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Study of phase transitions in carbon materials at the atomic level using modern modeling methods

RSF grant No. 22-72-00138

Competition 2022 “Conducting proactive research by young scientists” of the Presidential program of research projects implemented by leading scientists, including young scientists

Various first-order phase transitions in their development pass through the same stages, the first of which is the nucleation stage, which is of the greatest interest and greatest difficulty in studying. In the theory of this stage, questions of the thermodynamics of small systems and the description of the process of overcoming the energy barrier by nascent particles are closely intertwined. To achieve a detailed understanding of nucleation, it is necessary to use computer modeling methods. The small size of the nascent core of the new phase requires taking into account the contributions of the interface, surface energy, relaxation of mechanical stresses into the curvature energy and other features of low-dimensional materials. This requires high-precision modeling that takes into account all these parameters, which, however, is an extremely difficult task for the current tools of computational materials science. Indeed, traditional methods of electron density functional theory, although they make it possible to quite accurately calculate the properties of atomic systems from first principles, are nevertheless limited by the available computing power. This limits their applicability to periodic structures consisting of hundreds of atoms. At the same time, the task of describing the nucleation of new phases requires the description of systems with the number of atoms up to 10^4-10^6 atoms. On the other hand, empirical potentials that are not demanding on computational resources make it possible to describe large systems containing millions of atoms. But until recently, the parameterization of these potentials was limited to their own (often rather narrow) model systems, which were not intended for modeling transition states and new phases, which is a necessary condition for the study of phase transformations. However, the situation has changed dramatically recently with the advent of empirical machine learning capabilities that can be trained on large data sets obtained through first-principles calculations. Thus, one of the objectives of the project is to develop such potentials that describe the interaction with precision methods from first principles, allowing one to model the required number of atoms in structures. Parameterized potentials will be used for the scientific study of phase transformation in carbon systems, the graphite-diamond transition and multilayer graphene-ultrathin diamond film (diamane), and in the future can be used to describe phase transitions in other systems and nanomaterials.

Project implementers

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Main results of the project

Using electron density functional theory, it was shown that cubic diamond films in a graphite matrix can be stable only starting from 8 atomic layers, while hexagonal diamond films are stabilized starting from 4 layers. The advantage of the lonsdaleite phase in ultrathin films was explained by calculating the surface energy of the films. It was found that the surface energy of cubic diamond films is more than two times higher than that of hexagonal diamond. After studying the stability of films with different surfaces, it was shown that only the (111) film with the cubic diamond structure and the (10-10) film with the hexagonal diamond structure have the smallest discrepancies with the graphite lattice parameters and are suitable for studying the nucleation process. Machine learning potentials were trained on a training set of structures consisting of periodic structures of crystals of the studied phases under pressure, nonequilibrium configurations at temperature, films with various surfaces and semi-periodic models of nuclei. The training criterion was not only the small value of the standard deviation in the determination of forces and energies from density functional theory calculations, but also the correct determination of the elastic characteristics of volumetric phases. After comparing MTP- and GAP-type potentials, they were shown to provide similar accuracy. However, both in terms of computational costs and parallelization efficiency, the potential of MTP had a noticeable advantage. which was used in further calculations. Using the obtained machine learning potential, models of nuclei of cubic and hexagonal diamond phases in graphite at various pressures were built and optimized. Next, the thermodynamic Gibbs potential was calculated, the values of which were used to derive an analytical equation to describe the nucleation of diamond phases in graphite. Based on the dependences obtained from the analytical equation, the nucleation barriers and critical sizes of diamond phase nuclei were determined. In addition, it was shown that nuclei of too small thickness cannot exist at all even at a pressure of 15 GPa. With a thickness of ~6 to ~10 atomic layers, hexagonal diamond nuclei are more stable. And with a thickness of more than 30 layers, cubic diamond seeds become more stable.

Conference reports

1 / International Scientific Conference of Students, Postgraduate Students and Young Scientists “Lomonosov-2023”

Erokhin S.V., Sorokin P.B.,

Study of phase transitions in carbon materials at the atomic level using modern modeling methods

10-21 April 2023, 119991, Moscow, Leninskie Gory, 1

Oral report

2 / International Conference "New Carbon Nanomaterials: Ultrathin Diamond Films"

Sergey Erohin

The diamond nucleation in multilayered graphene. Theoretical description

December 06-09, 2021, NUST MISIS

Invited talk
 

3 / Fourth Russian conference “Graphene: molecule and 2D crystal”

Erokhin S.V., Larionov K.V., Builova M.A., Sorokin P.B.

Study of diamond nucleation in graphite at the atomic level using modern modeling methods

August 14-18, 2023, Novosibirsk, NSU

Oral report

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