Vacancy-mediated anomalous phononic and electronic transport in defective half-Heusler ZrNiBi

Abstract

Studies of vacancy-mediated anomalous transport properties have flourished in diverse fields since these properties endow solid materials with fascinating photoelectric, ferroelectric, and spin-electric behaviors. Although phononic and electronic transport underpin the physical origin of thermoelectrics, vacancy has only played a stereotyped role as a scattering center. Here we reveal the multifunctionality of vacancy in tailoring the transport properties of an emerging thermoelectric material, defective n-type ZrNiBi. The phonon kinetic process is mediated in both propagating velocity and relaxation time: vacancy-induced local soft bonds lower the phonon velocity while acoustic-optical phonon coupling, anisotropic vibrations, and point-defect scattering induced by vacancy shorten the relaxation time. Consequently, defective ZrNiBi exhibits the lowest lattice thermal conductivity among the half-Heusler family. In addition, a vacancy-induced flat band features prominently in its electronic band structure, which is not only desirable for electron-sufficient thermoelectric materials but also interesting for driving other novel physical phenomena. Finally, better thermoelectric performance is established in a ZrNiBi-based compound. Our findings not only demonstrate a promising thermoelectric material but also promote the fascinating vacancy-mediated anomalous transport properties for multidisciplinary explorations.

Fig. 1

Comparison of room-temperature lattice thermal conductivity among HHs and other typical thermoelectric (TE) materials^,,.

Fig. 2. Crystallographic properties of defective ZrNiBi.

a V_Zr-concentration-dependent XRD patterns for ZrNiBi-based compounds. b Crystal structure of phase-pure Zr_0.88NiBi. Green, red, purple, and white spheres represent Zr, Ni, Bi, and Zr vacancy, respectively. c Low-magnification TEM image of Zr_0.88NiBi. Twinning-structure-induced string contrasts are indicated by arrows. d Atomic-resolution HAADF-STEM image showing the twofold twinning structure of Zr_0.88NiBi. Yellow dash-dotted lines represent the boundary between the matrix and the primary twin T1 and blue dashed lines delineate the region of the secondary nanotwin T2. Inset: corresponding FFT diffraction pattern showing the superposition of diffraction spots from the matrix (red solid circles), the primary twin (yellow solid circles), and the secondary nanotwin (blue dotted circles). e HAADF-STEM image showing the atomic configuration of a single domain of Zr_0.88NiBi and f the corresponding intensity profile within the 4a plane (region marked by the yellow dashed rectangle in e).

Fig. 3. Phononic properties of defective ZrNiBi.

a Comparison of temperature-dependent lattice thermal conductivity among Zr_0.88NiBi, ZrCoBi, and Nb_0.8CoSb. b Experimentally determined sound velocity of various HHs with respect to their average atomic mass^,–. The gray shaded region shows the trend of $v_s~{\left(\overline{M}\right)}^{-1/2}$ and the corresponding data of possible HHs are from the AFLOWLIB.org database (see details in the Supplemental Material). Calculated two-dimensional ELFs along the $\left(01\overline{1}\right)$ plane together with corresponding bond lengths for c Zr_0.88NiBi and d ZrCoBi. Thin gray circle-like and thick black crescent-like contour lines correspond to the ELF values of 0.8 and 0.85, respectively. Calculated phonon dispersion, PDOS, and ADPs for e Zr_0.88NiBi and f ZrCoBi. Ranges of ADPs for all atoms in the supercell of Zr_0.88NiBi (see Figure S4) are shown in (e).

Fig. 4. Electronic properties of defective ZrNiBi.

a Calculated unfolded electronic band structure of Zr_0.88NiBi. b Pisarenko relation of Zr_0.88NiBi in comparison to that of ZrNiSn, ZrNiPb, ZrCoSb, and ZrCoBi. Symbols: experimental data. Dashed lines: obtained from the SPB model. Temperature-dependent c Seebeck coefficient and d electrical conductivity of Zr_0.88Ni_1-xCo_xBi. e Comparison of the electronic contribution to total heat conduction between Zr_0.88NiBi (top panel) and Zr_0.88Ni_0.57Co_0.43Bi (bottom panel). f Composition-dependent electronic thermal conductivity and power factor (top panel) and reduced Fermi energy (bottom panel) for Zr_0.88Ni_1-xCo_xBi.

Fig. 5. Thermoelectric properties of defective ZrNiBi.

a Temperature-dependent ZT of Zr_0.88Ni_1-xCo_xBi and Zr_0.88Ni_0.57Co_0.43Bi_0.9Sb_0.1. Comparisons of b temperature-dependent ZT and c average ZT between Zr_0.88Ni_0.57Co_0.43Bi_0.9Sb_0.1 and various typical n-type HHs^,,,,,,–.