LAMMPS Fracture

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(Created page with '== Abstract == This example shows how to run an atomistic simulation of fracture of an iron symmetric tilt grain boundary. A parallel molecular dynamics code, LAMMPS<ref>S. Plim…')
 
(Grain boundary structure file)
Line 15: Line 15:
 
=== Grain boundary structure file ===
 
=== Grain boundary structure file ===
  
This grain boundary structure was generated prior to this example. To use it, store the text in "Fe_100_sig5_210.txt."
+
The grain boundary structure that was generated prior to this example can be found [Fe_100_sig5_210.txt | here]. Store the text in "Fe_100_sig5_210.txt" to use it.
 
+
{|border ="0"
+
|<pre>
+
# Minimum Energy GB Structure for LAMMPS 
+
 
+
380 atoms
+
2 atom types
+
0.000000 6.384670 xlo xhi 
+
-121.638000 121.638000 ylo yhi 
+
0.000000 2.855310 zlo zhi 
+
 
+
Atoms
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1 1 4.460670 -121.056000 1.427660 
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2 1 0.121831 -121.349998 0.000000 
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3 1 0.614806 -119.457001 1.427660 
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4 1 2.536320 -120.134003 0.000000 
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5 1 3.193350 -118.271004 1.427660 
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6 1 5.056950 -118.997002 0.000000 
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7 1 5.717690 -117.030998 1.427660 
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8 1 1.272510 -117.596001 0.000000 
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9 1 1.907410 -115.704002 1.427660 
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10 1 3.820340 -116.360001 0.000000 
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11 1 4.457650 -114.445999 1.427660 
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12 1 6.366010 -115.097000 0.000000 
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13 1 0.623987 -113.174004 1.427660 
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14 1 2.543940 -113.799004 0.000000 
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15 1 3.182210 -111.888000 1.427660 
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16 1 5.096380 -112.530998 0.000000 
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17 1 5.735870 -110.615997 1.427660 
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18 1 1.265040 -111.255997 0.000000 
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19 1 1.905550 -109.338997 1.427660 
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20 1 3.821420 -109.974998 0.000000 
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21 1 4.461220 -108.060997 1.427660 
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22 1 6.375800 -108.699997 0.000000 
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23 1 0.631379 -106.785004 1.427660 
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26 1 5.101420 -106.146004 0.000000 
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32 1 6.382440 -102.316002 0.000000 
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33 1 0.638419 -100.401001 1.427660 
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34 1 2.553070 -101.039001 0.000000 
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36 1 5.108410 -99.762802 0.000000 
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37 1 5.749090 -97.847702 1.427660 
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38 1 1.279090 -98.486000 0.000000 
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39 1 1.919780 -96.570999 1.427660 
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42 1 0.005111 -95.932602 0.000000 
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54 1 2.567930 -88.272102 0.000000 
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56 1 5.123310 -86.995300 0.000000 
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57 1 5.764040 -85.080002 1.427660 
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58 1 1.294010 -85.718399 0.000000 
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62 1 0.020102 -83.164803 0.000000 
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63 1 0.660844 -81.249496 1.427660 
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64 1 2.575490 -81.887901 0.000000 
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65 1 3.216230 -79.972603 1.427660 
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66 1 5.130870 -80.611099 0.000000 
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67 1 5.771630 -78.695801 1.427660 
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68 1 1.301590 -79.334198 0.000000 
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69 1 1.942350 -77.418900 1.427660 
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70 1 3.856990 -78.057297 0.000000 
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71 1 4.497740 -76.141998 1.427660 
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73 1 0.668470 -74.865196 1.427660 
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74 1 2.583110 -75.503601 0.000000 
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75 1 3.223870 -73.588303 1.427660 
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76 1 5.138510 -74.226700 0.000000 
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78 1 1.309240 -72.949799 0.000000 
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79 1 1.950010 -71.034500 1.427660 
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80 1 3.864640 -71.672997 0.000000 
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81 1 4.505410 -69.757698 1.427660 
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83 1 0.676151 -68.480797 1.427660 
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84 1 2.590780 -69.119202 0.000000 
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85 1 3.231560 -67.203903 1.427660 
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86 1 5.146190 -67.842400 0.000000 
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87 1 5.786980 -65.927002 1.427660 
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88 1 1.316930 -66.565498 0.000000 
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89 1 1.957720 -64.650200 1.427660 
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90 1 3.872350 -65.288597 0.000000 
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91 1 4.513140 -63.373299 1.427660 
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92 1 0.043091 -64.011703 0.000000 
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93 1 0.683885 -62.096401 1.427660 
