The diamond C13/12C isotope Raman pressure sensor system for high-temperature/pressure diamond-anvil cells with reactive samples

Abstract

By using a thin ${}^{13}\mathrm{C}$ diamond chip together with a ${}^{12}\mathrm{C}$ diamond chip as sensors, the diamond Raman spectra provide the means to measure pressure precisely (±0.3 GPa) at any temperature (10–1200 K) and simultaneous hydrostatic (or quasihydrostatic) pressure (0–25 GPa) for any sample compatible with an externally heated diamond-anvil cell. Minimum interference between the Raman spectrum from the diamond anvils and those of the pressure sensors is obtained by measuring pressures with the Raman signal from the ${}^{13}\mathrm{C}$ diamond chip up to 13 GPa, and that from the ${}^{12}\mathrm{C}$ chip above 10 GPa. The best crystallographic orientation of the diamond anvils is with the [100] direction along the direction of applied force, in order to further minimize the interference. At 298 K, the pressure dependence of the ${}^{13}\mathrm{C}$ diamond first-order Raman line is given by ${\mathrm{\nu (P)=\nu }}_{\mathrm{RT}}\mathrm{+aP}$ for 91 at. % ${}^{13}\mathrm{C}$ diamond, where ${\nu }_{\mathrm{RT}}{\mathrm{(}}^{\mathrm{13}}{\mathrm{C)=1287.79\pm 0.28\hspace{0.17em}cm}}^{\mathrm{-1}}$ and ${\mathrm{a(}}^{13}\mathrm{C}\text{)=2.83±0.05\hspace{0.17em}}{\mathrm{cm}}^{\mathrm{-1}}\mathrm{/GPa}.$ Analysis of values from the literature shows that the pressure dependence of the Raman line of ${}^{12}\mathrm{C}$ diamond is best described by the parameters ${\nu }_{\mathrm{RT}}{\mathrm{(}}^{\mathrm{12}}{\mathrm{C)=1332.5\hspace{0.17em}cm}}^{\mathrm{-1}}$ and ${\mathrm{a(}}^{12}{\mathrm{C)=2.90\pm 0.05\hspace{0.17em}cm}}^{\mathrm{-1}}\mathrm{/GPa}.$ The temperature dependence of the diamond Raman line is best described by ${\mathrm{\nu (T)-\nu }}_{\mathrm{RT}}{\mathrm{=b}}_0$ for $\text{T⩽200\hspace{0.17em}}\mathrm{K},$ and ${\mathrm{\nu (T)-\nu }}_{\mathrm{RT}}{\mathrm{=b}}_0{\mathrm{+b}}_{\text{1.5}}{T}_k^{\text{1.5}}$ for $\text{200\hspace{0.17em}}\mathrm{K}\text{⩽T⩽1500\hspace{0.17em}}\mathrm{K},$ where $T_k\text{=T−200\hspace{0.17em}}\mathrm{K}.$ For 91 at. % ${}^{13}\mathrm{C}$ diamond, the parameters are $b_0\text{=0.450±0.025\hspace{0.17em}}{\mathrm{cm}}^{\mathrm{-1}};$ $b_{\text{1.5}}{\text{=−(7.36±0.09)×10}}^{\text{−4}}\hspace{0.17em}{\mathrm{cm}}^{\mathrm{-1}}{\mathrm{\hspace{0.17em}K}}^{\mathrm{-1.5}};$ and for ${}^{12}\mathrm{C}$ diamond, the parameters are $b_0\text{=0.467±0.033\hspace{0.17em}}{\mathrm{cm}}^{\mathrm{-1}},$ $b_{\text{1.5}}{\text{=−(7.56±0.10)×10}}^{\text{−4}}\hspace{0.17em}{\mathrm{cm}}^{\mathrm{-1}}{\mathrm{\hspace{0.17em}K}}^{\mathrm{-1.5}}.$ Although no quantitative theoretical models are available for calculating the Raman shift as a function of temperature, the excellent fits to the data suggest that the $T_k^{\text{1.5}}$ dependence above has a physical basis.