Divacancy superstructures in thermoelectric calcium-doped sodium cobaltate

D. G. Porter, M. Roger, M. J. Gutmann, S. Uthayakumar, D. Prabhakaran, A. T. Boothroyd, M. S. Pandiyan, and J. P. Goff

Phys. Rev. B 90, 054101 – Published 4 August 2014

Abstract

We have grown single crystals of ${Na}_{x} {Ca}_{y} Co O_{2}$ and determined their superstructures as a function of composition using neutron and x-ray diffraction. Inclusion of ${Ca}^{2 +}$ stabilizes a single superstructure across a wide range of temperatures and concentrations. The superstructure in the ${Na}^{+}$ layers is based on arrays of divacancy clusters with ${Ca}^{2 +}$ ions occupying the central site, and it has an ideal concentration ${Na}_{4 / 7} {Ca}_{1 / 7} Co O_{2}$ . Previous measurements of the thermoelectric properties on this system are discussed in light of this superstructure. ${Na}_{4 / 7} {Ca}_{1 / 7} Co O_{2}$ corresponds to the maximum in thermoelectric performance of this system.

Received 2 May 2014
Revised 18 July 2014

DOI:https://doi.org/10.1103/PhysRevB.90.054101

Authors & Affiliations

D. G. Porter^1,*, M. Roger², M. J. Gutmann³, S. Uthayakumar¹, D. Prabhakaran⁴, A. T. Boothroyd⁴, M. S. Pandiyan¹, and J. P. Goff¹

¹Department of Physics, Royal Holloway, University of London, Egham TW20 0EX, United Kingdom
²Service de Physique de l'Etat Condensé, (CNRS/MIPPU/URA 2464), DSM/DRECAM/SPEC, CEA Saclay, P.C. 135, F-91191 Gif Sur Yvette, France
³ISIS, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom
⁴Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom

^*D.G.Porter@rhul.ac.uk

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Vol. 90, Iss. 5 — 1 August 2014

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Images

Figure 1
Reciprocal space cuts through the $(h, k, 0)$ layer for different compositions of Na $_{x}$ Ca $_{y}$ CoO $_{2}$ , measured by single-crystal x-ray diffraction. (a) Na $_{0.65}$ Ca $_{0.1}$ CoO $_{2}$ shows a 12-fold ring of satellite peaks around the principal Bragg reflections which can be indexed on a hexagonal grid with spacing $a^{*} / 7$ . (b) Na $_{0.57}$ Ca $_{0.14}$ CoO $_{2}$ displays the same superlattice structure, but with stronger intensity. (c) Na $_{0.55}$ Ca $_{0.2}$ CoO $_{2}$ also displays the $a^{*} / 7$ superlattice peaks, plus additional peaks that lay on a $a^{*} / 4$ lattice.
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Figure 2
(a) Cuts through the reciprocal space volume for Na $_{0.57}$ Ca $_{0.14}$ CoO $_{2}$ at integer $l$ values, illustrating the variation of intensity in the superlattice peaks with $l$ . Gaps in the data are a result of missing coverage. (b) Calculated intensities from the model generated by reverse Monte Carlo, for comparison with (a).
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Figure 3
Temperature dependence of the superlattice peaks for three compositions of Na $_{x}$ Ca $_{y}$ CoO $_{2}$ . Each peak intensity is normalized by a close principal hexagonal reflection, therefore indicating the relative intensity variation between compositions. Fitting an order parameter to each data set gives disorder temperatures of $T_{d} = 379 \pm 6$ K for Na $_{0.65}$ Ca $_{0.1}$ CoO $_{2}$ , $T_{d} = 401 \pm 2$ K for Na $_{0.57}$ Ca $_{0.14}$ CoO $_{2}$ , and $T_{d} = 410 \pm 10$ K for Na $_{0.55}$ Ca $_{0.2}$ CoO $_{2}$ . The neutron data points indicate measurements during heating and cooling, showing no sign of hysteresis behavior and are consistent with the x-ray measurement.
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Figure 4
A cut in the $(h, k, 0)$ plane for Na $_{0.7}$ Ca $_{0.1}$ CoO $_{2}$ SXD data at 40 K. Satellite peaks appear in the same positions as found in the x-ray data, indicating that this is a bulk phase. Black circles and squares distinguish the two domains for the superlattice, and the red diamonds mark the {220} reflections of the epitaxial CaO impurity. Other nonindexed peaks are a result detector anomalies and noise resulting at low detector angles.
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Figure 5
Results from the RMC calculation of Na $_{0.57}$ Ca $_{0.14}$ CoO $_{2}$ x-ray data. (a) The resultant structure, where blue balls are sodium ions, purple are calcium ions, the other balls are cobalt ions, where dark green is a large negative distortion, and light green is a large positive distortion. Oxygen ions have been omitted for clarity. (b) Annealing of $χ^{2}$ during the calculation. Inset: Final comparison of calculated ( $I_{c}$ ) and experimental ( $I_{o}$ ) intensities, where the black line displays $I_{c} = I_{o}$ .
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Figure 6
Na $_{0.55}$ Ca $_{0.2}$ CoO $_{2}$ can be described by a coexistence of the Na $_{0.57}$ Ca $_{0.14}$ CoO $_{2}$ supercell in (b) and the $x = 0.5$ supercell in (c). The calculation of the $(h, k, 0)$ layer in (a) gives good agreement with the x-ray data from Fig. 1. Superlattice peaks generated by the Na $_{0.57}$ Ca $_{0.14}$ CoO $_{2}$ supercell are indicated with circles, whereas the peaks produced by the $x = 0.5$ supercell are marked by triangles.
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