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94 1 2.598510 -62.734901 0.000000 
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95 1 5.153930 -61.458000 0.000000 
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96 1 3.239310 -60.819599 1.427660 
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98 1 1.324680 -60.181099 0.000000 
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99 1 1.965490 -58.265800 1.427660 
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104 1 2.606300 -56.350498 0.000000 
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106 1 5.161730 -55.073601 0.000000 
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107 1 5.802550 -53.158298 1.427660 
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110 1 3.887930 -52.519901 0.000000 
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111 1 4.528760 -50.604599 1.427660 
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119 1 3.895820 -46.135601 0.000000 
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125 1 3.262900 -41.666599 1.427660 
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126 1 5.177510 -42.305000 0.000000 
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127 1 5.818360 -40.389702 1.427660 
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128 1 1.348300 -41.028099 0.000000 
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129 1 1.989150 -39.112900 1.427660 
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130 1 3.903760 -39.751301 0.000000 
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132 1 0.074546 -38.474499 0.000000 
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133 1 0.715404 -36.559200 1.427660 
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134 1 2.630010 -37.197601 0.000000 
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135 1 3.270870 -35.282398 1.427660 
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136 1 5.185470 -35.920799 0.000000 
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137 1 5.826330 -34.005600 1.427660 
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138 1 1.356260 -34.644001 0.000000 
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144 1 0.723381 -30.175400 1.427660 
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145 1 3.278850 -28.898600 1.427660 
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146 1 5.193450 -29.537001 0.000000 
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147 1 5.834320 -27.621901 1.427660 
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148 1 1.364240 -28.260300 0.000000 
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152 1 0.090508 -25.706800 0.000000 
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154 1 2.645970 -24.430099 0.000000 
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155 1 3.286830 -22.515100 1.427660 
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159 1 2.013090 -19.961599 1.427660 
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161 1 4.568500 -18.685101 1.427660 
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162 1 0.098511 -19.323200 2.855310 
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163 1 0.739356 -17.408100 1.427660 
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164 1 2.653910 -18.046499 0.000000 
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165 1 3.294660 -16.131399 1.427660 
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167 1 1.380180 -15.492800 0.000000 
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168 1 5.849840 -14.855400 1.427660 
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169 1 2.021010 -13.577200 1.427660 
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170 1 3.935270 -14.216300 0.000000 
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171 1 4.575630 -12.301200 1.427660 
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173 1 0.745482 -11.027400 1.427660 
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174 1 2.661980 -11.660800 0.000000 
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175 1 3.303420 -9.742730 1.427660 
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177 1 5.854650 -8.472240 1.427660 
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179 1 2.023040 -7.207600 1.427660 
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180 1 3.946290 -7.820610 0.000000 
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182 1 0.107342 -6.560490 0.000000 
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183 1 0.736295 -4.654560 1.427660 
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184 1 2.661220 -5.308910 0.000000 
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185 1 3.308560 -3.425320 1.427660 
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186 1 5.251020 -3.931570 0.000000 
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187 1 5.922660 -1.878590 1.427660 
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188 1 1.382770 -2.796470 0.000000 
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196 1 2.076100 1.503900 1.427660 
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198 1 4.631090 6.541390 1.427660 
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202 1 3.339920 4.042430 1.427660 
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220 1 0.785341 18.045401 1.427660 
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222 1 3.340590 16.768700 1.427660 
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234 1 5.881280 28.259199 1.427660 
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236 1 2.051960 26.982500 1.427660 
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238 1 3.325920 29.535999 1.427660 
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240 1 0.129844 32.727901 0.000000 
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241 1 0.770558 30.812700 1.427660 
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248 1 4.592330 38.473598 1.427660 
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250 1 0.763037 37.196800 1.427660 
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256 1 2.036940 39.750500 1.427660 
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260 1 0.755441 43.581100 1.427660 
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266 1 2.029320 46.134800 1.427660 
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275 1 1.380860 54.434502 0.000000 
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276 1 2.021640 52.519199 1.427660 
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277 1 3.936280 53.157600 0.000000 
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278 1 4.569340 57.626701 1.427660 
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279 1 0.099290 58.265099 0.000000 
