Data-Driven Exploration and Insights into Temperature-Dependent Phonons in Inorganic Materials

TL;DR

This work presents a scalable, data-driven framework to map temperature-dependent phonons ($TDPH$) across thousands of inorganic materials by coupling a fine-tuned ML interatomic potential (M3GNet) with streamlined anharmonic lattice dynamics. The authors demonstrate a fourfold improvement in phonon prediction accuracy over the baseline model, enable high-throughput $TDPH$ calculations via a streamlined SSCHA, and analyze 4,669 compounds to reveal elemental and structural trends driving anharmonicity. They introduce global and local APRN metrics, $\mathcal{R}_{full}$ and $\mathcal{R}_{onsite}$, and deploy random-forest models to identify key atomic environments responsible for strong anharmonicity, highlighting motifs such as weak bonding around oversized sites and perovskite-like structures. First-principles validation on a dozen materials shows that anharmonic effects can modify lattice thermal conductivity, sometimes by factors of 2–4, underscoring the need to account for finite-temperature phonons in materials design. Overall, the framework enables efficient, large-scale discovery and design of materials with tailored vibrational and thermal properties for applications in thermal management, thermoelectrics, and phase-stability engineering.

Abstract

Phonons, quantized vibrations of the atomic lattice, are fundamental to understanding thermal transport, structural stability, and phase behavior in crystalline solids. Despite advances in computational materials science, most predictions of vibrational properties in large materials databases rely on the harmonic approximation and overlook crucial temperature-dependent anharmonic effects. Here, we present a scalable computational framework that combines machine learning interatomic potentials, anharmonic lattice dynamics, and high-throughput calculations to investigate temperature-dependent phonons across thousands of materials. By fine-tuning the universal M3GNet interatomic potential using high-quality phonon data, we improve phonon prediction accuracy by a factor of four while preserving computational efficiency. Integrating this refined model into a high-throughput implementation of the stochastic self-consistent harmonic approximation, we compute temperature-dependent phonons for 4,669 inorganic compounds. Our analysis identifies systematic elemental and structural trends governing anharmonic phonon renormalization, with particularly strong manifestations in alkali metals, perovskite-derived frameworks, and related systems. Machine learning models trained on this dataset identify key atomic-scale features driving strong anharmonicity, including weak bonding, large atomic radii, and specific coordination motifs. First-principles validation confirms that anharmonic effects can dramatically alter lattice thermal conductivity by factors of two to four in some materials. This work establishes a robust and efficient data-driven approach for predicting finite-temperature phonon behavior, offering new pathways for the design and discovery of materials with tailored thermal and vibrational properties.

Figures (4)

• Figure 1: (A) Illustration of the M3GNet model, based on a graph neural network (GNN) and fine-tuned with the MDR harmonic phonon database to improve phonon property predictions. (B) Comparisons of phonon frequencies predicted by the original M3GNet foundation model and those calculated using DFT. (C) Comparisons of phonon frequencies predicted by the fine-tuned M3GNet foundation model and DFT results.
• Figure 2: Overview of anharmonic phonon renormalization (APRN) calculation and validation. (A) Schematic illustrating configuration-dependent interatomic force constants (represented by springs) between atoms (solid circles) displaced from their equilibrium positions (dashed circles). (B) Schematic showing the symmetrization of these force constants using space group symmetry operations, wherein $\alpha$ denotes a pair interaction and $\hat{S}$ indicate a symmetry operator ($\hat{S}_{1/2/3}$ for rotations and $\hat{S}_{o}$ for reflection). (C) Validation of the APRN approach using cubic SrTiO$_{3}$ as a test case. The phonon dispersions are shown as calculated from DFT (gray dashed lines), fine-tuned M3GNet harmonic approximation (blue solid lines), and renormalized calculations using fine-tuned M3GNet model at 300 K (red solid lines). Green circles represent experimental measurements at 300 K stirling1972neutroncowley1969relationship.
• Figure 3: (A) Heatmap of the APRN-induced percentage change of onsite force constants ($\mathcal{R}_{\text{onsite}}$) across the periodic table, plotted on a logarithmic scale. Brighter colors indicate stronger APRN effects, highlighting element-wise trends in temperature-dependent phonons. (B) Bar plot showing the average APRN effect on phonon frequencies for each space group number. The colors represent different crystal systems, and the dashed horizontal line indicates the overall average across all materials. (C) Illustration of the Matminer featurization process and random forest model training. Global features (structural and compositional properties) are used to predict $\mathcal{R}_{\text{full}}$, while local features (site environments) are used to predict $\mathcal{R}_{\text{onsite}}$. These two features are used to train two separate models: global APRN model and local APRN model. (D) Feature importance rankings for the top 10 features in the global APRN model (left) and local APRN model (right). (E)-(F) Case studies of materials with weak vs. strong APRN effects, demonstrating how local structural properties such as bond length ($L$) and unit cell volume ($V_\text{unit}$) affect phonon renormalization. The phonon dispersions compare the harmonic predictions (M3GNet, black) with the APRN-corrected predictions at 300 K (M3GNet + APRN, blue).
• Figure 4: (A) Schematic workflow for screening materials with strong temperature-dependent phonons (TDPH). First, for computational feasibility, we selected $\sim$5,000 materials with fewer than 20 atoms per unit cell from the MDR phonon database. This subset was then filtered to $\sim$1,200 candidate materials based on their APRN-induced onsite force constant change ratio $(\mathcal{R}_{\text{onsite}})$, using a threshold of $\mathcal{R}_{\text{onsite}} \geq 0.15$. This threshold corresponds to a 15% change in onsite force constants due to the APRN effect. The screening was followed by validation with SCPH theory. (B) Boxen plot showing $\mathcal{R}_{\text{onsite}}$ values for various material prototypes within the 1,200 selected crystals. Top-ranked prototypes exhibiting strong APRN contributions are shown, providing insight into structural trends associated with significant temperature-dependent APRN effects. (C) Distribution of material prototypes among the 1,200 screened materials, along with structural representations of key prototypes. The blue-colored polyhedral structures such as cuboctahedra and octahedra illustrate typical local atomic environments where onsite atoms exhibit strong temperature-dependent phonon behavior. (D) Comparisons of lattice thermal conductivities ($\kappa_{\rm{L}}$) for 12 selected materials at 300 K, calculated using different levels of theory: harmonic approximation (without anharmonic renormalization) with three-phonon scattering (HA + 3ph), self-consistent phonon approximation (with anharmonic renormalization) with three-phonon scattering (SCPH + 3ph), and SCPH with both 3- and 4-phonon scattering (SCPH 3,4ph). (E) Phonon dispersion and phonon density of states (DOS) for Cs$_2$RbGaF$_6$ at 0 K (black) and 300 K (red), showing an APRN effect primarily driven by contributions from F$^-$ ions. (F) Phonon scattering rates ($\tau^{-1}$) of Cs$_2$RbGaF$_6$ computed using HA + 3ph, SCPH + 3ph, and SCPH + 4ph approximations. The solid black line represents the Mott-loffe-Regel limit, where the scattering rate equals the phonon frequency.