Incongruent Melting and Phase Diagram of SiC from Machine Learning Molecular Dynamics

TL;DR

This work employs a Bayesian active-learning–trained Gaussian-process force field to perform large-scale MLMD of SiC under high temperature and pressure, enabling direct observation of incongruent melting and decomposition into Si-rich liquid and carbon-rich phases. By combining a 64-atom and a 512-atom active-learning trajectory with 512,000-atom simulations and two-phase coexistence methods, the authors map a comprehensive $P$-$T$ phase diagram, quantify transition temperatures, and analyze nucleation and spinodal decomposition of carbon clusters. The results reconcile long-standing experimental inconsistencies, showing that at high $P$ SiC decomposes upon heating and reverts to a homogeneous liquid upon heating, while at lower temperatures a crystal–decomposed boundary emerges and a distinct sublimation boundary exists at low pressure. The study demonstrates the power of uncertainty-aware MLFFs for predicting complex phase behavior in covalent ceramics and provides atomic-level insights with potential implications for SiC processing and deposition technologies.

Abstract

Silicon carbide (SiC) is an important technological material, but its high-temperature phase diagram has remained unclear due to conflicting experimental results about congruent versus incongruent melting. Here, we employ large-scale machine learning molecular dynamics (MLMD) simulations to gain insights into SiC decomposition and phase transitions. Our approach relies on a Bayesian active learning workflow to efficiently train an accurate machine learning force field on density functional theory data. Our large-scale simulations provide direct indication that melting of SiC proceeds incongruently via decomposition into silicon-rich and carbon phases at high temperature and pressure. During cooling at high pressures, carbon nanoclusters nucleate and grow within the homogeneous molten liquid. During heating, the decomposed mixture reversibly transitions back into a homogeneous SiC liquid. The full pressure-temperature phase diagram of SiC is systematically constructed using MLMD simulations, providing new understanding of the nature of phases, resolving long-standing inconsistencies from previous experiments and yielding technologically relevant implications for processing and deposition of this material.

Figures (7)

• Figure 1: a. Bayesian active learning workflow for collecting DFT training data on the fly during MD simulations. The MLFF predicts forces and uncertainties; configurations exceeding the uncertainty threshold trigger DFT labeling. b. Training data composition and coverage. Multiple Bayesian active learning trajectories were performed in parallel for different compositions (pure Si, pure C, and SiC) across various temperatures and pressures. For SiC, we started with a 64-atom supercell and then extended to a 512-atom supercell where phase separation spontaneouly occurred. c. Two-phase simulation protocol to determine phase transition temperatures. Interfaces between the solid/liquid and decomposed phases were created by inducing decomposition, followed by a two-phase coexistence simulation in the NPH ensemble to converge on the final transition temperature. d. Spontaneous decomposition during active learning. The collected data includes states where SiC decomposition occurred spontaneously during the active learning MD simulations, prior to any decomposed structures being present in the training set.
• Figure 2: Left: decomposed configuration of 512,000 atoms at the end of the simulation at 3000 K and 60 GPa. Yellow: Si, black: C. Middle: atoms colored with lattice type classified by polyhedral template matching. Blue: cubic diamond, orange: hexagonal diamond, purple: graphite, white: others. Right: radial distribution function of the structure shows the C-C peak dominates over the Si-C peak.
• Figure 3: SiC phase transitions and coexistence at 30 GPa from MD simulations. Top and middle panels (from 8,000-atom cooling and heating simulations) illustrate the reversibility of phase transition. Top: population distribution of local C atom fraction over time: a single peak indicates the homogeneous liquid phase, while multiple peaks indicate the decomposed (Si+C) phase (red: high population, blue: low population). Middle: temperature (blue) and largest carbon cluster size (red, number of atoms) with the simulation time, with blue shaded regions indicating the phase transition boundaries. Bottom panel (from 16,000-atom two-phase simulations) confirms the coexistence temperature by tracking the largest carbon cluster size (left) and temperature convergence at the $NPH$ stage (right).
• Figure 4: Snapshots of the four stages of the two-phase MD at 30 GPa (top) and 90 GPa (bottom) pressures. Each stage is simulated for 0.5 ns.
• Figure 5: Analysis of two-phase coexistence simulations. Panels (left to right) show: fraction of zinc-blende (rock-salt) structures, largest C cluster size (number of atoms), temperature convergence at the $NPH$ stage, over simulation time. Top: 30 GPa. Bottom: 90 GPa.