Fitting a pair potential with a user defined function¶
This example demonstrates the (ab)use of the embedded atom method (EAM) potential. A pair potential of the generalized Morse form is fitted to the lattice constant, bulk modulus, and cohesive energy of copper in the face-centered cubic (FCC) crystal structure. The example also illustrates the use of XML Inclusions. Note that the final potential is not particularly good, which is unsurprising given the fact that a pair potential form is being used with a limited number of parameters.
Location¶
examples/fitting_pair_potential
Input files¶
main.xml: main input file
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<?xml version="1.0" encoding="iso-8859-1"?> <job> <name>Fitting an EAM potential for copper</name> <verbosity>medium</verbosity> <fitting> <BFGS conv-threshold="1e-5" max-iter="200" /> </fitting> <atom-types> <species>Cu</species> </atom-types> <potentials> <xi:include href="potential.xml" xmlns:xi="http://www.w3.org/2003/XInclude" /> </potentials> <structures> <xi:include href="structures.xml" xmlns:xi="http://www.w3.org/2003/XInclude" /> </structures> </job>
potential.xml: initial parameter set (included in main input file via XML Inclusions)
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<eam id='Cu pair potential' species-a='*' species-b='*'> <export-functions>Cu_potential</export-functions> <mapping> <pair-interaction species-a='*' species-b='*' function='V' /> </mapping> <functions> <user-function id='V'> <input-var>r</input-var> <expression> D0 / (S-1) * exp(-beta * sqrt(2.0 * S) * (r-r0) ) - S * D0 / (S-1) * exp(-beta * sqrt(2.0 / S) * (r-r0) ) </expression> <derivative> - beta * ( sqrt(2 * S) * D0 / (S - 1) * exp(-beta * sqrt(2 * S) * (r - r0) ) - sqrt(2 / S) * S * D0 / (S - 1) * exp(- beta * sqrt(2/S) * (r - r0) ) ) </derivative> <param name='D0'>0.2</param> <param name='beta'>1.5</param> <param name='r0'>2.63</param> <param name='S'>1.84</param> <fit-dof> <D0/> <r0/> <beta/> </fit-dof> <screening> <user-function id='cutoff function'> <cutoff>5.5</cutoff> <input-var>r</input-var> <expression> 1 - 1/(1 + ((r - cutoff) / h)^4) </expression> <derivative> 4 * h^4 * (r - cutoff)^3 / ((h^4 + (r - cutoff)^4)^2) </derivative> <param name='h'>0.5</param> </user-function> </screening> </user-function> </functions> </eam>
structures.xml: input structures (included in main input file via XML Inclusions)
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<group> <fcc-lattice id="FCC"> <atom-type>Cu</atom-type> <lattice-parameter>3.615</lattice-parameter> <properties> <lattice-parameter fit='true' target='3.615' relative-weight='4'/> <atomic-energy fit='true' target='-3.540' relative-weight='4'/> <bulk-modulus fit='true' target='138'/> <C11 target='170.0'/> <C12 target='122.5'/> <C44 target= '75.8'/> </properties> </fcc-lattice> </group>
Output (files)¶
Cu_potential.V.table: pair potential suitable for plotting
