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Hopefully got compute_born_matrix numdiff method working. Also added two BORN_MATRIX examples.

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This commit is contained in:
Germain Clavier
2022-02-08 16:40:52 +01:00
parent ba89ad546a
commit 9833e5bc66
19 changed files with 200696 additions and 38 deletions
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3
examples/BORN_MATRIX/Analytical/born.out Normal file
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# Time-averaged data for fix CB
# TimeStep c_born[1] c_born[2] c_born[3] c_born[4] c_born[5] c_born[6] c_born[7] c_born[8] c_born[9] c_born[10] c_born[11] c_born[12] c_born[13] c_born[14] c_born[15] c_born[16] c_born[17] c_born[18] c_born[19] c_born[20] c_born[21]
100000 9577.85 9573.68 9585.15 5337.63 5342.81 5336.15 5336.15 5342.81 -9.85484 -4.88876 -2.9626 5337.63 12.6266 0.945491 0.397088 4.06348 4.42366 3.62678 3.62678 0.945491 -9.85484

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examples/BORN_MATRIX/Analytical/born_matrix.out Normal file
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# Cij Matrix from post process computation
3.36316 1.87373 1.87607 -0.00346 -0.00172 -0.00104
1.87373 3.36170 1.87425 0.00443 0.00033 0.00014
1.87607 1.87425 3.36573 0.00143 0.00155 0.00127
-0.00346 0.00443 0.00143 1.87425 0.00127 0.00033
-0.00172 0.00033 0.00155 0.00127 1.87607 -0.00346
-0.00104 0.00014 0.00127 0.00033 -0.00346 1.87373

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examples/BORN_MATRIX/Analytical/compute_born.py Normal file
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import sys
import numpy as np
def reduce_Born(Cf):
C = np.zeros((6,6), dtype=np.float64)
C[0,0] = Cf[0]
C[1,1] = Cf[1]
C[2,2] = Cf[2]
C[3,3] = Cf[3]
C[4,4] = Cf[4]
C[5,5] = Cf[5]
C[0,1] = Cf[6]
C[0,2] = Cf[7]
C[0,3] = Cf[8]
C[0,4] = Cf[9]
C[0,5] = Cf[10]
C[1,2] = Cf[11]
C[1,3] = Cf[12]
C[1,4] = Cf[13]
C[1,5] = Cf[14]
C[2,3] = Cf[15]
C[2,4] = Cf[16]
C[2,5] = Cf[17]
C[3,4] = Cf[18]
C[3,5] = Cf[19]
C[4,5] = Cf[20]
C = np.where(C,C,C.T)
return C
def compute_delta():
D = np.zeros((3,3,3,3))
for a in range(3):
for b in range(3):
for m in range(3):
for n in range(3):
D[a,b,m,n] = (a==m)*(b==n) + (a==n)*(b==m)
d = np.zeros((6,6))
d[0,0] = D[0,0,0,0]
d[1,1] = D[1,1,1,1]
d[2,2] = D[2,2,2,2]
d[3,3] = D[1,2,1,2]
d[4,4] = D[0,2,0,2]
d[5,5] = D[0,1,0,1]
d[0,1] = D[0,0,1,1]
d[0,2] = D[0,0,2,2]
d[0,3] = D[0,0,1,2]
d[0,4] = D[0,0,0,2]
d[0,5] = D[0,0,0,1]
d[1,2] = D[1,1,2,2]
d[1,3] = D[1,1,1,2]
d[1,4] = D[1,1,0,2]
d[1,5] = D[1,1,0,1]
d[2,3] = D[2,2,1,2]
d[2,4] = D[2,2,0,2]
d[2,5] = D[2,2,0,1]
d[3,4] = D[1,2,0,2]
d[3,5] = D[1,2,0,1]
d[4,5] = D[0,2,0,1]
d = np.where(d,d,d.T)
return d
def write_matrix(C, filename):
with open(filename, 'w') as f:
f.write("# Cij Matrix from post process computation\n")
for i in C:
f.write("{:8.5f} {:8.5f} {:8.5f} {:8.5f} {:8.5f} {:8.5f}\n".format(
i[0]*10**-9, i[1]*10**-9, i[2]*10**-9, i[3]*10**-9, i[4]*10**-9, i[5]*10**-9,
)
)
return
def main():
N = 500
vol = 27.047271**3 * 10**-30 # m^3
T = 60 # K
kb = 1.380649 * 10**-23 # J/K
kbT = T*kb # J
kcalmol2J = 4183.9954/(6.022*10**23)
born = np.loadtxt('born.out')
stre = np.loadtxt('vir.out')
stre[:, 1:] = -stre[:, 1:]*101325 # -> Pa
try:
mean_born = np.mean(born[:, 1:], axis=0)
except IndexError:
mean_born = born[1:]
CB = kcalmol2J/vol*reduce_Born(mean_born) # -> J/m^3=Pa
Cs = vol/kbT*np.cov(stre[:,1:].T)
Ct = N*kbT/vol * compute_delta()
C = CB - Cs + Ct
write_matrix(CB, 'born_matrix.out')
write_matrix(Cs, 'stre_matrix.out')
write_matrix(Ct, 'temp_matrix.out')
write_matrix(C, 'full_matrix.out')
C11 = np.mean([C[0,0], C[1,1], C[2,2]]) * 10**-9
C12 = np.mean([C[0,1], C[0,2], C[1,2]]) * 10**-9
C44 = np.mean([C[3,3], C[4,4], C[5,5]]) * 10**-9
eC11 = np.std([C[0,0], C[1,1], C[2,2]]) * 10**-9
eC12 = np.std([C[0,1], C[0,2], C[1,2]]) * 10**-9
eC44 = np.std([C[3,3], C[4,4], C[5,5]]) * 10**-9
print(C*10**-9)
print("C11 = {:f} ± {:f}; C12 = {:f} ± {:f}; C44 = {:f} ± {:f}".format(C11, eC11, C12, eC12, C44, eC44))
return
if __name__ == "__main__":
try:
main()
except KeyboardInterrupt:
raise SystemExit("User interruption.")

