, & G. Ceder. Formation enthalpies by mixing GGA and GGA + U 102 | calculations. Physical Review B, 2011, 84(4), 045115. 103 | 104 | 105 | [^5]: 106 | M. Wang, A. Navrotsky Enthalpy of formation of LiNiO2, LiCoO2 and 107 | their solid solution, LiNi1-xCoxO2, Solid State Ionics, vol. 166, 108 | no. 1-2, pp. 167-173, Jan. 2004. 109 | -------------------------------------------------------------------------------- /docs/user-guide/structure-similarity.md: -------------------------------------------------------------------------------- 1 | # Structure similarity 2 | 3 | ## Introduction 4 | 5 | The similarity between two structures _i_ and _j_ is assessed on the basis of local coordination information from all sites in the two structures.[^1] [^2] 6 | The four basic steps involved are: 7 | 8 | 1. Find near(est) neighbors of all sites in both structures. 9 | 2. Evaluate each coordination pattern via coordination descriptors observed at each site to define site fingerprints. 10 | 3. Compute statistics of the descriptor values across all sites in a structure to define structure fingerprints. 11 | 4. Use structure fingerprints to rate the (dis)similarity between the two (vectors representing the two) structures. 12 | 13 | ## Near-neighbor finding 14 | 15 | We use a novel method called CrystallNN to find near(est) neighbors in periodic structures. 16 | While the method will be introduced shortly[^3], it is already available through the python package [pymatgen](https://github.com/materialsproject/pymatgen). 17 | 18 | ## Site Fingerprints 19 | 20 | The second step of the structure similarity calculation is the computation of a crystal site fingerprint, $v^{site}$, for each site in the two structures. 21 | The fingerprint is a 61-dimensional vector in which each element carries information about the local coordination environment computed with the _site_ module of the python package [matminer](https://github.com/hackingmaterials/matminer). 22 | For example, the first two elements "wt $\ce{CN1}$" and "single bond $\ce{CN1}$" provide estimates of the likelihood (or weight) of how much the given site should be considered 1-fold coordinated (i.e., _w_$|_{CN=1}$). 23 | The third element "wt $\ce{CN2}$" provides a 2-fold coordination likelihood, whereas the fourth element "L-shaped $\ce{CN2}$" holds the resemblance similarity to an L-shaped coordination geometry (also called local structure order parameter) given that we find a coordination configuration with 2 atoms ($q_{L}|_{CN=2}$). 24 | The local structure order parameters can assume values between 0, meaning that the observed local environment has no resemblance with the target motif to which it is compared, and 1, which stands for perfect motif match. 25 | The remaining elements are: 26 | "water-like $\ce{CN2}$," 27 | "bent 120 degrees $\ce{CN2}$," 28 | "bent 150 degrees $\ce{CN2}$," 29 | "linear $\ce{CN2}$," 30 | "wt $\ce{CN3}$," 31 | "trigonal planar $\ce{CN3}$," 32 | "trigonal non-coplanar $\ce{CN3}$," 33 | "T-shaped $\ce{CN3}$," 34 | "wt $\ce{CN4}$," 35 | "square co-planar $\ce{CN4}$," 36 | "tetrahedral $\ce{CN4}$," 37 | "rectangular see-saw-like $\ce{CN4}$," 38 | "see-saw-like $\ce{CN4}$," 39 | "trigonal pyramidal $\ce{CN4}$," 40 | "wt $\ce{CN5}$," 41 | "pentagonal planar $\ce{CN5}$," 42 | "square pyramidal $\ce{CN5}$," 43 | "trigonal bipyramidal $\ce{CN5}$," 44 | "wt $\ce{CN6}$," 45 | "hexagonal planar $\ce{CN6}$," 46 | "octahedral $\ce{CN6}$," 47 | "pentagonal pyramidal $\ce{CN6}$," 48 | "wt $\ce{CN7}$," 49 | "hexagonal pyramidal $\ce{CN7}$," 50 | "pentagonal bipyramidal $\ce{CN7}$," 51 | "wt $\ce{CN8}$," 52 | "body-centered cubic $\ce{CN8}$," 53 | "hexagonal bipyramidal $\ce{CN8}$," 54 | "wt $\ce{CN9}$," 55 | "q2 $\ce{CN9}$," 56 | "q4 $\ce{CN9}$," 57 | "q6 $\ce{CN9}$," 58 | "wt $\ce{CN10}$," 59 | "q2 $\ce{CN10}$," 60 | "q4 $\ce{CN10}$," 61 | "q6 $\ce{CN10}$," 62 | "wt $\ce{CN11}$," 63 | "q2 $\ce{CN11}$," 64 | "q4 $\ce{CN11}$," 65 | "q6 $\ce{CN11}$," 66 | "wt $\ce{CN12}$," 67 | "cuboctahedral $\ce{CN12}$," 68 | "q2 $\ce{CN12}$," 69 | "q4 $\ce{CN12}$," 70 | "q6 $\ce{CN12}$," 71 | "wt $\ce{CN13}$," 72 | "wt $\ce{CN14}$," 73 | "wt $\ce{CN15}$," 74 | "wt $\ce{CN16}$," 75 | "wt $\ce{CN17}$," 76 | "wt $\ce{CN18}$," 77 | "wt $\ce{CN19}$," 78 | "wt $\ce{CN20}$," 79 | "wt $\ce{CN21}$," 80 | "wt $\ce{CN22}$," 81 | "wt $\ce{CN23}$," 82 | and "wt $\ce{CN24}$." Note that $q_{n}$ refers to Steinhardt bond orientational order parameter of order _n_. 83 | The resulting site fingerprint is thus defined as: 84 | 85 | $$ 86 | \mathbf{v}^\mathrm{site} = [w|_{\mathrm{CN}=1}, \quad w|_{\mathrm{CN}=2}, \quad q_\mathrm{L}|_{\mathrm{CN}=2}, \quad q_\mathrm{water}|_{\mathrm{CN}=2}, \quad \dots, \quad w|_{\mathrm{CN}=24}]^\mathrm{T} 87 | $$ 88 | 89 | ## Structure Fingerprints 90 | 91 | The fingerprints from sites in a given structure are subsequently statistically processed to yield the minimum, maximum, mean, and standard deviation of each coordination information element," 92 | The resultant ordered vector defines a structure fingerprint, $v^{struct}$: 93 | 94 | $$ 95 | \mathbf{v}^\mathrm{struct} = [ 96 | 97 | \min(w|_{\mathrm{CN}=1}), \quad \max(w|_{\mathrm{CN}=1}), \quad \mathrm{mean}(w|_{\mathrm{CN}=1}), \quad \mathrm{std}(w|_{\mathrm{CN}=1}), \dots, 98 | 99 | \min(w|_{\mathrm{CN}=24}), \quad \max(w|_{\mathrm{CN}=24}), \quad \mathrm{mean}(w|_{\mathrm{CN}=24}), \quad \mathrm{std}(w|_{\mathrm{CN}=24}) 100 | 101 | ]^\mathrm{T} 102 | $$ 103 | 104 | ## Structure Distance/Dissimilarity 105 | 106 | Finally, structure similarity is determined by the distance, _d_, between two structure fingerprints $v_{i}^{struct}$ and $v_{j}^{struct}$: 107 | 108 | $$ 109 | d = || \mathbf{v}_{i}^\mathrm{struct} - \mathbf{v}_{j}^\mathrm{struct} || 110 | $$ 111 | 112 | A small distance value indicates high similarity between two structures, whereas a large distance (>1) suggests that the structures are very dissimilar," 113 | The spinel example below gives an approximate threshold up to which **distance you can still consider two structures to be similar (0.9)**," 114 | Anything beyond 0.9 is most certainly not the same structure prototype. 115 | 116 | ## Examples 117 | 118 | - Diamond ([mp-66](https://materialsproject.org/materials/mp-66/)) vs. $\ce{GaAs}$ ([mp-2534](https://materialsproject.org/materials/mp-2534/)) $\rightarrow$ _d_ = 0 119 | - Diamond ([mp-66](https://materialsproject.org/materials/mp-66/)) vs. rocksalt ([mp-22862](https://materiahttps://materialsproject.org/materials/mp-5827/lsproject.org/materials/mp-22862/)) $\rightarrow$ _d_ = 3.5724 120 | - Diamond ([mp-66](https://materialsproject.org/materials/mp-66/)) vs. perfect $\ce{CaTiO3}$ perovskite ([mp-5827](https://materialsproject.org/materials/mp-5827/)) $\rightarrow$ _d_ = 3.5540 121 | - Rocksalt ([mp-22862](https://materialsproject.org/materials/mp-22862/)) vs. perfect $\ce{CaTiO3}$ perovskite ([mp-5827](https://materialsproject.org/materials/mp-5827/)) $\rightarrow$ _d_ = 2.7417 122 | - $\ce{Ca(CoS2)2}$-spinel ([mvc-12728](https://materialsproject.org/materials/mvc-12728/)) vs. $\ce{Si(CdO2)2}$-spinel ([mp-560842](https://materialsproject.org/materials/mp-560842/)) $\rightarrow$ _d_ = 0.8877 123 | 124 | Below is a python code snippet that allows you to quickly reproduce above results," 125 | You will need to install [pymatgen](https://github.com/materialsproject/pymatgen) and [matminer](https://github.com/hackingmaterials/matminer) for this to work," 126 | Both are easily accessible via the [Python Package Index](https://pypi.python.org/pypi). 127 | 128 | ```python 129 | import numpy as np 130 | from pymatgen import MPRester 131 | from matminer.featurizers.site import CrystalNNFingerprint 132 | from matminer.featurizers.structure import SiteStatsFingerprint 133 | 134 | with MPRester() as mpr: 135 | 136 | # Get structures. 137 | diamond = mpr.get_structure_by_material_id("mp-66") 138 | gaas = mpr.get_structure_by_material_id("mp-2534") 139 | rocksalt = mpr.get_structure_by_material_id("mp-22862") 140 | perovskite = mpr.get_structure_by_material_id("mp-5827") 141 | spinel_caco2s4 = mpr.get_structure_by_material_id("mvc-12728") 142 | spinel_sicd2O4 = mpr.get_structure_by_material_id("mp-560842") 143 | 144 | # Calculate structure fingerprints. 145 | ssf = SiteStatsFingerprint( 146 | CrystalNNFingerprint.from_preset('ops', distance_cutoffs=None, x_diff_weight=0), 147 | stats=('mean', 'std_dev', 'minimum', 'maximum')) 148 | v_diamond = np.array(ssf.featurize(diamond)) 149 | v_gaas = np.array(ssf.featurize(gaas)) 150 | v_rocksalt = np.array(ssf.featurize(rocksalt)) 151 | v_perovskite = np.array(ssf.featurize(perovskite)) 152 | v_spinel_caco2s4 = np.array(ssf.featurize(spinel_caco2s4)) 153 | v_spinel_sicd2O4 = np.array(ssf.featurize(spinel_sicd2O4)) 154 | 155 | # Print out distance between structures. 156 | print('Distance between diamond and GaAs: {:.4f}'.format(np.linalg.norm(v_diamond - v_gaas))) 157 | print('Distance between diamond and rocksalt: {:.4f}'.format(np.linalg.norm(v_diamond - v_rocksalt))) 158 | print('Distance between diamond and perovskite: {:.4f}'.format(np.linalg.norm(v_diamond - v_perovskite))) 159 | print('Distance between rocksalt and perovskite: {:.4f}'.format(np.linalg.norm(v_rocksalt - v_perovskite))) 160 | print('Distance between Ca(CoS2)2-spinel and Si(CdO2)2-spinel: {:.4f}'.format(np.linalg.norm(v_spinel_caco2s4 - v_spinel_sicd2O4))) 161 | ``` 162 | 163 | ## References 164 | 165 | [^1]: N. E. R. Zimmermann, D. Winston, K. A. Persson, A. Jain, in preparation (2018) 166 | [^2]: 10.3389/fmats.2017.00034 167 | [^3]: H. Pan, J. Dagdelen, N. E. R. Zimmermann, A. Jain, in preparation (2018) 168 | 169 | ## Authors 170 | 171 | Nils Zimmermann, Donny Winston, Handong Ling, Oxana Andriuc 172 | -------------------------------------------------------------------------------- /docs/methodology/piezoelectricity.md: -------------------------------------------------------------------------------- 1 | # Piezoelectricity Calculations 2 | 3 | ## Introduction 4 | 5 | Piezoelectricity is a reversible physical process that occurs in some 6 | materials whereby an electric moment is generated upon the application 7 | of a stress. This is often referred to as the direct piezoelectric 8 | effect. Conversely, the indirect piezoelectric effect refers to the case 9 | when a strain is generated in a material upon the application of an 10 | electric field. The mathematical description of piezoelectricity relates 11 | the strain (or stress) to the electric field via a third order tensor. 