Errors in vacuum microbalances caused by unequal thermal expansion of the balance arms

Abstract

A detailed analysis is made of the magnitude of the error that arises from temperature inhomogeneities along the balance case when a microbalance operates at low pressures. A general equation is derived which enables the influence of the nature of the constructional material and the geometrical dimensions of the balance and case to be assessed. The validity of this equation when applied to a particular balance material, Dural, for a specified type of temperature inhomogeneity, has been tested experimentally. The calculations reveal that, contrary to accepted practice in vacuum microbalance techniques, the use of a material with very low coefficient of expansion (such as silica) does not secure the minimum error arising from temperature inhomogeneities. It emerges that two other properties, the thermal conductivity and emissivity, are equally important; and there is much to be said in favour of choosing certain metals or alloys (such as Dural) as constructional materials for the balance beam. The error discussed here is likely to be most serious when the ambient pressure is less than about 10 μtorr, and, for most materials, if a measuring accuracy in the region of 1 μg is required, temperature inhomogeneities along the balance case of up to 1 degC may be tolerated.