🔬 materials science

HEACalculator: An Open-Source Python Tool for Thermodynamic Property Calculation and Solid Solution Prediction in High-Entropy Alloys

HEACalculator is an open-source Python tool that streamlines high-entropy alloy design by computing key thermodynamic descriptors and evaluating solid-solution formation rules through a unified command-line, graphical, and programmatic interface.

Original authors: Doğuhan Sarıtürk, Yunus Eren Kalay, Raymundo Arróyave

Published 2026-06-19

📖 3 min read☕ Coffee break read

CC BY 4.0

Original authors: Doğuhan Sarıtürk, Yunus Eren Kalay, Raymundo Arróyave

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a chef trying to invent a new, super-powerful metal alloy. You have a pantry full of different elements (like iron, nickel, chromium, etc.), and you want to mix them together to create a "High-Entropy Alloy" (HEA). The goal is to mix them in a way that they all stay happily blended together in a single, smooth phase (like a perfect smoothie) rather than separating into chunks or forming weird, brittle crystals (like a salad with too many distinct layers).

The problem? There are dozens of different "recipes" or rules written by different scientists over the years to predict if your mix will work. Some rules say, "Check the size of the atoms," others say, "Check the electron count," and others say, "Check the energy." Trying to use all these rules is like trying to bake a cake while following eight different cookbooks at once, where every book uses different units of measurement and different names for the same ingredients. It's confusing, messy, and hard to trust.

Enter HEACalculator.

Think of HEACalculator as a universal, open-source kitchen assistant built specifically for these metal chefs. It's a free tool written in Python (a popular coding language) that does three main things:

It speaks one language: Instead of you having to translate between eight different scientific rulebooks, HEACalculator takes your list of ingredients and calculates 16 different "flavor profiles" (scientific descriptors) all at once. These include things like how different the atom sizes are, how much energy is released when they mix, and how many electrons are hanging around.
It runs the tests for you: Once it has those numbers, it instantly runs all eight of the famous scientific "rules" to tell you: "Will this mix stay smooth, or will it break apart?" It does this in one go, so you don't have to do the math eight times.
It fits anywhere: Whether you are a person who likes clicking buttons on a desktop app, a scientist who likes typing commands in a terminal, or a programmer who wants to plug this tool into a larger automated system, HEACalculator has a version for you.

Why is this a big deal?

Before this tool, if a scientist wanted to compare two different theories, they often had to rebuild the calculations from scratch, which is prone to errors. It's like trying to compare two maps of the same city when one uses miles and the other uses kilometers, and neither has a legend.

HEACalculator fixes this by being the single source of truth. It uses a curated database of 118 elements and thousands of known interactions between them. It's designed so that if you run the same mix today, tomorrow, or next year, you get the exact same result, no matter which interface you use.

Who uses it?

The paper highlights that this tool isn't just for looking at one alloy at a time. It's being used by other researchers to:

Screen thousands of potential alloys quickly to find the best candidates for experiments.
Generate data for machine learning models (teaching computers to predict metal properties).
Study specific metals like shape-memory alloys (used in medical devices) and super-hard refractory alloys.

In short, HEACalculator takes the messy, confusing world of high-entropy alloy prediction and organizes it into a clean, transparent, and reusable toolkit, making it much easier for scientists to design better metals without getting lost in the math.

Technical Summary of HEACalculator

Problem Statement
The design of High-Entropy Alloys (HEAs) faces a practical bottleneck in predicting whether a candidate composition will form a single-phase solid solution or separate into multiple phases and intermetallic compounds. While numerous phenomenological criteria exist to address this, they are currently distributed across separate publications, each utilizing distinct notations, parameter definitions, and validation sets. This fragmentation forces researchers to reconstruct overlapping calculations, assemble disparate supporting datasets, and track subtle implementation differences. Consequently, routine composition screening becomes unnecessarily difficult, and reproducible comparison across studies is complicated.

Methodology
To address these challenges, the authors developed HEACalculator, an open-source Python package designed to centralize thermodynamic property calculations and solid-solution predictions. The software architecture is built around a shared calculation core that separates the user interface from the computational engine.

Data Foundation: The package utilizes a curated dataset comprising 118 elements, 2,628 binary mixing enthalpies (derived from Takeuchi and Inoue, 2005), and 435 binary formation enthalpies (derived from DFT data by Troparevsky et al., 2015).
Computational Core: Upon receiving a composition via Command-Line Interface (CLI), Graphical User Interface (GUI), or Python API, the system normalizes the input into an internal representation. A thermodynamic engine then lazily evaluates and caches sixteen key descriptors. These include mixing enthalpy ( $\Delta H_{mix}$ ), mixing entropy ( $\Delta S_{mix}$ ), valence electron concentration (VEC), atomic size mismatch ( $\delta$ ), electronegativity mismatch, and derived stability parameters such as $\Omega$ , $\lambda$ , and $\phi$ .
Prediction Models: Using the cached descriptors, the package evaluates eight published solid-solution formation criteria (Guo et al., 2011; King et al., 2016; Senkov & Miracle, 2016; Singh et al., 2014; Troparevsky et al., 2015; Wang et al., 2015; Yang & Zhang, 2012; Ye et al., 2015). These models classify compositions as Solid Solution, Intermetallic, or Multiple Phases based on specific thresholds.
Implementation Strategy: The design prioritizes reproducibility by ensuring that a single set of descriptors is used for all model evaluations, preventing inconsistencies caused by re-computing intermediate values. The package raises typed exceptions for missing data rather than silently substituting values, ensuring data provenance is transparent.

Key Contributions

Unified Implementation: HEACalculator provides the first unified, validated implementation of eight distinct solid-solution prediction criteria within a single Python package.
Multi-Interface Accessibility: The tool offers three access modes: a CLI for batch processing and scripting, a PyQt6-based desktop GUI for interactive exploration, and a documented Python API for integration into notebooks and automated screening pipelines.
Reproducible Workflow: By decoupling property calculation from model evaluation and utilizing explicit JSON-backed reference data, the software ensures that results are consistent regardless of the access mode used.
Open-Source Licensing: Released under a Creative Commons Attribution 4.0 International License (CC BY 4.0), the software is freely available with full source code and documentation.

Results and Validation
The software's scientific correctness is verified through a test suite that reproduces phase predictions for 120 reference compositions drawn from the eight source-model papers. The results demonstrate close agreement with published continuous parameters and classification outcomes. The package has already been adopted in subsequent materials informatics studies, including:

Zadeh et al. (2024), who utilized HEACalculator for descriptor generation in a data-driven study of NiTi shape memory alloys.
Sheikh et al. (2025), who used the tool to generate domain-specific features for machine-learning predictions of hardness in refractory HEAs.

Significance and Scope
The authors position HEACalculator not as the broadest HEA design environment, but as a transparent, literature-validated tool specifically for the evaluation of established thermodynamic and structural criteria. Unlike machine-learning-based tools (e.g., pyMPEALab) where predictions emerge from learned weights, HEACalculator produces predictions that are directly traceable to specific published formulas and thresholds.

The paper argues that while tools like HEAPS offer broader screening scopes, they are often constrained by proprietary software requirements (MATLAB) and platform limitations (Windows-only). In contrast, HEACalculator fills a complementary niche by providing a cross-platform, Python-native solution that can be inspected, cited, and embedded directly into reproducible computational materials workflows. Its primary contribution lies in removing the friction of reconstructing overlapping calculations, thereby facilitating more rigorous and comparable alloy design research.

More like this