781 lines
29 KiB
C++
781 lines
29 KiB
C++
// clang-format off
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/* ----------------------------------------------------------------------
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LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
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https://www.lammps.org/, Sandia National Laboratories
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LAMMPS development team: developers@lammps.org
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Copyright (2003) Sandia Corporation. Under the terms of Contract
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DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
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certain rights in this software. This software is distributed under
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the GNU General Public License.
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See the README file in the top-level LAMMPS directory.
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------------------------------------------------------------------------- */
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#include "meam.h"
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#include "math_special.h"
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#include <algorithm>
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#include <cmath>
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using namespace LAMMPS_NS;
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void MEAM::meam_force(int i, int eflag_global, int eflag_atom, int vflag_global, int vflag_atom,
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double *eng_vdwl, double *eatom, int /*ntype*/, int *type, int *fmap,
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double **scale, double **x, int numneigh, int *firstneigh, int numneigh_full,
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int *firstneigh_full, int fnoffset, double **f, double **vatom,
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double *virial)
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{
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int j, jn, k, kn, kk, m, n, p, q;
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int nv2, nv3, elti, eltj, eltk, ind;
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int eflag_either = eflag_atom || eflag_global;
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int vflag_either = vflag_atom || vflag_global;
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double xitmp, yitmp, zitmp, delij[3], rij2, rij, rij3;
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double v[6], fi[3], fj[3];
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double third, sixth;
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double pp, dUdrij, dUdsij, dUdrijm[3], force, forcem;
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double recip, phi, phip;
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double sij;
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double a1, a1i, a1j, a2, a2i, a2j;
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double a3i, a3j;
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double shpi[3], shpj[3];
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double ai, aj, ro0i, ro0j, invrei, invrej;
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double rhoa0j, drhoa0j, rhoa0i, drhoa0i;
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double rhoa1j, drhoa1j, rhoa1i, drhoa1i;
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double rhoa2j, drhoa2j, rhoa2i, drhoa2i;
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double a3, a3a, rhoa3j, drhoa3j, rhoa3i, drhoa3i;
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double drho0dr1, drho0dr2, drho0ds1, drho0ds2;
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double drho1dr1, drho1dr2, drho1ds1, drho1ds2;
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double drho1drm1[3], drho1drm2[3];
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double drho2dr1, drho2dr2, drho2ds1, drho2ds2;
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double drho2drm1[3], drho2drm2[3];
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double drho3dr1, drho3dr2, drho3ds1, drho3ds2;
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double drho3drm1[3], drho3drm2[3];
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double dt1dr1, dt1dr2, dt1ds1, dt1ds2;
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double dt2dr1, dt2dr2, dt2ds1, dt2ds2;
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double dt3dr1, dt3dr2, dt3ds1, dt3ds2;
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double drhodr1, drhodr2, drhods1, drhods2, drhodrm1[3], drhodrm2[3];
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double arg;
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double arg1i1, arg1j1, arg1i2, arg1j2, arg1i3, arg1j3, arg3i3, arg3j3;
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double dsij1, dsij2, force1, force2;
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double t1i, t2i, t3i, t1j, t2j, t3j;
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double scaleij;
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double rhoa1mj,drhoa1mj,rhoa1mi,drhoa1mi;
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double rhoa2mj,drhoa2mj,rhoa2mi,drhoa2mi;
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double rhoa3mj, drhoa3mj, rhoa3mi, drhoa3mi;
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double arg1i1m, arg1j1m, arg1i2m, arg1j2m, arg1i3m, arg1j3m, arg3i3m, arg3j3m;
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double drho1mdr1, drho1mdr2, drho1mds1, drho1mds2;
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double drho1mdrm1[3], drho1mdrm2[3];
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double drho2mdr1, drho2mdr2, drho2mds1, drho2mds2;
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double drho2mdrm1[3], drho2mdrm2[3];
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double drho3mdr1, drho3mdr2, drho3mds1, drho3mds2;
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double drho3mdrm1[3], drho3mdrm2[3];
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third = 1.0 / 3.0;
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sixth = 1.0 / 6.0;
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// Compute forces atom i
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elti = fmap[type[i]];
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if (elti < 0) return;
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xitmp = x[i][0];
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yitmp = x[i][1];
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zitmp = x[i][2];
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// Treat each pair
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for (jn = 0; jn < numneigh; jn++) {
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j = firstneigh[jn];
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eltj = fmap[type[j]];
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scaleij = scale[type[i]][type[j]];
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if (!iszero(scrfcn[fnoffset + jn]) && eltj >= 0) {
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sij = scrfcn[fnoffset + jn] * fcpair[fnoffset + jn];
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delij[0] = x[j][0] - xitmp;
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delij[1] = x[j][1] - yitmp;
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delij[2] = x[j][2] - zitmp;
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rij2 = delij[0] * delij[0] + delij[1] * delij[1] + delij[2] * delij[2];
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if (rij2 < cutforcesq) {
