Experimental X-ray Charge-Density Studies─A Suitable Probe for Superconductivity? A Case Study on MgB₂

Case studies of 1T-TiSe₂ and YBa₂Cu₃O_7-δ have demonstrated that X-ray diffraction (XRD) studies can be used to trace even subtle structural phase transitions which are inherently connected with the onset of superconductivity in these benchmark systems. However, the utility of XRD in the investigation of superconductors like MgB₂ lacking an additional symmetry-breaking structural phase transition is not immediately evident. Nevertheless, high-resolution powder XRD experiments on MgB₂ in combination with maximum entropy method analyses hinted at differences between the electron density distributions at room temperature and 15 K, that is, below the T_c of approx. 39 K. The high-resolution single-crystal XRD experiments in combination with multipolar refinements presented here can reproduce these results but show that the observed temperature-dependent density changes are almost entirely due to a decrease of atomic displacement parameters as a natural consequence of a reduced thermal vibration amplitude with decreasing temperature. Our investigations also shed new light on the presence or absence of magnesium vacancies in MgB₂ samples─a defect type claimed to control the superconducting properties of the compound. We propose that previous reports on the tendency of MgB₂ to form non-stoichiometric Mg_1-B₂ phases (1 - x ∼ 0.95) during high-temperature (HT) synthesis might result from the interpretation of XRD data of insufficient resolution and/or usage of inflexible refinement models. Indeed, advanced refinements based on an Extended Hansen-Coppens multipolar model and high-resolution X-ray data, which consider explicitly the contraction of core and valence shells of the magnesium cations, do not provide any significant evidence for the formation of non-stoichiometric Mg_1-B₂ phases during HT synthesis.