12 | This tensor describes the response of any piezoelectric bulk material, 13 | when subjected to an electric field or a mechanical load. 14 | 15 | The piezoelectric constants from the Materials Project (MP) are 16 | calculated from first principles Density Functional Perturbation Theory 17 | (DFPT) [^1] and are approximated as the superimposed effect of an 18 | electronic and ionic contribution. From the full piezoelectric tensor, 19 | several properties are derived such as the maximum longitudinal 20 | piezoelectric modulus and the corresponding crystallographic direction. 21 | Just as with the elastic constants, multiple consistency checks are 22 | performed on all the calculated piezoelectric data to ensure its 23 | reliability and accuracy. 24 | 25 | ![Cubic_pic1](/methodology/img/piezoelectricity/Cubic_pic1.png) 26 | _Figure 1: longitudinal piezoelectric modulus-surface 27 | for a cubic compound, showing the maximum response in the <111> 28 | family of directions._ 29 | 30 | ## Formalism 31 | 32 | In this work, we calculate the piezoelectric stress coefficients, 33 | $\textstyle e_{ijk}^{T}$ from DFPT, with units of 34 | $\textstyle C/m^{2}$. These can be defined in terms of thermodynamic 35 | derivatives as shown below [^2]. 36 | 37 | $$ 38 | e_{ijk}^{T}= \left(\frac{\partial D_{i}}{\partial \varepsilon_{jk}}\right)_{E, T} = -\left(\frac{\partial \sigma_{jk}}{\partial E_{i}}\right)_{\varepsilon, T} \! 39 | $$ 40 | 41 | where $\textstyle D$, $\textstyle E$, 42 | $\textstyle \varepsilon$, $\textstyle \sigma$ and 43 | $\textstyle T$ represent the electric displacement field, the 44 | electric field, the strain tensor, the stress tensor and the 45 | temperature, respectively. 46 | 47 | The above relations can be written in Voigt-notation as shown below. 48 | 49 | $$ 50 | e_{ij}^{T}= \left(\frac{\partial D_{i}}{\partial \varepsilon_{j}}\right)_{E, T} = -\left(\frac{\partial \sigma_{j}}{\partial E_{i}}\right)_{\varepsilon, T} \! 51 | $$ 52 | 53 | We note that the most commonly used piezoelectric constants appearing in 54 | the (experimental) literature are the piezoelectric strain constants, 55 | usually denoted by $\textstyle d_{ijk}$. These can be readily 56 | related to the constants $\textstyle e_{ijk}$ if the elastic 57 | compliances $\textstyle s_{lmjk}^{T}$ (at constant electric field 58 | and temperature) of the materials are known: 59 | $\textstyle d_{ijk}^{T} = e_{ilm} s_{lmjk}^{ET}$. In particular, the 60 | piezoelectric strain constants can be expressed thermodynamically as 61 | shown below 62 | 63 | $$ 64 | d_{kij}^{T} = \left(\frac{\partial \varepsilon_{ij}}{\partial E_{k}}\right)_{\sigma, T} = \left(\frac{\partial D_{k}}{\partial \sigma_{ij}}\right)_{E, T} \! 65 | $$ 66 | 67 | It is well-known that the piezoelectric behavior can only occur in 68 | crystals that lack inversion symmetry. This is the direct consequence of 69 | the symmetry properties of the piezoelectric tensor, which is of order 3. Another fundamental requirement for piezoelectric behavior is that 70 | the material has a band gap. Combined, these criteria severely limit the 71 | amount of compounds in nature that have the potential to exhibit 72 | piezoelectric behavior. 73 | 74 | For the Materials Project in particular, potential piezoelectric 75 | materials in the database are identified by i) allowing only structures 76 | with space groups 1, 3-9, 16-46, 75-82, 89-122, 143-146, 149-161, 77 | 168-174, 177-190, 195-199, 207-220 (since these space groups lack 78 | inversion symmetry), and in addition ii) the calculated DFT bandgap of 79 | the material > 0.1 eV. Compounds in the Materials Project database 80 | that satisfy these criteria are selected for a full-DFT calculation of 81 | the piezoelectric tensor and derived properties (see below). 82 | 83 | ## Derived piezoelectric properties 84 | 85 | For elastic properties, which are based on a tensor of order 4, 86 | isotropic Voigt and Reuss averages can be derived on the bulk and shear 87 | moduli. For piezoelectric properties, this isotropic averaging-approach 88 | does not quite work due to the requirement that inversion symmetry 89 | cannot occur in piezoelectric materials. On MP, in addition to the 90 | piezoelectric tensor in Voigt-notation, we report the maximum 91 | longitudinal piezoelectric modulus of the compound and the corresponding 92 | crystallographic direction in which this occurs. One can think of these 93 | quantities as the piezoelectric counterpart of the well-known Young's 94 | modulus and the stiffest elastic direction in the context of 95 | elasticity-theory. Fig. 1 shows an example of how the longitudinal 96 | piezoelectric modulus can be represented in 3D. This is for the case of 97 | a cubic material. As can be seen clearly, the maximum modulus occurs in 98 | the <111> family of crystallographic directions. By symmetry, this 99 | is always the case for cubic piezoelectric materials. Fig. 2 shows a 100 | more complicated longitudinal piezoelectric modulus-surface for an 101 | orthorhombic compound. In that case, the relative magnitudes of the 102 | tensor components dictate in which crystallographic direction, the 103 | maximum response occurs. Finally, note that for some compounds, a 104 | piezoelectric response is only induced by shear deformation rather than 105 | tensile or compressive deformation. For these cases, the response cannot 106 | be depicted such as in Figs. 1 and 2. The representations such as in 107 | Figs. 1 and 2 and created using the open-source MTEX package [^3][^4][^5]. 108 | 109 | ![ortho_1](/methodology/img/piezoelectricity/Ortho_1.png) 110 | _Figure 2: longitudinal piezoelectric modulus-surface 111 | for an orthorhombic compound._ 112 | 113 | ## DFT parameters 114 | 115 | The first-principles results presented in this work are performed using 116 | the projector augmented wave (PAW) method as implemented in the Vienna 117 | Ab Initio Simulation Package (VASP). In all calculations, we employ the 118 | Perdew, Becke and Ernzerhof (PBE) Generalized Gradient Approximation 119 | (GGA) for the exchange-correlation functional. A cut-off for the plane 120 | waves of 1000 eV is used and a uniform k-point density of approximately 121 | 2,000 per reciprocal atom (pra) is employed, which means that the number 122 | of atoms per cell multiplied by the number of k-points equals 123 | approximately 2,000. For the compounds that contain magnetic elements, a 124 | ferromagnetic state is initialized in the calculation. Similarly to our 125 | previous work, we expect to correctly converge to ferromagnetic and 126 | non-magnetic states in this way, but not to anti-ferromagnetic states. 127 | Due to the presence of strongly correlated electrons in some of the 128 | oxides, the GGA+U method is employed, with U representing the 129 | Hubbard-parameter. The values of U are chosen consistent with those 130 | employed in MP. 131 | 132 | ![piezomain](/methodology/img/piezoelectricity/Piezomain.png) 133 | *Figure 3: A graphical representation of the 134 | piezoelectric dataset, currently containing over 900 materials. A series 135 | of concentric circles indicate constant values of the maximum 136 | longitudinal piezoelectric modulus, $e_{ij,max}$. The compounds are broken 137 | up according to the crystal system and the different point group 138 | symmetry-classes considered in this work. See the paper [*A database to 139 | enable discovery and design of piezoelectric 140 | materials*](http://www.nature.com/articles/sdata201553) for 141 | details.* 142 | 143 | ## Crystal symmetry 144 | 145 | The crystal symmetry and in particular the point group dictates the 146 | symmetry of the piezoelectric tensor, relates components of the tensor 147 | to each other and imposes that certain components equal zero. All 148 | piezoelectric tensors in the Materials Project have been symmetrized for 149 | consistency with the underlying point group of the compound. Figure 4 150 | gives an overview of the symmetrized piezoelectric tensors in MP, broken 151 | up by the different piezoelectric point groups. Also, typical surface 152 | representations are shown. The point group that only yields 153 | piezoelectric behavior upon the application of shear is not included in 154 | the representation in Fig. 4. 155 | 156 | ![piezo_wiki](/methodology/img/piezoelectricity/Piezo_wiki_fig.png) 157 | *Figure 4: Piezoelectric tensors and symmetry 158 | classes considered in this work. Typical representations of the 159 | longitudinal piezoelectric modulus in 3D are also shown for each crystal 160 | point group. Note that depending on the components of the piezoelectric 161 | tensor, the surface representation can differ from those shown here. See 162 | the paper [*A database to enable discovery and design of piezoelectric 163 | materials*](http://www.nature.com/articles/sdata201553) for 164 | details.* 165 | 166 | ## Citation 167 | 168 | To cite the piezoelectric properties within the Materials Project, 169 | please reference the following work: 170 | 171 | - de Jong, Maarten and Chen, Wei and Geerlings, Henry and Asta, Mark and 172 | Persson, Kristin Aslaug. _A database to enable discovery and design of 173 | piezoelectric materials_, [Scientific Data 2 (2015)](http://www.nature.com/articles/sdata201553) 174 | 175 | The paper presents the results of our piezoelectric 176 | constant-calculations for the first batch of 941 compounds. Our 177 | DFT-parameters, the workflow and comparison to experiments are described 178 | in detail. Also, the filters in the workflow used for detecting 179 | anomalies in the calculations are described in the paper. 180 | 181 | ## Authors 182 | 183 | 1. Maarten de Jong 184 | 185 | ## References 186 | 187 | [^1]: 188 | Baroni, Giannozzi S. P. and Testa, A. Phys. Rev. Lett. 58, 1861 189 | (1987) 190 | 191 | [^2]: 192 | Nye, J. F. Physical properties of crystals (Clarendon press, 193 | 1985). 194 | 195 | [^3]: 196 | Bachmann, F., Hielscher, R. & Schaeben, H. Texture analysis with 197 | MTEX-free and open source software toolbox. Solid State Phenomena 160, 198 | 63–68 (2010). 199 | 200 | [^4]: 201 | Hielscher, R. & Schaeben, H. A novel pole figure inversion method: 202 | specification of the MTEX algorithm. Journal of Applied Crystallography 203 | 41, 1024–1037 (2008). 204 | 205 | [^5]: 206 | Mainprice, D., Hielscher, R. & Schaeben, H. Calculating 207 | anisotropic physical properties from texture data using the MTEX 208 | open-source package. Geological Society, London, Special Publications 209 | 360, 175–192 (2011). 