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rij = sqrt(rij2);
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recip = 1.0 / rij;
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// Compute phi and phip
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ind = eltind[elti][eltj];
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pp = rij * rdrar;
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kk = (int)pp;
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kk = std::min(kk, nrar - 2);
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pp = pp - kk;
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pp = std::min(pp, 1.0);
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phi = ((phirar3[ind][kk] * pp + phirar2[ind][kk]) * pp + phirar1[ind][kk]) * pp + phirar[ind][kk];
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phip = (phirar6[ind][kk] * pp + phirar5[ind][kk]) * pp + phirar4[ind][kk];
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if (eflag_either != 0) {
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double phi_sc = phi * scaleij;
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if (eflag_global != 0)
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*eng_vdwl = *eng_vdwl + phi_sc * sij;
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if (eflag_atom != 0) {
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eatom[i] = eatom[i] + 0.5 * phi_sc * sij;
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eatom[j] = eatom[j] + 0.5 * phi_sc * sij;
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}
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}
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// write(1,*) "force_meamf: phi: ",phi
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// write(1,*) "force_meamf: phip: ",phip
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// Compute pair densities and derivatives
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invrei = 1.0 / re_meam[elti][elti];
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ai = rij * invrei - 1.0;
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ro0i = rho0_meam[elti];
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rhoa0i = ro0i * MathSpecial::fm_exp(-beta0_meam[elti] * ai);
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drhoa0i = -beta0_meam[elti] * invrei * rhoa0i;
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rhoa1i = ro0i * MathSpecial::fm_exp(-beta1_meam[elti] * ai);
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drhoa1i = -beta1_meam[elti] * invrei * rhoa1i;
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rhoa2i = ro0i * MathSpecial::fm_exp(-beta2_meam[elti] * ai);
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drhoa2i = -beta2_meam[elti] * invrei * rhoa2i;
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rhoa3i = ro0i * MathSpecial::fm_exp(-beta3_meam[elti] * ai);
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drhoa3i = -beta3_meam[elti] * invrei * rhoa3i;
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if (msmeamflag) {
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rhoa1mi = ro0i * MathSpecial::fm_exp(-beta1m_meam[elti] * ai) * t1m_meam[elti];
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drhoa1mi = -beta1m_meam[elti] * invrei * rhoa1mi;
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rhoa2mi = ro0i * MathSpecial::fm_exp(-beta2m_meam[elti] * ai) * t2m_meam[elti];
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drhoa2mi = -beta2m_meam[elti] * invrei * rhoa2mi;
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rhoa3mi = ro0i * MathSpecial::fm_exp(-beta3m_meam[elti] * ai) * t3m_meam[elti];
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drhoa3mi = -beta3m_meam[elti] * invrei * rhoa3mi;
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}
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if (elti != eltj) {
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invrej = 1.0 / re_meam[eltj][eltj];
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aj = rij * invrej - 1.0;
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ro0j = rho0_meam[eltj];
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rhoa0j = ro0j * MathSpecial::fm_exp(-beta0_meam[eltj] * aj);
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drhoa0j = -beta0_meam[eltj] * invrej * rhoa0j;
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rhoa1j = ro0j * MathSpecial::fm_exp(-beta1_meam[eltj] * aj);
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drhoa1j = -beta1_meam[eltj] * invrej * rhoa1j;
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rhoa2j = ro0j * MathSpecial::fm_exp(-beta2_meam[eltj] * aj);
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drhoa2j = -beta2_meam[eltj] * invrej * rhoa2j;
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rhoa3j = ro0j * MathSpecial::fm_exp(-beta3_meam[eltj] * aj);
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drhoa3j = -beta3_meam[eltj] * invrej * rhoa3j;
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if (msmeamflag) {
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rhoa1mj = ro0j * t1m_meam[eltj] * MathSpecial::fm_exp(-beta1m_meam[eltj] * aj);
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drhoa1mj = -beta1m_meam[eltj] * invrej * rhoa1mj;
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rhoa2mj = ro0j * t2m_meam[eltj] * MathSpecial::fm_exp(-beta2m_meam[eltj] * aj);
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drhoa2mj = -beta2m_meam[eltj] * invrej * rhoa2mj;
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rhoa3mj = ro0j * t3m_meam[eltj] * MathSpecial::fm_exp(-beta3m_meam[eltj] * aj);
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drhoa3mj = -beta3m_meam[eltj] * invrej * rhoa3mj;
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}
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} else {
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rhoa0j = rhoa0i;
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drhoa0j = drhoa0i;
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rhoa1j = rhoa1i;
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drhoa1j = drhoa1i;
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rhoa2j = rhoa2i;
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drhoa2j = drhoa2i;
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rhoa3j = rhoa3i;
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drhoa3j = drhoa3i;
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if (msmeamflag) {
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rhoa1mj = rhoa1mi;
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drhoa1mj = drhoa1mi;
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rhoa2mj = rhoa2mi;
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drhoa2mj = drhoa2mi;
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rhoa3mj = rhoa3mi;
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drhoa3mj = drhoa3mi;
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}
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}
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const double t1mi = t1_meam[elti];
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const double t2mi = t2_meam[elti];
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const double t3mi = t3_meam[elti];
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const double t1mj = t1_meam[eltj];
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const double t2mj = t2_meam[eltj];
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const double t3mj = t3_meam[eltj];
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// ialloy mod not needed in MS-MEAM, but similarity here is that we multply rhos by t.
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// We did this above with rhoa1mj, rhoa2mj, etc.
