potentials/albe.c

   1 /*
   2  * albe.c - albe potential
   3  *
   4  * author: Frank Zirkelbach <frank.zirkelbach@physik.uni-augsburg.de>
   5  *
   6  */
   7
   8 #define _GNU_SOURCE
   9 #include <stdio.h>
  10 #include <stdlib.h>
  11 #include <string.h>
  12 #include <sys/types.h>
  13 #include <sys/stat.h>
  14 #include <fcntl.h>
  15 #include <unistd.h>
  16 #include <math.h>
  17
  18 #include "../moldyn.h"
  19 #include "../math/math.h"
  20 #include "albe.h"
  21
  22 /* create mixed terms from parameters and set them */
  23 int albe_mult_set_params(t_moldyn *moldyn,int element1,int element2) {
  24
  25         t_albe_mult_params *p;
  26
  27         // set cutoff before parameters (actually only necessary for some pots)
  28         if(moldyn->cutoff==0.0) {
  29                 printf("[albe] WARNING: no cutoff!\n");
  30                 return -1;
  31         }
  32
  33         /* alloc mem for potential parameters */
  34         moldyn->pot_params=malloc(sizeof(t_albe_mult_params));
  35         if(moldyn->pot_params==NULL) {
  36                 perror("[albe] pot params alloc");
  37                 return -1;
  38         }
  39
  40         /* these are now albe parameters */
  41         p=moldyn->pot_params;
  42
  43         // only 1 combination by now :p
  44         switch(element1) {
  45                 case SI:
  46                         /* type: silicon */
  47                         p->S[0]=ALBE_S_SI;
  48                         p->R[0]=ALBE_R_SI;
  49                         p->A[0]=ALBE_A_SI;
  50                         p->B[0]=ALBE_B_SI;
  51                         p->r0[0]=ALBE_R0_SI;
  52                         p->lambda[0]=ALBE_LAMBDA_SI;
  53                         p->mu[0]=ALBE_MU_SI;
  54                         p->gamma[0]=ALBE_GAMMA_SI;
  55                         p->c[0]=ALBE_C_SI;
  56                         p->d[0]=ALBE_D_SI;
  57                         p->h[0]=ALBE_H_SI;
  58                         switch(element2) {
  59                                 case C:
  60                                         /* type: carbon */
  61                                         p->S[1]=ALBE_S_C;
  62                                         p->R[1]=ALBE_R_C;
  63                                         p->A[1]=ALBE_A_C;
  64                                         p->B[1]=ALBE_B_C;
  65                                         p->r0[1]=ALBE_R0_C;
  66                                         p->lambda[1]=ALBE_LAMBDA_C;
  67                                         p->mu[1]=ALBE_MU_C;
  68                                         p->gamma[1]=ALBE_GAMMA_C;
  69                                         p->c[1]=ALBE_C_C;
  70                                         p->d[1]=ALBE_D_C;
  71                                         p->h[1]=ALBE_H_C;
  72                                         /* mixed type: silicon carbide */
  73                                         p->Smixed=ALBE_S_SIC;
  74                                         p->Rmixed=ALBE_R_SIC;
  75                                         p->Amixed=ALBE_A_SIC;
  76                                         p->Bmixed=ALBE_B_SIC;
  77                                         p->r0_mixed=ALBE_R0_SIC;
  78                                         p->lambda_m=ALBE_LAMBDA_SIC;
  79                                         p->mu_m=ALBE_MU_SIC;
