Based on geometric model of metal fiber sintering nodes, with Caputo fractional differential equations, a time fractional surface diffusion model is established. Numerical solution by finite difference method is made. Numerical simulation of metal fiber sintering process is realized. Numerical simulation of sintering process and variation of neck length as fractional order varies from 0 to 1 are obtained. As the order is fixed at 0.9, sintering process at initial included angles of 0°, 30°, 60° and 90° are simulated. It shows that as the order is equal to 1 the result is consistent with integer order diffusion model. Neck radius with integer order and fractional order grows rapidly in initial stage of sintering. With progress of sintering, fractional simulation of sintering neck length appears local fluctuation, and finally grows at an increase rate greater than the integer order. As the order is fixed, the smaller the initial angle, the greater the rate of growth. The fractional order surface diffusion model describes well the complex change of sintering node during fiber sintering process than the integer order surface diffusion model.

Structure and elastic property of ZrV₂ under high pressure are investigated with first-principles calculations based on plane-wave pseudo-potetial in the framework of density functional theory within generalized gradient approximation (GGA). With a quasi-harmonic Debye model, in which phonon effects are considered, we calculated thermodynamic properties of ZrV₂ in a pressure range from 0 to 20 GPa and temperature range from 0 to 1200 K. Pressure dependence of elastic constants, bulk modulus and heat capacity, and thermal expansion with pressure and temperature are presented. It shows that calculated lattice parameters of ZrV₂ are in good agreement with existing experimental data and other theoretical results. Elastic constants, Debye temperature and bulk modulus increases with increasing pressure. Relative volume, heat capacity decreases with increasing pressure. Temperature effect is weaker than pressure effect in thermal expansion of ZrV₂ under high pressures.