├── 1. Phonon Participation Ratios
    ├── .ipynb_checkpoints
    │   └── Phonon Participation Ratios-checkpoint.ipynb
    ├── Phonon Participation Ratios.ipynb
    ├── defect_graphene
    │   ├── dos.out
    │   ├── run.in
    │   └── xyz.in
    ├── graphene_construct.py
    └── prsitine_graphene
    │   ├── dos.out
    │   ├── run.in
    │   └── xyz.in
├── 2. Elastic Constants Based on Strain Fluctuation Method
    ├── .ipynb_checkpoints
    │   └── Elastic Constants Based on Strain Fluctuation Method-checkpoint.ipynb
    ├── Elastic Constants Based on Strain Fluctuation Method.ipynb
    ├── create_xyz.m
    ├── run.in
    ├── thermo.out
    └── xyz.in
├── 3. Phonon Dispersion and Vibration Mode Visualization of Graphene
    ├── D.out
    ├── Eigenvector
    │   ├── basis.in
    │   ├── eigenvector.out
    │   ├── kpoints.in
    │   ├── run.in
    │   └── xyz.in
    ├── Phonon_39.73067THz_first_frame.data
    ├── Phonon_39.73067THz_second_frame.data
    ├── Phonon_Dispersion_&_Mode_Viewer.ipynb
    ├── basis.in
    ├── eigenvector - binary.out
    ├── eigenvector.out
    ├── gr_uc.vasp
    ├── graphene_construct.py
    ├── kpoints.in
    ├── lammps.data
    ├── omega2.out
    ├── run.in
    └── xyz.in
├── 4. Quantum-corrected thermal conductivity of amorphous carbon
    ├── Quantum-corrected thermal conductivity of amorphous carbon.ipynb
    ├── kappa.out
    ├── run.in
    ├── shc.out
    └── xyz.in
├── LICENSE
└── README.md


/1. Phonon Participation Ratios/Phonon Participation Ratios.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# Phonon Participation Ratios\n",
  8 |     "# 1. Introduction\n",
  9 |     "- In this example, we calculate the phonon participation ratios (PPR) of prsitine and defect graphene at 300 K and zero pressure.Based on the atomic phonon density of states (PDOS) [[Dickey 1969]](https://doi.org/10.1103/PhysRev.188.1407), the PPR is calculated to approximately measure the phonon localization with the following form [[Bell 1970]](https://doi.org/10.1039/DF9705000055):\n",
 10 |     "$$\n",
 11 |     "PPR(\\omega) = \\frac{1}{N} \\frac{(\\sum_{i}PDOS_{i}^{2}(\\omega))^{2}}{\\sum_{i}PDOS_{i}^{4}(\\omega)},\n",
 12 |     "$$\n",
 13 |     "where $PDOS_{i}$ is the atomic PDOS and $N$ s the total number of atoms involved in the calculation. The specific details on the PDOS calculation can be found in our [PDOS tutorial](https://github.com/brucefan1983/GPUMD/blob/master/examples/empirical_potentials/density_of_states/Density%20of%20States.ipynb)."
 14 |    ]
 15 |   },
 16 |   {
 17 |    "cell_type": "markdown",
 18 |    "metadata": {},
 19 |    "source": [
 20 |     "# 2. Preparing the Inputs\n",
 21 |     "- We use a prsitine graphene consisting of 1008 carbon atoms and a defect graphene consisting of 978 carbon atoms (about 3% atomic vacancy). The atomic interactions are described by the Tersoff potential [[Tersoff 1989]](https://doi.org/10.1103/PhysRevB.39.5566) parameterized by Lindsay *et al.* [[Lindsay 2010]](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.81.205441).\n",
 22 |     "\n",
 23 |     "## Generate the  [xyz.in](https://gpumd.zheyongfan.org/index.php/The_xyz.in_input_file) file:"
 24 |    ]
 25 |   },
 26 |   {
 27 |    "cell_type": "markdown",
 28 |    "metadata": {},
 29 |    "source": [
 30 |     "- The xyz.in files for prsitine graphene and defect graphene are constructed by the python code graphene_construct.py as provided in the same path.\n",
 31 |     "- The first few lines of the [xyz.in](https://gpumd.zheyongfan.org/index.php/The_xyz.in_input_file) file are (taking the defect graphene as an example):\n",
 32 |     "```\n",
 33 |     "978 3 2.1 0 0 1 \n",
 34 |     "1 1 0 51.6497550817 51.12 3.35 \n",
 35 |     "0   0.614878036 0.710000001 10  12.011  0\n",
 36 |     "0   1.844634109 1.420000001 10  12.011  1\n",
 37 |     "0   1.844634109 2.840000002 10  12.011  2\n",
 38 |     "0   0.614878036 3.549999998 10  12.011  3\n",
 39 |     "0   0.614878036 4.969999999 10  12.011  4\n",
 40 |     "0   1.844634109 5.679999999 10  12.011  5\n",
 41 |     "```\n",
 42 |     "\n",
 43 |     "- Explanations for the first line:\n",
 44 |     "  - The first number states that the number of particles is 978.\n",
 45 |     "  - The second number in this line, 3, is good for graphene described by the Tersoff potential because no atom can have more than 3 neighbor atoms at room temperature. Making this number larger only results in more memory usage. If this number is not large enough, GPUMD will give an error message and exit.\n",
 46 |     "  - The next number, 2.1, means that the initial cutoff distance for the neighbor list construction is 2.1 A. Here, we only need to consider the first nearest neighbors. Any number larger than the first nearest neighbor distance and smaller than the second nearest neighbor distance is OK here. Note that we will also not update the neighbor list. There is no such need in this problem. \n",
 47 |     "  - The remaining three zeros in the first line mean:\n",
 48 |     "    - the box is orthogonal;\n",
 49 |     "    - the initial velocities are not contained in this file;\n",
 50 |     "    - there are one grouping methods defined here.\n",
 51 |     "\n",
 52 |     " - Explanations for the second line:\n",
 53 |     "   - The numbers 1 1 0 mean that the $x$ and $y$ (in-plane) directions are periodic and the $z$ direction is open (free).\n",
 54 |     "   - The remaining three numbers are the box lengths in the three directions. The box length in a free direction is chosen based on some convention. This number will only affect the system volume.\n",
 55 |     "\n",
 56 |     "- Starting from the third line, the numbers in the first column are all 0 here, which means that all the atoms are of type 0 (single atom-type system). The next three columns are the initial coordinates of the atoms. The penultimate column gives the masses of the atoms. The last column gives the group labels of each atom in the defined grouping method.\n",
 57 |     "- It is noted that, we give each atom a distinct group label to obtain the corresponding atomic PDOS here. "
 58 |    ]
 59 |   },
 60 |   {
 61 |    "cell_type": "markdown",
 62 |    "metadata": {},
 63 |    "source": [
 64 |     "## The <code>run.in</code> file:\n",
 65 |     "The <code>run.in</code> input file is given below:<br>\n",
 66 |     "```\n",
 67 |     "potential       potentials/tersoff/Graphene_Lindsay_2010_modified.txt 0\n",
 68 |     "velocity        300\n",
 69 |     "\n",
 70 |     "ensemble        npt_ber 300 300 0.01 0 0 0 0.0005 \n",
 71 |     "time_step       1     \n",
 72 |     "dump_thermo     100  \n",
 73 |     "run             200000\n",
 74 |     "\n",
 75 |     "ensemble        nve \n",
 76 |     "compute_dos     5 200 400.0 group 0 -1 num_dos_points 300\n",
 77 |     "run             200000\n",
 78 |     "```\n",
 79 |     " - The first line uses the [potential](https://gpumd.zheyongfan.org/index.php/The_potential_keyword) keyword to define the potential to be used, which is specified in the file [Graphene_Lindsay_2010_modified.txt](https://github.com/brucefan1983/GPUMD/blob/master/potentials/tersoff/Graphene_Lindsay_2010_modified.txt).\n",
 80 |     "\n",
 81 |     " - The second line uses the [velocity](https://gpumd.zheyongfan.org/index.php/The_velocity_keyword) keyword and sets the velocities to be initialized with a temperature of 300 K. \n",
 82 |     "\n",
 83 |     " - There are two runs:\n",
 84 |     "   - The first [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword) serves as the equilibration stage, where the NPT [ensemble](https://gpumd.zheyongfan.org/index.php/The_ensemble_keyword) (the Berendsen method) is used. The temperature is 300 K and the pressures are zero in all the directions. The coupling constants are 0.01 (dimensionless) and 0.0005 (in the natural unit system adopted by GPUMD) for the thermostat and the barostat, respectively. The [time_step](https://gpumd.zheyongfan.org/index.php/The_time_step_keyword) for integration is 1 fs. There are $2\\times 10^5$ steps (200 ps) for this [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword) and the thermodynamic quantities will be output every 1000 steps. \n",
 85 |     "   - The second [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword) serves as the production [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword), where the NVE [ensemble](https://gpumd.zheyongfan.org/index.php/The_ensemble_keyword) is used. The line with [compute_dos](https://gpumd.zheyongfan.org/index.php/The_compute_dos_keyword) means that velocities will be recorded every 5 steps (5 fs) and 200 VAC data (the maximum correlation time is then about 1 ps) will be calculated. The third parameter in this line is the maximum angular frequency considered, $\\omega_{\\rm max} = 2\\pi\\nu_{\\rm max} =400$ THz, which is large enough for graphene. Here, we use \"group 0 -1\" here to calculate the PDOS for each atom of graphene, and \"num_dos_points 300\" means total 300 points for each atom will be calculated, and therefore, it is expected to obtain the PDOS data with 300 $\\times$ N rows. The production [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword) lasts 200 ps."
 86 |    ]
 87 |   },
 88 |   {
 89 |    "cell_type": "markdown",
 90 |    "metadata": {},
 91 |    "source": [
 92 |     "# 3. Results and Discussion\n",
 93 |     "### Calculate the PPR\n",
 94 |     "Based on the [dos.out](https://gpumd.zheyongfan.org/index.php/The_dos.out_output_file) output files for each atom in prsitine and defect graphene, according to the PPR defined previously, we can obtain their corresponding PPR with the following codes. "
 95 |    ]
 96 |   },
 97 |   {
 98 |    "cell_type": "code",
 99 |    "execution_count": 8,
100 |    "metadata": {},
101 |    "outputs": [
102 |     {
103 |      "name": "stdout",
104 |      "output_type": "stream",
105 |      "text": [
106 |       "2922.3424473811947\n",
107 |       "3017.278477666552\n"
108 |      ]
109 |     }
110 |    ],
111 |    "source": [
112 |     "from pylab import *\n",
113 |     "\n",
114 |     "def ppr_calc(path):\n",
115 |     "    dos_raw = np.loadtxt(path + 'dos.out')\n",
116 |     "    N = int(len(dos_raw)/300) #atom number\n",
117 |     "    dos_collect = np.zeros((300, N))\n",
118 |     "    for i in range(N):\n",
119 |     "        dos_slice = dos_raw[300*i:300*(i+1)] #Phonon DOS for each atom\n",
120 |     "        dos_xyz_slice = dos_slice[:,1] + dos_slice[:,2] + dos_slice[:,3] #We calculate the total dos\n",
121 |     "        dos_collect[:,i] = dos_xyz_slice\n",
122 |     "    ppr = np.zeros((300,2))\n",
123 |     "    ppr[:,0]=dos_raw[:300][:,0] / (2*np.pi) \n",
124 |     "    print(trapz(sum(dos_collect,axis=1),ppr[:,0])) #equal to 3N\n",
125 |     "    for j in range(300):\n",
126 |     "        ppr[j,1] = (sum(dos_collect[j]**2))**2/sum(dos_collect[j]**4)/N\n",
127 |     "    return ppr\n",
128 |     "\n",
129 |     "\n",
130 |     "ppr_defect  = ppr_calc(\"defect_graphene/\")\n",
131 |     "ppr_prsitine = ppr_calc(\"prsitine_graphene/\")\n"
132 |    ]
133 |   },
134 |   {
135 |    "cell_type": "markdown",
136 |    "metadata": {},
137 |    "source": [
138 |     "## Plot PPR\n"
139 |    ]
140 |   },
141 |   {
142 |    "cell_type": "code",
143 |    "execution_count": 9,
144 |    "metadata": {
145 |     "scrolled": true
146 |    },
147 |    "outputs": [
148 |     {
149 |      "data": {
150 |       "text/plain": [
151 |        "<matplotlib.legend.Legend at 0x1b6afac0130>"
152 |       ]
153 |      },
154 |      "execution_count": 9,
155 |      "metadata": {},
156 |      "output_type": "execute_result"
157 |     },
158 |     {
159 |      "data": {
160 |       "image/png": 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\n",
161 |       "text/plain": [
162 |        "<Figure size 576x360 with 1 Axes>"
163 |       ]
164 |      },
165 |      "metadata": {
166 |       "needs_background": "light"
167 |      },
168 |      "output_type": "display_data"
169 |     }
170 |    ],
171 |    "source": [
172 |     "aw = 2\n",
173 |     "fs = 16\n",
174 |     "font = {'size'   : fs}\n",
175 |     "matplotlib.rc('font', **font)\n",
176 |     "matplotlib.rc('axes' , linewidth=aw)\n",
177 |     "\n",
178 |     "def set_fig_properties(ax_list):\n",
179 |     "    tl = 6\n",
180 |     "    tw = 1.5\n",
181 |     "    tlm = 3\n",
182 |     "    \n",
183 |     "    for ax in ax_list:\n",
184 |     "        ax.tick_params(which='major', length=tl, width=tw)\n",
185 |     "        ax.tick_params(which='minor', length=tlm, width=tw)\n",
186 |     "        ax.tick_params(which='both', axis='both', direction='in', right=True, top=True)\n",
187 |     "      \n",
188 |     "figure(figsize=(8, 5))\n",
189 |     "set_fig_properties([gca()])\n",
190 |     "plot(ppr_prsitine[:,0], ppr_prsitine[:,1], \n",
191 |     "     color='C1', \n",
192 |     "     marker=\"o\", \n",
193 |     "     linewidth=0,  \n",
194 |     "     markersize=5, \n",
195 |     "     label='Prsitine Graphene')\n",
196 |     "plot(ppr_defect[:,0], ppr_defect[:,1], \n",
197 |     "     color='C4', \n",
198 |     "     marker=\"o\", \n",
199 |     "     linewidth=0,  \n",
200 |     "     markersize=5, \n",
201 |     "     label='Defect Graphene')\n",
202 |     "xlim([0.0, 60.0])\n",
203 |     "gca().set_xticks(linspace(0,60,7))\n",
204 |     "ylim([-0.05, 1.05])\n",
205 |     "gca().set_yticks(linspace(0,1.0,6))\n",
206 |     "xlabel(r'$\\nu$ (THz)')\n",
207 |     "ylabel(\"PPR\")\n",
208 |     "legend(loc=\"lower center\")\n"
209 |    ]
210 |   },
211 |   {
212 |    "cell_type": "markdown",
213 |    "metadata": {},
214 |    "source": [
215 |     "From the above figure, it can be clearly found that the weakening of the PPR by the defects covered the entire frequency domain, indicating a significant phonon localization effect in defect graphene when compared to the prsitine graphene counterpart."
216 |    ]
217 |   },
218 |   {
219 |    "cell_type": "markdown",
220 |    "metadata": {},
221 |    "source": [
222 |     "# 4. References\n",
223 |     "- [Dickey 1969] J. M. Dickey and A. Paskin, [Computer Simulation of the Lattice Dynamics of Solids](https://doi.org/10.1103/PhysRev.188.1407), Phys. Rev. **188**, 1407 (1969).\n",
224 |     "- [Bell 1970] R. J. Bell, P. Dean, [Atomic vibrations in vitreous silica](https://doi.org/10.1039/DF9705000055), Discussions of the Faraday society **50**, 55-61 (1970).\n",
225 |     "- [Lindsay 2010] L. Lindsay and D.A. Broido, [Optimized Tersoff and Brenner emperical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene](https://doi.org/10.1103/PhysRevB.39.5566), Phys. Rev. B, **81**, 205441 (2010).\n",
226 |     "- [Tersoff 1989] J. Tersoff, [Modeling solid-state chemistry: Interatomic potentials for multicomponent systems](https://doi.org/10.1103/PhysRevB.39.5566), Phys. Rev. B **39**, 5566(R) (1989)."
227 |    ]
228 |   }
229 |  ],
230 |  "metadata": {
231 |   "kernelspec": {
232 |    "display_name": "Python 3",
233 |    "language": "python",
234 |    "name": "python3"
235 |   },
236 |   "language_info": {
237 |    "codemirror_mode": {
238 |     "name": "ipython",
239 |     "version": 3
240 |    },
241 |    "file_extension": ".py",
242 |    "mimetype": "text/x-python",
243 |    "name": "python",
244 |    "nbconvert_exporter": "python",
245 |    "pygments_lexer": "ipython3",
246 |    "version": "3.8.5"
247 |   }
248 |  },
249 |  "nbformat": 4,
250 |  "nbformat_minor": 2
251 | }
252 | 


--------------------------------------------------------------------------------
/1. Phonon Participation Ratios/defect_graphene/run.in:
--------------------------------------------------------------------------------
 1 | potential       potentials/tersoff/Graphene_Lindsay_2010_modified.txt 0
 2 | velocity        300
 3 | 
 4 | ensemble        npt_ber 300 300 0.01 0 0 0 0.0005 
 5 | time_step       1     
 6 | dump_thermo     100
 7 | run             200000
 8 | 
 9 | 
10 | ensemble        nve 
11 | compute_dos     5 200 400.0 group 0 -1 num_dos_points 300
12 | run             200000
13 | 
14 | 
15 | 
16 | 
17 | 
18 | 
19 | 
20 | 
21 | 