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examples/BORN_MATRIX/Analytical/full_matrix.out Normal file
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# Cij Matrix from post process computation
2.18161 1.13726 1.16596 -0.01607 -0.02637 0.00291
1.13726 2.20242 1.16714 0.00386 -0.05820 0.02644
1.16596 1.16714 2.24704 -0.00354 -0.00368 0.02714
-0.01607 0.00386 -0.00354 1.43706 0.00210 0.01003
-0.02637 -0.05820 -0.00368 0.00210 1.37530 0.01401
0.00291 0.02644 0.02714 0.01003 0.01401 1.42403

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examples/BORN_MATRIX/Analytical/in.ljcov Normal file
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# Numerical difference calculation
# of Born matrix
# Note that because of cubic symmetry and central forces, we have:
# C11, pure axial == positive mean value: 1,2,3
# C44==C23, pure shear == positive mean value, exactly match in pairs: (4,12),(5,8),(6,7)
# C14==C56, shear/axial(normal) == zero mean, exactly match in pairs: (9,21),(14,20),(18,19)
# C15, shear/axial(in-plane) == zero mean: 10,11,13,15,16,17
# adjustable parameters
units real
variable nsteps index 100000 # length of run
variable nthermo index 1000 # thermo output interval
variable nlat equal 5 # size of box
variable T equal 60. # Temperature in K
variable rho equal 5.405 # Lattice spacing in A
atom_style atomic
lattice fcc ${rho}
region box block 0 ${nlat} 0 ${nlat} 0 ${nlat}
create_box 1 box
create_atoms 1 box
mass * 39.948
velocity all create ${T} 87287 loop geom
velocity all zero linear
pair_style lj/cut 12.
pair_coeff 1 1 0.238067 3.405
neighbor 0.0 bin
neigh_modify every 1 delay 0 check no
variable vol equal vol
thermo 100
fix aL all ave/time 1 1 1 v_vol ave running
fix NPT all npt temp $T $T 100 aniso 1. 1. 1000 fixedpoint 0. 0. 0.
run 20000
unfix NPT
variable newL equal "f_aL^(1./3.)"
change_box all x final 0 ${newL} y final 0. ${newL} z final 0. ${newL} remap units box
unfix aL
reset_timestep 0
# Conversion variables
variable kb equal 1.38065e-23 # J/K
variable Myvol equal "vol*10^-30" # Volume in m^3
variable kbt equal "v_kb*v_T"
variable Nat equal atoms
variable Rhokbt equal "v_kbt*v_Nat/v_Myvol"
variable at2Pa equal 101325
variable kcalmol2J equal "4183.9954/(6.022e23)"
variable C1 equal "v_kcalmol2J/v_Myvol" # Convert Cb from energy to pressure units
variable C2 equal "v_Myvol/v_kbt" # Factor for Cfl terms
variable Pa2GPa equal 1e-9
# Born compute giving <C^b> terms
compute born all born/matrix
# The six virial stress component to compute <C^fl>
compute VIR all pressure NULL virial
variable s1 equal "-c_VIR[1]*v_at2Pa"
variable s2 equal "-c_VIR[2]*v_at2Pa"
variable s3 equal "-c_VIR[3]*v_at2Pa"
variable s6 equal "-c_VIR[4]*v_at2Pa"
variable s5 equal "-c_VIR[5]*v_at2Pa"
variable s4 equal "-c_VIR[6]*v_at2Pa"
variable press equal press
# Average of Born term and vector to store stress
# for post processing
fix CB all ave/time 1 ${nthermo} ${nthermo} c_born[*] ave running file born.out overwrite
fix CPR all ave/time 1 1 1 c_VIR[*] file vir.out
fix APR all ave/time 1 1 1 v_press ave running
fix VEC all vector 1 v_s1 v_s2 v_s3 v_s4 v_s5 v_s6
thermo ${nthermo}
thermo_style custom step temp press f_APR c_born[1] f_CB[1] c_born[12] f_CB[12] c_born[4] f_CB[4]
thermo_modify line multi
fix 1 all nvt temp $T $T 100
run ${nsteps}
# Compute vector averages
# Note the indice switch.
# LAMMPS convention is NOT the Voigt notation.
variable aves1 equal "ave(f_VEC[1])"
variable aves2 equal "ave(f_VEC[2])"
variable aves3 equal "ave(f_VEC[3])"
variable aves4 equal "ave(f_VEC[6])"
variable aves5 equal "ave(f_VEC[5])"
variable aves6 equal "ave(f_VEC[4])"
# Computing the covariance through the <s_{i}s_{j}>-<s_i><s_j>
# is numerically instable. Here we go through the <(s-<s>)^2>
# definition.
# Computing difference relative to average values
variable ds1 vector "f_VEC[1]-v_aves1"
variable ds2 vector "f_VEC[2]-v_aves2"
variable ds3 vector "f_VEC[3]-v_aves3"
variable ds4 vector "f_VEC[4]-v_aves4"
variable ds5 vector "f_VEC[5]-v_aves5"
variable ds6 vector "f_VEC[6]-v_aves6"
# Squaring and averaging
variable dds1 vector "v_ds1*v_ds1"
variable dds2 vector "v_ds2*v_ds2"
variable dds3 vector "v_ds3*v_ds3"
variable vars1 equal "ave(v_dds1)"
variable vars2 equal "ave(v_dds2)"
variable vars3 equal "ave(v_dds3)"
variable C11 equal "v_Pa2GPa*(v_C1*f_CB[1] - v_C2*v_vars1 + 2*v_Rhokbt)"
variable C22 equal "v_Pa2GPa*(v_C1*f_CB[2] - v_C2*v_vars2 + 2*v_Rhokbt)"
variable C33 equal "v_Pa2GPa*(v_C1*f_CB[3] - v_C2*v_vars3 + 2*v_Rhokbt)"
variable dds12 vector "v_ds1*v_ds2"
variable dds13 vector "v_ds1*v_ds3"
variable dds23 vector "v_ds2*v_ds3"
variable vars12 equal "ave(v_dds12)"
variable vars13 equal "ave(v_dds13)"
variable vars23 equal "ave(v_dds23)"
variable C12 equal "v_Pa2GPa*(v_C1*f_CB[7] - v_C2*v_vars12)"
variable C13 equal "v_Pa2GPa*(v_C1*f_CB[8] - v_C2*v_vars13)"
variable C23 equal "v_Pa2GPa*(v_C1*f_CB[12] - v_C2*v_vars23)"
variable dds4 vector "v_ds4*v_ds4"
variable dds5 vector "v_ds5*v_ds5"
variable dds6 vector "v_ds6*v_ds6"
variable vars4 equal "ave(v_dds4)"
variable vars5 equal "ave(v_dds5)"
variable vars6 equal "ave(v_dds6)"
variable C44 equal "v_Pa2GPa*(v_C1*f_CB[4] - v_C2*v_vars4 + v_Rhokbt)"
variable C55 equal "v_Pa2GPa*(v_C1*f_CB[5] - v_C2*v_vars5 + v_Rhokbt)"
variable C66 equal "v_Pa2GPa*(v_C1*f_CB[6] - v_C2*v_vars6 + v_Rhokbt)"
variable aC11 equal "(v_C11 + v_C22 + v_C33)/3."
variable aC12 equal "(v_C12 + v_C13 + v_C23)/3."
variable aC44 equal "(v_C44 + v_C55 + v_C66)/3."
print """
C11 = ${aC11}
C12 = ${aC12}
C44 = ${aC44}
"""