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280 1 0.740080 56.349800 1.427660 
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281 1 2.654710 56.988201 0.000000 
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282 1 3.295490 55.072899 1.427660 
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283 1 5.843170 60.180401 1.427660 
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284 1 1.373120 60.818802 0.000000 
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285 1 2.013920 58.903500 1.427660 
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286 1 3.928540 59.542000 0.000000 
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287 1 5.202370 62.095699 0.000000 
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288 1 4.561560 64.011002 1.427660 
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289 1 0.091508 64.649399 0.000000 
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290 1 0.732316 62.734100 1.427660 
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291 1 2.646940 63.372601 2.855310 
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292 1 3.287740 61.457298 1.427660 
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293 1 5.194550 68.480003 0.000000 
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294 1 5.835370 66.564697 1.427660 
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295 1 1.365310 67.203201 0.000000 
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296 1 2.006130 65.287903 1.427660 
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297 1 3.920750 65.926300 0.000000 
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298 1 4.553720 70.395401 1.427660 
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299 1 0.083667 71.033798 0.000000 
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300 1 0.724493 69.118500 1.427660 
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302 1 3.279930 67.841599 1.427660 
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303 1 5.186670 74.864403 0.000000 
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304 1 5.827510 72.949097 1.427660 
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305 1 1.357450 73.587502 0.000000 
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306 1 1.998280 71.672203 1.427660 
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310 1 4.545830 76.779701 1.427660 
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313 1 5.178740 81.248703 0.000000 
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315 1 1.349520 79.971802 0.000000 
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316 1 1.990370 78.056503 1.427660 
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330 1 0.700700 88.271103 1.427660 
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331 1 2.615300 88.909500 0.000000 
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332 1 3.256160 86.994301 1.427660 
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333 1 1.974440 90.824699 1.427660 
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334 1 5.162780 94.016502 0.000000 
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336 1 1.333580 92.739799 0.000000 
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340 1 0.692713 94.654900 1.427660 
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341 1 2.607320 95.293198 0.000000 
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342 1 3.248180 93.378098 1.427660 
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344 1 5.795650 98.485001 1.427660 
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345 1 1.325590 99.123299 0.000000 
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346 1 1.966450 97.208298 1.427660 
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347 1 3.881050 97.846603 0.000000 
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348 1 4.513920 102.315002 1.427660 
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349 1 0.043927 102.953003 0.000000 
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350 1 0.684743 101.038002 1.427660 
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351 1 2.599330 101.677002 0.000000 
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352 1 3.240190 99.761703 1.427660 
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353 1 5.787860 104.867996 1.427660 
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354 1 1.317770 105.507004 0.000000 
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355 1 1.958510 103.592003 1.427660 
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356 1 3.873070 104.230003 0.000000 
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357 1 3.232240 106.146004 1.427660 
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358 1 5.147260 106.782997 0.000000 
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359 1 4.506900 108.696999 1.427660 
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360 1 0.036794 109.336998 0.000000 
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361 1 0.677159 107.421997 1.427660 
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362 1 2.591410 108.060997 0.000000 
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363 1 5.142450 113.166000 0.000000 
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364 1 5.781540 111.251999 1.427660 
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365 1 1.309010 111.896004 0.000000 
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366 1 1.950450 109.977997 1.427660 
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367 1 3.866940 110.611000 0.000000 
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368 1 4.505080 115.078003 1.427660 
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369 1 0.019188 115.750000 0.000000 
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370 1 0.666139 113.818001 1.427660 
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371 1 2.589390 114.431000 0.000000 
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372 1 3.227590 112.523003 1.427660 
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373 1 5.074440 119.760002 0.000000 
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374 1 5.746080 117.707001 1.427660 
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375 1 1.303870 118.212997 0.000000 
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376 1 1.951210 116.329002 1.427660 
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377 1 3.876130 116.984001 0.000000 
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378 1 0.728234 120.060997 1.427660 
+
379 1 2.656320 120.772003 0.000000 
+
380 1 3.229660 118.842003 1.427660 
+
</pre>
+
|}
+
  
