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meam_setup_done.F
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c Declaration in pair_meam.h:
c
c void meam_setup_done(double *)
c
c Call from pair_meam.cpp:
c
c meam_setup_done(&cutmax)
c
subroutine meam_setup_done(cutmax)
use meam_data
implicit none
real*8 cutmax
integer nv2, nv3, m, n, p
c Force cutoff
cutforce = rc_meam
cutforcesq = cutforce*cutforce
c Pass cutoff back to calling program
cutmax = cutforce
c Augment t1 term
t1_meam(:) = t1_meam(:) + augt1 * 3.d0/5.d0 * t3_meam(:)
c Compute off-diagonal alloy parameters
call alloyparams
c indices and factors for Voight notation
nv2 = 1
nv3 = 1
do m = 1,3
do n = m,3
vind2D(m,n) = nv2
vind2D(n,m) = nv2
nv2 = nv2+1
do p = n,3
vind3D(m,n,p) = nv3
vind3D(m,p,n) = nv3
vind3D(n,m,p) = nv3
vind3D(n,p,m) = nv3
vind3D(p,m,n) = nv3
vind3D(p,n,m) = nv3
nv3 = nv3+1
enddo
enddo
enddo
v2D(1) = 1
v2D(2) = 2
v2D(3) = 2
v2D(4) = 1
v2D(5) = 2
v2D(6) = 1
v3D(1) = 1
v3D(2) = 3
v3D(3) = 3
v3D(4) = 3
v3D(5) = 6
v3D(6) = 3
v3D(7) = 1
v3D(8) = 3
v3D(9) = 3
v3D(10) = 1
nv2 = 1
do m = 1,neltypes
do n = m,neltypes
eltind(m,n) = nv2
eltind(n,m) = nv2
nv2 = nv2+1
enddo
enddo
c Compute pair potentials and setup arrays for interpolation
nr = 1000
dr = 1.1*rc_meam/nr
call compute_pair_meam
return
end
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c Fill off-diagonal alloy parameters
subroutine alloyparams
use meam_data
implicit none
integer i,j,k
real*8 eb
c Loop over pairs
do i = 1,neltypes
do j = 1,neltypes
c Treat off-diagonal pairs
c If i>j, set all equal to i<j case (which has aready been set,
c here or in the input file)
if (i.gt.j) then
re_meam(i,j) = re_meam(j,i)
Ec_meam(i,j) = Ec_meam(j,i)
alpha_meam(i,j) = alpha_meam(j,i)
lattce_meam(i,j) = lattce_meam(j,i)
c If i<j and term is unset, use default values (e.g. mean of i-i and j-j)
else if (j.gt.i) then
if (Ec_meam(i,j).eq.0.d0) then
Ec_meam(i,j) = (Ec_meam(i,i)+Ec_meam(j,j))/2.d0
$ - delta_meam(i,j)
endif
if (alpha_meam(i,j).eq.0.d0) then
alpha_meam(i,j) = (alpha_meam(i,i)+alpha_meam(j,j))/2.d0
endif
if (re_meam(i,j).eq.0.d0) then
re_meam(i,j) = (re_meam(i,i)+re_meam(j,j))/2.d0
endif
endif
enddo
enddo
c Cmin(i,k,j) is symmetric in i-j, but not k. For all triplets
c where i>j, set equal to the i<j element. Likewise for Cmax.
