WMoNbZrTiTa Diffusion Pipeline

High-throughput molecular-dynamics pipeline for computing vacancy-mediated tracer diffusivities, short-range order, and melting temperatures across W-Mo-Nb-Zr-Ti-Ta refractory high-entropy alloy compositions.

---

Overview

For each alloy composition sampled from the six-element composition space, the pipeline automates the following calculations:

1. Pure-element baselines - ADP-relaxed lattice parameters and vacancy formation entropies via phonopy.
2. Alloy constants - vacancy formation energy, rule-of-mixtures melting temperature, and the temperature grid.
3. True melting temperature - phase coexistence via the Modified Z-method using the GRACE-2L-OMAT machine-learning potential.
4. Diffusion and SRO - Monte Carlo chemical equilibration followed by long MD diffusion with a single vacancy, using the fast ADP potential.
5. Tracer diffusivity - per-element diffusion rates via the Einstein relation and Arrhenius fits.
6. Chemical ordering - Warren-Cowley short-range order parameters.
7. Global predictive model - a Ridge-regularised composition-property polynomial fitted across all compositions.

---

Architecture

The codebase is split into two strictly separated layers:

Layer	Directory	Responsibility
Generation	pipeline/	Build LAMMPS and phonopy inputs (Stages 1-4)
Post-processing	analysis/	Parse outputs and compute physics (Stages 5-10)

Supporting modules:

Module	Responsibility
config.py	Single source of truth for constants, paths, and mode
run_pipeline.py	Orchestrator and unified CLI entry point
logging_config.py	Central logging configuration
reporting.py	Aligned plain-text table rendering

pipeline/ never reads simulation output, and analysis/ never writes LAMMPS input. The only shared state is the file system, described below.

---

Data flow

config.py  (constants, paths, TEST_MODE)
    |
    v
[Stage 1]  pipeline/compositions.py
    |         -> results/compositions.csv
    v
[Stage 2]  pipeline/constants.py
    |         -> results/constants_all.csv
    |         -> results/constants/<comp_id>.json
    v
[Stage 3b] pipeline/lammps_tm.py
    |         -> runs/<comp_id>/tm_coexistence/T_<guess>/coexistence.in
    |         -> slurm/submit_Tm_array.sh
    |   (sbatch; GRACE MLIP)
    v
[Stage 3c] pipeline/lammps_tm.py
    |         -> results/constants_all.csv   (real Tm, rebuilt T_grid)
    v
[Stage 3]  pipeline/lammps_diffusion.py
    |         -> runs/<comp_id>/sim_<T>/bcc_vac_adv.in
    |         -> results/job_list.csv
    v
[Stage 4]  run_pipeline.py
    |         -> slurm/submit_diffusion.sh
    |   (sbatch; ADP potential)
    v
[Stage 5]  analysis/msd.py
    |         -> results/<comp_id>/sim_x/<T>/msd_all.txt
    |         -> results/<comp_id>/sim_x/<T>/msd_solo.txt
    v
[Stage 6]  analysis/vacancy_diffusion.py
    |         -> results/<comp_id>/txt/Dv.txt
    v
[Stage 7]  analysis/vacancy_concentration.py
    |         -> results/<comp_id>/txt/Cv.txt
    v
[Stage 8]  analysis/tracer_diffusion.py
    |         -> results/<comp_id>/txt/D2_components.txt
    v
[Stage 9]  analysis/sro.py
    |         -> results/<comp_id>/txt/sro_vs_temp.csv
    v
[Stage 10] analysis/postprocess.py
              -> results/master_results.csv
              -> results/poly_fit_coeffs.csv
              -> results/plots/*.png

