BraWl: Simulating the thermodynamics and phase stability of multicomponent alloys using conventional and enhanced sampling techniques

We present BraWl, a Fortran package implementing a range of conventional and enhanced sampling algorithms for exploration of the phase space of the Bragg-Williams model, facilitating study of diffusional solid-solid transformations in binary and multicomponent alloys. These sampling algorithms include Metropolis-Hastings Monte Carlo, Wang-Landau sampling, and Nested Sampling. We demonstrate the capabilities of the package by applying it to some prototypical binary and multicomponent alloys, including high-entropy alloys.

💡 Research Summary

This paper introduces “BraWl,” an open-source Fortran software package designed to simulate the thermodynamics and phase stability of multicomponent alloys. The core methodology of BraWl centers on applying advanced sampling algorithms to the Bragg-Williams lattice model, a physically intuitive Hamiltonian that describes the internal energy of an alloy as a sum of pairwise effective interactions (EPIs) between constituent atoms. These EPIs can be derived from first-principles density functional theory (DFT) calculations, providing a crucial link between quantum-mechanical accuracy and computational tractability for large-scale statistical sampling.

The primary motivation for developing BraWl is the combinatorial explosion of the configuration space in alloys, especially in multicomponent systems like high-entropy alloys (HEAs). Direct evaluation of the partition function is impossible, necessitating efficient sampling techniques. While other packages exist for cluster expansion methods, BraWl specifically focuses on the simpler Bragg-Williams formalism, which is more parameter-efficient and thus particularly suitable for systems with many chemical components.

BraWl implements a suite of three key sampling algorithms to explore the alloy configuration space:

1. Metropolis-Hastings Monte Carlo (MC): A conventional algorithm for sampling the equilibrium state at a fixed temperature via trial atom swaps.
2. Wang-Landau Sampling: An enhanced sampling technique that directly calculates the density of states, enabling the determination of thermodynamic properties (like free energy and specific heat) over a wide temperature range from a single simulation run.
3. Nested Sampling: Another enhanced method designed to compute the Bayesian evidence, which is particularly useful for comparing the relative stability of competing phases and constructing phase diagrams.

By leveraging these algorithms, BraWl can predict phase equilibria as a function of temperature and composition, visualize representative atomic configurations, and generate data for complementary modeling approaches. The authors demonstrate the package’s capabilities by applying it to prototypical binary and multicomponent alloys.

The paper is careful to outline the inherent limitations of the underlying Bragg-Williams model as implemented. First, it assumes a fixed underlying crystal lattice, neglecting local lattice distortions caused by atomic size mismatches. Second, it includes only configurational entropy, omitting other potentially significant contributions such as vibrational, magnetic, or electronic entropy. Users are advised to interpret results with these constraints in mind.

In summary, BraWl fills a niche in the materials simulation ecosystem by providing a dedicated, open-source platform for performing efficient and scalable thermodynamic sampling on the Bragg-Williams model. Its modular architecture promises future extensibility to more complex Hamiltonians and additional sampling algorithms, making it a valuable tool for researchers studying phase stability and transformations in complex alloy systems.