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# Elastic constants and stress-strain in thin films: application in fiber-textured gold film by X-Ray diffraction

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## Abstract

The purpose of the present article is to make a model using analytical equations, based on elasticity theory of continuous media for small deformations, with the aim of completely characterizing the material in their mechanical properties as well as the principal stresses-strains of thin films. The approach differs from the standard literature which usually brings crystal symmetries or is directly concerned with crystalline materials. It is entirely possible to define and to analyze anisotropy in elastic media from first principles in thin films. Therefore, the constitutive relation between strain and stress will be considered orthotropic, obeying the generalized Hooke's law. A new equation for the stress of the film-substrate system is proposed based on Newton's laws and energy conservation. As an application, it use the technique and data developed by Faurie et al (2005) in fiber-textured gold film deposited onto Kapton substrate by combining synchrotron X-Ray diffraction in situ tensile testing. As the gold thin film and substrate are considered transversely isotropic, therefore, is firstly required a texture analysis with the purpose of determining the possible Euler angles ($\phi$) and ($\psi$) for each crystallographic direction that can be used in the model equations. With the data, it is possible to make graphics, $\varepsilon$ (strain) X F, for every force applied to the sample. Comparing the experimental graphs with the theoretical equations it was possible obtained their mechanical properties and the principal stresses-strains of the anisotropic gold thin film. The results are compared with the results of Faurie et al (2005).

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