A simple and effective simulation for electrical conductivity of warm dense titanium

Abstract

A linear mixture rule has been used to calculate the electrical conductivity of warm dense titanium plasmas in the density and temperature ranges of 10-510 gcm-3 and 1043104 K, in which the interactions among electrons, atoms, and ions are considered systemically. In the first place, the coupling and degeneracy parameters of titanium plasma are shown as a function of density and temperature in the warm dense range. The warm dense titanium plasmas span from weakly coupled, nondegenerate region to strongly coupled, degenerate domain in the whole density and temperature regime. The titanium plasma becomes strongly coupled plasma at higher than 0.22 gcm-3 and almost in the whole temperature range where the coupling parameter ii 1. In particular, the Coulomb interactions become stronger at higher than 0.56 gcm-3 where 10 ii 216. At the same time, the titanium plasma is in the degenerate regime at higher than 0.35 gcm-3 where the degeneracy parameter 1, and is in the nondegenerate or partial degenerate regime at lower than 0.35 gcm-3 where 1. The influence of temperature on the coupling and degeneracy parameters is less than that of the density, and the plasma composition is calculated by the nonideal Saha equation felicitously. Thus the ionization degree decreases with increasing density at lower density, which is due to the thermal ionization in that regime where the free electrons have sufficiently high thermal energy. Meanwhile, the ionization degree increases with the increase of density at higher than 0.1 gcm-3, in which the pressure ionization takes place in the region where the electrons have sufficiently high density and the collisions increase rapidly. There is a minimum for the ionization degree at about 0.1 gcm-3, while the maximum ionization degree reaches 4 at 10 gcm-3. In the whole temperature regime, the titanium plasma is mostly in the partial plasma domain at lower than 1 gcm-3, and becomes completely ionized at higher than 1 gcm-3. The calculated conductivity is in reasonable agreement with the experimental data. At a fixed temperature, there is a minimum in each of the ionization curves at lower than 3104 K. And the position of the minimum is shifted towards decreasing density with increasing temperature. The conductivity monotonously increases as the density increases at a temprature of 3104 K. At a constant density, the conductivity increases with increasing temperature for lower than 0.56 gcm-3, while it decreases with increasing temperature for higher than 0.56 gcm-3. This behavior is connected with the nonmetal to metal transition in a dense plasma regime. So the nonmetal to metal transition in dense titanium plasma occurs at about 0.56 gcm-3 and its corresponding electrical conductivity is 1.5105 -1m-1. Finally, the contour of electrical conductivity of titanium plasma is shown as a function of density and temperature in the whole range. Its electrical conductivity spans a range from 103 to 106 -1m-1. It can be seen that the titanium plasma gradually approaches the semiconducting regime as temperature increases. When the order of magnitude of the electrical conductivity reaches 105 -1m-1, the plasma almost becomes conducting fluid in the higher density range. This also demonstrates that a nonmetal-metal transition has taken place in the warm dense titanium plasma.