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examples/BORN_MATRIX/Analytical/stre_matrix.out Normal file
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# Cij Matrix from post process computation
1.22342 0.73647 0.71011 0.01261 0.02465 -0.00395
0.73647 1.20115 0.70711 0.00057 0.05854 -0.02630
0.71011 0.70711 1.16055 0.00497 0.00524 -0.02587
0.01261 0.00057 0.00497 0.45813 -0.00083 -0.00969
0.02465 0.05854 0.00524 -0.00083 0.52170 -0.01747
-0.00395 -0.02630 -0.02587 -0.00969 -0.01747 0.47064

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examples/BORN_MATRIX/Analytical/temp_matrix.out Normal file
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# Cij Matrix from post process computation
0.04187 0.00000 0.00000 0.00000 0.00000 0.00000
0.00000 0.04187 0.00000 0.00000 0.00000 0.00000
0.00000 0.00000 0.04187 0.00000 0.00000 0.00000
0.00000 0.00000 0.00000 0.02093 0.00000 0.00000
0.00000 0.00000 0.00000 0.00000 0.02093 0.00000
0.00000 0.00000 0.00000 0.00000 0.00000 0.02093

100003
examples/BORN_MATRIX/Analytical/vir.out Normal file
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File diff suppressed because it is too large Load Diff

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examples/BORN_MATRIX/Numdiff/born.out Normal file
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# Time-averaged data for fix CB
# TimeStep c_born[1] c_born[2] c_born[3] c_born[4] c_born[5] c_born[6] c_born[7] c_born[8] c_born[9] c_born[10] c_born[11] c_born[12] c_born[13] c_born[14] c_born[15] c_born[16] c_born[17] c_born[18] c_born[19] c_born[20] c_born[21]
100000 9564.72 9600.27 9617.45 5363.27 5360.5 5353.08 5322.45 5329.46 6.62317 6.21194 -5.09248 5333.63 3.19349 2.42725 -0.188514 -1.65451 1.07531 -1.6134 -1.10109 1.86461 6.88031

