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Describes a method for chemical analysis of ceramic coatings by means of electron probe microanalysis (EPMA) using a scanning electron microscope (SEM) or an electron-probe microanalyser. The methods described are limited to the examination of single layer coatings when the analysis is carried out normal to the sample surface, but graded and multilayer coatings may also be analysed in cross-section if the thickness of the individual layers or gradations are greater than the maximum width of the volume of material within which characteristic or fluorescent X-rays are generated.