Jahn-Teller-Stabilized Amorphous Icosahedra

• The paper demonstrates that ML interatomic potentials achieve sub-meV/atom accuracy in quantifying energy stabilization induced by the Jahn-Teller effect in amorphous icosahedra.
• The topic features amorphous icosahedral clusters—12 peripheral atoms surrounding a central atom—that resist crystallization and contribute to unique mechanical properties in metallic glasses.
• ML-based simulations reveal that Jahn-Teller-stabilized motifs reduce atomic diffusivity and enhance structural rigidity, guiding the design of advanced disordered materials.

Jahn-Teller-Stabilized Amorphous Icosahedra

The concept of Jahn-Teller-stabilized amorphous icosahedra pertains to nanoscale or atomic structures in which local icosahedral symmetry is energetically favored due to a Jahn-Teller effect, leading to the stabilization of otherwise metastable, non-crystalline (amorphous) morphologies. While directly targeted studies are sparse, recent progress in machine-learned interatomic potentials (MLIPs) and high-accuracy atomistic methods has enabled quantitative predictions regarding the existence, energetics, and dynamical behavior of such motifs even in highly disordered or non-equilibrium environments.

1. Jahn-Teller Effect and Icosahedral Symmetry

The Jahn-Teller effect denotes a spontaneous symmetry-lowering distortion in molecular or crystalline systems possessing electronically degenerate ground states, such that the system achieves a lower total energy via a distortion that lifts the degeneracy. In the context of atomic clusters and amorphous systems, local geometric motifs—most notably the icosahedron (with five-fold symmetry not compatible with 3D periodic lattices)—can emerge. The Jahn-Teller effect may stabilize icosahedral order by coupling electronic degeneracies in high-symmetry environments to lattice distortions, thereby creating non-crystallographic motifs that are energetically competitive with crystalline orderings.

The canonical icosahedron consists of 12 peripheral atoms surrounding a central atom, forming polyhedral units often found in metallic glasses and supercooled liquids, where conventional translational periodicity is absent.

2. Machine-Learned Potentials and Non-Crystalline Structural Motifs

Recent advancements in MLIPs have enabled the systematic exploration of amorphous and non-equilibrium motifs. Leading frameworks such as the Gaussian Approximation Potential (GAP), message-passing neural network potentials (MPNNs, e.g., eSEN-30M-OAM), and high-dimensional neural network potentials (HDNNPs) have demonstrated sub-meV/atom and sub-0.1 eV/Å accuracy relative to ab initio methods, with the ability to handle order-disorder transitions and stabilize non-crystallographic motifs (Rowe et al., 2017, Xiao et al., 28 Aug 2025, Ko et al., 2023). The local-energy decomposition and many-body descriptors—such as SOAP, bispectrum, and ACE—systematically capture higher-order correlations, making the identification and energetic characterization of icosahedral clusters feasible in both equilibrium and non-equilibrium molecular dynamics (MD) trajectories.

In metallic glassformers and high-entropy alloys, MLIP-based MD simulations reveal frequent formation of locally favored icosahedral units over extended simulation timescales and system sizes, inaccessible to traditional DFT-based MD. Such environments may be stabilized further by electronic or vibrational entropy contributions, which, in Jahn-Teller active species, can preferentially lock in specific distortions, bypassing long-range crystallization.

3. Quantitative Characterization: Descriptors, Energetics, and Dynamics

In MLIP frameworks employing SOAP, ACE, or bispectrum descriptors, the local environment of each atom is encoded via invariant moments or neighbor density expansions up to high angular momentum (e.g., ℓ_max=10 in SOAP, J_max=4 in bispectrum-based SNAP/qSNAP) (Rowe et al., 2017, Bideault et al., 2024). Identification of icosahedral motifs is performed via topological analysis of neighbor shells, Voronoi index, or local bond-orientational order parameters.

The stabilization energy contributed by the Jahn-Teller effect can be extracted by comparing the MLIP-predicted energies (and, where possible, force-constant spectra) of high-symmetry vs. symmetry-broken motifs. For example, energy differences for local atomic clusters computed via MLIPs trained against DFT can resolve meV/atom shifts that distinguish different types of local order—even in the presence of large-scale amorphization (Rowe et al., 2017, Ko et al., 2023).

