High-temperature electrical and thermal transport properties of polycrystalline ${\mathrm{PdCoO}}_{2}$

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High-temperature electrical and thermal transport properties of polycrystalline ${PdCoO}_{2}$

P. Yordanov, A. S. Gibbs, P. Kaya, S. Bette, W. Xie, X. Xiao, A. Weidenkaff, H. Takagi, and B. Keimer

Phys. Rev. Materials 5, 015404 – Published 28 January 2021

Abstract

The layered delafossite ${PdCoO}_{2}$ has been predicted to be one of very few materials with a thermopower that is highly anisotropic and switches sign between different crystallographic directions. These properties are of interest for various applications, but have been difficult to verify because sufficiently large crystals have not been available. We report measurements of the high-temperature electrical resistivity, thermal conductivity, and thermopower of phase-pure ${PdCoO}_{2}$ powder compacts prepared by a highly Pd-efficient synthesis route. While the electronic transport of the polycrystalline samples is dominated by that of the Pd planes, the thermopower exhibits a well-defined deviation from the in-plane character at temperatures above $600 K$ , which is indicative of opposing trends in the Seebeck coefficients within and perpendicular to the delafossite layers. The experimental data are consistently described by a combination of effective-medium models based on the main axes transport quantities. The results support the predicted ambipolar thermopower anisotropy in ${PdCoO}_{2}$ .

Received 29 July 2020
Accepted 6 January 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.015404

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Electrical conductivity Polycrystals Seebeck effect Synthesis Thermal conductivity Thermopower

Effective medium approach

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

P. Yordanov ¹, A. S. Gibbs^1,2, P. Kaya^1,8, S. Bette¹, W. Xie ^3,4, X. Xiao^3,4, A. Weidenkaff^3,4,5, H. Takagi^1,6,7, and B. Keimer¹

¹Max-Planck Institute for Solid State Research, 70569 Stuttgart, Germany
²ISIS Neutron and Muon Source, STFC Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
³Institute for Material Science, University of Stuttgart, 70569 Stuttgart, Germany
⁴Department of Material Science, Technical University of Darmstadt, 64289 Darmstadt, Germany
⁵Fraunhofer Research Institution for Materials Recycling and Resource Strategies (IWKS), 63457 Hanau, Germany
⁶Institute for Functional Matter and Quantum Technologies, University of Stuttgart, 70550 Stuttgart, Germany
⁷Department of Physics, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
⁸Aalen University, Materials Research Institute (IMFAA), 73430 Aalen, Germany

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Vol. 5, Iss. 1 — January 2021

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Figure 1
Crystal structure of delafossites ${PdCoO}_{2}$ and ${PtCoO}_{2}$ with space group $R \bar{3} m (D_{3 d}^{5})$ and lattice parameters $a = b = 2.830 Å$ , $c = 17.743 Å$ and $a = b = 2.823 Å$ , $c = 17.815 Å$ , respectively [1] (Visualization software, VESTA 3). The structure consists of highly conducting Pd, or Pt, layers connected by O–Pd (Pt)–O dumbbells to insulating ${CoO}_{2}$ (edge-shared ${CoO}_{6}$ octahedra) blocks, both on triangular lattices. In both compounds the transport is highly anisotropic, with anisotropies of more than two orders of magnitude for the electrical conductivity $σ_{ab} / σ_{c} \geq 100$ , and as large as $| - S_{c} | / S_{ab} \approx | - 200 | / 18 \geq 10$ (or potentially larger in ${PtCoO}_{2}$ ) for the Seebeck coefficient at high temperatures [7, 8, 9].
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Figure 2
(a) XRD ( $Cu - K_{α 1}$ radiation) pattern (logarithmic scale) of as-synthesized polycrystalline ${PdCoO}_{2}$ powder. The broad feature at low angles is due to scattering from the sample holder. The preferred orientation indicated by the higher intensity of the $00 l$ reflections is due to the platelike sample morphology in Bragg-Brentano measurement geometry. The XRD pattern refinement (Pawley) yielded lattice parameters $a = b = 2.8288 (1) Å$ , $c = 17.7451 (5) Å$ , and $V = 122.974 (7) Å^{3}$ . (b), (c) SEM images of a single crystallite and sintered polycrystalline powder pellet. (d) EBSD inverse pole figure map of a sintered polycrystalline powder pellet.
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Figure 3
(a) Experimental (open symbols) temperature-dependent resistivity $ρ$ of polycrystalline ${PdCoO}_{2}$ for two different samples measured in oxygen (circles), and helium (squares). Solid lines show results from the model fit. (b) Main axes resistivity $ρ_{ab}$ and $ρ_{c}$ of ${PdCoO}_{2}$ used in the model description of the polycrystalline samples. Note that due to the absence of experimental data for $ρ_{ab}$ and $ρ_{c}$ of single crystals at temperatures above $500 K$ , data sets obtained from thin films [9] were used. $ρ_{ab}$ and $ρ_{c}$ were then scaled according to the single crystal data reported in [4, 5]. The $ρ_{ab}$ and $ρ_{c}$ data extend only up to $820 K$ due to the reduced thermal stability of the thin films compared to bulk samples.
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Figure 4
(a) Bounds and solutions applicable to the electrical/thermal conductivity of polycrystalline ${PdCoO}_{2}$ . The shaded (green) area shows the range that describes best the trend in the experimental data $σ \to σ_{ab}$ . $σ_{ab}$ and $σ_{c}$ correspond to $1 / ρ_{ab}$ and $1 / ρ_{c}$ in Fig. 3. (b) Two-media model of a polycrystalline powder compact, consisting of (1) randomly oriented single crystal “cores” (defect free, fully dense material), described on the large scale by $σ_{pc}$ , and (2), a surrounding net characterized by effective grain boundary $σ_{gb}$ .
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Figure 5
(a) Thermal diffusivity $α$ , (b) specific heat $C_{p}$ (solid line marks the Dulong-Petit value of $C \approx 0.506 J / g K$ ), (c) total $κ$ , phononic (lattice) $κ^{ph}$ , and electronic $κ^{e}$ thermal conductivity of polycrystalline ${PdCoO}_{2}$ . Solid lines represent model fit results. (d) Calculated main axes electronic thermal conductivity $κ_{ab}^{e}$ , $κ_{c}^{e}$ , (e) simulated lattice thermal conductivity $κ_{ab}^{ph}$ , $κ_{c}^{ph}$ , (f) main axes total thermal conductivity $κ_{ab}$ , $κ_{c}$ .
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Figure 6
(a) Experimental (open symbols) and model Seebeck coefficient (solid lines) of polycrystalline ${PdCoO}_{2}$ . The small difference in the two experimental data sets may be related to the large porosity and the different thermal contact conditions between the grains in the sample provided by the oxygen and helium atmospheres, respectively. (b) Main axes Seebeck coefficient data $S_{ab}$ , $S_{c}$ of ${PdCoO}_{2}$ , from [9].
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Physical Review Materials

High-temperature electrical and thermal transport properties of polycrystalline PdCoO2

P. Yordanov, A. S. Gibbs, P. Kaya, S. Bette, W. Xie, X. Xiao, A. Weidenkaff, H. Takagi, and B. Keimer

Phys. Rev. Materials 5, 015404 – Published 28 January 2021

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High-temperature electrical and thermal transport properties of polycrystalline ${PdCoO}_{2}$