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# 1st col: index # 2nd col: x # 3rd col: y # 4th col: derivative 0 0.2 351.883 -1010.26 1 0.2265 326.086 -937.589 2 0.253 302.146 -870.092 3 0.2795 279.929 -807.407 4 0.306 259.314 -749.191 5 0.3325 240.185 -695.129 6 0.359 222.438 -644.924 7 0.3855 205.972 -598.304 8 0.412 190.698 -555.014 9 0.4385 176.529 -514.818 10 0.465 163.387 -477.496 11 0.4915 151.199 -442.844 12 0.518 139.895 -410.673 13 0.5445 129.413 -380.805 14 0.571 119.693 -353.078 15 0.5975 110.682 -327.339 16 0.624 102.328 -303.447 17 0.6505 94.584 -281.27 18 0.677 87.4065 -260.687 19 0.7035 80.7545 -241.583 20 0.73 74.5904 -223.854 21 0.7565 68.879 -207.401 22 0.783 63.5877 -192.134 23 0.8095 58.6862 -177.968 24 0.836 54.1463 -164.824 25 0.8625 49.9421 -152.63 26 0.889 46.0492 -141.317 27 0.9155 42.445 -130.823 28 0.942 39.1088 -121.09 29 0.9685 36.0211 -112.062 30 0.995 33.1638 -103.689 31 1.0215 30.5202 -95.9247 32 1.048 28.0748 -88.7252 33 1.0745 25.8131 -82.0501 34 1.101 23.7218 -75.8617 35 1.1275 21.7884 -70.1251 36 1.154 20.0015 -64.8079 37 1.1805 18.3502 -59.8799 38 1.207 16.8247 -55.3131 39 1.2335 15.4156 -51.0816 40 1.26 14.1146 -47.1612 41 1.2865 12.9135 -43.5294 42 1.313 11.8052 -40.1656 43 1.3395 10.7826 -37.0502 44 1.366 9.83946 -34.1654 45 1.3925 8.96992 -31.4946 46 1.419 8.16849 -29.0221 47 1.4455 7.43012 -26.7337 48 1.472 6.7501 -24.616 49 1.4985 6.12408 -22.6565 50 1.525 5.54801 -20.8439 51 1.5515 5.01815 -19.1673 52 1.578 4.53103 -17.617 53 1.6045 4.08342 -16.1837 54 1.631 3.67233 -14.8588 55 1.6575 3.29501 -13.6344 56 1.684 2.94889 -12.5032 57 1.7105 2.63158 -11.4583 58 1.737 2.34089 -10.4934 59 1.7635 2.07478 -9.60258 60 1.79 1.83135 -8.78043 61 1.8165 1.60885 -8.02186 62 1.843 1.40567 -7.32217 63 1.8695 1.2203 -6.67701 64 1.896 1.05134 -6.08232 65 1.9225 0.897522 -5.53437 66 1.949 0.757641 -5.02966 67 1.9755 0.630597 -4.56497 68 2.002 0.515371 -4.13731 69 2.0285 0.411018 -3.7439 70 2.055 0.316664 -3.38217 71 2.0815 0.231504 -3.04973 72 2.108 0.15479 -2.74437 73 2.1345 0.0858312 -2.46405 74 2.161 0.0239908 -2.20685 75 2.1875 -0.0313208 -1.97103 76 2.214 -0.0806481 -1.75495 77 2.2405 -0.124494 -1.55709 78 2.267 -0.163322 -1.37605 79 2.2935 -0.197562 -1.21055 80 2.32 -0.227608 -1.05937 81 2.3465 -0.253825 -0.921399 82 2.373 -0.27655 -0.795614 83 2.3995 -0.296092 -0.681058 84 2.426 -0.312737 -0.576848 85 2.4525 -0.326749 -0.482165 86 2.479 -0.338369 -0.396255 87 2.5055 -0.347822 -0.318416 88 2.532 -0.355311 -0.248003 89 2.5585 -0.361026 -0.184415 90 2.585 -0.36514 -0.127101 91 2.6115 -0.367813 -0.0755472 92 2.638 -0.369191 -0.0292818 93 2.6645 -0.369408 0.0121324 94 2.691 -0.368587 0.0490992 95 2.7175 -0.366842 0.0819914 96 2.744 -0.364275 0.111153 97 2.7705 -0.360981 0.136903 98 2.797 -0.357046 0.159533 99 2.8235 -0.352551 0.179315 100 2.85 -0.347566 0.196497 101 2.8765 -0.342157 0.211311 102 2.903 -0.336385 0.223967 103 2.9295 -0.330304 0.234662 104 2.956 -0.323964 0.243576 105 2.9825 -0.317409 0.250873 106 