Dynamic crystallography reveals spontaneous anisotropy in cubic GeTe

Abstract

Cubic energy materials such as thermoelectrics or hybrid perovskite materials are often understood to be highly disordered^1,2. In GeTe and related IV-VI compounds, this is thought to provide the low thermal conductivities needed for thermoelectric applications¹. Since conventional crystallography cannot distinguish between static disorder and atomic motions, we develop the energy-resolved variable-shutter pair distribution function technique. This collects structural snapshots with varying exposure times, on timescales relevant for atomic motions. In disagreement with previous interpretations^3-5, we find the time-averaged structure of GeTe to be crystalline at all temperatures, but with anisotropic anharmonic dynamics at higher temperatures that resemble static disorder at fast shutter speeds, with correlated ferroelectric fluctuations along the <100>_c direction. We show that this anisotropy naturally emerges from a Ginzburg-Landau model that couples polarization fluctuations through long-range elastic interactions⁶. By accessing time-dependent atomic correlations in energy materials, we resolve the long-standing disagreement between local and average structure probes^1,7-9 and show that spontaneous anisotropy is ubiquitous in cubic IV-VI materials.

Fig. 1. Local distortion in GeTe and fits to X-ray PDFs in the R3m and Fm-3m phases.

a, Electronic structure of IV–VI materials consists of orthogonal one-dimensional bands made up of valence p orbitals. These are susceptible to Peierls distortions, resolved in GeTe by a <111> shift in the Ge sublattice. b, Apparent disorder in c-GeTe; note the splitting of the purple Ge sites. c, Fit to the room-temperature PDF of GeTe using the R3m structure (goodness-of-fit R_w = 0.087) (top). Peaks corresponding to several important distances are highlighted. The best fit of our split-site model for c-GeTe at 825 K (R_w = 0.104) (bottom).

Fig. 2. Instantaneous and time-averaged neutron scattering results for c-GeTe at 720 K using 300 meV neutrons.

a, Instantaneous (total) PDF fitted with the average rock-salt c-GeTe structure. Obvious peak splittings and sharpening are found at low r. The first coordination shell splitting is shown in the inset, and the purely inelastic PDF extracted by the PCA analysis is shown to replicate the misfits between the average and instantaneous structures. The asterisk highlights the <100>_c peak. b, Elastic PDF extracted using the PCA analysis, also showing a fit to the average NaCl structure. The peak splitting of the first coordination shell and <100>_c sharpening are completely absent. The asterisk highlights the <100>_c peak. c, Structure factors, Q × [S(Q) – 1], determined for the total (instantaneous) and elastic (time-averaged) scattering of GeTe at 720 K using ARCS. A significant extra oscillation is present in the total integrated structure factor, showing that the 2.88 Å real-space splitting is dynamic.

Fig. 3. Calculated TDS and phonon dispersion for c-GeTe.

a, Comparison of the energy-integrated (E_i = 120 meV) scattering and simulation at 720 K. Note the excellent agreement of the background TDS intensity. b, Phonon dispersion extracted from ab initio MD simulations. In contrast to T = 0 K DFT, the structure is found to be dynamically stable. c, Observed and calculated PDOS for c-GeTe at 720 K. The results are shown for a harmonic calculation from phonon dispersion and directly from the MD simulation using the velocity autocorrelation function (VACF).

Fig. 4. Temperature dependence of real-space dynamics and emergence of strain in GeTe.

a, Real-space TDS for c-GeTe at 898 K. This signal (which appears in the residual) was isolated by fitting the average structure to the xPDF data in 20 < r < 50 Å, and calculating G_obs(r) − G_calc(r) over the r range shown. b, Temperature dependence of the anisotropic correlated motion in GeTe. The plot shows the peak height of the selected features in the residual (G(r) – G_obs(r)); lines are guides to the eye. The data are normalized by the fitted scale factor at each temperature. c, Schematic of the real-space anisotropy that arises from our model of coupled ferroelectric fluctuations and shear strains. The coupling along <10> is enhanced whereas those along <11> are reduced in this two-dimensional schematic.