Volatilization kinetics in vacuum metallurgy

During metal processing, the melting conducted under vacuum or at low pressures leads to volatile metal losses. It is the case in the metallurgical processing of the nickel-based, titanium-based or zirconium-based alloys where the evaporation losses make it difficult to control the alloy chemical composition. A theoretical approach has been carried out involving both an hydrodynamic description of the liquid phase and a kinetic description of the gas phase. In the liquid phase, the coupled transport equations are solved by using the finite volume method where the turbulence mechanism is described by a k-epsilon model. In the gas phase, the vapour transport is modelled by the Boltzmann equation which is solved using a Monte Carlo method : the velocity distribution function of the vapour is approximated by a set of particles, each having a specific velocity and position. For each time step, the particle evolution is split in two steps, a free molecular motion and a random collision step. At the liquid metal and metallic vapour interface, the volatilization and recondensation fluxes link the two calculations. The models calculate the behaviours of the liquid metal and the vapour phase. The recondensation coefficients, which represent the fraction of evaporated molecules which return to the surface of the liquid, are also given by the simulation. Simulation results are given for the electron beam melting and refining of a reactive metal under vacuum, a titanium alloy (Ti-6 wt % Al) in particular, where the control of the chemical composition remains a major difficulty. For standard operating conditions, the recondensation coefficients are close to zero. The small recondensation flux values corroborate the low calculated partial pressures above the liquid pool and the expansion of the vapour towards the chamber walls. The deviation from Langmuir's law due to recondensation is thus negligible in this case. The numerical tool has also been used so as to study the influence of the volatilization rate on the recondensation coefficients. The recondensation fluxes increase with the thermal power, and therefore the liquid metal superheat. The aluminium recondensation coefficient reaches 20 % in the case of intense evaporation (which is the case of PVD for instance).