210 | -------------------------------------------------------------------------------- /docs/methodology/dielectricity.md: -------------------------------------------------------------------------------- 1 | # Dielectric Calculations 2 | 3 | ## Introduction 4 | 5 | A dielectric is a material that can be polarized by an applied electric 6 | field. This limits the dielectric effect to materials with a non-zero 7 | band gap. The mathematical description of the dielectric effect is a 8 | tensor constant of proportionality that relates an externally applied 9 | electric field to the field within the material. Along with the 10 | elastic and piezoelectric tensors, the dielectric tensor provides all 11 | the information necessary for the solution of the constitutive equations 12 | in applications where electric and mechanical stresses are coupled. 13 | 14 | The dielectric tensors from the Materials Project (MP) are calculated 15 | from first principles Density Functional Perturbation Theory (DFPT) [^1] 16 | and are approximated as the superimposed effect of an electronic and 17 | ionic contribution. From the full piezoelectric tensor, several 18 | properties are derived such as the refractive index and potential for 19 | ferroelectricity. Just as with the piezoelectric and elastic constants, 20 | multiple consistency checks are performed on all the calculated 21 | dielectric data to ensure its reliability and accuracy. 22 | 23 | ## Formalism 24 | 25 | Formally, the dielectric tensor ε relates the externally applied 26 | electric field to the field within the material and can be defined as: 27 | 28 | $$ 29 | E_i=\sum_j \epsilon^{-1}_{ij}E_{0j} 30 | $$ 31 | 32 | where $E$ is the electric 33 | field inside the material and $E_0$ is the externally applied 34 | electric field. the indices *i*,*j* refer to the direction in space and 35 | take the values: ${1, 2, 3}$. The dielectric tensor can be split in 36 | the ionic ($\epsilon_0$) and electronic ($\epsilon*\infty$) 37 | contributions: 38 | 39 | $$ 40 | \epsilon_{ij}=\epsilon_{ij}^0+\epsilon_{ij}^\infty 41 | $$ 42 | 43 | Here, we consider only the response of non-zero band gap materials to 44 | time-invariant fields. In the hypothetical case that a material does not 45 | respond at all to the external field, $\epsilon_{ij}^\infty$ would 46 | be equal to the identity tensor and  $\epsilon_{ij}^0$ would be 47 | zero. In fact, materials with zero ionic contribution do exist. In 48 | general, for $\epsilon_{ij}^0$ to be non-zero, compounds need to 49 | have at least 2 atoms per primitive cell, each having a different atomic 50 | charge. The dielectric tensor is symmetric and respects all the symmetry 51 | operations of the corresponding point group. This limits the number of 52 | independent elements in the tensor to a minimum of 1 and a maximum of 6 53 | depending on the crystal symmetry. 54 | 55 | The dielectric response calculated herein corresponds to that of a 56 | single crystal. In polycrystalline samples, grains are oriented randomly 57 | and hence, the actual response will be different. Generally, the 58 | dielectric response varies with the frequency of the applied external 59 | field however here, we consider the static response (i.e., the response 60 | at constant electric fields or the long wavelength limit). Since the 61 | ionic contribution vanishes at high frequencies, our results can be used 62 | to obtain an estimate of the refractive index, n, at optical frequencies 63 | and far from resonance effects using the well known formula[^2]: 64 | 65 | $$ 66 | n=\sqrt{\epsilon^\infty_{poly}} 67 | $$ 68 | 69 | where $\epsilon^\infty_{poly}$ is the average of the eigenvalues of 70 | the electronic contribution to the dielectric tensor. It should be noted 71 | this equation for the refractive index assumes the material is 72 | non-magnetic. 73 | 74 | ## DFT Parameters 75 | 76 | The initial set of 1,056 dielectric tensors were calculated using the 77 | Vienna Ab-Initio Simulation Package[^3][^4][^5][^6] (VASP version 5.3.4) 78 | combined with the Generalized Gradient Approximation 79 | GGA/PBE[^7][^8]+U[^9][^10] exchange-correlation functional and Projector 80 | Augmented Wave pseudopotentials[^11][^12]. The U values are energy 81 | corrections that address the spurious self-interaction energy introduced 82 | by GGA. Here, we used U values for d orbitals only that were fitted to 83 | experimental binary formation enthalpies using Wang et al.[^13] method. 84 | The full list of U values used, can be found in ref.[^10]. The k-point 85 | density was set at 3,000 per reciprocal atom and the plane wave energy 86 | cut-off at 600 eV (ref. 4). For detailed information on the calculation 87 | of the dielectric tensor within the DFPT framework we refer to Baroni et 88 | al.[^14][^15] and Gonze & Lee[^16]. 89 | 90 | [Piezoelectricity calculations](/methodology/piezoelectricity) use the same 91 | DFPT methodology with a tighter parameter set to achieve convergence. As 92 | a result, the dielectric tensor is already converged in these 93 | calculations and is reported for any non-centrosymmetric material, not 94 | in the initial dataset of dielectrics. 95 | 96 | ## Benchmarking 97 | 98 | We see that in most cases, it is possible to predict the dielectric 99 | constant of materials with a relative deviation of less than +/−25% from 100 | experimental values at room temperature. Including local field effects 101 | gives the smallest mean absolute relative deviation ( MARD= 16.2 % for 102 | GGA). Furthermore, we note a tendency to overestimate rather than 103 | underestimate the dielectric constant relative to experiments, which is 104 | a well-known effect of DFPT [^17][^18][^19] for the electronic 105 | contribution. Although it has often been related to the band gap 106 | underestimation problem of DFT, DFPT is a ground state theory and hence, 107 | the dielectric constant should, in principle, be described exactly 108 | [^20]. In fact, as described by various authors, the problem is likely 109 | linked to the exchange-correlation functional 110 | [^21][^22][^23][^24][^25][^26]. Specifically, the exchange correlation 111 | functional has been found to depend on polarization but the actual 112 | dependence formula is, unfortunately, not known [^27][^28][^29]. 113 | Additionally, the validity of GGA depends on the charge density varying 114 | slowly—an assumption that may be broken when an external electric field 115 | is applied [^30]. 116 | ![Benchmarking DFPT dielectric constants](/methodology/img/dielectricity/Dielectric_benchmarking.png) 117 | 118 | ## Citation 119 | 120 | To cite the dielectric properties within the Materials Project, please 121 | reference the following work: 122 | 123 | - Benchmarking density functional perturbation theory to enable 124 | high-throughput screening of materials for dielectric constant and 125 | refractive index. Ioannis Petousis, Wei Chen, Geoffroy Hautier, Tanja 126 | Graf, Thomas D. Schladt, Kristin A. Persson, and Fritz B. Prinz. Phys. 127 | Rev. B 93(11). [DOI:10.1103/PhysRevB.93.115151](https://doi.org/10.1103/PhysRevB.93.115151) 128 | 129 | - High-throughput screening of inorganic compounds for the discovery of 130 | novel dielectric and optical materials. Ioannis Petousis, David 131 | Mrdjenovich, Eric Ballouz, Miao Liu, Donald Winston, Wei Chen, Tanja 132 | Graf, Thomas D. Schladt, Kristin A. Persson, and Fritz B. Prinz. 133 | Scientific Data 4. [DOI:10.1038/sdata.2016.134](https://doi.org/10.1038/sdata.2016.134) 134 | 135 | These papers present the results of our dielectric constant-calculations 136 | for the first batch of 1,056 compounds. Our DFT-parameters, the 137 | workflow, the workflow filters used for detecting anomalies in the 138 | calculations and comparison to experiments are described in detail. 139 | 140 | ## Authors 141 | 142 | 1. Shyam Dwaraknath 143 | 2. Ioannis Petousis 144 | 145 | ## References 146 | 147 | [^1]: 148 | Baroni, Giannozzi S. P. and Testa, A. Phys. Rev. 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B 268 | 60, 14224 (1999). 269 | -------------------------------------------------------------------------------- /docs/user-guide/structure-predictor.md: -------------------------------------------------------------------------------- 1 | # Structure Predictor 2 | 3 | ## Manual 4 | 5 | ### Background on Data Mined Crystal Structure and Compound Prediction 6 | 7 | Crystal structure and compound prediction is an essential step of computational materials 8 | design. 9 | Indeed, while many materials properties can be computed nowadays with _ab-initio_ 10 | computations. 11 | Those computed properties are only relevant if they are evaluated on a compound (i.e., a 12 | stoichiometry and crystal structure) stable enough to be formed. 13 | Crystal structure prediction can be quite useful 14 | for experimentalists too. 15 | For instance, when only powder XRD experiments are available after synthesis of a new compound, a theoretical suggestion of a likely structure can tremendously help the structure refinement and determination for example. 16 | 17 | The most common approach in the field of crystal structure prediction is to treat it as an optimization problem. [^1] 18 | Researchers use optimization algorithms to search for the minimum of the relevant thermodynamic potential (e.g., the energy at 0 K, 0 atm) by varying the crystal's degrees of freedom (lattice constants, atomic positions). 19 | This optimization is extremely challenging as the energy landscape is very rugged and full of local minima. 20 | Very computationally expensive advanced optimization techniques (e.g., simulated annealing and genetic algorithm) are usually necessary to tackle this optimization problem. 21 | 22 | In a departure to this traditional approach, the methods we have developed use a combination of data mining and _ab-initio_ computations in the density functional theory (DFT) framework to tackle this problem with a limited computational budget. 23 | The basic idea is to learn the chemical rules governing phase stability from a database of experimentally known compounds. 24 | Embedding those rules in a mathematical model, we can predict what are the most likely compounds to form in a given chemical system. 25 | Finally, the last step consists of testing those candidates for stability using _ab-initio_ computations ([see Phase Diagram](phase-diagram.md)). 