Added elastic constant example at finite temperature

git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@14097 f3b2605a-c512-4ea7-a41b-209d697bcdaa

examples/ELASTIC/in.elastic

@@ -42,12 +42,6 @@
 #  that minimization is not required, you can set maxiter = 0.0 in 
 #  init.mod. 
 #
-#  There are two alternate versions of displace.mod provided.
-#  They are displace_restart.mod and displace_reverse.mod. 
-#  The former resets the box using a restart file while 
-#  the latter reverses the deformation. Copy whichever
-#  one you like best to displace.mod.
-#
 
 include init.mod
 include potential.mod

examples/ELASTIC_T/Si.sw

+# DATE: 2007-06-11 CONTRIBUTOR: Aidan Thompson, athomps@sandia.gov CITATION: Stillinger and Weber,  Phys Rev B, 31, 5262, (1985)
+# Stillinger-Weber parameters for various elements and mixtures
+# multiple entries can be added to this file, LAMMPS reads the ones it needs
+# these entries are in LAMMPS "metal" units:
+#   epsilon = eV; sigma = Angstroms
+#   other quantities are unitless
+
+# format of a single entry (one or more lines):
+#   element 1, element 2, element 3, 
+#   epsilon, sigma, a, lambda, gamma, costheta0, A, B, p, q, tol
+
+# Here are the original parameters in metal units, for Silicon from:
+#
+# Stillinger and Weber,  Phys. Rev. B, v. 31, p. 5262, (1985)
+#
+
+Si Si Si 2.1683  2.0951  1.80  21.0  1.20  -0.333333333333
+         7.049556277  0.6022245584  4.0  0.0 0.0

examples/ELASTIC_T/displace.mod

+# NOTE: This script should not need to be
+# modified. See in.elastic for more info.
+#
+# Find which reference length to use
+
+if "${dir} == 1" then &
+   "variable len0 equal ${lx0}" 
+if "${dir} == 2" then &
+   "variable len0 equal ${ly0}" 
+if "${dir} == 3" then &
+   "variable len0 equal ${lz0}" 
+if "${dir} == 4" then &
+   "variable len0 equal ${lz0}" 
+if "${dir} == 5" then &
+   "variable len0 equal ${lz0}" 
+if "${dir} == 6" then &
+   "variable len0 equal ${ly0}" 
+
+# Reset box and simulation parameters
+
+clear
+box tilt large
+read_restart restart.equil
+include potential.mod
+
+# Negative deformation
+
+variable delta equal -${up}*${len0}
+variable deltaxy equal -${up}*xy
+variable deltaxz equal -${up}*xz
+variable deltayz equal -${up}*yz
+if "${dir} == 1" then &
+   "change_box all x delta 0 ${delta} xy delta ${deltaxy} xz delta ${deltaxz} remap units box"
+if "${dir} == 2" then &
+   "change_box all y delta 0 ${delta} yz delta ${deltayz} remap units box"
+if "${dir} == 3" then &
+   "change_box all z delta 0 ${delta} remap units box"
+if "${dir} == 4" then &
+   "change_box all yz delta ${delta} remap units box"
+if "${dir} == 5" then &
+   "change_box all xz delta ${delta} remap units box"
+if "${dir} == 6" then &
+   "change_box all xy delta ${delta} remap units box"
+
+# Run MD
+
+run ${nequil}
+include potential.mod
+run ${nrun}
+
+# Obtain new stress tensor
+ 
+variable pxx1 equal f_avp[1]
+variable pyy1 equal f_avp[2]
+variable pzz1 equal f_avp[3]
+variable pxy1 equal f_avp[4]
+variable pxz1 equal f_avp[5]
+variable pyz1 equal f_avp[6]
+
+# Compute elastic constant from pressure tensor
+
+variable C1neg equal ${d1}
+variable C2neg equal ${d2}
+variable C3neg equal ${d3}
+variable C4neg equal ${d4}
+variable C5neg equal ${d5}
+variable C6neg equal ${d6}
+
+# Reset box and simulation parameters
+
+clear
+box tilt large
+read_restart restart.equil
+include potential.mod
+
+# Positive deformation
+
+variable delta equal ${up}*${len0}
+variable deltaxy equal ${up}*xy
+variable deltaxz equal ${up}*xz
+variable deltayz equal ${up}*yz
+if "${dir} == 1" then &
+   "change_box all x delta 0 ${delta} xy delta ${deltaxy} xz delta ${deltaxz} remap units box"
+if "${dir} == 2" then &
+   "change_box all y delta 0 ${delta} yz delta ${deltayz} remap units box"
+if "${dir} == 3" then &
+   "change_box all z delta 0 ${delta} remap units box"
+if "${dir} == 4" then &
+   "change_box all yz delta ${delta} remap units box"
+if "${dir} == 5" then &
+   "change_box all xz delta ${delta} remap units box"
+if "${dir} == 6" then &
+   "change_box all xy delta ${delta} remap units box"
+
+# Run MD
+
+run ${nequil}
+include potential.mod
+run ${nrun}
+
+# Obtain new stress tensor
+ 
+variable tmp equal pe
+variable e1 equal ${tmp}
+variable tmp equal press
+variable p1 equal ${tmp}
+variable tmp equal pxx
+variable pxx1 equal ${tmp}
+variable tmp equal pyy
+variable pyy1 equal ${tmp}
+variable tmp equal pzz
+variable pzz1 equal ${tmp}
+variable tmp equal pxy
+variable pxy1 equal ${tmp}
+variable tmp equal pxz
+variable pxz1 equal ${tmp}
+variable tmp equal pyz
+variable pyz1 equal ${tmp}
+
+# Compute elastic constant from pressure tensor
+
+variable C1pos equal ${d1}
+variable C2pos equal ${d2}
+variable C3pos equal ${d3}
+variable C4pos equal ${d4}
+variable C5pos equal ${d5}
+variable C6pos equal ${d6}
+
+# Combine positive and negative 
+
+variable C1${dir} equal 0.5*(${C1neg}+${C1pos})
+variable C2${dir} equal 0.5*(${C2neg}+${C2pos})
+variable C3${dir} equal 0.5*(${C3neg}+${C3pos})
+variable C4${dir} equal 0.5*(${C4neg}+${C4pos})
+variable C5${dir} equal 0.5*(${C5neg}+${C5pos})
+variable C6${dir} equal 0.5*(${C6neg}+${C6pos})
+
+# Delete dir to make sure it is not reused
+
+variable dir delete

