Liquid Metals: From Atomistic Potentials to Properties, Shock Compression, Earth’s Core and Nanoclusters

Contents......Page 8
Preface......Page 10
List of Abbreviations......Page 12
Introduction......Page 14
1.1. Method of Classical Molecular Dynamics......Page 18
1.2. Method of Static Relaxation......Page 22
1.3. The Ab Initio Method of the Model Creation  (“from the First Principles”)......Page 23
1.4. The Monte–Carlo Method......Page 24
1.5.1. Structural Functions......Page 25
1.5.2. Reverse Monte–Carlo Method......Page 29
1.5.3. Force Algorithm......Page 31
1.5.4. Restoration of Interparticle Potentials According to Diffraction Data.  The Schommers’ Algorithm......Page 32
1.5.5. The Problem of the Uniqueness of the Solution......Page 34
References......Page 39
2.1. Pair Interatomic Potentials......Page 42
2.2. Calculation of the Coulomb Forces......Page 45
2.3. Pseudopotential Calculation of Pair Potentials......Page 49
2.4. Three-Particle Interatomic Potentials......Page 50
2.5. Multiparticle Interatomic Potentials......Page 52
2.6. Ab Initio Calculation of Interparticle Interactions  (“from the First Principles”)......Page 61
References......Page 62
Static Structure Factor (SF)......Page 66
Dynamic Structure Factor......Page 67
Coordination Number......Page 68
Three-Particle Correlation Function......Page 69
The Distribution of Voronoi Polyhedrons......Page 70
The Distribution of Pores......Page 72
The Distribution of Bound Groups......Page 73
Velocity Autocorrelation Function and Density of Vibration States......Page 74
Oscillatory Entropy......Page 76
Viscosity......Page 77
Crystallinity Degree......Page 79
References......Page 81
The Method of Reverse Monte Carlo.  One-Component Systems......Page 84
The Reverse Monte Carlo Method. Binary Systems......Page 86
Approximate BGB and PY Equations......Page 88
Creation of Models of One-Component  Liquids by Schommers, Reatto,  Mendelev–Belashchenko (MB) Methods......Page 89
Other Methods of Simulation According  to Diffraction Data......Page 95
Binary Models......Page 96
The Problem of Unambiguity of Potentials Inference, Applying Diffraction Data......Page 97
Creation of Computer Models and Restoration of Interparticle Potentials of Amorphous Systems......Page 98
“Universal Algorithm”......Page 101
The Case of Multiparticle Potentials......Page 103
References......Page 104
Real Hard-Sphere System (HSS)......Page 108
Computer Simulation of Amorphous HSS......Page 109
Fluid HSS......Page 110
The Binary System of Hard Spheres......Page 111
The Diffusion in HSS......Page 114
Isotopic Effect in Simple Liquids......Page 117
Non-Crystalline Structures with the Inverse Power Potential (“Canonic”)......Page 118
Binary Canonic Structures......Page 122
The Case of Potentials with Negative Curvature......Page 125
References......Page 126
Basic Data......Page 128
Selection of Interparticle Interaction of Liquid Lithium. Pair Contribution......Page 129
Embedding Potential......Page 131
The Creation of Lithium Models......Page 134
Properties of Lithium Models on the Binodal......Page 135
Energy and Pressure......Page 138
Bulk Modulus......Page 142
The Coefficient of Thermal Expansion......Page 143
Grüneisen Coefficient......Page 144
Compressibility Factor......Page 145
Calculation of the Equilibrium Crystal – Liquid......Page 147
Structural Characteristics of the Models  at High Pressures......Page 151
References......Page 153
Basic Data......Page 156
Selection of Interparticle Potential for Liquid Sodium. Pair Contribution......Page 157
Embedding Potential......Page 158
Van Der Waals Loop......Page 162
Properties of Sodium Models on the Binodal......Page 163
Calculations of Thermodynamic Properties......Page 164
Approximation of Data......Page 168
Heat Capacity Cp and Sound Speed......Page 170
Compressibility Factor......Page 172