3.009 -0.31068 0.256706 107 3.0355 -0.303815 0.261216 108 3.062 -0.296847 0.26453 109 3.0885 -0.289805 0.266769 110 3.115 -0.282716 0.26804 111 3.1415 -0.275606 0.268443 112 3.168 -0.268496 0.26807 113 3.1945 -0.261405 0.267005 114 3.221 -0.25435 0.265324 115 3.2475 -0.247347 0.263098 116 3.274 -0.24041 0.260391 117 3.3005 -0.23355 0.257263 118 3.327 -0.226778 0.253766 119 3.3535 -0.220103 0.249951 120 3.38 -0.213533 0.245861 121 3.4065 -0.207075 0.241537 122 3.433 -0.200734 0.237017 123 3.4595 -0.194514 0.232334 124 3.486 -0.188421 0.227518 125 3.5125 -0.182457 0.222597 126 3.539 -0.176624 0.217597 127 3.5655 -0.170925 0.212539 128 3.592 -0.16536 0.207445 129 3.6185 -0.15993 0.202332 130 3.645 -0.154636 0.197217 131 3.6715 -0.149478 0.192115 132 3.698 -0.144454 0.187038 133 3.7245 -0.139564 0.182 134 3.751 -0.134808 0.17701 135 3.7775 -0.130182 0.172077 136 3.804 -0.125687 0.167209 137 3.8305 -0.12132 0.162415 138 3.857 -0.117078 0.1577 139 3.8835 -0.112961 0.15307 140 3.91 -0.108965 0.148529 141 3.9365 -0.105088 0.144083 142 3.963 -0.101327 0.139734 143 3.9895 -0.097681 0.135485 144 4.016 -0.0941458 0.13134 145 4.0425 -0.0907191 0.1273 146 4.069 -0.087398 0.123368 147 4.0955 -0.0841796 0.119545 148 4.122 -0.0810611 0.115833 149 4.1485 -0.0780395 0.112234 150 4.175 -0.0751117 0.108748 151 4.2015 -0.0722748 0.105376 152 4.228 -0.0695258 0.102121 153 4.2545 -0.0668614 0.0989824 154 4.281 -0.0642786 0.0959629 155 4.3075 -0.0617743 0.0930638 156 4.334 -0.0593452 0.0902867 157 4.3605 -0.056988 0.087634 158 4.387 -0.0546995 0.0851082 159 4.4135 -0.0524761 0.0827123 160 4.44 -0.0503145 0.0804497 161 4.4665 -0.0482111 0.0783247 162 4.493 -0.0461621 0.0763419 163 4.5195 -0.0441636 0.0745067 164 4.546 -0.0422118 0.0728251 165 4.5725 -0.0403025 0.071304 166 4.599 -0.0384313 0.0699504 167 4.6255 -0.0365936 0.0687717 168 4.652 -0.0347847 0.0677754 169 4.6785 -0.0329998 0.0669678 170 4.705 -0.0312337 0.0663537 171 4.7315 -0.0294814 0.0659344 172 4.758 -0.0277375 0.0657062 173 4.7845 -0.0259973 0.0656571 174 4.811 -0.0242563 0.0657639 175 4.8375 -0.0225108 0.0659872 176 4.864 -0.0207585 0.0662667 177 4.8905 -0.0189989 0.0665164 178 4.917 -0.0172344 0.0666205 179 4.9435 -0.0154706 0.0664326 180 4.97 -0.0137176 0.0657803 181 4.9965 -0.01199 0.0644776 182 5.023 -0.0103076 0.0623473 183 5.0495 -0.00869415 0.0592528 184 5.076 -0.00717626 0.055134 185 5.1025 -0.00578071 0.0500387 186 5.129 -0.00453137 0.0441373 187 5.1555 -0.00344608 0.0377116 188 5.182 -0.00253416 0.031116 189 5.2085 -0.00179515 0.0247206 190 5.235 -0.00121929 0.0188515 191 5.2615 -0.000789239 0.0137466 192 5.288 -0.000482796 0.00953506 193 5.3145 -0.000275746 0.0062417 194 5.341 -0.000144375 0.00380814 195 5.3675 -6.73101e-05 0.00212131 196 5.394 -2.65902e-05 0.00104062 197 5.4205 -8.10173e-06 0.000419336 198 5.447 -1.53971e-06 0.000118464 199 5.4735 -9.2548e-08 1.41062e-05 200 5.5 -0 0
The final properties (as well as parameters) are written to standard output.
