Raman scattering yields cubic crystal grain orientation

Abstract

The paper proposes a fully optical method for determination of a cubic crystal grain orientation in a sample inspected by a Raman microscope. The method is based on a universal and strong polarisation anisotropy of the Raman scattering by doubly degenerate optic phonon modes and it only requires a standard Raman microscope equipped with a polarisation analysis. Explicit formulas for the orientation of the crystal grain are derived. The feasibility of the approach is demonstrated by comparing grain orientations in a polycrystalline cubic lacunar spinel GaV₄S₈ determined independently using electron backscatter diffraction and Raman scattering methods.

Figure 1

Typical parallel-polarised Raman spectrum detected from an arbitrarily oriented grain.

Figure 2

Polar plot of the polarisation-dependent factor $\mathrm{\Lambda }$ of Raman scattering by (a) A₁ and (b) E-symmetry modes in a cubic crystal calculated using equations (1, 2, 4 and 5) for a = b = 1. B1 − B3 stand for the three perpendicular directions parallel to the fourfold symmetry axes of the crystal. Projections along the B3 axis are shown in (c and d) panels, respectively.

Figure 3

Grain morphology of the investigated GaV₄S₈ ceramics. (a) Scanning electron microscope image of an area of interest with sample coordinate system as an inset; (b) Inverse pole figure map from EBSD analysis of the area in (a); (c) positions of four grains chosen for detailed Raman measurements ($A:\{1\overline{15}1\}\langle \overline{5}\overline{1}\overline{10}\rangle$, $B:\{\overline{7}08\}\langle 8\overline{11}7\rangle$, $C:\{7\overline{3}12\}\langle 041\rangle$, $D:\{\overline{17}14\overline{10}\}\langle 89\overline{1}\rangle$), indicated projections of elementary cubic cells clarify their crystallographic orientation; (d) unit triangle with the color code of the inverse pole figure map; (e) surface normals of the chosen grains as determined from EBSD.

Figure 4

Parallel-polarised Raman scattering intensity ratios detected from the grain A (circles), B (squares) and C (triangles with vertex down) and D (triangles with vertex up) at selected frequencies as a function of the angle $\varphi$ between the polariser and the reference direction A1 on the sample surface (indicated in Fig. 3). The intensity ratios are obtained from the raw measured data after the flat background subtraction as the integrated intensity at 330 ± 5 cm⁻¹, divided by the integrated intensity at 277 ± 5 cm⁻¹, I₃₃₀/I₂₇₇.