do i = 2,neltypes
do j = 1,i-1
do k = 1,neltypes
Cmin_meam(i,j,k) = Cmin_meam(j,i,k)
Cmax_meam(i,j,k) = Cmax_meam(j,i,k)
enddo
enddo
enddo
c ebound gives the squared distance such that, for rik2 or rjk2>ebound,
c atom k definitely lies outside the screening function ellipse (so
c there is no need to calculate its effects). Here, compute it for all
c triplets (i,j,k) so that ebound(i,j) is the maximized over k
do i = 1,neltypes
do j = 1,neltypes
do k = 1,neltypes
eb = (Cmax_meam(i,j,k)*Cmax_meam(i,j,k))
$ /(4.d0*(Cmax_meam(i,j,k)-1.d0))
ebound_meam(i,j) = max(ebound_meam(i,j),eb)
enddo
enddo
enddo
return
end
c-----------------------------------------------------------------------
c compute MEAM pair potential for each pair of element types
c
subroutine compute_pair_meam
use meam_data
implicit none
real*8 r, temp
integer j,a,b,nv2
real*8 astar,frac,phizbl
integer n,nmax,Z1,Z2
real*8 arat,scrn
real*8 phitmp
real*8, external :: phi_meam
real*8, external :: zbl
c allocate memory for array that defines the potential
allocate(phir(nr,(neltypes*(neltypes+1))/2))
c allocate coeff memory
allocate(phirar(nr,(neltypes*(neltypes+1))/2))
allocate(phirar1(nr,(neltypes*(neltypes+1))/2))
allocate(phirar2(nr,(neltypes*(neltypes+1))/2))
allocate(phirar3(nr,(neltypes*(neltypes+1))/2))
allocate(phirar4(nr,(neltypes*(neltypes+1))/2))
allocate(phirar5(nr,(neltypes*(neltypes+1))/2))
allocate(phirar6(nr,(neltypes*(neltypes+1))/2))
c loop over pairs of element types
nv2 = 0
do a = 1,neltypes
do b = a,neltypes
nv2 = nv2 + 1
c loop over r values and compute
do j = 1,nr
r = (j-1)*dr
phir(j,nv2) = phi_meam(r,a,b)
c if using second-nearest neighbor, solve recursive problem
c (see Lee and Baskes, PRB 62(13):8564 eqn.(21))
if (nn2_meam(a,b).eq.1) then
if (a.ne.b) then
write(6,*) 'Second-neighbor currently only valid '
write(6,*) 'if element types are the same.'
c call error(' ')
endif
call get_Zij(Z1,lattce_meam(a,b))
call get_Zij2(Z2,arat,scrn,lattce_meam(a,b),
$ Cmin_meam(a,a,b),Cmax_meam(a,a,b))
nmax = 10
do n = 1,nmax
phir(j,nv2) = phir(j,nv2) +
$ (-Z2*scrn/Z1)**n * phi_meam(r*arat**n,a,b)
enddo
endif
c if astar <= -3
c potential is zbl potential
c else if -3 < astar < -1
c potential is linear combination with zbl potential
c endif
astar = alpha_meam(a,b) * (r/re_meam(a,b) - 1.d0)
if (astar.le.-3.d0) then
phir(j,nv2) = zbl(r,ielt_meam(a),ielt_meam(b))
else if (astar.gt.-3.d0.and.astar.lt.-1.d0) then
call fcut(1-(astar+1.d0)/(-3.d0+1.d0),frac)
phizbl = zbl(r,ielt_meam(a),ielt_meam(b))
phir(j,nv2) = frac*phir(j,nv2) + (1-frac)*phizbl
endif
enddo
c call interpolation
call interpolate_meam(nv2)
enddo
enddo
return
end
c----------------------------------------------------------------------c
c Compute MEAM pair potential for distance r, element types a and b
c
real*8 recursive function phi_meam(r,a,b)result(phi_m)
use meam_data
implicit none
integer a,b
real*8 r
real*8 a1,a2,a12
real*8 t11av,t21av,t31av,t12av,t22av,t32av
real*8 G1,G2,s1(3),s2(3),s12(3),rho0_1,rho0_2
real*8 Gam1,Gam2,Z1,Z2
real*8 rhobar1,rhobar2,F1,F2
real*8 rhoa01,rhoa11,rhoa21,rhoa31
real*8 rhoa02,rhoa12,rhoa22,rhoa32
real*8 rho01,rho11,rho21,rho31