  80                                         p->gamma_m=ALBE_GAMMA_SIC;
  81                                         p->c_mixed=ALBE_C_SIC;
  82                                         p->d_mixed=ALBE_D_SIC;
  83                                         p->h_mixed=ALBE_H_SIC;
  84                                         break;
  85                                 default:
  86                                         printf("[albe] WARNING: element2\n");
  87                                         return -1;
  88                         }
  89                         break;
  90                 default:
  91                         printf("[albe] WARNING: element1\n");
  92                         return -1;
  93         }
  94
  95         printf("[albe] parameter completion\n");
  96         p->S2[0]=p->S[0]*p->S[0];
  97         p->S2[1]=p->S[1]*p->S[1];
  98         p->S2mixed=p->Smixed*p->Smixed;
  99         p->c2[0]=p->c[0]*p->c[0];
 100         p->c2[1]=p->c[1]*p->c[1];
 101         p->c2_mixed=p->c_mixed*p->c_mixed;
 102         p->d2[0]=p->d[0]*p->d[0];
 103         p->d2[1]=p->d[1]*p->d[1];
 104         p->d2_mixed=p->d_mixed*p->d_mixed;
 105         p->c2d2[0]=p->c2[0]/p->d2[0];
 106         p->c2d2[1]=p->c2[1]/p->d2[1];
 107         p->c2d2_m=p->c2_mixed/p->d2_mixed;
 108
 109         printf("[albe] mult parameter info:\n");
 110         printf("  S (A)  | %f | %f | %f\n",p->S[0],p->S[1],p->Smixed);
 111         printf("  R (A)  | %f | %f | %f\n",p->R[0],p->R[1],p->Rmixed);
 112         printf("  A (eV) | %f | %f | %f\n",p->A[0]/EV,p->A[1]/EV,p->Amixed/EV);
 113         printf("  B (eV) | %f | %f | %f\n",p->B[0]/EV,p->B[1]/EV,p->Bmixed/EV);
 114         printf("  lambda | %f | %f | %f\n",p->lambda[0],p->lambda[1],
 115                                           p->lambda_m);
 116         printf("  mu     | %f | %f | %f\n",p->mu[0],p->mu[1],p->mu_m);
 117         printf("  gamma  | %f | %f\n",p->gamma[0],p->gamma[1]);
 118         printf("  c      | %f | %f\n",p->c[0],p->c[1]);
 119         printf("  d      | %f | %f\n",p->d[0],p->d[1]);
 120         printf("  h      | %f | %f\n",p->h[0],p->h[1]);
 121
 122         return 0;
 123 }
 124
 125 /* albe 3 body potential function (first ij loop) */
 126 int albe_mult_3bp_j1(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
 127
 128         t_albe_mult_params *params;
 129         t_albe_exchange *exchange;
 130         unsigned char brand;
 131         double S2;
 132         t_3dvec dist_ij;
 133         double d_ij2,d_ij;
 134
 135         params=moldyn->pot_params;
 136         exchange=&(params->exchange);
 137
 138         /* reset zeta sum */
 139         exchange->zeta_ij=0.0;
 140
 141         /*
 142          * set ij depending values
 143          */
 144
 145         brand=ai->brand;
 146         if(brand==aj->brand) {
 147                 S2=params->S2[brand];
 148         }
 149         else {
 150                 S2=params->S2mixed;
 151         }
 152
 153         /* dist_ij, d_ij2 */
 154         v3_sub(&dist_ij,&(aj->r),&(ai->r));
 155         if(bc) check_per_bound(moldyn,&dist_ij);
 156         d_ij2=v3_absolute_square(&dist_ij);
 157
 158         /* if d_ij2 > S2 => no force & potential energy contribution */
 159         if(d_ij2>S2) {
 160                 moldyn->run3bp=0;
 161                 return 0;
 162         }
 163
 164         /* d_ij */
 165         d_ij=sqrt(d_ij2);
 166