Transition to Dependences of F(p, T)......Page 174
Structure of Liquid Sodium Models......Page 176
Sodium Melting......Page 177
References......Page 178
Selection of Parameters of Interparticle Interaction. Pair Contribution......Page 182
Embedding Potential......Page 184
The Creation of Potassium Models......Page 185
The States along Hugoniot Adiabat......Page 186
The Calculations of Thermodynamic Properties......Page 187
Compressibility Factor......Page 195
Cold Pressure......Page 196
The Melting of Potassium Models......Page 197
References......Page 198
Basic Data......Page 202
The Selection of Interparticle Interaction  of Liquid Rubidium. Pair Contribution......Page 203
Embedding Potential......Page 204
Van Der Waals Loop......Page 206
The Properties of Rubidium Models on the Binodal......Page 207
The Calculations of Thermodynamic Properties......Page 208
Energy and Pressure......Page 209
Temperature Derivatives......Page 210
Heat Capacity Cp......Page 212
The Coefficient of Thermal Expansion......Page 213
Grüneisen Coefficient......Page 214
Transition to Dependencies F(p,T)......Page 215
The States with the Compressibility Factor Z = 1......Page 216
Structure of Liquid Rubidium Models......Page 217
The Melting of Rubidium Models......Page 218
The Solidification of Rb......Page 219
References......Page 220
Basic Data......Page 224
Selection of Interparticle Interaction of Liquid Cesium. Pair Contribution......Page 225
Embedding Potential......Page 226
The Creation of Cesium Models......Page 228
The States along Hugoniot Adiabat......Page 229
Van Der Waals Loop......Page 231
The Energy and Pressure......Page 232
Heat Capacity Cp and Sound Speed......Page 235
The Coefficient of Thermal Expansion......Page 236
Compressibility Factor Z = pV/RT......Page 237
The Line of Compressibility Factor Z = 1......Page 238
Structure of Liquid Cesium Models......Page 240
Melting Temperature......Page 243
References......Page 244
Basic Data......Page 248
The Selection of Parameters of Interparticle Interaction......Page 249
The Properties of Copper Models under Small Pressure......Page 254
The States Along Hugoniot Adiabat......Page 256
The Calculations of Thermodynamic Properties......Page 257
Melting Temperature......Page 262
References......Page 263
The Selection of Interparticle Interaction Parameters. Pair Contribution......Page 266
Embedding Potential......Page 269
The Properties of Silver Models under Small Pressure......Page 272
The States along Hugoniot Adiabat......Page 273
The Calculations of Thermodynamic Properties......Page 274
Solidification Mechanism......Page 279
References......Page 280
Basic Data......Page 282
The Selection of Interparticle Interaction of Liquid Zinc. Pair Contribution......Page 283
Embedding Potential......Page 284
The Creation of Zinc Models......Page 286
The States along Hugoniot Adiabat......Page 287
The Calculations of Thermodynamic Properties......Page 289
References......Page 293
Basic Data......Page 296
The Selection of Interparticle Potential of  Liquid Mercury. Pair Contribution......Page 299
Embedding Potential......Page 301
The Creation of Mercury Models......Page 302
The Calculations of Thermodynamic Properties......Page 305
Compressibility Factor......Page 311
The Melting of Mercury Models......Page 312
Conclusion......Page 314
References......Page 315
The Selection of Interparticle Potential  of Liquid Aluminum......Page 318
Embedding Potential......Page 320
The Properties of Aluminum Models on the Binodal......Page 322
The States along the Hugoniot Adiabat......Page 324
Structure of Liquid Aluminum Models......Page 328
Melting Temperature......Page 329
Conclusion......Page 330
References......Page 331
Basic Data......Page 334
Embedding Potential......Page 335
The Creation of Gallium Models......Page 338
