Quantifying strain birefringence halos around inclusions in diamond

The pressure and temperature conditions of formation of natural diamond can be estimated by measuring the residual stress that an inclusion remains under within a diamond. Raman spectroscopy has been the most commonly used technique for determining this stress by utilising pressure-sensitive peak shifts in the Raman spectrum of both the inclusion and the diamond host. Here, we present a new approach to measure the residual stress using quantitative analysis of the birefringence induced in the diamond. As the analysis of stress-induced birefringence is very different from that of normal birefringence, an analytical model is developed that relates the spherical inclusion size, R _i, host diamond thickness, L, and measured value of birefringence at the edge of the inclusion, Updelta n(R_texti )_textav Updelta n(R_{text{i}} )_{text{av}} , to the peak value of birefringence that has been encountered; to first order Updelta n_textpk = (3/4)(L/R_texti )  Updelta n(R_texti )_textav Updelta n_{text{pk}} = (3/4)(L/R_{text{i}} ) , Updelta n(R_{text{i}} )_{text{av}} . From this birefringence, the remnant pressure (P _i) can be calculated using the photoelastic relationship Updelta n_textpk = - (3/4)n³ q_textiso P_texti Updelta n_{text{pk}} = - (3/4)n^{3} q_{text{iso}} P_{text{i}} , where q _iso is a piezo-optical coefficient, which can be assumed to be independent of crystallographic orientation, and n is the refractive index of the diamond. This model has been used in combination with quantitative birefringence analysis with a MetriPol system and compared to the results from both Raman point and 2D mapping analysis for a garnet inclusion in a diamond from the Udachnaya mine (Russia) and coesite inclusions in a diamond from the Finsch mine (South Africa). The birefringence model and analysis gave a remnant pressure of 0.53 ± 0.01 GPa for the garnet inclusion, from which a source pressure was calculated as 5.7 GPa at 1,175°C (temperature obtained from IR analysis of the diamond host). The Raman techniques could not be applied quantitatively to this sample to support the birefringence model; they were, however, applied to the largest coesite inclusion in the Finsch sample. The remnant pressure values obtained were 2.5 ± 0.1 GPa (birefringence), 2.5 ± 0.3 GPa (2D Raman map), and 2.5–2.6 GPa (Raman point analysis from all four inclusions). However, although the remnant pressures from the three methods were self-consistent, they led to anomalously low source pressure of 2.9 GPa at 1,150°C (temperature obtained from IR analysis) raising serious concerns about the use of the coesite-in-diamond geobarometer.