Computational Simulation Of Structures And Energies For Symmetrical Tilt Grain Boundaries

Metal materials usually exist in polycrystalline form. A great many of grain boundaries (GB) are included, which have significant influences on the properties of materials, such as grain growth, diffusion, grain boundary sliding and rotation, impurity segregation, atoms migration, deformation, precipitation, corrosion and fracture. The structures and energies are two important parameters characterizing GB properties, the investigations on which will help to performances prediction, properties modification, and design of new materials. Therefore it is one of the great interesting fields in the society of materials. In this thesis, we have calculated and analyzed the energies and structures of [001] symmetrical tilt grain boundaries (STGB) for body centered cubic (BCC) metal Fe and [1|- 10] STGB for three noble metals Au, Ag and Cu. This is based on coincidence site lattice (CSL) model and performed by using modified analytical embedded atom method (MAEAM). In addition, the influences of translations and expansions on GB energies and structures are studied. Finally our theoretical results are compared with relevant experimental observations. The main results can be concluded as follows:(1) The distances between atoms in initial rigidly jointed GB are so small that the energies increase unrealistically high. Obviously such GB configuration is unstable and can not exit in nature.(2) For 27 [001] STGB involved in this work, GB energies vary with relative translation, and have minimum values at a certain translation distance. Every minimum energy appears at a translation distance of 50% during translating along tilt axis, and three minimum energies correspond to (310) (θ = 36.87°, E = 2.1548J/m~2), (210) (θ= 53.13°,E = 4.9388J/m~2) 和 (510) (θ = 22.62°, E = 7.5744J/m~2)successively, while for the translation in GB plane and perpendicular to the tilt axis, three minimum energies correspond to (310) (θ = 36.87°, E = 2.1023J/m~2), (530) (θ = 61.93°, E = 4.0826J / m~2) and (510) (θ = 22.62°, E = 4.5879J / m~2) successively. From the viewpoint of energy minimization, (310), (530), (510) and (210) GB are preferred in (hk0) STGB. Results also show that GB energy increases oscillatorily with increasingS, especially for smaller I. As the samel is concerned, the GB energy decreases with increasing interplanar spacing, this is true for other (hkO) GB planes. It was also obtained for Ag/Ni and Ag/Si interfaces.(3) For expansion between adjacent grains in [001] STGB, the minimum energy of each (hkO) GB varies with rotation angle, energy cusps appear at certain angles. The four lowest energies correspond to (310) (0 = 36.87°), (210) (0 = 53.13*), (510) (0 = 22.62°) and (530) (0 = 61.93°) successively. From energy minimization, these GBs are preferred in (hkO) STGB. The calculation of energy and excess volume 5VIA shows that the minimum GB energy E^ increases linearly with increasing excess volume SVI A, so the GB energy can be approximately measured with SV I A, which is consistent with rotating sphere-on-a-plate experiments. For the 27 considered GB planes, four lowest energies correspond to four minimum C(m) respectively.(4) In the investigation on the correlation between energy and translation for these three noble metals in [110] STGB, we find that the energies vary with translations for each (hhk) GB, the minimum energies can be obtained at certain translation distance. The relative translation distances corresponding to the minimum energies for the three metals Au> Ag^ Cu are the same for both translations in GB plane, moreover, except for (ill) and (113), the other 42 GB planes corresponding to the minimum energies have the same translation distance of 50% for translation along tilt axis. For both translations of various GB planes, the minimum energy of Cu is much higher than that of Ag and Au, while the minimum energy of Ag is slightly higher than that of Au. This is consistent with the calculated results of surface energy and twist GB energy. And for both translations in three metals, the three lowest energies are all corresponding to (111) (0 = 70.53°) , (113) (0 = 129.52*) and (331) (0 = 26.53°) boundary successively. In addition, the minimum GB energies obtained from translation in the GB plane and perpendicular to the tilt axis are much lower than that along the tilt axis, therefore we conclude that the main translation direction should be perpendicular to the tilt axis. The minimum energies in three metals increase oscillatorily with increasing 2 especially for smaller 2, the minimum GB energy decreases with increasing relative interplanar distance d I a.(5) During the simulation of [T10] STGB in three metals, it is found that for expansion between adjacent grains, the minimum energy appears at certain rotationangle, four lowest energies are all corresponding to (111) (0 = 70.53")> (113) (0 = 129.52') > (331) (0 = 26.53°) and (112) (0 = 109.47) GB plane, from minimization of energy, these GB planes are preferred in (hhk) STGB. The minimum GB energy E^ increases linearly with increasing excess volume 5VIA, in addition, four lowest energies are corresponding to four minimum C(m) respectively.