Measurement of in-plane elastic constants of crystalline solid films by X-ray diffraction coupled with four-point bending

A non-destructive method for measuring elastic constants of solid films using X-ray diffraction technique is explored in this study. To measure both in-plane Youngʹs modulus and Poissonʹs ratio of the crystalline solid films, a four-point bending technique is incorporated in the X-ray diffraction measurement. Applied stress of the four-point bend composite beam of film on substrate is analyzed. The Youngʹs modulus and Poissonʹs ratio can be expressed as the changes in the slope and intercept of the d–sin2 ψ curve respectively at the maximum deflection of the beam. Poissonʹs ratio may be obtained without knowing the material properties and geometries of both the substrate and the film while only the elastic modulus of the substrate and thickness of both substrate and film are required in determining the Youngʹs modulus of the film. The advantage of the present approach is that neither complicated nor expensive loading facilities are necessary in the evaluation process.