Data-Driven Exploration of AB₂X₄ (X = O, S, Se, Te) Spinel Chemical Space

This repository contains the complete high-throughput screening (HTS) workflow, data, and code for identifying potentially synthesizable AB₂X₄ spinel compounds. The framework integrates materials databases, empirical heuristics, and machine learning predictions to uncover novel, unexplored candidates.

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Overview

Spinels are a versatile class of materials used in applications ranging from energy storage to catalysis. Their crystal structures are similar to the mineral MgAl₂O₄, where the A- and B-site cations fill the tetrahedral and octahedral sites, respectively, within a tightly packed cubic structure of X anions, resulting in the space group Fd3̅m. They also possess cation disordering behavior where A and B cations can exchange their positions, forming either "normal" or "inverse" phases. This behavior can be explained using the cation inversion parameter (x), where x ∈ [0,1] corresponds to the degree of inversion from fully normal to fully and inverse spinel structures.

However, much of their chemical space remains underexplored. This project aims to explore spinel chemical space for potentially synthesisable compounds within the first 83 elements in the periodic table. We focus our investigation on oxide and chalcogen (sulfides, selenides, and tellurides) spinels. To tackle this vast design space, we developed a high-throughput screening (HTS) framework by combining several computational tools that systematically filters candidates through three main filtering stages:

• Chemical filtering (charge neutrality, electronegativity balance)
• Thermodynamic filtering (E_hull)
• Data-driven filtering (CLscore)

A key feature of this work is the introduction of a new unified crystal likelihood metric, the 'super score' (S_score), which combines thermodynamic filter (E_hull) with data-driven filter (CLscore). This allows for more robust candidate ranking across thousands of compositions.

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Workflow and Tools

The screening workflow and tools includes:

• Chemical validity check using SMACT
• Structural optimization with MACE-MP-0a
• E_hull calculation via Pymatgen
• CLscore prediction using Synthesizability-stoi-CGNF
• Unified crystal likelihood scoring (S_score)
• Phonon dispersion analysis via MatCalc using MACE-MP-0a

We begin by generating all possible spinel compositions composed of the first 83 elements in the periodic table and four anions (O, S, Se, and Te). These compositions are first filtered using SMACT for chemically valid spinel compounds and pass through structural optimisation using MACE-MP-0a. Pymatgen package is then used to calculate E_hull using energy from MACE-MP-0a. Synthesizability-stoi-CGNF model is adopted to further refine the screening through a metric called CLscore. Both E_hull and CLscore are combined to introduce a single unified metric, S_score to quantify crytal likelihood of a compound based on two different perspectives. To determine preferred configurations between normal or inverse, configuration with lower E_hull is chosen as the representative of the composition. To validate our S_score, we compare our results with known spinels on Materials Project (MP) and Inorganic Crystal Structure Database (ICSD). Furthermore, phonon dispersion calculations are carried out on the top 10 candidates, ranked by S_score, for each anion type to confirm the dynamical stability of the structures.

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Repository Structure

Spinel-chemical-space/
├── 1_MP_ICSD_SMACT.ipynb              # Chemical space generation and database retrieval
├── 2_screening.ipynb                  # Candidates screening
├── 3_plotting.ipynb                   # Results visualization
├── calculation_scripts/
│   ├── MACE/                          # Structure optimisation with MACE-MP-0a
│   ├── Ehull/                         # Energy above hull calculations
│   └── PUL_CLscore/                   # CLscore data preparation
├── data/                              # All intermediate and final datasets
│   ├── SMACT/                         # SMACT-filtered compositions
│   ├── MP/ & ICSD/ & MP_ICSD/         # Experimental spinel data
│   ├── MACE/                          # MACE optimisation results
│   ├── Ehull/                         # Ehull results
│   ├── PUL/                           # CLscore predictions
│   └── Final_data/                    # Final merged results per anion type
├── MACE_verifications/                # MACE vs DFT (VASP) validation
├── Orbital_radii/                     # Orbital radii analysis
├── plots/                             # Generated publication figures (PDF)
├── configs/                           # Matplotlib configuration
├── font/                              # Font files for plotting
└── LICENSE                            # MIT License

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Getting Started

Prerequisites

• Python 3.9+
• A Materials Project API key (required for querying MP data in 1_MP_ICSD_SMACT.ipynb)

Installation

Install all required packages using pip:

pip install numpy matplotlib seaborn pandas smact pymatgen mp-api==0.45 mace-torch ase

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Notebooks and Usage

This repository contains three main notebooks:

Notebook
1_MP_ICSD_SMACT.ipynb
2_screening.ipynb.ipynb
3_plotting.ipynb

All necessary data is already included in the data/ directory. If you would like to explore a different chemical system, you can change the chemical system in 1_MP_ICSD_SMACT.ipynb to the targeted system.

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Calculation Scripts

To reproduce the full workflow from scratch, follow the steps below:

1. Chemical filtering and MP data retrieval
   → 1_MP_ICSD_SMACT.ipynb

   Performs SMACT-based chemical validation and extracts relevant entries from the Materials Project.
   (Note: ICSD data must be downloaded and processed manually due to licensing restrictions.)

2. Structure optimization using MACE
   → calculation_scripts/MACE/MACE_calculation.py

   Optimizes spinel structures using the MACE-MP-0a model.

3. CLscore prediction via Positive-Unlabeled Learning (PUL)
   → calculation_scripts/PUL_CLscore/PUL_data_preparation.ipynb

   Prepares input for the Synthesizability-stoi-CGNF model. The PUL model cannot currently be installed via pip or imported directly into Jupyter notebooks. Instead, it must be cloned and executed from its own repository. Follow the instructions in the Synthesizability-stoi-CGNF repository to run the calculations and then bring the results back into this workflow.

4. Thermodynamic stability via E_hull
   → calculation_scripts/Ehull/Ehull_calculation.ipynb

   Calculates the E_hull using formation energies from MACE.

5. Final filtering and ranking with S_score → 2_screening.ipynb.ipynb and 3_plotting.ipynb

   Combines E_hull and CLscore into S_score to identify the promising candidates.

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Supplementary Analysis

Directory	Description
MACE_verifications/	Validation of MACE-MP-0a predictions against DFT (VASP) calculations, including parity plots for lattice parameters and total energies.
Orbital_radii/	Analysis of the relationship between element orbital radii and spinel formation preferences.

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License

This project is licensed under the MIT License. See LICENSE for details.