Thermal expansion coefficients of Bi2Se3 and Sb2Te3 crystals from 10 K to 270 K

Abstract

Lattice constant of Bi 2 Se 3 and Sb 2 Te 3 crystals is determined by X-ray powder diffraction measurement in a wide temperature range. Linear thermal expansion coefficients (α) of the crystals are extracted, and considerable anisotropy between α and α ⊥ is observed. The low temperature values of α can be fit well by the Debye model, while an anomalous behavior at above 150 K is evidenced and explained. Grüneisen parameters of the materials are also estimated at room temperature.Recently, much attention has been given to an intriguing class of materials, the so-called topological insulators (TIs). This type of material exhibits a band gap in the bulk, but gapless states on the edge or surface, which are protected by topological order and cannot be analogized to conventional semiconductors or insulators 1,2 . Bi 2 Se 3 , Bi 2 Te 3 and Sb 2 Te 3 are among the most interested compounds of three-dimensional TIs, owing to their robust and simple surface states 3 . Although these compounds were under extensive studies in 1950s and 1960s as excellent thermoelectric materials, some basic physical properties still remain unexplored. In this letter, we present the measurements of the temperature dependent linear thermal expansion coefficients of Bi 2 Se 3 and Sb 2 Te 3 crystals using X-ray powder diffraction (XRD). Thermal expansion is the tendency of materials to change in size and shape as they heat and cool. It is essential to device design and engineering, as the induced strain could cause the deformation of the device and affect its phonon dynamics. Indeed, our recent Raman spectroscopy study of TIs has uncovered significant contributions in the temperature dependent phonon frequency shifts from the thermal expansion of the materials 4 . In addition, the knowledge of thermal expansion coefficients is necessary for the directional growth of TI crystals and the understanding of the high thermoelectric efficiency 5 .Large grain polycrystalline Bi 2 Se 3 materials (single crystal grain size >1 mm) were synthesized at Sandia National Laboratories. First, Bi 2 Se 3 pieces (99.999%, from VWR international, LLC.) were placed in an evacuated (<10 −7 Torr) quartz ampoule and melted at 800 • C for 16 hours. The melt was then cooled at 10 • C/h to 550 • C, held for 3 days at this temperature, and finally allowed to furnace cool to room temperature. Single crystals of Sb 2 Te 3 were grown by Bridgman method at Purdue University. Stoichiometric amount of high purity antimony and tellurium (99.999%) was deoxidized and purified by multiple vacuum distillations under dynamic vacuum of <10 −7 Torr, and then heated up to 900 • C.This was followed by a slow cool down under a controlled pressure to minimize tellurium defects. Afterwards, the crystals were grown at a speed of 0.5-1.5 mm/h with a linear temperature gradient set to 5 • C/cm. Bi 2 Se 3 and Sb 2 Te 3 crystals have similar rhombohedral structure with five atoms in the trigonal primitive cell. A straightforward way to visualize the structure is to use a hexagonal lattice with th...

Electrical and optical properties of epitaxial binary and ternary GeTe-Sb2Te3 alloys

“…In order to verify if this is indeed the origin of the decrease of p in Sb 2 Te 3 , the change in the hole concentration Δ p and the change in unit cell volume Δ V evaluated from Chen et al . 27 are compared with each other in Fig. 3(d).…”

Anomalous thermal expansion of Sb2Te3 topological insulator

“…Previous reports show that the thermal expansion in these materials is quite anisotropic and exhibits an anomalous temperature dependence, presumably because of the weak bonding. [3][4][5][6] Chen et al 6 studied the temperature dependence of the lattice parameters of Bi 2 Se 3 and Sb 2 Te 3 single crystals. Below 150 K, the extracted coefficient of linear thermal expansion a can be described well by the Debye model.…”

Temperature dependence of Raman-active optical phonons in Bi2Se3 and Sb2Te3

“…For Sb 2 Te 3 , the polynomial approximation with better than 1.5% accuracy in the same temperature range is given by: a(T ) = 4.24 + 9.3×10 −6 T + 1.25×10 −7 T 2 , and c(T ) = 30.18 + 3.5×10 −4 T + 7.4×10 −7 T 2 . Estimated Grüneisen parameters at 270 K are 1.4 for Bi 2 Se 3 , and 2.3 for Sb 2 Te 3 [20].…”

“…We employed X-ray powder diffraction (XRD) to measure lattice constants of Bi 2 Se 3 and Sb 2 Te 3 at temperatures between 10 K and 270 K. Details about the XRD results and their analysis are described elsewhere [20]. Using the XRD data, we find that the temperature dependence of lattice parameters in Bi 2 Se 3 can be approximated between 10 K and 270 K with better than 0.8% accuracy by the following polinomials: a(T ) = 4.13 + 1.59×10 −5 T + 8.87×10 −8 T 2 , and c(T ) = 28.48 + 2.26×10 −4 T + 6.86×10 −7 T 2 .…”