Amorphous Bismuth: Structure-Property Relations and the Size of the Supercell
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Amorphous Bismuth: Structure-Property Relations and the Size of the Supercell Zaahel Mata-Pinzón†, Ariel A. Valladares†, Alexander Valladares§, R. M. Valladares§ † Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México. Apartado Postal 70-360, México D. F. 04510, México. § Facultad de Ciencias, Universidad Nacional Autónoma de México. Apartado Postal 70-542, México D. F. 04510, México. ABSTRACT It has been argued that for the simulation of amorphous materials, the larger the periodic supercell the better the representation. We contend that for certain properties there is a minimum supercell size above which one obtains a good representation of the topological and electronic collective properties of the material independent of the size. To show this contention we have chosen two periodic supercells of bismuth, one with 64 atoms and another with 216 atoms, which were amorphized using our undermelt-quench approach [1]. The originally crystalline structures were subjected to a heating-and-cooling process starting at an initial temperature of 300 K and linearly going up to 540 K, in 100 simulational steps, 4.5 K just below the melting temperature of bismuth (the undermelt section of the process) under normal conditions of pressure. Next, the sample was cooled down to 0K (the quench section of the process), in 225 simulational steps with the same absolute cooling rate as the heating process. Then the samples obtained were geometry-optimized to find the final metastable amorphous structures. These structures were analyzed by calculating their radial (pair) distribution functions, the plane angle distributions and the electron densities of states. Results will be presented that manifest that after proper normalization due to the difference in the number of atoms and the number of electron energy levels, the two structures are, for all practical purpose, the same, indicating that in this case, the size of the cell does not seem to play a major role in the properties determined. INTRODUCTION The structure of amorphous materials has been studied for many years and structural properties, as the Radial Distribution Function (RDF), were obtained experimentally by diffraction (neutron, electron or x-ray) for some amorphous materials but since they are metastable phases, the measurements were commonly made with in situ techniques in order to maintain the conditions so that the sample remained in the amorphous state. In general, the properties of amorphous materials are an experimental challenge and several features cannot be easily measured. The difficulties on the experimental processes to generate and obtain amorphous materials have turned the scene to the computer simulation ground but if we try to simulate an amorphous material the challenge is to describe the atomic arrangements, because their properties are strongly dependent on the short and middle range order. For that reason the simulated structure must describe accurately the topological characteristics of the real amorphous sample in order to
