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chuckv |
492 |
module calc_eam |
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use definitions, ONLY : DP |
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use force_globals |
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#ifdef MPI |
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use mpiSimulation |
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#endif |
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!! standard eam stuff |
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integer :: n_eam_atypes |
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integer, allocatable, dimension(:) :: eam_atype |
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real( kind = DP ), allocatable, dimension(:) :: eam_dr |
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integer, allocatable, dimension(:) :: eam_nr |
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integer, allocatable, dimension(:) :: eam_nrho |
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real( kind = DP ), allocatable, dimension(:) :: eam_lattice |
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real( kind = DP ), allocatable, dimension(:) :: eam_drho |
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integer , allocatable, dimension(:) :: eam_atype_map |
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real( kind = DP ), allocatable, dimension(:,:) :: eam_rvals |
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real( kind = DP ), allocatable, dimension(:,:) :: eam_rhovals |
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real( kind = DP ), allocatable, dimension(:) :: eam_rcut |
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real( kind = DP ), allocatable, dimension(:,:) :: eam_F_rho |
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real( kind = DP ), allocatable, dimension(:,:) :: eam_Z_r |
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real( kind = DP ), allocatable, dimension(:,:) :: eam_rho_r |
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real( kind = DP ), allocatable, dimension(:,:) :: eam_phi_r |
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real( kind = DP ), allocatable, dimension(:,:) :: eam_F_rho_pp |
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real( kind = DP ), allocatable, dimension(:,:) :: eam_Z_r_pp |
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real( kind = DP ), allocatable, dimension(:,:) :: eam_rho_r_pp |
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real( kind = DP ), allocatable, dimension(:,:) :: eam_phi_r_pp |
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real( kind = DP ), private :: time0,time1,time2,time3 |
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integer, private :: eam_err |
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private :: mass_weight |
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private :: allocate_eam_atype,allocate_eam_module,deallocate_eam_module |
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private :: read_eam_pot, get_eam_sizes |
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contains |
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subroutine initialize_eam() |
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character(len=80) :: eam_pot_file |
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integer :: i, j, max_size, prev_max_size |
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integer :: number_rho, number_r |
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integer :: eam_unit |
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integer :: this_error |
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character(len=300) :: msg |
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integer, external :: nfiles |
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!for mpi |
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#ifdef MPI |
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if (node == 0) & |
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n_eam_atypes = nfiles(trim(eam_pot_dir)//char(0)) |