--------------------------------------------------------------------------------
/1. Phonon Participation Ratios/defect_graphene/xyz.in:
--------------------------------------------------------------------------------
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  2 | 1 1 0 51.6497550817 51.12 20.0 
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  5 | 0   1.844634109 2.840000002 10  12.011  2
  6 | 0   0.614878036 3.549999998 10  12.011  3
  7 | 0   0.614878036 4.969999999 10  12.011  4
  8 | 0   1.844634109 5.679999999 10  12.011  5
  9 | 0   1.844634109 7.100000001 10  12.011  6
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129 | 0   5.533902328 39.05   10  12.011  126
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134 | 0   6.763658406 44.02   10  12.011  131
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141 | 0   7.993414479 0.710000001 10  12.011  138
142 | 0   9.223170552 1.420000001 10  12.011  139
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144 | 0   7.993414479 3.549999998 10  12.011  141
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146 | 0   9.223170552 5.679999999 10  12.011  143
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149 | 0   7.993414479 9.230000002 10  12.011  146
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189 | 0   11.6826827  1.420000001 10  12.011  186
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229 | 0   10.45292662 46.15   10  12.011  226
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234 | 0   12.91243877 0.710000001 10  12.011  231
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273 | 0   14.14219484 44.02   10  12.011  270
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280 | 0   15.37195092 0.710000001 10  12.011  277
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283 | 0   15.37195092 3.549999998 10  12.011  280
284 | 0   15.37195092 4.969999999 10  12.011  281
285 | 0   16.60170699 5.679999999 10  12.011  282
286 | 0   16.60170699 7.100000001 10  12.011  283
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289 | 0   16.60170699 9.939999998 10  12.011  286
290 | 0   16.60170699 11.36   10  12.011  287
291 | 0   15.37195092 12.07   10  12.011  288
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293 | 0   16.60170699 14.2    10  12.011  290
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306 | 0   15.37195092 29.11   10  12.011  303
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309 | 0   15.37195092 33.37   10  12.011  306
310 | 0   15.37195092 34.79   10  12.011  307
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313 | 0   15.37195092 39.05   10  12.011  310
314 | 0   16.60170699 39.76   10  12.011  311
315 | 0   16.60170699 41.18   10  12.011  312
316 | 0   15.37195092 41.89   10  12.011  313
317 | 0   15.37195092 43.31   10  12.011  314
318 | 0   16.60170699 44.02   10  12.011  315
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320 | 0   15.37195092 46.15   10  12.011  317
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324 | 0   15.37195092 50.41   10  12.011  321
325 | 0   17.83146306 0.710000001 10  12.011  322
326 | 0   19.06121913 1.420000001 10  12.011  323
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328 | 0   17.83146306 3.549999998 10  12.011  325
329 | 0   17.83146306 4.969999999 10  12.011  326
330 | 0   19.06121913 5.679999999 10  12.011  327
331 | 0   19.06121913 7.100000001 10  12.011  328
332 | 0   17.83146306 7.810000001 10  12.011  329
333 | 0   19.06121913 9.939999998 10  12.011  330
334 | 0   19.06121913 11.36   10  12.011  331
335 | 0   17.83146306 12.07   10  12.011  332
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339 | 0   17.83146306 16.33   10  12.011  336
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347 | 0   17.83146306 24.85   10  12.011  344
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349 | 0   19.06121913 26.98   10  12.011  346
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351 | 0   17.83146306 29.11   10  12.011  348
352 | 0   17.83146306 30.53   10  12.011  349
353 | 0   19.06121913 31.24   10  12.011  350
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355 | 0   17.83146306 33.37   10  12.011  352
356 | 0   17.83146306 34.79   10  12.011  353
357 | 0   19.06121913 35.5    10  12.011  354
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359 | 0   17.83146306 37.63   10  12.011  356
360 | 0   17.83146306 39.05   10  12.011  357
361 | 0   19.06121913 39.76   10  12.011  358
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363 | 0   17.83146306 41.89   10  12.011  360
364 | 0   17.83146306 43.31   10  12.011  361
365 | 0   19.06121913 44.02   10  12.011  362
366 | 0   19.06121913 45.44   10  12.011  363
367 | 0   17.83146306 46.15   10  12.011  364
368 | 0   17.83146306 47.57   10  12.011  365
369 | 0   19.06121913 48.28   10  12.011  366
370 | 0   19.06121913 49.7    10  12.011  367
371 | 0   17.83146306 50.41   10  12.011  368
372 | 0   20.29097521 0.710000001 10  12.011  369
373 | 0   21.52073129 1.420000001 10  12.011  370
374 | 0   21.52073129 2.840000002 10  12.011  371
375 | 0   20.29097521 3.549999998 10  12.011  372
376 | 0   20.29097521 4.969999999 10  12.011  373
377 | 0   21.52073129 5.679999999 10  12.011  374
378 | 0   21.52073129 7.100000001 10  12.011  375
379 | 0   20.29097521 7.810000001 10  12.011  376
380 | 0   20.29097521 9.230000002 10  12.011  377
381 | 0   21.52073129 9.939999998 10  12.011  378
382 | 0   21.52073129 11.36   10  12.011  379
383 | 0   20.29097521 12.07   10  12.011  380
384 | 0   20.29097521 13.49   10  12.011  381
385 | 0   21.52073129 14.2    10  12.011  382
386 | 0   21.52073129 15.62   10  12.011  383
387 | 0   20.29097521 16.33   10  12.011  384
388 | 0   20.29097521 17.75   10  12.011  385
389 | 0   21.52073129 18.46   10  12.011  386
390 | 0   21.52073129 19.88   10  12.011  387
391 | 0   20.29097521 22.01   10  12.011  388
392 | 0   21.52073129 22.72   10  12.011  389
393 | 0   21.52073129 24.14   10  12.011  390
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395 | 0   20.29097521 26.27   10  12.011  392
396 | 0   21.52073129 26.98   10  12.011  393
397 | 0   21.52073129 28.4    10  12.011  394
398 | 0   20.29097521 29.11   10  12.011  395
399 | 0   20.29097521 30.53   10  12.011  396
400 | 0   21.52073129 31.24   10  12.011  397
401 | 0   21.52073129 32.66   10  12.011  398
402 | 0   20.29097521 33.37   10  12.011  399
403 | 0   20.29097521 34.79   10  12.011  400
404 | 0   21.52073129 35.5    10  12.011  401
405 | 0   21.52073129 36.92   10  12.011  402
406 | 0   20.29097521 37.63   10  12.011  403
407 | 0   20.29097521 39.05   10  12.011  404
408 | 0   21.52073129 39.76   10  12.011  405
409 | 0   21.52073129 41.18   10  12.011  406
410 | 0   20.29097521 41.89   10  12.011  407
411 | 0   20.29097521 43.31   10  12.011  408
412 | 0   21.52073129 44.02   10  12.011  409
413 | 0   21.52073129 45.44   10  12.011  410
414 | 0   20.29097521 46.15   10  12.011  411
415 | 0   20.29097521 47.57   10  12.011  412
416 | 0   21.52073129 48.28   10  12.011  413
417 | 0   21.52073129 49.7    10  12.011  414
418 | 0   20.29097521 50.41   10  12.011  415
419 | 0   22.75048736 0.710000001 10  12.011  416
420 | 0   23.98024343 1.420000001 10  12.011  417
421 | 0   23.98024343 2.840000002 10  12.011  418
422 | 0   22.75048736 3.549999998 10  12.011  419
423 | 0   22.75048736 4.969999999 10  12.011  420
424 | 0   23.98024343 5.679999999 10  12.011  421
425 | 0   23.98024343 7.100000001 10  12.011  422
426 | 0   22.75048736 7.810000001 10  12.011  423
427 | 0   22.75048736 9.230000002 10  12.011  424
428 | 0   23.98024343 9.939999998 10  12.011  425
429 | 0   23.98024343 11.36   10  12.011  426
430 | 0   22.75048736 12.07   10  12.011  427
431 | 0   22.75048736 13.49   10  12.011  428
432 | 0   23.98024343 14.2    10  12.011  429
433 | 0   23.98024343 15.62   10  12.011  430
434 | 0   22.75048736 16.33   10  12.011  431
435 | 0   22.75048736 17.75   10  12.011  432
436 | 0   23.98024343 18.46   10  12.011  433
437 | 0   23.98024343 19.88   10  12.011  434
438 | 0   22.75048736 20.59   10  12.011  435
439 | 0   22.75048736 22.01   10  12.011  436
440 | 0   23.98024343 22.72   10  12.011  437
441 | 0   23.98024343 24.14   10  12.011  438
442 | 0   22.75048736 24.85   10  12.011  439
443 | 0   22.75048736 26.27   10  12.011  440
444 | 0   23.98024343 26.98   10  12.011  441
445 | 0   23.98024343 28.4    10  12.011  442
446 | 0   22.75048736 29.11   10  12.011  443
447 | 0   22.75048736 30.53   10  12.011  444
448 | 0   23.98024343 31.24   10  12.011  445
449 | 0   23.98024343 32.66   10  12.011  446
450 | 0   22.75048736 33.37   10  12.011  447
451 | 0   22.75048736 34.79   10  12.011  448
452 | 0   23.98024343 35.5    10  12.011  449
453 | 0   23.98024343 36.92   10  12.011  450
454 | 0   22.75048736 37.63   10  12.011  451
455 | 0   22.75048736 39.05   10  12.011  452
456 | 0   23.98024343 39.76   10  12.011  453
457 | 0   23.98024343 41.18   10  12.011  454
458 | 0   22.75048736 41.89   10  12.011  455
459 | 0   22.75048736 43.31   10  12.011  456
460 | 0   23.98024343 44.02   10  12.011  457
461 | 0   23.98024343 45.44   10  12.011  458
462 | 0   22.75048736 46.15   10  12.011  459
463 | 0   22.75048736 47.57   10  12.011  460
464 | 0   23.98024343 48.28   10  12.011  461
465 | 0   23.98024343 49.7    10  12.011  462
466 | 0   22.75048736 50.41   10  12.011  463
467 | 0   25.2099995  0.710000001 10  12.011  464
468 | 0   26.43975558 1.420000001 10  12.011  465
469 | 0   26.43975558 2.840000002 10  12.011  466
470 | 0   25.2099995  3.549999998 10  12.011  467
471 | 0   25.2099995  4.969999999 10  12.011  468
472 | 0   26.43975558 5.679999999 10  12.011  469
473 | 0   26.43975558 7.100000001 10  12.011  470
474 | 0   25.2099995  7.810000001 10  12.011  471
475 | 0   25.2099995  9.230000002 10  12.011  472
476 | 0   26.43975558 9.939999998 10  12.011  473
477 | 0   26.43975558 11.36   10  12.011  474
478 | 0   25.2099995  12.07   10  12.011  475
479 | 0   25.2099995  13.49   10  12.011  476
480 | 0   26.43975558 14.2    10  12.011  477
481 | 0   26.43975558 15.62   10  12.011  478
482 | 0   25.2099995  16.33   10  12.011  479
483 | 0   25.2099995  17.75   10  12.011  480
484 | 0   26.43975558 18.46   10  12.011  481
485 | 0   26.43975558 19.88   10  12.011  482
486 | 0   25.2099995  20.59   10  12.011  483
487 | 0   25.2099995  22.01   10  12.011  484
488 | 0   26.43975558 22.72   10  12.011  485
489 | 0   26.43975558 24.14   10  12.011  486
490 | 0   25.2099995  24.85   10  12.011  487
491 | 0   25.2099995  26.27   10  12.011  488
492 | 0   26.43975558 26.98   10  12.011  489
493 | 0   26.43975558 28.4    10  12.011  490
494 | 0   25.2099995  29.11   10  12.011  491
495 | 0   25.2099995  30.53   10  12.011  492
496 | 0   26.43975558 31.24   10  12.011  493
497 | 0   26.43975558 32.66   10  12.011  494
498 | 0   25.2099995  33.37   10  12.011  495
499 | 0   25.2099995  34.79   10  12.011  496
500 | 0   26.43975558 35.5    10  12.011  497
501 | 0   26.43975558 36.92   10  12.011  498
502 | 0   25.2099995  37.63   10  12.011  499
503 | 0   25.2099995  39.05   10  12.011  500
504 | 0   26.43975558 39.76   10  12.011  501
505 | 0   26.43975558 41.18   10  12.011  502
506 | 0   25.2099995  41.89   10  12.011  503
507 | 0   25.2099995  43.31   10  12.011  504
508 | 0   26.43975558 44.02   10  12.011  505
509 | 0   26.43975558 45.44   10  12.011  506
510 | 0   25.2099995  46.15   10  12.011  507
511 | 0   25.2099995  47.57   10  12.011  508
512 | 0   26.43975558 48.28   10  12.011  509
513 | 0   26.43975558 49.7    10  12.011  510
514 | 0   25.2099995  50.41   10  12.011  511
515 | 0   27.66951165 0.710000001 10  12.011  512
516 | 0   28.89926772 1.420000001 10  12.011  513
517 | 0   28.89926772 2.840000002 10  12.011  514
518 | 0   27.66951165 3.549999998 10  12.011  515
519 | 0   27.66951165 4.969999999 10  12.011  516
520 | 0   28.89926772 5.679999999 10  12.011  517
521 | 0   27.66951165 7.810000001 10  12.011  518
522 | 0   27.66951165 9.230000002 10  12.011  519
523 | 0   28.89926772 9.939999998 10  12.011  520
524 | 0   28.89926772 11.36   10  12.011  521
525 | 0   27.66951165 12.07   10  12.011  522
526 | 0   27.66951165 13.49   10  12.011  523
527 | 0   28.89926772 14.2    10  12.011  524
528 | 0   28.89926772 15.62   10  12.011  525
529 | 0   27.66951165 16.33   10  12.011  526
530 | 0   27.66951165 17.75   10  12.011  527
531 | 0   28.89926772 18.46   10  12.011  528
532 | 0   28.89926772 19.88   10  12.011  529
533 | 0   27.66951165 20.59   10  12.011  530
534 | 0   27.66951165 22.01   10  12.011  531
535 | 0   28.89926772 22.72   10  12.011  532
536 | 0   28.89926772 24.14   10  12.011  533
537 | 0   27.66951165 24.85   10  12.011  534
538 | 0   27.66951165 26.27   10  12.011  535
539 | 0   28.89926772 26.98   10  12.011  536
540 | 0   28.89926772 28.4    10  12.011  537
541 | 0   27.66951165 29.11   10  12.011  538
542 | 0   27.66951165 30.53   10  12.011  539
543 | 0   28.89926772 31.24   10  12.011  540
544 | 0   28.89926772 32.66   10  12.011  541
545 | 0   27.66951165 33.37   10  12.011  542
546 | 0   27.66951165 34.79   10  12.011  543
547 | 0   28.89926772 35.5    10  12.011  544
548 | 0   28.89926772 36.92   10  12.011  545
549 | 0   27.66951165 37.63   10  12.011  546
550 | 0   27.66951165 39.05   10  12.011  547
551 | 0   28.89926772 39.76   10  12.011  548
552 | 0   28.89926772 41.18   10  12.011  549
553 | 0   27.66951165 41.89   10  12.011  550
554 | 0   27.66951165 43.31   10  12.011  551
555 | 0   28.89926772 44.02   10  12.011  552
556 | 0   28.89926772 45.44   10  12.011  553
557 | 0   27.66951165 46.15   10  12.011  554
558 | 0   27.66951165 47.57   10  12.011  555
559 | 0   28.89926772 48.28   10  12.011  556
560 | 0   28.89926772 49.7    10  12.011  557
561 | 0   27.66951165 50.41   10  12.011  558
562 | 0   30.1290238  0.710000001 10  12.011  559
563 | 0   31.35877987 1.420000001 10  12.011  560
564 | 0   31.35877987 2.840000002 10  12.011  561
565 | 0   30.1290238  3.549999998 10  12.011  562
566 | 0   30.1290238  4.969999999 10  12.011  563
567 | 0   31.35877987 5.679999999 10  12.011  564
568 | 0   31.35877987 7.100000001 10  12.011  565
569 | 0   30.1290238  7.810000001 10  12.011  566
570 | 0   30.1290238  9.230000002 10  12.011  567
571 | 0   31.35877987 9.939999998 10  12.011  568
572 | 0   31.35877987 11.36   10  12.011  569
573 | 0   30.1290238  12.07   10  12.011  570
574 | 0   30.1290238  13.49   10  12.011  571
575 | 0   31.35877987 14.2    10  12.011  572
576 | 0   31.35877987 15.62   10  12.011  573
577 | 0   30.1290238  16.33   10  12.011  574
578 | 0   30.1290238  17.75   10  12.011  575
579 | 0   31.35877987 18.46   10  12.011  576
580 | 0   31.35877987 19.88   10  12.011  577
581 | 0   30.1290238  20.59   10  12.011  578
582 | 0   30.1290238  22.01   10  12.011  579
583 | 0   31.35877987 22.72   10  12.011  580
584 | 0   31.35877987 24.14   10  12.011  581
585 | 0   30.1290238  24.85   10  12.011  582
586 | 0   30.1290238  26.27   10  12.011  583
587 | 0   31.35877987 26.98   10  12.011  584
588 | 0   31.35877987 28.4    10  12.011  585
589 | 0   30.1290238  29.11   10  12.011  586
590 | 0   30.1290238  30.53   10  12.011  587
591 | 0   31.35877987 31.24   10  12.011  588
592 | 0   31.35877987 32.66   10  12.011  589
593 | 0   30.1290238  33.37   10  12.011  590
594 | 0   30.1290238  34.79   10  12.011  591
595 | 0   31.35877987 35.5    10  12.011  592
596 | 0   31.35877987 36.92   10  12.011  593
597 | 0   30.1290238  37.63   10  12.011  594
598 | 0   30.1290238  39.05   10  12.011  595
599 | 0   31.35877987 39.76   10  12.011  596
600 | 0   31.35877987 41.18   10  12.011  597
601 | 0   30.1290238  41.89   10  12.011  598
602 | 0   30.1290238  43.31   10  12.011  599
603 | 0   31.35877987 44.02   10  12.011  600
604 | 0   31.35877987 45.44   10  12.011  601
605 | 0   30.1290238  46.15   10  12.011  602
606 | 0   30.1290238  47.57   10  12.011  603
607 | 0   31.35877987 48.28   10  12.011  604
608 | 0   31.35877987 49.7    10  12.011  605
609 | 0   30.1290238  50.41   10  12.011  606
610 | 0   32.58853595 0.710000001 10  12.011  607
611 | 0   33.81829202 1.420000001 10  12.011  608
612 | 0   33.81829202 2.840000002 10  12.011  609
613 | 0   32.58853595 3.549999998 10  12.011  610
614 | 0   32.58853595 4.969999999 10  12.011  611
615 | 0   33.81829202 5.679999999 10  12.011  612
616 | 0   33.81829202 7.100000001 10  12.011  613
617 | 0   32.58853595 7.810000001 10  12.011  614
618 | 0   32.58853595 9.230000002 10  12.011  615
619 | 0   33.81829202 9.939999998 10  12.011  616
620 | 0   33.81829202 11.36   10  12.011  617
621 | 0   32.58853595 12.07   10  12.011  618
622 | 0   32.58853595 13.49   10  12.011  619
623 | 0   33.81829202 14.2    10  12.011  620
624 | 0   33.81829202 15.62   10  12.011  621
625 | 0   32.58853595 16.33   10  12.011  622
626 | 0   32.58853595 17.75   10  12.011  623
627 | 0   33.81829202 18.46   10  12.011  624
628 | 0   33.81829202 19.88   10  12.011  625
629 | 0   32.58853595 20.59   10  12.011  626
630 | 0   32.58853595 22.01   10  12.011  627
631 | 0   33.81829202 22.72   10  12.011  628
632 | 0   33.81829202 24.14   10  12.011  629
633 | 0   32.58853595 24.85   10  12.011  630
634 | 0   32.58853595 26.27   10  12.011  631
635 | 0   33.81829202 26.98   10  12.011  632
636 | 0   33.81829202 28.4    10  12.011  633
637 | 0   32.58853595 29.11   10  12.011  634
638 | 0   32.58853595 30.53   10  12.011  635
639 | 0   33.81829202 31.24   10  12.011  636
640 | 0   33.81829202 32.66   10  12.011  637
641 | 0   32.58853595 33.37   10  12.011  638
642 | 0   32.58853595 34.79   10  12.011  639
643 | 0   33.81829202 35.5    10  12.011  640
644 | 0   33.81829202 36.92   10  12.011  641
645 | 0   32.58853595 37.63   10  12.011  642
646 | 0   32.58853595 39.05   10  12.011  643
647 | 0   33.81829202 39.76   10  12.011  644
648 | 0   33.81829202 41.18   10  12.011  645
649 | 0   32.58853595 41.89   10  12.011  646
650 | 0   32.58853595 43.31   10  12.011  647
651 | 0   33.81829202 44.02   10  12.011  648
652 | 0   33.81829202 45.44   10  12.011  649
653 | 0   32.58853595 46.15   10  12.011  650
654 | 0   32.58853595 47.57   10  12.011  651
655 | 0   33.81829202 48.28   10  12.011  652
656 | 0   33.81829202 49.7    10  12.011  653
657 | 0   32.58853595 50.41   10  12.011  654
658 | 0   35.04804809 0.710000001 10  12.011  655
659 | 0   36.27780417 1.420000001 10  12.011  656
660 | 0   36.27780417 2.840000002 10  12.011  657
661 | 0   36.27780417 5.679999999 10  12.011  658
662 | 0   36.27780417 7.100000001 10  12.011  659
663 | 0   35.04804809 7.810000001 10  12.011  660
664 | 0   35.04804809 9.230000002 10  12.011  661
665 | 0   36.27780417 9.939999998 10  12.011  662
666 | 0   36.27780417 11.36   10  12.011  663
667 | 0   35.04804809 12.07   10  12.011  664
668 | 0   35.04804809 13.49   10  12.011  665
669 | 0   36.27780417 14.2    10  12.011  666
670 | 0   36.27780417 15.62   10  12.011  667
671 | 0   35.04804809 16.33   10  12.011  668
672 | 0   35.04804809 17.75   10  12.011  669
673 | 0   36.27780417 18.46   10  12.011  670
674 | 0   36.27780417 19.88   10  12.011  671
675 | 0   35.04804809 20.59   10  12.011  672
676 | 0   35.04804809 22.01   10  12.011  673
677 | 0   36.27780417 22.72   10  12.011  674
678 | 0   36.27780417 24.14   10  12.011  675
679 | 0   35.04804809 24.85   10  12.011  676
680 | 0   35.04804809 26.27   10  12.011  677
681 | 0   36.27780417 26.98   10  12.011  678
682 | 0   36.27780417 28.4    10  12.011  679
683 | 0   35.04804809 29.11   10  12.011  680
684 | 0   35.04804809 30.53   10  12.011  681
685 | 0   36.27780417 31.24   10  12.011  682
686 | 0   36.27780417 32.66   10  12.011  683
687 | 0   35.04804809 33.37   10  12.011  684
688 | 0   35.04804809 34.79   10  12.011  685
689 | 0   36.27780417 36.92   10  12.011  686
690 | 0   35.04804809 37.63   10  12.011  687
691 | 0   35.04804809 39.05   10  12.011  688
692 | 0   36.27780417 39.76   10  12.011  689
693 | 0   36.27780417 41.18   10  12.011  690
694 | 0   35.04804809 41.89   10  12.011  691
695 | 0   35.04804809 43.31   10  12.011  692
696 | 0   36.27780417 44.02   10  12.011  693
697 | 0   36.27780417 45.44   10  12.011  694
698 | 0   35.04804809 46.15   10  12.011  695
699 | 0   35.04804809 47.57   10  12.011  696
700 | 0   36.27780417 48.28   10  12.011  697
701 | 0   36.27780417 49.7    10  12.011  698
702 | 0   35.04804809 50.41   10  12.011  699
703 | 0   37.50756024 0.710000001 10  12.011  700
704 | 0   38.73731631 1.420000001 10  12.011  701
705 | 0   38.73731631 2.840000002 10  12.011  702
706 | 0   37.50756024 3.549999998 10  12.011  703
707 | 0   37.50756024 4.969999999 10  12.011  704
708 | 0   38.73731631 5.679999999 10  12.011  705
709 | 0   38.73731631 7.100000001 10  12.011  706
710 | 0   37.50756024 7.810000001 10  12.011  707
711 | 0   37.50756024 9.230000002 10  12.011  708
712 | 0   38.73731631 9.939999998 10  12.011  709
713 | 0   38.73731631 11.36   10  12.011  710
714 | 0   37.50756024 12.07   10  12.011  711
715 | 0   37.50756024 13.49   10  12.011  712
716 | 0   38.73731631 14.2    10  12.011  713
717 | 0   38.73731631 15.62   10  12.011  714
718 | 0   37.50756024 16.33   10  12.011  715
719 | 0   37.50756024 17.75   10  12.011  716
720 | 0   38.73731631 18.46   10  12.011  717
721 | 0   38.73731631 19.88   10  12.011  718
722 | 0   37.50756024 20.59   10  12.011  719
723 | 0   37.50756024 22.01   10  12.011  720
724 | 0   38.73731631 22.72   10  12.011  721
725 | 0   38.73731631 24.14   10  12.011  722
726 | 0   37.50756024 24.85   10  12.011  723
727 | 0   37.50756024 26.27   10  12.011  724
728 | 0   38.73731631 26.98   10  12.011  725
729 | 0   38.73731631 28.4    10  12.011  726
730 | 0   37.50756024 29.11   10  12.011  727
731 | 0   37.50756024 30.53   10  12.011  728
732 | 0   38.73731631 31.24   10  12.011  729
733 | 0   38.73731631 32.66   10  12.011  730
734 | 0   37.50756024 34.79   10  12.011  731
735 | 0   38.73731631 35.5    10  12.011  732
736 | 0   38.73731631 36.92   10  12.011  733
737 | 0   37.50756024 37.63   10  12.011  734
738 | 0   37.50756024 39.05   10  12.011  735
739 | 0   38.73731631 39.76   10  12.011  736
740 | 0   38.73731631 41.18   10  12.011  737
741 | 0   37.50756024 41.89   10  12.011  738
742 | 0   37.50756024 43.31   10  12.011  739
743 | 0   38.73731631 44.02   10  12.011  740
744 | 0   38.73731631 45.44   10  12.011  741
745 | 0   37.50756024 46.15   10  12.011  742
746 | 0   37.50756024 47.57   10  12.011  743
747 | 0   38.73731631 48.28   10  12.011  744
748 | 0   38.73731631 49.7    10  12.011  745
749 | 0   37.50756024 50.41   10  12.011  746
750 | 0   39.96707238 0.710000001 10  12.011  747
751 | 0   41.19682846 2.840000002 10  12.011  748
752 | 0   39.96707238 3.549999998 10  12.011  749
753 | 0   39.96707238 4.969999999 10  12.011  750
754 | 0   41.19682846 5.679999999 10  12.011  751
755 | 0   41.19682846 7.100000001 10  12.011  752
756 | 0   39.96707238 7.810000001 10  12.011  753
757 | 0   39.96707238 9.230000002 10  12.011  754
758 | 0   41.19682846 9.939999998 10  12.011  755
759 | 0   41.19682846 11.36   10  12.011  756
760 | 0   39.96707238 12.07   10  12.011  757
761 | 0   39.96707238 13.49   10  12.011  758
762 | 0   41.19682846 14.2    10  12.011  759
763 | 0   41.19682846 15.62   10  12.011  760
764 | 0   39.96707238 16.33   10  12.011  761
765 | 0   39.96707238 17.75   10  12.011  762
766 | 0   41.19682846 18.46   10  12.011  763
767 | 0   41.19682846 19.88   10  12.011  764
768 | 0   39.96707238 20.59   10  12.011  765
769 | 0   39.96707238 22.01   10  12.011  766
770 | 0   41.19682846 24.14   10  12.011  767
771 | 0   39.96707238 24.85   10  12.011  768
772 | 0   39.96707238 26.27   10  12.011  769
773 | 0   41.19682846 26.98   10  12.011  770
774 | 0   41.19682846 28.4    10  12.011  771
775 | 0   39.96707238 29.11   10  12.011  772
776 | 0   39.96707238 30.53   10  12.011  773
777 | 0   41.19682846 31.24   10  12.011  774
778 | 0   41.19682846 32.66   10  12.011  775
779 | 0   39.96707238 33.37   10  12.011  776
780 | 0   39.96707238 34.79   10  12.011  777
781 | 0   41.19682846 35.5    10  12.011  778
782 | 0   41.19682846 36.92   10  12.011  779
783 | 0   39.96707238 37.63   10  12.011  780
784 | 0   39.96707238 39.05   10  12.011  781
785 | 0   41.19682846 39.76   10  12.011  782
786 | 0   41.19682846 41.18   10  12.011  783
787 | 0   39.96707238 41.89   10  12.011  784
788 | 0   39.96707238 43.31   10  12.011  785
789 | 0   41.19682846 44.02   10  12.011  786
790 | 0   41.19682846 45.44   10  12.011  787
791 | 0   39.96707238 46.15   10  12.011  788
792 | 0   39.96707238 47.57   10  12.011  789
793 | 0   41.19682846 48.28   10  12.011  790
794 | 0   41.19682846 49.7    10  12.011  791
795 | 0   39.96707238 50.41   10  12.011  792
796 | 0   43.6563406  1.420000001 10  12.011  793
797 | 0   43.6563406  2.840000002 10  12.011  794
798 | 0   42.42658453 3.549999998 10  12.011  795
799 | 0   42.42658453 4.969999999 10  12.011  796
800 | 0   43.6563406  5.679999999 10  12.011  797
801 | 0   43.6563406  7.100000001 10  12.011  798
802 | 0   42.42658453 7.810000001 10  12.011  799
803 | 0   42.42658453 9.230000002 10  12.011  800
804 | 0   43.6563406  9.939999998 10  12.011  801
805 | 0   43.6563406  11.36   10  12.011  802
806 | 0   42.42658453 12.07   10  12.011  803
807 | 0   43.6563406  14.2    10  12.011  804
808 | 0   43.6563406  15.62   10  12.011  805
809 | 0   42.42658453 16.33   10  12.011  806
810 | 0   42.42658453 17.75   10  12.011  807
811 | 0   43.6563406  18.46   10  12.011  808
812 | 0   43.6563406  19.88   10  12.011  809
813 | 0   42.42658453 20.59   10  12.011  810
814 | 0   42.42658453 22.01   10  12.011  811
815 | 0   43.6563406  22.72   10  12.011  812
816 | 0   43.6563406  24.14   10  12.011  813
817 | 0   42.42658453 24.85   10  12.011  814
818 | 0   42.42658453 26.27   10  12.011  815
819 | 0   43.6563406  26.98   10  12.011  816
820 | 0   43.6563406  28.4    10  12.011  817
821 | 0   42.42658453 29.11   10  12.011  818
822 | 0   42.42658453 30.53   10  12.011  819
823 | 0   43.6563406  31.24   10  12.011  820
824 | 0   43.6563406  32.66   10  12.011  821
825 | 0   42.42658453 34.79   10  12.011  822
826 | 0   43.6563406  35.5    10  12.011  823
827 | 0   43.6563406  36.92   10  12.011  824
828 | 0   42.42658453 37.63   10  12.011  825
829 | 0   42.42658453 39.05   10  12.011  826
830 | 0   43.6563406  39.76   10  12.011  827
831 | 0   43.6563406  41.18   10  12.011  828
832 | 0   42.42658453 41.89   10  12.011  829
833 | 0   42.42658453 43.31   10  12.011  830
834 | 0   43.6563406  44.02   10  12.011  831
835 | 0   43.6563406  45.44   10  12.011  832
836 | 0   42.42658453 46.15   10  12.011  833
837 | 0   42.42658453 47.57   10  12.011  834
838 | 0   43.6563406  48.28   10  12.011  835
839 | 0   43.6563406  49.7    10  12.011  836
840 | 0   42.42658453 50.41   10  12.011  837
841 | 0   44.88609668 0.710000001 10  12.011  838
842 | 0   46.11585275 1.420000001 10  12.011  839
843 | 0   44.88609668 3.549999998 10  12.011  840
844 | 0   44.88609668 4.969999999 10  12.011  841
845 | 0   46.11585275 5.679999999 10  12.011  842
846 | 0   46.11585275 7.100000001 10  12.011  843
847 | 0   44.88609668 7.810000001 10  12.011  844
848 | 0   44.88609668 9.230000002 10  12.011  845
849 | 0   46.11585275 9.939999998 10  12.011  846
850 | 0   46.11585275 11.36   10  12.011  847
851 | 0   44.88609668 12.07   10  12.011  848
852 | 0   44.88609668 13.49   10  12.011  849
853 | 0   46.11585275 14.2    10  12.011  850
854 | 0   46.11585275 15.62   10  12.011  851
855 | 0   44.88609668 16.33   10  12.011  852
856 | 0   44.88609668 17.75   10  12.011  853
857 | 0   46.11585275 18.46   10  12.011  854
858 | 0   46.11585275 19.88   10  12.011  855
859 | 0   44.88609668 20.59   10  12.011  856
860 | 0   44.88609668 22.01   10  12.011  857
861 | 0   46.11585275 22.72   10  12.011  858
862 | 0   46.11585275 24.14   10  12.011  859
863 | 0   44.88609668 24.85   10  12.011  860
864 | 0   44.88609668 26.27   10  12.011  861
865 | 0   46.11585275 26.98   10  12.011  862
866 | 0   46.11585275 28.4    10  12.011  863
867 | 0   44.88609668 29.11   10  12.011  864
868 | 0   44.88609668 30.53   10  12.011  865
869 | 0   46.11585275 31.24   10  12.011  866
870 | 0   46.11585275 32.66   10  12.011  867
871 | 0   44.88609668 33.37   10  12.011  868
872 | 0   44.88609668 34.79   10  12.011  869
873 | 0   46.11585275 35.5    10  12.011  870
874 | 0   46.11585275 36.92   10  12.011  871
875 | 0   44.88609668 37.63   10  12.011  872
876 | 0   44.88609668 39.05   10  12.011  873
877 | 0   46.11585275 39.76   10  12.011  874
878 | 0   46.11585275 41.18   10  12.011  875
879 | 0   44.88609668 41.89   10  12.011  876
880 | 0   44.88609668 43.31   10  12.011  877
881 | 0   46.11585275 44.02   10  12.011  878
882 | 0   46.11585275 45.44   10  12.011  879
883 | 0   44.88609668 46.15   10  12.011  880
884 | 0   44.88609668 47.57   10  12.011  881
885 | 0   46.11585275 48.28   10  12.011  882
886 | 0   46.11585275 49.7    10  12.011  883
887 | 0   44.88609668 50.41   10  12.011  884
888 | 0   47.34560883 0.710000001 10  12.011  885
889 | 0   48.5753649  1.420000001 10  12.011  886
890 | 0   48.5753649  2.840000002 10  12.011  887
891 | 0   47.34560883 3.549999998 10  12.011  888
892 | 0   47.34560883 4.969999999 10  12.011  889
893 | 0   48.5753649  5.679999999 10  12.011  890
894 | 0   48.5753649  7.100000001 10  12.011  891
895 | 0   47.34560883 9.230000002 10  12.011  892
896 | 0   48.5753649  9.939999998 10  12.011  893
897 | 0   48.5753649  11.36   10  12.011  894
898 | 0   47.34560883 12.07   10  12.011  895
899 | 0   47.34560883 13.49   10  12.011  896
900 | 0   48.5753649  14.2    10  12.011  897
901 | 0   48.5753649  15.62   10  12.011  898
902 | 0   47.34560883 16.33   10  12.011  899
903 | 0   47.34560883 17.75   10  12.011  900
904 | 0   48.5753649  18.46   10  12.011  901
905 | 0   48.5753649  19.88   10  12.011  902
906 | 0   47.34560883 20.59   10  12.011  903
907 | 0   47.34560883 22.01   10  12.011  904
908 | 0   48.5753649  22.72   10  12.011  905
909 | 0   48.5753649  24.14   10  12.011  906
910 | 0   47.34560883 24.85   10  12.011  907
911 | 0   47.34560883 26.27   10  12.011  908
912 | 0   48.5753649  26.98   10  12.011  909
913 | 0   48.5753649  28.4    10  12.011  910
914 | 0   47.34560883 29.11   10  12.011  911
915 | 0   47.34560883 30.53   10  12.011  912
916 | 0   48.5753649  31.24   10  12.011  913
917 | 0   48.5753649  32.66   10  12.011  914
918 | 0   47.34560883 33.37   10  12.011  915
919 | 0   47.34560883 34.79   10  12.011  916
920 | 0   48.5753649  35.5    10  12.011  917
921 | 0   48.5753649  36.92   10  12.011  918
922 | 0   47.34560883 37.63   10  12.011  919
923 | 0   47.34560883 39.05   10  12.011  920
924 | 0   48.5753649  39.76   10  12.011  921
925 | 0   48.5753649  41.18   10  12.011  922
926 | 0   47.34560883 41.89   10  12.011  923
927 | 0   47.34560883 43.31   10  12.011  924
928 | 0   48.5753649  44.02   10  12.011  925
929 | 0   48.5753649  45.44   10  12.011  926
930 | 0   47.34560883 46.15   10  12.011  927
931 | 0   47.34560883 47.57   10  12.011  928
932 | 0   48.5753649  48.28   10  12.011  929
933 | 0   48.5753649  49.7    10  12.011  930
934 | 0   47.34560883 50.41   10  12.011  931
935 | 0   49.80512097 0.710000001 10  12.011  932
936 | 0   51.03487705 1.420000001 10  12.011  933
937 | 0   51.03487705 2.840000002 10  12.011  934
938 | 0   49.80512097 3.549999998 10  12.011  935
939 | 0   51.03487705 5.679999999 10  12.011  936
940 | 0   51.03487705 7.100000001 10  12.011  937
941 | 0   49.80512097 7.810000001 10  12.011  938
942 | 0   49.80512097 9.230000002 10  12.011  939
943 | 0   51.03487705 9.939999998 10  12.011  940
944 | 0   51.03487705 11.36   10  12.011  941
945 | 0   49.80512097 12.07   10  12.011  942
946 | 0   49.80512097 13.49   10  12.011  943
947 | 0   51.03487705 14.2    10  12.011  944
948 | 0   51.03487705 15.62   10  12.011  945
949 | 0   49.80512097 16.33   10  12.011  946
950 | 0   49.80512097 17.75   10  12.011  947
951 | 0   51.03487705 18.46   10  12.011  948
952 | 0   51.03487705 19.88   10  12.011  949
953 | 0   49.80512097 20.59   10  12.011  950
954 | 0   49.80512097 22.01   10  12.011  951
955 | 0   51.03487705 22.72   10  12.011  952
956 | 0   51.03487705 24.14   10  12.011  953
957 | 0   49.80512097 24.85   10  12.011  954
958 | 0   49.80512097 26.27   10  12.011  955
959 | 0   51.03487705 26.98   10  12.011  956
960 | 0   51.03487705 28.4    10  12.011  957
961 | 0   49.80512097 29.11   10  12.011  958
962 | 0   51.03487705 31.24   10  12.011  959
963 | 0   51.03487705 32.66   10  12.011  960
964 | 0   49.80512097 33.37   10  12.011  961
965 | 0   49.80512097 34.79   10  12.011  962
966 | 0   51.03487705 35.5    10  12.011  963
967 | 0   51.03487705 36.92   10  12.011  964
968 | 0   49.80512097 37.63   10  12.011  965
969 | 0   49.80512097 39.05   10  12.011  966
970 | 0   51.03487705 39.76   10  12.011  967
971 | 0   51.03487705 41.18   10  12.011  968
972 | 0   49.80512097 41.89   10  12.011  969
973 | 0   49.80512097 43.31   10  12.011  970
974 | 0   51.03487705 44.02   10  12.011  971
975 | 0   51.03487705 45.44   10  12.011  972
976 | 0   49.80512097 46.15   10  12.011  973
977 | 0   49.80512097 47.57   10  12.011  974
978 | 0   51.03487705 48.28   10  12.011  975
979 | 0   51.03487705 49.7    10  12.011  976
980 | 0   49.80512097 50.41   10  12.011  977
981 | 


