exaPD: A highly parallelizable workflow for multi-element phase diagram (PD) construction

TL;DR

This work tackles the challenge of constructing reliable multi-element phase diagrams by needing extensive free-energy calculations over many phases. It introduces exaPD, a scalable TI-based workflow that orchestrates MD/MC sampling in LAMMPS, supports neural-network potentials, and leverages a Parsl-driven global controller to manage massive parallelism. Free-energy results for line compounds, solid solutions, and liquids are integrated into CALPHAD via PyCALPHAD to produce phase diagrams, with validation examples illustrating accuracy and scalability. Overall, exaPD provides a practical exascale framework to accelerate materials discovery and guide synthesis by delivering thermodynamic data and phase equilibria efficiently.

Abstract

Phase diagrams (PDs) illustrate the relative stability of competing phases under varying conditions, serving as critical tools for synthesizing complex materials. Reliable phase diagrams rely on precise free energy calculations, which are computationally intensive. We introduce exaPD, a user-friendly workflow that enables simultaneous sampling of multiple phases across a fine mesh of temperature and composition for free energy calculations. The package employs standard molecular dynamics (MD) and Monte Carlo (MC) sampling techniques, as implemented in the LAMMPS package. Various interatomic potentials are supported, including the neural network potentials with near {\it ab initio} accuracy. A global controller, built with Parsl, manages the MD/MC jobs to achieve massive parallelization with near ideal scalability. The resulting free energies of both liquid and solid phases, including solid solutions, are integrated into CALPHAD modeling using the PYCALPHAD package for constructing the phase diagram.

Figures (8)

• Figure 1: Gibbs free energy as a function of the temperature for various compoinds in (a) the Cu-Zr system; and (b) the La-Si-P system. EAM-FS and NNP potentials are used for the Cu-Zr and La-Si-P system, respectively. The solid circles in (a) are results from Ref. Tang2012 for comparison.
• Figure 2: Gibbs free energy of fcc-Al as a function of the temperature calculated using the Einstein model, an EAM-FS potential, or a neural-network trained potential. The Einstein crystal is used as the reference for the EAM-FS potential in the thermodynamic integration; while the EAM-FS potential is used as the reference for the NNP.
• Figure 3: Semi-grand canonical calculation of the bcc phase in the Cu-Zr system. (a) The chemical potential difference as a function of the Zr composition at T = 1600 K. The red circles are from the MD simulations, and the solid line is a fitting to the derivative of the RK polynomial. (b) The calculated Gibbs free energy of both the liquid and bcc phase as a function of the Zr composition at T = 1600 K. The pure Zr and Cu$_{70}$Zr$_{30}$ liquids are used as the reference states. The dashed red line is a common tangent construction, which gives the Zr compositions in the liquid and bcc phases.
• Figure 4: The Gibbs free energy of the CuZr B2 phase and the Cu$_{50}$Zr$_{50}$ liquid as a function of the temperature. The liquid free energy is calculated using thermodynamic integration along an alchemical pathway starting from the pure Cu liquid. The free energy of the B2 phase is calculated using the Einstein crystal as the reference. The crossing point gives the melting point $T_m=890$ K.
• Figure 5: Measurement of the melting point of the Cu-Zr B$_2$ phase using the SLC method. (a) The initial configuration of the solid-liquid interface at $T=800$ K. On the left is the crystalline Cu-Zr B$_2$ phase and on the left is the liquid structure with $x_\textbf{Zr}=0.5$. (b) The rate of the internal energy change as a function of the temperature during the melting or the crystallization process. The solid line is a cubic interpolation, which gives the melting point $T_m=903$ K when the interpolated $\frac{\partial E}{\partial t}=0$.