real*8 rho02,rho12,rho22,rho32
real*8 scalfac,phiaa,phibb
real*8 Eu
integer Z12
character*3 latta,lattb
real*8, external :: erose
c Equation numbers below refer to:
c I. Huang et.al., Modelling simul. Mater. Sci. Eng. 3:615
c get number of neighbors in the reference structure
c Nref(i,j) = # of i's neighbors of type j
call get_Zij(Z12,lattce_meam(a,b))
call get_densref(r,a,b,rho01,rho11,rho21,rho31,
$ rho02,rho12,rho22,rho32)
c calculate average weighting factors for the reference structure
if (lattce_meam(a,b).eq.'c11') then
scalfac = 1.0/(rho01+rho02)
t11av = scalfac*(t1_meam(a)*rho01 + t1_meam(b)*rho02)
t12av = t11av
t21av = scalfac*(t2_meam(a)*rho01 + t2_meam(b)*rho02)
t22av = t21av
t31av = scalfac*(t3_meam(a)*rho01 + t3_meam(b)*rho02)
t32av = t31av
else
c average weighting factors for the reference structure, eqn. I.8
call get_tavref(t11av,t21av,t31av,t12av,t22av,t32av,
$ t1_meam(a),t2_meam(a),t3_meam(a),
$ t1_meam(b),t2_meam(b),t3_meam(b),lattce_meam(a,b))
endif
c for c11b structure, calculate background electron densities
if (lattce_meam(a,b).eq.'c11') then
latta = lattce_meam(a,a)
if (latta.eq.'dia') then
rhobar1 = ((Z12/2)*(rho02+rho01))**2 +
$ t11av*(rho12-rho11)**2 +
$ t21av/6.0*(rho22+rho21)**2 +
$ 121.0/40.*t31av*(rho32-rho31)**2
rhobar1 = sqrt(rhobar1)
rhobar2 = (Z12*rho01)**2 + 2.0/3.0*t21av*rho21**2
rhobar2 = sqrt(rhobar2)
else
rhobar2 = ((Z12/2)*(rho01+rho02))**2 +
$ t12av*(rho11-rho12)**2 +
$ t22av/6.0*(rho21+rho22)**2 +
$ 121.0/40.*t32av*(rho31-rho32)**2
rhobar2 = sqrt(rhobar2)
rhobar1 = (Z12*rho02)**2 + 2.0/3.0*t22av*rho22**2
rhobar1 = sqrt(rhobar1)
endif
else
c for other structures, use formalism developed in Huang's paper
c
c composition-dependent scaling, equation I.7
c -- note: The shape factors for the individual elements are used, since
c this function should cancel the F(rho) terms when the atoms are
c in the reference structure.
Z1 = Z_meam(a)
Z2 = Z_meam(b)
if (ibar_meam(a).le.0) then
G1 = 1.d0
else
call get_shpfcn(s1,lattce_meam(a,a))
Gam1 = (s1(1)*t11av+s1(2)*t21av+s1(3)*t31av)/(Z1*Z1)
call G_gam(Gam1,ibar_meam(a),gsmooth_factor,G1)
endif
if (ibar_meam(b).le.0) then
G2 = 1.d0
else
call get_shpfcn(s2,lattce_meam(b,b))
Gam2 = (s2(1)*t12av+s2(2)*t22av+s2(3)*t32av)/(Z2*Z2)
call G_gam(Gam2,ibar_meam(b),gsmooth_factor,G2)
endif
rho0_1 = rho0_meam(a)*Z1*G1
rho0_2 = rho0_meam(b)*Z2*G2
c get number of neighbors in the reference structure
c Nref(i,j) = # of i's neighbors of type j
c call get_Zij(Z12,lattce_meam(a,b))
c
c call get_densref(r,a,b,rho01,rho11,rho21,rho31,
c $ rho02,rho12,rho22,rho32)
c compute total background density, eqn I.6
Gam1 = (t11av*rho11+t21av*rho21+t31av*rho31)
Gam1 = Gam1/(rho01*rho01)
Gam2 = (t12av*rho12+t22av*rho22+t32av*rho32)
Gam2 = Gam2/(rho02*rho02)
call G_gam(Gam1,ibar_meam(a),gsmooth_factor,G1)
call G_gam(Gam2,ibar_meam(b),gsmooth_factor,G2)
rhobar1 = rho01/rho0_1*G1
rhobar2 = rho02/rho0_2*G2
endif
c compute embedding functions, eqn I.5
if (rhobar1.eq.0.d0) then
F1 = 0.d0
else
F1 = A_meam(a)*Ec_meam(a,a)*rhobar1*log(rhobar1)
endif
if (rhobar2.eq.0.d0) then
F2 = 0.d0
else
F2 = A_meam(b)*Ec_meam(b,b)*rhobar2*log(rhobar2)
endif