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if (ialloy == 1 || msmeamflag) {
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rhoa1j *= t1mj;
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rhoa2j *= t2mj;
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rhoa3j *= t3mj;
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rhoa1i *= t1mi;
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rhoa2i *= t2mi;
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rhoa3i *= t3mi;
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drhoa1j *= t1mj;
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drhoa2j *= t2mj;
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drhoa3j *= t3mj;
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drhoa1i *= t1mi;
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drhoa2i *= t2mi;
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drhoa3i *= t3mi;
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}
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nv2 = 0;
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nv3 = 0;
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arg1i1 = 0.0;
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arg1j1 = 0.0;
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arg1i2 = 0.0;
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arg1j2 = 0.0;
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arg1i3 = 0.0;
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arg1j3 = 0.0;
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arg3i3 = 0.0;
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arg3j3 = 0.0;
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for (n = 0; n < 3; n++) {
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for (p = n; p < 3; p++) {
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for (q = p; q < 3; q++) {
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arg = delij[n] * delij[p] * delij[q] * v3D[nv3];
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arg1i3 = arg1i3 + arho3[i][nv3] * arg;
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arg1j3 = arg1j3 - arho3[j][nv3] * arg;
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nv3 = nv3 + 1;
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}
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arg = delij[n] * delij[p] * v2D[nv2];
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arg1i2 = arg1i2 + arho2[i][nv2] * arg;
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arg1j2 = arg1j2 + arho2[j][nv2] * arg;
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nv2 = nv2 + 1;
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}
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arg1i1 = arg1i1 + arho1[i][n] * delij[n];
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arg1j1 = arg1j1 - arho1[j][n] * delij[n];
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arg3i3 = arg3i3 + arho3b[i][n] * delij[n];
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arg3j3 = arg3j3 - arho3b[j][n] * delij[n];
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}
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// msmeam arhom args
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nv2 = 0;
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nv3 = 0;
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arg1i1m = 0.0;
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arg1j1m = 0.0;
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arg1i2m = 0.0;
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arg1j2m = 0.0;
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arg1i3m = 0.0;
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arg1j3m = 0.0;
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arg3i3m = 0.0;
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arg3j3m = 0.0;
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if (msmeamflag) {
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for (n = 0; n < 3; n++) {
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for (p = n; p < 3; p++) {
