Close-packed layer spacing as a practical guideline for structure symmetry manipulation of IV-VI/I-V-VI₂ thermoelectrics

Abstract

The crystal-structure symmetry in real space can be inherited in the reciprocal space, making high-symmetry materials the top candidates for thermoelectrics due to their potential for significant electronic band degeneracy. A practical indicator that can quantitatively describe structural changes would help facilitate the advanced thermoelectric material design. In face-centered cubic structures, the spatial environment of the same crystallographic plane family is isotropic, such that the distances between the close-packed layers can be derived from the atomic distances within the layers. Inspired by this, the relationship between inter- and intra-layer geometric information can be used to compare crystal structures with their desired cubic symmetry. The close-packed layer spacing was found to be a practical guideline of crystal structure symmetry in IV-VI chalcogenides and I-V-VI₂ ternary semiconductors, both of which are historically important thermoelectrics. The continuous structural evolution toward high symmetry can be described by the layer spacing when temperature or/and composition change, which is demonstrated by a series of pristine and alloyed thermoelectric materials in this work. The layer-spacing-based guideline provides a quantitative pathway for manipulating crystal structures to improve the electrical and thermal properties of thermoelectric materials.

Keywords

phase transition / structure manipulation / thermoelectric materials / x-ray diffraction

References

[1] Mori T. Novel principles and nanostructuring methods for enhanced thermoelectrics. Small. 2017;13(45):1702013.

[2] Bell LE. Cooling, heating, generating power, and recovering waste heat with thermoelectric systems. Science. 2008;321(5895):1457-1461.

[3] Zhu T, Liu Y, Fu C, Heremans JP, Snyder JG, Zhao X. Compromise and synergy in high-efficiency thermoelectric materials. Adv Mater. 2017;29(14):1605884.

[4] Goldsmid HJ. Introduction to Thermoelectricity. Vol 121. Springer; 2016.

[5] Pei YZ, Wang H, Snyder GJ. Band engineering of thermoelectric materials. Adv Mater. 2012;24(46):6125-6135.

[6] Pei YZ, Shi XY, LaLonde A, Wang H, Chen LD, Snyder GJ. Convergence of electronic bands for high performance bulk thermoelectrics. Nature. 2011;473(7345):66-69.

[7] Lin SQ, Li W, Chen ZW, Shen JW, Ge BH, Pei YZ. Tellurium as a high-performance elemental thermoelectric. Nat Commun. 2016;7(1):7.

[8] Heremans JP, Jovovic V, Toberer ES, et al. Enhancement of thermoelectric efficiency in PbTe by distortion of the electronic density of states. Science. 2008;321(5888):554-557.

[9] Li W, Zheng LL, Ge BH, et al. Promoting SnTe as an eco-friendly solution for p-PbTe thermoelectric via band convergence and interstitial defects. Adv Mater. 2017;29(17):29.

[10] Pei YZ, LaLonde AD, Wang H, Snyder GJ. Low effective mass leading to high thermoelectric performance. Energ Environ Sci. 2012;5(7):7963.

[11] Wang H, Pei YZ, LaLonde AD, Snyder GJ. Weak electron-phonon coupling contributing to high thermoelectric performance in n-type PbSe. Proc Natl Acad Sci U S A. 2012;109(25):9705-9709.

[12] Li J, Zhang XY, Chen ZW, et al. Low-symmetry rhombohedral GeTe thermoelectrics. Joule. 2018;2(5):976-987.

[13] Vining CB. CRC Handbook of Thermoelectrics. CRC Press; 1995:329.

[14] Kim SI, Lee KH, Mun HA, et al. Dense dislocation arrays embedded in grain boundaries for high-performance bulk thermoelectrics. Science. 2015;348(6230):109-114.

[15] Chen Z, Ge B, Li W, et al. Vacancy-induced dislocations within grains for high-performance PbSe thermoelectrics. Nat Commun. 2017;8(1):13828.