c compute Rose function, I.16
Eu = erose(r,re_meam(a,b),alpha_meam(a,b),
$ Ec_meam(a,b),repuls_meam(a,b),attrac_meam(a,b))
c calculate the pair energy
if (lattce_meam(a,b).eq.'c11') then
latta = lattce_meam(a,a)
if (latta.eq.'dia') then
phiaa = phi_meam(r,a,a)
phi_m = (3*Eu - F2 - 2*F1 - 5*phiaa)/Z12
else
phibb = phi_meam(r,b,b)
phi_m = (3*Eu - F1 - 2*F2 - 5*phibb)/Z12
endif
c phi_m = 0.d0
else
c
c potential is computed from Rose function and embedding energy
phi_m = (2*Eu - F1 - F2)/Z12
c
endif
c if r = 0, just return 0
if (r.eq.0.d0) then
phi_m = 0.d0
endif
return
end
c----------------------------------------------------------------------c
c Shape factors for various configurations
subroutine get_shpfcn(s,latt)
implicit none
real*8 s(3)
character*3 latt
if (latt.eq.'fcc'.or.latt.eq.'bcc'.or.latt.eq.'b1') then
s(1) = 0.d0
s(2) = 0.d0
s(3) = 0.d0
else if (latt.eq.'hcp') then
s(1) = 0.d0
s(2) = 0.d0
s(3) = 1.d0/3.d0
else if (latt.eq.'dia') then
s(1) = 0.d0
s(2) = 0.d0
s(3) = 32.d0/9.d0
else if (latt.eq.'dim') then
s(1) = 1.d0
s(2) = 2.d0/3.d0
c s(3) = 1.d0
s(3) = 0.4d0
else
s(1) = 0.0
c call error('Lattice not defined in get_shpfcn.')
endif
return
end
c------------------------------------------------------------------------------c
c Average weighting factors for the reference structure
subroutine get_tavref(t11av,t21av,t31av,t12av,t22av,t32av,
$ t11,t21,t31,t12,t22,t32,latt)
implicit none
real*8 t11av,t21av,t31av,t12av,t22av,t32av
real*8 t11,t21,t31,t12,t22,t32
character*3 latt
if (latt.eq.'fcc'.or.latt.eq.'bcc'.or.latt.eq.'dia'
$ .or.latt.eq.'hcp'.or.latt.eq.'b1'
$ .or.latt.eq.'dim') then
c all neighbors are of the opposite type
t11av = t12
t21av = t22
t31av = t32
t12av = t11
t22av = t21
t32av = t31
else
c call error('Lattice not defined in get_tavref.')
endif
return
end
c------------------------------------------------------------------------------c
c Number of neighbors for the reference structure
subroutine get_Zij(Zij,latt)
implicit none
integer Zij
character*3 latt
if (latt.eq.'fcc') then
Zij = 12
else if (latt.eq.'bcc') then
Zij = 8
else if (latt.eq.'hcp') then
Zij = 12
else if (latt.eq.'b1') then
Zij = 6
else if (latt.eq.'dia') then
Zij = 4
else if (latt.eq.'dim') then
Zij = 1
else if (latt.eq.'c11') then
Zij = 10
else
c call error('Lattice not defined in get_Zij.')
endif
return
end
c------------------------------------------------------------------------------c
c Zij2 = number of second neighbors, a = distance ratio R1/R2, and S = second
c neighbor screening function for lattice type "latt"
subroutine get_Zij2(Zij2,a,S,latt,cmin,cmax)
implicit none
integer Zij2
real*8 a,S,cmin,cmax
character*3 latt
real*8 rratio,C,x,sijk
integer numscr
if (latt.eq.'bcc') then
Zij2 = 6
a = 2.d0/sqrt(3.d0)
numscr = 4
else if (latt.eq.'fcc') then
Zij2 = 6
a = sqrt(2.d0)
numscr = 4
else if (latt.eq.'dia') then
Zij2 = 0
a = sqrt(8.d0/3.d0)
numscr = 4
if (cmin.lt.0.500001) then
c call error('can not do 2NN MEAM for dia')
endif
else if (latt.eq.'hcp') then
Zij2 = 6
a = sqrt(2.d0)
numscr = 4
else if (latt.eq.'b1') then
Zij2 = 6
a = sqrt(2.d0)
numscr = 4
else
c call error('Lattice not defined in get_Zij2.')