26 | 27 | ### The Ionic Substitution based Structure Prediction Method 28 | 29 | The compound prediction model available on the Materials Project now, through the structure predictor app, is based on our recent work on the data mining of ionic substitutions. 30 | In this section we will briefly explain the idea of the approach and how to use the explorer. 31 | More details can be found in Hautier et al.[^2] 32 | 33 | ### The basic idea 34 | 35 | ![substitution example](img/structure-predictor/substitution-example.png) 36 | _Figure 1: An example of ionic substitution._ 37 | 38 | It is common for chemists to propose new compounds from the substitution of 39 | another, chemically similar, ion. 40 | For instance, as illustrated in Figure 1, knowing that BaTiO3 forms a perovskite structure, 41 | one can deduct that it is likely for another chemically similar ion as Ca2+ to form the same structure. 42 | We have 43 | implemented a mathematical model that learns these substitution rules from a database of experimentally 44 | observed crystal structure (e.g., the ICSD). 45 | Basically, what the model provides is a probability 46 | distribution for any ionic substitution. 47 | In Figure 2 we show the matrix indicating the data mined 48 | substitution tendency for two ionic species obtained from this work. 49 | The ions have been sorted by Mendeleev number and therefore groups of chemically similar ions (e.g., the transition metals) are grouped together. 50 | Red colors indicate that two ions 51 | tend to substitute while blue is associated with pair of species not substituting to each other. 52 | 53 | ![ionic substitution correlations](img/structure-predictor/ions-correlation.png) 54 | _Figure 2: Data mined tendency for ionic substitutions. 55 | Red indicates high substitution tendency. 56 | Blue indicates that the tow ions tend to not substitute._ 57 | 58 | ### The compound prediction procedure 59 | 60 | The product of our data mining approach is a probability function indicating how likely is a specific set of ionic substitutions. 61 | The model we used was inspired by previous work in the field of machine translation. 62 | In this field, it is the probability for a word in one language to be able to be substituted by a word in another language. 63 | In our case, we substitute ions rather than words. 64 | After we built this probability function, from a database of experimental data (here the ICSD), we can perform compound predictions. 65 | Figure 3 illustrates the procedure for 4 ions (but this can be generalized to any number of species). 66 | Targeting a specific combination of 4 ions (e.g., Ba2+, Fe3+, La3+, O2- ), we look for any substitution from known compounds (in the ICSD) that have a high enough probability to be likely to form a new stable compound. 67 | If the substitution is higher than a certain threshold we keep it as a possible candidate, otherwise we discard it and go to the next ICSD compound. 68 | There is also a check to make sure we do not form duplicate structures and only predict charge balanced compounds. 69 | 70 | ![substitution flowchart](img/structure-predictor/substitution-flowchart.png) 71 | _Figure 3: Procedure for proposing new compound candidates in a quaternary system using the ionic substitution probability._ 72 | 73 | From this procedure, we can see that the threshold set is quite important. 74 | A higher threshold will give you less false positives (suggested compounds that are not stable), but also less true positives. 75 | On the other hand, too low a threshold will give more true positives, but consequently, more false positives. 76 | There is a compromise to find between how exhaustive you want to be and how many candidates you can have, in terms of computational budget (that you will have to test down the road for stability using DFT). 77 | 78 | ### Performance and Limitations 79 | 80 | ### Using the Structure Predictor 81 | 82 | #### Entering Inputs 83 | 84 | Practically, the procedure for getting predictions consists in 3 steps 85 | 86 | 1. Pick elements: Select on the periodic table what constituent elements comprise the chemical space you are interested in. 87 | For instance if you want to make predictions for battery materials based on Li, Mn and O, you should pick those three elements. 88 | 89 | 2. Pick oxidation states: The model uses the oxidation states to make predictions. 90 | V3+ does not substitute with the same elements as V5+, so if you want to study Mn3+ compounds, you should pick +3 for Mn, +1 for Li (no other choices anyway) and -2 for O. 91 | Sometimes you do not know what oxidation states you are interest in. 92 | Let say you want all Li-Mn-O compounds regardless of the oxidation state of Mn. 93 | Then, I would suggest running the model several times, one for Mn2+, one for Mn3+, and lastly one for Mn4+. 94 | This should cover all the chemical space you are looking at. 95 | 96 | 3. Start the prediction: click 'Predict Structure' to begin the prediction. 97 | Predictions are not immediately available and will require some time to complete. 98 | You can monitor the status of your request in the [dashboard](https://materialsproject.org/dashboard). 99 | 100 | 4. Examine results: Upon completion of the task, you will be given a link to a landing page providing details on the candidate structures. 101 | We also provide cif files for the predicted compounds as well as VASP files ready to be run with standard parameters. 102 | We do not provide any DFT results due our limited computational budget for the moment. 103 | It is the responsibility of the user to run the predictions. 104 | Also, as the pseudopotentials are proprietary in VASP (POTCARs) we do not provide those but a script is sent along that can be run to make sure the POTCARs are built from a directory containing all pseudopotentials. 105 | 106 | #### Interpreting the Results 107 | 108 | The results pages provides a set of structure id's corresponding to the candidate structures. 109 | A link is provided for each structure id, which provides structure visualization, lattice vectors, atomic positions, and simulated x-ray spectra. 110 | Cif and POSCAR files for each candidate can be downloaded. 111 | Typically, the candidates need to be tested for stability against each other (seeing what is the lowest energy structure amongst the candidates at a given composition) but also against other phases known in nature. 112 | For instance, if a AB compound is proposed and its energy is higher than a combination of half A2B and half AB2. 113 | This stability analysis can be performed using the convex hull construction that will effectively test the stability of the phases against each other and come with a set of stable phases that are on the hull. 114 | Figure 4 shows a convex hull (in green) for an A-B system. 115 | Blue points indicate phases that are not on the hull and therefore unstable and red points indicate stable phases. 116 | For instance, the construction shows directly that the phase γ at AB will decompose into α1 and β2. 117 | 118 | ![convex hull example](img/structure-predictor/convex-hull.png) 119 | _Figure 4: An example of the convex hull construction._ 120 | 121 | More information about phase stability and convex hull can be obtained in the [phase diagram app manual](phase-diagram.md). 122 | 123 | Please note that we only presented an approach for building zero K, zero pressure phase diagrams. 124 | It is possible to use the candidates proposed by the model to perform more advanced stability studies for instance at finite temperature. 125 | This is more expensive computationally though as the different entropy components (configuration, vibration, etc...) need to be taken into account. 126 | 127 | Finally, as we present a usage of our candidates for computations, an experimentalist can also use these candidates to test different structures versus a powder diffraction pattern. 128 | 129 | ### Future features 130 | 131 | In the future, we want to give the user the option to perform substitution of several ions for one ion in a starting structure. 132 | For instance, if one is interested in ternary oxychlorides (M, O2-, Cl1-) there will be only few ternary compounds that will be good candidates for a substitution generating oxychlorides (e.g., oxybromides). 133 | A strategy to increase the pool of possible structure is to allow substitution of one ion by O2- and Cl-. 134 | For instance, we would start with an oxide and substitute the O2- by a mixture of O2- and Cl-. 135 | The amount of O and Cl will be set to achieve charge balance and a simple model (electrostatics or other) could be used to pick an ordering of the two substituted species. 136 | 137 | The only data mined model accessible now is the substitution predictor. 138 | We have developed another model based on correlations between crystal structures at different compositions.[^3][^4] We plan to give access to this model in the future. 139 | The two models are complimentary: the model based on correlations between structure is more efficient in data rich regions (e.g., ternary oxides) while the ionic substitution model is more efficient in data sparse regions (e.g., quaternaries). 140 | 141 | ### Citations 142 | 143 | To cite the Structure Predictor App, please reference the following works: 144 | 145 | - G. Hautier, V. Ehrlacher, C.C. Fischer, A. Jain, G. Ceder, Data Mined Ionic Substitutions for the Discovery of New Compounds, Inorganic Chemistry, vol. 50, 2011, pp. 656-663. 146 | - A. Jain, G. Hautier, C. J. Moore, S. P. Ong, C. C. Fischer, T. Mueller, K. A. Persson, and G. Ceder, A high-throughput infrastructure for density functional theory calculations, Computational Materials Science, vol. 50, 2011, pp. 2295-2310. 147 | 148 | [^1]: 10.1038/nmat2321 149 | [^2]: 10.1021/ic102031h 150 | [^3]: 10.1021/cm100795d 151 | [^4]: 10.1038/nmat1691 152 | 153 | ### Authors 154 | 155 | - Geoffroy Hautier 156 | - Anubhav Jain 157 | -------------------------------------------------------------------------------- /docs/user-guide/pourbaix-tool.md: -------------------------------------------------------------------------------- 1 | # Pourbaix App 2 | 3 | ## Introduction 4 | 5 | A Pourbaix diagram, also frequently called a potential-pH diagram, or E-pH diagram, is a representation of aqueous phase electrochemical equilibria. 6 | It is a two-dimensional representation of a three-dimensional free energy-pH-potential diagram. 