Multiple low angles of incidence x-ray-diffraction method for nondestructively determining the depth-dependent fraction of a phase in the surface layer

Abstract

An x-ray-diffraction technique for nondestructively determining the depth-dependent fraction of a phase in the surface layer of a polycrystalline solid is presented using the data at low angles of incidence above the critical angle for the total reflection of x rays. The fraction, which is expressed as a polynomial in depth, is given by solving the equation of the kinematic diffracted intensity under the ratios of diffracted intensities from the phase to the bulk measured with multiple angles of incidence. The method utilizes the fact that at a lower angle of incidence the diffracted intensity from a deep layer attenuates more steeply and also the degree of the attenuation largely varies depending upon the angle of incidence. An application of the method to ground plates of yttria-doped tetragonal zirconia polycrystals revealed that the fraction of monoclinic phase induced by the machining was maximum (∼0.2) near the surface and decreased gradually in the deeper layer up to a few microns.