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examples/BORN_MATRIX/Numdiff/born_matrix.out Normal file
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# Cij Matrix from post process computation
3.35855 1.86892 1.87139 0.00233 0.00218 -0.00179
1.86892 3.37104 1.87285 0.00112 0.00085 -0.00007
1.87139 1.87285 3.37707 -0.00058 0.00038 -0.00057
0.00233 0.00112 -0.00058 1.88326 -0.00039 0.00065
0.00218 0.00085 0.00038 -0.00039 1.88229 0.00242
-0.00179 -0.00007 -0.00057 0.00065 0.00242 1.87968

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examples/BORN_MATRIX/Numdiff/compute_born.py Normal file
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import sys
import numpy as np
def reduce_Born(Cf):
C = np.zeros((6,6), dtype=np.float64)
C[0,0] = Cf[0]
C[1,1] = Cf[1]
C[2,2] = Cf[2]
C[3,3] = Cf[3]
C[4,4] = Cf[4]
C[5,5] = Cf[5]
C[0,1] = Cf[6]
C[0,2] = Cf[7]
C[0,3] = Cf[8]
C[0,4] = Cf[9]
C[0,5] = Cf[10]
C[1,2] = Cf[11]
C[1,3] = Cf[12]
C[1,4] = Cf[13]
C[1,5] = Cf[14]
C[2,3] = Cf[15]
C[2,4] = Cf[16]
C[2,5] = Cf[17]
C[3,4] = Cf[18]
C[3,5] = Cf[19]
C[4,5] = Cf[20]
C = np.where(C,C,C.T)
return C
def compute_delta():
D = np.zeros((3,3,3,3))
for a in range(3):
for b in range(3):
for m in range(3):
for n in range(3):
D[a,b,m,n] = (a==m)*(b==n) + (a==n)*(b==m)
d = np.zeros((6,6))
d[0,0] = D[0,0,0,0]
d[1,1] = D[1,1,1,1]
d[2,2] = D[2,2,2,2]
d[3,3] = D[1,2,1,2]
d[4,4] = D[0,2,0,2]
d[5,5] = D[0,1,0,1]
d[0,1] = D[0,0,1,1]
d[0,2] = D[0,0,2,2]
d[0,3] = D[0,0,1,2]
d[0,4] = D[0,0,0,2]
d[0,5] = D[0,0,0,1]
d[1,2] = D[1,1,2,2]
d[1,3] = D[1,1,1,2]
d[1,4] = D[1,1,0,2]
d[1,5] = D[1,1,0,1]
d[2,3] = D[2,2,1,2]
d[2,4] = D[2,2,0,2]
d[2,5] = D[2,2,0,1]
d[3,4] = D[1,2,0,2]
d[3,5] = D[1,2,0,1]
d[4,5] = D[0,2,0,1]
d = np.where(d,d,d.T)
return d
def write_matrix(C, filename):
with open(filename, 'w') as f:
f.write("# Cij Matrix from post process computation\n")
for i in C:
f.write("{:8.5f} {:8.5f} {:8.5f} {:8.5f} {:8.5f} {:8.5f}\n".format(
i[0]*10**-9, i[1]*10**-9, i[2]*10**-9, i[3]*10**-9, i[4]*10**-9, i[5]*10**-9,
)
)
return
def main():
N = 500
vol = 27.047271**3 * 10**-30 # m^3
T = 60 # K
kb = 1.380649 * 10**-23 # J/K
kbT = T*kb # J
kcalmol2J = 4183.9954/(6.022*10**23)
born = np.loadtxt('born.out')
stre = np.loadtxt('vir.out')
stre[:, 1:] = -stre[:, 1:]*101325 # -> Pa
try:
mean_born = np.mean(born[:, 1:], axis=0)
except IndexError:
mean_born = born[1:]
CB = kcalmol2J/vol*reduce_Born(mean_born) # -> J/m^3=Pa
Cs = vol/kbT*np.cov(stre[:,1:].T)
Ct = N*kbT/vol * compute_delta()
C = CB - Cs + Ct
write_matrix(CB, 'born_matrix.out')
write_matrix(Cs, 'stre_matrix.out')
write_matrix(Ct, 'temp_matrix.out')
write_matrix(C, 'full_matrix.out')
C11 = np.mean([C[0,0], C[1,1], C[2,2]]) * 10**-9
C12 = np.mean([C[0,1], C[0,2], C[1,2]]) * 10**-9
C44 = np.mean([C[3,3], C[4,4], C[5,5]]) * 10**-9
eC11 = np.std([C[0,0], C[1,1], C[2,2]]) * 10**-9
eC12 = np.std([C[0,1], C[0,2], C[1,2]]) * 10**-9
eC44 = np.std([C[3,3], C[4,4], C[5,5]]) * 10**-9
print(C*10**-9)
print("C11 = {:f} ± {:f}; C12 = {:f} ± {:f}; C44 = {:f} ± {:f}".format(C11, eC11, C12, eC12, C44, eC44))
return
if __name__ == "__main__":
try:
main()
except KeyboardInterrupt:
raise SystemExit("User interruption.")