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call mpi_bcast(n_eam_atypes,1,mpi_integer,0,mpi_comm_world,mpi_err) |
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if (n_eam_atypes == -1) then |
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call error("INITIALIZE_EAM","NO EAM potentials found!") |
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endif |
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write(msg,'(a5,i4,a12,i5,a14)') 'Node: ',node,' reading ...', & |
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n_eam_atypes, ' eam atom types' |
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call info('INITIALIZE_EAM', trim(msg)) |
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#else |
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n_eam_atypes = nfiles(trim(eam_pot_dir)//char(0)) |
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if (n_eam_atypes == -1) then |
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call error("INITIALIZE_EAM","NO EAM potentials found!") |
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endif |
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write(msg,'(a12,i5,a14)') ' Reading ...', & |
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n_eam_atypes, ' eam atom types' |
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call info('INITIALIZE_EAM', trim(msg)) |
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#endif |
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call allocate_eam_atype(n_eam_atypes) |
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!! get largest number of data points for any potential |
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#ifdef MPI |
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if (node == 0) then |
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#endif |
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prev_max_size = 0 |
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do i = 1, n_eam_atypes |
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call getfilename(i, eam_pot_file) |
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max_size = max(get_eam_sizes( & |
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trim(eam_pot_dir) // '/' // eam_pot_file), & |
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prev_max_size) |
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prev_max_size = max_size |
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end do |
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#ifdef MPI |
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end if |
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call mpi_bcast(max_size,1,mpi_integer,0,mpi_comm_world,mpi_err) |
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#endif |
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call allocate_eam_module(n_eam_atypes,max_size) |
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allocate(eam_atype_map(get_max_atype())) |
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#ifdef MPI |
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if (node == 0) then |
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#endif |
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do i = 1, n_eam_atypes |
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call getfilename(i, eam_pot_file) |
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call read_eam_pot(i,trim(eam_pot_dir) // '/' // eam_pot_file, & |
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this_error) |
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do j = 1, eam_nr(i) |
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eam_rvals(j,i) = dble(j-1)*eam_dr(i) |
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enddo |
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do j = 1, eam_nrho(i) |
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eam_rhovals(j,i) = dble(j-1)*eam_drho(i) |
| 120 |
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enddo |
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! convert from eV to kcal / mol: |
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do j = 1, eam_nrho(i) |
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eam_F_rho(j,i) = eam_F_rho(j,i)*23.06054E0_DP |
