Since the original observation that the surfaces of materials undergo radiation damage in the electron microscope similar to that observed by more conventional surface science techniques there has been substantial interest in understanding these phenomena in more detail; for a review see. For instance, surface damage in a microscope mimics damage in the space environment due to the solar wind and electron beam lithographic operations.However, purely qualitative experiments that have been done in the past are inadequate. In addition, many experiments performed in conventional microscopes may be inaccurate. What is needed is careful quantitative analysis including comparisons of the behavior in UHV versus that in a conventional microscope. In this paper we will present results of quantitative analysis which clearly demonstrate that the phenomena of importance are diffusion controlled; more detailed presentations of the data have been published elsewhere.As an illustration of the results, Figure 1 shows a plot of the shrinkage of a single, roughly spherical particle of WO3 versus time (dose) driven by oxygen desorption from the surface.