[16] Xin J, Wu H, Liu X, Zhu T, Yu G, Zhao X. Mg vacancy and dislocation strains as strong phonon scatterers in Mg₂Si_1−xSb_x thermoelectric materials. Nano Energy. 2017;34:428-436.

[17] Carruthers P. Scattering of phonons by elastic strain fields and the thermal resistance of dislocations. Phys Rev. 1959;114(4):995-1001.

[18] Liu W, Tan XJ, Yin K, et al. Convergence of conduction bands as a means of enhancing thermoelectric performance of n-Type Mg₂Si_1−xSn_x solid solutions. Phys Rev Lett. 2012;108:166601.

[19] Cheng K, Bu ZL, Tang J, et al. Efficient Mg₂Si_0.3Sn_0.7 thermoelectrics demonstrated for recovering heat of about 600 K. Mater Today Phys. 2022;28:100887.

[20] Liu X, Zhu T, Wang H, et al. Low electron scattering potentials in high performance Mg₂Si_0.45Sn_0.55 based thermoelectric solid solutions with band convergence. Adv Energy Mater. 2013;3(9):1238-1244.

[21] Tang YL, Gibbs ZM, Agapito LA, et al. Convergence of multi-valley bands as the electronic origin of high thermoelectric performance in CoSb₃ skutterudites. Nat Mater. 2015;14(12):1223-1228.

[22] Kajikawa Y. Refined analysis of the transport properties of Co1-NiSb₃ according to a model including a deep donor level and the second lowest valleys of the conduction band. J Alloys Compd. 2015;621:170-178.

[23] Tyagi K, Gahtori B, Bathula S, Auluck S, Dhar A. Band structure and transport studies of copper selenide: an efficient thermoelectric material. Appl Phys Lett. 2014;105(17):105.

[24] Barabash S, Ozolins V. Order, miscibility, and electronic structure ofAg(Bi,Sb)Te₂ alloys and (Ag,Bi,Sb)Te precipitates in rocksalt matrix: a first-principles study. Phys Rev B. 2010;81(7):075212.

[25] May AF, Flage-Larsen E, Snyder GJ. Electron and phonon scattering in the high-temperature thermoelectric La₃Te_4−zM_z(M = Sb,Bi). Phys Rev B. 2010;81(12):125205.

[26] Wunderlich W, Amano M, Matsumura Y. Electronic band-structure calculations of Ba₈Me_xSi_46−x clathrates with me = Mg, Pd, Ni, Au, Ag, Cu, Zn, Al, Sn. J Electron Mater. 2014;43(6):1527-1532.

[27] Fu C, Bai S, Liu Y, et al. Realizing high figure of merit in heavy-band p-type half-Heusler thermoelectric materials. Nat Commun. 2015;6(1):8144.

[28] Li S, Hou S, Xue W, et al. Manipulation of phase structure and Se vacancy to enhance the average thermoelectric performance of AgBiSe₂. Mater Today Phys. 2022;27:100837.

[29] Sarkar D, Roychowdhury S, Arora R, et al. Metavalent bonding in GeSe leads to high thermoelectric performance. Angew Chem Int ed. 2021;60(18):10350-10358.

[30] Roychowdhury S, Ghosh T, Arora R, Waghmare UV, Biswas K. Stabilizing n-type cubic GeSe by entropy-driven alloying of AgBiSe₂: ultralow thermal conductivity and promising thermoelectric performance. Angew Chem Int Ed. 2018;57(46):15167-15171.

[31] Chandra S, Arora R, Waghmare UV, Biswas K. Modulation of the electronic structure and thermoelectric properties of orthorhombic and cubic SnSe by AgBiSe₂ alloying. Chem Sci. 2021;12(39):13074-13082.

[32] Liu H-X, Zhang X-Y, Bu Z-L, Li W, Pei Y-Z. Thermoelectric properties of (GeTe)_1−x[(Ag₂Te)_0.4(Sb₂Te₃)_0.6]_x alloys. Rare Metals. 2022;41(3):921-930.

