# Finite difference calculation of the clamped-ion
# piezoelectric constants of AlP
#
# The calculation proceeds by computing the change in cell
# polarization by a Berrys phase formula, due to changes
# in the strain of the unit cell. "Clamped-ion" refers to the
# fact that the ions move with the strains but are not
# allowed to relax to their new equilibrium positions
# Berry phase calculation of the polarization
# berryopt -1 triggers the implementation of M. Viethen
berryopt -1
rfdir 1 1 1
# three cell geometries will be computed
ndtset 3
#Definition of the unit cell
acell 3*7.2728565836E+00
# rprim = strain tensor x rprim0, where
# rprim0 is the unstrained rprim
# strain: e4 = 0.00
rprim1
0.0000000000E+00 7.0710678119E-01 7.0710678119E-01
7.0710678119E-01 0.0000000000E+00 7.0710678119E-01
7.0710678119E-01 7.0710678119E-01 0.0000000000E+00
#strain: e4 = 0.01
rprim2
0.0000000000E+00 7.1064231509E-01 7.1064231509E-01
7.0710678119E-01 3.535533906E-03 7.0710678119E-01
7.0710678119E-01 7.0710678119E-01 3.535533906E-03
# strain: e4 = -0.01
rprim3
0.0000000000E+00 7.0357124728E-01 7.0357124728E-01
7.0710678119E-01 -3.535533906E-03 7.0710678119E-01
7.0710678119E-01 7.0710678119E-01 -3.535533906E-03
tolsym 1.0e-8 # Since we make rather small lattice vector changes, with the default value of tolsym
# ABINIT will recognize that we are close to a more symmetric
# configuration, and will resymmetrize the primitive vectors, something we want to avoid ...
#Definition of the atom types and pseudopotentials
ntypat 2 # two types of atoms
znucl 15 13 # the atom types are Phosphorous and Aluminum
# the following norm-conserving pseudopotentials are stored in the abinit distribution, but are freely
# available through www.pseudo-dojo.org
# this set uses the Perdew-Wang parameterization of LDA for the xc model
pp_dirpath "$ABI_PSPDIR"
pseudos "Pseudodojo_nc_sr_04_pw_standard_psp8/P.psp8, Pseudodojo_nc_sr_04_pw_standard_psp8/Al.psp8"
#Definition of the atoms
natom 2 # two atoms in the cell
typat 1 2 # type 1 is Phosphorous, type 2 is Aluminum (order defined by znucl above and pseudos list)
nband 4 # nband is restricted here to the number of filled bands only, no empty bands. The theory of
# the Berrys phase polarization formula assumes filled bands only. Our pseudopotential choice
# includes 5 valence electrons on P, 3 on Al, for 8 total in the primitive unit cell, hence
# 4 filled bands.
#atomic positions, given in units of the cell vectors. Thus as the cell vectors
#change due to strain the atoms will move as well.
xred
1/4 1/4 1/4
0 0 0
#Numerical parameters of the calculation : planewave basis set and k point grid
ecut 5 # this value is very low but is used here to achieve very low calculation times.
# in a production environment this should be checked carefully for convergence and
# a more reasonable value is probably around 20
ecutsm 0.5
dilatmx 1.05
ngkpt 6 6 6
nshiftk 4 # this Monkhorst-Pack shift pattern is used so that the symmetry of the shifted grid
# is correct. A gamma-centered grid would also have the correct symmetry but would be
# less efficient.
shiftk 0.5 0.5 0.5
0.5 0.0 0.0
0.0 0.5 0.0
0.0 0.0 0.5
#Parameters for the SCF procedure
toldfe 1.0d-15
nstep 8
# suppress printing of density, wavefunctions, etc for this tutorial
prtwf 0
prtden 0
prteig 0
##############################################################
# This section is used only for regression testing of ABINIT #
##############################################################
#%%
#%% [setup]
#%% executable = abinit
#%% [files]
#%% files_to_test =
#%% tffield_4.abo, tolnlines= 10, tolabs= 9.999e-9, tolrel= 1.224e-04
#%% [paral_info]
#%% max_nprocs = 2
#%% [extra_info]
#%% authors = J. Zwanziger, M. Veithen
#%% keywords = NC, DFPT
#%% description =
#%% Finite difference calculation of the clamped-ion
#%% piezoelectric constants of AlP
#%%