Monte Carlo study of Knudsen layers in evaporation from elemental and binary media

Selective Vacuum Evaporation by the Control of the Chemistry of Gas Phase in Vacuum Refining of Si

The evaporation of P from liquid Si under vacuum and reduced pressures of H₂, He, and Ar was studied to evaluate the feasibility of effective P removal with insignificant Si loss. It was found that the introduction of Ar and He inert gases at low pressures reduces the rate of P removal, and their pressure decrease will increase the process rate. Moreover, the kinetics of P removal was higher in He than in Ar, with simultaneous lower Si loss. Under reduced pressures of H₂ gas, however, the P removal rate was higher than that under vacuum conditions with the lowest Si loss. Quantum chemistry and dynamics simulations were applied, and the results indicated that P can maintain its momentum for longer distances in H₂ once it is evaporated from the melt surface and then can travel far away from the surface, while Si atoms lose their momentum in closer distances, yielding less net Si flux to the gas phase. Moreover, this distance is significantly increased with decreasing pressure for H₂, He, and Ar gases; however, it is the largest for H₂ and the lowest for Ar for a given pressure, while the temperature effect is insignificant. The rate of P evaporation was accelerated by applying an additional vacuum tube close to the melt surface for taking out the hot gas particles before they lose their temperature and velocity. It was shown that this technique contributes to the rate of process by preventing condensing gas stream back to the melt surface.

Transport phenomena in the Knudsen layer near an evaporating surface

Using the combination of the kinetic theory of gases (KTG), Boltzmann transport equation (BTE), and molecular dynamics (MD) simulations, we study the transport phenomena in the Knudsen layer near a planar evaporating surface. The MD simulation is first used to validate the assumption regarding the anisotropic velocity distribution of vapor molecules in the Knudsen layer. Based on this assumption, we use the KTG to formulate the temperature and density of vapor at the evaporating surface as a function of the evaporation rate and the mass accommodation coefficient (MAC), and we use these vapor properties as the boundary conditions to find the solution to the BTE for the anisotropic vapor flow in the Knudsen layer. From the study of the evaporation into a vacuum, we show the ratio of the macroscopic speed of vapor to the most probable thermal speed of vapor molecules in the flow direction will always reach the maximum value of sqrt[1.5] at the vacuum boundary. The BTE solutions predict that the maximum evaporation flux from a liquid surface at a given temperature depends on both the MAC and the distance between the evaporating surface and the vacuum boundary. From the study of the evaporation and condensation between two parallel plates, we show the BTE solutions give good predictions of transport phenomena in both the anisotropic vapor flow within the Knudsen layer and the isotropic flow out of the Knudsen layer. All the predictions from the BTE are verified by the MD simulation results.