[33] Zhao T, Yang L-Z, Zhou Y, et al. Thermoelectric performance of (AgBiTe₂)_1−x(SnTe)_x with stable cubic enabled by enhanced configurational entropy. Rare Metals. 2022;41(12):4149-4155.

[34] Luo Y, Hao S, Cai S, et al. High thermoelectric performance in the new cubic semiconductor AgSnSbSe₃ by high-entropy engineering. J Am Chem Soc. 2020;142(35):15187-15198.

[35] Yan M, Geng H, Jiang P, Bao X. Glass-like electronic and thermal transport in crystalline cubic germanium selenide. J Energy Chem. 2020;45:83-90.

[36] Samanta M, Ghosh T, Arora R, Waghmare UV, Biswas K. Realization of both n- and p-type GeTe thermoelectrics: electronic structure modulation by AgBiSe₂ alloying. J Am Chem Soc. 2019;141(49):19505-19512.

[37] Shu HW, Jaulmes S, Ollitrault-Fichet R, Flahaut J. Système As-Ge-Te. J Solid State Chem. 1987;69(1):48-54.

[38] Glatz AC, Pinella A. X-ray and neutron diffraction studies of the high-temperature-phase of the AgBiSe₂/AgBiS₂ system. J Mater Sci. 1968;3(5):498-501.

[39] Böcher F, Culver SP, Peilstöcker J, Weldert KS, Zeier WG. Vacancy and anti-site disorder scattering in AgBiSe₂ thermoelectrics. Dalton Trans. 2017;46(12):3906-3914.

[40] Shuling W, Meng J, Lianjun W, Wan J. n-type Pb-free AgBiSe₂ based thermoelectric materials with stable cubic phase structure. J Inorg Mater. 2023;38(7):807-814.

[41] Liu H, Zhang X, Li J, et al. Band and phonon engineering for thermoelectric enhancements of rhombohedral GeTe. ACS Appl Mater Interfaces. 2019;11(34):30756-30762.

[42] Chattopadhyay T, Boucherle JX, VonSchnering HG. Neutron diffraction study on the structural phase transition in GeTe. J Phys C: Solid State Phys. 1987;20(10):1431-1440.

[43] Bierly JN, Muldawer L, Beckman O. The continuous rhombohedral-gubic transformation in GeTe-SnTe alloys. Acta Metall. 1963;11(5):447-454.

[44] Goto Y, Nishida A, Nishiate H, et al. Effect of Te substitution on crystal structure and transport properties of AgBiSe₂ thermoelectric material. Dalton Trans. 2018;47(8):2575-2580.

[45] Wang D-Z, Liu W-D, Li M, et al. Hierarchical architectural structures induce high performance in n-type GeTe-based thermoelectrics. Adv Funct Mater. 2023;33(14):2213040.

[46] Woolley JC, Nikolić PM. Some properties of GeTe-PbTe alloys. J Electrochem Soc. 1965;112(1):82.

[47] Parker SG, Pinnell JE, Johnson RE. Growth of large crystals of (Pb,Ge)Te and (Pb,Sn)Te. J Electron Mater. 1974;3(4):731-746.

[48] Hohnke DK, Holloway H, Kaiser S. Phase relations and transformations in the system PbTe-GeTe. J Phys Chem Solid. 1972;33(11):2053-2062.

[49] Toby BH, Von Dreele RB. GSAS-II: the genesis of a modern open-source all purpose crystallography software package. J Appl Cryst. 2013;46(2):544-549.

[50] Bergerhoff G, Hundt R, Sievers R, Brown I. The inorganic crystal structure data base. J Chem Inf Comput Sci. 1983;23(2):66-69.

[51] Belsky A, Hellenbrandt M, Karen VL, Luksch P. New developments in the inorganic crystal structure database (ICSD): accessibility in support of materials research and design. Acta Crystallogr Sect B: Struct Sci. 2002;58(3):364-369.

RIGHTS & PERMISSIONS

2023 The Authors. InfoMat published by UESTC and John Wiley & Sons Australia, Ltd.