 
=== LAMMPS input script ===
 
=== LAMMPS input script ===

Revision as of 15:53, 28 April 2011

Contents

Abstract

This example shows how to run an atomistic simulation of fracture of an iron symmetric tilt grain boundary. A parallel molecular dynamics code, LAMMPS[1], is used to calculate stresses at the grain boundary as the strain of the bicrystal is incrementally increased. A stress-strain curve is plotted as a result of the simulation.

Author(s): Mark A. Tschopp, Nathan R. Rhodes

Corresponding Author: Mark Tschopp

Input

Description of Simulation

This molecular dynamics simulation calculates the stress-strain relationship of an iron symmetric tilt grain boundary under fracture. The grain boundary structure used in this example is a <100> Σ5(210) symmetric tilt grain boundary. The potential used to generate the structure, the Hepburn and Ackland (2008) Fe-C interatomic potential[2], is also used in this script. The simulation cell is defined such that the bicrystal is pulled in the y-direction, or perpendicular to the boundary interface, to increase strain. The strain in increased for a specified number of times in a loop, and the stress is calculated at each point before the simulation loops. The stress and strain values are output to a separate file which can be imported in a graphing application for plotting.

Grain boundary structure file

The grain boundary structure that was generated prior to this example can be found [Fe_100_sig5_210.txt | here]. Store the text in "Fe_100_sig5_210.txt" to use it.

LAMMPS input script

This input script was run using the November 2010 version of LAMMPS. Changes in some commands in more recent versions may require revision of the input script. This script runs the simulation with a previously generated grain boundary file, which is fed to the variable "datfile." The variable "nloop" defines how many times the strain will be increased and the number of points at which the stress is calculated. To run this script, store it in "in.gb_fracture.txt" and use "lmp_exe < in.gb_fracture.txt" in a UNIX environment where "lmp_exe" refers to the LAMMPS executable.

############################################################################
# Interfacial fracture
# Mark Tschopp, 2010

# lmp_exe -var datfile Fe_100_sig52_10.txt -var strain 0.001 -var nloop 100 -var minlength 20 < in.gb_fracture.txt
############################################################################

variable datfile index Fe_100_sig5_210.txt
variable strain equal 0.001
variable nloop equal 100
#variable repl equal 1
variable strain2 equal "1+v_strain"

######################################
# INITIALIZATION
units 		metal
dimension		3
boundary		p	p	p
atom_style		atomic
atom_modify map array

######################################
# SIMULATION CELL VARIABLES (in Angstroms)

read_data ${datfile}

#variable minlength equal 100
variable xlen equal lx
variable ylen equal ly
variable zlen equal lz

print "lx: ${xlen}"
print "ly: ${ylen}"
print "lz: ${zlen}"

# Determine number of increments for displacement grid in the in-plane GB directions 
variable xrepl equal "ceil(v_minlength / v_xlen)" 
variable zrepl equal "ceil(v_minlength / v_zlen)" 

replicate ${xrepl} 1 ${zrepl}

######################################
# INTERATOMIC POTENTIAL
pair_style	eam/fs
pair_coeff	* * Fe-C_Hepburn_Ackland.eam.fs Fe C

##########################################
# Minimize first?
reset_timestep 0
thermo		10
thermo_style custom step lx ly lz press pxx pyy pzz pe
min_style cg
fix 1 all box/relax x 0.0 z 0.0 couple none vmax 0.001 
minimize 1.0e-25 1.0e-25 1000 10000
unfix 1

variable ly1 equal ly
variable ly0 equal ${ly1}
variable lydelta equal "v_strain*v_ly0/2"

# Setup file output (time in ps, pressure in GPa)
variable p1 equal "(ly-v_ly0)/v_ly0"
variable p2 equal "-pxx/10000"
variable p3 equal "-pyy/10000"
variable p4 equal "-pzz/10000"
variable p5 equal "-pxy/10000"
variable p6 equal "-pxz/10000"
variable p7 equal "-pyz/10000"
variable p8 equal "pe"

fix equil1 all print 1 "${p1} ${p2} ${p3} ${p4} ${p5} ${p6} ${p7} ${p8}" file data.${datfile}_${minlength}.txt screen no
fix 1 all nve
run 1
unfix 1
variable pressf1 equal pyy
variable pressf equal ${pressf1}