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enddo |
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! precompute the pair potential and get it into kcal / mol: |
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eam_phi_r(1,i) = 0.0E0_DP |
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do j = 2, eam_nr(i) |
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eam_phi_r(j,i) = (eam_Z_r(j,i)**2)/eam_rvals(j,i) |
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eam_phi_r(j,i) = eam_phi_r(j,i)*331.999296E0_DP |
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enddo |
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end do |
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#ifdef MPI |
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call info('INITIALIZE_EAM','NODE 0: Distributing spline arrays') |
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endif |
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call mpi_bcast(this_error,n_eam_atypes,mpi_integer,0, & |
| 140 |
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mpi_comm_world,mpi_err) |
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if (this_error /= 0) then |
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call error('INITIALIZE_EAM',"Cannot read eam files") |
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endif |
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call mpi_bcast(eam_atype,n_eam_atypes,mpi_integer,0, & |
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mpi_comm_world,mpi_err) |
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| 148 |
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!! distribute values to cluster...... |
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call mpi_bcast(eam_nr,n_eam_atypes,mpi_integer,& |
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0,mpi_comm_world,mpi_err) |
| 151 |
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call mpi_bcast(eam_nrho,n_eam_atypes,mpi_integer,& |
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0,mpi_comm_world,mpi_err) |
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call mpi_bcast(eam_rvals,n_eam_atypes*max_size,mpi_double_precision, & |
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0,mpi_comm_world,mpi_err) |
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call mpi_bcast(eam_rcut,n_eam_atypes,mpi_double_precision, & |
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0,mpi_comm_world,mpi_err) |
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call mpi_bcast(eam_rhovals,n_eam_atypes*max_size,mpi_double_precision, & |
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0,mpi_comm_world,mpi_err) |
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!! distribute arrays |
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call mpi_bcast(eam_rho_r,n_eam_atypes*max_size,mpi_double_precision, & |
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0,mpi_comm_world,mpi_err) |
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call mpi_bcast(eam_Z_r,n_eam_atypes*max_size,mpi_double_precision, & |
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0,mpi_comm_world,mpi_err) |
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call mpi_bcast(eam_F_rho,n_eam_atypes*max_size,mpi_double_precision, & |
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0,mpi_comm_world,mpi_err) |
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call mpi_bcast(eam_phi_r,n_eam_atypes*max_size,mpi_double_precision, & |
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0,mpi_comm_world,mpi_err) |
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#endif |
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call info('INITIALIZE_EAM', 'creating splines') |
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do i = 1, n_eam_atypes |
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number_r = eam_nr(i) |
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number_rho = eam_nrho(i) |
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call eam_spline(i, number_r, eam_rvals, eam_rho_r, eam_rho_r_pp, & |
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0.0E0_DP, 0.0E0_DP, 'N') |