 167         /* store values */
 168         exchange->dist_ij=dist_ij;
 169         exchange->d_ij2=d_ij2;
 170         exchange->d_ij=d_ij;
 171
 172         /* reset k counter for first k loop */
 173         exchange->kcount=0;
 174
 175         return 0;
 176 }
 177
 178 /* albe 3 body potential function (first k loop) */
 179 int albe_mult_3bp_k1(t_moldyn *moldyn,
 180                      t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
 181
 182         t_albe_mult_params *params;
 183         t_albe_exchange *exchange;
 184         unsigned char brand;
 185         double R,S,S2;
 186         t_3dvec dist_ij,dist_ik;
 187         double d_ik2,d_ik,d_ij;
 188         double cos_theta,h_cos,d2_h_cos2,frac,g,dg,s_r,arg;
 189         double f_c_ik,df_c_ik;
 190         int kcount;
 191
 192         params=moldyn->pot_params;
 193         exchange=&(params->exchange);
 194         kcount=exchange->kcount;
 195
 196         if(kcount>ALBE_MAXN) {
 197                 printf("FATAL: neighbours = %d\n",kcount);
 198                 printf("  -> %d %d %d\n",ai->tag,aj->tag,ak->tag);
 199         }
 200
 201         /* ik constants */
 202         brand=ai->brand;
 203         if(brand==ak->brand) {
 204                 R=params->R[brand];
 205                 S=params->S[brand];
 206                 S2=params->S2[brand];
 207                 /* albe needs i,k depending c,d,h and gamma values */
 208                 exchange->gamma_i=&(params->gamma[brand]);
 209                 exchange->c_i=&(params->c[brand]);
 210                 exchange->d_i=&(params->d[brand]);
 211                 exchange->h_i=&(params->h[brand]);
 212         }
 213         else {
 214                 R=params->Rmixed;
 215                 S=params->Smixed;
 216                 S2=params->S2mixed;
 217                 /* albe needs i,k depending c,d,h and gamma values */
 218                 exchange->gamma_i=&(params->gamma_m);
 219                 exchange->c_i=&(params->c_mixed);
 220                 exchange->d_i=&(params->d_mixed);
 221                 exchange->h_i=&(params->h_mixed);
 222         }
 223         exchange->ci2=*(exchange->c_i)**(exchange->c_i);
 224         exchange->di2=*(exchange->d_i)**(exchange->d_i);
 225         exchange->ci2di2=exchange->ci2/exchange->di2;
 226
 227         /* dist_ik, d_ik2 */
 228         v3_sub(&dist_ik,&(ak->r),&(ai->r));
 229         if(bc) check_per_bound(moldyn,&dist_ik);
 230         d_ik2=v3_absolute_square(&dist_ik);
 231
 232         /* store data for second k loop */
 233         exchange->dist_ik[kcount]=dist_ik;
 234         exchange->d_ik2[kcount]=d_ik2;
 235
 236         /* return if not within cutoff */
 237         if(d_ik2>S2) {
 238                 exchange->kcount++;
 239                 return 0;
 240         }
 241
 242         /* d_ik */
 243         d_ik=sqrt(d_ik2);
 244
 245         /* dist_ij, d_ij */
 246         dist_ij=exchange->dist_ij;
 247         d_ij=exchange->d_ij;
 248
 249         /* cos theta */
 250         cos_theta=v3_scalar_product(&dist_ij,&dist_ik)/(d_ij*d_ik);
 251
 252         /* g_ijk */
 253         h_cos=*(exchange->h_i)+cos_theta; // + in albe formalism
 254         d2_h_cos2=exchange->di2+(h_cos*h_cos);
 255         frac=exchange->ci2/d2_h_cos2;
 256         g=*(exchange->gamma_i)*(1.0+exchange->ci2di2-frac);
 257         dg=2.0*frac**(exchange->gamma_i)*h_cos/d2_h_cos2; // + in albe f..