##########################################
# MS Deformation loop

variable a loop ${nloop}
label loop

# Increase box bound and minimize again
reset_timestep 0
#displace_box all y scale ${strain2}
#fix 1 all box/relax x 10000.0 z 10000.0 couple none vmax 0.001 
displace_box all y delta -${lydelta} ${lydelta} units box
minimize 1.0e-25 1.0e-25 1000 10000

run 1

print "Pressf: ${pressf}"
variable pdiff equal "pyy - v_pressf"
print "Pressf: ${pressf}"
print "Pdiff: ${pdiff}"
if ${pdiff} > 10000 then "exit"
variable pressf1 equal pyy
variable pressf equal ${pressf1}

next a
jump in.gb_fracture.txt loop 

unfix equil1

######################################
# SIMULATION DONE
print "All done"

Output

LAMMPS datafile

The following file, named "data.Fe_100_sig52_10.txt" should have been created in addition to the log.lammps file. This file stores strain information in the first column, stress tensor information in the second through seventh columns, and stores the total potential energy of the cell in the eight column. The simulation should have looped 100 times (as per the "nloop" variable), so there should be 100 entries (which end at a strain of 0.1) plus the initial entry of stress and strain at zero.

# Fix print output for fix equil1
0 -2.219884235e-05 -0.09436668009 5.407552011e-06 1.221556825e-05 1.110009611e-09 4.462377068e-12 -48716.72405
0.001 0.1468487572 0.1387359115 0.1431841846 -6.180770704e-09 -2.564170766e-12 -2.40791993e-12 -48716.76403
0.002 0.2598702618 0.4058469325 0.2847557426 -4.808171999e-12 9.566142713e-16 -3.41722654e-15 -48716.52319
0.003 0.3720478051 0.6731956939 0.4254156925 1.311052574e-10 3.449206559e-15 -2.636944941e-14 -48716.04581
0.004 0.483977058 0.9402201271 0.5652029445 -6.629325468e-12 1.129857588e-15 2.416966446e-14 -48715.3319
0.005 0.5948099239 1.207643528 0.7041151176 -9.516316287e-13 2.79361336e-15 7.471854238e-15 -48714.38144
...


Post-Processing

Stress-Strain Plot

The stress-strain curve in Figure 1 can be generated using the following MATLAB script. Note that the definitions of stress and strain are negative. This is done to counteract the negative values of compressive stress and strain so that positive axes and a familiar shape are retained. The "exportfig" command saves the plot to a tiff files, but the plot can also be saved as a Mathcad figure once it appears.

% Analyze def1.txt files and plot the responses

d = dir('*.def1.txt');
for i = 1:length(d)
    fname = d(i).name;
    A = importdata(fname);
    strain = -A.data(:,1);
    stress = -A.data(:,2:4);
    
    plot(strain,stress(:,1),'-or','LineWidth',2,'MarkerEdgeColor','r',...
        'MarkerFaceColor','r','MarkerSize',5),hold on
    plot(strain,stress(:,2),'-ob','LineWidth',2,'MarkerEdgeColor','b',...
        'MarkerFaceColor','b','MarkerSize',5),hold on
    plot(strain,stress(:,3),'-og','LineWidth',2,'MarkerEdgeColor','g',...
        'MarkerFacecolor','g','MarkerSize',5),hold on
    axis square
    ylim([0 7])
    xlim([0 0.2])
    set(gca,'LineWidth',2,'FontSize',24,'FontWeight','normal','FontName','Times')
    set(get(gca,'xlabel'),'String','Strain','FontSize',32,'FontWeight','bold','FontName','Times')
    set(get(gca,'ylabel'),'String','Stress (GPa)','FontSize',32','FontWeight','bold','FontName','Times')
    set(gcf,'Position',[1 1 round(1000) round(1000)])
    
    % Export the figure to a tif file
    exportfig(gcf,strrep(fname,'.def1.txt','.tif'),'Format','tiff',...
        'Color','rgb','Resolution',300)
end
Figure 1. Stress-strain curve for uniaxial compressive loading of single crystal aluminum in the <100> loading direction.

Deformation Movie

This assumes that you already have AtomEye and ImageJ downloaded.