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for (q = p; q < 3; q++) {
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arg = delij[n] * delij[p] * delij[q] * v3D[nv3];
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arg1i3m = arg1i3m - arho3m[i][nv3] * arg;
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arg1j3m = arg1j3m + arho3m[j][nv3] * arg;
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nv3 = nv3 + 1;
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}
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arg = delij[n] * delij[p] * v2D[nv2];
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arg1i2m = arg1i2m + arho2m[i][nv2] * arg;
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arg1j2m = arg1j2m + arho2m[j][nv2] * arg;
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nv2 = nv2 + 1;
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}
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arg1i1m = arg1i1m - arho1m[i][n] * delij[n];
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arg1j1m = arg1j1m + arho1m[j][n] * delij[n];
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arg3i3m = arg3i3m - arho3mb[i][n] * delij[n];
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arg3j3m = arg3j3m + arho3mb[j][n] * delij[n];
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}
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}
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// rho0 terms
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drho0dr1 = drhoa0j * sij;
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drho0dr2 = drhoa0i * sij;
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// rho1 terms
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a1 = 2 * sij / rij;
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drho1dr1 = a1 * (drhoa1j - rhoa1j / rij) * arg1i1;
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drho1dr2 = a1 * (drhoa1i - rhoa1i / rij) * arg1j1;
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a1 = 2.0 * sij / rij;
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for (m = 0; m < 3; m++) {
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drho1drm1[m] = a1 * rhoa1j * arho1[i][m];
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drho1drm2[m] = -a1 * rhoa1i * arho1[j][m];
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}
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// rho2 terms
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a2 = 2 * sij / rij2;
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drho2dr1 = a2 * (drhoa2j - 2 * rhoa2j / rij) * arg1i2 - 2.0 / 3.0 * arho2b[i] * drhoa2j * sij;
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drho2dr2 = a2 * (drhoa2i - 2 * rhoa2i / rij) * arg1j2 - 2.0 / 3.0 * arho2b[j] * drhoa2i * sij;
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a2 = 4 * sij / rij2;
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for (m = 0; m < 3; m++) {
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drho2drm1[m] = 0.0;
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drho2drm2[m] = 0.0;
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for (n = 0; n < 3; n++) {
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drho2drm1[m] = drho2drm1[m] + arho2[i][vind2D[m][n]] * delij[n];
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drho2drm2[m] = drho2drm2[m] - arho2[j][vind2D[m][n]] * delij[n];
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}
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drho2drm1[m] = a2 * rhoa2j * drho2drm1[m];
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drho2drm2[m] = -a2 * rhoa2i * drho2drm2[m];
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}
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// rho3 terms
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rij3 = rij * rij2;
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a3 = 2 * sij / rij3;
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a3a = 6.0 / 5.0 * sij / rij;
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drho3dr1 = a3 * (drhoa3j - 3 * rhoa3j / rij) * arg1i3 - a3a * (drhoa3j - rhoa3j / rij) * arg3i3;
