Dear Abinit community,

I want to determine the elastic and piezoelectric properties of Wurtzite-AlN . Both atomic positions and the lattice constants have been optimized before beginning DFPT calculations.

#AlN in hypothetical wurzite (hexagonal) structure

#Response function calculation for:

# * rigid-atom elastic tensor

# * rigid-atom piezoelectric tensor

# * interatomic force constants at gamma

# * Born effective charges

ndtset 3

# Set 1 : Initial self-consistent run

kptopt1 1

tolvrs1 1.0d-18 #need excellent convergence of GS quantities for RF runs

# Set 2 : Calculate the ddk wf’s - needed for piezoelectric tensor and

# Born effective charges in dataset 3

getwfk2 -1

iscf2 -3 #this option is needed for ddk

kptopt2 2 #use time-reversal symmetry only for k points

nqpt2 1 #one wave vector will be specified

qpt2 0 0 0 #need to specify gamma point

rfelfd2 2 #set for ddk wf’s only

tolwfr2 1.0d-20 #only wf convergence can be monitored here

# Set 3 : response-function calculations for all needed perturbations

getddk3 -1

getwfk3 -2

kptopt3 2 #use time-reversal symmetry only for k points

nqpt3 1

qpt3 0 0 0

rfphon3 1 #do atomic displacement perturbation

rfstrs3 3 #do strain perturbation

tolvrs3 1.0d-10 #need reasonable convergence of 1st-order quantities

#Common input data

# acell COPY RELAXED RESULT FROM PREVIOUS CALCULATION

# Here is a default value, for automatic testing : suppress it and fill with values from the previous run

acell 5.8963399059E+00 5.8963399059E+00 9.5183958753E+00 Bohr

rprim sqrt(0.75) 0.5 0.0 #Better to specify hexagonal primitive vectors

-sqrt(0.75) 0.5 0.0 #with high accuracy to be

0.0 0.0 1.0 #sure that the symmetry is recognized

#and preserved in the optimization process

#Definition of the atom types and atoms

ntypat 2

znucl 13 7

natom 4

typat 1 1 2 2

# xred COPY RELAXED RESULT FROM PREVIOUS CALCULATION

# Here is a set of default values, for automatic testing : suppress it and fill with values from the previous run

xred 3.3333333333E-01 6.6666666667E-01 0.0000000000E+00

6.6666666667E-01 3.3333333333E-01 5.0000000000E-01

3.3333333333E-01 6.6666666667E-01 3.8056006731E-01

6.6666666667E-01 3.3333333333E-01 8.8056006731E-01

#Gives the number of bands, explicitely (do not take the default)

nband 8 # For an insulator (if described correctly as an

# insulator by DFT), conduction bands should not

# be included in response-function calculations

#Definition of the plane wave basis set

ecut 20 # Maximum kinetic energy cutoff (Hartree)

ecutsm 0.5 # Smoothing energy needed for lattice paramete

# optimization. This will be retained for

# consistency throughout.

#Definition of the k-point grid

kptopt 1 # Use symmetry and treat only inequivalent points

ngkpt 4 4 4 # 4x4x4 Monkhorst-Pack grid

nshiftk 1 # Use one copy of grid only (default)

shiftk 0.0 0.0 0.5 # This choice of origin for the k point grid

# preserves the hexagonal symmetry of the grid,

# which would be broken by the default choice.

#Definition of the self-consistency procedure

diemac 9.0 # Model dielectric preconditioner

nstep 40 # Maxiumum number of SCF iterations

# enforce calculation of forces at each SCF step

optforces 1

I checked all scf are convergenced . the stresses are relaxed. I also confirm that the convergence in term of WFK had achieved.

I get a large value of c33 elastic constant :

Elastic Tensor (clamped ion) (unit:10^2GP):

5.3966224 1.2721801 2.4291300 0.0000056 0.0000554 0.0006669

1.2721801 5.3977411 2.4292820 0.0000192 0.0000184 0.0004970

2.4292622 2.4291530 13.2992211 0.0000026 0.0000139 0.0000556

0.0000007 0.0001086 0.0000183 3.0872582 0.0000238 0.0000000

0.0000000 0.0000000 0.0000000 0.0000238 3.0871503 0.0000008

0.0002840 0.0000908 0.0000237 0.0000000 0.0000008 2.0617493

Elastic Tensor (relaxed ion) (unit:10^2GP):

(at fixed electric field boundary condition)

4.7008113 1.5952688 2.8114591 0.0000055 0.0000553 0.0006680

1.5952689 4.7017499 2.8116392 0.0000193 0.0000185 0.0004956

2.8115913 2.8115101 12.5149861 0.0000026 0.0000139 0.0000551

0.0000006 0.0001088 0.0000183 2.9364613 0.0000239 -0.0000000

-0.0000001 0.0000001 0.0000000 0.0000239 2.9363546 0.0000008

0.0002851 0.0000894 0.0000232 -0.0000000 0.0000008 1.5522459

1329 GPa for clamped ion and 1251 GPa for the relaxed ion, while the experimental value is about 350 GPa.

Can someone tells me what wrong and should I take the value of clamped or relaxed ion?

Many thnaks