A calculation of the temperature distribution in electron-microscope specimens

A general equation is derived which describes the circularly symmetrical flow of heat in a multi-layered specimen of variable thickness irradiated with a non-uniform electron beam. As an example the general equation is integrated numerically to provide a solution describing the effect that an uneven layer of surface contamination has on the temperature distribution in a platelet specimen. The results show that, in general, the temperature increases as the contamination thickens, although in some cases the increase is preceded initially by a reduction in the maximum rise in temperature. In the latter cases there is also a significant change in the shape of the temperature distribution within the specimen. Sometimes an almost linear increase in maximum temperature is obtained when contamination is deposited on metallic specimens; this rise is predicted approximately by a rough analytical solution to the appropriate differential equation.