7 | In other words, it shows water-stable phases as a function of pH and potential, where, potential is defined with respect to the standard hydrogen electrode. 8 | 9 | Experimentally determining Pourbaix Diagrams is painstaking work, as we need not only the free energy of aqueous ions, but also that of all solid phases that a system can exist in. 10 | The Materials Project offers a very convenient and powerful database of materials properties which has been used to generate Pourbaix diagrams in a high-throughput manner. 11 | 12 | This manual outlines the usage of the Pourbaix App to calculate Pourbaix diagrams, and the thermodynamic formalism underlying the app. 13 | 14 | ## Thermodynamic Formalism of Pourbaix Diagrams 15 | 16 | To calculate a Pourbaix diagram, free energies of the solid phases, and of the aqueous ions is required. 17 | Calculating free energies of ions is tricky, and time-consuming. 18 | To overcome this problem, a methodology utilizing experimentally measured free energies of aqueous ions and the calculated DFT energies for solid phases available in the Materials Project was developed. 19 | [^1] Note that the correction scheme described below is applied over and above any compatibilities/corrections which are applied to the species. 20 | 21 | ### Referencing Energies of Aqueous Ions 22 | 23 | Briefly, for each ion, a reference solid is chosen, and the correction term is calculated for the ion as the energy difference between the experimental and the DFT calculated energies of the reference solid. 24 | The basic idea behind this scheme is that, if we have a reference energy for an aqueous ion which reproduces the correct dissolution for one solid, then accurate DFT solid-solid energy differences ensure that all other solids dissolve accurately with respect to that ion. 25 | The better the solid is represented by DFT, the more transferable the reference aqueous energy becomes. 26 | We therefore prefer to choose simple chemical systems (primarily binaries with an uncomplicated electronic structure) as representative solids. 27 | 28 | For an aqueous ion i at standard state conditions (e.g., room temperature, atmospheric pressure, and $10^{-6}$ M concentration) using a representative solid s, we define the chemical potential as: 29 | 30 | ![Pourbaix Reference Energies](img/pourbaix-app/Ion_ref_energy.png) 31 | _Figure 1: Schematic to reference experimental aqueous ion energies to DFT data_ 32 | 33 | $$ 34 | \begin{align} \mu_{i(aq)}^0 &= \mu_{i(aq)}^{0,{\rm exp}} + \left[\Delta g_s^{0,{\rm DFT}} - \Delta g_s^{0,{\rm exp}}\right] \ 35 | & = \mu_{i(aq)}^{0,{\rm exp}} + \Delta\mu_s^{0, {\rm DFT - exp}} 36 | \end{align} 37 | $$ 38 | 39 | Figure 1 shows this schematically. 40 | 41 | ### Correction for Water 42 | 43 | In an aqueous environment, many chemical and electrochemical reactions are enabled by the breakdown, formation, or incorporation of water molecules. 44 | It is therefore important that the free energy of formation of water is captured accurately. 45 | This is known accurately from experiments as $-2.46~eV$. 46 | So, at standard state, the free energy of formation of water is set as follows: 47 | 48 | $$ 49 | \begin{align} 50 | \mu^0_{{\rm H_2O}} &= \Delta g^{0, {\rm exp}}_{\rm H_2O} \ 51 | & = -2.46 eV 52 | \end{align} 53 | $$ 54 | 55 | ### Correction for Elemental Gaseous, and Liquid States, except $\ce{H2}$ 56 | 57 | For all gaseous elements, the experimentally determined entropic contribution at 298 K is added to the DFT/corrected energy of the element as follows: 58 | 59 | $$\mu_i^{\rm ref} = E_i^{0, {\rm DFT}} + \Delta E_i^{\rm correction} - Ts_i^{\rm exp}$$ 60 | 61 | This is implemented for the following elements: $\ce{O_2, F_2, Cl_2, Br_2, Hg}$ 62 | 63 | ### Correction for $\ce{H_2}$ 64 | 65 | In an aqueous environment, $\ce{O_2}$ and $\ce{H_2}$ in their gaseous states are in equilibrium with water through the reaction 66 | 67 | $\ce{H2(g) + 1/2O2(g) <-> H2O(l)}$ 68 | 69 | Hence, the hydrogen energy is corrected such that the experimental free energy of formation of $\ce{H_2O}$ is reproduced. 70 | 71 | $$ 72 | \begin{align} 73 | \mu_{\rm H}^{\rm ref} & = \frac{1}{2}\left[g_{\rm H_2O}^0 - \mu_O^0 - \Delta g_{\rm H_2O}^{0, {\rm exp}} \right] \ 74 | & \approx \frac{1}{2}\left[ E_{\rm H_2O}^{0, {\rm DFT}} -Ts_{\rm H_2O}^0 - \mu_O^0 - \mu_{\rm H_2O}^{0, {\rm exp}} \right] 75 | \end{align} 76 | $$ 77 | 78 | ### Electrochemical Stability of Metastable Materials 79 | 80 | In principle, Pourbaix diagrams account for materials only at thermodynamic equilibrium, providing no insight into the electrochemical stability of metastable materials which find practical applications in many commercial applications. 81 | However, one can compute the Gibbs free energy difference for an arbitrary material with respect to the Pourbaix stable domains as a function of pH and E, providing an electrochemical (in)stability map for this material. 82 | For detailed information on the formalism and its applications see reference 2.[^2] 83 | 84 | ## Using the Computational Pourbaix App 85 | 86 | The Pourbaix app is capable of plotting elemental, and multi-element Pourbaix diagrams. 87 | To construct an Elemental Pourbaix diagram, enter the element of choice, and click on the Generate button. 88 | 89 | To generate a multi-elemental Pourbaix diagram, choose the desired multiple elements from the periodic table, and click the Generate button. 90 | Note that oxygen and hydrogen are included by default, since these elements are always "open" in a Pourbaix diagram. 91 | 92 | For multi-elemental diagrams, sliders are provided to specify a composition of the elements. 93 | Note that for each composition, a new Pourbaix diagram is generated from scratch. 94 | 95 | To generate electrochemical stability maps of a specific material go to the material's details page and click on the "Aqueous Stability (Pourbaix)" tab which can be found in the "Generate Phase Diagram" tab. 96 | A new tab will open which will show the electrochemical stability map superimposed on a Pourbaix diagram. 97 | The ratio of elements used to generate the Pourbaix diagram are same as that of the material in consideration. 98 | Electrochemical stability maps are available for materials with up to three non H and O elements. 99 | For materials with more than three elements, one can use pymatgen to generate the maps programmatically. 100 | 101 | ### Interfacing With the Data 102 | 103 | To ensure a clutter-free diagram, the domains on the Pourbaix diagram are not labeled by default. 104 | To view labels on the plot, select the "Domain Labels" check box. 105 | Each domain has a mouse-over point located at the center of the domain. 106 | Mousing over these points displays the entries corresponding to the domain. 107 | Domains which contain a solid in solution are shaded. 108 | This helps identify passivation regions, especially in multi-elemental systems, were identifying passivation regions is tricky. 109 | Zooming into domains is quite simple! Just drag a selection window using your mouse. 110 | To reset zoom, click on the reset zoom button which appears on the upper right corner. 111 | Data tables are shown to the right of the Pourbaix diagram. 112 | Mousing over rows in the "Stable" column of the table highlights the corresponding entries in the Pourbaix diagram. 113 | Some stable entries may not get highlighted. 114 | This is because the domains corresponding to these entries lies outside the standard limits of the Pourbaix diagram. 115 | The "Unstable" column in the table lists the unstable entries, and their corresponding energies above hull. 116 | Links in the data tables lead to more information about the corresponding entries. 117 | Unlinked entries are ions. 118 | Mousing over the book icon next to the ions shows the reference for the free energy of formation of the aqueous ion. 119 | 120 | ## Demonstration of the Pourbaix App 121 | 122 | This section briefly demonstrates an elemental Pourbaix diagram, a multi-elemental Pourbaix diagram, and an electrochemical stability map. 123 | 124 | ### Elemental Pourbaix Diagram 125 | 126 | Figure 2 shows the elemental Pourbaix diagram for Fe. 127 | The default concentration of ions is $10^{-8}$ M, but can be varied using the "Concentration" slider above the diagram. 128 | 129 | ![fe_pourbaix_diagram](img/pourbaix-app/Fe_pourbaix.png) 130 | _Figure 2: Pourbaix diagram for elemental Fe._ 131 | 132 | The two orange lines are the hydrogen reduction line, and the line denoting water oxidation to $\ce{O_2}$. 133 | These are clearly labeled in Figure 3. 134 | These lines show the stability region of H2O. 135 | For example, water is unstable below the $\ce{H_2}$ line, and so, hydrogen gas evolves at the cathode at conditions below this line. 136 | Similarly, above the $\ce{O_2}$ line, oxygen gas is evolved at the anode. 137 | 138 | ![fe_pourbaix_diagram_ox_red_marked](img/pourbaix-app/Fe_Lines_marked.png) 139 | _Figure 3: Orange lines are the water oxidation and reduction lines in the Pourbaix diagram._ 140 | 141 | ### Multi-elemental Pourbaix diagram 142 | 143 | The stability of multiple-elements in aqueous environments is predicted using multi-elemental Pourbaix diagrams like the one shown in Figure 4. 144 | The composition slider bar can be seen above the plot. 145 | Here, the small white bar separating the two colors can be clicked on and dragged to change the ratio of Fe to Cr. 146 | This may, or may not have any effect on the Pourbaix diagram. 147 | More information about how multi-elemental Pourbaix diagrams vary as a function of composition can be found elsewhere.[^3] 148 | 149 | ![fe_cr_pourbaix_diagram](img/pourbaix-app/FeCr_pourbaix.png) 150 | _Figure 4: Multi-elemental Fe-Cr Pourbaix diagram at a composition of 18% Cr, 82% Fe._ 151 | 152 | For an n-element diagram, there are n coexisting phases. 153 | Note that these can be any mixture of solid, and aqueous phases. 154 | So, for the two-element diagram shown in Figure 4, there are two coexisting phases in each domain. 155 | As mentioned above, domains shaded blue indicate purely solid domains. 156 | For multi-elemental diagrams, shaded domains indicate those in which purely solid phases coexist. 157 | 158 | ### Electrochemical Stability Map 159 | 160 | Figure 5 shows the Gibbs free energy of $\ce{Fe_2O_3}$, as a scatter plot, superimposed over the Pourbaix diagram of Fe. 161 | For a material with more than one non H and O elements, the ratio of these elements is fixed to the ratio of elements of the material but the concentration of ions can be varied similar to the single- and multi-element Pourbaix diagrams. 