Thermal expansion measurements by x-ray scattering and breakdown of Ehrenfest's relation in alloy liquids

Measurements of sharp diffraction peaks as a function of temperature are routinely used to obtain precise linear expansion coefficients of crystalline solids. In this case, the relation between temperature dependent changes in peak position in momentum transfer (q1) and volume expansion is straightforward (Ehrenfest's relation: q1 = K(2π/d), where K is a constant and d is the interatomic spacing) and the data obtained are usually in close agreement with more direct measurements. With high intensity synchrotron x-ray and spallation neutron sources, it is also possible to accurately measure the positions of the much broader peaks for liquids and glasses. This has led to a debate on whether linear expansion coefficients derived from these data are an accurate representation of the volume expansion coefficients. We present here volume thermal expansion and x-ray diffraction data for a large number of glass-forming alloy liquids acquired in a containerless environment using the beamline electrostatic levitation technique. The data show a large difference in the values obtained from the two different techniques. Moreover, the position of the first peak (q1) in the scattered intensity in the structure factor (S(q)) and the atomic volume v for all liquids follow a simple relationship, v∝(q1)−ε. The exponent, ε = 2.28 (±0.11), is much different from the expected value of 3 from Ehrenfest's relation and shows no temperature dependence over the temperature range of the data collected