Available online at www.sciencedirect.com ScienceDirect Materials Today: Proceedings 11 (2019) 118–123 www.materialstoday.com/proceedings 2214-7853 © 2019 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Modern Trends in Manufacturing Technologies and Equipment 2018: Materials Science. ICMTMTE_2018 Crystal structures predicted by the PFC method with atomic density fluctuations Ilya Starodumov a, *, Vladimir Ankudinov b,c , Peter Galenko c 0F0F a Laboratory of Multi-scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, 620000 Ekaterinburg, Russia b Udmurt State University, Universitetskaya str. 1, building 4, 426034, Izhevsk, Russia c Friedrich-Schiller-Universitat Jena, Physikalisch-Astronomische Fakultat, D-07743 Jena, Germany Abstract The mathematical modeling of crystal structures and their dynamics during the structural transitions can be performed by the method of phase field crystal in the hyperbolic formulation (MPFC method). This method is suitable for a continual modeling of the atomic density field at diffusion time intervals. The unstable behavior of the solution near local energy minima is discussed. The authors propose the hypothesis of the formation of metastable structures during the relaxation of domain to the stable state. Due to the presence of the set of different possible structures on the system’s transformation path, the pattern of the atomic density field could remain still when the system is in the vicinity of local free energy minima. In the absence of fluctuations the system can remain in that condition for arbitrarily long. We propose the simple stochastic extension of hyperbolic PFC-model to find the effect of fluctuations on the dynamics of atomic density field. © 2019 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Modern Trends in Manufacturing Technologies and Equipment 2018: Materials Science. Keywords: crystal structure; phase field crystal; simulation; metastability 1. Introduction The phase field crystal model (PFC model) is modern continuum approach for simulations of the atomic density evolution on the diffusion time scales [1–3]. The PFC model predicts the coexistence of structures having various * Corresponding author. Tel.: +7 343 3899477. E-mail address: ilya.starodumov@urfu.ru