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drho3dr2 = a3 * (drhoa3i - 3 * rhoa3i / rij) * arg1j3 - a3a * (drhoa3i - rhoa3i / rij) * arg3j3;
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a3 = 6 * sij / rij3;
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a3a = 6 * sij / (5 * rij);
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for (m = 0; m < 3; m++) {
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drho3drm1[m] = 0.0;
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drho3drm2[m] = 0.0;
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nv2 = 0;
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for (n = 0; n < 3; n++) {
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for (p = n; p < 3; p++) {
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arg = delij[n] * delij[p] * v2D[nv2];
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drho3drm1[m] = drho3drm1[m] + arho3[i][vind3D[m][n][p]] * arg;
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drho3drm2[m] = drho3drm2[m] + arho3[j][vind3D[m][n][p]] * arg;
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nv2 = nv2 + 1;
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}
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}
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drho3drm1[m] = (a3 * drho3drm1[m] - a3a * arho3b[i][m]) * rhoa3j;
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drho3drm2[m] = (-a3 * drho3drm2[m] + a3a * arho3b[j][m]) * rhoa3i;
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}
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if (msmeamflag) {
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// rho1m terms
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a1 = 2 * sij / rij;
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drho1mdr1 = a1 * (drhoa1mj - rhoa1mj / rij) * arg1i1m;
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drho1mdr2 = a1 * (drhoa1mi - rhoa1mi / rij) * arg1j1m;
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drho1mdr1 *= -1.0;
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drho1mdr2 *= -1.0;
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a1 = 2.0 * sij / rij;
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for (m = 0; m < 3; m++) {
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drho1mdrm1[m] = a1 * rhoa1mj * arho1m[i][m];
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drho1mdrm2[m] = -a1 * rhoa1mi * arho1m[j][m];
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}
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// rho2m terms
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a2 = 2 * sij / rij2;
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drho2mdr1 = a2 * (drhoa2mj - 2 * rhoa2mj / rij) * arg1i2m - 2.0 / 3.0 * arho2mb[i] * drhoa2mj * sij;
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drho2mdr2 = a2 * (drhoa2mi - 2 * rhoa2mi / rij) * arg1j2m - 2.0 / 3.0 * arho2mb[j] * drhoa2mi * sij;
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a2 = 4 * sij / rij2;
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for (m = 0; m < 3; m++) {
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drho2mdrm1[m] = 0.0;
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drho2mdrm2[m] = 0.0;
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for (n = 0; n < 3; n++) {
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drho2mdrm1[m] += arho2m[i][vind2D[m][n]] * delij[n];
|
|
drho2mdrm2[m] -= arho2m[j][vind2D[m][n]] * delij[n];
|
|
}
|
|
drho2mdrm1[m] = a2 * rhoa2mj * drho2mdrm1[m];
|
|
drho2mdrm2[m] = -a2 * rhoa2mi * drho2mdrm2[m];
|
|
}
|
|
|
|
// rho3m terms
|
|
rij3 = rij * rij2;
|
|
a3 = 2 * sij / rij3;
|
|
a3a = 6.0 / 5.0 * sij / rij;
|
|
drho3mdr1 = a3 * (drhoa3mj - 3 * rhoa3mj / rij) * arg1i3m - a3a * (drhoa3mj - rhoa3mj / rij) * arg3i3m;
|
|
drho3mdr2 = a3 * (drhoa3mi - 3 * rhoa3mi / rij) * arg1j3m - a3a * (drhoa3mi - rhoa3mi / rij) * arg3j3m;
|
|
drho3mdr1 *= -1.0;
|
|
drho3mdr2 *= -1.0;
|
|
|
|
a3 = 6 * sij / rij3;
|
|
a3a = 6 * sij / (5 * rij);
|
|
for (m = 0; m < 3; m++) {
|
|
drho3mdrm1[m] = 0.0;
