Hertz-Knudsen relation

In order to avoid surface contamination by the residual atmosphere of the spectrometer, it is necessary to work under UHV conditions (10 Pa). This is apparent from the Hertz-Knudsen relation ... 

This is the Hertz-Knudsen relation expressed in SI units. This relation can be made more accessible by expressing pressure in units of torr and merging all the conversion factors into a single constant, i.e. ... 

By solving the Hertz-Knudsen relation and assuming interaction with a Silicon surface for which the sticking coefficient is close to unity and the surface density is 1 X lO atoms/cm, one quickly realizes that a monolayer of Oxygen will form in 1 ns at atmospheric pressure and room temperature (298 K). This drops to 1 s at 10 Torr but really does not reach any kind of acceptable value for Static SIMS ( 1000 s) until into the 10" Torr pressure range. 

Figure 48.1 illustrates a typical Knudsen cell. The Knudsen cell provides a way to probe the vapor in equilibrium with the condensed sample of interest plus cell material. Under the low-pressure conditions used (<10 bar), the fugacities of real gases are equal to their partial pressure, and the behavior of the vapor phase is readily described by the kinetic theory of gases. There are several excellent texts on this subject [19,20]. The key relationship derived from kinetic theory to this technique is the Hertz-Knudsen-Langmuir (HKL) expression, which relates the flux of a molecular species striking a surface, Ja (mol area s ), to its equilibrium vapor pressure in a closed container ... 

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