Clausing factors

An optimized relationship is obtained between the beU jar, 60° swing-leaf valve, LN trap, baffle for the oil, and the plane of action for the diffusion pump (DP) top jet. The valve open area equals 0.38 of the cross-sectional area of the inside diameter of the furnace. The volumetric speed factor for water vapor is thus 0.38 x 0.9 crr 0.34, where 0.9 is the Clausing factor. 

The equilibrium constants can be approximated by ratios of ion currents in some instances otherwise, the currents are converted to partial pressures by comparison with the evaporation of known amounts of a standard material. Various geometric corrections (K) such as the solid angle subtended by the sample at the orifice, the Clausing factor for orifice geometry, molecular cross-section (o-), which control ionization efficiency, and detector efficiency are included in the general relationship... 

Example A tube with a length of 1 m and an internal diameter of 5 cm has an (uncorrected) conductance C of around 17 l/s in the molecular flow region, as determined using the appropriate connecting lines between the T scale and the d scale. The conductance C found In this manner must be multiplied by the clausing factor y = 0.963 (intersection of connecting line with the y scale) to obtain the true conductance in the molecular flow region ... 

M is the molecular weight and, qa, is the area of the effusion orifice corrected by the Clausing factor, a, [87]. An example of the application of this method is given in Ref. 88. 

Clausing factor considering the orifice shape in the effusion cell Decomposition degree... 

TABLE 48.1 Clausing Factors for Different Orifices from Monte Carlo Modeling... 

Length/ Radius (Ur) Clausing Factor Average Number of Wall Collisions for Returns Average Number of Wall Collisions for Escapes Fraction of Escapes with no Wall Collisions... 

A large Clausing factor for vapor transport from the sample surface to the orifice. 

A low Clausing factor for the cell orifice (as discussed in the previous section). 

Here Pe is the equilibrium pressure inside the Knudsen cell,pm is the measured vapor pressure, Wc is the Clausing factor for the orifice, C is the surface area of the orifice, D is the surface area of the bottom of the cell cavity, Ov is the vaporization coefficient, and Wd is the Clausing factor for the cell itself. A number of assumptions have been made in this derivation, most notably that the condensation coefficient equals the vaporization coefficient. However, the important points about the design of a Knudsen cell are captured in the basic Whitman-Motzfeld equation. Our cells have a cavity with a diameter of 10 mm and height of 7.6 mm, and a typical orifice has a diameter of 1.5 mm and a length of 4.0 mm. If tabulated Clausing factors [27] and a vaporization coefficient of 1 are assumed, the ratio Pe. Pm has a value of 1.005. 

Our goal in this section is to describe the molecular beam mathematically. We need to understand how the intensity varies a function of the pressure in the cell, the Clausing factor of the cell orifice, the distance from the cell orifice, the area of the cell orifice, and the placement of defining apertures in the molecular beam. 

Here Wc(0 ) is the Clausing factor discussed earlier in Equation 48.7, but it is for the limited angle from the normal 0 defined by the field and source apertures (Equation 48.13). Note also that the number distribution is not the same everywhere in the molecular beam. This is evident if a portion of the beam distribution is sampled as shown in Figure 48.3C. If the center of the collimating apertures is collinear with the center of the distribution, then there is a symmetric number density about this center ... 

Wc(0 ) Clausing factor for limited angle from normal defined by the field and source apertures... 

---