162 | 163 | ![fe_cr_pourbaix_diagram](img/pourbaix-app/Fe2O3_stability_map.png) 164 | _Figure 5: Electrochemical stability map of Fe2O3 (mp-24972)._ 165 | 166 | A color bar is shown above the electrochemical stability maps. 167 | Note that Gibbs free energies larger than 1 eV/atom are not marked in the map. 168 | Stable and unstable phase energies can be found in the table to the right of the electrochemical stability map. 169 | 170 | ## Literature References for Ions 171 | 172 | The free energies of ions in the aqueous phase have been taken from standard references/recent publications. 173 | The acronyms which show up on the tool-tips associated with the aqueous ions, and their corresponding references are as follows. 174 | 175 | NBS Tables: NBS Thermodynamic tables.[^4] 176 | M. Pourbaix (1974): Atlas of Electrochemical Equilibria in Aqueous Solutions. [^5] 177 | Barin Knacke Kubaschewski: Thermochemical Properties of Inorganic Substances [^6] 178 | Barner and Scheuerman (1978): Handbook of thermochemical data for compounds and aqueous species [^7] 179 | Beverskog and Puigdomenech (1997): Beverskog and Puigdomenech, Corr. Sci. (1997) [^8] 180 | 181 | [^1]: K. A. Persson, B. Waldwick, P. Lazic, and G. Ceder, Phys. Rev. B, 85, 235438 (2012) 182 | [^2]: A. K. Singh, L. Zhou, A. Shinde, S. K. Suram, J. H. Montoya, D. Winston, J. M. Gregoire, K. A. Persson, Chem. Mater. 29, 10159 (2017) 183 | [^3]: Pourbaix Diagrams for Multielement Systems, Thompson, W. T., Kaye, M. H., Bale, C. W. and Pelton, A. D. (2011), in Uhlig's Corrosion Handbook, Third Edition (ed R. W. Revie), John Wiley & Sons, Inc., Hoboken, NJ, USA. 184 | [^4]: NBS Technical Note 270-1 to 270-8. D. D. Wagman et. al, U. S. Department of Commerce (1973) 185 | [^5]: Atlas of Electrochemical Equilibria in Aqueous Solutions, M. Pourbaix,, NACE (1974) 186 | [^6]: Thermochemical Properties of Inorganic Substances, I. Barin, O. Knacke, and O. Kubaschewski, Springer-Verlag, Berlin (1977) 187 | [^7]: Handbook of thermochemical data for compounds and aqueous species, H. E. Barner, and R. V. Scheuerman, Wiley, New York, 1978 188 | [^8]: Revised Pourbaix diagrams for Ni at 25-300^oC, B. Beverskog and I. Puigdomenech, Corr. Sci., 39, 969-980 (1997) 189 | 190 | ## Authors 191 | 192 | - Sai Jayaraman 193 | - Arunima K. Singh 194 | - Rebecca Stern 195 | - Eric Sivonxay 196 | -------------------------------------------------------------------------------- /docs/user-guide/interface-reactions.md: -------------------------------------------------------------------------------- 1 | # Introduction 2 | 3 | Interfaces between solid phases are critical in determining the optical, mechanical and transport properties of a system. 4 | Interfacial reactions can occur when two contacting materials are not thermodynamically stable against each other. 5 | Information about interface reactions is valuable in various aspects: the reaction energy reflects the reactivity of the interface, and the reaction products affect the performance of devices such as Li-ion batteries that are built from these materials. 6 | 7 | Experimental investigation of interface reactions is challenging as accessing the interface between two solids is difficult and the reaction layers have only limited thickness. 8 | It is thus highly valuable to predict possible interface reactions from a computational approach. 9 | 10 | Materials Project database provides calculated energies of a wide range of materials. 11 | By using all compounds in the relevant chemical system from Materials Project database, one can construct the reaction energy plots for the interface systems at 0 K and 0 atm. 12 | 13 | The Manual outlines the usage of the Interface Reactions App and the computational methods employed. 14 | 15 | ## Using the Interface Reactions App 16 | 17 | To construct the reaction energy plot for a closed system, enter the two reactants in contact into the fields “Reactant 1” and "Reactant 2" and click on “Compute” button. 18 | 19 | In the case where the interface system is open to a particular element at a constant chemical potential (e.g., solid-state synthesis under constant $O_2$ gas flow), after entering the reactants, click on "Advanced options", and then check the "Open element?" box, select the element from the drop-down list, and enter the desired relative chemical potential. 20 | Note that the relative chemical potential of an element is referenced to the chemical potential of pure substance of that element. 21 | For example, for element Li the reference chemical potential is that of Li metal. 22 | Users can also use the slider bar to change the chemical potential for gaseous phases. 23 | For gaseous phases such as $O_2$, increasing temperature and/or decreasing the pressure leads to a lower chemical potential of the element. 24 | 25 | As the plot is generated, it shows the reactivity (normalized reaction energy) of the interface as a function of molar fraction $x$of the first reactant. 26 | There are multiple ways to get the reaction information: 27 | 28 | - When mousing over a node on the plot, the pop-up window shows the reactivity (eV/atom) and the reaction equation. 29 | - You can zoom into a portion of the plot by defining a zoom area: click and hold at the upper-left corner of the desired area, and drag down and right, releasing the mouse at the lower-right corner of the desired area. 30 | The window should be replaced by the zoomed-in portion. 31 | To return to the original phase diagram, click on the “Autoscale” button in the tool bar at the upper-right corner. 32 | - The reaction energy plot can be downloaded in PNG format by clicking on the first button in the tool bar at the upper-right corner. 33 | - The table below the plot shows the detailed information of the reactions at critical molar fractions. 34 | 35 | ## Interpreting Reaction Energy Plots 36 | 37 | The section shows how to interpret reaction energy plot generated by the Interface Reactions App. 38 | In the table below the plot, you can review, for each node in the plot, the corresponding quantities: 39 | 40 | - **mol fraction**: The molar fraction of the first input reactant 41 | - **reactivity (eV/atom)**: The reaction energy normalized to the total number of atoms in reactants. 42 | (For an open system, the element in the reservoir is excluded for the normalization.) 43 | - **reaction equation**: A reaction equation chosen to normalize one of the reactants. 44 | - **reaction energy (kJ/mol)**: The reaction energy (per mol) of the displayed reaction equation. 45 | 46 | All input reactants are converted to reduced cell formulae in reaction equations. 47 | For example, the reactant $Li_2Co_2O_4$ will be converted to $LiCoO_2$. 48 | 49 | ### Reaction Plots in Closed Systems 50 | 51 | ![Figure 1](img/interface-reactions/plot_LiCoO2-Li3PS4_close_MP_release.png) 52 | _Figure 1. Calculated reaction energy plot for LiCoO2-Li3PS4 closed system_ 53 | 54 | To illustrate the reaction information generated by the Interface Reactions App, we use $LiCoO_2-Li_3PS_4$ system as an example. 55 | $LiCoO_2$ and $Li_3PS_4$ are commonly used cathode material and solid-state electrolyte material in Li-ion batteries, respectively. 56 | The cathode/electrolyte interface is of particular interest in battery research as it largely affects the battery performance. 57 | 58 | Figure 1 shows the reactivity as a function of molar fraction $x$ of $LiCoO_2$. 59 | Table 1 lists all the critical reaction equations, corresponding molar fraction of the first reactant and reaction energies per mole of reaction equation. 60 | There are 8 nodes in Figure 1 corresponding to 8 critical reactions. 61 | For example, the second node from the left with molar fraction of $LiCoO_2$ being 0.667 corresponds to the reaction: 62 | 63 | $$Li_3PS_4 + 2 LiCoO_2 = 0.5 CoS_2 + 0.5 Co_3S_4 + Li_3PO_4 + Li_2S$$ 64 | 65 | The reactivity for this node is -0.399 eV/atom. 66 | The reaction energy of the reaction above is -616.0 kJ/mol. 67 | 68 | The largest reaction driving force (magnitude of reactivity) is found for two reactions with the molar fraction of $LiCoO_2$ being 0.686 and 0.742, respectively. 69 | The corresponding reactivity is -0.402 eV/atom. 70 | 71 | ![Table 1](img/interface-reactions/table_LiCoO2-Li3PS4_close_MP_releasee.png) 72 | _Table 1. Critical reaction information for LiCoO2-Li3PS4 closed system_ 73 | 74 | Since in reality the reaction between two phases can consume arbitrary amounts of either phase, the molar fraction in the mixed region is not necessarily the critical molar fraction in Table 1, but can be any value from 0 to 1. 75 | If the molar fraction is not exactly equal to the critical fraction, the reaction is a linear combination of the critical reactions for its left neighbor node and right neighbor node, by the lever rule. 76 | As a consequence, all reaction products in Table 1 are possible phases that may be generated at the interface. 77 | 78 | ### Reaction Plots in Open Systems 79 | 80 | ![Figure 2](img/interface-reactions/plot_LiCoO2-Li3PS4_open_MP_release.png) 81 | _Figure 2. Calculated reaction energy plot for LiCoO2-Li3PS4 system open to Li reservoir at relative chemical potential - 3 eV vs. Li metal._ 82 | 83 | ![Table 2](img/interface-reactions/table_LiCoO2-Li3PS4_open_MP_release.png) 84 | _Table 2. Critical reaction information for LiCoO2-Li3PS4 system open to Li reservoir at relative chemical potential - 3 eV vs. Li metal._ 85 | 86 | We use the $LiCoO_2-Li_3PS_4$ system that opens to Li reservoir to illustrate the reaction energy plot for an open system. 87 | The Li reservoir is at relative chemical potential - 3 eV vs. 88 | Li metal, corresponding to μ = -3 eV in the App. 89 | 90 | In Figure 2, there are 16 labeled nodes that corresponds to 16 critical reactions. 91 | The reaction energy at $x$ = 0 is negative, meaning that $Li_3PS_4$ is not stable at the given Li chemical potential. 92 | The corresponding decomposition reaction is: 93 | 94 | $$Li_3PS_4 = 2.875 Li + 0.5 P_2S_7 + 0.125 LiS_4$$ 95 | 96 | The reaction equation shows that Li is extracted from the reactants to the Li reservoir during the decomposition of $Li_3PS_4$. 97 | In contrast, $LiCoO_2$ is stable at the given Li chemical potential as the reactivity is 0 eV/atom at $x$ = 1. 