|
|
drho3mdrm2[m] = 0.0;
|
|
nv2 = 0;
|
|
for (n = 0; n < 3; n++) {
|
|
for (p = n; p < 3; p++) {
|
|
arg = delij[n] * delij[p] * v2D[nv2];
|
|
drho3mdrm1[m] += arho3m[i][vind3D[m][n][p]] * arg;
|
|
drho3mdrm2[m] += arho3m[j][vind3D[m][n][p]] * arg;
|
|
nv2 = nv2 + 1;
|
|
}
|
|
}
|
|
drho3mdrm1[m] = (a3 * drho3mdrm1[m] - a3a * arho3mb[i][m]) * rhoa3mj;
|
|
drho3mdrm2[m] = (-a3 * drho3mdrm2[m] + a3a * arho3mb[j][m]) * rhoa3mi;
|
|
}
|
|
} else {
|
|
for (m = 0; m < 3; m++) {
|
|
drho1mdrm1[m] = 0.0;
|
|
drho1mdrm2[m] = 0.0;
|
|
drho2mdrm1[m] = 0.0;
|
|
drho2mdrm2[m] = 0.0;
|
|
drho3mdrm1[m] = 0.0;
|
|
drho3mdrm2[m] = 0.0;
|
|
}
|
|
}
|
|
|
|
// compute derivatives of weighting functions t wrt rij
|
|
// weighting functions t set to unity for MS-MEAM
|
|
|
|
if (msmeamflag) {
|
|
|
|
t1i = 1.0;
|
|
t2i = 1.0;
|
|
t3i = 1.0;
|
|
t1j = 1.0;
|
|
t2j = 1.0;
|
|
t3j = 1.0;
|
|
dt1dr1 = 0.0;
|
|
dt1dr2 = 0.0;
|
|
dt2dr1 = 0.0;
|
|
dt2dr2 = 0.0;
|
|
dt3dr1 = 0.0;
|
|
dt3dr2 = 0.0;
|
|
|
|
} else {
|
|
|
|
t1i = t_ave[i][0];
|
|
t2i = t_ave[i][1];
|
|
t3i = t_ave[i][2];
|
|
t1j = t_ave[j][0];
|
|
t2j = t_ave[j][1];
|
|
t3j = t_ave[j][2];
|
|
|
|
if (ialloy == 1) {
|
|
|
|
a1i = fdiv_zero(drhoa0j * sij, tsq_ave[i][0]);
|
|
a1j = fdiv_zero(drhoa0i * sij, tsq_ave[j][0]);
|
|
a2i = fdiv_zero(drhoa0j * sij, tsq_ave[i][1]);
|
|
a2j = fdiv_zero(drhoa0i * sij, tsq_ave[j][1]);
|
|
a3i = fdiv_zero(drhoa0j * sij, tsq_ave[i][2]);
|
|
a3j = fdiv_zero(drhoa0i * sij, tsq_ave[j][2]);
|
|
|
|
dt1dr1 = a1i * (t1mj - t1i * MathSpecial::square(t1mj));
|
|
dt1dr2 = a1j * (t1mi - t1j * MathSpecial::square(t1mi));
|
|
dt2dr1 = a2i * (t2mj - t2i * MathSpecial::square(t2mj));
|
|
dt2dr2 = a2j * (t2mi - t2j * MathSpecial::square(t2mi));
|
|
dt3dr1 = a3i * (t3mj - t3i * MathSpecial::square(t3mj));
|
|
dt3dr2 = a3j * (t3mi - t3j * MathSpecial::square(t3mi));
|
|
|
|
} else if (ialloy == 2) {
|
|
|
|
dt1dr1 = 0.0;
|
|
dt1dr2 = 0.0;
|
|
dt2dr1 = 0.0;
|
|
dt2dr2 = 0.0;
|
|
dt3dr1 = 0.0;
|
|
dt3dr2 = 0.0;
|
|
|
|
} else {
|
|
|
|
ai = 0.0;
|
|
if (!iszero(rho0[i]))
|
|
ai = drhoa0j * sij / rho0[i];
|
|
aj = 0.0;
|
|
if (!iszero(rho0[j]))
|
|
aj = drhoa0i * sij / rho0[j];
|
|
|
|
dt1dr1 = ai * (t1mj - t1i);
|
|
dt1dr2 = aj * (t1mi - t1j);
|
|
dt2dr1 = ai * (t2mj - t2i);
|
|
dt2dr2 = aj * (t2mi - t2j);
|
|
dt3dr1 = ai * (t3mj - t3i);
|
|
dt3dr2 = aj * (t3mi - t3j);
|
|
}
|
|
|
|
}
|
|
|
|
// Compute derivatives of total density wrt rij, sij and rij(3)
|
|
get_shpfcn(lattce_meam[elti][elti], stheta_meam[elti][elti], ctheta_meam[elti][elti], shpi);
|
|
get_shpfcn(lattce_meam[eltj][eltj], stheta_meam[elti][elti], ctheta_meam[elti][elti], shpj);
|
|
|
|
if (msmeamflag) {
|
|
drhodr1 = dgamma1[i] * drho0dr1 +
|
|
dgamma2[i] * (dt1dr1 * rho1[i] + t1i * (drho1dr1 - drho1mdr1) +
|
|
dt2dr1 * rho2[i] + t2i * (drho2dr1 - drho2mdr1) +
|
|
dt3dr1 * rho3[i] + t3i * (drho3dr1 - drho3mdr1)) -
|
|
dgamma3[i] * (shpi[0] * dt1dr1 + shpi[1] * dt2dr1 + shpi[2] * dt3dr1);
|
|
drhodr2 = dgamma1[j] * drho0dr2 +
|
|
dgamma2[j] * (dt1dr2 * rho1[j] + t1j * (drho1dr2 - drho1mdr2) +
|
|
dt2dr2 * rho2[j] + t2j * (drho2dr2 - drho2mdr2) +
|
|
dt3dr2 * rho3[j] + t3j * (drho3dr2 - drho3mdr2)) -
|
|
dgamma3[j] * (shpj[0] * dt1dr2 + shpj[1] * dt2dr2 + shpj[2] * dt3dr2);
|
|
for (m = 0; m < 3; m++) {
|
|
drhodrm1[m] = 0.0;
|
|
drhodrm2[m] = 0.0;
|
|
drhodrm1[m] = dgamma2[i] * (t1i * (drho1drm1[m] - drho1mdrm1[m]) +
|
|
t2i * (drho2drm1[m] - drho2mdrm1[m]) +
|
|
t3i * (drho3drm1[m] - drho3mdrm1[m]) );
|
|
drhodrm2[m] = dgamma2[j] * (t1j * (drho1drm2[m] - drho1mdrm2[m]) +
|
|
t2j * (drho2drm2[m] - drho2mdrm2[m]) +
|
|
t3j * (drho3drm2[m] - drho3mdrm2[m]) );
|
|
}
|
|
} else {
|
|
|
|
drhodr1 = dgamma1[i] * drho0dr1 +
|
|
dgamma2[i] * (dt1dr1 * rho1[i] + t1i * drho1dr1 + dt2dr1 * rho2[i] + t2i * drho2dr1 +
|
|
dt3dr1 * rho3[i] + t3i * drho3dr1) -
|
|
dgamma3[i] * (shpi[0] * dt1dr1 + shpi[1] * dt2dr1 + shpi[2] * dt3dr1);
|
|
drhodr2 = dgamma1[j] * drho0dr2 +
|
|
dgamma2[j] * (dt1dr2 * rho1[j] + t1j * drho1dr2 + dt2dr2 * rho2[j] + t2j * drho2dr2 +
|
|
dt3dr2 * rho3[j] + t3j * drho3dr2) -
|
|