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call eam_spline(i, number_r, eam_rvals, eam_Z_r, eam_Z_r_pp, & |
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0.0E0_DP, 0.0E0_DP, 'N') |
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call eam_spline(i, number_rho, eam_rhovals, eam_F_rho, eam_F_rho_pp, & |
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0.0E0_DP, 0.0E0_DP, 'N') |
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call eam_spline(i, number_r, eam_rvals, eam_phi_r, eam_phi_r_pp, & |
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0.0E0_DP, 0.0E0_DP, 'N') |
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enddo |
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do i = 1, n_eam_atypes |
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eam_atype_map(eam_atype(i)) = i |
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end do |
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call info('INITIALIZE_EAM','Done creating splines') |
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return |
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end subroutine initialize_eam |
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subroutine allocate_eam_atype(n_size_atype) |
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integer, intent(in) :: n_size_atype |
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allocate(eam_atype(n_size_atype)) |
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allocate(eam_drho(n_size_atype)) |
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allocate(eam_dr(n_size_atype)) |
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allocate(eam_nr(n_size_atype)) |
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allocate(eam_nrho(n_size_atype)) |
| 207 |
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allocate(eam_lattice(n_size_atype)) |
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allocate(eam_rcut(n_size_atype)) |
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| 210 |
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end subroutine allocate_eam_atype |
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subroutine allocate_eam_module(n_size_atype,n_eam_points) |
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integer, intent(in) :: n_eam_points |
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integer, intent(in) :: n_size_atype |
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allocate(eam_rvals(n_eam_points,n_size_atype)) |
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allocate(eam_rhovals(n_eam_points,n_size_atype)) |
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allocate(eam_F_rho(n_eam_points,n_size_atype)) |
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allocate(eam_Z_r(n_eam_points,n_size_atype)) |
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allocate(eam_rho_r(n_eam_points,n_size_atype)) |
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allocate(eam_phi_r(n_eam_points,n_size_atype)) |
| 222 |
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allocate(eam_F_rho_pp(n_eam_points,n_size_atype)) |
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allocate(eam_Z_r_pp(n_eam_points,n_size_atype)) |
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allocate(eam_rho_r_pp(n_eam_points,n_size_atype)) |
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allocate(eam_phi_r_pp(n_eam_points,n_size_atype)) |
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end subroutine allocate_eam_module |
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subroutine deallocate_eam_module() |
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| 231 |
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deallocate(eam_atype) |
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deallocate(eam_drho) |
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deallocate(eam_dr) |
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deallocate(eam_nr) |
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deallocate(eam_nrho) |
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deallocate(eam_lattice) |
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deallocate(eam_atype_map) |