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examples/BORN_MATRIX/Numdiff/full_matrix.out Normal file
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# Cij Matrix from post process computation
2.29922 1.17439 1.20854 -0.01653 -0.01684 0.01188
1.17439 2.20673 1.21718 -0.00781 -0.00753 0.00867
1.20854 1.21718 2.30804 0.01535 -0.01596 0.00426
-0.01653 -0.00781 0.01535 1.47647 -0.01355 -0.01601
-0.01684 -0.00753 -0.01596 -0.01355 1.37905 0.01975
0.01188 0.00867 0.00426 -0.01601 0.01975 1.40170

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examples/BORN_MATRIX/Numdiff/in.ljcov Normal file
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# Numerical difference calculation
# of Born matrix
# Note that because of cubic symmetry and central forces, we have:
# C11, pure axial == positive mean value: 1,2,3
# C44==C23, pure shear == positive mean value, exactly match in pairs: (4,12),(5,8),(6,7)
# C14==C56, shear/axial(normal) == zero mean, exactly match in pairs: (9,21),(14,20),(18,19)
# C15, shear/axial(in-plane) == zero mean: 10,11,13,15,16,17
# adjustable parameters
units real
variable nsteps index 100000 # length of run
variable nthermo index 1000 # thermo output interval
variable nlat equal 5 # size of box
variable T equal 60. # Temperature in K
variable rho equal 5.405 # Lattice spacing in A
atom_style atomic
lattice fcc ${rho}
region box block 0 ${nlat} 0 ${nlat} 0 ${nlat}
create_box 1 box
create_atoms 1 box
mass * 39.948
velocity all create ${T} 87287 loop geom
velocity all zero linear
pair_style lj/cut 12.
pair_coeff 1 1 0.238067 3.405
neighbor 0.0 bin
neigh_modify every 1 delay 0 check no
variable vol equal vol
thermo 100
fix aL all ave/time 1 1 1 v_vol ave running
fix NPT all npt temp $T $T 100 aniso 1. 1. 1000 fixedpoint 0. 0. 0.
run 20000
unfix NPT
variable newL equal "f_aL^(1./3.)"
change_box all x final 0 ${newL} y final 0. ${newL} z final 0. ${newL} remap units box
unfix aL
reset_timestep 0
# Conversion variables
variable kb equal 1.38065e-23 # J/K
variable Myvol equal "vol*10^-30" # Volume in m^3
variable kbt equal "v_kb*v_T"
variable Nat equal atoms
variable Rhokbt equal "v_kbt*v_Nat/v_Myvol"
variable at2Pa equal 101325
variable kcalmol2J equal "4183.9954/(6.022e23)"
variable C1 equal "v_kcalmol2J/v_Myvol" # Convert Cb from energy to pressure units
variable C2 equal "v_Myvol/v_kbt" # Factor for Cfl terms
variable Pa2GPa equal 1e-9
# Born compute giving <C^b> terms
# The six virial stress component to compute <C^fl>
compute VIR all pressure NULL virial
compute born all born/matrix numdiff 1e-6 VIR
variable s1 equal "-c_VIR[1]*v_at2Pa"
variable s2 equal "-c_VIR[2]*v_at2Pa"
variable s3 equal "-c_VIR[3]*v_at2Pa"
variable s6 equal "-c_VIR[4]*v_at2Pa"
variable s5 equal "-c_VIR[5]*v_at2Pa"
variable s4 equal "-c_VIR[6]*v_at2Pa"
variable press equal press
# Average of Born term and vector to store stress
# for post processing
fix CB all ave/time 1 ${nthermo} ${nthermo} c_born[*] ave running file born.out overwrite
fix CPR all ave/time 1 1 1 c_VIR[*] file vir.out
fix APR all ave/time 1 1 1 v_press ave running
fix VEC all vector 1 v_s1 v_s2 v_s3 v_s4 v_s5 v_s6
thermo ${nthermo}
thermo_style custom step temp press f_APR c_born[1] f_CB[1] c_born[12] f_CB[12] c_born[4] f_CB[4]
thermo_modify line multi
fix 1 all nvt temp $T $T 100
run ${nsteps}
# Compute vector averages
# Note the indice switch.
# LAMMPS convention is NOT the Voigt notation.
variable aves1 equal "ave(f_VEC[1])"
variable aves2 equal "ave(f_VEC[2])"
variable aves3 equal "ave(f_VEC[3])"
variable aves4 equal "ave(f_VEC[6])"
variable aves5 equal "ave(f_VEC[5])"
variable aves6 equal "ave(f_VEC[4])"
# Computing the covariance through the <s_{i}s_{j}>-<s_i><s_j>
# is numerically instable. Here we go through the <(s-<s>)^2>
# definition.
# Computing difference relative to average values
variable ds1 vector "f_VEC[1]-v_aves1"
variable ds2 vector "f_VEC[2]-v_aves2"
variable ds3 vector "f_VEC[3]-v_aves3"
variable ds4 vector "f_VEC[4]-v_aves4"
variable ds5 vector "f_VEC[5]-v_aves5"
variable ds6 vector "f_VEC[6]-v_aves6"
# Squaring and averaging
variable dds1 vector "v_ds1*v_ds1"
variable dds2 vector "v_ds2*v_ds2"
variable dds3 vector "v_ds3*v_ds3"
variable vars1 equal "ave(v_dds1)"
variable vars2 equal "ave(v_dds2)"
variable vars3 equal "ave(v_dds3)"
variable C11 equal "v_Pa2GPa*(v_C1*f_CB[1] - v_C2*v_vars1 + 2*v_Rhokbt)"
variable C22 equal "v_Pa2GPa*(v_C1*f_CB[2] - v_C2*v_vars2 + 2*v_Rhokbt)"
variable C33 equal "v_Pa2GPa*(v_C1*f_CB[3] - v_C2*v_vars3 + 2*v_Rhokbt)"
variable dds12 vector "v_ds1*v_ds2"
variable dds13 vector "v_ds1*v_ds3"
variable dds23 vector "v_ds2*v_ds3"
variable vars12 equal "ave(v_dds12)"
variable vars13 equal "ave(v_dds13)"
variable vars23 equal "ave(v_dds23)"
variable C12 equal "v_Pa2GPa*(v_C1*f_CB[7] - v_C2*v_vars12)"
variable C13 equal "v_Pa2GPa*(v_C1*f_CB[8] - v_C2*v_vars13)"
variable C23 equal "v_Pa2GPa*(v_C1*f_CB[12] - v_C2*v_vars23)"
variable dds4 vector "v_ds4*v_ds4"
variable dds5 vector "v_ds5*v_ds5"
variable dds6 vector "v_ds6*v_ds6"
variable vars4 equal "ave(v_dds4)"
variable vars5 equal "ave(v_dds5)"
variable vars6 equal "ave(v_dds6)"
variable C44 equal "v_Pa2GPa*(v_C1*f_CB[4] - v_C2*v_vars4 + v_Rhokbt)"
variable C55 equal "v_Pa2GPa*(v_C1*f_CB[5] - v_C2*v_vars5 + v_Rhokbt)"
variable C66 equal "v_Pa2GPa*(v_C1*f_CB[6] - v_C2*v_vars6 + v_Rhokbt)"
variable aC11 equal "(v_C11 + v_C22 + v_C33)/3."
variable aC12 equal "(v_C12 + v_C13 + v_C23)/3."
variable aC44 equal "(v_C44 + v_C55 + v_C66)/3."
print """
C11 = ${aC11}
C12 = ${aC12}
C44 = ${aC44}
"""

