Reconciling Crystallographic and Physical Property Measurements on Thermoelectric Lead Sulfide

Abstract

For many decades the lead chalcogenides PbTe, PbSe, and PbS (and their solid solutions) have been preferred high-performance thermoelectric materials due to their exceptional electronic and thermal properties as well as great stability during operation. However, there is a lack of understanding about the fundamental relation between the reported high-defect crystal structure containing cation disorder and vacancies and the observed transport properties, which follow expectations for an ideal rock salt crystal structure. Here we have studied a series of undoped lead sulfide samples (Pb 1−x S) with presumed small chemical variations. Crystallographic refinements of high-resolution synchrotron powder X-ray diffraction data give unphysically low lead occupancies (0.75−0.98), in contradiction with the measured charge carrier concentration, resistivity, mobility, and Seebeck coefficient, which show no signs of lead vacancies. A new Rietveld refinement model including preferred orientation parameters and anisotropic strain gives almost full lead occupancy and improved agreement factors. However, transmission electron microscopy analysis reveals that there is no preferred orientation in this system. Instead it is the diffuse scattering due to directional correlated disorder in the structure that necessitates the additional parameters when modeling Bragg intensities. The present approach is a general method for absorbing effects of direction-dependent correlations in advanced materials.

Accurate high-resolution single-crystal diffraction data from a Pilatus3 X CdTe detector

“…This parameter has been implemented for a completely different purpose, and to rely on it as a correction should be considered highly unsatisfactory. A similar fudge parameter was recently reported for the Rietveld refinement of powder X-ray diffraction where the physically incorrect modelling of preferred orientation and anisotropic strain was able to mimic and completely absorb the underlying effect of thermal diffuse scattering (Zeuthen et al, 2019).…”

Tuneable correlated disorder in alloys

“…Nanoscale complexity, like that observed in this study, has been shown to be of great importance in phonon engineering for emerging thermoelectrics [54], efficiently scattering mid-to long-wavelength phonons that are responsible for the majority of phonon-mediated heat transport in alloys [55], and possibly contributing to the destruction of longwavelength phonon coherence [56]. Spontaneous structural modulations have been observed in numerous promising candidates [11][12][13][57][58][59][60]. These systems are vastly more complex than the binary alloy investigated in our study, often involving chemical ordering in conjunction with structural distortions, however we observe similarly extraordinary phonon broadening, in both magnitude and the proportion of the dispersion affected.…”

High‐Density Frenkel Defects as Origin of N‐Type Thermoelectric Performance and Low Thermal Conductivity in Mg3Sb2‐Based Materials

“…reported that fictitious modeling using preferred orientation and anisotropic strain coincidentally improved profile fitting and led to a reliable structural model consistent with physical properties of lead sulfides that exhibit anisotropic diffuse scattering. [ 26 ] In the case of Mg 3 Sb 2 , we do not observe any distinct diffuse scattering by single crystal XRD measurement (Figure S2, Supporting Information), and we consider that the anisotropic strain essentially exists in Mg 3 Sb 2 . We confirm presence of the interstitial defects by MEM analysis of both single crystal XRD and SPXRD data using structure factors refined without assuming any occupancy at the interstitial sites (Figure S3, Supporting Information).…”