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deallocate(eam_rvals) |
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deallocate(eam_rhovals) |
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deallocate(eam_rcut) |
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deallocate(eam_Z_r) |
| 242 |
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deallocate(eam_rho_r) |
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deallocate(eam_phi_r) |
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deallocate(eam_F_rho_pp) |
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deallocate(eam_Z_r_pp) |
| 246 |
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deallocate(eam_rho_r_pp) |
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deallocate(eam_phi_r_pp) |
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| 249 |
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end subroutine deallocate_eam_module |
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| 252 |
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subroutine calc_eam_pair(atom1,atom2,d,rij,r2,pot,f,do_pot,do_stress) |
| 253 |
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!Arguments |
| 254 |
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integer, intent(in) :: atom1, atom2 |
| 255 |
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real( kind = dp ), intent(in) :: rij, r2 |
| 256 |
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real( kind = dp ) :: pot |
| 257 |
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real( kind = dp ), dimension(3,getNlocal()) :: f |
| 258 |
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real( kind = dp ), intent(in), dimension(3) :: d |
| 259 |
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logical, intent(in) :: do_pot, do_stress |
| 260 |
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| 261 |
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!Local Variables |
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| 264 |
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if (rij .lt. EAM_rcut) then |
| 265 |
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| 266 |
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r = dsqrt(rijsq) |
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efr(1,j) = -rxij |
| 268 |
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efr(2,j) = -ryij |
| 269 |
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efr(3,j) = -rzij |
| 270 |
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| 271 |
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| 272 |
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call calc_eam_rho(r, rha, drha, d2rha, atype1) |
| 273 |
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call calc_eam_phi(r, pha, dpha, d2pha, atype1) |
| 274 |
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rci = eam_rcut(eam_atype_map(atype1)) |
| 275 |
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#ifdef MPI |
| 276 |
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atype2 = ident_col(j) |
| 277 |
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#else |
| 278 |
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atype2 = ident(j) |
| 279 |
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#endif |
| 280 |
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| 281 |
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call calc_eam_rho(r, rhb, drhb, d2rhb, atype2) |
| 282 |
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call calc_eam_phi(r, phb, dphb, d2phb, atype2) |
| 283 |
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rcj = eam_rcut(eam_atype_map(atype2)) |
| 284 |
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| 285 |
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phab = 0.0E0_DP |
| 286 |
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dvpdr = 0.0E0_DP |
| 287 |
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d2vpdrdr = 0.0E0_DP |
| 288 |
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| 289 |
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if (r.lt.rci) then |
| 290 |
