Stress tensor dependence of the polarized Raman spectrum of tetragonal barium titanate

The stress tensor dependence of the polarized Raman spectrum of the barium titanate (BaTiO 3 ) tetragonal structure has been theoretically elucidated and the phonon deformation potential (PDP) constants of its A 1 (TO) and E (TO) vibrational modes measured by means of a spectroscopic analysis of single-crystalline samples under controlled stress fields. Two types of stress field were employed: (i) A uniaxial (compressive) stress field generated with loading along different crystallographic axes and (ii) a biaxial (tensile) stress field stored at the tip of a surface crack propagated across the a -plane of the crystal. This latter stress field enabled us unfolding the full set of PDP values for the E (TO) vibrational mode. However, the highly graded (multiaxial) stress field stored at the crack tip required both rationalizing the dependence of oblique phonons on crystal orientation and applying a spatial deconvolution routine based on the three-dimensional response of the Raman probe. According to a combination of experimental and computational procedures, we quantitatively uncoupled the effects of crystallographic orientation and spatial convolution from the locally collected Raman spectra. Uniaxial compression and biaxial tensile stress calibrations led to consistent PDP values, thus allowing the establishment of a working algorithm for stress analysis in the technologically important class of perovskitic material. Finally, as an application of the newly developed procedure, a tensor-resolved stress analysis was performed to evaluate the unknown (elastic) magnitude of the residual stress components and the extent of the plastic deformation zone generated around a Vickers indentation print in BaTiO 3 single crystal. The present findings open the way to tensor resolved Raman analysis of the complex strain fields stored in advanced ferroelectric devices.