Composite wall materials

Practical ion chambers do not consist of graphite alone, since the collector electrode must be held in place and insulated by another material. As seen in Fig. 2 the insulator in the NRC chamber is a ring of polystyrene, and in the BIPM chamber there are holders made of Duralumin (aluminium alloy). To take this into account one introduces a correction factor $K_{\rm comp}$ into Eq. ()s another of the $K$ factors[25]. The correction is not required for the investigation of the agreement with Spencer-Attix cavity theory, but for obtaining the dose or air kerma from a measurement, this correction, in principle, should be applied although usually it does not appear to be considered[8,9,42].

Using Monte Carlo simulations the value of $K_{\rm comp}$ is calculated as the ratio of the calculated dose to the air (corrected for attenuation and scatter) for a model with only graphite walls and end caps to the calculated dose for a model with graphite walls and a polystyrene insulator (for the NRC chamber) or a model with holders of Duralumin (for the BIPM chamber).

$$K_{\rm comp,MC}= {{\left( D~K_{\rm wall}\right) _{\rm graphi... ..._{\rm wall}\right) _{\rm polystyrene ~ or ~ duralumin \it }}}$$ (5)

The Monte Carlo calculated $K_{\rm comp}$ values for the NRC chamber as a function of photon energy are shown in Fig. 13.

To estimate the $K_{\rm comp}$ value through Monte Carlo calculations for the BIPM chamber the two holders for the collector plate are modelled as two rings, one on the side of the collector and one behind the collector with outer radius equal to that of the collector. Care is taken to have the same mass and the same area of Duralumin exposed to the air as in the real BIPM ion chamber. Modelling the holders correctly is not possible with the user-code CAVRZnrc, since it models cylindrical geometries only.

An analytical expression of the effect of composite walls is generally used for calculating the influence of a buildup cap made of a different material than the chamber wall [25]:

$$K_{\rm comp,ana}= { 1 \over { {\left({\bar{L}} \over {\rho} ... ...n}} \over {\rho} \right)^{\rm cap} _{\rm air}}}\right]}} ~ ~ ,$$ (6)

where $\alpha$ is the fraction of the ionization in the cavity due to electrons originating in the wall material and $(1-\alpha)$ is the fraction from the buildup cap. In the present case, we make the rough approximation that this expression applies for the effect of different materials near the cavity, e.g. polystyrene or Duralumin. For the analytical calculation of $K_{\rm comp}$, $\alpha$ must be estimated. For the NRC chamber the fraction of the dose to the air in the cavity originating from the graphite is calculated using the user-code DOSRZnrc. For the BIPM chamber the $\alpha$ value is estimated from the surface area of Duralumin compared to that of graphite. This latter value is only a very crude estimate! A worst case scenario for the BIPM chamber is obtained by fitting the mass of Duralumin into the two rings and covering the actual area of graphite in the Monte Carlo model. This means that much more Duralumin surface is exposed to the air and $K_{\rm comp,MC}$ is $0.9970 \pm 0.0003$.

Table I shows the results of calculations of $K_{\rm comp}$ from Equations (5) and (6) for the NRC chamber and for the BIPM chamber with polystyrene and Duralumin, respectively, as part of the chamber material. The results of calculations using the simple analytical expression agree well with the Monte Carlo calculated values, and $K_{\rm comp}$ indicates either a decrease ( $K_{\rm comp}> 1$) or an increase ( $K_{\rm comp}< 1$) in the dose to the cavity compared to the dose in a homogeneous chamber, depending on what material is used in addition to the graphite. The values calculated are surprisingly large given that standards laboratories have not traditionally considered this correction factor of 0.4% for the NRC chamber and of -0.07% for the BIPM chamber.