Carrier concentration dependence of structural disorder in thermoelectric Sn1−xTe

SnTe is a promising thermoelectric and topological insulator material. Here, the presumably simple rock salt crystal structure of SnTe is studied comprehensively by means of high-resolution synchrotron single-crystal and powder X-ray diffraction from 20 to 800 K. Two samples with different carrier concentrations (sample A = high, sample B = low) have remarkably different atomic displacement parameters, especially at low temperatures. Both samples contain significant numbers of cation vacancies (1–2%) and ordering of Sn vacancies possibly occurs on warming, as corroborated by the appearance of multiple phases and strain above 400 K. The possible presence of disorder and anharmonicity is investigated in view of the low thermal conductivity of SnTe. Refinement of anharmonic Gram–Charlier parameters reveals marginal anharmonicity for sample A, whereas sample B exhibits anharmonic effects even at low temperature. For both samples, no indications are found of a low-temperature rhombohedral phase. Maximum entropy method (MEM) calculations are carried out, including nuclear-weighted X-ray MEM calculations (NXMEM). The atomic electron densities are spherical for sample A, whereas for sample B the Te electron density is elongated along the 〈100〉 direction, with the maximum being displaced from the lattice position at higher temperatures. Overall, the crystal structure of SnTe is found to be defective and sample-dependent, and therefore theoretical calculations of perfect rock salt structures are not expected to predict the properties of real materials

Understanding the Reorientational Dynamics of Solid-State MBH₄ (M = Li–Cs)

The reorientational dynamics of crystalline MBH₄ (M = Li–Cs) have been characterized with the interacting quantum atom theory. This interpretive approach enables an atomistic deciphering of the energetic features involved in BH₄^– reorientation using easily graspable chemical terms. It reveals a complex construction of the activation energy that extends beyond interatomic distances and chemical interactions. BH₄^– reorientations are in LiBH₄ and NaBH₄ regulated by their interaction with the nearest metal cation; however, higher metal electronic polarizability and more covalent M···H interactions shift the source of destabilization to internal deformations in the heavier systems. Underlying electrostatic contributions cease abruptly at CsBH₄, triggering a departure in the otherwise monotonically increasing activation energy. Such knowledge concurs to the fundamental understanding and advancement of energy solutions in the field of hydrogen storage and solid-state batteries

Synchrotron powder diffraction of silicon: high-quality structure factors and electron density

Crystalline silicon is an ideal compound to test the current state of experimental structure factors and corresponding electron densities. High-quality structure factors have been measured on crystalline silicon with synchrotron powder X-ray diffraction. They are in excellent agreement with benchmark Pendellösung data having comparable accuracy and precision, but acquired in far less time and to a much higher resolution (sin θ\λ < 1.7 Å$^{-1}$). The extended data range permits an experimental modelling of not only the valence electron density but also the core deformation in silicon, establishing an increase of the core density upon bond formation in crystalline silicon. Furthermore, a physically sound procedure for evaluating the standard deviation of powder-derived structure factors has been applied. Sampling statistics inherently account for contributions from photon counts as well as the limited number of diffracting particles, where especially the latter are particularly difficult to handle

A Theoretical Study on the Rotational Motion and Interactions in the Disordered Phase of MBH₄ (M = Li, Na, K, Rb, Cs)

The rotational motion in the high-temperature disordered phase of MBH₄ (M = Li, Na, K, Rb, Cs) is investigated utilizing two complementary theoretical approaches. The first one consists of high-level periodic DFT calculations which systematically consider several instantaneous representations of the structural disorder. The second approach is based on a series of in vacuo calculations on molecular complexes suitably extracted from the crystal and chosen as to possibly disentangle the energetic factors leading to the observed rotational barriers. The results of the first part demonstrate that the motion of the BH₄^– anion is dominated by 90° reorientations around the 4-fold symmetry axes of the cubic crystal, and depending on the instantaneous structural disorder activation energies are found to be between 0.00 and 0.31 eV for LiBH₄, 0.05 and 0.26 eV for NaBH₄, 0.16 and 0.27 eV for KBH₄, 0.22 and 0.31 eV for RbBH₄, and 0.21 and 0.32 eV for CsBH₄. The increasing rotational barriers as well as the movement of the transition state from 7° to 44° observed along the series of alkaline metals, M = Li–Rb, appear to be simply accounted for by an analysis of the energy profiles for the <i>C</i>₂ rotation of a BH₄^– group in M⁺–BH₄^– and BH₄^––BH₄^– in vacuo complexes. The energy gained from the introduction of disorder shows a trend opposite to that of the rotational barriers as it decreases along the Li–Rb series. Similar considerations apply to the <i>C</i>₃ rotational motion of the BH₄^– anion, which likewise has been studied in the crystal and in the in vacuo molecular complexes. CsBH₄ deviates from the systematic trends observed for LiBH₄–RbBH₄. Depending on the structural starting point of the rotation, its <i>C</i>₂ rotational barriers are found to be slightly higher or slightly lower than for RbBH₄, whereas its energy gain due to the introduction of disorder is found to be positioned between that of KBH₄ and RbBH₄. The <i>C</i>₃ rotational barriers of CsBH₄ are instead significantly smaller compared to those of RbBH₄ and even marginally below those of KBH₄