--------------------------------------------------------------------------------
/1. Phonon Participation Ratios/graphene_construct.py:
--------------------------------------------------------------------------------
 1 | # -*- coding: utf-8 -*-
 2 | """
 3 | Created on Thu Jul  8 12:15:44 2021
 4 | 
 5 | @author: Penghua Ying (hityingph@163.com)
 6 | """
 7 | import numpy as np
 8 | import random as rd
 9 | 
10 | lx = 50
11 | ly = 50
12 | lz = 3.35
13 | bond_length = 1.42
14 | defect_dens = 0.03 #For pristine graphene without defect, one should set this as zero.
15 | 
16 | uc_lx = np.sqrt(3) * bond_length
17 | uc_ly = 3 * bond_length
18 | uc_lz = 20
19 | rp_x = int(lx/uc_lx) + 1
20 | rp_y = int(ly/uc_ly) + 1
21 | 
22 | atom_num = int(4*rp_x*rp_y)
23 | defect_num = int(atom_num*defect_dens)
24 | defect_id = []
25 | for i in range(defect_num):
26 |     defect_id.append(rd.randint(1, atom_num))
27 |     
28 | atom1 = [0.25, 1/6, 0.5]
29 | atom2 = [0.75, 1/3, 0.5]
30 | atom3 = [0.75, 2/3, 0.5]
31 | atom4 = [0.25, 5/6, 0.5]
32 | atoms = [atom1, atom2, atom3, atom4]
33 | 
34 | atom_id = 0
35 | new_atom_id = 0
36 | atom_type = 0
37 | atom_mass = 12.011
38 | 
39 | coord_type = []
40 | coord_x = []
41 | coord_y = []
42 | coord_z = []
43 | coord_mass = []
44 | coord_id = []
45 | for i in range(rp_x):
46 |     for j in range(rp_y):
47 |         for k in range(4):
48 |             atom_id += 1
49 |             position_x = atoms[k][0]*uc_lx + i*uc_lx
50 |             position_y = atoms[k][1]*uc_ly + j*uc_ly
51 |             position_z = atoms[k][2]*uc_lz
52 |             if atom_id not in defect_id:
53 |                 coord_type.append(atom_type)
54 |                 coord_x.append(position_x)
55 |                 coord_y.append(position_y)
56 |                 coord_z.append(position_z)
57 |                 coord_mass.append(atom_mass)
58 |                 coord_id.append(new_atom_id)
59 |                 new_atom_id +=1
60 |                 # print(atom_id, atom_type, position_x, position_y, position_z)
61 | 
62 | ### line 0
63 | N = new_atom_id     #number of atoms
64 | M = 3               #maximum number of neighbors
65 | cutoff = 2.1        #initial cutoff distance used for building the neighbor list
66 | box_shape = 0       #0:orthogonal; 1:triclinic
67 | has_velocity = 0    #0:has initial velocity; 1:not has initial velocity 
68 | number_of_grouping_methods = 1 #we use one grouping method here
69 | 
70 | ### line 1
71 | pbc_x = 1 #1:periodic; 0:free
72 | pbc_y = 1 #1:periodic; 0:free
73 | pbc_z = 0 #1:periodic; 0:free
74 | L_x = uc_lx*rp_x
75 | L_y = uc_ly*rp_y
76 | L_z = lz
77 | 
78 | 
79 | f = open("xyz.in", "w")
80 | line0 = ' '.join(str(val) for val in [N, M, cutoff, box_shape, has_velocity, number_of_grouping_methods]) 
81 | f.write(line0)
82 | f.write("\n")
83 | line1 = ' '.join(str(val) for val in [pbc_x, pbc_y, pbc_z, L_x, L_y, L_z]) 
84 | f.write(line1)
85 | f.write("\n")
86 | # line m+2                 
87 | for i in range(new_atom_id):
88 |     line_coord = ' '.join(str(val) for val in [coord_type[i], coord_x[i], coord_y[i], coord_z[i], coord_mass[i], coord_id[i]])
89 |     f.write(line_coord)                                           
90 |     f.write(str("\n"))
91 | f.close()
92 | 
93 |         
94 | 
95 | 


--------------------------------------------------------------------------------
/1. Phonon Participation Ratios/prsitine_graphene/run.in:
--------------------------------------------------------------------------------
 1 | potential       potentials/tersoff/Graphene_Lindsay_2010_modified.txt 0
 2 | velocity        300
 3 | 
 4 | ensemble        npt_ber 300 300 0.01 0 0 0 0.0005 
 5 | time_step       1     
 6 | dump_thermo     100     
 7 | run             200000
 8 | 
 9 | 
10 | ensemble        nve 
11 | compute_dos     5 200 400.0 group 0 -1 num_dos_points 300
12 | run             200000
13 | 
14 | 
15 | 
16 | 
17 | 
18 | 
19 | 
20 | 
21 | 