7
examples/BORN_MATRIX/Numdiff/stre_matrix.out Normal file
View File

@ -0,0 +1,7 @@
# Cij Matrix from post process computation
1.10120 0.69454 0.66285 0.01885 0.01902 -0.01367
0.69454 1.20617 0.65567 0.00893 0.00839 -0.00873
0.66285 0.65567 1.11090 -0.01593 0.01634 -0.00483
0.01885 0.00893 -0.01593 0.42772 0.01316 0.01666
0.01902 0.00839 0.01634 0.01316 0.52416 -0.01733
-0.01367 -0.00873 -0.00483 0.01666 -0.01733 0.49891

7
examples/BORN_MATRIX/Numdiff/temp_matrix.out Normal file
View File

@ -0,0 +1,7 @@
# Cij Matrix from post process computation
0.04187 0.00000 0.00000 0.00000 0.00000 0.00000
0.00000 0.04187 0.00000 0.00000 0.00000 0.00000
0.00000 0.00000 0.04187 0.00000 0.00000 0.00000
0.00000 0.00000 0.00000 0.02093 0.00000 0.00000
0.00000 0.00000 0.00000 0.00000 0.02093 0.00000
0.00000 0.00000 0.00000 0.00000 0.00000 0.02093

100003
examples/BORN_MATRIX/Numdiff/vir.out Normal file
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File diff suppressed because it is too large Load Diff

12
examples/BORN_MATRIX/README.md Normal file
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@ -0,0 +1,12 @@
This repository is a test case for the compute born/matrix. It provides short
scripts creating argon fcc crystal and computing the Born term using the two
methods described in the documentation.
In the __Analytical__ directory the terms are computed using the analytical
derivation of the lj/cut pair style.
In the __Numdiff__ directory, the born term is evaluated through small
numerical differences of the stress tensor. This method can be used with any
interaction potential.
Both script show examples on how to compute the full Cij tensor in LAMMPS.