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phab = phab + 0.5E0_DP*(rhb/rha)*pha |
| 291 |
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dvpdr = dvpdr + 0.5E0_DP*((rhb/rha)*dpha + & |
| 292 |
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pha*((drhb/rha) - (rhb*drha/rha/rha))) |
| 293 |
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d2vpdrdr = d2vpdrdr + 0.5E0_DP*((rhb/rha)*d2pha + & |
| 294 |
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2.0E0_DP*dpha*((drhb/rha) - (rhb*drha/rha/rha)) + & |
| 295 |
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pha*((d2rhb/rha) - 2.0E0_DP*(drhb*drha/rha/rha) + & |
| 296 |
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(2.0E0_DP*rhb*drha*drha/rha/rha/rha) - (rhb*d2rha/rha/rha))) |
| 297 |
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endif |
| 298 |
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| 299 |
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| 300 |
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if (r.lt.rcj) then |
| 301 |
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phab = phab + 0.5E0_DP*(rha/rhb)*phb |
| 302 |
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dvpdr = dvpdr + 0.5E0_DP*((rha/rhb)*dphb + & |
| 303 |
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phb*((drha/rhb) - (rha*drhb/rhb/rhb))) |
| 304 |
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d2vpdrdr = d2vpdrdr + 0.5E0_DP*((rha/rhb)*d2phb + & |
| 305 |
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2.0E0_DP*dphb*((drha/rhb) - (rha*drhb/rhb/rhb)) + & |
| 306 |
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phb*((d2rha/rhb) - 2.0E0_DP*(drha*drhb/rhb/rhb) + & |
| 307 |
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(2.0E0_DP*rha*drhb*drhb/rhb/rhb/rhb) - (rha*d2rhb/rhb/rhb))) |
| 308 |
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endif |
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#ifdef MPI |
| 312 |
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| 313 |
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e_row(i) = e_row(i) + phab*0.5 |
| 314 |
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e_col(i) = e_col(i) + phab*0.5 |
| 315 |
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#else |
| 316 |
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if (do_pot) pot = pot + phab |
| 317 |
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#endif |
| 318 |
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| 319 |
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drhoidr = drha |
| 320 |
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drhojdr = drhb |
| 321 |
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d2rhoidrdr = d2rha |
| 323 |
|
|
d2rhojdrdr = d2rhb |
| 324 |
|
|
#ifdef MPI |
| 325 |
|
|
dudr = drhojdr*dfrhodrho_row(i)+drhoidr*dfrhodrho_col(j) & |
| 326 |
|
|
+ dvpdr |
| 327 |
|
|
|
| 328 |
|
|
if (nmflag) then |
| 329 |
|
|
d2 = d2vpdrdr + & |
| 330 |
|
|
d2rhoidrdr*dfrhodrho_col(j) + & |
| 331 |
|
|
d2rhojdrdr*dfrhodrho_row(i) + & |
| 332 |
|
|
drhoidr*drhoidr*d2frhodrhodrho_col(j) + & |
| 333 |
|
|
drhojdr*drhojdr*d2frhodrhodrho_row(i) |
| 334 |
|
|
endif |
| 335 |
|
|
#else |
| 336 |
|
|
dudr = drhojdr*dfrhodrho(i)+drhoidr*dfrhodrho(j) & |
| 337 |
|
|
+ dvpdr |
| 338 |
|
|
|
| 339 |
|
|
d2 = d2vpdrdr + & |
| 340 |
|
|
d2rhoidrdr*dfrhodrho(j) + & |
| 341 |
|
|
d2rhojdrdr*dfrhodrho(i) + & |
| 342 |
|
|
drhoidr*drhoidr*d2frhodrhodrho(j) + & |
| 343 |
|
|
drhojdr*drhojdr*d2frhodrhodrho(i) |
| 344 |
|
|
#endif |
| 345 |
|
|
|
| 346 |
|
|
|
| 347 |
|
|
do dim = 1, 3 |
| 348 |
|
|
|
| 349 |
|
|
drdx1 = efr(dim,j) / r |
| 350 |
|
|
ftmp = dudr * drdx1 |
| 351 |
|
|
|
| 352 |
|
|
#ifdef MPI |
| 353 |
|
|
f_col(dim,j) = f_col(dim,j) - ftmp |
| 354 |
|
|
f_row(dim,i) = f_row(dim,i) + ftmp |
| 355 |
|
|
#else |
| 356 |
|
|
f(dim,j) = f(dim,j) - ftmp |
| 357 |
|
|
f(dim,i) = f(dim,i) + ftmp |
| 358 |
|
|
#endif |
| 359 |
|
|
|
| 360 |
|
|
if (nmflag) then |
| 361 |
|
|
idim = 3 * (i-1) + dim |
| 362 |
|
|
jdim = 3 * (j-1) + dim |
| 363 |
|
|
|
| 364 |
|
|
do dim2 = 1, 3 |
| 365 |
|
|
|
| 366 |
|
|
kt1 = d2 * efr(dim,j) * efr(dim2,j)/r/r |
| 367 |
|
|
kt2 = - dudr * efr(dim,j) * efr(dim2,j)/r/r/r |
