Structural disorder, anisotropic micro-strain and cation vacancies in thermo-electric lead chalcogenides.

Thermoelectric materials can interconvert heat and electricity, and the extraordinary thermoelectric properties of lead chalcogenides (PbX, X = S, Se, Te) attract immense scientific interest. A key topic is the role of the cation in reaching a very low thermal conductivity necessary for efficient energy conversion. Here we present new structural insights about the deceptively simple rock-salt lead chalcogenides through a comparative multi-temperature synchrotron powder X-ray diffraction study. For the first time, the presence of anisotropic microstrain broadening as well as lead vacancies are quantified for all three compounds. The microstrain implies extended breakage of cubic symmetry as a sign of the incipient ferroelectric nature of PbX. The degree of microstrain is correlated to the transition pressure of a symmetry reducing phase transition, and this trend can be explained by anion mediated s-p hybridization on lead. The observed number of vacancies is greatest for PbS (4-8%), but two samples of PbS show different cation occupancy, and thus sample-dependent vacancies might be the property that unifies conflicting results reported for PbX. Gram-Charlier analysis identifies a local non-spherical distribution of Pb; however, model unbiased maximum entropy analysis indicates that any static displacement of Pb, if present, is less than 0.2 Å at 100 K.

Carrier concentration dependence of structural disorder in thermoelectric Sn1-x Te.

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.

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.

Nuclear-weighted X-ray maximum entropy method - NXMEM.

Subtle structural features such as disorder and anharmonic motion may be accurately characterized from nuclear density distributions (NDDs). As a viable alternative to neutron diffraction, this paper introduces a new approach named the nuclear-weighted X-ray maximum entropy method (NXMEM) for reconstructing pseudo NDDs. It calculates an electron-weighted nuclear density distribution (eNDD), exploiting that X-ray diffraction delivers data of superior quality, requires smaller sample volumes and has higher availability. NXMEM is tested on two widely different systems: PbTe and Ba(8)Ga(16)Sn(30). The first compound, PbTe, possesses a deceptively simple crystal structure on the macroscopic level that is unable to account for its excellent thermoelectric properties. The key mechanism involves local distortions, and the capability of NXMEM to probe this intriguing feature is established with simulated powder diffraction data. In the second compound, Ba(8)Ga(16)Sn(30), disorder among the Ba guest atoms is analysed with both experimental and simulated single-crystal diffraction data. In all cases, NXMEM outperforms the maximum entropy method by substantially enhancing the nuclear resolution. The induced improvements correlate with the amount of available data, rendering NXMEM especially powerful for powder and low-resolution single-crystal diffraction. The NXMEM procedure can be implemented in existing software and facilitates widespread characterization of disorder in functional materials.

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.

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) Å(2). 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.

Maximum-entropy-method charge densities based on structure-factor extraction with the commonly used Rietveld refinement programs GSAS, FullProf and Jana2006.

Structure-factor extractions in commonly used Rietveld refinement programs (FullProf, Jana2006 and GSAS) were examined with respect to subsequent calculation of electron-density distributions (EDDs) using the maximum entropy method (MEM). As a test case, 90 K synchrotron powder X-ray diffraction data were collected on the potential hydrogen storage material, NaGaH(4), at SPring-8, Japan. To support the model, neutron powder diffraction data were collected on the fully deuterated sample at PSI, Switzerland. Firstly, it was established whether the programs can produce observed structure factors, F(obs), corrected for anomalous dispersion and scaled to the scattering power of one unit cell. Secondly, different models for background and peak-shape description were investigated with respect to the extracted F(obs), and the effect on the subsequent MEM EDDs was analysed within the quantum theory of atoms in molecules. Substantial differences are observed in the estimated standard deviations, σ(obs), produced by the different programs. Since σ(obs) is a vital parameter in the calculation of MEM EDDs this leads to substantial variation between the MEM EDDs obtained with different Rietveld programs even in cases with similar F(obs). A new approach for selecting an optimized MEM EDD and thereby minimizing the effect of variation in σ(obs) is suggested.