100
src/EXTRA-COMPUTE/compute_born_matrix.cpp
View File

@ -165,48 +165,59 @@ ComputeBornMatrix::ComputeBornMatrix(LAMMPS *lmp, int narg, char **arg) :
}
if (pairflag) {
if (numflag) error->all(FLERR, "Illegal compute born/matrix command");
if (numflag) error->all(FLERR, "Illegal compute born/matrix command: cannot mix numflag and other flags");
if (force->pair) {
if (force->pair->born_matrix_enable == 0) {
if (comm->me == 0) error->warning(FLERR, "Pair style does not support compute born/matrix");
}
} else {
pairflag = 0;
}
}
if (bondflag) {
if (numflag) error->all(FLERR, "Illegal compute born/matrix command");
if (numflag) error->all(FLERR, "Illegal compute born/matrix command: cannot mix numflag and other flags");
if (force->bond) {
if (force->bond->born_matrix_enable == 0) {
if (comm->me == 0) error->warning(FLERR, "Bond style does not support compute born/matrix");
}
} else {
bondflag = 0;
}
}
if (angleflag) {
if (numflag) error->all(FLERR, "Illegal compute born/matrix command");
if (numflag) error->all(FLERR, "Illegal compute born/matrix command: cannot mix numflag and other flags");
if (force->angle) {
if (force->angle->born_matrix_enable == 0) {
if (comm->me == 0) error->warning(FLERR, "Angle style does not support compute born/matrix");
}
} else {
angleflag = 0;
}
}
if (dihedflag) {
if (numflag) error->all(FLERR, "Illegal compute born/matrix command");
if (numflag) error->all(FLERR, "Illegal compute born/matrix command: cannot mix numflag and other flags");
if (force->dihedral) {
if (force->dihedral->born_matrix_enable == 0) {
if (comm->me == 0) error->warning(FLERR, "Dihedral style does not support compute born/matrix");
}
} else {
dihedflag = 0;
}
}
if (impflag) {
if (numflag) error->all(FLERR, "Illegal compute born/matrix command");
if (numflag) error->all(FLERR, "Illegal compute born/matrix command: cannot mix numflag and other flags");
if (force->improper) {
if (force->improper->born_matrix_enable == 0) {
if (comm->me == 0) error->warning(FLERR, "Improper style does not support compute born/matrix");
}
} else {
impflag = 0;
}
}
if (force->kspace) {
if (!numflag) error->warning(FLERR, "KSPACE contribution not supported by compute born/matrix");
}
// Initialize some variables
values_local = values_global = vector = nullptr;
@ -292,18 +303,18 @@ void ComputeBornMatrix::init()
// set up reverse index lookup
for (int m = 0; m < nvalues; m++) {
int a = albe[m][0];
int b = albe[m][1];
int a = C_albe[m][0];
int b = C_albe[m][1];
revalbe[a][b] = m;
revalbe[b][a] = m;
}
for (int a = 0; a < NDIR_VIRIAL; a++) {
for (int b = 0; b < NDIR_VIRIAL; b++) {
printf("%d ",revalbe[a][b]);
}
printf("\n");
}
// for (int a = 0; a < NDIR_VIRIAL; a++) {
// for (int b = 0; b < NDIR_VIRIAL; b++) {
// printf("%d ",revalbe[a][b]);
// }
// printf("\n");
// }
// voigt3VtoM notation in normal physics sense,
// 3x3 matrix and vector indexing
@ -358,6 +369,13 @@ void ComputeBornMatrix::init()
voigt6MtoV[row][col] = voigt6MtoV[col][row] = indcounter;
indcounter++;
}
// printf("Voigt6MtoV:\n");
// for (int a = 0; a < NDIR_VIRIAL; a++) {
// for (int b = 0; b < NDIR_VIRIAL; b++) {
// printf("%d ", voigt6MtoV[a][b]);
// }
// printf("\n");
// }
// set up 3x3 kronecker deltas
@ -415,6 +433,13 @@ void ComputeBornMatrix::compute_vector()
// calculate Born matrix using stress finite differences
compute_numdiff();
// for consistency this is returned in energy units
double inv_nktv2p = 1.0/force->nktv2p;
double volume = domain->xprd * domain->yprd * domain->zprd;
for (int m = 0; m < nvalues; m++) {
values_global[m] *= inv_nktv2p * volume;
}
}
for (int m = 0; m < nvalues; m++) vector[m] = values_global[m];
@ -527,7 +552,7 @@ void ComputeBornMatrix::compute_pairs()
void ComputeBornMatrix::compute_numdiff()
{
double energy;
int m;
int vec_indice;
// grow arrays if necessary
@ -547,6 +572,10 @@ void ComputeBornMatrix::compute_numdiff()
// loop over 6 strain directions
// compute stress finite difference in each direction
// It must be noted that, as stated in Yoshimoto's eq. 15, eq 16.
// and eq. A3, this tensor is NOT the true Cijkl tensor.
// We have the relationship
// C_ijkl=1./4.(\hat{C}_ijkl+\hat{C}_jikl+\hat{C}_ijlk+\hat{C}_jilk)
int flag, allflag;
@ -555,8 +584,8 @@ void ComputeBornMatrix::compute_numdiff()
force_clear(nall);
update_virial();
for (int jdir = 0; jdir < NDIR_VIRIAL; jdir++) {
m = revalbe[idir][jdir];
values_global[m] = compute_virial->vector[virialVtoV[jdir]];
vec_indice = revalbe[idir][jdir];
values_global[vec_indice] = compute_virial->vector[virialVtoV[jdir]];
}
restore_atoms(nall, idir);
@ -564,9 +593,11 @@ void ComputeBornMatrix::compute_numdiff()
force_clear(nall);
update_virial();
for (int jdir = 0; jdir < NDIR_VIRIAL; jdir++) {
m = revalbe[idir][jdir];
values_global[m] -= compute_virial->vector[virialVtoV[jdir]];
vec_indice = revalbe[idir][jdir];
values_global[vec_indice] -= compute_virial->vector[virialVtoV[jdir]];
}
// End of the strain
restore_atoms(nall, idir);
}
@ -588,6 +619,7 @@ void ComputeBornMatrix::compute_numdiff()
for (int i = 0; i < nall; i++)
for (int k = 0; k < 3; k++)
f[i][k] = temp_f[i][k];
}
/* ----------------------------------------------------------------------
@ -598,14 +630,22 @@ void ComputeBornMatrix::displace_atoms(int nall, int idir, double magnitude)
{
double **x = atom->x;
// this works for 7,8,9,12,14,18, and 15,16,17
// A.T.
// this works for vector indices 7, 8, 9, 12, 14, 18 and 15, 16, 17
// corresponding i,j indices 12, 13, 14, 23, 25, 36 and 26, 34, 35
int k = dirlist[idir][1];
int l = dirlist[idir][0];
// this works for 7,8,9,12,14,18, and 10,11,13
// A.T.
// this works for vector indices 7, 8, 9, 12, 14, 18 and 10, 11, 13
// corresponding i,j indices 12, 13, 14, 23, 25, 36 and 15, 16, 24
// G.C.:
// I see no difference with a 0 step simulation between both
// methods.
// int k = dirlist[idir][0];
// int l = dirlist[idir][1];
for (int i = 0; i < nall; i++)
x[i][k] = temp_x[i][k] + numdelta * magnitude * (temp_x[i][l] - fixedpoint[l]);
x[i][k] = temp_x[i][k] + numdelta * magnitude * (temp_x[i][l] - fixedpoint[l]);
}
/* ----------------------------------------------------------------------
@ -631,7 +671,8 @@ void ComputeBornMatrix::restore_atoms(int nall, int idir)
void ComputeBornMatrix::update_virial()
{
int eflag = 0;
int vflag = VIRIAL_FDOTR; // Need to generalize this
// int vflag = VIRIAL_FDOTR; // Need to generalize this
int vflag = 1;
if (force->pair) force->pair->compute(eflag, vflag);
@ -662,14 +703,17 @@ void ComputeBornMatrix::virial_addon()
// Note: in calculation kl is all there from 0 to 6, and ij=(id,jd)
// each time there are six numbers passed for (Dijkl+Djikl)
// and the term I need should be div by 2.
// Job is to arrange the 6 numbers with ij indexing to the 21 element data structure.
// Job is to arrange the 6 numbers with ij indexing to the 21
// element data structure.
// the sigv is the virial stress at current time. It is never touched.
// Note the symmetry of (i-j), (k-n), and (ij, kn)
// so we only need to evaluate 6x6 matrix with symmetry
int kd, nd, id, jd;
int m;
double* sigv = compute_virial->vector;
double modefactor[6] = {1.0, 1.0, 1.0, 0.5, 0.5, 0.5};
for (int idir = 0; idir < NDIR_VIRIAL; idir++) {
int ijvgt = idir; // this is it.
@ -680,19 +724,18 @@ void ComputeBornMatrix::virial_addon()
id = voigt3VtoM[ijvgt][0];
jd = voigt3VtoM[ijvgt][1];
int SHEAR = 0;
if( id != jd) SHEAR = 1;
for (int knvgt=ijvgt; knvgt < NDIR_VIRIAL; knvgt++) {
kd = voigt3VtoM[knvgt][0];
nd = voigt3VtoM[knvgt][1];
addon = kronecker[id][nd]*sigv[virialMtoV[jd][kd]] +
kronecker[id][kd]*sigv[virialMtoV[jd][nd]];
if(SHEAR)
if(id != jd)
addon += kronecker[jd][nd]*sigv[virialMtoV[id][kd]] +
kronecker[jd][kd]*sigv[virialMtoV[id][nd]];
values_global[revalbe[ijvgt][knvgt]] += addon;
m = revalbe[ijvgt][knvgt];
values_global[revalbe[ijvgt][knvgt]] += 0.5*modefactor[idir]*addon;
}
}
}
@ -841,7 +884,6 @@ void ComputeBornMatrix::compute_bonds()
all atoms in interaction must be known to proc
if bond is deleted or turned off (type <= 0)
do not count or count contribution
<<<<<<< HEAD
---------------------------------------------------------------------- */
void ComputeBornMatrix::compute_angles()
{

