Short-range order in crystalline, amorphous, liquid, and supercooled germanium probed by x-ray-absorption spectroscopy

A detailed experimental investigation of the short-range structural properties in condensed phases of germanium is presented. X-ray-absorption measurements at the Ge K edge have been collected in a wide temperature range for different samples. Polycrystalline c-Ge was measured at 77, 296, 450, 620, 782, 920, and 1110 K, close to the Ge melting-point temperature ${\mathit{T}}_{\mathit{m}}$=1210.4 K. Evaporated amorphous Ge was measured at 297 K. Eight independent measurements for liquid germanium have been collected from about 950 K in highly supercooled conditions up to about 1600 K. The spectra show a remarkable temperature trend. By comparison, previous diffraction measurements on l-Ge were limited to two narrow temperature regions only, either above ${\mathit{T}}_{\mathit{m}}$ or around 1500 K, and no measurements in the supercooled liquid region existed. Data analysis has been performed with the GNXAS approach and account has been taken for the presence of double-excitation channels involving 3d and 3p electrons in addition to the 1s. The c-Ge structural results are found in excellent agreement with the known properties. The expansion of the average bond length R is in agreement with thermal expansion data. Mean-square vibrational amplitudes are in excellent agreement with both previous measurements and calculations in the harmonic approximation. The analysis of the signal in liquid Ge has been performed using a technique that allows to extract information on the radial distribution function g(r) directly comparable with molecular dynamics (MD) simulations or previous diffraction determinations.