endif
c Compute screening for each first neighbor
C = 4.d0/(a*a) - 1.d0
x = (C-cmin)/(cmax-cmin)
call fcut(x,sijk)
c There are numscr first neighbors screening the second neighbors
S = sijk**numscr
return
end
c------------------------------------------------------------------------------c
c Calculate density functions, assuming reference configuration
subroutine get_densref(r,a,b,rho01,rho11,rho21,rho31,
$ rho02,rho12,rho22,rho32)
use meam_data
implicit none
real*8 r,rho01,rho11,rho21,rho31,rho02,rho12,rho22,rho32
real*8 a1,a2
real*8 rhoa01,rhoa11,rhoa21,rhoa31,rhoa02,rhoa12,rhoa22,rhoa32
real*8 C,Cmin,Cmax,fc,s(3)
character*3 lat
integer a,b
integer Zij1nn,Zij2nn
real*8 rhoa01nn,rhoa02nn
real*8 arat,scrn
a1 = r/re_meam(a,a) - 1.d0
a2 = r/re_meam(b,b) - 1.d0
rhoa01 = rho0_meam(a)*exp(-beta0_meam(a)*a1)
rhoa11 = rho0_meam(a)*exp(-beta1_meam(a)*a1)
rhoa21 = rho0_meam(a)*exp(-beta2_meam(a)*a1)
rhoa31 = rho0_meam(a)*exp(-beta3_meam(a)*a1)
rhoa02 = rho0_meam(b)*exp(-beta0_meam(b)*a2)
rhoa12 = rho0_meam(b)*exp(-beta1_meam(b)*a2)
rhoa22 = rho0_meam(b)*exp(-beta2_meam(b)*a2)
rhoa32 = rho0_meam(b)*exp(-beta3_meam(b)*a2)
lat = lattce_meam(a,b)
rho11 = 0.d0
rho21 = 0.d0
rho31 = 0.d0
rho12 = 0.d0
rho22 = 0.d0
rho32 = 0.d0
call get_Zij(Zij1nn,lat)
if (lat.eq.'fcc') then
rho01 = 12.d0*rhoa02
rho02 = 12.d0*rhoa01
else if (lat.eq.'bcc') then
rho01 = 8.d0*rhoa02
rho02 = 8.d0*rhoa01
else if (lat.eq.'b1') then
c Warning: this assumes that atoms of element 1 are not completely
c screened from each other, but that atoms of element 2 are. So
c Cmin_meam(1,1,2) can be less than 1.0, but Cmin_meam(2,2,1) cannot.
c This should be made more general in the future.
c Cmin = Cmin_meam(1,1,2)
c Cmax = Cmax_meam(1,1,2)
c C = (1.0-Cmin)/(Cmax-Cmin)
c call fcut(C,fc)
c a1 = sqrt(2.0)*r/re_meam(1,1) - 1.d0
c rho01 = 6*rhoa02 + 12*fc*fc*rho0_meam(1)*exp(-beta0_meam(1)*a1)
c rho02 = 6*rhoa01
rho01 = 6*rhoa02
rho02 = 6*rhoa01
else if (lat.eq.'dia') then
rho01 = 4*rhoa02
rho02 = 4*rhoa01
rho31 = 32.d0/9.d0*rhoa32*rhoa32
rho32 = 32.d0/9.d0*rhoa31*rhoa31
else if (lat.eq.'hcp') then
rho01 = 12*rhoa02
rho02 = 12*rhoa01
rho31 = 1.d0/3.d0*rhoa32*rhoa32
rho32 = 1.d0/3.d0*rhoa31*rhoa31
else if (lat.eq.'dim') then
call get_shpfcn(s,'dim')
rho01 = rhoa02
rho02 = rhoa01
rho11 = s(1)*rhoa12*rhoa12
rho12 = s(1)*rhoa11*rhoa11
rho21 = s(2)*rhoa22*rhoa22
rho22 = s(2)*rhoa21*rhoa21
rho31 = s(3)*rhoa32*rhoa32
rho32 = s(3)*rhoa31*rhoa31
else if (lat.eq.'c11') then
rho01 = rhoa01
rho02 = rhoa02
rho11 = rhoa11
rho12 = rhoa12
rho21 = rhoa21
rho22 = rhoa22
rho31 = rhoa31
rho32 = rhoa32
else
c call error('Lattice not defined in get_densref.')