---

Repository layout

config.py                  Central configuration - edit before running
run_pipeline.py            Orchestrator and unified CLI entry point
logging_config.py          Central logging configuration
reporting.py               Aligned plain-text table rendering
pyproject.toml             Packaging metadata and pinned dependencies
requirements.txt           Locked dependency list
Makefile                   Workflow shortcuts

pipeline/                  LAMMPS and phonopy input generation
    lammps_common.py       Shared composition algebra and LAMMPS blocks
    compositions.py        Stage 1  - composition sampling
    constants.py           Stage 2  - a0, Tm_rom, Ef, Sf, C0, T_grid
    lammps_diffusion.py    Stage 3  - ADP diffusion inputs
    lammps_tm.py           Stage 3b/3c - GRACE coexistence inputs, Tm patch
    compute_sf_phonopy.py  Standalone phonopy Sf calculation

analysis/                  Post-processing and analytics
    logparse.py            Shared LAMMPS text-parsing helpers
    arrhenius.py           Weighted Arrhenius fitting
    msd.py                 Stage 5  - mean-square displacement
    vacancy_diffusion.py   Stage 6  - Dv(T)
    vacancy_concentration.py Stage 7 - Cv(T)
    tracer_diffusion.py    Stage 8  - D*(T)
    sro.py                 Stage 9  - Warren-Cowley parameters
    postprocess.py         Stage 10 - aggregation, fit, plots

docs/                      Physics, logic, workflow, and testing guides
slurm/                     Cluster submission scripts (generated + static)
tests/                     pytest suite

---

Installation

git clone https://github.com/akmal523/high-entropy-alloy-pipeline.git
cd high-entropy-alloy-pipeline

# Editable install with pinned dependencies and the test runner
make setup

make setup runs pip install -e ".[dev]". To install only the runtime dependencies, use pip install -r requirements.txt.

Before running, edit config.py to set LAMMPS_EXE, LAMMPS_CMD_TMPL, SLURM_PARTITION, and GRACE_MODEL_DIR, and place WMoNbZrTiTa.nist.adp.txt in the project root.

---

Quick start

The Makefile wraps the common workflow:

make generate            # Stages 0-2: validate, compositions, constants
make tm-inputs           # Stage 3b: write GRACE coexistence inputs
make submit-tm           # sbatch slurm/submit_Tm_array.sh
# [wait for Tm jobs]
make tm-patch            # Stage 3c: patch real Tm into constants
make diffusion-inputs    # Stages 3-4: write ADP inputs and submit script
make submit              # sbatch slurm/submit_diffusion.sh
# [wait for diffusion jobs]
make analyze             # Stages 5-10: MSD, Dv, Cv, D*, SRO, postprocess

The equivalent direct commands are:

python run_pipeline.py --from_stage 0 --to_stage 2
python run_pipeline.py --only_stage 31
sbatch slurm/submit_Tm_array.sh
python run_pipeline.py --only_stage 32
python run_pipeline.py --from_stage 3 --to_stage 4
sbatch slurm/submit_diffusion.sh
python run_pipeline.py --from_stage 5

A fast validation run uses the reduced configuration:

make generate TEST=1
# or
python run_pipeline.py --test --from_stage 0 --to_stage 2

---

Configuration

All tuneable parameters live in config.py.

Parameter	Default	Description
TEST_MODE	False	Full production run; override with --test
N_COMPOSITIONS	100	Number of alloy compositions to sample
LAMMPS_EXE	(set this)	Path to the LAMMPS binary
GRACE_MODEL_DIR	(set this)	Path to the GRACE-2L-OMAT weights
SLURM_PARTITION	compute	Cluster partition name
T_FRAC_MAX	0.80	Upper temperature bound as a fraction of Tm

TEST_MODE defaults to False. It can be overridden at runtime, before any stage executes, with the --test flag (or forced back with --production). The mode switch changes only sampling counts, run lengths, and walltimes; physical constants are never modified.