98 | The interpretation of other reactions in Table 2 is similar to those in the closed system. 99 | 100 | By comparing Table 1 and Table 2, it can be seen that the reaction products in the closed system and the open system for the same interface are quite different. 101 | This is because the stable materials in the closed system are not necessarily stable in the open system. 102 | Users can refer to Phase Diagram App to explore the phase diagrams of the corresponding systems. 103 | 104 | ## Thermodynamic Methodology 105 | 106 | The Interface Reactions App uses the computed energies of materials from the Materials Project database. 107 | The computational methodology, default total energy corrections and accuracy can be found in the [Calculations Guide](../methodology/total-energies.md). 108 | 109 | We consider two conditions for interface systems where chemical mixing occurs: 1) interfaces that are closed to any element (closed system), and 2) interfaces that are open to a particular element in the chemical system (open system). 110 | These two scenarios are treated separately as below: 111 | 112 | ### Chemical Mixing in Closed Systems 113 | 114 | For closed systems, we calculate the reaction energy of two reactants A and B at varying mixing fraction $x$ of the first reactant using the equation: 115 | 116 | $$\Delta E[A, B, x] = E_{pd} [x c_A + (1 - x) c_B] - x E_A - (1 - x) E_B$$ 117 | 118 | where $c_A$ and $c_B$ are the normalized compositions (i.e., the total number of atoms = 1) for reactants A and B, $E_A$ and $E_B$ are energies of ground-state structures for reactants A and B, respectively. 119 | $E_{pd}[c]$ is the energy on the energy convex hull at composition $c$. 120 | 121 | In the case where there is no structure in the database that matches the composition of reactant A or B, the energy on the convex hull $E_{pd}[c_A]$ or $E_{pd}[c_B]$ for that composition will be used instead. 122 | It should be noted that at endpoints (x = 0 or 1), the reaction energies can be zero or negative, depending on whether the ground-state structure energy of reactant A or B is on the hull or above the hull. 123 | In the generated reaction energy plot and the table, the App converts the mixing fraction $x$ to the corresponding molar fraction of the original first reactant for display. 124 | 125 | ### Chemical Mixing in Open Systems 126 | 127 | In many applications, interface systems are open to a particular element at a constant chemical potential. 128 | For example, in battery conditions, the electrode/electrolyte interface is open to Li reservoir during battery cycling. 129 | The relevant thermodynamic potential for an open system is the grand potential Φ. 130 | For instance, for a system open to a Li reservoir at chemical potential $\mu_{Li}$, the grand potential for reactant with composition $c$ is obtained using the equation: 131 | 132 | $\Phi[c, \mu_{Li}] = (E[c] - n*{Li}[c] \mu*{Li})/n\_{non-Li}[c] $ 133 | 134 | where $E[c]$ is the energy of the ground-state structure that has composition $c$. 135 | $n_{Li}[c]$ and $n_{non-Li}[c]$ are the number of Li and non-Li atoms in composition formula $c$, respectively. 136 | PV and TS terms are ignored when calculating Φ. 137 | Because the system is open to Li, the grand potential is normalized by the number of non-Li atoms. 138 | The convex hull of $\Phi$ is constructed using the grand potentials of all phases in the chemical system. 139 | As a result, the grand potential on the grand potential convex hull $\Phi_{pd}$ is a function of composition $c$ and chemical potential $\mu_{Li}$ of the reservoir: 140 | 141 | $$\Phi_{pd}[c, \mu_{Li}] = \min_{c_{Li}}{\{(E_{pd}[c+c_{Li}] - n_{Li}[c+c_{Li}] \mu_{Li}) / n_{non-Li}[c]\}}$$ 142 | 143 | where $c_{Li}$ is the number of Li atoms extracted from or added to the Li reservoir and therefore can take positive or negative value. 144 | 145 | The reaction energy is calculated using: 146 | 147 | $$\Delta \Phi[A, B, \mu_{Li}, x] = \Phi_{pd}[xc_A + (1 - x) c_B, \mu_{Li}] - x \Phi[c_A, \mu_{Li}] - (1 - x) \Phi[c_B, \mu_{Li}]$$ 148 | 149 | Since the Interface Reactions App is based on the analysis of the energy convex hull, compounds that are metastable at 0 K will not show up in the reaction products, although they might be stable or kinetically stabilized under experimental conditions. 150 | Therefore, reactions not listed in the table are possible to happen under experimental conditions. 151 | 152 | ## Citing 153 | 154 | To cite the Interface Reactions App, please reference the following work: 155 | 156 | Note that the methodology used in this paper is slightly different from the one employed in the Interface Reactions App. 157 | In the paper, the energies for reactants are always the energies on the convex hull at the compositions of reactants, whereas in the Interface Reactions App the default reactant energies are the energies of corresponding ground-state structures. 158 | Only when no structure in the database matches the reactant composition will the energy on the convex hull be used. 159 | Users can restore the methodology used in the paper by additionally checking the "Always use hull energies?" box in the "Advanced options". 160 | 161 | Note that the methodology used in this paper is slightly different from the one employed in the Interface Reactions App. 162 | In the paper, the energies for reactants are always the energies on the convex hull at the compositions of reactants, whereas in the Interface Reactions App the default reactant energies are the energies of corresponding ground-state structures. 163 | Only when no structure in the database matches the reactant composition will the energy on the convex hull be used. 164 | Users can restore the methodology used in the paper by additionally checking the "Always use hull energies?" box in the "Advanced options". 165 | 166 | ## Authors 167 | 168 | Yihan Xiao 169 | -------------------------------------------------------------------------------- /docs/methodology/total-energies.md: -------------------------------------------------------------------------------- 1 | # Total Energy Calculations 2 | 3 | ## Calculation Details 4 | 5 | We use density functional theory as implemented in the Vienna Ab Initio 6 | Simulation Package (VASP) software[^1] to evaluate the total energy of 7 | compounds. For the exchange-correlational functional, we employ a mix of 8 | Generalized Gradient Approximation (GGA) and GGA+U, as 9 | described [later in this manual](#ggau_tag). 10 | We use the Projector Augmented Wave (PAW) method for modeling core 11 | electrons with an energy cutoff of 520 eV. This cutoff corresponds to 12 | 1.3 times the highest cutoff recommended among all the pseudopotentials 13 | we use (more details can be found in the [Pseudopotentials 14 | Choice](/methodology/pseudopotentials) manual). All calculations 15 | are performed at 0K and 0atm. All computations are performed with spin 16 | polarization on and with magnetic ions in a high-spin ferromagnetic 17 | initialization (the system can of course relax to a low spin state 18 | during the DFT relaxation). We used a k-point mesh of 1000/(number of 19 | atoms in the cell) for all computations, the Monkhorst-Pack method for 20 | the k-point choices (but $\Gamma$-centered for hexagonal cells) and 21 | the tetrahedron method to perform the k-point integration. Pymatgen 22 | could change those default parameters if they are not adequate for the 23 | computation (e.g., switch to another k-point integration scheme). Some 24 | details of our calculation method can be found in ref [^2]; however, the 25 | Materials Project has updated many parameters as documented throughout 26 | the Methodology sections. 27 | 28 | ### Crystal structures 29 | 30 | We use input structures from the Inorganic Crystal Structure Database 31 | (ICSD),[^3] and relax all cell and atomic positions in our calculation 32 | two times in consecutive runs. When multiple crystal structures are 33 | present for a single chemical composition, we attempt to evaluate all 34 | unique structures as determined by an affine mapping technique.[^4] 35 | 36 | ### Total energy convergence 37 | 38 | We currently employ a k-point mesh of 1000 per reciprocal atom (pra). We performed 39 | a convergence test of total energy with respect to k-point 40 | density and convergence energy difference for a subset of chemically 41 | diverse compounds for a previous parameter set, which employed a smaller 42 | k-point mesh of 500 pra. Using a 500 pra k-point mesh, the numerical 43 | convergence for most compounds tested was within 5 meV/atom, and 96% of 44 | compounds tested were converged to within 15 meV/atom. Results for the 45 | new parameter set will be better due to the denser k-point mesh 46 | employed. Convergence will depend on chemical system; for example, 47 | oxides were generally converged to less than 1 meV/atom.[^6] 48 | 49 | ### Structure convergence 50 | 51 | The energy difference for ionic convergence is set to 0.0005 \* natoms 52 | in the cell. Data on expected accuracy on cell volumes can be found in a 53 | previous paper.[^2] We have found these parameters to yield 54 | well-converged structures in most instances; however, if the structures 55 | are to be used for further calculations that require strictly converged 56 | atomic positions and cell parameters (e.g. elastic constants, phonon 57 | modes, etc.), we recommend that users re-optimize the structures with 58 | tighter cutoffs or in force convergence mode. 59 | 60 | ## Total Energy Adjustments 61 | 62 | To better model energies across diverse chemical spaces, we apply 63 | several adjustments to the total energy. These adjustments fall into two categories, 64 | each of which is briefly described below. Our correction scheme assumes independent, 65 | linear corrections associated with each corrected element. For example, $\ce{VO_2}$ 66 | would receive both a 'V' and an 'oxide' correction (as explained below), while 67 | elemental $\ce{V}$ would receive no corrections. For complete details of our correction 68 | scheme, refer to Wang et al[^5] 69 | 70 | ### Anion corrections 71 | 72 | For many elements that take on negative oxidation states in solids, differences 73 | in electron localization between the elements and the solid can result in substantial 74 | errors in formation energies computed from DFT calculations. This is especially 75 | true for elements that are gaseous in their standard state - $\ce{O2}$, 76 | $\ce{N2}$, $\ce{Cl2}$, $\ce{F2}$, and $\ce{H2}$. 