how to get bulk modulus by Birch-Murnaghan equation?

[lzl8181]

hello,everyone!
in lectures, i know two methods are often adopted to caculate bulk modulus by Birch-Murnaghan equation:
one is increasing isotrpic static pressure on the unit cell (Bravais lattice) step by step, then get the relevant energy, finally using Energy-Pressure-type Birch-Murnaghan equation to obtain the bulk modulus.
the other is by changing the "acell' Parameters, get the relevant energy, through Energy-Volume-type Birch-Murnaghan equation to obtain the bulk modulus; to do this, it is easy to obtain the bulk modulus of cubic cell (Bravais lattice), for the change of "acell" is equal for the three directions; but i don't know how to get bulk modulus of orthogonal, tetragonal, hexagonal, and other types by using this method? can anybody give some detailed guidance?
thanks!
best whishs
lzl

[jzwanzig]

relax your structure using the strtarget input variable, you can then relax in the presence of hydrostatic pressure and get P as a function of ucvol (the unit cell volume) and then you don't need to go through the Eq of state.

[lzl8181]

Dear Pro. Zwanziger
thanks! I see.

[sunnyone]

Dear lzl8181,

I want to caclulate the bulk module for a cubic zinc Blende crystal structure of the binary compound CdS by methods you entioned , i prefer the second one i.e by increasing the "acell", i tried firstly through the toturespon (elastic toturial 6) and i got alot of warnings, actually i don't know how to calcuate it so please can you explain for me how i do that step by step and in below is my input file :


Best regards...



ndtset 12 # Total number of datasets (3*4)
udtset 3 4 # Double loop for k-sample convergence study

nspden 2
nsppol 2
nspinor 1

# Set 1 : Initial self-consistent and lattice optimization run

getwfk?1 0
ionmov?1 2 # Broyden lattice optimization scheme
ntime?1 5 # Maximim lattice optimization steps
optcell?1 1 # Optimize cell volume only
strfact?1 100 # Test convergence of stresses (Hartree/bohr^3) by
# multiplying by this factor and applying force
# convergence test
tolmxf?1 1.0e-6 # Convergence limit for forces as above
tolvrs?1 1.0d-18 # Need excellent convergence of GS quantities for RF runs

# Set 2 : Additional iteration to print density just at converged acell

prtden?2 1 # Third dataset needs density
tolvrs?2 1.0d-18

# Set 3 : Converge unoccupied wave functions

getden?3 -1 # Use density from previout set
tolwfr?3 5.0d-19 # Only wave function convergence can be used with
# non-self-consistent calculation
tolwfr23 1.0d-30 # This is simply for a reason of portability of automatic tests
nstep23 25 # This is simply for a reason of portability of automatic tests
nstep33 35 # This is simply for a reason of portability of automatic tests

# Set 4 : response-function calculations for all needed perturbations

kptopt?4 2 # Time-reversal only for RF calculation
nqpt?4 1
qpt?4 0 0 0 # By symmetry, only need one direction
rfdir?4 1 0 0
rfstrs?4 3 # Need both unaxial and shear strains
tolvrs?4 1.0d-12 # Need reasonable convergence of 1st-order quantities

#Common input data

#Double loop data passing

getcell -1 # Start from optimized (datasets ?2-?4) or previously
# optimized (datasets ?1) acell
getwfk -1 # Use last set of wave functions (except datasets ?1)


#Lattice definition
acell 3*10.96 # Starting value
dilatmx 1.05 # Allow for optimization
rprim 0.0 0.5 0.5
0.5 0.0 0.5
0.5 0.5 0.0

#Definition of the atom types and atoms
ntypat 2
znucl 48 16
natom 2
typat 1 2

#Atomic position
xred 0.0 0.0 0.0
0.25 0.25 0.25

#Definition of the plane wave basis set
ecut 20.947118 # Maximum kinetic energy cutoff (Hartree)
ecutsm 0.5 # Smoothing energy needed for lattice parameter
# optimization. This will be retained for
# consistency throughout.