--------------------------------------------------------------------------------
/2. Elastic Constants Based on Strain Fluctuation Method/.ipynb_checkpoints/Elastic Constants Based on Strain Fluctuation Method-checkpoint.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# Elastic Constants Calculations Based on Strain Fluctuations Method\n",
  8 |     "# 1. Introduction\n",
  9 |     "- In this example, we calculate the elastic constants of diamond Si at 300 K and zero pressure. Based on the strain fluctuations method [[Parrinello 1982]](https://doi.org/10.1063/1.443248), one can directly measure the elastic constants from the fluctuations of unit cell vectors in the constant-stress (N, $\\sigma$, T) molecular dynamics simulations:\n",
 10 |     "$$\n",
 11 |     "C_{ijkl}^{-1} = \\frac{V}{k_{B}T}\\left\\langle\\epsilon_{ij}\\epsilon_{kl}\\right\\rangle-\\left\\langle\\epsilon_{ij}\\right\\rangle\\left\\langle\\epsilon_{kl}\\right\\rangle,\n",
 12 |     "$$\n",
 13 |     "where $\\epsilon$ is the unit cell strain, $V$ is the unit cell volume, $T$ is the temperature and $k_{B}$ is the Boltzmann constant. $\\left\\langle\\right\\rangle$ represents the ensemble average and calculated as the the average over a period of time in molecular dynamics simulations. \n",
 14 |     "\n",
 15 |     "\n",
 16 |     "- In this tutorial, we use the stochastic cell rescaling (scr) ensemble [[Bernetti 2020]](https://doi.org/10.1063/5.0020514), which is a first-order barostat that samples the correct volume fluctuations by including a suitable noise term. The scr ensemble has been implemented in GPUMD recently. However, we stress that the strain fluctuation methods **cannot** be performed using **the Berendsen method**, due to the fact that the Berendsen method cannot give the correct volume fluctuations. "
 17 |    ]
 18 |   },
 19 |   {
 20 |    "cell_type": "markdown",
 21 |    "metadata": {},
 22 |    "source": [
 23 |     "# 2. Preparing the Inputs\n",
 24 |     "- We use a diamond Si consisting of 8000 atoms. \n",
 25 |     "\n",
 26 |     "\n",
 27 |     "- The atomic interactions are described by the minimal Tersoff potential [[Fan 2020]](https://doi.org/10.1088/1361-648X/ab5c5f).\n",
 28 |     "\n",
 29 |     "## Generate the  [xyz.in](https://gpumd.zheyongfan.org/index.php/The_xyz.in_input_file) file:"
 30 |    ]
 31 |   },
 32 |   {
 33 |    "cell_type": "markdown",
 34 |    "metadata": {},
 35 |    "source": [
 36 |     "- The xyz.in file for diamond silicon is contructed by the matlab code create_xyz.m as provided in the same path, which is replicated from the [cohesive_energy tutorial](https://github.com/brucefan1983/GPUMD/tree/master/examples/empirical_potentials/cohesive_energy). Because we need to obtain the fluctuation of lattice angle, we use the triclinic box  instead of orthogonal box here.   "
 37 |    ]
 38 |   },
 39 |   {
 40 |    "cell_type": "markdown",
 41 |    "metadata": {},
 42 |    "source": [
 43 |     "## The <code>run.in</code> file:\n",
 44 |     "The <code>run.in</code> input file is given below:<br>\n",
 45 |     "```\n",
 46 |     "potential   potentials/tersoff/Si_Fan_2019.txt 0\n",
 47 |     "velocity    300\n",
 48 |     "\n",
 49 |     "ensemble    npt_scr 300 300 100 0 0 0 0 0 0 2000\n",
 50 |     "time_step   1\n",
 51 |     "dump_thermo  100         \n",
 52 |     "run       1100000\n",
 53 |     "```\n",
 54 |     " - The first line uses the [potential](https://gpumd.zheyongfan.org/index.php/The_potential_keyword) keyword to define the potential to be used, which is specified in the file [Si_Fan_2019.txt](https://github.com/brucefan1983/GPUMD/blob/master/potentials/tersoff/Si_Fan_2019.txt).\n",
 55 |     "\n",
 56 |     "\n",
 57 |     " - The second line uses the [velocity](https://gpumd.zheyongfan.org/index.php/The_velocity_keyword) keyword and sets the velocities to be initialized with a temperature of 300 K. \n",
 58 |     "\n",
 59 |     "\n",
 60 |     "- For the [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword), the constant-stress (N, $\\sigma$, T), specifically, NPT [ensemble](https://gpumd.zheyongfan.org/index.php/The_ensemble_keyword) (the scr method) is used. The temperature is 300 K and the pressures are zero in all the directions. Currently, all the box components will be controlled independently according to the 6 target pressure components. Therefore, we can obtain the fluctuation of all lattice constants including three lattice length and three lattice angles. \n",
 61 |     "\n",
 62 |     "\n",
 63 |     "- The coupling constants are 100 (dimensionless) and 2000 (in the natural unit system adopted by GPUMD) for the thermostat and the barostat, respectively. The [time_step](https://gpumd.zheyongfan.org/index.php/The_time_step_keyword) for integration is 1 fs. There are $1.1\\times 10^6$ steps (1100 ps) for this [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword) and the thermodynamic quantities will be output every 100 steps. The first 100 ps serves as the equilibration stage, and the last 1000 ps serves as the production stage.\n"
 64 |    ]
 65 |   },
 66 |   {
 67 |    "cell_type": "markdown",
 68 |    "metadata": {},
 69 |    "source": [
 70 |     "# 3. Results and Discussion\n",
 71 |     "Based on the [thermo.out](https://gpumd.zheyongfan.org/index.php/The_thermo.out_output_file) output files, according to the strain fluctuation method defined above, one can obtain the four-order elastic tensor based on fluctuation of corresponding strain compoments, and then obtain the two-order elastic constants under Voigt notation. Specifically, dimaond Si considered here has a cubic symmestry, there are only three elastic constants, i.e., C11, C12, C44. Based on this simple example, one can be easily extended to the structures with other symmetry.  "
 72 |    ]
 73 |   },
 74 |   {
 75 |    "cell_type": "code",
 76 |    "execution_count": 1,
 77 |    "metadata": {},
 78 |    "outputs": [
 79 |     {
 80 |      "name": "stdout",
 81 |      "output_type": "stream",
 82 |      "text": [
 83 |       "[C11, C12, C44] (unit in GPa) of Si estimated by gpumd with npt_scr for 1ns:\n",
 84 |       "[153.99128892  65.06584192  77.93512353]\n",
 85 |       "With standard error (unit in GPa) of: \n",
 86 |       "[4.00294202 5.43223573 2.30484482]\n"
 87 |      ]
 88 |     }
 89 |    ],
 90 |    "source": [
 91 |     "from thermo.gpumd.data import load_thermo\n",
 92 |     "from pylab import *\n",
 93 |     "import math\n",
 94 |     "\n",
 95 |     "def calc_angle(v1, v2):\n",
 96 |     "    alpha = math.acos(np.dot(v1, v2)/(np.linalg.norm(v1)*np.linalg.norm(v2)))\n",
 97 |     "    return alpha\n",
 98 |     "\n",
 99 |     "def calc_elstic(strain_ij, strain_kl):\n",
100 |     "    s_ijkl = average(strain_ij*strain_kl)-average(strain_ij)*average(strain_kl)\n",
101 |     "    return s_ijkl\n",
102 |     "\n",
103 |     "def output_elastic_gpumd(path, slice_num):\n",
104 |     "    #Obtain the strain tensor     \n",
105 |     "    thermo = load_thermo(directory=path)\n",
106 |     "    for keys in thermo:\n",
107 |     "        thermo[keys]=thermo[keys][1000:] #Discard the first 100 ps data\n",
108 |     "    Cij = np.zeros((slice_num,3))\n",
109 |     "    for i in range(slice_num): #Split to 10 slices\n",
110 |     "        # print(i)\n",
111 |     "        thermo_slice = dict()\n",
112 |     "        for keys in thermo:\n",
113 |     "            thermo_slice[keys]=thermo[keys][1000*i:1000*(i+1)]\n",
114 |     "        alpha = np.zeros(len(thermo_slice[\"ax\"]))\n",
115 |     "        beta  = np.zeros_like(alpha)\n",
116 |     "        gamma = np.zeros_like(alpha)\n",
117 |     "        for j in range(len(thermo_slice[\"ax\"])):\n",
118 |     "            va = [thermo_slice[\"ax\"][j], thermo_slice[\"ay\"][j], thermo_slice[\"az\"][j]]\n",
119 |     "            vb = [thermo_slice[\"bx\"][j], thermo_slice[\"by\"][j], thermo_slice[\"bz\"][j]]\n",
120 |     "            vc = [thermo_slice[\"cx\"][j], thermo_slice[\"cy\"][j], thermo_slice[\"cz\"][j]]\n",
121 |     "            alpha[j] = calc_angle(vb, vc)\n",
122 |     "            beta[j]  = calc_angle(va, vc)\n",
123 |     "            gamma[j] = calc_angle(va, vb)\n",
124 |     "           \n",
125 |     "        strain = dict()\n",
126 |     "        strain[\"11\"] = thermo_slice[\"ax\"]/average(thermo_slice[\"ax\"])-1 #xx \n",
127 |     "        strain[\"22\"] = thermo_slice[\"by\"]/average(thermo_slice[\"by\"])-1 #yy\n",
128 |     "        strain[\"33\"] = thermo_slice[\"cz\"]/average(thermo_slice[\"cz\"])-1 #zz\n",
129 |     "        strain[\"23\"] = (alpha-pi/2)/2 #yz\n",
130 |     "        strain[\"13\"] = (beta-pi/2)/2 #xz\n",
131 |     "        strain[\"12\"] = (gamma-pi/2)/2 #xy\n",
132 |     "        \n",
133 |     "        #Calculate the cubic compliance tensor\n",
134 |     "        #S11=S1111=S2222=S3333,S12=S1122=S1133=S2233; S44=S2323=S1313=S1212\n",
135 |     "        V = average(thermo[\"ax\"]*thermo[\"by\"]*thermo[\"cz\"]) #volue, unit in angstrom^{3}\n",
136 |     "        T = 300 #temperature, unit in K\n",
137 |     "        kB = 1.38064852 #unit in e-23 J/K\n",
138 |     "        scale = 100/(T*kB)*V #unit in GPa^{-1}, scale=V/(KB*T)\n",
139 |     "        S1111 = scale*calc_elstic(strain[\"11\"], strain[\"11\"])\n",
140 |     "        S2222 = scale*calc_elstic(strain[\"22\"], strain[\"22\"])\n",
141 |     "        S3333 = scale*calc_elstic(strain[\"33\"], strain[\"33\"])\n",
142 |     "        S1122 = scale*calc_elstic(strain[\"11\"], strain[\"22\"])\n",
143 |     "        S1133 = scale*calc_elstic(strain[\"11\"], strain[\"33\"])\n",
144 |     "        S2233 = scale*calc_elstic(strain[\"22\"], strain[\"33\"])\n",
145 |     "        S2323 = scale*calc_elstic(strain[\"23\"], strain[\"23\"])\n",
146 |     "        S1313 = scale*calc_elstic(strain[\"13\"], strain[\"13\"])\n",
147 |     "        S1212  = scale*calc_elstic(strain[\"12\"], strain[\"12\"])\n",
148 |     "        \n",
149 |     "        # All the below value should be very close to zero\n",
150 |     "        S1123 = scale*calc_elstic(strain[\"11\"], strain[\"23\"])\n",
151 |     "        S1113 = scale*calc_elstic(strain[\"11\"], strain[\"13\"])\n",
152 |     "        S1112 = scale*calc_elstic(strain[\"11\"], strain[\"12\"])\n",
153 |     "        \n",
154 |     "        # Convert Sijkl to  Spq \n",
155 |     "        # NOTED that the Spq = Sijkl when p q = 1, 2, 3 BUT Spq = 4*Sijkl when p q = 4, 5, 6.\n",
156 |     "        S11 = (S1111+S2222+S3333)/3\n",
157 |     "        S12 = (S1122+S1133+S2233)/3\n",
158 |     "        S44 = 4*(S2323+S1313+S1212)/3\n",
159 |     "        Spq = np.array([[S11, S12, S12,   0,   0,   0], \n",
160 |     "                        [S12, S11, S12,   0,   0,   0],\n",
161 |     "                        [S12, S12, S11,   0,   0,   0],\n",
162 |     "                        [0,     0,   0, S44,   0,   0],\n",
163 |     "                        [0,     0,   0,   0, S44,   0],\n",
164 |     "                        [0,     0,   0,   0,   0, S44]])\n",
165 |     "        \n",
166 |     "        # Convert Spq to Cpq and \n",
167 |     "        Cpq = np.linalg.inv(Spq)\n",
168 |     "        C11 = Cpq[1,1]\n",
169 |     "        C12 = Cpq[1,2]\n",
170 |     "        C44 = Cpq[4,4]\n",
171 |     "        # print(np.array([C11, C12, C44]))\n",
172 |     "        Cij[i] = np.array([C11, C12, C44])\n",
173 |     "    return Cij\n",
174 |     "\n",
175 |     "def calc_ste(array): # calculate the standard error\n",
176 |     "    ste = np.zeros(3)\n",
177 |     "    for i in range(array.shape[1]):\n",
178 |     "        ste[i] = sqrt(sum(abs(array[:,i] - array[:,i].mean())**2))/len(array[:,i])\n",
179 |     "    return ste\n",
180 |     "        \n",
181 |     "\n",
182 |     "Cij_Si_gpumd_1ns = output_elastic_gpumd(\"./\", 10)\n",
183 |     "print(\"[C11, C12, C44] (unit in GPa) of Si estimated by gpumd with npt_scr for 1ns:\")\n",
184 |     "print(np.average(Cij_Si_gpumd_1ns, axis=0))\n",
185 |     "print(\"With standard error (unit in GPa) of: \")\n",
186 |     "print(calc_ste(Cij_Si_gpumd_1ns))"
187 |    ]
188 |   },
189 |   {
190 |    "cell_type": "markdown",
191 |    "metadata": {},
192 |    "source": [
193 |     "- Noted that we evenly divide the 1 ns simulation to ten independent simulations of 100 ps. Based on each independent simulation, we can obtain three elastic constants, and the final elastic constants is obtained averaging on ten simulations. We also compute the corresponding standard deviation.\n",
194 |     "\n",
195 |     "\n",
196 |     "- According to the [cohesive_energy tutorial](https://github.com/brucefan1983/GPUMD/tree/master/examples/empirical_potentials/cohesive_energy), one can also straightly calculate the elastic constants at 0 K based on stress-strain relationship by deforming the box with small strain. The elastic constants at 0 K are calculated as C11 = 148.686 Gpa, C12 = 65.5985 GPa ,C44 = 74.9417 GPa, which is in good agreement with our result obtained from strain fluctuation method at 300 K. \n",
197 |     "\n",
198 |     "\n",
199 |     "- Rather than the case at finite temperature, the strain fluctuation method can also been extended to the case under pressure loading. Combined with the Born stability criteria [[Born 1954]](https://en.wikipedia.org/wiki/Dynamical_Theory_of_Crystal_Lattices), strain fluctuation method is a powerful method to investigate the mechanical stability under pressure loading. \n"
200 |    ]
201 |   },
202 |   {
203 |    "cell_type": "markdown",
204 |    "metadata": {},
205 |    "source": [
206 |     "# 4. References\n",
207 |     "- [Parrinello 1982] M. Parrinello and A. Rahman. [Strain fluctuations and elastic constants](https://doi.org/10.1063/1.443248), J. Chem. Phys. **76**, 2662 (1982).\n",
208 |     "- [Bernetti 2020] Mattia Bernetti and  Giovanni Bussia, [Pressure control using stochastic cell rescaling](https://doi.org/10.1063/5.0020514), J. Chem. Phys. **153**, 114107 (2020).\n",
209 |     "- [Fan 2020] Zheyong Fan, Yanzhou Wang, Xiaokun Gu, Ping Qian, Yanjing Su, and Tapio Ala-Nissila, [A minimal Tersoff potential for diamond silicon with improved descriptions of elastic and phonon transport properties](https://doi.org/10.1088/1361-648X/ab5c5f), J. Phys.: Condens. Matter 32 135901 (2020).\n",
210 |     "- [Born 1954] M. Born, K. Huang, Dynamical Theory of Crystal Lattices, Clarendon Press, 1954.\n",
211 |     "\n"
212 |    ]
213 |   }
214 |  ],
215 |  "metadata": {
216 |   "kernelspec": {
217 |    "display_name": "Python 3",
218 |    "language": "python",
219 |    "name": "python3"
220 |   },
221 |   "language_info": {
222 |    "codemirror_mode": {
223 |     "name": "ipython",
224 |     "version": 3
225 |    },
226 |    "file_extension": ".py",
227 |    "mimetype": "text/x-python",
228 |    "name": "python",
229 |    "nbconvert_exporter": "python",
230 |    "pygments_lexer": "ipython3",
231 |    "version": "3.8.8"
232 |   }
233 |  },
234 |  "nbformat": 4,
235 |  "nbformat_minor": 2
236 | }
237 | 


