Combined electronic and thermodynamic approaches for enhancing the thermoelectric properties of Ti-doped PbTe

Abstract

Lead telluride based compounds are of great interest due to their enhanced thermoelectric transport properties. Nevertheless, the donor type impurities in this class of materials are currently mainly limited and alternative types of donor impurities are still required for optimizing the thermoelectric performance. In the current research titanium as a donor impurity in PbTe is examined. Although titanium is known to form resonant levels above the conduction band in PbTe, it does not enhance the thermo-power beyond the classical predictions. Recent experiments showed that alloying with a small amount of Ti (∼0.1 at%) gives a significant increase in the figure of merit. In the current research ab initio calculations were applied in order to correlate the reported experimental results with a thermoelectric optimization model. It was found that a Ti concentration of ∼1.4 at% in the Pb sublattice is expected to maximize the thermoelectric power factor. Using a statistical thermodynamic approach and in agreement with the previously reported appearance of a secondary intermetallic phase, the actual Ti solubility limit in PbTe is found to be ∼0.3 at%. Based on the proposed model, the mechanism for the formation of the previously observed secondary phase is attributed to phase separation reactions, characterized by a positive enthalpy of formation in the system. With extrapolation of the obtained ab initio results, it is demonstrated that lower Ti-doping concentrations than previously experimentally reported ones are expected to provide power factor values close to the maximal one, making doping with Ti a promising opportunity for the generation of highly efficient n-type PbTe-based thermoelectric materials.

Optimized Strategies for Advancing n-Type PbTe Thermoelectrics: A Review

“…Theoretical calculations also show that alloying divalent IIB group elements (Zn, Cd, and Hg) ,− ,− or transition metals (Cr, Fe, Co, Ni, Ti, and Ta) − can introduce resonance states near the bottom of the conduction band of PbTe. However, it shows no significant increase in the density of states in both n-type PbTe–ZnTe and PbTe–CdTe alloys at 298 K (Figure b).…”

“…(a) Schematic image of resonate states, and (b) Hall carrier concentration-dependent Seebeck coefficient for n-PbTe thermoelectrics at room temperature. ,,,,,,,,,,,,− ,− …”

“…Similar phenomena also occur in transitional elements. Experimentally, Ti − and Cr − supply resonance impurity levels located in the conduction band at low temperatures, whereas the energy level moves to the gap as the temperature increases. Generally, the lower energy and the more localized d-electron of transition metals are not conducive to achieving a significant resonance effect, and high temperature will invalidate the resonance effect due to the Fermi level pinning.…”

Physical Metallurgy Inspired Nano‐Features for Enhancement of Thermoelectric Conversion Efficiency

“…For systems that are more complicated than the above, computational methods are required to evaluate PDs. A unique combination of total energy DFT calculations and statistical thermodynamics is employed to predict solubility limit of Ti in PbTe, providing us with better predictive power and accuracy at elevated temperatures . Hence, the determination of phase decomposition in supersaturated states is enabled.…”

Dopant solubility in ceria: alloy thermodynamics combined with the DFT+U calculations

“…the atom B (Tb, in our case) at the site ⃗ of the lattice. Such approach was successfully used previously to analyze the initial stages of the growth of thin metallic films on the ceramic substrate[43][44][45][46], to explain the behavior of complex perovskites[47- 50], and for description of the phase competition and solubility of doping elements in some thermoelectric compounds[51][52][53]. It is based on the treatment of the ordering phases in the crystalline structure of solid solution which are stable with respect to the formation of antiphase domains.…”