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The "x-ray tensile test" is the combination of the standard uniaxial tensile test with x-ray diffraction techniques. In this test, in addition to the mechanical stress-strain values usually obtained from a tensile test, one measures the x-ray strain and stress in the diffracting regions of the sample. In multilayer thin films or in multiphase materials, x-ray diffraction enables the determination of strains and stresses in the individual layers or phases. Correlation of the x-ray data with the mechanical stress-strain values may be used to analyze strain and load partitioning within the specimen. In this paper an extended theoretical analysis of this technique and its application to evaporated Cu films on Ni substrates is presented.

I. INTRODUCTION The increased usage of thin films in advanced technology products has necessitated the development of accurate mechanical testing.1"4 For such structures, the parameters of interest are not the mechanical properties of the film alone, but rather, the mechanical response of the film-substrate composite to the applied load. This "composite response" contains contributions from the "stand-alone" properties of the film and the substrate, the compatibility conditions imposed by the presence of the interface between the film and the substrate, and the residual stresses within the film and the substrate. Residual stresses exist in free bodies that have no tractions (forces or moments) applied on their boundaries.5 In thin-film structures, such stresses may be created during plating or evaporation. Various factors, such as thermal mismatch between the film(s) and the substrate, the incorporation of defects into the film during the deposition, phase transformations, etc., can cause residual stresses. Residual stresses in thin films can be quite large and exceed the yield point of bulk materials of the same composition. The stress distribution in the composite is also constrained by the equations of equilibrium, which must be obeyed within the composite volume.5 Thus, the strain/stress values within the individual layers can be quite different, and the determination of the strain/stress values in the individual layers is desirable in the analysis of the overall mechanical response. Diffraction-based techniques, such as x-ray strain/ stress analysis, are particularly suitable for the measurement of strain/stress in such systems. The measurement volume can be completely confined to a given individual layer through the selection of an appropriate Bragg reflection.6"17 Traditionally, x-ray techniques have been used mainly for the determination of residual stresses.18 ^Presently at the Department of Mining and Metallurgy, Tehran Polytechnic University, Tehran, Iran. 764 http://journals.cambridge.org

J. Mater. Res., Vol. 8, No. 4, Apr 1993 Downloaded: 24 Mar 2015

In recent years, these techniques have been extended to the determination of mechanical properties of the individual layers of thin film-substrate composites. The basic principle of mechanical response analysis in thin-film