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

Abstract

Case studies of 1T-TiSe 2 and YBa 2 Cu 3 O 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 MgB 2 lacking an additional symmetry-breaking structural phase transition is not immediately evident. Nevertheless, high-resolution powder XRD experiments on MgB 2 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 MgB 2 samples�a defect type claimed to control the superconducting properties of the compound. We propose that previous reports on the tendency of MgB 2 to form non-stoichiometric Mg 1−x B 2 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 nonstoichiometric Mg 1−x B 2 phases during HT synthesis.

Trapped flux in pure and Mn-substituted CaKFe4As4and MgB2superconducting single crystals

“…Figure 14 presents temperature-dependent, low field ZFC and FC magnetic susceptibility M/H. The superconducting transition temperature T c ≈ 37.7 K, is consistent with other single crystal data [20,22]. Note that, in contrast to CaKFe 4 As 4 and CaK(Fe 0.983 Mn 0.017 ) 4 As 4 crystals discussed earlier, the pinning in MgB 2 crystal is rather small, resulting in only ≈8% difference in ZFC and FC data for H∥ab (figure 14 for a shoulder observed for high H M values at temperatures close to T c for FC and ZFC protocols in both orientations of the magnetic field.…”

“…The Mn substitution level x was determined by performing energy dispersive x-ray spectroscopy. MgB 2 single crystals [19][20][21] were grown from a solution with excess Mg under high pressure and high temperature in boron nitride crucibles (see supporting information in [20] for more details), similarly to the procedure described in [22].…”

Critical Crystallographic Transition in Violation of Kasha’s Rule of Size-Specific ZnO Quantum Dots

“…The change in the crystal structure and volume of the unit cell dictates the excited electronic and vibrational states through diverse electron–phonon or electron–lattice interactions in the semiconductor. Therefore, the excited vibrational energy states lose the degeneracy on a different mode for different categories of unit cell patterns and exhibit the anti-Kasha behavior …”

“…In general, the decrease in lattice constants means that the electrons are more tightly bound to the atoms and hence require more energy to transfer, corresponding to an increased band gap. Since the volume of a particular unit cell is determined by the free electron concentration, the width of the conduction band is inversely proportional to the lattice dimension. When the lattice becomes distorted to the smaller dimension, the conduction band becomes narrower and generates a band gap or there would be an increase in the band gap.…”

Peierls-type structural phase transition in the low-dimensional superconductor Sc3CoC4

“…Up to now, a wide and diverse field of compounds is known, where small structural changes occur that are either in a competition with the onset of superconductivity, leave it unaffected or even lead to its stabilization [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. These structural changes can be subtle and solely indicated by an anomaly in the thermal expansion directly above the T c as exemplified by the broadly known MgB 2 [27][28][29]. But they may also break the rotational and/or translational symmetry of the crystal structure as demonstrated by the trigonal-to-triclinic phase transitions in the Chevrel phases [8-10, 26, 30-32] or the tetragonal-to-orthorhombic phase transitions in the iron-based superconductors [12][13][14][15][16]33].…”