Vacuum Evaporation of Pure Metals
- PDF / 459,041 Bytes
- 7 Pages / 593.972 x 792 pts Page_size
- 83 Downloads / 245 Views
THE kinetics of materials’ evaporation in vacuum is important in many areas such as materials’ processing and materials’ application in vacuum and space systems. In metallurgical processes, the kinetics of materials’ evaporation is important when mass transfer occurs from a condensed phase to a gas phase. Developing basic knowledge of the evaporation kinetics of pure metals is crucially important. The distillation of metals and vacuum refining for eliminating the impurities are typical processes in which the application of low pressures is the key process. Studying the mass transport phenomena in such processes, where the evaporation is taking place from a multicomponent condensed phase, requires basic knowledge of the evaporation of the single component systems. For instance, in the vacuum refining of metals, useful information about the mass transfer coefficient of the volatile impurity in the gas phase can be determined from the gas velocity above the melt, which mainly consists of the solvent metal vapor, and is relatively close to the vapor velocity of the pure solvent metal. The vacuum removal of phosphorus (P) from liquid silicon (Si) is a typical case in which very low concentrations of P such as 10 ppmw are eliminated from Si to achieve the concentrations required for the fabrication of silicon solar cells, i.e., below 0.1 ppmw.[1] Considering the above points, the vacuum evaporation of pure elements is studied in this paper as follows.
JAFAR SAFARIAN, Researcher, and THORVALD A. ENGH, Professor, are with the Department of Materials Science and Engineering, Norwegian University of Science and Technology (NTNU), Alfred Getz Vei 2, 7491 Trondheim, Norway. Contact e-mail: [email protected] Manuscript submitted June 5, 2012. Article published online October 17, 2012 METALLURGICAL AND MATERIALS TRANSACTIONS A
II.
KINETIC THEORIES OF EVAPORATION
In a perfect vacuum condition, the maximum molar flux of substance Me from the condensed form to its gaseous form is expressed by the Hertz-Knudsen equation.[2] p n_ Max ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2pMRT
½1
where M is the molecular weight, R is the universal gas constant, and T is the absolute temperature at the evaporating surface. p is the standard vapor pressure of the substance Me, which is a function of the absolute temperature[3] log p ¼
A þ B log T þ CT þ D T
½2
The coefficients A, B, C, and D are constants. When perfect vacuum is not used, the net flux of Me from the condense phase to its vapor is expressed as p p n_ evap: ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2pMRT
½3
where p is the pressure above the condensed phase. Equation [3] is based on considering a certain distribution function of velocity for the gas particles (full range Maxwellian), where the particles do not interact with each other, but move freely between collisions.[4] Schrage[4] introduced a simple correction to take the continuum into account and argued that the Maxwellian due to the mass movement of the vapor must be shifted by the mean velocity of the gas. According to Schrage, Eq. [3] becomes
Data Loading...
