Sebastian Christensen

Phase transition enhanced thermoelectric figure-of-merit in copper chalcogenides

While thermoelectric materials can be used for solid state cooling, waste heat recovery, and solar electricity generation, low values of the thermoelectric figure of merit, zT, have led to an efficiency too low for widespread use. Thermoelectric effects are characterized by the Seebeck coefficient or thermopower, which is related to the entropy associated with charge transport. For example, coupling spin entropy with the presence of charge carriers has enabled the enhancement of zT in cobalt oxides. We demonstrate that the coupling of a continuous phase transition to carrier transport in Cu 2Se over a broad (360–410 K) temperature range results in a dramatic peak in thermopower, an increase in phonon and electron scattering, and a corresponding doubling of zT (to 0.7 at 406 K), and a similar but larger increase over a wider temperature range in the zT of Cu 1.97 Ag .03Se (almost 1.0 at 400 K). The use of structural entropy for enhanced thermopower could lead to new engineering approaches for thermoelectric materials with high zT and new green applications for thermoelectrics.

Combined X-ray and neutron diffraction study of vacancies and disorder in the dimorphic clathrate Ba8Ga16Sn30 of type i and VIII

We report detailed structural investigations of the dimorphic clathrate Ba8Ga16Sn30 that crystallizes in both type I and VIII clathrate structures. Single crystals of type I and VIII have been examined using single crystal X-ray and Laue neutron diffraction in the temperature range T = 10 K-500 K. The utilization of both X-ray and neutron diffraction gives a unique ability to reveal the occurrence of minute vacancy occupancies in the host structure. The vacancies are shown to be located on the 6c (type I) and 24g (type VIII) framework sites. Largest vacancy densities are observed for type I p-Ba8Ga16Sn30, 1.3(4)%, and type VIII n-Ba8Ga16Sn30, 0.7(2)%. The relation between guest atom disorder and occurrence of glasslike thermal conductivity in intermetallic clathrates was also investigated. In type VIII Ba8Ga16Sn30 neither n-type (crystalline thermal conductivity) nor p-type (glasslike thermal conductivity) showed any significant disorder of the guest atoms; they do however show anharmonic motion. The glasslike thermal conductivity of p-type Ba8Ga16Sn30 is interpretable as a result of higher effective mass of p-type charge-carriers affecting phonon scattering. In type I Ba8Ga16Sn30 guest atoms are highly disordered for both carrier types and samples of both charge carrier types have glasslike thermal conductivity.

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.

“Glass-like” thermal conductivity gradually induced in thermoelectric Sr8Ga16Ge30 clathrate by off-centered guest atoms

The origin of the “glass-like” plateau in thermal conductivity of inorganic type I clathrates has been debated for more than a decade. Here, it is demonstrated that the low temperature thermal conductivity of Sr8Ga16Ge30 can be controlled by the synthesis method: A flux-grown sample has a “glass-like” plateau in thermal conductivity at low temperature, while a zone-melted sample instead has a crystalline peak. A combination of flux-growth and zone-melting produces an intermediate thermal conductivity. In a comprehensive study of three single crystal samples, it is shown by neutron diffraction that the transition from crystalline peak to “glass-like” plateau is related to an increase in Sr guest atom off-centering distance from 0.24 A to 0.43 A. By modifying ab initio calculated force constants for the guest atom to an isotropic model, we reproduce both measured heat capacity and inelastic neutron scattering data. The transition from peak to plateau in the thermal conductivity can be modeled by a combined ...

Carrier concentration dependence of structural disorder in thermoelectric Sn1−xTe

The crystal structure of SnTe is investigated from 20 to 800 K in two samples with different carrier concentrations by single-crystal and powder synchrotron X-ray diffraction, coupled with maximum entropy analysis.

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 Straaso, 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 sinθ/λ = 2.2 A−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.

Guest host interaction and low energy host structure dynamics in tin clathrates

The two binary clathrates with vacancies (□) Rb8Sn44□2 and Cs8Sn44□2 have been examined using powder inelastic neutron scattering (INS). Rattling energies of Rb and Cs are found to be similar by both experiment and calculations, ℏωCs/ℏωRb|Exp.=0.98(1) and ℏωCs/ℏωRb|Calc.=1.0, despite the significant mass difference: mCs/mRb=1.6, which shows that guest-host interaction is non-negligible for the studied system. For Rb8Sn44□2, a low energy phonon mode is observed at ≈3.5 meV, below the phonon mode which in the literature is attributed to the guest atom. The 3.5 meV mode is interpreted to have significant spectral weight of Sn host atoms based on temperature dependence and comparison with published theoretical phonon calculations. The record of low thermal conductivity of the tin clathrates can be attributed to the host structure dynamics rather than the guest atom rattling.

