Equation of State using Birch-Murnaghan EOS#

Dataset Download#

The complete dataset (inputs, scripts, and example workflow) is available here:

The archive contains all files required to reproduce the calculation for the FeNi₃ alloy in the L1₂ phase.

Overview#

This tutorial describes how to compute the equation of state (EOS) by fitting total energy vs. volume data using the Birch-Murnaghan EOS.

The goal is to determine:

Equilibrium volume \(V_0\)
Minimum energy \(E_0\)
Bulk modulus \(B_0\)
Pressure derivative \(B_0'\)

Required Files#

File	Description	Usage
i_mst	Main input file	Controls the simulation
Evec_input.dat	Moment direction data
Fe_mt_v	Fe pseudopotential
Ni_mt_v	Ni pseudopotential
position.dat	Structure file	Atomic positions
volume.dat	Volume scaling factors	Scales lattice constant
job.sh	Job submission script	Adjust for cluster and MPI
job-submit	Batch execution script	Run multiple volume calculations
extract.sh	Data extraction script	Generates energy-volume data
eos.py	EOS fitting script	Computes equation of state

Step 1: Extract Dataset#

tar -xzf FeNi3_EV.tar.gz

Step 2: Prepare Volume Scaling#

Edit volume.dat:

The lattice constant scales as:

\(a = a_0 \times s\)

Step 3: Configure Input File#

Edit i_mst:

Set pseudopotentials
Ensure SCF calculation
Use tight convergence

Step 4: Configure Job Script#

mpirun -np 32 ./mst.x > output.log

MPI tasks should satisfy:

\(N_{\text{MPI}} = k \times N_{\text{atoms}}\)

Step 5: Run Calculations#

./job-submit

Step 6: Extract Energy-Volume Data#

./extract.sh

Output:

Volume, Energy
V_1, E_1
V_2, E_2

Step 7: Fit Birch-Murnaghan EOS#

python eos.py

The EOS is given by:

\(E(V) = E_0 + \frac{9 V_0 B_0}{16} \left[ \left( \left( \frac{V_0}{V} \right)^{2/3} - 1 \right)^3 B_0' + \left( \left( \frac{V_0}{V} \right)^{2/3} - 1 \right)^2 \left( 6 - 4 \left( \frac{V_0}{V} \right)^{2/3} \right) \right]\)

_images/FeNi3_EV.png — Energy vs. volume curve for FeNi₃ in the L1₂ phase. The discrete points correspond to calculated total energies at different volumes, while the smooth curve represents the Birch-Murnaghan EOS fit. The minimum of the curve gives the equilibrium volume \(V_0\).#

Outputs:

\(V_0\)
\(E_0\)
\(B_0\)
\(B_0'\)

Workflow Summary#

FeNi3_EV.tar.gz -> extract -> run jobs -> extract.sh -> result.csv -> eos.py

Equation of State using Birch-Murnaghan EOS

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