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This is program version 0.1.6 Reading job file main.xml ------------------------------------------------------- Parsing input file(s) ------------------------------------------------------- ------------------------------------------------------- Potential parameters being optimized (#dof=3): elemental EAM potential[EAM].V[user-function].D0: 0.2 elemental EAM potential[EAM].V[user-function].beta: 1.5 elemental EAM potential[EAM].V[user-function].r0: 2.63 ------------------------------------------------------- ------------------------------------------------------- Number of properties being fitted: 3 ------------------------------------------------------- iter= 1 residual= 14077.2 grad= 142826 iter= 2 residual= 467034 grad= 2.33932e+06 iter= 3 residual= 1463.38 grad= 27202.1 iter= 4 residual= 1463.38 grad= 27202.1 iter= 5 residual= 914.83 grad= 11131.5 iter= 6 residual= 914.83 grad= 11131.5 iter= 7 residual= 695.498 grad= 12252 iter= 8 residual= 96.1781 grad= 9763.98 iter= 9 residual= 96.1781 grad= 9763.98 iter= 10 residual= 16.3463 grad= 3264.58 ------------------------------------------------------- Potential parameters being optimized (#dof=3): elemental EAM potential[EAM].V[user-function].D0: 0.421798 elemental EAM potential[EAM].V[user-function].beta: 1.5293 elemental EAM potential[EAM].V[user-function].r0: 2.76538 ------------------------------------------------------- iter= 11 residual= 16.3463 grad= 3264.58 iter= 12 residual= 17.2543 grad= 3555.34 iter= 13 residual= 7.98951 grad= 1445.09 iter= 14 residual= 7.98951 grad= 1445.09 iter= 15 residual= 8.90514 grad= 2132.15 iter= 16 residual= 7.56993 grad= 1323.44 iter= 17 residual= 7.56993 grad= 1323.44 iter= 18 residual= 10.5635 grad= 2330.62 iter= 19 residual= 6.97667 grad= 898.806 iter= 20 residual= 6.97667 grad= 898.806 ------------------------------------------------------- Potential parameters being optimized (#dof=3): elemental EAM potential[EAM].V[user-function].D0: 0.424874 elemental EAM potential[EAM].V[user-function].beta: 1.52458 elemental EAM potential[EAM].V[user-function].r0: 2.76091 ------------------------------------------------------- iter= 21 residual= 7.0202 grad= 537.2 iter= 22 residual= 6.97784 grad= 1497.81 iter= 23 residual= 6.97561 grad= 987.668 iter= 24 residual= 6.97797 grad= 1786.67 iter= 25 residual= 6.97688 grad= 373.522 iter= 26 residual= 6.97569 grad= 1531.91 iter= 27 residual= 6.97569 grad= 1531.91 iter= 28 residual= 114.257 grad= 10793.4 iter= 29 residual= 7.12217 grad= 1337.44 iter= 30 residual= 6.97273 grad= 538.562 ------------------------------------------------------- Potential parameters being optimized (#dof=3): elemental EAM potential[EAM].V[user-function].D0: 0.424779 elemental EAM potential[EAM].V[user-function].beta: 1.52381 elemental EAM potential[EAM].V[user-function].r0: 2.76096 ------------------------------------------------------- iter= 31 residual= 6.97273 grad= 538.562 iter= 32 residual= 6.81371 grad= 264.436 iter= 33 residual= 6.81371 grad= 264.436 iter= 34 residual= 6.79466 grad= 601.69 iter= 35 residual= 6.79466 grad= 601.69 iter= 36 residual= 7.8179 grad= 875.562 iter= 37 residual= 6.80111 grad= 473.237 iter= 38 residual= 6.7948 grad= 901.646 iter= 39 residual= 6.79405 grad= 400.6 iter= 40 residual= 6.7953 grad= 711.802 ------------------------------------------------------- Potential parameters being optimized (#dof=3): elemental EAM potential[EAM].V[user-function].D0: 0.424077 