--------------------------------------------------------------------------------
/2. Elastic Constants Based on Strain Fluctuation Method/Elastic Constants Based on Strain Fluctuation Method.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# Elastic Constants Calculations Based on Strain Fluctuations Method\n",
  8 |     "# 1. Introduction\n",
  9 |     "- In this example, we calculate the elastic constants of diamond Si at 300 K and zero pressure. Based on the strain fluctuations method [[Parrinello 1982]](https://doi.org/10.1063/1.443248), one can directly measure the elastic constants from the fluctuations of unit cell vectors in the constant-stress (N, $\\sigma$, T) molecular dynamics simulations:\n",
 10 |     "$$\n",
 11 |     "C_{ijkl}^{-1} = \\frac{V}{k_{B}T}\\left\\langle\\epsilon_{ij}\\epsilon_{kl}\\right\\rangle-\\left\\langle\\epsilon_{ij}\\right\\rangle\\left\\langle\\epsilon_{kl}\\right\\rangle,\n",
 12 |     "$$\n",
 13 |     "where $\\epsilon$ is the unit cell strain, $V$ is the unit cell volume, $T$ is the temperature and $k_{B}$ is the Boltzmann constant. $\\left\\langle\\right\\rangle$ represents the ensemble average and calculated as the the average over a period of time in molecular dynamics simulations. \n",
 14 |     "\n",
 15 |     "\n",
 16 |     "- In this tutorial, we use the stochastic cell rescaling (scr) ensemble [[Bernetti 2020]](https://doi.org/10.1063/5.0020514), which is a first-order barostat that samples the correct volume fluctuations by including a suitable noise term. The scr ensemble has been implemented in GPUMD recently. However, we stress that the strain fluctuation methods **cannot** be performed using **the Berendsen method**, due to the fact that the Berendsen method cannot give the correct volume fluctuations. "
 17 |    ]
 18 |   },
 19 |   {
 20 |    "cell_type": "markdown",
 21 |    "metadata": {},
 22 |    "source": [
 23 |     "# 2. Preparing the Inputs\n",
 24 |     "- We use a diamond Si consisting of 8000 atoms. \n",
 25 |     "\n",
 26 |     "\n",
 27 |     "- The atomic interactions are described by the minimal Tersoff potential [[Fan 2020]](https://doi.org/10.1088/1361-648X/ab5c5f).\n",
 28 |     "\n",
 29 |     "## Generate the  [xyz.in](https://gpumd.zheyongfan.org/index.php/The_xyz.in_input_file) file:"
 30 |    ]
 31 |   },
 32 |   {
 33 |    "cell_type": "markdown",
 34 |    "metadata": {},
 35 |    "source": [
 36 |     "- The xyz.in file for diamond silicon is contructed by the matlab code create_xyz.m as provided in the same path, which is replicated from the [cohesive_energy tutorial](https://github.com/brucefan1983/GPUMD/tree/master/examples/empirical_potentials/cohesive_energy). Because we need to obtain the fluctuation of lattice angle, we use the triclinic box  instead of orthogonal box here.   "
 37 |    ]
 38 |   },
 39 |   {
 40 |    "cell_type": "markdown",
 41 |    "metadata": {},
 42 |    "source": [
 43 |     "## The <code>run.in</code> file:\n",
 44 |     "The <code>run.in</code> input file is given below:<br>\n",
 45 |     "```\n",
 46 |     "potential   potentials/tersoff/Si_Fan_2019.txt 0\n",
 47 |     "velocity    300\n",
 48 |     "\n",
 49 |     "ensemble    npt_scr 300 300 100 0 0 0 0 0 0 2000\n",
 50 |     "time_step   1\n",
 51 |     "dump_thermo  100         \n",
 52 |     "run       1100000\n",
 53 |     "```\n",
 54 |     " - The first line uses the [potential](https://gpumd.zheyongfan.org/index.php/The_potential_keyword) keyword to define the potential to be used, which is specified in the file [Si_Fan_2019.txt](https://github.com/brucefan1983/GPUMD/blob/master/potentials/tersoff/Si_Fan_2019.txt).\n",
 55 |     "\n",
 56 |     "\n",
 57 |     " - The second line uses the [velocity](https://gpumd.zheyongfan.org/index.php/The_velocity_keyword) keyword and sets the velocities to be initialized with a temperature of 300 K. \n",
 58 |     "\n",
 59 |     "\n",
 60 |     "- For the [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword), the constant-stress (N, $\\sigma$, T), specifically, NPT [ensemble](https://gpumd.zheyongfan.org/index.php/The_ensemble_keyword) (the scr method) is used. The temperature is 300 K and the pressures are zero in all the directions. Currently, all the box components will be controlled independently according to the 6 target pressure components. Therefore, we can obtain the fluctuation of all lattice constants including three lattice length and three lattice angles. \n",
 61 |     "\n",
 62 |     "\n",
 63 |     "- The coupling constants are 100 (dimensionless) and 2000 (in the natural unit system adopted by GPUMD) for the thermostat and the barostat, respectively. The [time_step](https://gpumd.zheyongfan.org/index.php/The_time_step_keyword) for integration is 1 fs. There are $1.1\\times 10^6$ steps (1100 ps) for this [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword) and the thermodynamic quantities will be output every 100 steps. The first 100 ps serves as the equilibration stage, and the last 1000 ps serves as the production stage.\n"
 64 |    ]
 65 |   },
 66 |   {
 67 |    "cell_type": "markdown",
 68 |    "metadata": {},
 69 |    "source": [
 70 |     "# 3. Results and Discussion\n",
 71 |     "Based on the [thermo.out](https://gpumd.zheyongfan.org/index.php/The_thermo.out_output_file) output files, according to the strain fluctuation method defined above, one can obtain the four-order elastic tensor based on fluctuation of corresponding strain compoments, and then obtain the two-order elastic constants under Voigt notation. Specifically, dimaond Si considered here has a cubic symmestry, there are only three elastic constants, i.e., C11, C12, C44. Based on this simple example, one can be easily extended to the structures with other symmetry.  "
 72 |    ]
 73 |   },
 74 |   {
 75 |    "cell_type": "code",
 76 |    "execution_count": 1,
 77 |    "metadata": {},
 78 |    "outputs": [
 79 |     {
 80 |      "name": "stdout",
 81 |      "output_type": "stream",
 82 |      "text": [
 83 |       "[C11, C12, C44] (unit in GPa) of Si estimated by gpumd with npt_scr for 1ns:\n",
 84 |       "[153.99128892  65.06584192  77.93512353]\n",
 85 |       "With standard error (unit in GPa) of: \n",
 86 |       "[4.00294202 5.43223573 2.30484482]\n"
 87 |      ]
 88 |     }
 89 |    ],
 90 |    "source": [
 91 |     "from thermo.gpumd.data import load_thermo\n",
 92 |     "from pylab import *\n",
 93 |     "import math\n",
 94 |     "\n",
 95 |     "def calc_angle(v1, v2):\n",
 96 |     "    alpha = math.acos(np.dot(v1, v2)/(np.linalg.norm(v1)*np.linalg.norm(v2)))\n",
 97 |     "    return alpha\n",
 98 |     "\n",
 99 |     "def calc_elstic(strain_ij, strain_kl):\n",
100 |     "    s_ijkl = average(strain_ij*strain_kl)-average(strain_ij)*average(strain_kl)\n",
101 |     "    return s_ijkl\n",
102 |     "\n",
103 |     "def output_elastic_gpumd(path, slice_num):\n",
104 |     "    #Obtain the strain tensor     \n",
105 |     "    thermo = load_thermo(directory=path)\n",
106 |     "    for keys in thermo:\n",
107 |     "        thermo[keys]=thermo[keys][1000:] #Discard the first 100 ps data\n",
108 |     "    Cij = np.zeros((slice_num,3))\n",
109 |     "    for i in range(slice_num): #Split to 10 slices\n",
110 |     "        # print(i)\n",
111 |     "        thermo_slice = dict()\n",
112 |     "        for keys in thermo:\n",
113 |     "            thermo_slice[keys]=thermo[keys][1000*i:1000*(i+1)]\n",
114 |     "        alpha = np.zeros(len(thermo_slice[\"ax\"]))\n",
115 |     "        beta  = np.zeros_like(alpha)\n",
116 |     "        gamma = np.zeros_like(alpha)\n",
117 |     "        for j in range(len(thermo_slice[\"ax\"])):\n",
118 |     "            va = [thermo_slice[\"ax\"][j], thermo_slice[\"ay\"][j], thermo_slice[\"az\"][j]]\n",
119 |     "            vb = [thermo_slice[\"bx\"][j], thermo_slice[\"by\"][j], thermo_slice[\"bz\"][j]]\n",
120 |     "            vc = [thermo_slice[\"cx\"][j], thermo_slice[\"cy\"][j], thermo_slice[\"cz\"][j]]\n",
121 |     "            alpha[j] = calc_angle(vb, vc)\n",
122 |     "            beta[j]  = calc_angle(va, vc)\n",
123 |     "            gamma[j] = calc_angle(va, vb)\n",
124 |     "           \n",
125 |     "        strain = dict()\n",
126 |     "        strain[\"11\"] = thermo_slice[\"ax\"]/average(thermo_slice[\"ax\"])-1 #xx \n",
127 |     "        strain[\"22\"] = thermo_slice[\"by\"]/average(thermo_slice[\"by\"])-1 #yy\n",
128 |     "        strain[\"33\"] = thermo_slice[\"cz\"]/average(thermo_slice[\"cz\"])-1 #zz\n",
129 |     "        strain[\"23\"] = (alpha-pi/2)/2 #yz\n",
130 |     "        strain[\"13\"] = (beta-pi/2)/2 #xz\n",
131 |     "        strain[\"12\"] = (gamma-pi/2)/2 #xy\n",
132 |     "        \n",
133 |     "        #Calculate the cubic compliance tensor\n",
134 |     "        #S11=S1111=S2222=S3333,S12=S1122=S1133=S2233; S44=S2323=S1313=S1212\n",
135 |     "        V = average(thermo[\"ax\"]*thermo[\"by\"]*thermo[\"cz\"]) #volue, unit in angstrom^{3}\n",
136 |     "        T = 300 #temperature, unit in K\n",
137 |     "        kB = 1.38064852 #unit in e-23 J/K\n",
138 |     "        scale = 100/(T*kB)*V #unit in GPa^{-1}, scale=V/(KB*T)\n",
139 |     "        S1111 = scale*calc_elstic(strain[\"11\"], strain[\"11\"])\n",
140 |     "        S2222 = scale*calc_elstic(strain[\"22\"], strain[\"22\"])\n",
141 |     "        S3333 = scale*calc_elstic(strain[\"33\"], strain[\"33\"])\n",
142 |     "        S1122 = scale*calc_elstic(strain[\"11\"], strain[\"22\"])\n",
143 |     "        S1133 = scale*calc_elstic(strain[\"11\"], strain[\"33\"])\n",
144 |     "        S2233 = scale*calc_elstic(strain[\"22\"], strain[\"33\"])\n",
145 |     "        S2323 = scale*calc_elstic(strain[\"23\"], strain[\"23\"])\n",
146 |     "        S1313 = scale*calc_elstic(strain[\"13\"], strain[\"13\"])\n",
147 |     "        S1212  = scale*calc_elstic(strain[\"12\"], strain[\"12\"])\n",
148 |     "        \n",
149 |     "        # All the below value should be very close to zero\n",
150 |     "        S1123 = scale*calc_elstic(strain[\"11\"], strain[\"23\"])\n",
151 |     "        S1113 = scale*calc_elstic(strain[\"11\"], strain[\"13\"])\n",
152 |     "        S1112 = scale*calc_elstic(strain[\"11\"], strain[\"12\"])\n",
153 |     "        \n",
154 |     "        # Convert Sijkl to  Spq \n",
155 |     "        # NOTED that the Spq = Sijkl when p q = 1, 2, 3 BUT Spq = 4*Sijkl when p q = 4, 5, 6.\n",
156 |     "        S11 = (S1111+S2222+S3333)/3\n",
157 |     "        S12 = (S1122+S1133+S2233)/3\n",
158 |     "        S44 = 4*(S2323+S1313+S1212)/3\n",
159 |     "        Spq = np.array([[S11, S12, S12,   0,   0,   0], \n",
160 |     "                        [S12, S11, S12,   0,   0,   0],\n",
161 |     "                        [S12, S12, S11,   0,   0,   0],\n",
162 |     "                        [0,     0,   0, S44,   0,   0],\n",
163 |     "                        [0,     0,   0,   0, S44,   0],\n",
164 |     "                        [0,     0,   0,   0,   0, S44]])\n",
165 |     "        \n",
166 |     "        # Convert Spq to Cpq and \n",
167 |     "        Cpq = np.linalg.inv(Spq)\n",
168 |     "        C11 = Cpq[1,1]\n",
169 |     "        C12 = Cpq[1,2]\n",
170 |     "        C44 = Cpq[4,4]\n",
171 |     "        # print(np.array([C11, C12, C44]))\n",
172 |     "        Cij[i] = np.array([C11, C12, C44])\n",
173 |     "    return Cij\n",
174 |     "\n",
175 |     "def calc_ste(array): # calculate the standard error\n",
176 |     "    ste = np.zeros(3)\n",
177 |     "    for i in range(array.shape[1]):\n",
178 |     "        ste[i] = sqrt(sum(abs(array[:,i] - array[:,i].mean())**2))/len(array[:,i])\n",
179 |     "    return ste\n",
180 |     "        \n",
181 |     "\n",
182 |     "Cij_Si_gpumd_1ns = output_elastic_gpumd(\"./\", 10)\n",
183 |     "print(\"[C11, C12, C44] (unit in GPa) of Si estimated by gpumd with npt_scr for 1ns:\")\n",
184 |     "print(np.average(Cij_Si_gpumd_1ns, axis=0))\n",
185 |     "print(\"With standard error (unit in GPa) of: \")\n",
186 |     "print(calc_ste(Cij_Si_gpumd_1ns))"
187 |    ]
188 |   },
189 |   {
190 |    "cell_type": "markdown",
191 |    "metadata": {},
192 |    "source": [
193 |     "- Noted that we evenly divide the 1 ns simulation to ten independent simulations of 100 ps. Based on each independent simulation, we can obtain three elastic constants, and the final elastic constants is obtained averaging on ten simulations. We also compute the corresponding standard deviation.\n",
194 |     "\n",
195 |     "\n",
196 |     "- According to the [cohesive_energy tutorial](https://github.com/brucefan1983/GPUMD/tree/master/examples/empirical_potentials/cohesive_energy), one can also straightly calculate the elastic constants at 0 K based on stress-strain relationship by deforming the box with small strain. The elastic constants at 0 K are calculated as C11 = 148.686 Gpa, C12 = 65.5985 GPa ,C44 = 74.9417 GPa, which is in good agreement with our result obtained from strain fluctuation method at 300 K. \n",
197 |     "\n",
198 |     "\n",
199 |     "- Rather than the case at finite temperature, the strain fluctuation method can also been extended to the case under pressure loading. Combined with the Born stability criteria [[Born 1954]](https://en.wikipedia.org/wiki/Dynamical_Theory_of_Crystal_Lattices), strain fluctuation method is a powerful method to investigate the mechanical stability under pressure loading. \n"
200 |    ]
201 |   },
202 |   {
203 |    "cell_type": "markdown",
204 |    "metadata": {},
205 |    "source": [
206 |     "# 4. References\n",
207 |     "- [Parrinello 1982] M. Parrinello and A. Rahman. [Strain fluctuations and elastic constants](https://doi.org/10.1063/1.443248), J. Chem. Phys. **76**, 2662 (1982).\n",
208 |     "- [Bernetti 2020] Mattia Bernetti and  Giovanni Bussia, [Pressure control using stochastic cell rescaling](https://doi.org/10.1063/5.0020514), J. Chem. Phys. **153**, 114107 (2020).\n",
209 |     "- [Fan 2020] Zheyong Fan, Yanzhou Wang, Xiaokun Gu, Ping Qian, Yanjing Su, and Tapio Ala-Nissila, [A minimal Tersoff potential for diamond silicon with improved descriptions of elastic and phonon transport properties](https://doi.org/10.1088/1361-648X/ab5c5f), J. Phys.: Condens. Matter 32 135901 (2020).\n",
210 |     "- [Born 1954] M. Born, K. Huang, Dynamical Theory of Crystal Lattices, Clarendon Press, 1954.\n",
211 |     "\n"
212 |    ]
213 |   }
214 |  ],
215 |  "metadata": {
216 |   "kernelspec": {
217 |    "display_name": "Python 3",
218 |    "language": "python",
219 |    "name": "python3"
220 |   },
221 |   "language_info": {
222 |    "codemirror_mode": {
223 |     "name": "ipython",
224 |     "version": 3
225 |    },
226 |    "file_extension": ".py",
227 |    "mimetype": "text/x-python",
228 |    "name": "python",
229 |    "nbconvert_exporter": "python",
230 |    "pygments_lexer": "ipython3",
231 |    "version": "3.8.8"
232 |   }
233 |  },
234 |  "nbformat": 4,
235 |  "nbformat_minor": 2
236 | }
237 | 


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/2. Elastic Constants Based on Strain Fluctuation Method/create_xyz.m:
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https://raw.githubusercontent.com/hityingph/Tutorial-on-atomic-simulations/4e059f908c9361e86d2997ff784a19f7134acdf1/2. Elastic Constants Based on Strain Fluctuation Method/create_xyz.m


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/2. Elastic Constants Based on Strain Fluctuation Method/run.in:
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 1 | potential   potentials/tersoff/Si_Fan_2019.txt 0
 2 | velocity    300
 3 | 
 4 | ensemble    npt_scr 300 300 100 0 0 0 0 0 0 2000
 5 | time_step   1
 6 | dump_thermo 100         
 7 | run         1100000
 8 | 
 9 | 
10 | 


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/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/Eigenvector/basis.in:
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  1 | 50	
  2 | 0	12.011
  3 | 1	12.011
  4 | 2	12.011
  5 | 3	12.011
  6 | 4	12.011
  7 | 5	12.011
  8 | 6	12.011
  9 | 7	12.011
 10 | 8	12.011
 11 | 9	12.011
 12 | 10	12.011
 13 | 11	12.011
 14 | 12	12.011
 15 | 13	12.011
 16 | 14	12.011
 17 | 15	12.011
 18 | 16	12.011
 19 | 17	12.011
 20 | 18	12.011
 21 | 19	12.011
 22 | 20	12.011
 23 | 21	12.011
 24 | 22	12.011
 25 | 23	12.011
 26 | 24	12.011
 27 | 25	12.011
 28 | 26	12.011
 29 | 27	12.011
 30 | 28	12.011
 31 | 29	12.011
 32 | 30	12.011
 33 | 31	12.011
 34 | 32	12.011
 35 | 33	12.011
 36 | 34	12.011
 37 | 35	12.011
 38 | 36	12.011
 39 | 37	12.011
 40 | 38	12.011
 41 | 39	12.011
 42 | 40	12.011
 43 | 41	12.011
 44 | 42	12.011
 45 | 43	12.011
 46 | 44	12.011
 47 | 45	12.011
 48 | 46	12.011
 49 | 47	12.011
 50 | 48	12.011
 51 | 49	12.011
 52 | 0
 53 | 1
 54 | 2
 55 | 3
 56 | 4
 57 | 5
 58 | 6
 59 | 7
 60 | 8
 61 | 9
 62 | 10
 63 | 11
 64 | 12
 65 | 13
 66 | 14
 67 | 15
 68 | 16
 69 | 17
 70 | 18
 71 | 19
 72 | 20
 73 | 21
 74 | 22
 75 | 23
 76 | 24
 77 | 25
 78 | 26
 79 | 27
 80 | 28
 81 | 29
 82 | 30
 83 | 31
 84 | 32
 85 | 33
 86 | 34
 87 | 35
 88 | 36
 89 | 37
 90 | 38
 91 | 39
 92 | 40
 93 | 41
 94 | 42
 95 | 43
 96 | 44
 97 | 45
 98 | 46
 99 | 47
100 | 48
101 | 49


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/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/Eigenvector/kpoints.in:
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1 | 1
2 | 0 0 0


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/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/Eigenvector/run.in:
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1 | potential       potentials/tersoff/Graphene_Lindsay_2010_modified.txt 0
2 | compute_phonon  5 0.005 # in units of A
3 | 


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/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/Eigenvector/xyz.in:
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 1 | 50 3 2.1 1 0 0 
 2 | 1 1 0 12.302199601999998 0.0 0.0 -6.151099800999999 10.654017378 0.0 0.0 0.0 10.0 
 3 | 0 -6.177549530139714e-06 0.7102713712121174 5.0 12.011
 4 | 0 1.23022613774953 1.4205321043878827 5.0 12.011
 5 | 0 -1.23022613774953 2.841074846812117 5.0 12.011
 6 | 0 6.177549530139714e-06 3.5513355799878825 5.0 12.011
 7 | 0 -2.46044609794953 4.971878322412118 5.0 12.011
 8 | 0 -1.2302137826504698 5.682139055587883 5.0 12.011
 9 | 0 -3.69066605814953 7.102681798012117 5.0 12.011
10 | 0 -2.4604337428504697 7.812942531187883 5.0 12.011
11 | 0 -4.920886018349529 9.233485273612118 5.0 12.011
12 | 0 -3.6906537030504696 9.943746006787883 5.0 12.011
13 | 0 2.4604337428504697 0.7102713712121174 5.0 12.011
14 | 0 3.69066605814953 1.4205321043878827 5.0 12.011
15 | 0 1.2302137826504698 2.841074846812117 5.0 12.011
16 | 0 2.46044609794953 3.5513355799878825 5.0 12.011
17 | 0 -6.177549530139714e-06 4.971878322412118 5.0 12.011
18 | 0 1.23022613774953 5.682139055587883 5.0 12.011
19 | 0 -1.23022613774953 7.102681798012117 5.0 12.011
20 | 0 6.177549530139714e-06 7.812942531187883 5.0 12.011
21 | 0 -2.46044609794953 9.233485273612118 5.0 12.011
22 | 0 -1.2302137826504698 9.943746006787883 5.0 12.011
23 | 0 4.92087366325047 0.7102713712121174 5.0 12.011
24 | 0 6.15110597854953 1.4205321043878827 5.0 12.011
25 | 0 3.6906537030504696 2.841074846812117 5.0 12.011
26 | 0 4.920886018349529 3.5513355799878825 5.0 12.011
27 | 0 2.4604337428504697 4.971878322412118 5.0 12.011
28 | 0 3.69066605814953 5.682139055587883 5.0 12.011
29 | 0 1.2302137826504698 7.102681798012117 5.0 12.011
30 | 0 2.46044609794953 7.812942531187883 5.0 12.011
31 | 0 -6.177549530139714e-06 9.233485273612118 5.0 12.011
32 | 0 1.23022613774953 9.943746006787883 5.0 12.011
33 | 0 7.381313583650469 0.7102713712121174 5.0 12.011
34 | 0 8.61154589894953 1.4205321043878827 5.0 12.011
35 | 0 6.151093623450469 2.841074846812117 5.0 12.011
36 | 0 7.381325938749529 3.5513355799878825 5.0 12.011
37 | 0 4.92087366325047 4.971878322412118 5.0 12.011
38 | 0 6.15110597854953 5.682139055587883 5.0 12.011
39 | 0 3.6906537030504696 7.102681798012117 5.0 12.011
40 | 0 4.920886018349529 7.812942531187883 5.0 12.011
41 | 0 2.4604337428504697 9.233485273612118 5.0 12.011
42 | 0 3.69066605814953 9.943746006787883 5.0 12.011
43 | 0 9.84175350405047 0.7102713712121174 5.0 12.011
44 | 0 11.071985819349528 1.4205321043878827 5.0 12.011
45 | 0 8.61153354385047 2.841074846812117 5.0 12.011
46 | 0 9.841765859149529 3.5513355799878825 5.0 12.011
47 | 0 7.381313583650469 4.971878322412118 5.0 12.011
48 | 0 8.61154589894953 5.682139055587883 5.0 12.011
49 | 0 6.151093623450469 7.102681798012117 5.0 12.011
50 | 0 7.381325938749529 7.812942531187883 5.0 12.011
51 | 0 4.92087366325047 9.233485273612118 5.0 12.011
52 | 0 6.15110597854953 9.943746006787883 5.0 12.011


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/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/Phonon_39.73067THz_first_frame.data:
--------------------------------------------------------------------------------
 1 | Phonon_39.73067THz_first_frame.data (written by ASE) 
 2 | 
 3 | 50 	 atoms 
 4 | 1  atom types
 5 | 0.0      12.302199601999998  xlo xhi
 6 | 0.0      10.654017378000001  ylo yhi
 7 | 0.0                      10  zlo zhi
 8 |     -6.1510998009999991                       0                       0  xy xz yz
 9 | 
10 | 
11 | Atoms 
12 | 
13 |      1   1 -6.1775495301397143e-06     0.71027137121211736                       5
14 |      2   1        1.23022613774953      1.4205321043878827                       5
15 |      3   1       -1.23022613774953      2.8410748468121172                       5
16 |      4   1  6.1775495301397143e-06      3.5513355799878825                       5
17 |      5   1       -2.46044609794953      4.9718783224121177                       5
18 |      6   1     -1.2302137826504698       5.682139055587883                       5
19 |      7   1     -3.6906660581495299      7.1026817980121173                       5
20 |      8   1     -2.4604337428504697      7.8129425311878826                       5
21 |      9   1     -4.9208860183495293      9.2334852736121178                       5
22 |     10   1     -3.6906537030504696      9.9437460067878831                       5
23 |     11   1      2.4604337428504697     0.71027137121211736                       5
24 |     12   1      3.6906660581495299      1.4205321043878827                       5
25 |     13   1      1.2302137826504698      2.8410748468121172                       5
26 |     14   1        2.46044609794953      3.5513355799878825                       5
27 |     15   1 -6.1775495301397143e-06      4.9718783224121177                       5
28 |     16   1        1.23022613774953       5.682139055587883                       5
29 |     17   1       -1.23022613774953      7.1026817980121173                       5
30 |     18   1  6.1775495301397143e-06      7.8129425311878826                       5
31 |     19   1       -2.46044609794953      9.2334852736121178                       5
32 |     20   1     -1.2302137826504698      9.9437460067878831                       5
33 |     21   1      4.9208736632504699     0.71027137121211736                       5
34 |     22   1      6.1511059785495297      1.4205321043878827                       5
35 |     23   1      3.6906537030504696      2.8410748468121172                       5
36 |     24   1      4.9208860183495293      3.5513355799878825                       5
37 |     25   1      2.4604337428504697      4.9718783224121177                       5
38 |     26   1      3.6906660581495299       5.682139055587883                       5
39 |     27   1      1.2302137826504698      7.1026817980121173                       5
40 |     28   1        2.46044609794953      7.8129425311878826                       5
41 |     29   1 -6.1775495301397143e-06      9.2334852736121178                       5
42 |     30   1        1.23022613774953      9.9437460067878831                       5
43 |     31   1      7.3813135836504689     0.71027137121211736                       5
44 |     32   1      8.6115458989495295      1.4205321043878827                       5
45 |     33   1      6.1510936234504694      2.8410748468121172                       5
46 |     34   1      7.3813259387495291      3.5513355799878825                       5
47 |     35   1      4.9208736632504699      4.9718783224121177                       5
48 |     36   1      6.1511059785495297       5.682139055587883                       5
49 |     37   1      3.6906537030504696      7.1026817980121173                       5
50 |     38   1      4.9208860183495293      7.8129425311878826                       5
51 |     39   1      2.4604337428504697      9.2334852736121178                       5
52 |     40   1      3.6906660581495299      9.9437460067878831                       5
53 |     41   1      9.8417535040504696     0.71027137121211736                       5
54 |     42   1      11.071985819349528      1.4205321043878827                       5
55 |     43   1      8.6115335438504701      2.8410748468121172                       5
56 |     44   1      9.8417658591495289      3.5513355799878825                       5
57 |     45   1      7.3813135836504689      4.9718783224121177                       5
58 |     46   1      8.6115458989495295       5.682139055587883                       5
59 |     47   1      6.1510936234504694      7.1026817980121173                       5
60 |     48   1      7.3813259387495291      7.8129425311878826                       5
61 |     49   1      4.9208736632504699      9.2334852736121178                       5
62 |     50   1      6.1511059785495297      9.9437460067878831                       5
63 | 


