In the harmonic approximation, the atomic force constants are derived and the phonon dispersion curves along four major symmetry directions [00ζ], [0ζζ], [ζζζ] and [0ζ1] （or △∑, A and Z in group-theory nota...In the harmonic approximation, the atomic force constants are derived and the phonon dispersion curves along four major symmetry directions [00ζ], [0ζζ], [ζζζ] and [0ζ1] （or △∑, A and Z in group-theory notation） are calculated for four noble metals Cu, Ag, Au and Pt by combining the modified analytic embedded atom method （MAEAM） with the theory of lattice dynamics. A good agreement between calculations and measurements, especially for lower frequencies, shows that the MAEAM provides a reasonable description of lattice dynamics in noble metals.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
基金Project supported by the State Key Program of Basic Research of China （Grant No 2004CB619302） and the National Natural Science Foundation of China （Grant No 50271038）.
文摘In the harmonic approximation, the atomic force constants are derived and the phonon dispersion curves along four major symmetry directions [00ζ], [0ζζ], [ζζζ] and [0ζ1] （or △∑, A and Z in group-theory notation） are calculated for four noble metals Cu, Ag, Au and Pt by combining the modified analytic embedded atom method （MAEAM） with the theory of lattice dynamics. A good agreement between calculations and measurements, especially for lower frequencies, shows that the MAEAM provides a reasonable description of lattice dynamics in noble metals.
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.