elemental EAM potential[EAM].V[user-function].beta: 1.52379 elemental EAM potential[EAM].V[user-function].r0: 2.76089 ------------------------------------------------------- iter= 41 residual= 6.79581 grad= 592.135 iter= 42 residual= 6.79527 grad= 842.651 iter= 43 residual= 6.79412 grad= 994.064 iter= 44 residual= 6.79412 grad= 994.064 iter= 45 residual= 6.7906 grad= 913.106 iter= 46 residual= 6.7906 grad= 913.106 iter= 47 residual= 6.76243 grad= 542.524 iter= 48 residual= 6.76243 grad= 542.524 iter= 49 residual= 6.82223 grad= 752.146 iter= 50 residual= 6.76024 grad= 1402.08 ------------------------------------------------------- Potential parameters being optimized (#dof=3): elemental EAM potential[EAM].V[user-function].D0: 0.42355 elemental EAM potential[EAM].V[user-function].beta: 1.52278 elemental EAM potential[EAM].V[user-function].r0: 2.76094 ------------------------------------------------------- iter= 51 residual= 6.76223 grad= 1325.41 iter= 52 residual= 6.76061 grad= 704.579 iter= 53 residual= 6.76038 grad= 1078.16 iter= 54 residual= 6.75934 grad= 930.737 iter= 55 residual= 6.75934 grad= 930.737 iter= 56 residual= 6.96147 grad= 1045.85 iter= 57 residual= 6.7702 grad= 792.081 iter= 58 residual= 6.76002 grad= 1230.7 iter= 59 residual= 6.76052 grad= 1135.03 iter= 60 residual= 6.76138 grad= 1151.42 ------------------------------------------------------- Potential parameters being optimized (#dof=3): elemental EAM potential[EAM].V[user-function].D0: 0.423544 elemental EAM potential[EAM].V[user-function].beta: 1.52277 elemental EAM potential[EAM].V[user-function].r0: 2.76095 ------------------------------------------------------- iter= 61 residual= 6.76134 grad= 842.388 iter= 62 residual= 6.76055 grad= 552.923 iter= 63 residual= 6.75985 grad= 859.367 iter= 64 residual= 6.75845 grad= 969.45 iter= 65 residual= 6.76031 grad= 1497 iter= 66 residual= 6.75959 grad= 1022.64 iter= 67 residual= 6.75952 grad= 460.327 iter= 68 residual= 6.75952 grad= 460.327 ------------------------------------------------------- Potential parameters being optimized (#dof=3): elemental EAM potential[EAM].V[user-function].D0: 0.42355 elemental EAM potential[EAM].V[user-function].beta: 1.52278 elemental EAM potential[EAM].V[user-function].r0: 2.76094 ------------------------------------------------------- Fitting process complete. ------------------------------------------------------- Computing structure properties Structure 'FCC': total-energy: -3.53491 eV atomic-energy: -3.53491 eV/atom (target: -3.54 eV/atom) Abs. weight: 0.444444; Tolerance: 0.01; Weighted residual: 0.115302 total-volume: 11.8546 A^3 atomic-volume: 11.8546 A^3/atom bulk-modulus: 153.04 GPa (target: 138 GPa) Abs. weight: 0.111111; Tolerance: 2; Weighted residual: 6.28344 C11: 201.423 GPa C12: 128.859 GPa C44: 128.857 GPa lattice-parameter: 3.6195 A (target: 3.615 A) Abs. weight: 0.444444; Tolerance: 0.005; Weighted residual: 0.360779 (relaxed) [0:] ------------------------------------------------------- Writing EAM function tables to Cu_potential.* -------------------------------------------------------
Other files¶
pairpotential_reference.table: the pair potential from the embedded atom method (EAM) potential presented in [MisMehPap01]
