🔬 materials science

Pressure-dependent melting and crystallization of B2-NiAl from neural-network molecular dynamics

This study employs neural-network molecular dynamics with a Deep Potential model to establish a thermodynamically consistent pressure-dependent melting curve for B2-NiAl, revealing a steeper increase in melting temperature at high pressures and confirming that the melting process remains congruent with an essentially equiatomic liquid phase.

Original authors: A. S. Onegin, P. R. Levashov, N. M. Chtchelkatchev

Published 2026-09-18

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CC BY 4.0

Original authors: A. S. Onegin, P. R. Levashov, N. M. Chtchelkatchev

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

Nickel aluminide is a material that engineers have long admired for its ability to withstand extreme heat without losing its strength. It is a compound made of equal parts nickel and aluminum, arranged in a rigid, ordered pattern that makes it ideal for protective coatings and high-temperature machinery. For decades, scientists have known that this material melts at a specific temperature when left alone at normal atmospheric pressure. However, the behavior of this material changes dramatically when it is squeezed. In the deep interiors of planets or during high-speed impacts, materials are subjected to immense pressure, which forces their atoms closer together and alters how they hold onto each other. Understanding exactly how pressure changes the temperature at which a solid turns into a liquid is crucial for predicting how materials behave in these extreme environments. While researchers have measured this for many substances, the precise relationship for nickel aluminide under high pressure has remained uncertain, leaving a gap in our knowledge of how this important material transforms when compressed.

To fill this gap, a team of researchers turned to a powerful new way of simulating matter using artificial intelligence. Instead of relying on older, simplified models of how atoms interact, they trained a neural network—a type of computer program that learns from data—to understand the complex forces between nickel and aluminum atoms. They fed this program with thousands of calculations based on the fundamental laws of quantum physics, teaching it to predict how the atoms would behave under various conditions of heat and pressure. Once the model was trained, the researchers used it to run massive simulations on a computer. They created virtual blocks of the material, half solid and half liquid, and watched what happened when they adjusted the pressure and temperature. By observing the point where the solid and liquid parts stopped growing or shrinking and remained stable side by side, they could pinpoint the exact melting temperature at different levels of compression.

The simulations revealed a clear and steady trend: as the pressure increased, the temperature required to melt the material rose significantly. The researchers tested pressures ranging from normal atmospheric levels up to fifty gigapascals, a force equivalent to the weight of a small car pressing down on a single fingernail. At the lowest pressure, the material melted at approximately 1896 Kelvin. As the pressure climbed to fifty gigapascals, the melting point surged to nearly 3569 Kelvin. This increase was sharper than what previous computer models had predicted, suggesting that the new, more accurate model captures how the material resists melting under extreme compression better than earlier attempts. The researchers also checked their work by calculating the energy and volume changes that occur when the solid turns to liquid. These independent checks matched their melting curve perfectly, confirming that their results were internally consistent and reliable.

Beyond just finding the melting point, the team investigated a subtle but important question: does the material melt evenly, or do the nickel and aluminum atoms separate into different layers as they turn to liquid? In some materials, the liquid that forms has a different chemical makeup than the solid it came from, which can complicate how the material behaves. The researchers analyzed the composition of the liquid layer in their simulations with extreme precision. They found that even under the highest pressures, the liquid remained perfectly balanced, containing equal amounts of nickel and aluminum. The difference from a perfect fifty-fifty mix was so small it was barely measurable. This provided direct evidence that the material melts in a congruent manner, meaning the solid and liquid phases stay chemically identical throughout the process, even when squeezed to the limits of the simulation.

To understand how the material reforms after melting, the researchers also simulated what happens when the liquid is cooled back down. They watched the atoms as they lost heat and began to lock into place. They discovered that the speed of cooling mattered greatly. If the material was cooled very quickly, the atoms froze into a disordered, glass-like state. However, if they cooled more slowly, the atoms had time to arrange themselves into the specific, ordered pattern characteristic of nickel aluminide. Interestingly, higher pressure made the material more eager to crystallize into this ordered structure. The simulations showed that the atoms first formed a basic geometric framework, and only afterward did the nickel and aluminum atoms sort themselves into their correct, alternating positions. This step-by-step process confirmed that the material has a strong natural preference to return to its original, ordered state rather than forming a different kind of crystal.

These findings offer a complete and consistent picture of how nickel aluminide behaves under pressure. By combining advanced machine learning with rigorous simulation techniques, the researchers have established a reliable map of the material's melting behavior from normal conditions to extreme compression. They have shown that the material becomes much harder to melt as it is squeezed, that it maintains its chemical balance throughout the process, and that it naturally seeks to return to its ordered structure when cooled. This work not only clarifies the fundamental physics of a material used in high-temperature applications but also demonstrates the power of modern computational methods to solve long-standing questions about how matter transforms under the most intense conditions.

Technical Summary: Pressure-Dependent Melting and Crystallization of B2-NiAl

Problem Statement
Nickel aluminide (NiAl) is a prototypical ordered intermetallic compound with significant high-temperature structural applications. While its melting behavior at ambient pressure is well-characterized as congruent, its melting behavior under high pressure remains insufficiently constrained. Existing molecular dynamics (MD) studies have relied primarily on embedded-atom method (EAM) potentials, which may lack the transferability required for accurate high-pressure thermodynamics. Furthermore, experimental data at elevated pressures are limited and exhibit scatter due to measurement difficulties. A critical open question is whether the melting of stoichiometric B2-NiAl remains congruent (where solid and liquid phases share the same composition) under compression, or if chemical partitioning occurs. This study addresses these gaps by employing high-accuracy machine-learning interatomic potentials to determine the pressure-dependent melting curve ( $T_m(P)$ ), verify thermodynamic consistency, and characterize the congruence of melting and subsequent crystallization.