| 368 |
|
|
|
| 369 |
|
|
if (dim.eq.dim2) then |
| 370 |
|
|
kt3 = dudr / r |
| 371 |
|
|
else |
| 372 |
|
|
kt3 = 0.0E0_DP |
| 373 |
|
|
endif |
| 374 |
|
|
|
| 375 |
|
|
! The factor of 2 below is to compensate for |
| 376 |
|
|
! overcounting. |
| 377 |
|
|
! Mass weighting is done separately... |
| 378 |
|
|
|
| 379 |
|
|
ktmp = (kt1+kt2+kt3)/2.0E0_DP |
| 380 |
|
|
idim2 = 3 * (i-1) + dim2 |
| 381 |
|
|
jdim2 = 3 * (j-1) + dim2 |
| 382 |
|
|
|
| 383 |
|
|
d(idim, idim2) = d(idim,idim2) + ktmp |
| 384 |
|
|
d(idim2, idim) = d(idim2,idim) + ktmp |
| 385 |
|
|
|
| 386 |
|
|
d(idim, jdim2) = d(idim,jdim2) - ktmp |
| 387 |
|
|
d(idim2, jdim) = d(idim2,jdim) - ktmp |
| 388 |
|
|
|
| 389 |
|
|
d(jdim, idim2) = d(jdim,idim2) - ktmp |
| 390 |
|
|
d(jdim2, idim) = d(jdim2,idim) - ktmp |
| 391 |
|
|
|
| 392 |
|
|
d(jdim, jdim2) = d(jdim,jdim2) + ktmp |
| 393 |
|
|
d(jdim2, jdim) = d(jdim2,jdim) + ktmp |
| 394 |
|
|
|
| 395 |
|
|
enddo |
| 396 |
|
|
endif |
| 397 |
|
|
enddo |
| 398 |
|
|
|
| 399 |
|
|
endif |
| 400 |
|
|
enddo |
| 401 |
|
|
endif |
| 402 |
|
|
|
| 403 |
|
|
enddo |
| 404 |
|
|
|
| 405 |
|
|
|
| 406 |
|
|
|
| 407 |
|
|
|
| 408 |
|
|
end subroutine calc_eam_pair |
| 409 |
|
|
|
| 410 |
|
|
subroutine calc_eam_rho(r, rho, drho, d2rho, atype) |
| 411 |
|
|
|
| 412 |
|
|
! include 'headers/sizes.h' |
| 413 |
|
|
|
| 414 |
|
|
|
| 415 |
|
|
integer atype, etype, number_r |
| 416 |
|
|
real( kind = DP ) :: r, rho, drho, d2rho |
| 417 |
|
|
integer :: i |
| 418 |
|
|
|
| 419 |
|
|
|
| 420 |
|
|
etype = eam_atype_map(atype) |
| 421 |
|
|
|
| 422 |
|
|
if (r.lt.eam_rcut(etype)) then |
| 423 |
|
|
number_r = eam_nr(etype) |
| 424 |
|
|
call eam_splint(etype, number_r, eam_rvals, eam_rho_r, & |
| 425 |
|
|
eam_rho_r_pp, r, rho, drho, d2rho) |
| 426 |
|
|
else |
| 427 |
|
|
rho = 0.0E0_DP |
| 428 |
|
|
drho = 0.0E0_DP |
| 429 |
|
|
d2rho = 0.0E0_DP |
| 430 |
|
|
endif |
| 431 |
|
|
|
| 432 |
|
|
return |
| 433 |
|
|
end subroutine calc_eam_rho |
| 434 |
|
|
|
| 435 |
|
|
subroutine calc_eam_frho(dens, u, u1, u2, atype) |
| 436 |
|
|
|
| 437 |
|
|
! include 'headers/sizes.h' |
| 438 |
|
|
|
| 439 |
|
|
integer atype, etype, number_rho |
| 440 |
|
|
real( kind = DP ) :: dens, u, u1, u2 |
| 441 |
|
|
real( kind = DP ) :: rho_vals |
| 442 |
|
|
|
| 443 |
|
|
etype = eam_atype_map(atype) |
| 444 |
|
|
number_rho = eam_nrho(etype) |
| 445 |
|
|
if (dens.lt.eam_rhovals(number_rho, etype)) then |
| 446 |
|
|
call eam_splint(etype, number_rho, eam_rhovals, eam_f_rho, & |
| 447 |
|
|
eam_f_rho_pp, dens, u, u1, u2) |
| 448 |
|
|
else |
| 449 |
|
|
rho_vals = eam_rhovals(number_rho,etype) |
| 450 |
|
|
call eam_splint(etype, number_rho, eam_rhovals, eam_f_rho, & |
| 451 |
|
|
eam_f_rho_pp, rho_vals, u, u1, u2) |
| 452 |
|
|
endif |
| 453 |
|
|
|
| 454 |
|
|
return |
| 455 |
|
|
end subroutine calc_eam_frho |
| 456 |
|
|
|
| 457 |
|
|
subroutine calc_eam_phi(r, phi, dphi, d2phi, atype) |
| 458 |
|
|
|
| 459 |
|
|
|
| 460 |
|
|
|
| 461 |
|
|
|
| 462 |
|
|
integer atype, etype, number_r |
| 463 |
|
|
real( kind = DP ) :: r, phi, dphi, d2phi |
| 464 |
|
|
|
| 465 |
|
|
etype = eam_atype_map(atype) |
| 466 |
|
|
|
| 467 |
|
|
if (r.lt.eam_rcut(etype)) then |
| 468 |
|
|
number_r = eam_nr(etype) |
| 469 |
|
|
call eam_splint(etype, number_r, eam_rvals, eam_phi_r, & |
| 470 |
|
|
eam_phi_r_pp, r, phi, dphi, d2phi) |
| 471 |
|
|
else |
| 472 |
|
|
phi = 0.0E0_DP |
| 473 |
|
|
dphi = 0.0E0_DP |
| 474 |
|
|
d2phi = 0.0E0_DP |
| 475 |
|
|
endif |
| 476 |
|
|
|
| 477 |
|
|
return |
| 478 |
|
|
end subroutine calc_eam_phi |
| 479 |
|
|
|
| 480 |
|
|
|
| 481 |
|
|
subroutine eam_splint(atype, nx, xa, ya, yppa, x, y, dy, d2y) |
| 482 |
|
|
|
| 483 |
|
|
! include 'headers/sizes.h' |
| 484 |
|
|
|
| 485 |
|
|
real( kind = DP ), dimension(:,:) :: xa |
| 486 |
|
|
real( kind = DP ), dimension(:,:) :: ya |
| 487 |
|
|
real( kind = DP ), dimension(:,:) :: yppa |
| 488 |
|
|
real( kind = DP ) :: x, y, dy, d2y |
| 489 |
|
|
real( kind = DP ) :: del, h, a, b, c, d |
| 490 |
|
|
|
| 491 |
|
|
|
| 492 |
|
|
integer atype, nx, j |
| 493 |
|
|
|
| 494 |
|
|
|
| 495 |
|
|
! this spline code assumes that the x points are equally spaced |
| 496 |
|
|