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/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/Phonon_39.73067THz_second_frame.data:
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 1 | Phonon_39.73067THz_second_frame.data (written by ASE) 
 2 | 
 3 | 50 	 atoms 
 4 | 1  atom types
 5 | 0.0      12.302199601999998  xlo xhi
 6 | 0.0      10.654017378000001  ylo yhi
 7 | 0.0                      10  zlo zhi
 8 |     -6.1510998009999991                       0                       0  xy xz yz
 9 | 
10 | 
11 | Atoms 
12 | 
13 |      1   1    -0.16715717754953013     0.79807897121211735                       5
14 |      2   1        1.32916973774953      1.3548065043878827                       5
15 |      3   1       -1.12060113774953       2.793779646812117                       5
16 |      4   1   0.0035447575495301397      3.5604321299878827                       5
17 |      5   1     -2.4699877379495301      4.9609895224121177                       5
18 |      6   1     -1.3341997826504697       5.733541855587883                       5
19 |      7   1     -3.7846288581495298      7.1676666980121171                       5
20 |      8   1     -2.2955467428504699      7.7208327311878824                       5
21 |      9   1     -4.7598560183495291       9.138876373612117                       5
22 |     10   1     -3.8540367030504696      10.041082306787883                       5
23 |     11   1      2.5697427428504698     0.65793397121211739                       5
24 |     12   1        3.69369607814953      1.4324936043878826                       5
25 |     13   1      1.2202264126504698      2.8349591868121173                       5
26 |     14   1      2.3562380979495301      3.5976306799878826                       5
27 |     15   1   -0.093701677549530141      5.0337617224121178                       5
28 |     16   1        1.39523213774953      5.5949724555878833                       5
29 |     17   1       -1.06919713774953      7.0083804980121176                       5
30 |     18   1    -0.16330082245046987      7.9073436311878824                       5
31 |     19   1     -2.6271000979495298      9.3243565736121177                       5
32 |     20   1     -1.1307353826504698       9.878254906787884                       5
33 |     21   1      4.9105374632504697     0.70428751121211741                       5
34 |     22   1      6.0466469785495294      1.4636810043878827                       5
35 |     23   1      3.5975784030504694      2.9061270468121174                       5
36 |     24   1      5.0865810183495297      3.4644571799878827                       5
37 |     25   1      2.6215687428504695      4.8727774224121179                       5
38 |     26   1        3.52727205814953      5.7796488555878831                       5
39 |     27   1      1.0632517826504697      7.1983722980121172                       5
40 |     28   1      2.5598106979495299      7.7424424311878823                       5
41 |     29   1     0.10923282245046986      9.1778272736121185                       5
42 |     30   1      1.2330188877495301      9.9604656067878832                       5
43 |     31   1      7.2883537836504688     0.78038747121211738                       5
44 |     32   1      8.7775498989495286      1.3288905043878827                       5
45 |     33   1      6.3122966234504698      2.7386968468121173                       5
46 |     34   1      7.2178019387495294      3.6537005799878823                       5
47 |     35   1      4.7532256632504701       5.067484722412118                       5
48 |     36   1      6.2498630785495299      5.6083092555878826                       5
49 |     37   1      3.8001657030504696      7.0500153980121176                       5
50 |     38   1      4.9240414883495296      7.8297391311878828                       5
51 |     39   1      2.4503269428504697      9.2228070736121186                       5
52 |     40   1      3.5862730581495299      9.9900565067878837                       5
53 |     41   1      10.002891504050469     0.61066927121211734                       5
54 |     42   1      10.908467819349529      1.5227911043878828                       5
55 |     43   1      8.4437685438504708      2.9318082468121172                       5
56 |     44   1      9.9402617591495286      3.4804530799878823                       5
57 |     45   1      7.4910655836504692      4.9243832224121178                       5
58 |     46   1      8.6151636089495298      5.6942277555878826                       5
59 |     47   1      6.1414765634504693      7.0889692980121177                       5
60 |     48   1      7.2772249387495291      7.8643514311878828                       5
61 |     49   1      4.8273674632504697      9.3035617736121186                       5
62 |     50   1        6.31660997854953       9.848871306787883                       5
63 | 


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/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/basis.in:
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 1 | 2
 2 | 0 12.011
 3 | 1 12.011
 4 | 0
 5 | 1
 6 | 0
 7 | 1
 8 | 0
 9 | 1
10 | 0
11 | 1
12 | 0
13 | 1
14 | 0
15 | 1
16 | 0
17 | 1
18 | 0
19 | 1
20 | 0
21 | 1
22 | 0
23 | 1
24 | 0
25 | 1
26 | 0
27 | 1
28 | 0
29 | 1
30 | 0
31 | 1
32 | 0
33 | 1
34 | 0
35 | 1
36 | 0
37 | 1
38 | 0
39 | 1
40 | 0
41 | 1
42 | 0
43 | 1
44 | 0
45 | 1
46 | 0
47 | 1
48 | 0
49 | 1
50 | 0
51 | 1
52 | 0
53 | 1
54 | 


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/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/eigenvector - binary.out:
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https://raw.githubusercontent.com/hityingph/Tutorial-on-atomic-simulations/4e059f908c9361e86d2997ff784a19f7134acdf1/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/eigenvector - binary.out


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/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/gr_uc.vasp:
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 1 | Graphene
 2 | 1.0
 3 |         2.4604399204         0.0000000000         0.0000000000
 4 |        -1.2302199602         2.1308034756         0.0000000000
 5 |         0.0000000000         0.0000000000        10.0000000000
 6 |     C
 7 |     2
 8 | Direct
 9 |      0.000000000         0.000000000         0.000000000
10 |      0.666670024         0.333330005         0.000000000


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/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/graphene_construct.py:
--------------------------------------------------------------------------------
 1 | # -*- coding: utf-8 -*-
 2 | """
 3 | Created on Thu Jul  8 12:15:44 2021
 4 | 
 5 | @author: benwa
 6 | """
 7 | import numpy as np
 8 | import random as rd
 9 | 
10 | lx = 12
11 | ly = 12
12 | lz = 3.35
13 | bond_length = 1.42
14 | defect_dens = 0 #For pristine graphene without defect, one should set this as zero.
15 | 
16 | uc_lx = np.sqrt(3) * bond_length
17 | uc_ly = 3 * bond_length
18 | uc_lz = 20
19 | rp_x = int(lx/uc_lx) + 1
20 | rp_y = int(ly/uc_ly) + 1
21 | 
22 | atom_num = int(4*rp_x*rp_y)
23 | defect_num = int(atom_num*defect_dens)
24 | defect_id = []
25 | for i in range(defect_num):
26 |     defect_id.append(rd.randint(1, atom_num))
27 |     
28 | atom1 = [0.25, 1/6, 0.5]
29 | atom2 = [0.75, 1/3, 0.5]
30 | atom3 = [0.75, 2/3, 0.5]
31 | atom4 = [0.25, 5/6, 0.5]
32 | atoms = [atom1, atom2, atom3, atom4]
33 | 
34 | atom_id = 0
35 | new_atom_id = 0
36 | atom_type = 0
37 | atom_mass = 12.011
38 | 
39 | coord_type = []
40 | coord_x = []
41 | coord_y = []
42 | coord_z = []
43 | coord_mass = []
44 | coord_id = []
45 | for i in range(rp_x):
46 |     for j in range(rp_y):
47 |         for k in range(4):
48 |             atom_id += 1
49 |             position_x = atoms[k][0]*uc_lx + i*uc_lx
50 |             position_y = atoms[k][1]*uc_ly + j*uc_ly
51 |             position_z = atoms[k][2]*uc_lz
52 |             if atom_id not in defect_id:
53 |                 coord_type.append(atom_type)
54 |                 coord_x.append(position_x)
55 |                 coord_y.append(position_y)
56 |                 coord_z.append(position_z)
57 |                 coord_mass.append(atom_mass)
58 |                 coord_id.append(new_atom_id)
59 |                 new_atom_id +=1
60 |                 # print(atom_id, atom_type, position_x, position_y, position_z)
61 | 
62 | ### line 0
63 | N = new_atom_id     #number of atoms
64 | M = 3               #maximum number of neighbors
65 | cutoff = 2.1        #initial cutoff distance used for building the neighbor list
66 | box_shape = 0       #0:orthogonal; 1:triclinic
67 | has_velocity = 0    #0:has initial velocity; 1:not has initial velocity 
68 | number_of_grouping_methods = 1 #we use one grouping method here
69 | 
70 | ### line 1
71 | pbc_x = 1 #1:periodic; 0:free
72 | pbc_y = 1 #1:periodic; 0:free
73 | pbc_z = 0 #1:periodic; 0:free
74 | L_x = uc_lx*rp_x
75 | L_y = uc_ly*rp_y
76 | L_z = lz
77 | 
78 | 
79 | f = open("xyz.in", "w")
80 | line0 = ' '.join(str(val) for val in [N, M, cutoff, box_shape, has_velocity, number_of_grouping_methods]) 
81 | f.write(line0)
82 | f.write("\n")
83 | line1 = ' '.join(str(val) for val in [pbc_x, pbc_y, pbc_z, L_x, L_y, L_z]) 
84 | f.write(line1)
85 | f.write("\n")
86 | # line m+2                 
87 | for i in range(new_atom_id):
88 |     line_coord = ' '.join(str(val) for val in [coord_type[i], coord_x[i], coord_y[i], coord_z[i], coord_mass[i], coord_id[i]])
89 |     f.write(line_coord)                                           
90 |     f.write(str("\n"))
91 | f.close()
92 | 
93 |         
94 | 
95 | 


--------------------------------------------------------------------------------
/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/kpoints.in:
--------------------------------------------------------------------------------
  1 | 400
  2 | 0 0 0
  3 | 0.00880581 0.00508403 0
  4 | 0.0176116 0.0101681 0
  5 | 0.0264174 0.0152521 0
  6 | 0.0352232 0.0203361 0
  7 | 0.044029 0.0254202 0
  8 | 0.0528348 0.0305042 0
  9 | 0.0616406 0.0355882 0
 10 | 0.0704464 0.0406723 0
 11 | 0.0792523 0.0457563 0
 12 | 0.0880581 0.0508403 0
 13 | 0.0968639 0.0559244 0
 14 | 0.10567 0.0610084 0
 15 | 0.114475 0.0660924 0
 16 | 0.123281 0.0711765 0
 17 | 0.132087 0.0762605 0
 18 | 0.140893 0.0813445 0
 19 | 0.149699 0.0864286 0
 20 | 0.158505 0.0915126 0
 21 | 0.16731 0.0965967 0
 22 | 0.176116 0.101681 0
 23 | 0.184922 0.106765 0
 24 | 0.193728 0.111849 0
 25 | 0.202534 0.116933 0
 26 | 0.211339 0.122017 0
 27 | 0.220145 0.127101 0
 28 | 0.228951 0.132185 0
 29 | 0.237757 0.137269 0
 30 | 0.246563 0.142353 0
 31 | 0.255368 0.147437 0
 32 | 0.264174 0.152521 0
 33 | 0.27298 0.157605 0
 34 | 0.281786 0.162689 0
 35 | 0.290592 0.167773 0
 36 | 0.299397 0.172857 0
 37 | 0.308203 0.177941 0
 38 | 0.317009 0.183025 0
 39 | 0.325815 0.188109 0
 40 | 0.334621 0.193193 0
 41 | 0.343426 0.198277 0
 42 | 0.352232 0.203361 0
 43 | 0.361038 0.208445 0
 44 | 0.369844 0.213529 0
 45 | 0.37865 0.218613 0
 46 | 0.387455 0.223698 0
 47 | 0.396261 0.228782 0
 48 | 0.405067 0.233866 0
 49 | 0.413873 0.23895 0
 50 | 0.422679 0.244034 0
 51 | 0.431484 0.249118 0
 52 | 0.44029 0.254202 0
 53 | 0.449096 0.259286 0
 54 | 0.457902 0.26437 0
 55 | 0.466708 0.269454 0
 56 | 0.475514 0.274538 0
 57 | 0.484319 0.279622 0
 58 | 0.493125 0.284706 0
 59 | 0.501931 0.28979 0
 60 | 0.510737 0.294874 0
 61 | 0.519543 0.299958 0
 62 | 0.528348 0.305042 0
 63 | 0.537154 0.310126 0
 64 | 0.54596 0.31521 0
 65 | 0.554766 0.320294 0
 66 | 0.563572 0.325378 0
 67 | 0.572377 0.330462 0
 68 | 0.581183 0.335546 0
 69 | 0.589989 0.34063 0
 70 | 0.598795 0.345714 0
 71 | 0.607601 0.350798 0
 72 | 0.616406 0.355882 0
 73 | 0.625212 0.360966 0
 74 | 0.634018 0.36605 0
 75 | 0.642824 0.371135 0
 76 | 0.65163 0.376219 0
 77 | 0.660435 0.381303 0
 78 | 0.669241 0.386387 0
 79 | 0.678047 0.391471 0
 80 | 0.686853 0.396555 0
 81 | 0.695659 0.401639 0
 82 | 0.704464 0.406723 0
 83 | 0.71327 0.411807 0
 84 | 0.722076 0.416891 0
 85 | 0.730882 0.421975 0
 86 | 0.739688 0.427059 0
 87 | 0.748493 0.432143 0
 88 | 0.757299 0.437227 0
 89 | 0.766105 0.442311 0
 90 | 0.774911 0.447395 0
 91 | 0.783717 0.452479 0
 92 | 0.792523 0.457563 0
 93 | 0.801328 0.462647 0
 94 | 0.810134 0.467731 0
 95 | 0.81894 0.472815 0
 96 | 0.827746 0.477899 0
 97 | 0.836552 0.482983 0
 98 | 0.845357 0.488067 0
 99 | 0.854163 0.493151 0
100 | 0.862969 0.498235 0
101 | 0.871775 0.503319 0
102 | 0.880581 0.508403 0
103 | 0.889386 0.513487 0
104 | 0.898192 0.518572 0
105 | 0.906998 0.523656 0
106 | 0.915804 0.52874 0
107 | 0.92461 0.533824 0
108 | 0.933415 0.538908 0
109 | 0.942221 0.543992 0
110 | 0.951027 0.549076 0
111 | 0.959833 0.55416 0
112 | 0.968639 0.559244 0
113 | 0.977444 0.564328 0
114 | 0.98625 0.569412 0
115 | 0.995056 0.574496 0
116 | 1.00386 0.57958 0
117 | 1.01267 0.584664 0
118 | 1.02147 0.589748 0
119 | 1.03028 0.594832 0
120 | 1.03909 0.599916 0
121 | 1.04789 0.605 0
122 | 1.0567 0.610084 0
123 | 1.0655 0.615168 0
124 | 1.07431 0.620252 0
125 | 1.08311 0.625336 0
126 | 1.09192 0.63042 0
127 | 1.10073 0.635504 0
128 | 1.10953 0.640588 0
129 | 1.11834 0.645672 0
130 | 1.12714 0.650756 0
131 | 1.13595 0.65584 0
132 | 1.14475 0.660924 0
133 | 1.15356 0.666009 0
134 | 1.16237 0.671093 0
135 | 1.17117 0.676177 0
136 | 1.17998 0.681261 0
137 | 1.18878 0.686345 0
138 | 1.19759 0.691429 0
139 | 1.2064 0.696513 0
140 | 1.2152 0.701597 0
141 | 1.22401 0.706681 0
142 | 1.23281 0.711765 0
143 | 1.24162 0.716849 0
144 | 1.25042 0.721933 0
145 | 1.25923 0.727017 0
146 | 1.26804 0.732101 0
147 | 1.27684 0.737185 0
148 | 1.27178 0.745961 0
149 | 1.26671 0.754737 0
150 | 1.26164 0.763513 0
151 | 1.25657 0.772289 0
152 | 1.25151 0.781065 0
153 | 1.24644 0.789841 0
154 | 1.24137 0.798617 0
155 | 1.23631 0.807393 0
156 | 1.23124 0.816169 0
157 | 1.22617 0.824945 0
158 | 1.22111 0.833721 0
159 | 1.21604 0.842497 0
160 | 1.21097 0.851273 0
161 | 1.20591 0.860049 0
162 | 1.20084 0.868825 0
163 | 1.19577 0.877601 0
164 | 1.19071 0.886377 0
165 | 1.18564 0.895153 0
166 | 1.18057 0.903929 0
167 | 1.17551 0.912705 0
168 | 1.17044 0.921481 0
169 | 1.16537 0.930257 0
170 | 1.1603 0.939033 0
171 | 1.15524 0.947809 0
172 | 1.15017 0.956585 0
173 | 1.1451 0.965361 0
174 | 1.14004 0.974137 0
175 | 1.13497 0.982913 0
176 | 1.1299 0.991689 0
177 | 1.12484 1.00047 0
178 | 1.11977 1.00924 0
179 | 1.1147 1.01802 0
180 | 1.10964 1.02679 0
181 | 1.10457 1.03557 0
182 | 1.0995 1.04435 0
183 | 1.09444 1.05312 0
184 | 1.08937 1.0619 0
185 | 1.0843 1.07067 0
186 | 1.07924 1.07945 0
187 | 1.07417 1.08823 0
188 | 1.0691 1.097 0
189 | 1.06403 1.10578 0
190 | 1.05897 1.11455 0
191 | 1.0539 1.12333 0
192 | 1.04883 1.13211 0
193 | 1.04377 1.14088 0
194 | 1.0387 1.14966 0
195 | 1.03363 1.15843 0
196 | 1.02857 1.16721 0
197 | 1.0235 1.17599 0
198 | 1.01843 1.18476 0
199 | 1.01337 1.19354 0
200 | 1.0083 1.20231 0
201 | 1.00323 1.21109 0
202 | 0.998166 1.21987 0
203 | 0.993099 1.22864 0
204 | 0.988032 1.23742 0
205 | 0.982966 1.24619 0
206 | 0.977899 1.25497 0
207 | 0.972832 1.26375 0
208 | 0.967765 1.27252 0
209 | 0.962698 1.2813 0
210 | 0.957631 1.29007 0
211 | 0.952565 1.29885 0
212 | 0.947498 1.30763 0
213 | 0.942431 1.3164 0
214 | 0.937364 1.32518 0
215 | 0.932297 1.33395 0
216 | 0.92723 1.34273 0
217 | 0.922164 1.35151 0
218 | 0.917097 1.36028 0
219 | 0.91203 1.36906 0
220 | 0.906963 1.37783 0
221 | 0.901896 1.38661 0
222 | 0.896829 1.39539 0
223 | 0.891763 1.40416 0
224 | 0.886696 1.41294 0
225 | 0.881629 1.42171 0
226 | 0.876562 1.43049 0
227 | 0.871495 1.43927 0
228 | 0.866428 1.44804 0
229 | 0.861362 1.45682 0
230 | 0.856295 1.46559 0
231 | 0.851228 1.47437 0
232 | 0.846221 1.4657 0
233 | 0.841213 1.45702 0
234 | 0.836206 1.44835 0
235 | 0.831199 1.43968 0
236 | 0.826192 1.43101 0
237 | 0.821185 1.42233 0
238 | 0.816177 1.41366 0
239 | 0.81117 1.40499 0
240 | 0.806163 1.39632 0
241 | 0.801156 1.38764 0
242 | 0.796148 1.37897 0
243 | 0.791141 1.3703 0
244 | 0.786134 1.36162 0
245 | 0.781127 1.35295 0
246 | 0.77612 1.34428 0
247 | 0.771112 1.33561 0
248 | 0.766105 1.32693 0
249 | 0.761098 1.31826 0
250 | 0.756091 1.30959 0
251 | 0.751083 1.30091 0
252 | 0.746076 1.29224 0
253 | 0.741069 1.28357 0
254 | 0.736062 1.2749 0
255 | 0.731055 1.26622 0
256 | 0.726047 1.25755 0
257 | 0.72104 1.24888 0
258 | 0.716033 1.24021 0
259 | 0.711026 1.23153 0
260 | 0.706018 1.22286 0
261 | 0.701011 1.21419 0
262 | 0.696004 1.20551 0
263 | 0.690997 1.19684 0
264 | 0.68599 1.18817 0
265 | 0.680982 1.1795 0
266 | 0.675975 1.17082 0
267 | 0.670968 1.16215 0
268 | 0.665961 1.15348 0
269 | 0.660953 1.1448 0
270 | 0.655946 1.13613 0
271 | 0.650939 1.12746 0
272 | 0.645932 1.11879 0
273 | 0.640925 1.11011 0
274 | 0.635917 1.10144 0
275 | 0.63091 1.09277 0
276 | 0.625903 1.0841 0
277 | 0.620896 1.07542 0
278 | 0.615888 1.06675 0
279 | 0.610881 1.05808 0
280 | 0.605874 1.0494 0
281 | 0.600867 1.04073 0
282 | 0.59586 1.03206 0
283 | 0.590852 1.02339 0
284 | 0.585845 1.01471 0
285 | 0.580838 1.00604 0
286 | 0.575831 0.997368 0
287 | 0.570823 0.988695 0
288 | 0.565816 0.980022 0
289 | 0.560809 0.97135 0
290 | 0.555802 0.962677 0
291 | 0.550795 0.954004 0
292 | 0.545787 0.945331 0
293 | 0.54078 0.936659 0
294 | 0.535773 0.927986 0
295 | 0.530766 0.919313 0
296 | 0.525758 0.91064 0
297 | 0.520751 0.901968 0
298 | 0.515744 0.893295 0
299 | 0.510737 0.884622 0
300 | 0.50573 0.875949 0
301 | 0.500722 0.867276 0
302 | 0.495715 0.858604 0
303 | 0.490708 0.849931 0
304 | 0.485701 0.841258 0
305 | 0.480693 0.832585 0
306 | 0.475686 0.823913 0
307 | 0.470679 0.81524 0
308 | 0.465672 0.806567 0
309 | 0.460665 0.797894 0
310 | 0.455657 0.789222 0
311 | 0.45065 0.780549 0
312 | 0.445643 0.771876 0
313 | 0.440636 0.763203 0
314 | 0.435628 0.754531 0
315 | 0.430621 0.745858 0
316 | 0.425614 0.737185 0
317 | 0.420607 0.728512 0
318 | 0.4156 0.719839 0
319 | 0.410592 0.711167 0
320 | 0.405585 0.702494 0
321 | 0.400578 0.693821 0
322 | 0.395571 0.685148 0
323 | 0.390563 0.676476 0
324 | 0.385556 0.667803 0
325 | 0.380549 0.65913 0
326 | 0.375542 0.650457 0
327 | 0.370534 0.641785 0
328 | 0.365527 0.633112 0
329 | 0.36052 0.624439 0
330 | 0.355513 0.615766 0
331 | 0.350506 0.607094 0
332 | 0.345498 0.598421 0
333 | 0.340491 0.589748 0
334 | 0.335484 0.581075 0
335 | 0.330477 0.572402 0
336 | 0.325469 0.56373 0
337 | 0.320462 0.555057 0
338 | 0.315455 0.546384 0
339 | 0.310448 0.537711 0
340 | 0.305441 0.529039 0
341 | 0.300433 0.520366 0
342 | 0.295426 0.511693 0
343 | 0.290419 0.50302 0
344 | 0.285412 0.494348 0
345 | 0.280404 0.485675 0
346 | 0.275397 0.477002 0
347 | 0.27039 0.468329 0
348 | 0.265383 0.459657 0
349 | 0.260376 0.450984 0
350 | 0.255368 0.442311 0
351 | 0.250361 0.433638 0
352 | 0.245354 0.424965 0
353 | 0.240347 0.416293 0
354 | 0.235339 0.40762 0
355 | 0.230332 0.398947 0
356 | 0.225325 0.390274 0
357 | 0.220318 0.381602 0
358 | 0.215311 0.372929 0
359 | 0.210303 0.364256 0
360 | 0.205296 0.355583 0
361 | 0.200289 0.346911 0
362 | 0.195282 0.338238 0
363 | 0.190274 0.329565 0
364 | 0.185267 0.320892 0
365 | 0.18026 0.31222 0
366 | 0.175253 0.303547 0
367 | 0.170246 0.294874 0
368 | 0.165238 0.286201 0
369 | 0.160231 0.277528 0
370 | 0.155224 0.268856 0
371 | 0.150217 0.260183 0
372 | 0.145209 0.25151 0
373 | 0.140202 0.242837 0
374 | 0.135195 0.234165 0
375 | 0.130188 0.225492 0
376 | 0.125181 0.216819 0
377 | 0.120173 0.208146 0
378 | 0.115166 0.199474 0
379 | 0.110159 0.190801 0
380 | 0.105152 0.182128 0
381 | 0.100144 0.173455 0
382 | 0.0951372 0.164783 0
383 | 0.09013 0.15611 0
384 | 0.0851228 0.147437 0
385 | 0.0801156 0.138764 0
386 | 0.0751083 0.130091 0
387 | 0.0701011 0.121419 0
388 | 0.0650939 0.112746 0
389 | 0.0600867 0.104073 0
390 | 0.0550795 0.0954004 0
391 | 0.0500722 0.0867276 0
392 | 0.045065 0.0780549 0
393 | 0.0400578 0.0693821 0
394 | 0.0350506 0.0607094 0
395 | 0.0300433 0.0520366 0
396 | 0.0250361 0.0433638 0
397 | 0.0200289 0.0346911 0
398 | 0.0150217 0.0260183 0
399 | 0.0100144 0.0173455 0
400 | 0.00500722 0.00867276 0
401 | 0 0 0
402 | 


