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The allotropes composed of close-packed (CP) structures that differ only in the stacking order in the system are called the CP polytypes [1]. The CP polytype is also considered one of the physical systems realizing the Kepler conjecture [2]. Since the significant changes in physical properties due to the intentional polytype formation have been reported in various fields of metallic and semiconductive systems [3-5], the material engineering demand for polytype phase control is diverse. The acquisition and deepening of scientific knowledge for the polytype phase control is therefore promising to lead to the creation of new functional materials. However, the scientific control of the polytype stacking order is still incomplete in the field of practical materials engineering. This is because the polytype control technology has many uncertainties since the formation mechanism of polytype is physically unsolved yet. Predicting polytype phase stability for a material has also been a long-standing issue in condensed matter physics and/or materials science. This situation stems from the fact that the atomistic interactions on polytype energetics might be surprisingly quite complex and delicate despite the simplicity of their geometrical structure. In the previous paper, we have presented an analytical theory on the total energetics for the CP polytypes based on the geometrical analysis for the correlation between interlayer interactions and interatomic ones in CP polytypes [6]. Our theoretical studies have shown that the long-range nature of interatomic interactions is an important factor for reproducing the static polytype energetics [6,7]. Based on our theory submitted [6], we have tried to construct an EAM (Embedded Atom Method) [8] type interatomic model for metallic La reproducing the theoretical polytype energetics. Our primary motivation for the present study is to grasp why long periodic polytype structures other than 2H and 3C ones appear as the stable phase under the crystal growth for the specific elemental systems. Therefore, we aim to develop the interatomic potential to reproduce the theoretical polytype energetics and to adopt it to the dynamical simulations for the long-periodic polytypes systems. The ground state for La is the 4H structure which is the simplest long-periodic polytype and La can exist in both 4H phase and the 3C phase under 583K [9]. Thus, it is possible to investigate the essential factors determining the polytype selection rule through the atomistic dynamics for metallic La. From our research so far, we have succeeded in constructing an EAM-type potential that mimics the energetics of metallic La with the 4H as the ground structure [10]. The following three procedures are found to be essentially important for deriving an interatomic interaction model with the 4H structure as the ground state; (i) The cutoff radius should be set to have a relatively longer distance (three or more interlayer distances in the 4H stacking structure). (ii) The equations of state (EOS) for the energetics of 2H, 3C, and 4H structures need to be reproduced as accurately as possible. (iii) The adiabatic potential along important transition paths between crystal structures such as the Bain path for the bcc-fcc transition must be exactly considered [11]. These procedures have made the interaction model describable for not only the energetics but also the lattice dynamics such as dynamical instability, which is known to be generally significant for the phase transition phenomena [11, 12]. The transferability of the associated potential and some results adapted in the molecular dynamics (MD) simulations will be also discussed in the presentation of the day. [1] A. L.Ortiz et al., J. Appl. Cryst. 46, 242 (2013). [2] T. Hales et al., Forum of Mathematics, Pi, 5, E2 (2017). [3] R. Yakimova et al., J. Cryst. Grow. 217, 255 (2000). [4] Z. Fan et al., Nat. Commun. 6, 7684 (2015). [5] E. M. T. Fadaly et al., Nature. 580, 205 (2020). [6] S. Ogane and K. Moriguchi, MRS Advances 6, 170 (2021). [7] K. Moriguchi et al., MRS Advances 6, 163 (2021). [8] Murray S. Daw and M. I. Baskes, Phys. Rev. B 29, 6443 (1984). [9] B. Love, “Metal Handbook”, Vol. 1, American Society for Metals, Novelty, Ohio, 1961, pp 1230-1231. [10] S. Ogane, et al., 2021 MRS Fall Meeting & Exhibit, CH02.13.05 (2021). [11] K Moriguchi and M Igarashi, Phys. Rev. B 74, 024111 (2006). [12] G. Grimvall et al., Rev. Mod. Phys. 84, 945 (2012). [13] S. Baci et al., Phys. Rev. B 81 (2010) 144507. Figure 1 |
