Shock induced melting of sapphire

Abstract

The method for calculation the melting curves of crystalline bodies based on the Debye model of heat capacity and the Lindemann melting rule is proposed. Hugoniot shock adiabate, determined in dynamic experiments and thermophysical characteristics of the substance under normal conditions are used as input data. Mathematically, the calculation of the melting curveis reduced to the Cauchy problem for a system of ordinary differential equations. This system is solved numerically by the Runge-Kutta method. Using the proposed method, the melting curves of copper, silver, gold, and sapphire at high pressures are calculated. The results obtained for copper, silver and gold were compared with available calculated and experimental data to validate the method. Experiments on shock compression of transparent sapphire sampleswere performed, using a Mach-type cumulative explosive generators. Investigated pressure range (280-1350 GPa) covered a region of shock-induced melting. The temperature of shock front was registered by fast optical pyrometer together with shock velocity. Particle velocity andpressure were obtained by impedance matching technique. Satisfactory agreement of calculatedand experimental data on temperature of melting behind the shock wave front in sapphire was obtained.