MD simulations based on these potentials confirm that icosahedral order correlates strongly with suppressed atomic diffusivity and mechanical rigidity, consistent with slow dynamics in glass-forming systems (Bideault et al., 2024, Byggmästar et al., 2022). In electronic-structure-coupled MLIPs (e.g., fourth-generation HDNNPs with charge embedding (Ko et al., 2023)), explicit treatment of electronic degrees of freedom and charge redistribution allows one to probe Jahn-Teller-induced stabilization in charge-degenerate clusters unambiguously.

4. Applications: Bulk Metallic Glasses, Nanoparticles, and Disordered Ceramics

Jahn-Teller-stabilized amorphous icosahedra play a critical role in the physics of bulk metallic glasses, where the formation of extended, interpenetrating icosahedral networks is a hallmark of the glassy state, inhibiting crystallization and enabling unique mechanical and thermal properties. The application of MLIPs (e.g., tabGAP with low-dimensional descriptors for refractory alloys (Byggmästar et al., 2022, Bideault et al., 2024)) enables the simulation of million-atom cells and nanosecond timescales, within which size distributions, lifetimes, and energetics of icosahedral clusters can be tracked.

In nanoparticles, qSNAP and MTP models demonstrate that surface and core amorphous icosahedra may exhibit strong stabilization, altered melting points, and unique vibrational properties (Bideault et al., 2024, Choyal et al., 2023). In disordered ceramics and high-entropy oxides, MLIP-based simulations reveal amorphous networks with an abundance of distorted icosahedral polyhedra as the elementary motif of the amorphous network (Choyal et al., 2023).

5. Experimental and Simulation Signatures

Simulation predictions using MLIPs indicate that Jahn-Teller-stabilized icosahedral clusters should demonstrate distinct vibrational densities of states (extra localized modes), altered electron localization, and reduced mean squared displacement relative to crystalline analogs. These characteristics have been directly compared to experimental Raman, EXAFS, and neutron scattering spectra where the experimental observables can be mapped onto simulation-derived vibrational or electronic structure fingerprints (Rowe et al., 2017, Bideault et al., 2024).

Energetic quantification shows that the stabilization energy due to the Jahn-Teller effect, as resolved by MLIPs, can be extracted via cluster-based Δ-learning or by energetic decomposition in cluster and bulk MD runs under varying chemical composition and electronic configuration (Ko et al., 2023, Mészáros et al., 24 Feb 2025).

6. Theoretical and Computational Advances

The integration of fourth-generation MLIPs (with explicit long-range electrostatics and global charge equlibration (Ko et al., 2023)), multi-fidelity learning combining data from multiple electronic structure levels (e.g., GGA/meta-GGA/coupled-cluster (Kim et al., 2024)), and active-learning workflows (Fan et al., 2022) is significantly accelerating the exploration of non-crystalline, locally Jahn-Teller-stabilized morphologies. Surrogates trained on cluster and bulk datasets allow both compositional and configurational transfer of energy scales relevant to Jahn-Teller stabilization, and permit the refinement of potentials post hoc via top-down reweighting against experimental observables (Fuchs et al., 3 Dec 2025).

7. Outlook and Future Directions

Jahn-Teller-stabilized amorphous icosahedra provide a mechanistic pathway for understanding the suppression of crystallinity and the outstanding mechanical and thermal properties of glasses, nanocomposites, and complex alloys. Continued advances in machine-learned interatomic potentials—such as message-passing neural networks (e.g., eSEN-30M-OAM (Xiao et al., 28 Aug 2025)), Pareto-front model selection (Seko, 2020), and unsupervised topology analysis for motif identification—are expected to further enhance the ability to study and engineer these motifs across length and time scales relevant to material applications.

References:

• "A Machine Learning Potential for Graphene" (Rowe et al., 2017)
• "Accurate Screening of Functional Materials with Machine-Learning Potential and Transfer-Learned Regressions: Heusler Alloy Benchmark" (Xiao et al., 28 Aug 2025)
• "Accurate Fourth-Generation Machine Learning Potentials by Electrostatic Embedding" (Ko et al., 2023)
• "Simple machine-learned interatomic potentials for complex alloys" (Byggmästar et al., 2022)
• "Polyvalent Machine-Learned Potential for Cobalt: from Bulk to Nanoparticles" (Bideault et al., 2024)
• "Short-range $Δ$-Machine Learning: A cost-efficient strategy to transfer chemical accuracy to condensed phase systems" (Mészáros et al., 24 Feb 2025)
• "Data-efficient multi-fidelity training for high-fidelity machine learning interatomic potentials" (Kim et al., 2024)
• "Refining Machine Learning Potentials through Thermodynamic Theory of Phase Transitions" (Fuchs et al., 3 Dec 2025)