Methodology
The authors utilized neural-network molecular dynamics (NNMD) with a Deep Potential (DeepMD) interatomic model. The methodology comprised four main components:

Potential Development: A Deep Potential model was trained on an extended database of approximately 37,200 configurations. This database was constructed by combining first-principles (DFT) data for liquid Al–Cu–Ni alloys with ordered Al–Ni structures, distorted crystals, and surfaces. To ensure coverage of high-pressure states relevant to the study, an active learning loop was employed using the PET-MAD-S model as a configuration generator. Configurations were selected via Smooth Overlap of Atomic Positions (SOAP) descriptors and Farthest-Point Sampling (FPS), then labeled with DFT. The final model was trained to reproduce energies, forces, and stress tensors, achieving high accuracy (force RMSE < 0.16 eV/Å) across the 0–50 GPa range.
Melting Curve Determination: Melting temperatures were determined using the two-phase solid–liquid coexistence method. Simulations were performed in the constant-pressure, constant-enthalpy (NPH) ensemble for supercells containing 16,384 atoms. A solid–liquid interface was created, and the system was evolved until a stable coexistence state was reached, allowing the determination of $T_m$ at pressures from 0 to 50 GPa.
Thermodynamic Consistency Check: To validate the calculated melting line, independent single-phase simulations of the solid and liquid were conducted at the determined $T_m(P)$ . Enthalpy ( $\Delta h$ ) and volume ( $\Delta v$ ) changes upon melting were calculated. These values were used to compute the Clapeyron slope ( $dT_m/dP = T_m \Delta v / \Delta h$ ) and compared against the analytical derivative of the fitted $T_m(P)$ curve.
Congruence and Structural Analysis:
- Composition: Layer-resolved composition profiles along the [001] direction were analyzed to measure the aluminum fraction in the liquid phase relative to the stoichiometric value (0.5).
- Crystallization: Melt-quench simulations were performed at various cooling rates and pressures. Structural analysis utilized Polyhedral Template Matching (PTM) to identify local geometries (BCC, FCC, HCP, etc.) and a specific local order parameter ( $q_{B2}$ ) to distinguish chemically ordered B2 structures from disordered BCC-like geometries.

Key Results

Melting Curve ( $T_m(P)$ ): The melting temperature of B2-NiAl increases monotonically with pressure, rising from $1896 \pm 9$ K at 0 GPa to $3569 \pm 17$ K at 50 GPa. The results agree closely with experimental ambient-pressure values ( $\sim$ 1911 K) and previous EAM-based calculations up to ~20 GPa. However, at higher pressures (30–50 GPa), the DeepMD model predicts a significantly steeper increase in $T_m$ compared to previous EAM results, suggesting a different description of the relative thermodynamic stability of compressed solid and liquid phases.
Thermodynamic Consistency: The calculated Clapeyron slopes, derived from independent $\Delta h$ and $\Delta v$ measurements, show excellent agreement with the derivative of the fitted Simon–Glatzel melting curve across most of the pressure range. This confirms the internal thermodynamic consistency of the coexistence simulations. The enthalpy of melting increases with pressure, while the relative volume change ( $\Delta v/v_{sol}$ ) decreases, indicating a reduced density contrast between phases under compression.
Congruent Melting: Layer-resolved composition analysis reveals that the coexisting liquid phase remains essentially equiatomic (Al fraction $\approx$ 0.5) at all investigated pressures. Deviations from the stoichiometric value do not exceed $5 \times 10^{-3}$ . This provides direct atomistic evidence that the melting of B2-NiAl remains congruent within the present model, with no significant chemical partitioning between solid and liquid phases.
Crystallization Behavior: Melt-quench simulations demonstrate that the undercooled liquid crystallizes into a polycrystalline state dominated by a BCC-like geometric framework. Chemical B2 ordering develops progressively within this framework. The tendency for crystallization increases with slower cooling rates and higher pressure. At 30 GPa, the BCC fraction is substantially higher than at 0 GPa for the same cooling rates, indicating that compression promotes crystallization into bcc-derived structures.

Significance and Claims
The paper establishes a thermodynamically consistent, pressure-dependent description of B2-NiAl melting using a high-fidelity Deep Potential model. The primary contributions are:

Refined Melting Curve: Providing a more accurate $T_m(P)$ relation that diverges from previous EAM predictions at high pressures, suggesting the need for more accurate potentials to capture high-pressure thermodynamics.
Validation of Congruence: Offering direct atomistic evidence that B2-NiAl melting remains congruent under compression, resolving uncertainty regarding potential chemical partitioning.
Methodological Rigor: Demonstrating the utility of combining two-phase coexistence simulations with independent single-phase thermodynamic checks (Clapeyron relation) to ensure the reliability of machine-learning potential predictions.
Structural Insight: Clarifying the crystallization pathway, showing that a bcc-like geometric framework forms prior to the establishment of full chemical B2 order, and that pressure enhances this crystallization tendency.

The authors conclude that these results provide a coherent atomistic description of pressure-driven melting in B2-NiAl, clarifying both the melting line and the character of melting under compression within the scope of the developed interatomic model.

Technical Summary: Pressure-Dependent Melting and Crystallization of B2-NiAl

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