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
 100         printf("[albe] mult parameter info:\n");
 101         printf("  S (A)  | %f | %f | %f\n",p->S[0],p->S[1],p->Smixed);
 102         printf("  R (A)  | %f | %f | %f\n",p->R[0],p->R[1],p->Rmixed);
 103         printf("  A (eV) | %f | %f | %f\n",p->A[0]/EV,p->A[1]/EV,p->Amixed/EV);
 104         printf("  B (eV) | %f | %f | %f\n",p->B[0]/EV,p->B[1]/EV,p->Bmixed/EV);
 105         printf("  lambda | %f | %f | %f\n",p->lambda[0],p->lambda[1],
 106                                           p->lambda_m);
 107         printf("  mu     | %f | %f | %f\n",p->mu[0],p->mu[1],p->mu_m);
 108         printf("  gamma  | %f | %f\n",p->gamma[0],p->gamma[1]);
 109         printf("  c      | %f | %f\n",p->c[0],p->c[1]);
 110         printf("  d      | %f | %f\n",p->d[0],p->d[1]);
 111         printf("  h      | %f | %f\n",p->h[0],p->h[1]);
 112
 113         return 0;
 114 }
 115
 116 /* albe 3 body potential function (first ij loop) */
 117 int albe_mult_3bp_j1(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
 118
 119         t_albe_mult_params *params;
 120         t_albe_exchange *exchange;
 121         unsigned char brand;
 122         double S2;
 123         t_3dvec dist_ij;
 124         double d_ij2,d_ij;
 125
 126         params=moldyn->pot_params;
 127         exchange=&(params->exchange);
 128
 129         /* reset zeta sum */
 130         exchange->zeta_ij=0.0;
 131
 132         /*
 133          * set ij depending values
 134          */
 135
 136         brand=ai->brand;
 137         if(brand==aj->brand) {
 138                 S2=params->S2[brand];
 139         }
 140         else {
 141                 S2=params->S2mixed;
 142         }
 143
 144         /* dist_ij, d_ij2 */
 145         v3_sub(&dist_ij,&(aj->r),&(ai->r));
 146         if(bc) check_per_bound(moldyn,&dist_ij);
 147         d_ij2=v3_absolute_square(&dist_ij);
 148
 149         /* if d_ij2 > S2 => no force & potential energy contribution */
 150         if(d_ij2>S2) {
 151                 moldyn->run3bp=0;
 152                 return 0;
 153         }
 154
 155         /* d_ij */
 156         d_ij=sqrt(d_ij2);
 157
 158         /* store values */
 159         exchange->dist_ij=dist_ij;
 160         exchange->d_ij2=d_ij2;
 161         exchange->d_ij=d_ij;
 162
 163         /* reset k counter for first k loop */
 164         exchange->kcount=0;
 165
 166         return 0;
 167 }
 168
 169 /* albe 3 body potential function (first k loop) */
 170 int albe_mult_3bp_k1(t_moldyn *moldyn,
 171                      t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
 172
 173         t_albe_mult_params *params;
 174         t_albe_exchange *exchange;
 175         unsigned char brand;
 176         double R,S,S2;
 177         t_3dvec dist_ij,dist_ik;
 178         double d_ik2,d_ik,d_ij;
 179         double cos_theta,h_cos,d2_h_cos2,frac,g,dg,s_r,arg;
 180         double f_c_ik,df_c_ik;
 181         int kcount;
 182
 183         params=moldyn->pot_params;
 184         exchange=&(params->exchange);
 185         kcount=exchange->kcount;
 186
 187         if(kcount>ALBE_MAXN) {
 188                 printf("FATAL: neighbours = %d\n",kcount);
 189                 printf("  -> %d %d %d\n",ai->tag,aj->tag,ak->tag);
 190         }
 191
 192         /* ik constants */
 193         brand=ai->brand;
 194         if(brand==ak->brand) {
 195                 R=params->R[brand];
 196                 S=params->S[brand];
 197                 S2=params->S2[brand];
 198                 /* albe needs i,k depending c,d,h and gamma values */
 199                 exchange->gamma_i=&(params->gamma[brand]);
 200                 exchange->c_i=&(params->c[brand]);
 201                 exchange->d_i=&(params->d[brand]);
 202                 exchange->h_i=&(params->h[brand]);
 203         }
 204         else {
 205                 R=params->Rmixed;
 206                 S=params->Smixed;