dgamma3[j] * (shpj[0] * dt1dr2 + shpj[1] * dt2dr2 + shpj[2] * dt3dr2);
|
|
for (m = 0; m < 3; m++) {
|
|
drhodrm1[m] = 0.0;
|
|
drhodrm2[m] = 0.0;
|
|
drhodrm1[m] = dgamma2[i] * (t1i * drho1drm1[m] + t2i * drho2drm1[m] + t3i * drho3drm1[m]);
|
|
drhodrm2[m] = dgamma2[j] * (t1j * drho1drm2[m] + t2j * drho2drm2[m] + t3j * drho3drm2[m]);
|
|
}
|
|
}
|
|
|
|
// Compute derivatives wrt sij, but only if necessary
|
|
if (!iszero(dscrfcn[fnoffset + jn])) {
|
|
drho0ds1 = rhoa0j;
|
|
drho0ds2 = rhoa0i;
|
|
a1 = 2.0 / rij;
|
|
a2 = 2.0 / rij2;
|
|
a3 = 2.0 / rij3;
|
|
a3a = 6.0 / (5.0 * rij);
|
|
|
|
drho1ds1 = a1 * rhoa1j * arg1i1;
|
|
drho1ds2 = a1 * rhoa1i * arg1j1;
|
|
drho2ds1 = a2 * rhoa2j * arg1i2 - 2.0 / 3.0 * arho2b[i] * rhoa2j;
|
|
drho2ds2 = a2 * rhoa2i * arg1j2 - 2.0 / 3.0 * arho2b[j] * rhoa2i;
|
|
drho3ds1 = a3 * rhoa3j * arg1i3 - a3a * rhoa3j * arg3i3;
|
|
drho3ds2 = a3 * rhoa3i * arg1j3 - a3a * rhoa3i * arg3j3;
|
|
|
|
if (msmeamflag) {
|
|
|
|
drho1mds1 = a1 * rhoa1mj * arg1i1m;
|
|
drho1mds2 = a1 * rhoa1mi * arg1j1m;
|
|
drho2mds1 = a2 * rhoa2mj * arg1i2m - 2.0 / 3.0 * arho2mb[i] * rhoa2mj;
|
|
drho2mds2 = a2 * rhoa2mi * arg1j2m - 2.0 / 3.0 * arho2mb[j] * rhoa2mi;
|
|
drho3mds1 = a3 * rhoa3mj * arg1i3m - a3a * rhoa3mj * arg3i3m;
|
|
drho3mds2 = a3 * rhoa3mi * arg1j3m - a3a * rhoa3mi * arg3j3m;
|
|
drho1mds1 *= -1;
|
|
drho1mds2 *= -1;
|
|
drho3mds1 *= -1;
|
|
drho3mds2 *= -1;
|
|
|
|
t1i = 1.0;
|
|
t2i = 1.0;
|
|
t3i = 1.0;
|
|
t1j = 1.0;
|
|
t2j = 1.0;
|
|
t3j = 1.0;
|
|
dt1dr1 = 0.0;
|
|
dt1dr2 = 0.0;
|
|
dt2dr1 = 0.0;
|
|
dt2dr2 = 0.0;
|
|
dt3dr1 = 0.0;
|
|
dt3dr2 = 0.0;
|
|
|
|
// these formulae are simplifed by substituting t=1, dt=0 from above
|
|
|
|
drhods1 = dgamma1[i] * drho0ds1 + dgamma2[i]
|
|
* ((drho1ds1 - drho1mds1) + (drho2ds1 - drho2mds1) + (drho3ds1 - drho3mds1));
|
|
drhods2 = dgamma1[j] * drho0ds2 + dgamma2[j]
|
|
* ((drho1ds2 - drho1mds2) + (drho2ds2 - drho2mds2) + (drho3ds2 - drho3mds2));
|
|
} else {
|
|
|
|
drho1mds1 = 0.0;
|
|
drho1mds2 = 0.0;
|
|
drho2mds1 = 0.0;
|
|
drho2mds2 = 0.0;
|
|
drho3mds1 = 0.0;
|
|
drho3mds2 = 0.0;
|
|
|
|
if (ialloy == 1) {
|
|
|
|
a1i = fdiv_zero(rhoa0j, tsq_ave[i][0]);
|
|
a1j = fdiv_zero(rhoa0i, tsq_ave[j][0]);
|
|
a2i = fdiv_zero(rhoa0j, tsq_ave[i][1]);
|
|
a2j = fdiv_zero(rhoa0i, tsq_ave[j][1]);
|
|
a3i = fdiv_zero(rhoa0j, tsq_ave[i][2]);
|
|
a3j = fdiv_zero(rhoa0i, tsq_ave[j][2]);
|
|
|
|
dt1ds1 = a1i * (t1mj - t1i * MathSpecial::square(t1mj));
|
|
dt1ds2 = a1j * (t1mi - t1j * MathSpecial::square(t1mi));
|
|
dt2ds1 = a2i * (t2mj - t2i * MathSpecial::square(t2mj));
|
|
dt2ds2 = a2j * (t2mi - t2j * MathSpecial::square(t2mi));
|
|
dt3ds1 = a3i * (t3mj - t3i * MathSpecial::square(t3mj));
|
|
dt3ds2 = a3j * (t3mi - t3j * MathSpecial::square(t3mi));
|
|
|
|
} else if (ialloy == 2) {
|
|
|
|
dt1ds1 = 0.0;
|
|
dt1ds2 = 0.0;
|
|
dt2ds1 = 0.0;
|
|
dt2ds2 = 0.0;
|
|
dt3ds1 = 0.0;
|
|
dt3ds2 = 0.0;
|
|
|
|
} else {
|
|
|
|
ai = 0.0;
|
|
if (!iszero(rho0[i])) ai = rhoa0j / rho0[i];
|
|
aj = 0.0;
|
|
if (!iszero(rho0[j])) aj = rhoa0i / rho0[j];
|
|
|
|
dt1ds1 = ai * (t1mj - t1i);
|
|
dt1ds2 = aj * (t1mi - t1j);
|
|
dt2ds1 = ai * (t2mj - t2i);
|
|
dt2ds2 = aj * (t2mi - t2j);
|
|
dt3ds1 = ai * (t3mj - t3i);
|
|
dt3ds2 = aj * (t3mi - t3j);
|
|
}
|
|
|
|
drhods1 = dgamma1[i] * drho0ds1 +
|
|
dgamma2[i] * (dt1ds1 * rho1[i] + t1i * drho1ds1 + dt2ds1 * rho2[i] + t2i * drho2ds1 +
|
|
dt3ds1 * rho3[i] + t3i * drho3ds1) -
|
|
dgamma3[i] * (shpi[0] * dt1ds1 + shpi[1] * dt2ds1 + shpi[2] * dt3ds1);
|
|
drhods2 = dgamma1[j] * drho0ds2 +
|
|
dgamma2[j] * (dt1ds2 * rho1[j] + t1j * drho1ds2 + dt2ds2 * rho2[j] + t2j * drho2ds2 +
|
|
dt3ds2 * rho3[j] + t3j * drho3ds2) -
|
|
dgamma3[j] * (shpj[0] * dt1ds2 + shpj[1] * dt2ds2 + shpj[2] * dt3ds2);
|
|
}
|
|
}
|
|
|
|
// Compute derivatives of energy wrt rij, sij and rij[3]
|
|
// MS-MEAM affects phip
|
|
|
|
dUdrij = phip * sij + frhop[i] * drhodr1 + frhop[j] * drhodr2;
|
|
dUdsij = 0.0;
|
|
|
|
if (!iszero(dscrfcn[fnoffset + jn])) {
|
|
dUdsij = phi + frhop[i] * drhods1 + frhop[j] * drhods2;
|
|
}
|
|
for (m = 0; m < 3; m++) {
|
|
dUdrijm[m] = frhop[i] * drhodrm1[m] + frhop[j] * drhodrm2[m];
|
|
