X-Ray Diffraction Analysis of Residual Stress in Thin Polycrystalline Anatase Films and Elastic Anisotropy of Anatase
Abstract
The importance of residual stress in anatase thin films for their photo-induced hydrophilicity was proved recently. Detailed X-ray diffraction (XRD) studies of residual stresses in titanium dioxide films are presented here.
Measurements including multiple hkl reflections on several series of these films revealed the presence of tensile stresses in the films that were obtained by crystallization from amorphous state. Significant anisotropy of the strain was also found and compared with that of anatase, resulting from its theoretically calculated single-crystal elastic constants.
The XRD data support the experimental evidence of the hypothesis that the [00l] axis is the elastically soft anatase direction, whereas the directions in the [h00] x [hk0] plane are elastically stiff. This is in agreement with the anisotropy predicted by single-crystal elastic constants that are obtained from ab-initio calculations.
Residual stress analysis for materials with tetragonal symmetry is described and the theory is used to analyze the data. The anisotropy is very different from that for the rutile phase, and the experimental results agree well with the values calculated for anatase.
A simplified method of XRD residual stress analysis in thin anatase films by total pattern fitting (TPF) is also presented. Tensile stresses are formed during the crystallization process and increase rapidly with reduced film thickness.
They inhibit crystallization, which is then very slow in the thinnest films.