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# pair potential from Mishin's EAM potential (2001) # 1st col: index # 2nd col: x # 3rd col: y # 4th col: derivative 0 0.2 8379.04 -50890.7 1 0.226534 7132.66 -43259.4 2 0.253068 6073.32 -36763.4 3 0.279602 5173.15 -31235.8 4 0.306136 4408.4 -26534.2 5 0.33267 3758.81 -22536.8 6 0.359204 3207.12 -19139.7 7 0.385738 2738.59 -16254.1 8 0.412272 2340.69 -13804.3 9 0.438806 2002.75 -11725.5 10 0.465339 1715.66 -9962.36 11 0.491873 1471.69 -8467.78 12 0.518407 1264.27 -7201.46 13 0.544941 1087.81 -6129.04 14 0.571475 937.564 -5221.19 15 0.598009 809.501 -4452.93 16 0.624543 700.211 -3802.92 17 0.651077 606.803 -3253.01 18 0.677611 526.833 -2787.73 19 0.704145 458.233 -2393.93 20 0.730679 399.259 -2060.4 21 0.757213 348.443 -1777.64 22 0.783747 304.546 -1537.59 23 0.810281 266.529 -1333.42 24 0.836815 233.519 -1159.35 25 0.863349 204.782 -1010.5 26 0.889883 179.707 -882.781 27 0.916417 157.779 -772.746 28 0.942951 138.568 -677.522 29 0.969485 121.714 -594.718 30 0.996018 106.915 -522.36 31 1.02255 93.9159 -458.828 32 1.04909 82.5 -402.806 33 1.07562 72.4828 -353.239 34 1.10215 63.7047 -309.297 35 1.12869 56.0251 -270.339 36 1.15522 49.3185 -235.892 37 1.18176 43.4699 -205.62 38 1.20829 38.3717 -179.307 39 1.23482 33.922 -156.659 40 1.26136 30.0302 -137.166 41 1.28789 26.619 -120.37 42 1.31443 23.6221 -105.876 43 1.34096 20.983 -93.3484 44 1.36749 18.6535 -82.4975 45 1.39403 16.5924 -73.0768 46 1.42056 14.7647 -64.8758 47 1.4471 13.1404 -57.7145 48 1.47363 11.694 -51.44 49 1.50016 10.4039 -45.9222 50 1.5267 9.25134 -41.0509 51 1.55323 8.22051 -36.7331 52 1.57977 7.29779 -32.8903 53 1.6063 6.47147 -29.4572 54 1.63283 5.73142 -26.3792 55 1.65937 5.06884 -23.6115 56 1.6859 4.476 -21.1174 57 1.71244 3.94603 -18.8675 58 1.73897 3.47279 -16.8385 59 1.7655 3.05065 -15.0126 60 1.79204 2.67442 -13.3767 61 1.81857 2.33918 -11.9207 62 1.8451 2.04038 -10.6273 63 1.87164 1.77396 -9.47641 64 1.89817 1.53638 -8.45024 65 1.92471 1.32455 -7.53348 66 1.95124 1.13575 -6.71283 67 1.97777 0.967568 -5.97681 68 2.00431 0.817908 -5.31549 69 2.03084 0.684901 -4.72032 70 2.05738 0.566891 -4.18395 71 2.08391 0.462404 -3.70008 72 2.11044 0.370119 -3.26335 73 2.13698 0.288848 -2.86922 74 2.16351 0.217513 -2.51385 75 2.19005 0.155129 -2.19404 76 2.21658 0.100789 -1.90717 77 2.24311 0.0536478 -1.65107 78 2.26965 0.0129159 -1.42364 79 2.29618 -0.0221292 -1.22194 80 2.32272 -0.0521329 -1.04321 81 2.34925 -0.0776711 -0.884964 82 2.37578 -0.0992577 -0.745002 83 2.40232 -0.117351 -0.621352 84 2.42885 -0.13236 -0.512256 85 2.45539 -0.14465 -0.416144 86 2.48192 -0.154547 -0.331613 87 2.50845 -0.16234 -0.257409 88 2.53499 -0.168288 -0.192413 89 2.56152 -0.172623 -0.13562 90 2.58806 -0.17555 -0.0861355 91 2.61459 -0.177252 -0.0431567 92 2.64112 -0.177891 -0.00596593 93 2.66766 -0.177614 0.0260791 94 2.69419 -0.176548 0.0535531 95 2.72073 -0.174808 0.0769705 96 2.74726 -0.172495 0.0967917 97 2.77379 -0.169699 0.113428 98 2.80033 -0.1665 0.127249 99 2.82686 -0.162968 0.138583 100 2.85339 -0.159165 0.147726 101 2.87993 -0.155146 0.154939 102 2.90646 -0.150958 0.16046 103 2.933 -0.146644 0.164498 104 2.95953 -0.14224 0.167241 105 2.98606 -0.137779 0.168855 106 3.0126 -0.133288 0.169491 107 3.03913 -0.128791 0.169281 108 3.06567 -0.124311 0.168343 109 3.0922 -0.119863 0.166782 110 3.11873 -0.115465 0.164692 111 3.14527 -0.111127 0.162156 112 3.1718 -0.106863 0.159246 113 3.19834 -0.102679 0.156029 114 3.22487 -0.0985848 0.15256 115 3.2514 -0.094585 0.148891 116 3.27794 -0.0906848 0.145065 117 3.30447 -0.0868878 0.141123 118 3.33101 -0.0831965 0.137097 119 3.35754 -0.0796128 0.133018 120 3.38407 -0.0761377 0.128912 121 3.41061 -0.0727717 0.124801 122 3.43714 -0.0695146 0.120704 123 3.46368 -0.0663659 0.116638 124 3.49021 -0.0633245 0.112617 125 3.51674 -0.0603891 0.108653 126 3.54328 -0.0575579 0.104756 127 3.56981 -0.0548292 0.100934 128 3.59635 -0.0522008 0.0971953 129 3.62288 -0.0496705 0.0935438 130 3.64941 -0.0472358 0.0899845 131 3.67595 -0.0448944 0.0865207 132 3.70248 -0.0426435 0.0831548 133 3.72902 -0.0404806 0.0798884 134 3.75555 -0.0384031 0.0767224 135 3.78208 -0.0364082 0.0736573 136 3.80862 -0.0344934 0.0706928 137 3.83515 -0.0326558 0.0678284 138 3.86169 -0.030893 0.065063 139 3.88822 -0.0292022 0.0623954 140 3.91475 -0.0275809 0.0598239 141 3.94129 -0.0260266 0.0573468 142 3.96782 -0.0245369 0.054962 143 3.99435 -0.0231091 0.0526673 144 4.02089 -0.0217411 0.0504604 145 4.04742 -0.0204306 0.0483389 146 4.07396 -0.0191752 0.0463004 147 4.10049 -0.0179728 0.0443422 148 4.12702 -0.0168213 0.0424617 149 4.15356 -0.0157188 0.0406563 150 4.18009 -0.0146631 0.0389232 151 4.20663 -0.0136526 0.0372598 152 4.23316 -0.0126852 0.0356633 153 4.25969 -0.0117594 0.0341309 154 4.28623 -0.0108734 0.0326598 155 4.31276 -0.0100257 0.0312471 156 4.3393 -0.00921474 0.0298899 157 4.36583 -0.00843906 0.0285852 158 4.39236 -0.00769734 0.0273299 159 4.4189 -0.00698831 0.0261208 160 4.44543 -0.00631079 0.0249545 161 4.47197 -0.00566369 0.0238273 162 4.4985 -0.00504601 0.0227355 163 4.52503 -0.00445689 0.0216748 164 4.55157 -0.00389554 0.0206405 165 4.5781 -0.00336135 0.0196277 166 4.60464 -0.0028538 0.0186306 167 4.63117 -0.00237258 0.0176427 168 4.6577 -0.00191753 0.0166569 169 4.68424 -0.00148869 0.015665 170 4.71077 -0.00108635 0.0146581 171 4.73731 -0.000711038 0.0136259 172 4.76384 -0.00036357 0.0125576 173 4.79037 -4.50522e-05 0.0114418 174 4.81691 0.000243102 0.0102671 175 4.84344 0.000499188 0.00902306 176 4.86998 0.000721253 0.00770177 177 4.89651 0.00090719 0.00629994 178 4.92304 0.0010549 0.00482166 179 4.94958 0.00116251 0.00328152 180 4.97611 0.00122874 0.00170785 181 5.00264 0.00125324 0.00014482 182 5.02918 0.00123705 -0.00134747 183 5.05571 0.00118299 -0.0026966 184 5.08225 0.00109589 -0.00382582 185 5.10878 0.000982528 -0.00466597 186 5.13531 0.00085127 -0.00516907 187 5.16185 0.000711345 -0.00531972 188 5.18838 0.000571892 -0.00514044 189 5.21492 0.000440972 -0.00468847 190 5.24145 0.00032478 -0.00404508 191 5.26798 0.0002272 -0.00330065 192 5.29452 0.000149758 -0.00254022 193 5.32105 9.19208e-05 -0.00183278 194 5.34759 5.15999e-05 -0.00122598 195 5.37412 2.57372e-05 -0.000745547 196 5.40065 1.08566e-05 -0.00039786 197 5.42719 3.52603e-06 -0.000173891 198 5.45372 7.13171e-07 -5.31468e-05 199 5.48026 4.55553e-08 -6.83139e-06 200 5.50679 0 0
plot_pairpotential.py: a python script that plots a comparison between the pair potential fitted here and the pair potential from the EAM potential in [MisMehPap01]
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# creates: pairpotential.svg import matplotlib.pyplot as plt import numpy as np x_ref,y_ref = np.loadtxt('pairpotential_reference.table', usecols=(1,2), unpack=True) x_fit,y_fit = np.loadtxt('Cu_potential.V.table', usecols=(1,2), unpack=True) plt.figure(figsize=(4, 3)) plt.xlabel(r'Pair distance (A)') plt.ylabel(r'Pair potential (eV)') plt.axis([1.8, 5.5, -0.5, 2]) plt.plot(x_ref, y_ref, color='cornflowerblue', linestyle='-', label='from EAM potential') plt.plot(x_fit, y_fit, color='orange', linestyle='-', label='fitted potential') plt.legend() plt.savefig('pairpotential.svg', bbox_inches='tight')
Pair interaction from a pure pair and an EAM potential [MisMehPap01].¶