This paper gives the general expressions for the compliance s′ijkl, Young＇s modulus E（hkl） and Poisson＇s ratio v（hkl, θ） along arbitrary loading direction [hkl] for tetragonal crystals. The representation surf...This paper gives the general expressions for the compliance s′ijkl, Young＇s modulus E（hkl） and Poisson＇s ratio v（hkl, θ） along arbitrary loading direction [hkl] for tetragonal crystals. The representation surface for which the length of the radius vector in the [hkl] direction equals E（hkl） and representation curve for which the length of the radius vector with angle θ deviated from the reference directions [001^-], [100], [001^-], [101^-] and [112^-] equals v（100, θ）, v（001, θ）, v（110,θ）, v（101,θ） and v（111, θ） respectively, are constructed for nine tetragonal crystals （ammonium dihydrogen arsenate, ammonium dihydrogen phosphate, barium titanate, indium, nickel sulfate, potassium dihydrogen arsenate, potassium dihydrogen phosphate, tin and zircon）. The characteristics of them are analysed in detail.展开更多
This paper reports that an atomic scale study of [^-110] symmetrical tilt grain boundary （STGB） has been made with modified analytical embedded atom method （MAEAM） for 44 planes in three noble metals Au, Ag and Cu...This paper reports that an atomic scale study of [^-110] symmetrical tilt grain boundary （STGB） has been made with modified analytical embedded atom method （MAEAM） for 44 planes in three noble metals Au, Ag and Cu. For each metal, the energies of two crystals ideally joined together are unrealistically hlgh due to very short distance between atoms near the grain boundary （GB） plane. A relative slide between grains in the GB plane results in a significaut decrease in GB energy and a minimum value is obtained at specific translation distance. 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. For all the three metals, the three lowest energies correspond to identical （111）, （113） and （331） boundary successively for two translations considered; from minimization of GB energy, these boundaries should be preferable in [^-110] STGB for noble metals. This is consistent with the experimental results. In addition, the minimum energy increases with increasing reciprocal planar coincidence density ∑, but decreases with increasing relative interplanar distance d/a.展开更多
For crystals, the compliance (sij) and the stiffness (cij) matrices are specified in the orthogonal coordinate systems (Yi), which do not coincide with the crystal axes (Xi) commonly used except for cubic and orthorho...For crystals, the compliance (sij) and the stiffness (cij) matrices are specified in the orthogonal coordinate systems (Yi), which do not coincide with the crystal axes (Xi) commonly used except for cubic and orthorhombic crystal systems. Transformations have been done in this paper and the general compliance transformation relations from the orthogonal coordinate systems (Yi) to the measurement systems (Mi) are given for all seven crystal systems. Accordingly, useful expressions for Young's modulus E and Poisson's ratio are also derived.展开更多
基金supported by the State Key Development Program for Basic Research of China (Grant No 2004CB619302)the National Natural Science Foundation of China (Grant No 50271038)
文摘This paper gives the general expressions for the compliance s′ijkl, Young＇s modulus E（hkl） and Poisson＇s ratio v（hkl, θ） along arbitrary loading direction [hkl] for tetragonal crystals. The representation surface for which the length of the radius vector in the [hkl] direction equals E（hkl） and representation curve for which the length of the radius vector with angle θ deviated from the reference directions [001^-], [100], [001^-], [101^-] and [112^-] equals v（100, θ）, v（001, θ）, v（110,θ）, v（101,θ） and v（111, θ） respectively, are constructed for nine tetragonal crystals （ammonium dihydrogen arsenate, ammonium dihydrogen phosphate, barium titanate, indium, nickel sulfate, potassium dihydrogen arsenate, potassium dihydrogen phosphate, tin and zircon）. The characteristics of them are analysed in detail.
基金Project supported by the State Key Development for Basic Research of China （Grant No 2004CB619302） and the National Natural Science Foundation of China （Grant No 50271038）.
文摘This paper reports that an atomic scale study of [^-110] symmetrical tilt grain boundary （STGB） has been made with modified analytical embedded atom method （MAEAM） for 44 planes in three noble metals Au, Ag and Cu. For each metal, the energies of two crystals ideally joined together are unrealistically hlgh due to very short distance between atoms near the grain boundary （GB） plane. A relative slide between grains in the GB plane results in a significaut decrease in GB energy and a minimum value is obtained at specific translation distance. 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. For all the three metals, the three lowest energies correspond to identical （111）, （113） and （331） boundary successively for two translations considered; from minimization of GB energy, these boundaries should be preferable in [^-110] STGB for noble metals. This is consistent with the experimental results. In addition, the minimum energy increases with increasing reciprocal planar coincidence density ∑, but decreases with increasing relative interplanar distance d/a.
文摘For crystals, the compliance (sij) and the stiffness (cij) matrices are specified in the orthogonal coordinate systems (Yi), which do not coincide with the crystal axes (Xi) commonly used except for cubic and orthorhombic crystal systems. Transformations have been done in this paper and the general compliance transformation relations from the orthogonal coordinate systems (Yi) to the measurement systems (Mi) are given for all seven crystal systems. Accordingly, useful expressions for Young's modulus E and Poisson's ratio are also derived.
