Influence of the isotope ratio on the lattice constant of diamond

The lattice constants of diamond crystals consisting of an isotopic mixture of ¹³Cₓ¹²{C}_{(1{{-}}x)}$ 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^-4X+3.7×{}10^-4{X}²$, where X=${[}¹³$C]/(${[}¹²$C]+${[}¹³C]), 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}^{{{-}}4}$X.