Available on-demand - F.SF07.06.03
ANNNI Model Descriptions on Structural Energetics for a Wide Variety of Metallic Polytypes Composed of Close-Packed Layers
Koji Moriguchi1,2,Taku Miyakawa2,1,Shinya Ogane1,Kazumasa Tsutsui2,Yuta Tanaka2
Tohoku University1,Nippon Steel Corporation2
The local inhomogeneity such as defect, surface, interface, and nanostructure often assumes an important role for developing sophisticated materials since the functionalities of materials usually originate from the spatial inhomogeneity in the associated systems. In this work, among the many phenomena related to inhomogeneity in materials, we will report our computational research on the phenomenon called "Polytypism". Polytypism is a special case of polymorphism where two polymorphs differ only in the stacking sequences of the same two-dimensional sheets or layers.
Many crystalline compounds can be considered to be composed of one or more structural units. When these units can be stacked in different ways to form stable or metastable phases, the resulting phases are known as polytypes. Among the polytypes for these compounds, the silicon carbide (SiC) systems have been the most attractive and motivated tremendous amounts of theoretical and experimental investigations on their fundamental and technological properties for many years. Many SiC polytypes located around the ground state have been found to be energetically degenerated with energy of about ΔT = 2K . It is, therefore, very difficult to control the phase stability during the growth of a single crystal in order to obtain the desired stacking polytype in SiC systems. For this reason, a variety of physical perspectives are being investigated in order to establish better single crystal growing techniques . In addition, the long period stacking ordered (LPSO) Mg alloys with light weight, high specific strength, and high heat resistance are also recently drawing attention as a metallic system with similar polytypism to that in SiC . For both systems, the physical mechanism behind polytype selection is not yet fully understood and remains challenging issues to be solved.
In this situation, we have proposed a computational method coupled with three theoretical tools (PGA: polytype generation algorithm; FPC-DFT: first-principles calculations based on the density functional theory; and ANNNI: axial next-nearest-neighbor Ising model), which can make us possible to efficiently investigate the structural energetics for diverse nonequivalent close-packed(CP) polytypes [1, 4]. In the present work, the static energetics of a wide variety polytypes for 17 kinds of metallic elements (M=Be, Mg, Sc, Y, Co, Zn, Cu, Ag, Au, Ni, Pd, Pt, Al, Ca, Sr, Ba, and La) is systematically evaluated based on the same computational method proposed by the authors [1, 4]. For all these elemental systems, the atomistic geometry, energetics, and electronic structure for all polytypes with up to the periodic stacking length of L=13 (165 kinds of polytypes in total) have been carefully calculated based on the DFT within the GGA. The equilibrium theories based on the ANNNI model that is well known in the field of statistical mechanics have played an efficient role in the study of the origins of polytypism [5, 6]. In this work, the ANNNI model including interactions up to the third-nearest neighbor layer with the four-spin term  is adopted for the systems considered. Using the ANNNI model extracted from the GGA calculations, we will describe the inter-layer interactions, the phase diagrams of ANNNI model with interactions up to third-nearest neighbor, and the stability of stacking faults for each element. The relation to polytypism in the metallic systems considered will be also discussed.
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