---

Stage reference

Stage	Module	Output
0	run_pipeline.py	Environment validation
1	pipeline/compositions.py	results/compositions.csv
2	pipeline/constants.py	results/constants_all.csv
3b	pipeline/lammps_tm.py	runs/*/tm_coexistence/, slurm/submit_Tm_array.sh
3c	pipeline/lammps_tm.py	Patched results/constants_all.csv
3	pipeline/lammps_diffusion.py	runs/*/sim_*/bcc_vac_adv.in
4	run_pipeline.py	slurm/submit_diffusion.sh
5	analysis/msd.py	results/*/sim_x/*/msd_*.txt
6	analysis/vacancy_diffusion.py	results/*/txt/Dv.txt
7	analysis/vacancy_concentration.py	results/*/txt/Cv.txt
8	analysis/tracer_diffusion.py	results/*/txt/D2_components.txt
9	analysis/sro.py	results/*/txt/sro_vs_temp.csv
10	analysis/postprocess.py	results/master_results.csv, plots

---

Output file structure

results/
    compositions.csv
    constants_all.csv
    tm_job_list.csv
    job_list.csv
    master_results.csv
    poly_fit_coeffs.csv
    constants/
        <comp_id>.json
    <comp_id>/
        txt/
            Dv.txt
            Cv.txt
            D2_components.txt
            sro_vs_temp.csv
        plots/
            Dv_total.png
            Dv_elements.png
            Dv_homologous.png
            cv_vs_invT_<comp_id>.png
            D2_vs_invT.png
            Dtotal_vs_invT.png
            sro_vs_temp.png
        sim_x/
            <T>/
                msd_all.txt
                msd_solo.txt
    plots/
        comparison_D_vs_Tm.png
        comparison_sro_vs_T.png
        parity_Dtotal.png
        arrhenius_summary.png

runs/
    <comp_id>/
        sim_<T>/
            bcc_vac_adv.in
            submit.sh
            dump/
        tm_coexistence/
            T_<guess>/
                coexistence.in
                dump/

---

Physics notes

The full derivations, with citations, are in docs/physics.md and docs/logic.md. Key points:

• Sequential-fraction composition assignment. LAMMPS set type/fraction is applied sequentially and overwrites earlier types. The conditional fractions are obtained by inverting P(X) = f_X * prod_{Y after X} (1 - f_Y) in reverse setting order. See pipeline/lammps_common.py.
• Modified Z-method. An elongated BCC supercell is split into solid and liquid halves; coexistence is detected from the volume and pressure trajectory under independent per-axis NPT barostats, followed by stress equalization. See pipeline/lammps_tm.py.
• Dynamic SRO cutoff. The cutoff is the midpoint between the BCC first and second neighbour shells, r_sro = a0 * (sqrt(3)/2 + 1) / 2, evaluated at the composition's lattice parameter. See config.py.
• Tracer versus vacancy diffusion. Dv is the vacancy diffusivity; D*_i = f_i * Cv * Dv_i / x_i is the tracer diffusivity. The BCC correlation factor f = 0.727 is already embedded in the MSD-derived data and must not be applied twice. See analysis/tracer_diffusion.py.

Key references:

• Starikov et al. Phys. Rev. Materials 8, 043603 (2024) - Ef, Sf, ADP validation.
• Karavaev et al. J. Chem. Phys. 144, 194507 (2016) - modified Z-method.
• Cowley, Phys. Rev. 77, 669 (1950) - Warren-Cowley SRO.
• Compaan & Haven, Trans. Faraday Soc. 52, 786 (1956) - BCC correlation factor.

---

Testing

make test        # python -m pytest
make lint        # byte-compile every module

The suite covers the sequential-fraction algebra, weighted Arrhenius fitting, graceful MSD log parsing, the mode switch, and composition sampling.

---

Requirements

• Python >= 3.10
• LAMMPS with the adp pair style (diffusion runs)
• LAMMPS with the grace pair style (Tm runs)
• Phonopy (vacancy formation entropy)
• GRACE-2L-OMAT model weights
• WMoNbZrTiTa.nist.adp.txt potential file (project root)
• SLURM cluster environment

Runtime dependencies are pinned in pyproject.toml and mirrored in requirements.txt.