Revisiting the lattice dynamics of cubic yttria-stabilized zirconia

Shelby R. Turner, Stéphane Pailhès, Leila Ben-Mahfoud, Marc de Boissieu, Frédéric Bourdarot, Helmut Schober, Yvan Sidis, John-Paul Castellan, Andrea Piovano, Alexandre Ivanov, and Valentina M. Giordano

Phys. Rev. Materials 7, 115401 – Published 7 November 2023

Abstract

Cubic yttria-stabilized zirconia has long been a ceramic material of interest for its many uses in thermal-based applications. Its very low and weakly temperature-dependent thermal conductivity has been ascribed to the large oxygen vacancies content, which introduces disorder and strongly scatters phonons. Still, despite many experimental works in the literature, phonon dynamics has not been fully understood yet, with several points to be clarified, such as the apparent absence of optic modes throughout the Brillouin zone. In this paper, we present findings on the phonon dispersions of this material, showing experimental evidence of low-lying optical branches throughout the Brillouin zone, which reduce the pure acoustic regime for some branches. Furthermore, the observed energy dependence of the intrinsic acoustic phonon linewidths clearly suggests the existence of competing Mie and Rayleigh scattering mechanisms. Our findings allow to uncover a different phonon dynamics scenario in this material and point to a deeper understanding of heat transport in yttria-stabilized zirconia, based on two different, concomitant mechanisms, generated by the large vacancy content.

Received 21 April 2023
Accepted 28 August 2023

DOI:https://doi.org/10.1103/PhysRevMaterials.7.115401

Physics Subject Headings (PhySH)

Acoustic phonons Lattice dynamics Lattice thermal conductivity Lifetimes & widths Optical phonons Vacancies

Functional materials

Inelastic X-ray scattering Inelastic neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shelby R. Turner ^1,2,3, Stéphane Pailhès ³, Leila Ben-Mahfoud⁴, Marc de Boissieu², Frédéric Bourdarot⁵, Helmut Schober ⁶, Yvan Sidis ⁷, John-Paul Castellan ^7,8, Andrea Piovano ¹, Alexandre Ivanov ¹, and Valentina M. Giordano ^3,*

¹Institut Laue-Langevin, Grenoble, F-38042 Grenoble Cedex, France
²Université Grenoble Alpes, CNRS, Grenoble-INP, SIMaP, F-38402 St. Martin d'Hères, France
³Institute of Light and Matter, UMR5306 Université Lyon 1-CNRS, Université de Lyon, F-69622 Villeurbanne Cedex, France
⁴Laboratoire Hubert Curien, UMR5516, Université St. Etienne, F-42000 Saint-Etienne, France
⁵Université Grenoble Alpes, CEA, IRIG, MEM, MDN, F-38000 Grenoble Cedex, France
⁶European Spallation Source ERIC, P.O. Box 176, SE-221 00 Lund, Sweden
⁷Laboratoire Léon Brillouin, CEA, CNRS, UMR-12, CE-Saclay, F-91191 Gif-sur-Yvette, France
⁸Institut für Festkörperphysik, Karlsruher Institut für Technologie, D-76021 Karlsruhe, Germany

^*Author to whom correspondence should be addressed: valentina.giordano@univ-lyon1.fr

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Issue

Vol. 7, Iss. 11 — November 2023

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Images

Figure 1
High-resolution energy scans, measured by inelastic neutron scattering, of the transverse acoustic (TA) phonons propagating along [100], and polarized along [010] are plotted. (a) shows the low- $q$ part of the dispersion, where the clearly defined TA mode disperses until 9 meV, as better seen in (b). In (b), we see that the TA mode is cut off by an optical branch at 9 meV. Three higher-energy optical branches are also highlighted using the fit for the $q = 0.45$ r.l.u. point, plotted as a solid black line. Measurements were done on IN8@ILL with a fixed $k_{f} = 2.662 Å^{- 1}$ .
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Figure 2
Top left: Sketch of the cubic YSZ crystalline structure ( ${CaF}_{2}$ type, space group No. 225), with Zr atoms in blue, O atoms in green, and Y atoms in red. Open dashed circles indicate O vacancies. Top right: Brillouin zone, with the main symmetry directions reported in red: [100] ( $Γ − X, Δ$ direction), the [110] ( $Γ − K, Σ$ direction) and the [111] ( $Γ − L, Λ$ direction). Bottom: Experimental phonon dispersions at 300 K. The longitudinal acoustic (LA) phonons (red circles) have been measured by IXS, with horizontal lines representing the energies of the optical branches that were fixed in position during analysis. TA phonons (blue) have been measured by INS on 4F2@LLB (diamonds), 1T@LLB with $20^{'}$ collimation (triangles), 1T@LLB with $60^{'}$ collimation (squares), and IN8@ILL (stars). The second TA polarization in the $[ζ ζ 0]$ direction (green) is similarly a combination of INS setups (same marker symbols apply). Data have been measured around the Bragg peaks (002), (200), (220), (111), and (222) as detailed in Table S1 of the Supplemental Material [26]. Data from Argyriou et al. [20] are also reported as open gray circles. The error bars for the leftmost transversely polarized optical branches in the $[00 ζ]$ direction represent width rather than error of the energy position.
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Figure 3
Temperature dependence of representative energy scans from the transverse acoustic (TA) phonon dispersion in which phonons propagate along [100] and are polarized along [010]. Scans have been made on 4F2@LLB at 300 K (blue) and 50 K (purple) and have been corrected according to the Bose-Einstein distribution.
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Figure 4
When possible according to the different experimental setups, intrinsic linewidths have been extracted. Colors and symbols follow from Fig. 2.
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Figure 5
Normalized intensity at 300 K (colors and symbols as in Fig. 2). Longitudinal acoustic modes have been measured by IXS. All intensities have been normalized by the analyzer efficiency to compare scans across different analyzers. Transverse acoustic modes were measured by various INS setups and have been scaled to match each other in each polarization.
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