# Compute elastic constant tensor for a crystal at finite temperature
#
# WARNING: This script attempts to measure small differences in 
# statistical averages generated by finite temperature MD simulations. 
# This creates many more opportunities for errors to occur, compared 
# to the zero temperature version provided in examples/ELASTIC.
# Hence, it is always a good idea to start with the zero temperature
# calculation, before attempting to use this script.
#
# Written by Aidan Thompson (Sandia, athomps@sandia.gov)
#
#  This script uses the following three include files.
#
#   init.mod      (must be modified for different crystal structures)
# 	       	  Define units, MD parameters, deformation parameters,
#		  and initial configuration of the atoms and simulation cell.  
#
#
#   potential.mod    (must be modified for different pair styles)
# 		     Define pair style and other attributes 
#		     not stored in restart file
#
#
#   displace.mod    (displace.mod should not need to be modified)
# 		    Perform positive and negative box displacements 
# 		    in direction ${dir} and size ${up}. 
# 		    It uses the resultant changes 
#		    in stress to compute one
# 		    row of the elastic stiffness tensor
#		    
#		    Inputs variables:
#		    	   dir = the Voigt deformation component 
#		    		    (1,2,3,4,5,6)  
#		    Global constants:
#       	    	   up = the deformation magnitude (strain units)
#       		   cfac = conversion from LAMMPS pressure units to 
#               	   output units for elastic constants 
#
#
#  To run this on a different system, it should only be necessary to 
#  modify the files init.mod and potential.mod. In order to calculate
#  the elastic constants correctly, care must be taken to specify
#  the correct units in init.mod (units, cfac and cunits). It is also
#  important to verify that the MD sampling of stress components
#  is generating accurate statistical averages.
#  One indication of this is that the elastic constants are insensitive
#  to the choice of the variable ${up} in init.mod. Another is to
#  check for finite size effects. 
#

include init.mod

# Compute initial state

variable thermostat equal 1
include potential.mod
run ${nequil}

if "${adiabatic} == 1" &
then "variable thermostat equal 0" &
else "variable thermostat equal 1"

print ${thermostat}

include potential.mod
run ${nrun}

variable pxx0 equal f_avp[1]
variable pyy0 equal f_avp[2]
variable pzz0 equal f_avp[3]
variable pxy0 equal f_avp[4]
variable pxz0 equal f_avp[5]
variable pyz0 equal f_avp[6]

variable tmp equal lx
variable lx0 equal ${tmp}
variable tmp equal ly
variable ly0 equal ${tmp}
variable tmp equal lz
variable lz0 equal ${tmp}

# These formulas define the derivatives w.r.t. strain components
# Constants uses $, variables use v_ 
variable d1 equal -(v_pxx1-${pxx0})/(v_delta/v_len0)*${cfac}
variable d2 equal -(v_pyy1-${pyy0})/(v_delta/v_len0)*${cfac}
variable d3 equal -(v_pzz1-${pzz0})/(v_delta/v_len0)*${cfac}
variable d4 equal -(v_pyz1-${pyz0})/(v_delta/v_len0)*${cfac}
variable d5 equal -(v_pxz1-${pxz0})/(v_delta/v_len0)*${cfac}
variable d6 equal -(v_pxy1-${pxy0})/(v_delta/v_len0)*${cfac}

# Write restart
write_restart restart.equil

# uxx Perturbation

variable dir equal 1
include displace.mod

# uyy Perturbation

variable dir equal 2
include displace.mod

# uzz Perturbation

variable dir equal 3
include displace.mod

# uyz Perturbation

variable dir equal 4
include displace.mod

# uxz Perturbation

variable dir equal 5
include displace.mod

# uxy Perturbation

variable dir equal 6
include displace.mod

# Output final values

variable C11all equal ${C11}
variable C22all equal ${C22}
variable C33all equal ${C33}

variable C12all equal 0.5*(${C12}+${C21})
variable C13all equal 0.5*(${C13}+${C31})
variable C23all equal 0.5*(${C23}+${C32})

variable C44all equal ${C44}
variable C55all equal ${C55}
variable C66all equal ${C66}

variable C14all equal 0.5*(${C14}+${C41})
variable C15all equal 0.5*(${C15}+${C51})
variable C16all equal 0.5*(${C16}+${C61})

variable C24all equal 0.5*(${C24}+${C42})
variable C25all equal 0.5*(${C25}+${C52})
variable C26all equal 0.5*(${C26}+${C62})

variable C34all equal 0.5*(${C34}+${C43})
variable C35all equal 0.5*(${C35}+${C53})
variable C36all equal 0.5*(${C36}+${C63})

variable C45all equal 0.5*(${C45}+${C54})
variable C46all equal 0.5*(${C46}+${C64})
variable C56all equal 0.5*(${C56}+${C65})

# Average moduli for cubic crystals

variable C11cubic equal (${C11all}+${C22all}+${C33all})/3.0
variable C12cubic equal (${C12all}+${C13all}+${C23all})/3.0
variable C44cubic equal (${C44all}+${C55all}+${C66all})/3.0

variable bulkmodulus equal (${C11cubic}+2*${C12cubic})/3.0
variable shearmodulus1 equal ${C44cubic}
variable shearmodulus2 equal (${C11cubic}-${C12cubic})/2.0
variable poissonratio equal 1.0/(1.0+${C11cubic}/${C12cubic})
  
# For Stillinger-Weber silicon, the analytical results
# are known to be (E. R. Cowley, 1988):
#               C11 = 151.4 GPa
#               C12 = 76.4 GPa
#               C44 = 56.4 GPa

print "========================================="
print "Components of the Elastic Constant Tensor"
print "========================================="

print "Elastic Constant C11all = ${C11all} ${cunits}"
print "Elastic Constant C22all = ${C22all} ${cunits}"
print "Elastic Constant C33all = ${C33all} ${cunits}"

print "Elastic Constant C12all = ${C12all} ${cunits}"
print "Elastic Constant C13all = ${C13all} ${cunits}"
print "Elastic Constant C23all = ${C23all} ${cunits}"

print "Elastic Constant C44all = ${C44all} ${cunits}"
print "Elastic Constant C55all = ${C55all} ${cunits}"
print "Elastic Constant C66all = ${C66all} ${cunits}"

print "Elastic Constant C14all = ${C14all} ${cunits}"
print "Elastic Constant C15all = ${C15all} ${cunits}"
print "Elastic Constant C16all = ${C16all} ${cunits}"

print "Elastic Constant C24all = ${C24all} ${cunits}"
print "Elastic Constant C25all = ${C25all} ${cunits}"
print "Elastic Constant C26all = ${C26all} ${cunits}"

print "Elastic Constant C34all = ${C34all} ${cunits}"
print "Elastic Constant C35all = ${C35all} ${cunits}"
print "Elastic Constant C36all = ${C36all} ${cunits}"

print "Elastic Constant C45all = ${C45all} ${cunits}"
print "Elastic Constant C46all = ${C46all} ${cunits}"
print "Elastic Constant C56all = ${C56all} ${cunits}"

print "========================================="
print "Average properties for a cubic crystal"
print "========================================="

print "Bulk Modulus = ${bulkmodulus} ${cunits}"
print "Shear Modulus 1 = ${shearmodulus1} ${cunits}"
print "Shear Modulus 2 = ${shearmodulus2} ${cunits}"
print "Poisson Ratio = ${poissonratio}"