Influence of the isotope ratio on the lattice constant of diamond

The lattice constants of diamond crystals consisting of an isotopic mixture of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}_{\mathit{x}}^{12}{}_{}{}^{}$ ${\mathrm{C}}_{\left(1\mathrm{}\mathrm{-}\mathit{x}\right)}$ were measured as a function of the isotopic composition by single-crystal diffractometry using the synchrotron x-ray radiation. The isotope ratio of the synthesized diamond samples was determined by secondary-ion-mass spectroscopy. The lattice constant can be expressed in quadratic form as a(X) =3.567 12-9.0×${10}^{\mathrm{-}4}$X+3.7×${10}^{\mathrm{-}4}$ ${\mathit{X}}^2$, where X=${[}^{13}$C]/(${[}^{12}$C]+${[}^{13}$C]), in contrast to the linear relation reported by Holloway, Hass, and Tamor [Phys. Rev. B 45, 6353 (1992)], namely a(X)=3.567 14-5.4×${10}^{\mathrm{-}4}$X.