endif
if (nn2_meam(a,b).eq.1) then
c Assume that second neighbor is of same type, first neighbor
c may be of different type
if (lat.ne.'bcc') then
c call error('Second-neighbor not defined for this lattice')
endif
call get_Zij2(Zij2nn,arat,scrn,lat,
$ Cmin_meam(a,a,b),Cmax_meam(a,a,b))
a1 = arat*r/re_meam(a,a) - 1.d0
a2 = arat*r/re_meam(b,b) - 1.d0
rhoa01nn = rho0_meam(a)*exp(-beta0_meam(a)*a1)
rhoa02nn = rho0_meam(b)*exp(-beta0_meam(b)*a2)
rho01 = rho01 + Zij2nn*scrn*rhoa02nn
rho02 = rho02 + Zij2nn*scrn*rhoa01nn
endif
return
end
c---------------------------------------------------------------------
c Compute ZBL potential
c
real*8 function zbl(r,z1,z2)
implicit none
integer i,z1,z2
real*8 r,c,d,a,azero,cc,x
dimension c(4),d(4)
data c /0.028171,0.28022,0.50986,0.18175/
data d /0.20162,0.40290,0.94229,3.1998/
data azero /0.4685/
data cc /14.3997/
c azero = (9pi^2/128)^1/3 (0.529) Angstroms
a = azero/(z1**0.23+z2**0.23)
zbl = 0.0
x = r/a
do i=1,4
zbl = zbl + c(i)*exp(-d(i)*x)
enddo
if (r.gt.0.d0) zbl = zbl*z1*z2/r*cc
return
end
c---------------------------------------------------------------------
c Compute Rose energy function, I.16
c
real*8 function erose(r,re,alpha,Ec,repuls,attrac)
implicit none
real*8 r,re,alpha,Ec,repuls,attrac,astar,a3
erose = 0.d0
if (r.gt.0.d0) then
astar = alpha * (r/re - 1.d0)
a3 = 0.d0
if (astar.ge.0) then
a3 = attrac
else if (astar.lt.0) then
a3 = repuls
endif
c erose = -Ec * (1 + astar + a3*(astar**3)/(r/re)) * exp(-astar)
erose = -Ec*(1+astar+(-attrac+repuls/r)*(astar**3))*exp(-astar)
endif
return
end
c -----------------------------------------------------------------------
subroutine interpolate_meam(ind)
use meam_data
implicit none
integer j,ind
real*8 drar
c map to coefficient space
nrar = nr
drar = dr
rdrar = 1.0D0/drar
c phir interp
do j = 1,nrar
phirar(j,ind) = phir(j,ind)
enddo
phirar1(1,ind) = phirar(2,ind)-phirar(1,ind)
phirar1(2,ind) = 0.5D0*(phirar(3,ind)-phirar(1,ind))
phirar1(nrar-1,ind) = 0.5D0*(phirar(nrar,ind)
$ -phirar(nrar-2,ind))
phirar1(nrar,ind) = 0.0D0
do j = 3,nrar-2
phirar1(j,ind) = ((phirar(j-2,ind)-phirar(j+2,ind)) +
$ 8.0D0*(phirar(j+1,ind)-phirar(j-1,ind)))/12.
enddo
do j = 1,nrar-1
phirar2(j,ind) = 3.0D0*(phirar(j+1,ind)-phirar(j,ind)) -
$ 2.0D0*phirar1(j,ind) - phirar1(j+1,ind)
phirar3(j,ind) = phirar1(j,ind) + phirar1(j+1,ind) -
$ 2.0D0*(phirar(j+1,ind)-phirar(j,ind))
enddo
phirar2(nrar,ind) = 0.0D0
phirar3(nrar,ind) = 0.0D0
do j = 1,nrar
phirar4(j,ind) = phirar1(j,ind)/drar
phirar5(j,ind) = 2.0D0*phirar2(j,ind)/drar
phirar6(j,ind) = 3.0D0*phirar3(j,ind)/drar
enddo
end
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