Analysis of some solid amorphous inorganic structures and the boson peak phenomenon with a computational random graph approach

In this study, a new alternative model algorithm has been proposed for assembling amorphous structures, unifying the bosonic paradigm applicable at low temperatures with crystalline models relevant at room and higher temperatures. Physical meaning of main model parameters is determined together with an explanation for the appearing bosonic peak using the random graph theory. Numerically, statistical atomic distribution in a multiphase amorphous system is provided without the melting simulation of base crystals, and the mean energy function has been determined analytically. The calculated table data are in good agreement with neutronography measurements of the actual amorphous alloy in its solid state. Programme optimisations were also implemented, and we outlined several effective steps to achieve the higher processing speed. The proposed programme code can be used for potential test assembling and simulations of amorphous systems with sorting by the optimal atomic content or proportion (i.e. glass forming ability).

💡 Research Summary

This paper introduces a novel computational framework for modeling the atomic structure of metallic glasses and explaining the low‑temperature boson peak, using a random‑graph‑based algorithm combined with Finnis‑Sinclair pair potentials. The authors focus on the AMAG‑225 alloy (Fe 73.5 %, Ni 25 %, Cr 1.5 %) as a benchmark system.

Instead of the conventional melt‑and‑quench molecular dynamics (MD) workflow, which requires explicit crystalline precursors, melting simulations, and thermostat‑controlled cooling, the proposed method proceeds in two conceptual steps: (1) generate a set of points randomly distributed in a simulation box, with the total number of points proportional to the prescribed elemental composition; (2) compute all inter‑particle distances, evaluate the Finnis‑Sinclair binding energy for each possible pair, and retain only the pair with the lowest energy for each atom, thereby constructing a set of bonds that can be interpreted as edges of a random graph. Duplicate distances (identical distance‑energy pairs) are flagged as potential local crystallization events; the frequency of such duplicates is suggested as a metric of glass‑forming ability.

The Finnis‑Sinclair potentials are parameterized for Fe‑Fe, Ni‑Ni, and Cr‑Cr interactions (quadratic polynomials multiplied by a (x‑10)² factor, active only for 0 < x < 10 Å). By using these physically motivated potentials, the model captures both the “pair‑dipole” contributions that dominate at cryogenic temperatures (the origin of the boson peak) and the many‑body interactions that become relevant at room temperature and above.

Computationally, the algorithm scales as O(N²) because every distance pair is examined. The authors implement the code in Python and accelerate it with MPI parallelism, nested loops, and list‑membership checks. Benchmarks on two JSC super‑computing nodes (96 Intel Xeon Platinum 8268 cores per node) show that expanding the system from 2 000 to 10 000 particles yields a speed‑up of roughly 19×, while preserving numerical accuracy (linear correlation coefficient 0.99 with respect to reference MD runs, absolute energy error ±0.011 eV). Additional optimisation ideas—compact NumPy arrays, GPU off‑loading, and a C‑language port—are discussed.

Experimental validation is performed by comparing the simulated radial distribution function (RDF) with neutron diffraction data obtained on the DN‑2 thermal neutron diffractometer. The simulated RDF reproduces the main peak at 5.6–5.8 Å, the overall shape, and the decay beyond 10 Å, achieving a correlation coefficient of 0.99. This agreement demonstrates that the random‑graph‑based construction can faithfully reproduce the short‑range order of a real metallic glass without an explicit melting step.

The most original contribution lies in the theoretical link between the boson peak and random‑graph matching statistics. The authors treat each bond as an edge; the number of matched edges follows a Poisson or Gaussian distribution, depending on temperature. By integrating the mean energy ⟨U(x)⟩ over a Gaussian distribution and differentiating with respect to temperature, they derive a heat‑capacity term C ∝ exp(−E/kT)/T², which exhibits a low‑temperature minimum identified as the boson peak. The magnitude of this peak is controlled by the stiffness parameters in the Finnis‑Sinclair potentials, implying that frozen atomic pairs are the microscopic source of the boson anomaly. At higher temperatures, the edge‑matching statistics become smoother, corresponding to a fully connected graph that mimics an ideal gas of interacting atoms, consistent with Johnson‑Mehl‑Avrami‑Kolmogorov (JMAK) and Kohlrausch‑Williams‑Watts (KWW) relaxation models.

In the conclusion, the authors acknowledge limitations: the current implementation is restricted to two dimensions, the Finnis‑Sinclair parameter set covers only Fe, Ni, and Cr, and the boson‑peak interpretation, while mathematically elegant, lacks a direct quantitative comparison with low‑temperature calorimetry. They propose future work on extending the method to three dimensions, incorporating a broader range of elements (including rare‑earths), and coupling the mean‑energy expression with experimental heat‑capacity data for a fully unified description across all temperature regimes.

Overall, the paper delivers a coherent, experimentally validated computational tool that unifies low‑temperature bosonic behavior and high‑temperature structural dynamics of metallic glasses within a random‑graph framework. By eliminating the need for explicit melt‑and‑quench simulations, it offers a potentially faster route to explore composition‑structure relationships, assess glass‑forming ability, and guide the design of new amorphous alloys.