 207                 S2=params->S2mixed;
 208                 /* albe needs i,k depending c,d,h and gamma values */
 209                 exchange->gamma_i=&(params->gamma_m);
 210                 exchange->c_i=&(params->c_mixed);
 211                 exchange->d_i=&(params->d_mixed);
 212                 exchange->h_i=&(params->h_mixed);
 213         }
 214         exchange->ci2=*(exchange->c_i)**(exchange->c_i);
 215         exchange->di2=*(exchange->d_i)**(exchange->d_i);
 216         exchange->ci2di2=exchange->ci2/exchange->di2;
 217
 218         /* dist_ik, d_ik2 */
 219         v3_sub(&dist_ik,&(ak->r),&(ai->r));
 220         if(bc) check_per_bound(moldyn,&dist_ik);
 221         d_ik2=v3_absolute_square(&dist_ik);
 222
 223         /* store data for second k loop */
 224         exchange->dist_ik[kcount]=dist_ik;
 225         exchange->d_ik2[kcount]=d_ik2;
 226
 227         /* return if not within cutoff */
 228         if(d_ik2>S2) {
 229                 exchange->kcount++;
 230                 return 0;
 231         }
 232
 233         /* d_ik */
 234         d_ik=sqrt(d_ik2);
 235
 236         /* dist_ij, d_ij */
 237         dist_ij=exchange->dist_ij;
 238         d_ij=exchange->d_ij;
 239
 240         /* cos theta */
 241         cos_theta=v3_scalar_product(&dist_ij,&dist_ik)/(d_ij*d_ik);
 242
 243         /* g_ijk */
 244         h_cos=*(exchange->h_i)+cos_theta; // + in albe formalism
 245         d2_h_cos2=exchange->di2+(h_cos*h_cos);
 246         frac=exchange->ci2/d2_h_cos2;
 247         g=*(exchange->gamma_i)*(1.0+exchange->ci2di2-frac);
 248         dg=2.0*frac**(exchange->gamma_i)*h_cos/d2_h_cos2; // + in albe f..
 249
 250         /* zeta sum += f_c_ik * g_ijk */
 251         if(d_ik<=R) {
 252                 exchange->zeta_ij+=g;
 253                 f_c_ik=1.0;
 254                 df_c_ik=0.0;
 255         }
 256         else {
 257                 s_r=S-R;
 258                 arg=M_PI*(d_ik-R)/s_r;
 259                 f_c_ik=0.5+0.5*cos(arg);
 260                 df_c_ik=0.5*sin(arg)*(M_PI/(s_r*d_ik));
 261                 exchange->zeta_ij+=f_c_ik*g;
 262         }
 263
 264         /* store even more data for second k loop */
 265         exchange->g[kcount]=g;
 266         exchange->dg[kcount]=dg;
 267         exchange->d_ik[kcount]=d_ik;
 268         exchange->cos_theta[kcount]=cos_theta;
 269         exchange->f_c_ik[kcount]=f_c_ik;
 270         exchange->df_c_ik[kcount]=df_c_ik;
 271
 272         /* increase k counter */
 273         exchange->kcount++;
 274
 275         return 0;
 276 }
 277
 278 int albe_mult_3bp_j2(t_moldyn *moldyn,t_atom *ai,t_atom *aj,u8 bc) {
 279
 280         t_albe_mult_params *params;
 281         t_albe_exchange *exchange;
 282         t_3dvec force;
 283         double f_a,df_a,b,db,f_c,df_c;
 284         double f_r,df_r;
 285         double scale;
 286         double mu,B;
 287         double lambda,A;
 288         double d_ij,r0;
 289         unsigned char brand;
 290         double S,R,s_r,arg;
 291         double energy;
 292
 293         params=moldyn->pot_params;
 294         exchange=&(params->exchange);
 295
 296         brand=aj->brand;
 297         if(brand==ai->brand) {
 298                 S=params->S[brand];
 299                 R=params->R[brand];
 300                 B=params->B[brand];
 301                 A=params->A[brand];
 302                 r0=params->r0[brand];
 303                 mu=params->mu[brand];
 304                 lambda=params->lambda[brand];
 305         }
 306         else {
 307                 S=params->Smixed;
 308                 R=params->Rmixed;
 309                 B=params->Bmixed;
 310                 A=params->Amixed;
 311                 r0=params->r0_mixed;
 312                 mu=params->mu_m;
 313                 lambda=params->lambda_m;
 314         }
 315
 316         d_ij=exchange->d_ij;
 317
 318         /* f_c, df_c */
 319         if(d_ij<R) {
 320                 f_c=1.0;
