Resolving stress tensor components in space from polarized Raman spectra: polycrystalline alumina

Abstract

A method of Raman spectroscopic analysis has been proposed for evaluating tensorial stress fields stored in alumina polycrystals with a corundum structure (α-Al₂O₃). Raman selection rules for all the vibrational modes of the structure were expanded into explicit functions of both 3 Euler angles in space and 4 Raman tensor elements (RTE) of corundum. A theoretical treatment was then worked out according to the phonon deformation potential (PDP) formalism, which explicitly expressed the changes in force constants under stress in matricial form. Close-form solutions could be obtained for the matrix eigenvalues as a function of 9 unknown variables, namely 6 independent stress tensor components and 3 Euler angles in space, the latter parameters being representatives of local crystal orientation. Successively, two separate sets of Raman calibration experiments were performed for the determination of both RTE and PDP constants of the corundum structure of alumina. Calibration experiments provided a quantitative frame to the newly developed Raman formalism. Polarized Raman spectra were systematically recorded in both single-crystalline and polycrystalline samples, with both A_1g and E_g vibrational bands being characterized. Regarding polycrystalline samples, a validation of the proposed Raman method could be done through a comparison between Raman and fluorescence data collected at the same locations across an alumina/metal interface embedded in a steeply graded residual stress field.