High-rate Knudsen cell

Evaluation of F() and r(i). In this section, the distribution of the incident flux is solved for two technologically important processes electron beam evaporation and evaporation from a high-rate Knudsen cell. 

The measurement of partial pressures over a liquid or solid mixture of two metals is not as simple. Mostly, it is restricted to higher temperatures or even to the molten phase. The direct measurement can be done, for example, in high or ultra high vacuum, using a Knudsen cell and a mass spectrometer for selective pressure determination. Dynamic measurements were developed, e.g., transportation methods. A steady stream of a reactive gas is passed over the sample transporting the reactive component to a cooled region of the apparatus. From the measured mass of the transported metal and the flow rate the vapor pressure can be calculated. Kubaschewski et alP have given a detailed description of the experimental possibilities. 

Knudsen effusion cells are used to determine vapor pressures of high-temperature materials. For example, a Knudsen cell is filled with tungsten and heated to 4500 K in a vacuum. Measurements show that the cell loses mass— assumed to be W vapor—at the rate of 2.113 grams per hour out of a hole that is 1.00 mm in area. Calculate the vapor pressure of W at 4500 K. 

A much better approach to this quantity is possible if special Knudsen cells are used the cover of these has an orifice (10-100 pm) whose size is comparable with the mean free path of a gas molecule. When the system is maintained under high vacuum (p < 0 mm Hg) and constant 7 , the release of the volatiles occurs at a constant rate and the relevant heat flux attains a constant level. Thus both DSC and DTG traces are horizontal straight lines the DSC/DTG ratio gives therefore the vaporization enthalpy at any moment of the weight-loss process [117] ... 

Most studies have assumed equation (3) to apply, so that equation (1) takes the form of Fick s law, with the composite (effective) diffusion taking account of both bulk and Knudsen diffusion. For the stealy state operation of the Wicke-Kallenbach cell, this can often be a reasonable assumption. Smith et al (18) have also used this description of the transport processes to analyze the situation when a pulse of the trace component is applied at z=0 and the concentration is monitored at z=L. For sufficiently high flow rates of the carrier gas, the first moment of the response curve to a pulse input is ... 

Gibson and Haire (1988a,b) decomposed several lanthanide and actinide tetrafluor-ides thermally in a Knudsen effusion cell, carried out (1992) high-temperature fluor-inations, and used mass spectrometry to identify the gaseous decomposition products (Fj or MFj) and the rate of change of pressure of these products with temperature. They showed that stability trends in the tetrafluorides differ slightly from those in the dioxides. These trends are discussed in sections 2.4.4 and 4.4.1. Similar studies have been carried out with trichlorides (Sapegin et al. 1984), tribromides, and triiodides but are not discussed further in this chapter. 

At the catalyst-electrolyte surface we have gas-phase diffusion, and there can also be additional surface diffusion. In surface diffusion, gas molecules physically or chemically absorb onto a solid surface. If it is physical absorption, the species are highly mobUe. If it is chemisorption and the molecule is more strongly bonded to the specific site, species are not directly mobile but can move via a hopping mechanism. Surface diffusion rates can be measured by direct measurement of the flux of a nonreacting gas across the material surface. The difference between the measured diffusion and predicted Knudsen diffusion is calculated to be the surface diffusion component. Values of the surface diffusion coefficient (Ds) are 10 cm /s in solids and liquids, but these vary widely since surface interaction is involved. Also, Ds is a strong function of temperature and surface concentration. Surface diffusion adds to the overall diffusion but is typically less than one-half of the Knudsen component and so has been mostly neglected in fuel cell analysis. 

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