The Properties of Gallium Models on the Binodal......Page 339
The States along Hugoniot Adiabat......Page 340
The Calculations of Thermodynamic Properties......Page 341
Structure of Liquid Gallium Models......Page 344
Conclusion......Page 345
References......Page 346
Basic Data......Page 348
The Selection of Parameters of Interparticle Interaction. Pair Contribution......Page 349
The Embedding Potential......Page 352
The States along Hugoniot Adiabat......Page 356
The Calculations of Thermodynamic Properties......Page 357
Melting Temperature......Page 361
References......Page 362
Basic Data......Page 364
The Selection of Interparticle Interaction  in the Liquid Lead. Pair Contribution......Page 365
Embedding Potential......Page 367
The Properties of Lead Models on the Binodal......Page 369
The Calculations of Thermodynamic Properties......Page 370
The Isotopic Effect in Diffusion......Page 375
References......Page 376
Basic Data......Page 380
The Selection of Interparticle Interaction of  Liquid Bismuth. Pair Contribution......Page 381
Embedding Potential......Page 383
The Properties of Bismuth Models on the Binodal......Page 385
The States along Hugoniot Adiabat......Page 386
The Calculations of Thermodynamic Properties......Page 387
Conclusion......Page 391
References......Page 392
Basic Data......Page 394
The Selection of Interparticle Interaction  in Liquid Uranium. Pair Contribution......Page 395
The Embedding Potential......Page 397
The Properties of Uranium Models on the Isobar P ≅ 0......Page 400
The States on Hugoniot Adiabat......Page 401
The Calculations of Thermodynamic Properties......Page 402
Melting Line of Uranium......Page 405
Conclusion......Page 409
References......Page 410
Basic Data......Page 412
The Simulation of Liquid Iron at Ambient Pressure. Potential EAM-1......Page 413
The Simulation of Iron Models......Page 415
The Simulation of Compressed States of Iron......Page 418
EAM-2 Potential......Page 419
The Calculations of Thermodynamic Properties,  Applying EAM-2......Page 425
An Evaluation of Electron Influence on Model Properties. EAM-2el Variant......Page 427
Conclusion......Page 431
References......Page 432
Basic Data......Page 436
The Selection of Interparticle Interaction of  Liquid Nickel......Page 440
The States along Hugoniot Adiabat......Page 442
The Calculations of Thermodynamic Properties......Page 444
Melting Line of Nickel Models......Page 449
The EAM-2 Potential......Page 451
Solidification Mechanism......Page 454
Conclusion......Page 455
References......Page 456
Solutions Iron–Carbon......Page 458
The Solutions Iron–Sulfur......Page 464
The Simulation of the Inner Structure of the Earth,  Moon and Jupiter Satellites......Page 471
Solutions Lithium–Lead......Page 475
The Solutions Sodium–Lanthanides......Page 476
The Segregation in Binary Solutions......Page 477
References......Page 481
Calculations of Shock Adiabats......Page 486
Shock Compression of Copper......Page 489
Shock Compression of Cesium......Page 492
Shock Compression of Lead......Page 494
Shock Compression of Nickel......Page 495
Shock Compression of Bismuth......Page 499
Shock Compression of Zinc......Page 500
References......Page 502
Simulation of Nanoclusters......Page 504
The Creation of Models......Page 505
Geometrical Characteristics......Page 506
The Thermodynamic Characteristics of Nanoclusters......Page 508
The Dependence of Cluster Energy on Its Size......Page 513
The Entropy, Helmholtz (A) and Gibbs (G) Energy  of Clusters......Page 517
The Dependence of Clusters Energy on Temperature......Page 520
The Melting of Nanoclusters......Page 522
The Non-Equilibrium Melting and Solidification  of Nanoclusters......Page 527
References......Page 528
Appendix......Page 532
Index......Page 552
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