X-ray standing wave analysis of the effect of isotopic composition on the lattice constants of Si and Ge

The x-ray standing wave (XSW) technique is used to measure the isotopic mass dependence of the lattice constants of Si and Ge. Backreflection allows substrates of moderate crystallinity to be used while high order reflection yields high accuracy. The XSW, generated by the substrate, serves as a reference for the lattice planes of an epilayer; of different isotopic composition. Employing XSW and photoemission, the position of the surface planes is determined from which the lattice constant difference Deltaa is calculated. Scaled to DeltaM = 1 amu we find (Deltaa/a) of -0.36 x 10(-5) and -0.88 x 10(-5) for Ge and -1.8 x 10(-5) and -3.0 X 10(-5) for Si at 300 and 30 K, respectively.