An integrated methodology to estimate the effective elastic parameters of amorphous TiO2 nanostructured films, combining SEM images, finite element simulations and homogenization techniques

Abstract

In this paper, a novel experimental-numerical methodology is outlined, which aims at estimating the homogenized elastic properties of thin nanostructured coatings, utilized in a variety of industrial contexts. Focus is posed on amorphous titanium dioxide (TiO2) films, a few micrometer thick, produced through Pulsed Laser Deposition in the form of columnar elements coating a Silicon flat substrate. The proposed inverse strategy rests on digital images acquired by a Scanning Electron Microscope on coated samples, with a nanometer resolution, and consists of the following steps: (i) within a representative volume element, cavities existing in between the nanostructured columns are identified in the raster images by an automatic edge detection procedure; (ii) information concerning the location of the pore borders are vectorized and passed through a Python script to a commercial finite element code; (iii) the homogenized stiffness matrix is reconstructed on the basis of finite element simulations of such a representative volume subjected to elementary loading conditions, each corresponding to a single component of the effective strain tensor. Diverse mechanical models with periodic boundary conditions have been comparatively assessed, fully three dimensional or under plane conditions, assuming for the TiO2 columns in an amorphous state (as corroborated by Raman spectroscopy) an isotropic behaviour, with a priori known Young’s modulus and Poisson’s ratio. The homogenized elastic moduli and coefficients of TiO2 thin films, at varying the deposition process parameter, are estimated by the novel procedure, resulting in an orthotropic, transversely-isotropic behaviour.