 321                 df_c=0.0;
 322         }
 323         else {
 324                 s_r=S-R;
 325                 arg=M_PI*(d_ij-R)/s_r;
 326                 f_c=0.5+0.5*cos(arg);
 327                 df_c=0.5*sin(arg)*(M_PI/(s_r*d_ij));
 328         }
 329
 330         /* f_a, df_a */
 331         f_a=-B*exp(-mu*(d_ij-r0));
 332         df_a=mu*f_a/d_ij;
 333
 334         /* f_r, df_r */
 335         f_r=A*exp(-lambda*(d_ij-r0));
 336         df_r=lambda*f_r/d_ij;
 337
 338         /* b, db */
 339         if(exchange->zeta_ij==0.0) {
 340                 b=1.0;
 341                 db=0.0;
 342         }
 343         else {
 344                 b=1.0/sqrt(1.0+exchange->zeta_ij);
 345                 db=-0.5*b/(1.0+exchange->zeta_ij);
 346         }
 347
 348         /* force contribution for atom i */
 349         scale=-0.5*(f_c*(df_r-b*df_a)+df_c*(f_r-b*f_a)); // - in albe formalism
 350         v3_scale(&force,&(exchange->dist_ij),scale);
 351         v3_add(&(ai->f),&(ai->f),&force);
 352
 353         /* force contribution for atom j */
 354         v3_scale(&force,&force,-1.0); // dri rij = - drj rij
 355         v3_add(&(aj->f),&(aj->f),&force);
 356
 357         /* virial */
 358         virial_calc(ai,&force,&(exchange->dist_ij));
 359
 360 #ifdef DEBUG
 361 if(moldyn->time>DSTART&&moldyn->time<DEND) {
 362         if((ai==&(moldyn->atom[DATOM]))|(aj==&(moldyn->atom[DATOM]))) {
 363                 printf("force 3bp (j2): [%d %d sum]\n",ai->tag,aj->tag);
 364                 printf("  adding %f %f %f\n",force.x,force.y,force.z);
 365                 if(ai==&(moldyn->atom[0]))
 366                         printf("  total i: %f %f %f\n",ai->f.x,ai->f.y,ai->f.z);
 367                 if(aj==&(moldyn->atom[0]))
 368                         printf("  total j: %f %f %f\n",aj->f.x,aj->f.y,aj->f.z);
 369                 printf("  energy: %f = %f %f %f %f\n",0.5*f_c*(b*f_a+f_r),
 370                                                     f_c,b,f_a,f_r);
 371                 printf("          %f %f %f\n",exchange->zeta_ij,.0,.0);
 372         }
 373 }
 374 #endif
 375
 376         /* dzeta prefactor = - f_c f_a db, (* -0.5 due to force calc) */
 377         exchange->pre_dzeta=0.5*f_a*f_c*db;
 378
 379         /* energy contribution */
 380         energy=0.5*f_c*(f_r-b*f_a); // - in albe formalism
 381         moldyn->energy+=energy;
 382         ai->e+=energy;
 383
 384         /* reset k counter for second k loop */
 385         exchange->kcount=0;
 386
 387         return 0;
 388 }
 389
 390 /* albe 3 body potential function (second k loop) */
 391 int albe_mult_3bp_k2(t_moldyn *moldyn,
 392                      t_atom *ai,t_atom *aj,t_atom *ak,u8 bc) {
 393
 394         t_albe_mult_params *params;
 395         t_albe_exchange *exchange;
 396         int kcount;
 397         t_3dvec dist_ik,dist_ij;
 398         double d_ik2,d_ik,d_ij2,d_ij;
 399         unsigned char brand;
 400         double S2;
 401         double g,dg,cos_theta;
 402         double pre_dzeta;
 403         double f_c_ik,df_c_ik;
 404         double dijdik_inv,fcdg,dfcg;
 405         t_3dvec dcosdrj,dcosdrk;
 406         t_3dvec force,tmp;
 407
 408         params=moldyn->pot_params;
 409         exchange=&(params->exchange);
 410         kcount=exchange->kcount;
 411
 412         if(kcount>ALBE_MAXN)
 413                 printf("FATAL: neighbours!\n");
 414
 415         /* d_ik2 */
 416         d_ik2=exchange->d_ik2[kcount];
 417
 418         brand=ak->brand;
 419         if(brand==ai->brand)
 420                 S2=params->S2[brand];
 421         else
 422                 S2=params->S2mixed;
 423
 424         /* return if d_ik > S */
 425         if(d_ik2>S2) {
 426                 exchange->kcount++;
 427                 return 0;
 428         }
 429
 430         /* prefactor dzeta */
 431         pre_dzeta=exchange->pre_dzeta;
 432
 433         /* dist_ik, d_ik */