--------------------------------------------------------------------------------
/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/lammps.data:
--------------------------------------------------------------------------------
 1 | lammps.data (written by ASE) 
 2 | 
 3 | 50 	 atoms 
 4 | 1  atom types
 5 | 0.0      12.302199601999998  xlo xhi
 6 | 0.0      10.654017378000001  ylo yhi
 7 | 0.0                      10  zlo zhi
 8 |     -6.1510998009999991                       0                       0  xy xz yz
 9 | 
10 | 
11 | Atoms 
12 | 
13 |      1   1 -6.1775495301397143e-06     0.71027137121211736                       5
14 |      2   1        1.23022613774953      1.4205321043878827                       5
15 |      3   1       -1.23022613774953      2.8410748468121172                       5
16 |      4   1  6.1775495301397143e-06      3.5513355799878825                       5
17 |      5   1       -2.46044609794953      4.9718783224121177                       5
18 |      6   1     -1.2302137826504698       5.682139055587883                       5
19 |      7   1     -3.6906660581495299      7.1026817980121173                       5
20 |      8   1     -2.4604337428504697      7.8129425311878826                       5
21 |      9   1     -4.9208860183495293      9.2334852736121178                       5
22 |     10   1     -3.6906537030504696      9.9437460067878831                       5
23 |     11   1      2.4604337428504697     0.71027137121211736                       5
24 |     12   1      3.6906660581495299      1.4205321043878827                       5
25 |     13   1      1.2302137826504698      2.8410748468121172                       5
26 |     14   1        2.46044609794953      3.5513355799878825                       5
27 |     15   1 -6.1775495301397143e-06      4.9718783224121177                       5
28 |     16   1        1.23022613774953       5.682139055587883                       5
29 |     17   1       -1.23022613774953      7.1026817980121173                       5
30 |     18   1  6.1775495301397143e-06      7.8129425311878826                       5
31 |     19   1       -2.46044609794953      9.2334852736121178                       5
32 |     20   1     -1.2302137826504698      9.9437460067878831                       5
33 |     21   1      4.9208736632504699     0.71027137121211736                       5
34 |     22   1      6.1511059785495297      1.4205321043878827                       5
35 |     23   1      3.6906537030504696      2.8410748468121172                       5
36 |     24   1      4.9208860183495293      3.5513355799878825                       5
37 |     25   1      2.4604337428504697      4.9718783224121177                       5
38 |     26   1      3.6906660581495299       5.682139055587883                       5
39 |     27   1      1.2302137826504698      7.1026817980121173                       5
40 |     28   1        2.46044609794953      7.8129425311878826                       5
41 |     29   1 -6.1775495301397143e-06      9.2334852736121178                       5
42 |     30   1        1.23022613774953      9.9437460067878831                       5
43 |     31   1      7.3813135836504689     0.71027137121211736                       5
44 |     32   1      8.6115458989495295      1.4205321043878827                       5
45 |     33   1      6.1510936234504694      2.8410748468121172                       5
46 |     34   1      7.3813259387495291      3.5513355799878825                       5
47 |     35   1      4.9208736632504699      4.9718783224121177                       5
48 |     36   1      6.1511059785495297       5.682139055587883                       5
49 |     37   1      3.6906537030504696      7.1026817980121173                       5
50 |     38   1      4.9208860183495293      7.8129425311878826                       5
51 |     39   1      2.4604337428504697      9.2334852736121178                       5
52 |     40   1      3.6906660581495299      9.9437460067878831                       5
53 |     41   1      9.8417535040504696     0.71027137121211736                       5
54 |     42   1      11.071985819349528      1.4205321043878827                       5
55 |     43   1      8.6115335438504701      2.8410748468121172                       5
56 |     44   1      9.8417658591495289      3.5513355799878825                       5
57 |     45   1      7.3813135836504689      4.9718783224121177                       5
58 |     46   1      8.6115458989495295       5.682139055587883                       5
59 |     47   1      6.1510936234504694      7.1026817980121173                       5
60 |     48   1      7.3813259387495291      7.8129425311878826                       5
61 |     49   1      4.9208736632504699      9.2334852736121178                       5
62 |     50   1      6.1511059785495297      9.9437460067878831                       5
63 | 


--------------------------------------------------------------------------------
/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/omega2.out:
--------------------------------------------------------------------------------
  1 | -9.04674e-05 -2.32518e-12 9.047e-05 61764.2 103730 103730 
  2 | 0.000888877 2.32194 4.96424 61761 103729 103729 
  3 | 0.00405913 9.28681 19.8559 61751.3 103725 103725 
  4 | 0.0110212 20.8924 44.6711 61735.2 103719 103720 
  5 | 0.0242912 37.1351 79.4035 61712.7 103711 103712 
  6 | 0.0473892 58.0099 124.045 61683.8 103701 103702 
  7 | 0.0848355 83.5098 178.583 61648.4 103688 103689 
  8 | 0.142149 113.627 243.004 61606.6 103673 103675 
  9 | 0.22584 148.352 317.292 61558.4 103655 103658 
 10 | 0.343409 187.673 401.43 61503.9 103636 103639 
 11 | 0.503335 231.578 495.393 61443 103614 103617 
 12 | 0.715077 280.053 599.16 61375.7 103589 103594 
 13 | 0.989065 333.084 712.706 61302.2 103563 103567 
 14 | 1.33664 390.647 835.989 61222.3 103534 103539 
 15 | 1.77021 452.734 968.999 61136.2 103502 103508 
 16 | 2.30301 519.32 1111.69 61043.8 103469 103475 
 17 | 2.94925 590.384 1264.03 60945.2 103433 103440 
 18 | 3.72406 665.903 1425.99 60840.4 103395 103402 
 19 | 4.64347 745.853 1597.5 60729.5 103354 103362 
 20 | 5.7243 830.201 1778.53 60612.5 103312 103319 
 21 | 6.98455 918.934 1969.06 60489.3 103267 103274 
 22 | 8.44279 1012.02 2169.01 60360.2 103220 103227 
 23 | 10.1185 1109.42 2378.34 60225 103170 103177 
 24 | 12.0321 1211.1 2597.01 60083.9 103119 103124 
 25 | 14.2046 1317.03 2824.92 59936.8 103065 103069 
 26 | 16.6582 1427.2 3062.08 59783.9 103009 103012 
 27 | 19.4156 1541.54 3308.38 59625.2 102950 102952 
 28 | 22.5003 1660.03 3563.79 59460.6 102889 102890 
 29 | 25.9364 1782.63 3828.22 59290.4 102823 102827 
 30 | 29.7488 1909.28 4101.6 59114.5 102755 102763 
 31 | 33.9636 2039.97 4383.9 58933 102685 102696 
 32 | 38.6069 2174.64 4675.02 58746 102611 102626 
 33 | 43.7057 2313.25 4974.89 58553.4 102535 102555 
 34 | 49.2877 2455.75 5283.45 58355.4 102456 102482 
 35 | 55.3805 2602.08 5600.58 58152 102375 102407 
 36 | 62.014 2752.21 5926.26 57943.4 102290 102329 
 37 | 69.217 2906.1 6260.39 57729.4 102203 102249 
 38 | 77.0195 3063.67 6602.88 57510.3 102113 102168 
 39 | 85.4519 3224.88 6953.64 57286.1 102019 102084 
 40 | 94.5442 3389.66 7312.56 57056.9 101923 101999 
 41 | 104.329 3557.98 7679.61 56822.7 101824 101911 
 42 | 114.838 3729.77 8054.68 56583.6 101722 101821 
 43 | 126.102 3904.98 8437.66 56339.6 101617 101730 
 44 | 138.155 4083.53 8828.47 56091 101508 101636 
 45 | 151.028 4265.36 9226.99 55837.6 101397 101541 
 46 | 164.756 4450.43 9633.16 55579.7 101282 101444 
 47 | 179.37 4638.66 10046.9 55317.3 101164 101344 
 48 | 194.906 4829.98 10468 55050.5 101043 101244 
 49 | 211.396 5024.32 10896.5 54779.3 100918 101141 
 50 | 228.872 5221.61 11332.1 54503.9 100791 101036 
 51 | 247.371 5421.8 11774.9 54224.4 100659 100930 
 52 | 266.927 5624.81 12224.7 53940.7 100525 100822 
 53 | 287.572 5830.56 12681.5 53653.1 100387 100712 
 54 | 309.34 6038.97 13145 53361.6 100245 100601 
 55 | 332.266 6249.98 13615.2 53066.3 100100 100487 
 56 | 356.381 6463.48 14092 52767.3 99951.4 100373 
 57 | 381.722 6679.43 14575.2 52464.6 99799.1 100257 
 58 | 408.322 6897.74 15064.8 52158.5 99643.2 100139 
 59 | 436.212 7118.32 15560.6 51849 99483.6 100019 
 60 | 465.426 7341.09 16062.5 51536.1 99320.2 99898.6 
 61 | 495.993 7565.94 16570.4 51220 99153.1 99776.4 
 62 | 527.951 7792.83 17084.2 50900.8 98982.2 99652.8 
 63 | 561.328 8021.66 17603.7 50578.7 98807.4 99527.8 
 64 | 596.156 8252.32 18128.9 50253.6 98628.7 99401.5 
 65 | 632.465 8484.74 18659.6 49925.7 98446.1 99273.9 
 66 | 670.281 8718.8 19195.6 49595.1 98259.5 99145.1 
 67 | 709.64 8954.45 19736.9 49261.9 98068.8 99015.1 
 68 | 750.566 9191.57 20283.4 48926.3 97874.2 98883.9 
 69 | 793.089 9430.06 20834.8 48588.3 97675.4 98751.6 
 70 | 837.233 9669.84 21391.1 48248 97472.5 98618.3 
 71 | 883.021 9910.79 21952.2 47905.7 97265.4 98484 
 72 | 930.486 10152.8 22517.9 47561.3 97054.2 98348.7 
 73 | 979.646 10395.9 23088.1 47215 96838.6 98212.5 
 74 | 1030.53 10639.8 23662.7 46866.9 96618.8 98075.4 
 75 | 1083.14 10884.5 24241.5 46517.1 96394.7 97937.6 
 76 | 1137.52 11129.8 24824.4 46165.8 96166.2 97799 
 77 | 1193.67 11375.7 25411.3 45813.1 95933.3 97659.7 
 78 | 1251.62 11622.1 26002 45459 95696 97519.8 
 79 | 1311.37 11868.8 26596.5 45103.8 95454.3 97379.3 
 80 | 1372.95 12115.8 27194.5 44747.5 95208 97238.3 
 81 | 1436.36 12362.8 27795.9 44390.3 94957.2 97096.8 
 82 | 1501.62 12610 28400.7 44032.3 94701.9 96955 
 83 | 1568.73 12857 29008.7 43673.6 94442 96812.8 
 84 | 1637.69 13103.7 29619.7 43314.3 94177.4 96670.4 
 85 | 1708.52 13350.2 30233.7 42954.7 93908.2 96527.8 
 86 | 1781.2 13596.2 30850.4 42594.8 93634.4 96385 
 87 | 1855.75 13841.6 31469.7 42234.7 93355.8 96242.2 
 88 | 1932.16 14086.4 32091.6 41874.7 93072.4 96099.5 
 89 | 2010.41 14330.3 32715.9 41514.8 92784.4 95956.8 
 90 | 2090.51 14573.4 33342.4 41155.1 92491.5 95814.2 
 91 | 2172.43 14815.3 33971.1 40795.9 92193.8 95672 
 92 | 2256.16 15056.1 34601.7 40437.3 91891.3 95530 
 93 | 2341.69 15295.6 35234.2 40079.4 91583.9 95388.4 
 94 | 2428.98 15533.7 35868.4 39722.4 91271.7 95247.3 
 95 | 2518.02 15770.2 36504.2 39366.3 90954.6 95106.8 
 96 | 2608.77 16005 37141.5 39011.5 90632.5 94966.9 
 97 | 2701.18 16238.1 37780.1 38658 90305.5 94827.7 
 98 | 2795.25 16469.2 38306 38419.9 89973.6 94689.4 
 99 | 2890.91 16698.2 37955.7 39060.7 89636.7 94551.9 
100 | 2988.11 16925.1 37607.2 39702.6 89294.8 94415.4 
101 | 3086.81 17149.6 37260.7 40345.2 88948 94279.9 
102 | 3186.93 17371.7 36916.4 40988.5 88596.2 94145.6 
103 | 3288.44 17591.2 36574.5 41632.4 88239.3 94012.5 
104 | 3391.24 17808 36235 42276.7 87877.4 93880.8 
105 | 3495.27 18022 35898.3 42921.3 87510.5 93750.5 
106 | 3600.44 18233 35564.6 43566.1 87138.6 93621.7 
107 | 3706.66 18440.9 35233.9 44210.9 86761.6 93494.5 
108 | 3813.84 18645.5 34906.6 44855.6 86379.6 93369 
109 | 3921.88 18846.8 34582.8 45500.2 85992.6 93245.2 
110 | 4030.67 19044.7 34262.7 46144.5 85600.6 93123.4 
111 | 4140.09 19238.9 33946.6 46788.3 85203.5 93003.5 
112 | 4249.99 19429.3 33634.6 47431.6 84801.4 92885.7 
113 | 4360.28 19615.9 33327 48074.2 84394.3 92770 
114 | 4470.8 19798.5 33024.1 48716 83982.1 92656.6 
115 | 4581.37 19976.9 32726.1 49356.8 83565.1 92545.5 
116 | 4691.91 20151.2 32433.1 49996.8 83142.8 92436.8 
117 | 4802.1 20321 32145.7 50635.2 82715.9 92330.8 
118 | 4911.96 20486.5 31863.7 51272.9 82283.7 92227.2 
119 | 5021.2 20647.3 31587.6 51909.2 81846.6 92126.4 
120 | 5129.52 20803.3 31317.9 52543.4 81404.9 92028.4 
121 | 5236.91 20954.6 31054.5 53176.6 80958 91933.2 
122 | 5342.98 21100.8 30798.1 53807.6 80506.5 91841 
123 | 5447.66 21242.1 30548.4 54437.2 80049.9 91751.8 
124 | 5550.56 21378.1 30306.4 55064.4 79588.8 91665.9 
125 | 5651.61 21509 30071.8 55690 79122.6 91583 
126 | 5750.46 21634.5 29845.2 56313.5 78651.6 91503.4 
127 | 5846.79 21754.4 29627.1 56934.2 78176.3 91427.3 
128 | 5940.48 21868.9 29417.4 57553 77696 91354.5 
129 | 6031.12 21977.6 29216.8 58168.7 77211.4 91285.3 
130 | 6118.59 22080.7 29025.2 58782.4 76722 91219.6 
131 | 6202.47 22177.9 28843.5 59392.7 76228.5 91157.6 
132 | 6282.62 22269.3 28671.4 60000.8 75730.2 91099.2 
133 | 6358.7 22354.8 28509.6 60605.7 75227.6 91044.6 
134 | 6430.38 22434.1 28358.5 61206.9 74721.2 90993.9 
135 | 6497.52 22507.4 28218 61805.2 74210.4 90946.9 
136 | 6559.76 22574.4 28088.8 62399.4 73696.2 90904 
137 | 6616.94 22635.3 27970.8 62990.2 73177.9 90864.9 
138 | 6668.79 22690 27864.5 63576.7 72656.4 90829.9 
139 | 6715.05 22738.2 27770.2 64157.8 72132.7 90798.9 
140 | 6755.61 22780.2 27687.9 64733.8 71606.5 90771.9 
141 | 6790.21 22815.7 27618 65302.1 71080.3 90749.1 
142 | 6818.77 22844.9 27560.5 65861.2 70555.7 90730.4 
143 | 6841.09 22867.5 27515.7 66404.4 70039.4 90715.8 
144 | 6857.13 22883.8 27483.5 66918 69545 90705.3 
145 | 6866.78 22893.5 27464.2 67355 69119.6 90699.1 
146 | 6870 22896.7 27457.8 67558.8 68919.6 90697 
147 | 6871.07 22901.5 27455.7 67552.5 68917 90702.8 
148 | 6874.27 22915.8 27449.3 67533.6 68909 90720.3 
149 | 6879.61 22939.7 27438.6 67502.2 68895.7 90749.4 
150 | 6887.08 22973.1 27423.7 67458.4 68877.1 90789.9 
151 | 6896.69 23016 27404.5 67402.5 68853.3 90841.7 
152 | 6908.44 23068.5 27381.1 67334.5 68824.1 90904.5 
153 | 6922.35 23130.4 27353.4 67254.9 68789.6 90978.1 
154 | 6938.39 23201.8 27321.6 67163.9 68749.8 91062 
155 | 6956.6 23282.7 27285.5 67061.8 68704.7 91156.1 
156 | 6976.97 23373 27245.2 66949 68654.3 91259.9 
157 | 6999.49 23472.7 27200.7 66826 68598.6 91372.9 
158 | 7024.2 23581.8 27152.1 66693.1 68537.7 91494.8 
159 | 7051.09 23700.3 27099.3 66550.7 68471.5 91625.1 
160 | 7080.15 23828.1 27042.4 66399.5 68400 91763.3 
161 | 7111.43 23965.2 26981.4 66239.6 68323.2 91909 
162 | 7144.91 24111.5 26916.3 66071.7 68241.2 92061.7 
163 | 7180.59 24266.9 26847.1 65896.3 68154 92220.9 
164 | 7218.52 24431.6 26774 65713.6 68061.5 92386.1 
165 | 7258.69 24605.4 26696.8 65524.2 67963.8 92556.9 
166 | 7301.08 24788.2 26615.6 65328.7 67860.9 92732.6 
167 | 7345.76 24980.1 26530.5 65127.3 67752.8 92913.1 
168 | 7392.71 25180.9 26441.5 64920.5 67639.5 93097.7 
169 | 7441.95 25390.7 26348.6 64708.8 67521 93286 
170 | 7493.47 25609.1 26251.9 64492.6 67397.4 93477.5 
171 | 7547.32 25836.5 26151.4 64272.1 67268.5 93671.9 
172 | 7603.51 26047.1 26072.5 64047.8 67134.6 93868.8 
173 | 7662.01 25939.2 26317.1 63820.2 66995.5 94067.6 
174 | 7722.9 25827.5 26570.4 63589.5 66851.3 94268.2 
175 | 7786.17 25712.1 26832.2 63356 66702 94470.1 
176 | 7851.82 25593.2 27102.4 63120 66547.6 94673 
177 | 7919.85 25470.8 27380.8 62882.1 66388.3 94876.3 
178 | 7990.37 25344.8 27667.7 62642.1 66223.7 95080.1 
179 | 8063.23 25215.5 27962.4 62400.9 66054.3 95283.6 
180 | 8138.64 25082.6 28265.7 62158.1 65879.7 95487 
181 | 8216.54 24946.3 28577 61914.3 65700.2 95689.8 
182 | 8296.83 24807 28895.7 61669.9 65515.8 95891.4 
183 | 8379.74 24664.2 29222.8 61424.7 65326.3 96092 
184 | 8465.11 24518.3 29557.3 61179.3 65132.1 96291.1 
185 | 8553.06 24369.2 29899.6 60933.7 64932.8 96488.6 
186 | 8643.63 24217 30249.7 60687.9 64728.6 96684.3 
187 | 8736.71 24061.9 30606.9 60442.6 64519.7 96877.6 
188 | 8832.48 23903.6 30971.8 60197.5 64305.8 97068.8 
189 | 8930.75 23742.7 31343.4 59953.2 64087.4 97257.2 
190 | 9031.8 23578.7 31722.7 59709.2 63863.9 97443.1 
191 | 9135.51 23411.9 32109.1 59466.1 63635.6 97626.1 
192 | 9241.77 23242.5 32501.9 59224.3 63403 97805.7 
193 | 9350.89 23070.3 32902 58983.2 63165.3 97982.3 
194 | 9462.63 22895.7 33308.5 58743.5 62923.2 98155.3 
195 | 9577.16 22718.4 33721.8 58505.1 62676.3 98324.8 
196 | 9694.52 22538.5 34141.8 58267.9 62424.7 98490.6 
197 | 9814.55 22356.5 34567.8 58032.3 62168.8 98652.5 
198 | 9937.44 22171.9 35000.2 57798.3 61908.2 98810.4 
199 | 10063.1 21985.2 35438.6 57565.9 61643.3 98964.1 
200 | 10191.7 21796.1 35883.4 57335.1 61373.6 99113.8 
201 | 10323.1 21605 36333.9 57106 61099.6 99259.1 
202 | 10457.4 21411.8 36789.9 56879 60821.3 99399.8 
203 | 10594.6 21216.6 37252 56653.6 60538.5 99536.2 
204 | 10734.6 21019.5 37719.1 56430.2 60251.6 99667.8 
205 | 10877.7 20820.4 38192 56208.7 59960.2 99794.8 
206 | 11023.7 20619.5 38670.3 55989 59664.5 99917.1 
207 | 11172.6 20417.1 39153.2 55771.5 59364.9 100034 
208 | 11324.6 20212.9 39641.5 55555.8 59060.8 100147 
209 | 11479.5 20007.2 40134.3 55342.3 58752.9 100255 
210 | 11637.5 19799.9 40632.2 55130.6 58440.7 100357 
211 | 11798.5 19591.1 41134.7 54920.9 58124.4 100455 
212 | 11962.5 19381.1 41641.3 54713.3 57804.4 100547 
213 | 12129.6 19169.7 42152.6 54507.6 57480.2 100635 
214 | 12299.7 18957.2 42667.6 54303.9 57152.4 100717 
215 | 12473 18743.4 43187.1 54102 56820.5 100794 
216 | 12649.4 18528.5 43710.5 53902 56484.8 100866 
217 | 12828.8 18312.8 44237.3 53704 56145.6 100933 
218 | 13011.4 18096 44768.1 53507.6 55802.5 100995 
219 | 13197.1 17878.5 45301.9 53313.1 55456 101051 
220 | 13386 17660 45839.5 53120.2 55105.7 101103 
221 | 13578.1 17440.9 46380.2 52929 54751.8 101149 
222 | 13773.2 17221.3 46923.5 52739.4 54394.9 101190 
223 | 13971.6 17000.9 47470.2 52551.3 54034.2 101227 
224 | 14173 16780.2 48019 52364.7 53670.5 101258 
225 | 14377.8 16558.9 48570.9 52179.4 53303.4 101284 
226 | 14585.8 16337.3 49125 51995.3 52933.2 101306 
227 | 14796.7 16115.6 49680.5 51812.7 52560.6 101322 
228 | 15011.1 15893.4 50237.5 51630.9 52185.6 101334 
229 | 15228.5 15671.3 50792 51450.4 51812.1 101341 
230 | 15448.9 15449.3 51270.3 51273.8 51510.5 101343 
231 | 15229.7 15670.1 51015.2 51096.7 51942.5 101341 
232 | 15010 15894.6 50638.3 50920.4 52494.9 101334 
233 | 14790.6 16122 50253.8 50744.8 53053.4 101323 
234 | 14571.4 16352.5 49865.4 50569.7 53614.5 101308 
235 | 14352.4 16586.2 49473.8 50395 54177.3 101289 
236 | 14133.6 16823.1 49079 50220.3 54741.9 101266 
237 | 13915.4 17063 48681.9 50045.9 55307 101239 
238 | 13697.6 17306 48282.3 49871.5 55872.9 101208 
239 | 13480.4 17552 47880.2 49696.9 56439.6 101173 
240 | 13263.5 17801.4 47475.5 49521.9 57007.2 101135 
241 | 13047.4 18053.6 47068.8 49346.6 57574.7 101093 
242 | 12832.1 18308.9 46659.9 49170.8 58142.5 101048 
243 | 12617.3 18567.4 46248.6 48994.1 58710.8 101000 
244 | 12403.5 18828.8 45835.6 48816.8 59278.6 100948 
245 | 12190.6 19093.2 45420.5 48638.5 59846.2 100894 
246 | 11978.6 19360.6 45003.6 48459 60413.5 100837 
247 | 11767.5 19631.2 44584.5 48278.1 60980.8 100778 
248 | 11557.5 19904.5 44164 48095.9 61547.1 100715 
249 | 11348.6 20180.8 43741.8 47912.2 62112.6 100651 
250 | 11140.7 20460.3 43317.7 47726.5 62677.9 100585 
251 | 10934.2 20742.4 42892.3 47539.1 63241.6 100516 
252 | 10729 21027.4 42465.6 47349.6 63804.2 100446 
253 | 10525 21315.3 42037.4 47158 64365.7 100374 
254 | 10322.2 21606.3 41607.6 46963.8 64926.2 100301 
255 | 10121 21899.9 41176.9 46767.2 65484.8 100226 
256 | 9921.25 22196.2 40745 46568 66041.8 100150 
257 | 9722.97 22495.2 40312.1 46366 66597.1 100073 
258 | 9526.07 22797.3 39877.8 46160.7 67151.1 99995.3 
259 | 9330.9 23101.8 39443 45952.6 67702.6 99917.1 
260 | 9137.36 23408.9 39007.3 45741.1 68252.1 99838.3 
261 | 8945.33 23718.9 38570.5 45526 68799.9 99759.2 
262 | 8755.16 24031.3 38133.3 45307.5 69344.8 99680.1 
263 | 8566.74 24346.2 37695.6 45085.3 69887.4 99601.1 
264 | 8380.09 24663.6 37257.3 44859.2 70427.5 99522.3 
265 | 8195.1 24983.8 36818.2 44628.9 70965.5 99443.8 
266 | 8012.14 25306.1 36379.1 44394.7 71500.2 99366 
267 | 7831.05 25630.8 35939.8 44156.2 72032.1 99288.9 
268 | 7651.73 25958.1 35499.8 43913.1 72561.5 99212.7 
269 | 7474.53 26287.4 35060.1 43665.8 73087.5 99137.6 
270 | 7299.3 26619 34620.3 43413.7 73610.3 99063.7 
271 | 7126.09 26952.8 34180.6 43157 74129.8 98991.2 
272 | 6954.78 27289.1 33740.6 42895.2 74646.5 98920.1 
273 | 6785.67 27627.2 33301.1 42628.7 75159.4 98850.8 
274 | 6618.67 27967.3 32862 42357.2 75668.7 98783.3 
275 | 6453.78 28309.4 32423.2 42080.5 76174.4 98717.8 
276 | 6290.9 28653.8 31984.4 41798.5 76676.9 98654.3 
277 | 6130.31 28999.8 31546.5 41511.4 77175.2 98593 
278 | 5971.91 29347.6 31109.2 41219.1 77669.6 98534.1 
279 | 5815.58 29697.5 30672.3 40921.1 78160.5 98477.5 
280 | 5661.61 30048.8 30236.4 40618 78647 98423.6 
281 | 5509.88 29801.4 30401.7 40309.4 79129.4 98372.3 
282 | 5360.39 29367.2 30756.3 39995.3 79607.6 98323.7 
283 | 5213.06 28933.7 31112.7 39675.5 80082 98278 
284 | 5068.13 28501.6 31470.3 39350.5 80551.7 98235.1 
285 | 4925.46 28070.6 31829.4 39019.8 81017.1 98195.3 
286 | 4785.09 27640.7 32189.8 38683.7 81478.1 98158.5 
287 | 4647.03 27212.1 32551.5 38342 81934.6 98124.9 
288 | 4511.3 26785 32914.4 37995 82386.5 98094.4 
289 | 4377.89 26359.3 33278.5 37642.4 82833.9 98067.1 
290 | 4246.82 25935 33643.6 37284.5 83276.5 98043.2 
291 | 4118.07 25512.4 34009.8 36921.1 83714.4 98022.5 
292 | 3991.69 25091.5 34376.8 36552.6 84147.5 98005.1 
293 | 3867.63 24672.3 34744.7 36178.8 84575.9 97991.1 
294 | 3745.92 24254.9 35113.4 35799.8 84999.3 97980.4 
295 | 3626.54 23839.4 35415.7 35482.8 85417.8 97973.1 
296 | 3509.52 23425.9 35026.7 35852.8 85831.4 97969.2 
297 | 3394.82 23014.4 34632.7 36223.4 86239.9 97968.7 
298 | 3282.46 22605 34234 36594.5 86643.5 97971.5 
299 | 3172.43 22197.7 33830.6 36965.9 87041.9 97977.6 
300 | 3064.72 21792.7 33422.6 37337.7 87435.3 97987.1 
301 | 2959.33 21390.1 33010.2 37709.7 87823.5 97999.9 
302 | 2856.24 20989.8 32593.5 38081.9 88206.6 98015.9 
303 | 2755.45 20591.9 32172.6 38454.1 88584.5 98035.1 
304 | 2656.94 20196.6 31747.7 38826.4 88957.2 98057.6 
305 | 2560.72 19803.8 31318.9 39198.5 89324.6 98083.1 
306 | 2466.75 19413.7 30886.4 39570.5 89686.8 98111.8 
307 | 2375.03 19026.3 30450.4 39942.2 90043.8 98143.4 
308 | 2285.54 18641.6 30010.9 40313.5 90395.5 98178.1 
309 | 2198.27 18259.8 29568.2 40684.5 90741.9 98215.6 
310 | 2113.2 17880.8 29122.5 41054.9 91083 98256 
311 | 2030.32 17504.8 28673.9 41424.7 91418.9 98299.2 
312 | 1949.59 17131.7 28222.5 41793.9 91749.4 98345.1 
313 | 1871.02 16761.8 27768.7 42162.2 92074.6 98393.5 
314 | 1794.57 16394.9 27312.5 42529.7 92394.6 98444.6 
315 | 1720.23 16031.3 26854.2 42896.2 92709.2 98498.1 
316 | 1647.97 15670.8 26394 43261.7 93018.6 98554 
317 | 1577.76 15313.6 25932 43626.1 93322.6 98612.3 
318 | 1509.6 14959.7 25468.5 43989.2 93621.4 98672.7 
319 | 1443.45 14609.3 25003.7 44351.1 93915 98735.3 
320 | 1379.29 14262.2 24537.6 44711.5 94203.3 98799.9 
321 | 1317.09 13918.6 24070.7 45070.4 94486.3 98866.5 
322 | 1256.82 13578.5 23603 45427.8 94764.1 98935 
323 | 1198.47 13242 23134.8 45783.5 95036.8 99005.3 
324 | 1142 12909.1 22666.3 46137.4 95304.2 99077.3 
325 | 1087.38 12579.9 22197.6 46489.5 95566.6 99150.8 
326 | 1034.59 12254.3 21729.1 46839.7 95823.7 99225.9 
327 | 983.592 11932.5 21260.8 47187.8 96075.8 99302.4 
328 | 934.362 11614.5 20793 47533.8 96322.8 99380.3 
329 | 886.869 11300.3 20326 47877.5 96564.8 99459.4 
330 | 841.087 10989.9 19859.9 48219 96801.8 99539.6 
331 | 796.973 10683.5 19395 48558.1 97033.8 99620.9 
332 | 754.505 10380.9 18931.3 48894.7 97260.8 99703.2 
333 | 713.649 10082.3 18469.2 49228.7 97483 99786.3 
334 | 674.373 9787.71 18008.9 49560.1 97700.3 99870.3 
335 | 636.646 9497.15 17550.6 49888.7 97912.8 99954.9 
336 | 600.432 9210.62 17094.4 50214.5 98120.4 100040 
337 | 565.7 8928.19 16640.5 50537.4 98323.4 100126 
338 | 532.417 8649.86 16189.3 50857.3 98521.6 100212 
339 | 500.551 8375.7 15740.8 51174 98715.2 100299 
340 | 470.063 8105.66 15295.2 51487.6 98904.2 100386 
341 | 440.924 7839.83 14852.9 51797.9 99088.6 100473 
342 | 413.099 7578.21 14413.8 52104.9 99268.5 100560 
343 | 386.557 7320.85 13978.4 52408.3 99444 100647 
344 | 361.257 7067.72 13546.6 52708.3 99615 100734 
345 | 337.17 6818.88 13118.8 53004.7 99781.7 100822 
346 | 314.261 6574.33 12695.1 53297.4 99944.1 100908 
347 | 292.499 6334.13 12275.8 53586.3 100102 100995 
348 | 271.844 6098.24 11860.9 53871.4 100256 101081 
349 | 252.265 5866.69 11450.6 54152.5 100406 101167 
350 | 233.729 5639.52 11045.2 54429.6 100551 101252 
351 | 216.202 5416.73 10644.8 54702.6 100693 101337 
352 | 199.652 5198.36 10249.7 54971.4 100831 101421 
353 | 184.041 4984.37 9859.83 55236.1 100964 101505 
354 | 169.341 4774.81 9475.52 55496.3 101094 101587 
355 | 155.516 4569.69 9096.9 55752.2 101220 101669 
356 | 142.537 4369.03 8724.17 56003.6 101342 101750 
357 | 130.367 4172.8 8357.41 56250.5 101461 101830 
358 | 118.977 3981.03 7996.8 56492.8 101575 101909 
359 | 108.335 3793.74 7642.54 56730.3 101687 101987 
360 | 98.41 3610.94 7294.77 56963.1 101794 102064 
361 | 89.1703 3432.61 6953.59 57191.1 101898 102139 
362 | 80.5855 3258.76 6619.15 57414.3 101999 102214 
363 | 72.6266 3089.42 6291.63 57632.4 102096 102287 
364 | 65.2643 2924.6 5971.18 57845.5 102190 102358 
365 | 58.4683 2764.27 5657.88 58053.6 102281 102429 
366 | 52.2107 2608.45 5351.88 58256.5 102369 102498 
367 | 46.4633 2457.14 5053.3 58454.3 102453 102565 
368 | 41.1993 2310.35 4762.29 58646.7 102534 102631 
369 | 36.3919 2168.09 4478.98 58833.9 102612 102695 
370 | 32.0141 2030.34 4203.45 59015.7 102687 102758 
371 | 28.0406 1897.11 3935.81 59192.1 102759 102819 
372 | 24.4467 1768.41 3676.21 59362.9 102829 102878 
373 | 21.2083 1644.24 3424.75 59528.3 102895 102936 
374 | 18.3011 1524.59 3181.51 59688.1 102958 102991 
375 | 15.7025 1409.47 2946.6 59842.2 103019 103045 
376 | 13.3901 1298.86 2720.11 59990.7 103077 103098 
377 | 11.3429 1192.8 2502.17 60133.5 103132 103148 
378 | 9.5397 1091.25 2292.82 60270.5 103185 103196 
379 | 7.96062 994.222 2092.17 60401.8 103235 103242 
380 | 6.58642 901.717 1900.29 60527.2 103282 103287 
381 | 5.39895 813.748 1717.3 60646.7 103327 103329 
382 | 4.38028 730.291 1543.22 60760.3 103369 103370 
383 | 3.51377 651.355 1378.14 60867.9 103408 103409 
384 | 2.78346 576.939 1222.14 60969.6 103444 103446 
385 | 2.17426 507.041 1075.27 61065.3 103479 103481 
386 | 1.67195 441.666 937.607 61154.9 103511 103514 
387 | 1.26307 380.801 809.182 61238.5 103541 103544 
388 | 0.935166 324.45 690.061 61316 103568 103572 
389 | 0.676627 272.615 580.295 61387.4 103594 103597 
390 | 0.47672 225.29 479.922 61452.6 103617 103620 
391 | 0.325641 182.477 388.987 61511.7 103639 103641 
392 | 0.214484 144.174 307.524 61564.6 103658 103660 
393 | 0.13527 110.379 235.567 61611.3 103675 103676 
394 | 0.0809383 81.0924 173.145 61651.9 103689 103691 
395 | 0.045363 56.3127 120.284 61686.2 103702 103703 
396 | 0.0233512 36.0395 77.0055 61714.3 103712 103712 
397 | 0.0106485 20.2719 43.3258 61736.1 103720 103720 
398 | 0.00394301 9.00959 19.259 61751.7 103725 103725 
399 | 0.000867291 2.25245 4.81519 61761.1 103729 103729 
400 | -9.04674e-05 -2.32518e-12 9.047e-05 61764.2 103730 103730 
401 | 