}
|
|
if (!isone(scaleij)) {
|
|
dUdrij *= scaleij;
|
|
dUdsij *= scaleij;
|
|
dUdrijm[0] *= scaleij;
|
|
dUdrijm[1] *= scaleij;
|
|
dUdrijm[2] *= scaleij;
|
|
}
|
|
|
|
// Add the part of the force due to dUdrij and dUdsij
|
|
|
|
force = dUdrij * recip + dUdsij * dscrfcn[fnoffset + jn];
|
|
for (m = 0; m < 3; m++) {
|
|
forcem = delij[m] * force + dUdrijm[m];
|
|
f[i][m] = f[i][m] + forcem;
|
|
f[j][m] = f[j][m] - forcem;
|
|
}
|
|
|
|
// Tabulate per-atom virial as symmetrized stress tensor
|
|
|
|
if (vflag_either) {
|
|
fi[0] = delij[0] * force + dUdrijm[0];
|
|
fi[1] = delij[1] * force + dUdrijm[1];
|
|
fi[2] = delij[2] * force + dUdrijm[2];
|
|
v[0] = -0.5 * (delij[0] * fi[0]);
|
|
v[1] = -0.5 * (delij[1] * fi[1]);
|
|
v[2] = -0.5 * (delij[2] * fi[2]);
|
|
v[3] = -0.25 * (delij[0] * fi[1] + delij[1] * fi[0]);
|
|
v[4] = -0.25 * (delij[0] * fi[2] + delij[2] * fi[0]);
|
|
v[5] = -0.25 * (delij[1] * fi[2] + delij[2] * fi[1]);
|
|
|
|
if (vflag_global) {
|
|
for (m = 0; m < 6; m++) {
|
|
virial[m] += 2.0*v[m];
|
|
}
|
|
}
|
|
if (vflag_atom) {
|
|
for (m = 0; m < 6; m++) {
|
|
vatom[i][m] += v[m];
|
|
vatom[j][m] += v[m];
|
|
}
|
|
}
|
|
}
|
|
|
|
// Now compute forces on other atoms k due to change in sij
|
|
|
|
if (iszero(sij) || isone(sij)) continue; //: cont jn loop
|
|
|
|
double dxik(0), dyik(0), dzik(0);
|
|
double dxjk(0), dyjk(0), dzjk(0);
|
|
|
|
for (kn = 0; kn < numneigh_full; kn++) {
|
|
k = firstneigh_full[kn];
|
|
eltk = fmap[type[k]];
|
|
if (k != j && eltk >= 0) {
|
|
double xik, xjk, cikj, sikj, dfc, a;
|
|
double dCikj1, dCikj2;
|
|
double delc, rik2, rjk2;
|
|
|
|
sij = scrfcn[jn+fnoffset] * fcpair[jn+fnoffset];
|
|
const double Cmax = Cmax_meam[elti][eltj][eltk];
|
|
const double Cmin = Cmin_meam[elti][eltj][eltk];
|
|
|
|
dsij1 = 0.0;
|
|
dsij2 = 0.0;
|
|
if (!iszero(sij) && !isone(sij)) {
|
|
const double rbound = rij2 * ebound_meam[elti][eltj];
|
|
delc = Cmax - Cmin;
|
|
dxjk = x[k][0] - x[j][0];
|
|
dyjk = x[k][1] - x[j][1];
|
|
dzjk = x[k][2] - x[j][2];
|
|
rjk2 = dxjk * dxjk + dyjk * dyjk + dzjk * dzjk;
|
|
if (rjk2 <= rbound) {
|
|
dxik = x[k][0] - x[i][0];
|
|
dyik = x[k][1] - x[i][1];
|
|
dzik = x[k][2] - x[i][2];
|
|
rik2 = dxik * dxik + dyik * dyik + dzik * dzik;
|
|
if (rik2 <= rbound) {
|
|
xik = rik2 / rij2;
|
|
xjk = rjk2 / rij2;
|
|
a = 1 - (xik - xjk) * (xik - xjk);
|
|
if (!iszero(a)) {
|
|
cikj = (2.0 * (xik + xjk) + a - 2.0) / a;
|
|
if (cikj >= Cmin && cikj <= Cmax) {
|
|
cikj = (cikj - Cmin) / delc;
|
|
sikj = dfcut(cikj, dfc);
|
|
dCfunc2(rij2, rik2, rjk2, dCikj1, dCikj2);
|
|
a = sij / delc * dfc / sikj;
|
|
dsij1 = a * dCikj1;
|
|
dsij2 = a * dCikj2;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
if (!iszero(dsij1) || !iszero(dsij2)) {
|
|
force1 = dUdsij * dsij1;
|
|
force2 = dUdsij * dsij2;
|
|
|
|
f[i][0] += force1 * dxik;
|
|
f[i][1] += force1 * dyik;
|
|
f[i][2] += force1 * dzik;
|
|
f[j][0] += force2 * dxjk;
|
|
f[j][1] += force2 * dyjk;
|
|
f[j][2] += force2 * dzjk;
|
|
f[k][0] -= force1 * dxik + force2 * dxjk;
|
|
f[k][1] -= force1 * dyik + force2 * dyjk;
|
|
f[k][2] -= force1 * dzik + force2 * dzjk;
|
|
|
|
// Tabulate per-atom virial as symmetrized stress tensor
|
|
|
|
if (vflag_either) {
|
|
fi[0] = force1 * dxik;
|
|
fi[1] = force1 * dyik;
|
|
fi[2] = force1 * dzik;
|
|
fj[0] = force2 * dxjk;
|
|
fj[1] = force2 * dyjk;
|
|
fj[2] = force2 * dzjk;
|
|
v[0] = -third * (dxik * fi[0] + dxjk * fj[0]);
|
|
v[1] = -third * (dyik * fi[1] + dyjk * fj[1]);
|
|
v[2] = -third * (dzik * fi[2] + dzjk * fj[2]);
|
|
v[3] = -sixth * (dxik * fi[1] + dxjk * fj[1] + dyik * fi[0] + dyjk * fj[0]);
|
|
v[4] = -sixth * (dxik * fi[2] + dxjk * fj[2] + dzik * fi[0] + dzjk * fj[0]);
|
|
v[5] = -sixth * (dyik * fi[2] + dyjk * fj[2] + dzik * fi[1] + dzjk * fj[1]);
|
|
|
|
if (vflag_global) {
|
|
for (m = 0; m < 6; m++) {
|
|
virial[m] += 3.0*v[m];
|
|
}
|
|
}
|
|
|
|
if (vflag_atom) {
|
|
for (m = 0; m < 6; m++) {
|
|
vatom[i][m] += v[m];
|
|
vatom[j][m] += v[m];
|
|
vatom[k][m] += v[m];
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// end of k loop
|
|
}
|
|
}
|
|
}
|
|
// end of j loop
|
|
}
|
|
}
|