on account of the temperature t and or stresses u03c3 the precipitations 22 change in such a way that the positive influence on the mechanical properties is at least considerably reduced this occurs through an increase in the size of the precipitations 25 fig4 right cracks may likewise be present in the substrate 4 and or in the layers 7 10 increasing the porosity since there are no direct unique parameters for the microstructure cracks pores precipitations etc the microstructure is integrally determined indirectly by means of one or more material parameters which are influenced by cracks pores and precipitations etc the measurements are for example non destructive measurements fig5 shows an example of a measurement arrangement for determining a material parameter of the substrate 4 and or of the layer 7 10 in this case electrodes 28 are applied at suitable locations of the substrate 4 or the layer 7 10 the electrical capacitance c f can be determined by means of a measurement appliance 31 the capacitance measurement is most suitable if the substrate 4 or the layer 7 10 consists of ceramic i e has a high dielectric constant u03b5 and a reduction in the porosity is expected the material parameters of the substrate 4 can be measured if the layers on top have been removed fig6 but also if the layers 7 on top are still present fig7 as an.