Effect of isotope concentration on the lattice parameter of germanium perfect crystals

Abstract

The difference in lattice parameters between germanium crystals of natural isotopic composition and an isotopically enriched crystal of $^{74}\mathrm{Ge}$ was calculated and measured by using a double-beam triple-axis x-ray spectrometer. The measured relative fractional difference was (-6.3\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ and (-14.9\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ at room and liquid-nitrogen temperatures, respectively. The corresponding calculated values are -6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ and -12\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$. The agreement is very good, given uncertainties in the values of physical constants used for the theoretical calculations.