Lattice parameter and Raman spectra of isotopically mixed diamond

The influence of isotope mass and anharmonicity on the lattice parameter of isotopically mixed diamond is studied in a simple theoretical model. The performed calculations confirm that in good approximation the lattice parameter changes linearly with the isotope concentration. We show that the stretching harmonic-force constants for pure 12C and 13C differ slightly and we explain why the Raman-frequency ratio is smaller than the square root of the ratio of the corresponding masses. Finally, the positive bowing of the Raman frequency in isotopically mixed diamond is discusse