10
src/pair.h
View File

@ -53,7 +53,6 @@ class Pair : protected Pointers {
int single_enable; // 1 if single() routine exists
int born_matrix_enable; // 1 if born_matrix() routine exists
int single_hessian_enable; // 1 if single_hessian() routine exists
int born_matrix_enable; // 1 if born_matrix() routine exists
int restartinfo; // 1 if pair style writes restart info
int respa_enable; // 1 if inner/middle/outer rRESPA routines
int one_coeff; // 1 if allows only one coeff * * call
@ -160,13 +159,6 @@ class Pair : protected Pointers {
return 0.0;
}
virtual void born_matrix(int /*i*/, int /*j*/, int /*itype*/, int /*jtype*/, double /*rsq*/,
double /*factor_coul*/, double /*factor_lj*/, double& du, double& du2)
{
du = 0.0;
du2 = 0.0;
}
void hessian_twobody(double fforce, double dfac, double delr[3], double phiTensor[6]);
virtual double single_hessian(int, int, int, int, double, double[3], double, double,
@ -178,7 +170,7 @@ class Pair : protected Pointers {
}
virtual void born_matrix(int /*i*/, int /*j*/, int /*itype*/, int /*jtype*/, double /*rsq*/,
double /*factor_coul*/, double /*factor_lj*/, double& du, double& du2)
double /*factor_coul*/, double /*factor_lj*/, double& du, double& du2)
{
du = 0.0;
du2 = 0.0;