Local Sn Dipolar-Character Displacements behind the Low Thermal Conductivity in SnSe Thermoelectric

E. S. Bozin, H. Xie, A. M. M. Abeykoon, S. M. Everett, M. G. Tucker, M. G. Kanatzidis, and S. J. L. Billinge

Phys. Rev. Lett. 131, 036101 – Published 17 July 2023

Abstract

The local atomic structure of SnSe was characterized across its orthorhombic-to-orthorhombic structural phase transition using x-ray pair distribution function analysis. Substantial Sn displacements with a dipolar character persist in the high-symmetry high-temperature phase, albeit with a symmetry different from that of the ordered displacements below the transition. The analysis implies that the transition is neither order-disorder nor displacive but rather a complex crossover. Robust ferrocoupled SnSe intralayer distortions suggest a ferroelectriclike instability as the driving force. These local symmetry-lowering Sn displacements are likely integral to the ultralow lattice thermal conductivity mechanism in SnSe.

Received 13 January 2023
Revised 10 May 2023
Accepted 20 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.036101

Physics Subject Headings (PhySH)

Anharmonic lattice dynamics Chemical bonding Crystal structure Electroluminescence Jahn-Teller effect Lattice thermal conductivity Order diagnosis Phase diagrams Thermoelectric effects

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

E. S. Bozin ^1,*, H. Xie ², A. M. M. Abeykoon ³, S. M. Everett ⁴, M. G. Tucker ⁴, M. G. Kanatzidis ², and S. J. L. Billinge ⁵

¹Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, New York 11973, USA
²Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
³Photon Sciences Division, Brookhaven National Laboratory, Upton, New York 11973, USA
⁴Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁵Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA

^*bozin@bnl.gov

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Vol. 131, Iss. 3 — 21 July 2023

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Figure 1
Crystal structure of SnSe and temperature-induced phase transition. The structure features two SnSe bilayers which are related by inversion symmetry. (a) Low-temperature $P n m a$ phase. Sn is displaced from the center of the plaquette of Se ions forming strongly bonded ${SnSe}_{3}$ pyramids. The associated atomic dipolar displacements exhibit intrabilayer “ferro” and interbilayer “antiferro” ordering, as indicated by the red arrows. (b) High-temperature $C m c m$ phase. Sn is centered in the plaquette on average, resulting in a Sn-Se dumbbell motif when viewed down the $c$ axis, the apical Sn-Se being the shortest bond in the structure. To enable comparison in (a) and (b), an arbitrary stack of unit cells, depicted in the middle for $P n m a$ , along the bilayer directions is shown. Rietveld fits of neutron powder diffraction data confirm the average sample structure across the transition: $P n m a$ at 300 K (c) and $C m c m$ at 975 K (d). Evolution of the in-plane lattice parameters and the $C m c m$ $(200) / (002)$ reflection across the transition ( $T_{s} \approx 840 K$ ) are shown in the insets in (c) and (d).
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Figure 2
Assessment of the structure of SnSe over different length scales. (a) Measured reduced x-ray total scattering function $F (Q)$ at 300 (blue line) and 1070 K (red line). (b),(c) Representative PDFs from different temperatures are shown (b) calculated from the average structure by Bragg scattering fits [43] (see Supplemental Material [53] for more information) and (c) from total scattering measurements. The PDFs from the extremal temperatures are plotted in red (hot) and blue (cool) colors. Intermediate temperatures are shown in gray. Solid (dotted) red arrows indicate the presence (absence) of features discussed in the text. (d) Temperature evolution of atomic displacement parameters (ADPs) obtained from $P n m a$ and $C m c m$ PDF models fit over the $r$ range $10 \leq r \leq 60 Å$ . The abscissa is the reduced temperature $τ = (T - T_{s}) / T_{s}$ , where $T_{s}$ is the phase transition temperature. Different colored curves are from anisotropic Sn ADPs, with components parallel and perpendicular to the layers, and isotropic Se ADPs, as indicated. A sizable enhancement of the in-plane ADP component is seen at $T > T_{s}$ , marked by a black arrow, indicative of planar disordering of the Sn in the high-temperature phase. The inset shows the fit residual $r_{w} (T)$ for the two models. Fits of average structure models over the entire $r$ range for 300 and 1070 K are shown in (e) and (f), respectively. Difference traces between the calculated and measured PDF, $Δ G$ , in green are offset for clarity. In (g) and (h), the same fits are shown expanded on the low- $r$ region. An observable discrepancy is seen between the $C m c m$ model and 1070 K data on a subnanometer length scale, resulting in an increase of $r_{w}$ . The Sn environments expected from the average structure by Bragg scattering are depicted in (i) and (j). In the $P n m a$ structure the Sn is displaced sideways from being directly below Se, whereas in the $C m c m$ average structure the Sn is directly below it. Labels $A$ and $P$ refer to apical and in-plane Se, respectively. The arrow in (h) marks a feature expected in the $C m c m$ symmetry model, associated with the Sn being centered in the Se plaquette, which is clearly absent in the data.
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Figure 3
Local symmetry-breaking Sn displacements in SnSe at $T > T_{s}$ . (a) The fit to 1070 K data of the local distorted model [shown in the inset in (b) and (c)] featuring split Sn sites. The corresponding difference trace $Δ G$ (black) is offset for clarity. The gray difference trace is that of the $C m c m$ model from Fig. 2, which is shown as a reference. (b) The distorted model, labeled here as “local,” results in ADP magnitudes substantially reduced as compared to these observed by undistorted models. The ADPs obtained from $P n m a$ and $C m c m$ , shown in Fig. 2, are reproduced as solid lines. (c) The magnitude of the Sn displacements away from the center of the plaquette vs reduced temperature, and absolute temperature, as seen by high-resolution powder diffraction [43], and $10 \leq r \leq 60 Å$ range PDF $P n m a$ model fits. The ${Se}_{4}$ plaquette is nearly a square in $C m c m$ , and, to preserve the average symmetry, the local model allows for displacements in four directions indicated by block arrows in the inset. (d) The estimated correlation length of local distortions, as described in the text. Insets to the left: the displacement coupling, shown in a $2 \times 1 \times 2 C m c m$ supercell, of the best model where the couplings are explicitly tested. Inset to the right: temperature-dependent lattice parameter along the bilayer stacking direction ( $b$ axis of the $C m c m$ model in red, $a$ axis of the $P n m a$ model in blue). Note the change in slope at temperature $T_{s}$ .
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