 258
 259         /* zeta sum += f_c_ik * g_ijk */
 260         if(d_ik<=R) {
 261                 exchange->zeta_ij+=g;
 262                 f_c_ik=1.0;
 263                 df_c_ik=0.0;
 264         }
 265         else {
 266                 s_r=S-R;
 267                 arg=M_PI*(d_ik-R)/s_r;
 268                 f_c_ik=0.5+0.5*cos(arg);
 269                 df_c_ik=0.5*sin(arg)*(M_PI/(s_r*d_ik));
 270                 exchange->zeta_ij+=f_c_ik*g;
 271         }
 272
 273 #ifdef DEBUG
 274         if(ai==&(moldyn->atom[DATOM]))
 275                 printf("zeta_ij: %f %f %f %f\n",f_c_ik*g,f_c_ik,g,d_ik);
 276 #endif
 277
 278         /* store even more data for second k loop */
 279         exchange->g[kcount]=g;
 280         exchange->dg[kcount]=dg;
 281         exchange->d_ik[kcount]=d_ik;
 282         exchange->cos_theta[kcount]=cos_theta;
 283         exchange->f_c_ik[kcount]=f_c_ik;
 284         exchange->df_c_ik[kcount]=df_c_ik;
 285
 286         /* increase k counter */
 287         exchange->kcount++;
 288
 289         return 0;
 290 }
 291
 292 int albe_mult_3bp_j2(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
 293
 294         t_albe_mult_params *params;
 295         t_albe_exchange *exchange;
 296         t_3dvec force;
 297         double f_a,df_a,b,db,f_c,df_c;
 298         double f_r,df_r;
 299         double scale;
 300         double mu,B;
 301         double lambda,A;
 302         double d_ij,r0;
 303         unsigned char brand;
 304         double S,R,s_r,arg;
 305         double energy;
 306
 307         params=moldyn->pot_params;
 308         exchange=&(params->exchange);
 309
 310         brand=aj->brand;
 311         if(brand==ai->brand) {
 312                 S=params->S[brand];
 313                 R=params->R[brand];
 314                 B=params->B[brand];
 315                 A=params->A[brand];
 316                 r0=params->r0[brand];
 317                 mu=params->mu[brand];
 318                 lambda=params->lambda[brand];
 319         }
 320         else {
 321                 S=params->Smixed;
 322                 R=params->Rmixed;
 323                 B=params->Bmixed;
 324                 A=params->Amixed;
 325                 r0=params->r0_mixed;
 326                 mu=params->mu_m;
 327                 lambda=params->lambda_m;
 328         }
 329
 330         d_ij=exchange->d_ij;
 331
 332         /* f_c, df_c */
 333         if(d_ij<R) {
 334                 f_c=1.0;
 335                 df_c=0.0;
 336         }
 337         else {
 338                 s_r=S-R;
 339                 arg=M_PI*(d_ij-R)/s_r;
 340                 f_c=0.5+0.5*cos(arg);
 341                 df_c=0.5*sin(arg)*(M_PI/(s_r*d_ij));
 342         }
 343
 344         /* f_a, df_a */
 345         f_a=-B*exp(-mu*(d_ij-r0));
 346         df_a=mu*f_a/d_ij;
 347
 348         /* f_r, df_r */
 349         f_r=A*exp(-lambda*(d_ij-r0));
 350         df_r=lambda*f_r/d_ij;
 351
 352         /* b, db */
 353         if(exchange->zeta_ij==0.0) {
 354                 b=1.0;
 355                 db=0.0;
 356         }
 357         else {
 358                 b=1.0/sqrt(1.0+exchange->zeta_ij);
 359                 db=-0.5*b/(1.0+exchange->zeta_ij);
 360         }
 361
 362         /* force contribution for atom i */
 363         scale=-0.5*(f_c*(df_r-b*df_a)+df_c*(f_r-b*f_a)); // - in albe formalism
 364         v3_scale(&force,&(exchange->dist_ij),scale);