Low-temperature powder X-ray diffraction measurements in vacuum: analysis of the thermal displacement of copper

A serious limitation of the all-in-vacuum diffractometer reported by Straasø, Dippel, Becker & Als-Nielsen [J. Synchrotron Rad. (2014), 21, 119-126] has so far been the inability to cool samples to near-cryogenic temperatures during measurement. The problem is solved by placing the sample in a jet of helium gas cooled by liquid nitrogen. The resulting temperature change is quantified by determining the change in unit-cell parameter and atomic displacement parameter of copper. The cooling proved successful, with a resulting temperature of ~95 (3) K. The measured powder X-ray diffraction data are of superb quality and high resolution [up to sin$\theta/\lambda$ = 2.2 Å$^{-1}$], permitting an extensive modelling of the thermal displacement. The anharmonic displacement of copper was modelled by a Gram-Charlier expansion of the temperature factor. As expected, the corresponding probability distribution function shows an increased probability away from neighbouring atoms and a decreased probability towards them

Experimental determination of core electron deformation in diamond

Synchrotron powder X-ray diffraction data are used to determine the core electron deformation of diamond. Core shell contraction inherently linked to covalent bond formation is observed in close correspondence with theoretical predictions. Accordingly, a precise and physically sound reconstruction of the electron density in diamond necessitates the use of an extended multipolar model, which abandons the assumption of an inert core. The present investigation is facilitated by negligible model bias in the extraction of structure factors, which is accomplished by simultaneous multipolar and Rietveld refinement accurately determining an atomic displacement parameter (ADP) of 0.00181 (1) Å2. The deconvolution of thermal motion is a critical step in experimental core electron polarization studies, and for diamond it is imperative to exploit the monatomic crystal structure by implementing Wilson plots in determination of the ADP. This empowers the electron-density analysis to precisely administer both the deconvolution of thermal motion and the employment of the extended multipolar model on an experimental basis

Contemporary X-ray electron-density studies using synchrotron radiation

Synchrotron radiation has many compelling advantages over conventional radiation sources in the measurement of accurate Bragg diffraction data. The variable photon energy and much higher flux may help to minimize critical systematic effects such as absorption, extinction and anomalous scattering. Based on a survey of selected published results from the last decade, the benefits of using synchrotron radiation in the determination of X-ray electron densities are discussed, and possible future directions of this field are examined

Carrier concentration dependence of structural disorder in thermoelectric Sn1−xTe

SnTe is a promising thermoelectric and topological insulator material. Here, the presumably simple rock salt crystal structure of SnTe is studied comprehensively by means of high-resolution synchrotron single-crystal and powder X-ray diffraction from 20 to 800 K. Two samples with different carrier concentrations (sample A = high, sample B = low) have remarkably different atomic displacement parameters, especially at low temperatures. Both samples contain significant numbers of cation vacancies (1–2%) and ordering of Sn vacancies possibly occurs on warming, as corroborated by the appearance of multiple phases and strain above 400 K. The possible presence of disorder and anharmonicity is investigated in view of the low thermal conductivity of SnTe. Refinement of anharmonic Gram–Charlier parameters reveals marginal anharmonicity for sample A, whereas sample B exhibits anharmonic effects even at low temperature. For both samples, no indications are found of a low-temperature rhombohedral phase. Maximum entropy method (MEM) calculations are carried out, including nuclear-weighted X-ray MEM calculations (NXMEM). The atomic electron densities are spherical for sample A, whereas for sample B the Te electron density is elongated along the 〈100〉 direction, with the maximum being displaced from the lattice position at higher temperatures. Overall, the crystal structure of SnTe is found to be defective and sample-dependent, and therefore theoretical calculations of perfect rock salt structures are not expected to predict the properties of real materials