! do not attempt to use this code if they are not. |
| 497 |
|
|
|
| 498 |
|
|
|
| 499 |
|
|
! find the closest point with a value below our own: |
| 500 |
|
|
j = FLOOR(dble(nx-1) * (x - xa(1,atype)) / (xa(nx,atype) - xa(1,atype))) + 1 |
| 501 |
|
|
|
| 502 |
|
|
! check to make sure we're inside the spline range: |
| 503 |
|
|
if ((j.gt.nx).or.(j.lt.1)) call error('eam_splint', & |
| 504 |
|
|
'x is outside bounds of spline') |
| 505 |
|
|
|
| 506 |
|
|
! check to make sure we haven't screwed up the calculation of j: |
| 507 |
|
|
if ((x.lt.xa(j,atype)).or.(x.gt.xa(j+1,atype))) then |
| 508 |
|
|
if (j.ne.nx) then |
| 509 |
|
|
call error('eam_splint', & |
| 510 |
|
|
'x is outside bounding range') |
| 511 |
|
|
endif |
| 512 |
|
|
endif |
| 513 |
|
|
|
| 514 |
|
|
del = xa(j+1,atype) - x |
| 515 |
|
|
h = xa(j+1,atype) - xa(j,atype) |
| 516 |
|
|
|
| 517 |
|
|
a = del / h |
| 518 |
|
|
b = 1.0E0_DP - a |
| 519 |
|
|
c = a*(a*a - 1.0E0_DP)*h*h/6.0E0_DP |
| 520 |
|
|
d = b*(b*b - 1.0E0_DP)*h*h/6.0E0_DP |
| 521 |
|
|
|
| 522 |
|
|
y = a*ya(j,atype) + b*ya(j+1,atype) + c*yppa(j,atype) + d*yppa(j+1,atype) |
| 523 |
|
|
|
| 524 |
|
|
dy = (ya(j+1,atype)-ya(j,atype))/h & |
| 525 |
|
|
- (3.0E0_DP*a*a - 1.0E0_DP)*h*yppa(j,atype)/6.0E0_DP & |
| 526 |
|
|
+ (3.0E0_DP*b*b - 1.0E0_DP)*h*yppa(j+1,atype)/6.0E0_DP |
| 527 |
|
|
|
| 528 |
|
|
d2y = a*yppa(j,atype) + b*yppa(j+1,atype) |
| 529 |
|
|
|
| 530 |
|
|
return |
| 531 |
|
|
end subroutine eam_splint |
| 532 |
|
|
|
| 533 |
|
|
subroutine eam_spline(atype, nx, xa, ya, yppa, yp1, ypn, boundary) |
| 534 |
|
|
|
| 535 |
|
|
! include 'headers/sizes.h' |
| 536 |
|
|
|
| 537 |
|
|
|
| 538 |
|
|
! yp1 and ypn are the first derivatives of y at the two endpoints |
| 539 |
|
|
! if boundary is 'L' the lower derivative is used |
| 540 |
|
|
! if boundary is 'U' the upper derivative is used |
| 541 |
|
|
! if boundary is 'B' then both derivatives are used |
| 542 |
|
|
! if boundary is anything else, then both derivatives are assumed to be 0 |
| 543 |
|
|
|
| 544 |
|
|
integer nx, i, k, atype, max_array_size |
| 545 |
|
|
|
| 546 |
|
|
real( kind = DP ), dimension(:,:) :: xa |
| 547 |
|
|
real( kind = DP ), dimension(:,:) :: ya |
| 548 |
|
|
real( kind = DP ), dimension(:,:) :: yppa |
| 549 |
|
|
real( kind = DP ), allocatable, dimension(:) :: u |
| 550 |
|
|
real( kind = DP ) :: yp1,ypn,un,qn,sig,p |
| 551 |
|
|
character boundary |
| 552 |
|
|
|
| 553 |
|
|
max_array_size = size(xa,1) |
| 554 |
|
|
allocate(u(max_array_size)) |
| 555 |
|
|
|
| 556 |
|
|
|
| 557 |
|
|
if ((boundary.eq.'l').or.(boundary.eq.'L').or. & |
| 558 |
|
|
(boundary.eq.'b').or.(boundary.eq.'B')) then |
| 559 |
|
|
yppa(1, atype) = -0.5E0_DP |
| 560 |
|
|
u(1) = (3.0E0_DP/(xa(2,atype)-xa(1,atype)))*((ya(2,atype)-& |
| 561 |
|
|
ya(1,atype))/(xa(2,atype)-xa(1,atype))-yp1) |
| 562 |
|
|
else |
| 563 |
|
|
yppa(1,atype) = 0.0E0_DP |
| 564 |
|
|
u(1) = 0.0E0_DP |
| 565 |
|
|
endif |
| 566 |
|
|
|
| 567 |
|
|
do i = 2, nx - 1 |
| 568 |
|
|
sig = (xa(i,atype) - xa(i-1,atype)) / (xa(i+1,atype) - xa(i-1,atype)) |
| 569 |
|
|
p = sig * yppa(i-1,atype) + 2.0E0_DP |
| 570 |
|
|
yppa(i,atype) = (sig - 1.0E0_DP) / p |
| 571 |
|
|
u(i) = (6.0E0_DP*((ya(i+1,atype)-ya(i,atype))/(xa(i+1,atype)-xa(i,atype)) - & |
| 572 |
|
|
(ya(i,atype)-ya(i-1,atype))/(xa(i,atype)-xa(i-1,atype)))/ & |
| 573 |
|
|
(xa(i+1,atype)-xa(i-1,atype)) - sig * u(i-1))/p |
| 574 |
|
|
enddo |
| 575 |
|
|
|
| 576 |
|
|
if ((boundary.eq.'u').or.(boundary.eq.'U').or. & |
| 577 |
|
|
(boundary.eq.'b').or.(boundary.eq.'B')) then |
| 578 |
|
|
qn = 0.5E0_DP |
| 579 |
|
|
un = (3.0E0_DP/(xa(nx,atype)-xa(nx-1,atype)))* & |
| 580 |
|
|
(ypn-(ya(nx,atype)-ya(nx-1,atype))/(xa(nx,atype)-xa(nx-1,atype))) |
| 581 |
|
|
else |
| 582 |
|
|
qn = 0.0E0_DP |
| 583 |
|
|
un = 0.0E0_DP |
| 584 |
|
|
endif |
| 585 |
|
|
|
| 586 |
|
|
yppa(nx,atype)=(un-qn*u(nx-1))/(qn*yppa(nx-1,atype)+1.0E0_DP) |
| 587 |
|
|
|
| 588 |
|
|
do k = nx-1, 1, -1 |
| 589 |
|
|
yppa(k,atype)=yppa(k,atype)*yppa(k+1,atype)+u(k) |
| 590 |
|
|
enddo |
| 591 |
|
|
|
| 592 |
|
|
deallocate(u) |
| 593 |
|
|
return |
| 594 |
|
|
end subroutine eam_spline |
| 595 |
|
|
|
| 596 |
|
|
|
| 597 |
|
|
|
| 598 |
|
|
|
| 599 |
|
|
end module calc_eam |
