The Relationship Between Parameters In The Dislocation Equation And Phonon Spectrum

The quasi-continuum dislocation equation derived from the lattice dynamics includes the corrections of the discrete effect which are important for the core structure of dislocation. The quasi-continuum dislocation equations for all kinds of lattices possess universal form except for the physical parameters in them. In this paper, the purpose is to discuss the physical significance of the discrete effect corrections in the equation and confirm the relationship between physical parameters and the phonon velocity and lattice structure.Assuming that one atom only have interaction with its first and second nearest neighbors, force constants matrixes of Two-dimensional triangular lattice and Simple cubic lattice which satisfy the rigid body translation and rotation sum rule are presented; Otherwise, those of Face-centred cubic lattice are also presented when the first nearst interaction only considered. Based on the lattice theory of dislocation, the physical significance of the discrete effect corrections of crystal in the equation is discussed and the relationship between coefficients of the corrections and the wave velocity of decoupled crystal plane is pressented. It's found that the corrections of discrete effect corresponding to the second-order derivative term which is mainly resulted from the interaction between the surface atoms.Within the lattice dynamics theory, the decoupled crystal plane wave velocity in crystal which is related with the bulk wave velocity and the lattice structure is obtained by analyzing the connection between bulk wave velocity and atomic interacting force in crystal and considering only the short-range central interacting force among atoms. The purpose is to establish the connection between the parameters of the correction of discrete effect in the dislocation equation and the measurable physical quantity in experiment. The relationship is approximately available for the case of the modification of non-central interacting force among atoms is further considered. Finally, the reliability of the relationship is validated by various representative lattice structures.