 365         v3_add(&(ai->f),&(ai->f),&force);
 366
 367         /* force contribution for atom j */
 368         v3_scale(&force,&force,-1.0); // dri rij = - drj rij
 369         v3_add(&(aj->f),&(aj->f),&force);
 370
 371         /* virial */
 372         virial_calc(ai,&force,&(exchange->dist_ij));
 373
 374 #ifdef DEBUG
 375         if((ai==&(moldyn->atom[DATOM]))|(aj==&(moldyn->atom[DATOM]))) {
 376                 printf("force 3bp (j2): [%d %d sum]\n",ai->tag,aj->tag);
 377                 printf("  adding %f %f %f\n",force.x,force.y,force.z);
 378                 if(ai==&(moldyn->atom[DATOM]))
 379                         printf("  total i: %f %f %f\n",ai->f.x,ai->f.y,ai->f.z);
 380                 if(aj==&(moldyn->atom[DATOM]))
 381                         printf("  total j: %f %f %f\n",aj->f.x,aj->f.y,aj->f.z);
 382                 printf("  energy: %f = %f %f %f %f\n",0.5*f_c*(b*f_a+f_r),
 383                                                     f_c,b,f_a,f_r);
 384                 printf("          %f %f %f\n",exchange->zeta_ij,.0,.0);
 385         }
 386 #endif
 387
 388         /* dzeta prefactor = - f_c f_a db, (* -0.5 due to force calc) */
 389         exchange->pre_dzeta=0.5*f_a*f_c*db;
 390
 391         /* energy contribution */
 392         energy=0.5*f_c*(f_r-b*f_a); // - in albe formalism
 393         moldyn->energy+=energy;
 394         ai->e+=energy;
 395
 396         /* reset k counter for second k loop */
 397         exchange->kcount=0;
 398
 399         return 0;
 400 }
 401
 402 /* albe 3 body potential function (second k loop) */
 403 int albe_mult_3bp_k2(t_moldyn *moldyn,
 404                      t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
 405
 406         t_albe_mult_params *params;
 407         t_albe_exchange *exchange;
 408         int kcount;
 409         t_3dvec dist_ik,dist_ij;
 410         double d_ik2,d_ik,d_ij2,d_ij;
 411         unsigned char brand;
 412         double S2;
 413         double g,dg,cos_theta;
 414         double pre_dzeta;
 415         double f_c_ik,df_c_ik;
 416         double dijdik_inv,fcdg,dfcg;
 417         t_3dvec dcosdrj,dcosdrk;
 418         t_3dvec force,tmp;
 419
 420         params=moldyn->pot_params;
 421         exchange=&(params->exchange);
 422         kcount=exchange->kcount;
 423
 424         if(kcount>ALBE_MAXN)
 425                 printf("FATAL: neighbours!\n");
 426
 427         /* d_ik2 */
 428         d_ik2=exchange->d_ik2[kcount];
 429
 430         brand=ak->brand;
 431         if(brand==ai->brand)
 432                 S2=params->S2[brand];
 433         else
 434                 S2=params->S2mixed;
 435
 436         /* return if d_ik > S */
 437         if(d_ik2>S2) {
 438                 exchange->kcount++;
 439                 return 0;
 440         }
 441
 442         /* prefactor dzeta */
 443         pre_dzeta=exchange->pre_dzeta;
 444
 445         /* dist_ik, d_ik */
 446         dist_ik=exchange->dist_ik[kcount];
 447         d_ik=exchange->d_ik[kcount];
 448
 449         /* f_c_ik, df_c_ik */
 450         f_c_ik=exchange->f_c_ik[kcount];
 451         df_c_ik=exchange->df_c_ik[kcount];
 452
 453         /* dist_ij, d_ij2, d_ij */
 454         dist_ij=exchange->dist_ij;
 455         d_ij2=exchange->d_ij2;
 456         d_ij=exchange->d_ij;
 457
 458         /* g, dg, cos_theta */
 459         g=exchange->g[kcount];