 434         dist_ik=exchange->dist_ik[kcount];
 435         d_ik=exchange->d_ik[kcount];
 436
 437         /* f_c_ik, df_c_ik */
 438         f_c_ik=exchange->f_c_ik[kcount];
 439         df_c_ik=exchange->df_c_ik[kcount];
 440
 441         /* dist_ij, d_ij2, d_ij */
 442         dist_ij=exchange->dist_ij;
 443         d_ij2=exchange->d_ij2;
 444         d_ij=exchange->d_ij;
 445
 446         /* g, dg, cos_theta */
 447         g=exchange->g[kcount];
 448         dg=exchange->dg[kcount];
 449         cos_theta=exchange->cos_theta[kcount];
 450
 451         /* cos_theta derivatives wrt j,k */
 452         dijdik_inv=1.0/(d_ij*d_ik);
 453         v3_scale(&dcosdrj,&dist_ik,dijdik_inv);         // j
 454         v3_scale(&tmp,&dist_ij,-cos_theta/d_ij2);
 455         v3_add(&dcosdrj,&dcosdrj,&tmp);
 456         v3_scale(&dcosdrk,&dist_ij,dijdik_inv);         // k
 457         v3_scale(&tmp,&dist_ik,-cos_theta/d_ik2);
 458         v3_add(&dcosdrk,&dcosdrk,&tmp);
 459
 460         /* f_c_ik * dg, df_c_ik * g */
 461         fcdg=f_c_ik*dg;
 462         dfcg=df_c_ik*g;
 463
 464         /* derivative wrt j */
 465         v3_scale(&force,&dcosdrj,fcdg*pre_dzeta);
 466
 467         /* force contribution */
 468         v3_add(&(aj->f),&(aj->f),&force);
 469
 470 #ifdef DEBUG
 471 if(moldyn->time>DSTART&&moldyn->time<DEND) {
 472         if(aj==&(moldyn->atom[DATOM])) {
 473                 printf("force 3bp (k2): [%d %d %d]\n",ai->tag,aj->tag,ak->tag);
 474                 printf("  adding %f %f %f\n",force.x,force.y,force.z);
 475                 printf("  total j: %f %f %f\n",aj->f.x,aj->f.y,aj->f.z);
 476                 printf("  angle: %f\n",acos(cos_theta)*360.0/(2*M_PI));
 477                 printf("    d ij ik = %f %f\n",d_ij,d_ik);
 478         }
 479 }
 480 #endif
 481
 482         /* virial */
 483         virial_calc(ai,&force,&dist_ij);
 484
 485         /* force contribution to atom i */
 486         v3_scale(&force,&force,-1.0);
 487         v3_add(&(ai->f),&(ai->f),&force);
 488
 489         /* derivative wrt k */
 490         v3_scale(&force,&dist_ik,-1.0*dfcg); // dri rik = - drk rik
 491         v3_scale(&tmp,&dcosdrk,fcdg);
 492         v3_add(&force,&force,&tmp);
 493         v3_scale(&force,&force,pre_dzeta);
 494
 495         /* force contribution */
 496         v3_add(&(ak->f),&(ak->f),&force);
 497
 498 #ifdef DEBUG
 499 if(moldyn->time>DSTART&&moldyn->time<DEND) {
 500         if(ak==&(moldyn->atom[DATOM])) {
 501                 printf("force 3bp (k2): [%d %d %d]\n",ai->tag,aj->tag,ak->tag);
 502                 printf("  adding %f %f %f\n",force.x,force.y,force.z);
 503                 printf("  total k: %f %f %f\n",ak->f.x,ak->f.y,ak->f.z);
 504                 printf("  angle: %f\n",acos(cos_theta)*360.0/(2*M_PI));
 505                 printf("    d ij ik = %f %f\n",d_ij,d_ik);
 506         }
 507 }
 508 #endif
 509
 510         /* virial */
 511         virial_calc(ai,&force,&dist_ik);
 512
 513         /* force contribution to atom i */
 514         v3_scale(&force,&force,-1.0);
 515         v3_add(&(ai->f),&(ai->f),&force);
 516
 517         /* increase k counter */
 518         exchange->kcount++;
 519
 520         return 0;
 521
 522 }
 523
 524 int albe_mult_check_2b_bond(t_moldyn *moldyn,t_atom *itom,t_atom *jtom,u8 bc) {
 525
 526         t_albe_mult_params *params;
 527         t_3dvec dist;
 528         double d;
 529         u8 brand;
 530
 531         v3_sub(&dist,&(jtom->r),&(itom->r));
 532         if(bc) check_per_bound(moldyn,&dist);
 533         d=v3_absolute_square(&dist);
 534
 535         params=moldyn->pot_params;
 536         brand=itom->brand;
 537
 538         if(brand==jtom->brand) {
 539                 if(d<=params->S2[brand])
 540                         return TRUE;
 541         }
 542         else {
 543                 if(d<=params->S2mixed)
 544                         return TRUE;
 545         }
 546
 547         return FALSE;
 548 }