Accurate charge densities from powder X-ray diffraction – a new version of the Aarhus vacuum imaging-plate diffractometer

In recent years powder X-ray diffraction has proven to be a valuable alternative to single-crystal X-ray diffraction for determining electron-density distributions in high-symmetry inorganic materials, including subtle deformation in the core electron density. This was made possible by performing diffraction measurements in vacuum using high-energy X-rays at a synchrotron-radiation facility. Here we present a new version of our custom-built in-vacuum powder diffractometer with the sample-to-detector distance increased by a factor of four. In practice this is found to give a reduction in instrumental peak broadening by approximately a factor of three and a large improvement in signal-to-background ratio compared to the previous instrument. Structure factors of silicon at room temperature are extracted using a combined multipole-Rietveld procedure and compared with ab initio calculations and the results from the previous diffractometer. Despite some remaining issues regarding peak asymmetry, the new diffractometer yields structure factors of comparable accuracy to the previous diffractometer at low angles and improved accuracy at high angles. The high quality of the structure factors is further assessed by modelling of core electron deformation with results in good agreement with previous investigations.

Nuclear Enhanced MEM Used to Analyze Local Distortions in Lead Chalcogenides

We introduce a novel method for reconstructing nuclear density distributions (NDDs): Nuclear Enhanced X-ray Maximum Entropy Method (NEXMEM). NEXMEM offers an alternative route to experimental NDDs, exploiting the superior quality of synchrotron X-ray data compared to neutron data. The method was conceived to analyse local distortions in the thermoelectric lead chalcogenides, PbX (X = S, Se, Te). Thermoelectric materials are functional materials with the unique ability to interconvert heat and electricity, holding much promise for green energy solutions such as waste heat recovery. The extraordinary thermoelectric performance of binary lead chalcogenides has caused huge research activity, but the mechanisms governing their unexpected low thermal conductivity still remain a controversial topic. It has been proposed to result from giant anharmonic phonon scattering or from local fluctuating dipoles on the Pb site.[1,2] No macroscopic symmetry change are associated with these effects, rendering them invisible to conventional crystallographic techniques. For this reason PbX was until recently believed to adopt the ideal, undistorted rock-salt structure. In the present study, we investigate PbX using multi-temperature synchrotron powder X-ray diffraction data in combination with the maximum entropy method (MEM) and NEXMEM. In addition NEXMEM has been validated by testing against simulated powder diffraction data of PbTe with known displacements of Pb. The increased resolution of NEXMEM proved essential for resolving Pbdisplacement of 0.2 Å in simulated data. The figure below shows Pb in the (100) plane for MEM, NEXMEM and the actual NDD of the test structure. Our findings outline the extent of disorder in lead chalcogenides, promoting our understanding of this class of highperformance thermoelectric materials. Furthermore we introduce NEXMEM which can be used for widespread characterization of subtle atomic features in crystals with unusual properties.

Characterization of Local Distortions in Thermoelectric Lead Chalcogenides

Thermoelectric materials are functional materials with the unique ability to interconvert heat and electricity, holding much promise for green energy solutions such as efficient waste heat recovery. The extraordinary thermoelectric performance of binary lead chalcogenides has caused huge research activity, but the mechanisms governing their unexpected low thermal conductivity still remain a controversial topic. It has been proposed to result from giant anharmonic phonon scattering or from local fluctuating dipoles on the Pb site, emerging with temperature on the Pb site.[1,2] No macroscopic symmetry change are associated with these effects, rendering them invisible to conventional crystallographic techniques. For this reason lead chalcogenides were until recently believed to adopt the ideal, undistorted rock-salt structure. In the present study, we probe the peculiar structural features in PbX (X = S, Se, Te) using multi-temperature synchrotron powder X-ray diffraction data in combination with the maximum entropy method. Distorted atoms are detected and quantified by refinement of anharmonic probability density functions. The charge density analysis is complemented by nuclear density distributions (NDDs) reconstructed from neutron diffraction data and by a novel method: Nuclear Enhanced X-ray Maximum Entropy Method (NEXMEM). NEXMEM offers an alternative route to experimental NDDs, exploiting the superior quality of synchrotron X-ray data compared to neutron diffraction data. The increased atomic resolution introduced by NEXMEM proved essential for resolving atomic distortions, see figure below showing Pb in the (100) plane. Our findings outline the extent of disorder and anharmonicity in binary lead chalcogenides, promoting our fundamental understanding of this class of highperformance thermoelectric materials. The applied approach can be used in general, opening up for widespread characterization of subtle features in crystals with unusual properties.