 460         dg=exchange->dg[kcount];
 461         cos_theta=exchange->cos_theta[kcount];
 462
 463         /* cos_theta derivatives wrt j,k */
 464         dijdik_inv=1.0/(d_ij*d_ik);
 465         v3_scale(&dcosdrj,&dist_ik,dijdik_inv);         // j
 466         v3_scale(&tmp,&dist_ij,-cos_theta/d_ij2);
 467         v3_add(&dcosdrj,&dcosdrj,&tmp);
 468         v3_scale(&dcosdrk,&dist_ij,dijdik_inv);         // k
 469         v3_scale(&tmp,&dist_ik,-cos_theta/d_ik2);
 470         v3_add(&dcosdrk,&dcosdrk,&tmp);
 471
 472         /* f_c_ik * dg, df_c_ik * g */
 473         fcdg=f_c_ik*dg;
 474         dfcg=df_c_ik*g;
 475
 476         /* derivative wrt j */
 477         v3_scale(&force,&dcosdrj,fcdg*pre_dzeta);
 478
 479         /* force contribution */
 480         v3_add(&(aj->f),&(aj->f),&force);
 481
 482 #ifdef DEBUG
 483         if(aj==&(moldyn->atom[DATOM])) {
 484                 printf("force 3bp (k2): [%d %d %d]\n",ai->tag,aj->tag,ak->tag);
 485                 printf("  adding %f %f %f\n",force.x,force.y,force.z);
 486                 printf("  total j: %f %f %f\n",aj->f.x,aj->f.y,aj->f.z);
 487                 printf("  angle: %f\n",acos(cos_theta)*360.0/(2*M_PI));
 488                 printf("    d ij ik = %f %f\n",d_ij,d_ik);
 489         }
 490 #endif
 491
 492         /* virial */
 493         virial_calc(ai,&force,&dist_ij);
 494
 495         /* force contribution to atom i */
 496         v3_scale(&force,&force,-1.0);
 497         v3_add(&(ai->f),&(ai->f),&force);
 498
 499         /* derivative wrt k */
 500         v3_scale(&force,&dist_ik,-1.0*dfcg); // dri rik = - drk rik
 501         v3_scale(&tmp,&dcosdrk,fcdg);
 502         v3_add(&force,&force,&tmp);
 503         v3_scale(&force,&force,pre_dzeta);
 504
 505         /* force contribution */
 506         v3_add(&(ak->f),&(ak->f),&force);
 507
 508 #ifdef DEBUG
 509         if(ak==&(moldyn->atom[DATOM])) {
 510                 printf("force 3bp (k2): [%d %d %d]\n",ai->tag,aj->tag,ak->tag);
 511                 printf("  adding %f %f %f\n",force.x,force.y,force.z);
 512                 printf("  total k: %f %f %f\n",ak->f.x,ak->f.y,ak->f.z);
 513                 printf("  angle: %f\n",acos(cos_theta)*360.0/(2*M_PI));
 514                 printf("    d ij ik = %f %f\n",d_ij,d_ik);
 515         }
 516 #endif
 517
 518         /* virial */
 519         virial_calc(ai,&force,&dist_ik);
 520
 521         /* force contribution to atom i */
 522         v3_scale(&force,&force,-1.0);
 523         v3_add(&(ai->f),&(ai->f),&force);
 524
 525         /* increase k counter */
 526         exchange->kcount++;
 527
 528         return 0;
 529
 530 }
 531
 532 int albe_mult_check_2b_bond(t_moldyn *moldyn,t_atom *itom,t_atom *jtom,u8 bc) {
 533
 534         t_albe_mult_params *params;
 535         t_3dvec dist;
 536         double d;
 537         u8 brand;
 538
 539         v3_sub(&dist,&(jtom->r),&(itom->r));
 540         if(bc) check_per_bound(moldyn,&dist);
 541         d=v3_absolute_square(&dist);
 542
 543         params=moldyn->pot_params;
 544         brand=itom->brand;
 545
 546         if(brand==jtom->brand) {
 547                 if(d<=params->S2[brand])
 548                         return TRUE;
 549         }
 550         else {
 551                 if(d<=params->S2mixed)
 552                         return TRUE;
 553         }
 554
 555         return FALSE;
 556 }