  • Visualize the dumpfile in AtomEye by typing the following command, "/A dump.tensile_0.cfg" (UNIX).
  • Use the AtomEye options to select how you want to visualize deformation. In this example, the centrosymmetry parameter was used to show only atoms in a non-centrosymmetric environment (see Fig. 2).
    • Use Alt+0 to activate centrosymmetric (csym) view.
    • Adjust threshold, or set of atoms to view, by using Shift+T. This will allow creation of a set for the current parameter (in this case, csym).
    • Make atoms with values outside of the threshold invisible by using Ctrl+A.
  • Press 'y' within AtomEye to produce an animation script.
  • The folder "Jpg" now contains snapshots of all dumpfiles.
  • Open ImageJ
  • Drag the folder Jpg into ImageJ
    • Select "Convert to RGB" to keep the color from the AtomEye images.
    • Choose "yes" to load a stack.
  • Adjust the size as needed (Image/Adjust/Size)
  • Adjust frame rate as desired (Image/Stacks/Animation Options)
  • Save as Animated Gif file
Figure 2. Image of nucleated dislocation near peak stress.
Movie showing compressive deformation of single crystal aluminum loaded in the <100> direction at a strain rate of 1010 s-1 and a temperature of 300 K. Only atoms in non-centrosymmetric environment are shown.

Cell Size Comparison

In order to test the difference that the number of atoms can have on a simulation, the above script was run with 32,000 and 108,000 atoms in addition 4,000 atoms. Editing the values (currently "10") in the following line in the input script will change the size of the simulation cell and the number of atoms used in the simulation. Values of "20" will result in 32,000 atoms, and values of "30" will result in 108,000 atoms.

region whole block 0 10 0 10 0 10 


Shown below are movies of the 4,000, 32,000, and 108,000 atom simulations, which show only atoms in a non-centrosymmetric environment. As one might expect, more slip planes become visible as the atom count of the simulation increases.

Movie showing compressive deformation of a 4,000 atom single crystal of aluminum loaded in the <100> direction. Only atoms in non-centrosymmetric environment are shown.
File:Al comp 32k.gif
Movie showing compressive deformation of a 32,000 atom single crystal of aluminum loaded in the <100> direction. Only atoms in non- centrosymmetric environment are shown.
Movie showing compressive deformation of a 108,000 atom single crystal of aluminum loaded in the <100> direction. Only atoms in non-centrosymmetric environment are shown.

Temperature Comparison

The temperature of the simulations also makes a difference in the outputs. To show this difference, the above simulations (previously at 300 K) were run at 10 K. In order to change the temperature of the simulation, three lines in the input script must be edited. Two lie under the 'Equilibraion' section while the third lies under 'Deformation.'

The velocity and fix commands shown below contain temperature data. The velocity command specifies the thermal velocity of the system while the fix command specifies the desired temperatures at the beginning and end of the simulation. In order to run the simulation at 10 K instead of 300 K, change the three '300' values to '10' in the velocity and fix command lines.

# EQUILIBRATION
reset_timestep	0
timestep 0.001
velocity all create 300 12345 mom yes rot no
fix 1 all npt temp 300 300 1 iso 0 0 1 drag 1 

The temperature values in the fix command under 'Deformation' also needs to be changed to '10' instead of '300.' The values are being changed again because between 'Equilibration' and 'Deformation' the fix ID 1 was unfixed. Here fix 1 is being redefined.

# DEFORMATION
reset_timestep	0

fix		1 all npt temp 300 300 1 y 0 0 1 z 0 0 1 drag 1

All three simulation cell sizes were run at 10 K. Below are the movies from the simulations. Once again, only atoms in a non-centrosymmetric environment are viewable. The difference between the 300 K and 10 K simulations is that there is less non-centrosymmetry induced by thermal velocity. At 10 K, many fewer atoms are seen before slip occurs, and the slip planes are more cleary visible and absent of "noise" created by atoms that are non-centrosymmetric solely due to thermal activity.

Movie showing compressive deformation of a 4,000 atom single crystal of aluminum at 10 K loaded in the <100> direction. Only atoms in non-centrosymmetric environment are shown.
Movie showing compressive deformation of a 32,000 atom single crystal of aluminum at 10 K loaded in the <100> direction. Only atoms in non-centrosymmetric environment are shown.
Movie showing compressive deformation of a 108,000 atom single crystal of aluminum at 10 Kloaded in the <100> direction. Only atoms in non-centrosymmetric environment are shown.

Go Back

Acknowledgments

The authors would like to acknowledge funding for this work through the Department of Energy.

References

  1. S. Plimpton, "Fast Parallel Algorithms for Short-Range Molecular Dynamics," J. Comp. Phys., 117, 1-19 (1995).
  2. D.J. Hepburn and G.J. Ackland, "Metallic-covalent interatomic potential for carbon in iron," Phys. Rev. B 78, 165115 (2008).
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