77 | 78 | To address this, we adjust the energies of materials containing certain elements 79 | by applying a correction to anionic species, as explained in ref [^5]. Specifically, 80 | we apply energy corrections to 14 anion species -- 'oxide', 'peroxide', 'superoxide', 81 | $\ce{S}$, $\ce{F}$, $\ce{Cl}$, $\ce{Br}$, $\ce{I}$, $\ce{N}$, $\ce{H}$, 82 | $\ce{Se}$, $\ce{Si}$, $\ce{Sb}$, and $\ce{Te}$. In the case of oxygen-containing compounds, 83 | separate corrections are applied to oxides, superoxides, and peroxides based 84 | on the specific bonding environment of oxygen in the material, as determined 85 | from nearest-neighbor bond lengths (e.g., <1.35 Å for superoxide, <1.49 Å 86 | for 'peroxide', and 'oxide' otherwise). Thus, $\ce{Na_2O}$ receives an 'oxide' 87 | correction while $\ce{NaO_2}$ receives a `superoxide' correction. 88 | 89 | Anion corrections are applied to a material only when it contains a corrected 90 | element _as an anion._ For example, the `H''correction is applied to LiH but not 91 | to H$_2$O. A specie is classified as an anion if its estimated oxidation state 92 | (when available) is negative, or if it is the most electronegative element in 93 | the formula. 94 | 95 | ### GGA / GGA+U Mixing Corrections 96 | 97 | 98 | 99 | Some compounds are better modeled with a U correction term to 100 | the density functional theory Hamiltonian while others are better 101 | modeled without (i.e., regular GGA). Energies from calculations with 102 | the +U correction are not directly comparable to those without. 103 | To obtain better accuracy across chemical systems, we use GGA+U when 104 | appropriate, GGA otherwise, and mix energies from the two 105 | calculation methodologies by adding an energy correction term to the 106 | GGA+U calculations to make them comparable to the GGA 107 | calculations. 108 | 109 | Specifically, we use GGA+U for oxide and fluoride 110 | compounds containing any of the transition metals $\ce{V}$, $\ce{Cr}$, 111 | $\ce{Mn}$, $\ce{Fe}$, $\ce{Co}$, $\ce{Ni}$, $\ce{W}$, and $\ce{Mo}$, and GGA for 112 | everything else. More details on this method can be found in ref [^5] and [^7]. 113 | 114 | ## Accuracy of Total Energies 115 | 116 | To estimate the accuracy of our total energy calculations, we compute 117 | reaction data and compare against experimental data. Note that this data 118 | set was compiled using a lower k-point mesh and pseudopotentials with 119 | fewer electrons than the current Materials Project parameter set. 120 | 121 | ### Estimating errors in calculated reaction energies 122 | 123 | The accuracy of calculated reaction energies depends on the chemical 124 | system investigated. In general, GGA calculations have similar errors 125 | among chemically similar systems. Hence, reaction energies between 126 | chemically similar systems (e.g., a reaction where the reactants and 127 | products are all oxides, such as $\ce{MgO + Al2O3 -> MgAl2O4}$) tend 128 | to have smaller errors than reactions between chemically dissimilar 129 | systems (e.g., between metals and insulators). 130 | 131 | ![formen errors](/methodology/img/calculations-manual/FormE_errors.png) 132 | _Figure 1: Errors in Calculated Formation Energies for 133 | 413 binaries in the Kubaschewski Tables. Energies are normalized to per 134 | mol atom._ 135 | 136 | To provide a quantitative indicator of the error we may expect from the 137 | reaction calculator, we have computed the reaction energies of 138 | [413 binaries](/methodology/static/KtablesBinaries.txt) in the Kubaschewski 139 | Tables formed with Group V, VI and VII anions. Figure 1 shows the errors 140 | in the calculated formation energies (compared to the experimental 141 | values) for these compounds. The mean absolute error (MAE) is around 14 142 | kJ mol$^{-1}$. 75% of the calculated formation energies are within 20 kJ 143 | mol$^{-1}$. We also found that compounds of certain elements tend to have 144 | larger errors. For example, Bi, Co, Pb, Eu, U, Tl and W compounds often 145 | have errors larger than 20 kJ mol$^{-1}$. 146 | 147 | It should be noted that while an MAE of 14 kJ mol$^{-1}$ is significantly 148 | higher than the desired chemical accuracy of 4 kJ mol$^{-1}$, it compares 149 | fairly well with the performance of most quantum chemistry 150 | calculations[^8]. Other than the most computationally expensive model 151 | chemistries such as G1-G3 and CBS, the reaction energy errors of most 152 | computational chemistry model chemistries are well above 10 kJ mol$^{-1}$. 153 | 154 | For oxidation of the elements into binary compounds, an average error of 155 | ~4% or 33 kJ/mol-$\ce{O2}$ is typical.[^9] For conventional ternary oxide 156 | formation from the elements, we have found a mean relative absolute 157 | error of about 2%.[^9] 158 | 159 | ### Sources of error 160 | 161 | The largest contribution to the error comes from the inability of the 162 | GGA to fully describe electronic exchange and correlation effects. In 163 | addition, there is some error associated with neglecting zero-point 164 | effects and with comparing 0K, 0atm computations with room-temperature 165 | enthalpy experiments. The latter effect was estimated to contribute less 166 | than 0.03 eV/atom by Lany.[^10] The stability of antiferromagnetic 167 | compounds may be underestimated, as the majority of our calculations are 168 | performed ferromagnetically only. The effect of magnetism may be small 169 | (under 10 meV/atom) or large (100 meV/atom or greater), depending on the 170 | compound. For compounds with heavy elements, relativistic effects may 171 | lead to greater-than-expected errors. 172 | 173 | ### GGA errors on reaction energies between chemically similar compounds 174 | 175 | We recently conducted a more in-depth study comparing GGA (+U) reaction 176 | energies of ternary oxides from binary oxides on 135 compounds. [^11] 177 | 178 | The main conclusions are: 179 | 180 | - The error in reaction energies for the binary oxide to ternary 181 | oxides reaction energies are an order of magnitude lower than for 182 | the more often reported formation energies from the element. An 183 | error intrinsic to GGA (+U) is estimated to follow a normal 184 | distribution centered in zero (no systematic underestimation 185 | or overestimation) and with a standard deviation around 24 meV/at. 186 | - When looking at phase stability (and for instance assessing if a 187 | phase is stable or not), the relevant reaction energies are most of 188 | the time not the formation energies from the elements but reaction 189 | energies from chemically similar compounds (e.g., two oxides forming 190 | a third oxide). Large cancellation of errors explain 191 | this observation. 192 | - The +U is necessary for accurate description of the energetics even 193 | when reactions do not involve change in formal oxidation states 194 | 195 | ## Accuracy of Calculated Volumes 196 | 197 | A discussion of errors in calculated volumes can be found in the [Volume 198 | Change Error manual](/methodology/volume-change-error). 199 | 200 | ## Citation 201 | 202 | To cite the calculation methodology, please reference the following 203 | works: 204 | 205 | 1. A. Jain, G. Hautier, C. Moore, S.P. Ong, C.C. Fischer, T. 206 | Mueller, K.A. Persson, G. Ceder., A High-Throughput Infrastructure 207 | for Density Functional Theory Calculations, Computational Materials 208 | Science, vol. 50, 2011, pp. 2295-2310. 209 | [DOI:10.1016/j.commatsci.2011.02.023](https://dx.doi.org/10.1016/j.commatsci.2011.02.023) 210 | 2. A. Jain, G. Hautier, S.P. Ong, C. Moore, C.C. Fischer, K.A. 211 | Persson, G. Ceder, Accurate Formation Enthalpies by Mixing GGA and 212 | GGA+U calculations, Physical Review B, vol. 84, 2011, p. 045115. 213 | [DOI:10.1103/PhysRevB.84.045115](https://doi.org/10.1103/PhysRevB.84.045115) 214 | 215 | ## Authors 216 | 217 | 1. Anubhav Jain 218 | 2. Shyue Ping Ong 219 | 3. Geoffroy Hautier 220 | 4. Charles Moore 221 | 222 | ## References 223 | 224 | [^1]: 225 | Kresse, G. & Furthmuller, J., 1996. Efficient iterative schemes 226 | for ab initio total-energy calculations using a plane-wave basis 227 | set. Physical Review B, 54, pp.11169-11186. 228 | 229 | [^2]: 230 | A. Jain, G. Hautier, C. Moore, S.P. Ong, C.C. Fischer, T. Mueller, 231 | K.A. Persson, G. Ceder., A High-Throughput Infrastructure for 232 | Density Functional Theory Calculations, Computational Materials 233 | Science. vol. 50 (2011) 2295-2310. 234 | 235 | [^3]: 236 | G. Bergerhoff, The inorganic crystal-structure data-base, Journal 237 | Of Chemical Information and Computer Sciences. 23 (1983) 66-69. 238 | 239 | [^4]: 240 | R. Hundt, J.C. Schön, M. Jansen, CMPZ - an algorithm for the 241 | efficient comparison of periodic structures, Journal Of Applied 242 | Crystallography. 39 (2006) 6-16. 243 | 244 | [^5]: 245 | A. Wang, R. Kingsbury, M. McDermott, M. Horton, A. Jain, S.P. Ong S. Dwaraknath, 246 | K. Persson, A framework for quantifying uncertainty in DFT energy corrections, 247 | ChemRxiv. Preprint. [DOI:10.26434/chemrxiv.14593476.v1](https://doi.org/10.26434/chemrxiv.14593476.v1). 248 | 249 | [^6]: 250 | L. Wang, T. Maxisch, G. Ceder, Oxidation energies of transition 251 | metal oxides within the GGA+U framework, Physical Review B. 73 252 | (2006) 1-6. 253 | 254 | [^7]: 255 | A. Jain, G. Hautier, S.P. Ong, C. Moore, C.C. Fischer, K.A. 256 | Persson, G. Ceder, Formation Enthalpies by Mixing GGA and GGA+U 257 | calculations, Physical Review B, vol. 84 (2011), 045115. 258 | 259 | [^8]: 260 | J.B. Foresman, A.E. Frisch, Exploring Chemistry With Electronic 261 | Structure Methods: A Guide to Using Gaussian, Gaussian. (1996). 262 | 263 | [^9]: 264 | A. Jain, S.-a Seyed-Reihani, C.C. Fischer, D.J. Couling, G. 265 | Ceder, W.H. Green, Ab initio screening of metal sorbents for 266 | elemental mercury capture in syngas streams, Chemical Engineering 267 | Science. 65 (2010) 3025-3033. 268 | 269 | [^10]: 270 | S. Lany, Semiconductor thermochemistry in density functional 271 | calculations, Physical Review B. 78 (2008) 1-8. 272 | 273 | [^11]: 274 | G. Hautier, S.P. Ong, A. Jain, C. J. Moore, G. Ceder, Accuracy of 275 | density functional theory in predicting formation energies of 276 | ternary oxides from binary oxides and its implication on phase 277 | stability, Physical Review B, 85 (2012), 155208 278 | --------------------------------------------------------------------------------