Isotopic Mass and Lattice Constant: X-ray Standing Wave Measurements

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Abstract
The molecular volume of crystals depends on their isotopic masses. This influence originates from the zero-point motion and the resulting small differences in lattice constants. This effect was measured with high precision by using an x-ray standing wave. The standing wave is generated during Bragg reflection and thus is in phase with the planes of the substrate crystal, which is covered with a homoepitaxial film that has a different isotopic composition than the substrate. The positions of the surface planes of the film with respect to the substrate planes are revealed by the photoelectrons excited by the maxima of the standing wave. For germanium-76 on natural germanium(111), a difference in lattice constant of −1.1 × 10 −5 and −2.5 × 10 −5 at 300 and 54 kelvin, respectively, was found. The results are in good agreement with theoretical predictions.