On-the-fly machine learning-augmented constrained AIMD to design new routes from glassy carbon to quenchable amorphous diamond with low pressure and temperature

TL;DR

This work addresses the challenge of modeling glassy carbon transformations under anisotropic stresses, which are crucial for forming quenchable amorphous diamond at lower pressures and temperatures. It introduces an on-the-fly ML-augmented constrained AIMD (CAIMD) framework implemented in VASP, enabling simulations under non-hydrostatic compression and rotational shear with explicit strain constraints. The study finds that GC is highly plastic under large strains, with a critical 30–40 GPa threshold for sp3 bond formation under pressure, and demonstrates pathways to quenchable a-D via carefully ordered pressure and temperature treatments, including shear-driven routes that yield high sp3 content at comparatively low P/T. The results reveal that non-hydrostatic loading and rotational shear can lower synthesis barriers, producing hard, sp3-rich amorphous carbon and offering a general modeling framework for disordered materials under anisotropic stresses with broad potential applications in materials design and synthesis.

Abstract

Recent advances in machine learning have enabled large-scale atomic simulations with first-principles accuracy, allowing precise modeling of disordered materials such as glassy carbon (GC). However, conventional ab initio molecular dynamics (AIMD) cannot effectively capture anisotropic stress effects, which are believed to play a key role in the transformation of GC into amorphous diamond under extreme conditions. In this work, we present an on-the-fly machine learning-augmented constrained AIMD (ML-augmented CAIMD) approach by modifying VASP 6.3.2. Our simulations not only reproduce major experimental features of GC but also provide restrictive synthesis conditions and microscopic insights. We show that GC exhibits unexpectedly high plasticity, with its compressive and shear strengths enhanced by large strains. Under pressure, increasing annealing temperature promotes the formation of quenchable amorphous diamond via enhanced sp3 preservation, but this trend reverses above 2900 K due to thermal graphitization. Under non-hydrostatic compression, GC transforms into a superhard structure sustaining large stress differences, which sharply increase when confining pressure exceeds 40 GPa. Finally, severe rotational shear at 30 GPa induces sp3 fractions up to 80 percent at 300 to 1000 K. A hardened amorphous carbon retaining 64 percent sp3 content is achieved by decompression at 300 K, marking the lowest pressure-temperature route ever predicted. Our ML-augmented CAIMD provides a general framework for modeling structural transformations in disordered materials under anisotropic stresses.

Figures (10)

• Figure 1: The temperature evolution as a function of AIMD time throughout the entire simulation process of GC preparation. Initially, the structure was melted at Tliquid (7000 K), followed by a rapid quenching to 300 K and subsequent annealing at Tanneal (3500 K). During these stages, an NVT ensemble was employed to maintain a constant volume (and thus a fixed density). Finally, the system was cooled to 300 K within an NpT ensemble, allowing for structural relaxation which induces a small density variation due to volume changes.
• Figure 2: Flowchart illustrating the modified VASP workflow for constrained deformation simulations under the NpT ensemble coupled with on-the-fly MLFF generation. The steps highlighted in Boldface (Apply strain and Constrain) represent our newly introduced procedures to impose and sustain applied anisotropic strains (tensile, compression, or shear) during simulations. {s$_l$} describes atomic positions of all atoms in the supercell at the $l$-th CAIMD step. {h$_l$} is a matrix with nine components from the three lattice vectors of the supercell at the $l$-th CAIMD step given in SM. FP is the abbreviation for first-principles (calculation). N$_{\rm MD}$ is the total CAIMD steps to be performed.
• Figure 3: Evolution of the percentage of sp2 bonds during the annealing (100 ps) and aging (100 ps) processes as a function of simulation time. Data was sampled at 1 ps intervals. The inset shows the final GC structure at 201 ps (including an extra 1 ps cooling stage before aging). Brown-colored atoms represent sp-bonded carbon, gray-colored atoms indicate sp2-bonded carbon, and red-colored atoms correspond to sp3-bonded carbon.
• Figure 4: Upper panels, the averaged stress--strain curves of GC at 300 K under 0 GPa for tensile (a), compression (b), and shear (c) loading, where the stresses are parallel to the directions of applied strains. The vertical dashed lines indicate the maximum strain at which the density and sp3 fraction remain within the typical range of GC, suggesting the upper limit of elastic behavior. Lower panels, the averaged stress--strain curves for other five stresses corresponding to tensile (d), compression (e), and shear (f) loading. Each curve represents an average over the three principal crystallographic directions and nearby 2000 data points.
• Figure 5: The average density (upper panels) and the percentage of sp3 bonds (lower panels) as a function of pressure under various temperatures, (a) 300 K, (b) 1000 K, (c) 2000 K, and (d) 3000 K. Each data point represents the time-averaged value obtained from at least 50 ps of simulation after equilibration. Solid lines indicate stepwise compression, while dashed lines represent stepwise decompression. The red sample marks the final density or sp3-bond percentage at 300 K and 0 GPa. The percentage of sp3 bonds is categorized into four distinct regions based on the bond percentage, each represented by a different color: 0--5% (GC or graphite structure), 5--80% (a-C structure), 8--88% (ta-C structure), and 88--100% (a-D structure).