--------------------------------------------------------------------------------
/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/run.in:
--------------------------------------------------------------------------------
1 | potential       potentials/tersoff/Graphene_Lindsay_2010_modified.txt 0
2 | compute_phonon  5 0.005 # in units of A
3 | 


--------------------------------------------------------------------------------
/3. Phonon Dispersion and Vibration Mode Visualization of Graphene/xyz.in:
--------------------------------------------------------------------------------
 1 | 50 3 2.1 1 0 0 
 2 | 1 1 0 12.302199601999998 0.0 0.0 -6.151099800999999 10.654017378 0.0 0.0 0.0 10.0 
 3 | 0 -6.177549530139714e-06 0.7102713712121174 5.0 12.011
 4 | 0 1.23022613774953 1.4205321043878827 5.0 12.011
 5 | 0 -1.23022613774953 2.841074846812117 5.0 12.011
 6 | 0 6.177549530139714e-06 3.5513355799878825 5.0 12.011
 7 | 0 -2.46044609794953 4.971878322412118 5.0 12.011
 8 | 0 -1.2302137826504698 5.682139055587883 5.0 12.011
 9 | 0 -3.69066605814953 7.102681798012117 5.0 12.011
10 | 0 -2.4604337428504697 7.812942531187883 5.0 12.011
11 | 0 -4.920886018349529 9.233485273612118 5.0 12.011
12 | 0 -3.6906537030504696 9.943746006787883 5.0 12.011
13 | 0 2.4604337428504697 0.7102713712121174 5.0 12.011
14 | 0 3.69066605814953 1.4205321043878827 5.0 12.011
15 | 0 1.2302137826504698 2.841074846812117 5.0 12.011
16 | 0 2.46044609794953 3.5513355799878825 5.0 12.011
17 | 0 -6.177549530139714e-06 4.971878322412118 5.0 12.011
18 | 0 1.23022613774953 5.682139055587883 5.0 12.011
19 | 0 -1.23022613774953 7.102681798012117 5.0 12.011
20 | 0 6.177549530139714e-06 7.812942531187883 5.0 12.011
21 | 0 -2.46044609794953 9.233485273612118 5.0 12.011
22 | 0 -1.2302137826504698 9.943746006787883 5.0 12.011
23 | 0 4.92087366325047 0.7102713712121174 5.0 12.011
24 | 0 6.15110597854953 1.4205321043878827 5.0 12.011
25 | 0 3.6906537030504696 2.841074846812117 5.0 12.011
26 | 0 4.920886018349529 3.5513355799878825 5.0 12.011
27 | 0 2.4604337428504697 4.971878322412118 5.0 12.011
28 | 0 3.69066605814953 5.682139055587883 5.0 12.011
29 | 0 1.2302137826504698 7.102681798012117 5.0 12.011
30 | 0 2.46044609794953 7.812942531187883 5.0 12.011
31 | 0 -6.177549530139714e-06 9.233485273612118 5.0 12.011
32 | 0 1.23022613774953 9.943746006787883 5.0 12.011
33 | 0 7.381313583650469 0.7102713712121174 5.0 12.011
34 | 0 8.61154589894953 1.4205321043878827 5.0 12.011
35 | 0 6.151093623450469 2.841074846812117 5.0 12.011
36 | 0 7.381325938749529 3.5513355799878825 5.0 12.011
37 | 0 4.92087366325047 4.971878322412118 5.0 12.011
38 | 0 6.15110597854953 5.682139055587883 5.0 12.011
39 | 0 3.6906537030504696 7.102681798012117 5.0 12.011
40 | 0 4.920886018349529 7.812942531187883 5.0 12.011
41 | 0 2.4604337428504697 9.233485273612118 5.0 12.011
42 | 0 3.69066605814953 9.943746006787883 5.0 12.011
43 | 0 9.84175350405047 0.7102713712121174 5.0 12.011
44 | 0 11.071985819349528 1.4205321043878827 5.0 12.011
45 | 0 8.61153354385047 2.841074846812117 5.0 12.011
46 | 0 9.841765859149529 3.5513355799878825 5.0 12.011
47 | 0 7.381313583650469 4.971878322412118 5.0 12.011
48 | 0 8.61154589894953 5.682139055587883 5.0 12.011
49 | 0 6.151093623450469 7.102681798012117 5.0 12.011
50 | 0 7.381325938749529 7.812942531187883 5.0 12.011
51 | 0 4.92087366325047 9.233485273612118 5.0 12.011
52 | 0 6.15110597854953 9.943746006787883 5.0 12.011


--------------------------------------------------------------------------------
/4. Quantum-corrected thermal conductivity of amorphous carbon/run.in:
--------------------------------------------------------------------------------
 1 | potential       ../potentials/nep.txt 0
 2 | 
 3 | time_step       1.0
 4 | 
 5 | velocity    	300
 6 | ensemble        nvt_nhc 300 300 100 
 7 | run             100000
 8 | 
 9 | ensemble        nvt_nhc 300 300 100
10 | compute_hnemd   1000 0 0 2e-4
11 | compute_shc     5 200 2 500 400
12 | run             2000000
13 | 
14 | 
15 | 
16 | 
17 | 
18 | 
19 | 
20 | 


--------------------------------------------------------------------------------
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675 | 


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/README.md:
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1 | # Tutorial-on-atomic-simulations
2 | Here, we give some tutorials on atomic simulations based on [GPUMD package](https://github.com/brucefan1983/GPUMD).
3 | 1. The phonon participation ratios are calculated with the [GPUMD-2.9.1](https://github.com/brucefan1983/GPUMD/releases/tag/v2.9.1).
4 | 2. The elastic constants based on strain fluctuation method are calculated with the [GPUMD-3.0](https://github.com/brucefan1983/GPUMD/releases/tag/v3.0).
5 | 3. Phonon Dispersion and Vibration Mode Visualization of Graphene [GPUMD-2.9.1](https://github.com/brucefan1983/GPUMD/releases/tag/v2.9.1).
6 | 4. Quantum-corrected thermal conductivity of amorphous carbon [GPUMD-3.3](https://github.com/brucefan1983/GPUMD/releases/tag/v3.3).
7 | 


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