Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Neural network potentials for modeling nonstoichiometric materials: a case of Chromium Sulfides Cr1-xS



Akram Ibrahim, Daniel Wines, Can Ataca


The chemical exfoliation of non-van der Waals (vdW) materials to ultrathin nanosheets remains a formidable challenge. This difficulty arises from the strong preference of these materials to engage in three-dimensional chemical bonding, resulting in uncontrolled atomic migration into the vdW gaps during cation deintercalation from the bulk structure, ultimately leading to unpredictable structural disorder. Computational models capable of comprehending the widespread nonstoichiometric local environments resulting from disordered atomic migrations during exfoliation of non-vdW materials are crucial for understanding the underlying mechanisms. Here, we propose a generic framework using neural network potentials (NNPs) to accurately model nonstoichiometric systems over a broad range of vacancy concentrations. We apply our framework to investigate the crystal structures and phase transformations occurring during the exfoliation of non-vdW nonstoichiometric Cr$_(1-x)}$S systems, a compelling material category with substantial potential for two-dimensional (2D) magnetic applications. The efficacy of the NNP outperforms the conventional cluster expansion, exhibiting superior accuracy and transferability to unexplored crystal structures and compositions. By employing the NNP in simulated annealing optimizations, we predict low-energy Cr1-xS structures anticipated to result from experimental synthesis. A notable structural transition is discerned at the Cr0.5S composition, with half of the Cr atoms preferentially migrating to vdW gaps. This aligns with experimental observations in the chemical exfoliation of 2D CrS2, and emphasizes the vital role of excess Cr atoms beyond the Cr/S = $1/2$ composition ratio in stabilizing vdW gaps. Additionally, we utilize the NNP in a large-scale vacancy diffusion Monte Carlo simulation, to illustrate the impact of lateral compressive strains in catalyzing the formation of vdW gaps within non-vdW CrS2 slabs through Poisson's axial expansion. This provides a direct pathway for more facile exfoliation of ultrathin nanosheets from non-vdW materials through strain engineering. The implemented methodology, leveraging machine learning potentials, is imperative to bridge the quantum-level accuracy to large scales necessary for modeling the intricate mechanisms underlying the chemical exfoliation of non-vdW materials.
npj Computational Materials


Ibrahim, A. , Wines, D. and Ataca, C. (2024), Neural network potentials for modeling nonstoichiometric materials: a case of Chromium Sulfides Cr1-xS, npj Computational Materials, [online],, (Accessed July 23, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created January 10, 2024, Updated January 17, 2024