examples/ELASTIC_T/in.elastic

+# Compute elastic constant tensor for a crystal at finite temperature
+#
+# 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
+
+include potential.mod
+run ${nequil}
+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}+${C65})
+
+variable C11cubic equal (${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 "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 "Bulk Modulus = ${bulkmodulus} ${cunits}"
+print "Shear Modulus 1 = ${shearmodulus1} ${cunits}"
+print "Shear Modulus 2 = ${shearmodulus2} ${cunits}"
+print "Poisson Ratio = ${poissonratio}"

examples/ELASTIC_T/init.mod

+# NOTE: This script can be modified for different atomic structures, 
+# units, etc. See in.elastic for more info.
+#
+
+# Define the finite deformation size. Try several values of this
+# variable to verify that results do not depend on it.
+variable up equal 1.0e-1
+ 
+# metal units, elastic constants in GPa
+units		metal
+variable cfac equal 1.0e-4
+variable cunits string GPa
+
+# Define MD parameters
+variable nevery equal 10
+variable nrepeat equal 10
+variable nfreq equal ${nevery}*${nrepeat}
+variable nthermo equal ${nfreq}
+variable nequil equal 10*${nthermo}
+variable nrun equal 3*${nthermo}
+variable temp equal 2000.0
+variable timestep equal 0.001
+variable mass1 equal 28.06
+variable tdamp equal 0.01
+variable seed equal 123457
+
+# generate the box and atom positions using a diamond lattice
+variable a equal 5.431
+
+boundary	p p p
+
+lattice         diamond $a
+region		box prism 0 3.0 0 3.0 0 3.0 0.0 0.0 0.0
+create_box	1 box
+create_atoms	1 box
+mass 1 ${mass1}
+

examples/ELASTIC_T/potential.mod

+# NOTE: This script can be modified for different pair styles 
+# See in.elastic for more info.
+
+reset_timestep 0
+
+# Choose potential
+pair_style	sw
+pair_coeff * * Si.sw Si
+
+# Setup neighbor style
+neighbor 1.0 nsq
+neigh_modify once no every 1 delay 0 check yes
+
+# Setup output
+
+fix avp all ave/time  ${nevery} ${nrepeat} ${nfreq} c_thermo_press mode vector
+thermo		${nthermo}
+thermo_style custom step temp pe press f_avp[1] f_avp[2] f_avp[3] f_avp[4] f_avp[5] f_avp[6]
+thermo_modify norm no
+
+# Setup MD
+
+timestep ${timestep}
+fix 4 all nve
+fix 5 all langevin ${temp} ${temp} ${tdamp} ${seed}
+
+

examples/README

@@ -144,9 +144,13 @@ either by itself or in tandem with another code or library.  See the
 COUPLE/README file to get started.
 
 The ELASTIC directory has an example script for computing elastic
-constants, using a zero temperature Si example.  See the
+constants at zero temperature, using an Si example.  See the
 ELASTIC/in.elastic file for more info.
 
+The ELASTIC_T directory has an example script for computing elastic
+constants at finite temperature, using an Si example.  See the
+ELASTIC_T/in.elastic file for more info.
+
 The KAPPA directory has example scripts for computing the thermal
 conductivity (kappa) of a LJ liquid using 4 different methods.  See
 the KAPPA/README file for more info.