#Definition of the k-point grid - loop over 3 k-point densities

ngkpt1? 6 6 6
ngkpt2? 8 8 8
ngkpt3? 10 10 10

nshiftk 4 # Use one copy of grid only (default)
shiftk 0.0 0.0 0.5 # This gives the usual fcc Monkhorst-Pack grid
0.0 0.5 0.0
0.5 0.0 0.0
0.5 0.5 0.5

#Definition of occupation numbers and number of bands
nband 10 # With metallic occup
occopt 4 # Femi-function smearing
tsmear 0.02

#Definition of the self-consistency procedure
iscf 5 # Use conjugate-gradient SCF cycle (datasets 1 & 3)
nstep 50 # Maximum number of SCF iterations
# This might not be enough for the very demanding tolwfr?3 above,
# but was chosen for portability reasons.
# enforce calculation of forces at each SCF step
optforces 1


#%%<BEGIN TEST_INFO>
#%% [setup]
#%% executable = abinit
#%% [files]
#%% files_to_test =
#%% telast_6.out, tolnlines= 0, tolabs= 0.000e+00, tolrel= 0.000e+00, fld_options = -medium
#%% psp_files = 13al.pspnc, 33as.pspnc
#%% [paral_info]
#%% max_nprocs = 1
#%% [extra_info]
#%% author =
#%% keywords =
#%% description =
#%%<END TEST_INFO>

[BAMGBOSE, M. K.]

relax your structure using the strtarget input variable, you can then relax in the presence of hydrostatic pressure and get P as a function of ucvol (the unit cell volume) and then you don't need to go through the Eq of state.

Dear Jzwanzig,
please help me out. I am working on cubic system and i have the following output

"Scale of Primitive Cell (acell) [bohr]
8.80000000000000E+00 8.80000000000000E+00 8.80000000000000E+00
Real space primitive translations (rprimd) [bohr]
0.00000000000000E+00 4.40000000000000E+00 4.40000000000000E+00
4.40000000000000E+00 0.00000000000000E+00 4.40000000000000E+00
4.40000000000000E+00 4.40000000000000E+00 0.00000000000000E+00
Unitary Cell Volume (ucvol) [Bohr^3]= 1.70368000000000E+02
Angles (23,13,12)= [degrees]
6.00000000000000E+01 6.00000000000000E+01 6.00000000000000E+01
Lengths [Bohr]
6.22253967444162E+00 6.22253967444162E+00 6.22253967444162E+00
Stress tensor in cartesian coordinates (strten) [Ha/bohr^3]
-9.31428390291595E-04 0.00000000000000E+00 0.00000000000000E+00
0.00000000000000E+00 -9.31428390291594E-04 0.00000000000000E+00
0.00000000000000E+00 0.00000000000000E+00 -9.31428390291593E-04
Total energy (etotal) [Ha]= -1.18290446959563E+01


Cartesian components of stress tensor (hartree/bohr^3)
sigma(1 1)= -9.31428390E-04 sigma(3 2)= 0.00000000E+00
sigma(2 2)= -9.31428390E-04 sigma(3 1)= 0.00000000E+00
sigma(3 3)= -9.31428390E-04 sigma(2 1)= 0.00000000E+00

-Cartesian components of stress tensor (GPa) [Pressure= 2.7404E+01 GPa]
- sigma(1 1)= -2.74035647E+01 sigma(3 2)= 0.00000000E+00
- sigma(2 2)= -2.74035647E+01 sigma(3 1)= 0.00000000E+00
- sigma(3 3)= -2.74035647E+01 sigma(2 1)= 0.00000000E+00"

I don't know values to pick from this output to calculate bulk modulus and pressure derivative of bulk modulus.
Thanks

[jzwanzig]

The unit cell volume is 1.70368E2 bohr^3 (see ucvol) and the pressure is 2.7404E1 GPa (look for the word Pressure).