- Email: [email protected]

Contents lists available at ScienceDirect

Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom

Exploration of thermoelectricity in ScRhTe and ZrPtPb Half Heusler compounds: A ﬁrst principle study Kulwinder Kaur*, Jaswinder Kaur Department of Physics, Panjab University, Chandigarh, 160014, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 February 2017 Received in revised form 1 April 2017 Accepted 1 May 2017 Available online 3 May 2017

Motivated by the results of other well known Half Heusler compounds, the structural, electronic, phonon and thermoelectric properties of two novel Half Heusler compounds ScRhTe and ZrPtPb are thoroughly investigated with the frame work of ﬁrst principle calculations and semi classical Boltzmann equations with constant relaxation time approximation. These materials show direct band semiconductors nature with band gap 0.43 eV (ScRhTe) and 0.83 eV (ZrPtPb) respectively. The phonon dispersion curves indicate that these compounds are thermodynamically stable. The Seebeck coefﬁcient, electrical conductivity, electronic thermal conductivity and power factor as function of chemical potential are evaluated in this report. These materials have high power factor for n-type doping. The lattice thermal conductivity of these materials decreases with increase in temperature. The calculated results divulge that these materials are potential candidates for thermoelectric applications. © 2017 Elsevier B.V. All rights reserved.

Keywords: Density functional theory Thermoelectric properties Half Heusler compounds Electronic structure

1. Introduction Thermoelectric materials are of contemporary attention because of their ability to convert heat into electricity and vice versa. The performances of these materials are characterized by dimensionless ﬁgure of merit (ZT). The ﬁgure of merit (ZT) is deﬁned as:

ZT ¼

S2 s T ke þ kl

(1)

where S, s, ke , T and kl are the Seebeck coefﬁcient, electrical conductivity, electronic thermal conductivity, absolute temperature and lattice thermal conductivity. Probing for novel thermoelectric materials with high power factor (S2 s) and low thermal conductivity (k ¼ ke þ kl) is challenging now days. Diverse materials have been identiﬁed like Bi2Te3 [1,2], Si1-xGex [3,4], complex chalcogenides [5,6] and Skutterudites [7,8] etc. as a potential thermoelectric materials. Heusler compounds have attractive intention in science community because of their applications like spintronics, thermoelectric, superconductors and topological insulators [9]. In the last decade, the Half Heusler compounds with 18 valence electrons have emerged as promising materials for thermoelectric * Corresponding author. E-mail address: [email protected] (K. Kaur). http://dx.doi.org/10.1016/j.jallcom.2017.05.005 0925-8388/© 2017 Elsevier B.V. All rights reserved.

applications [10e13]. These materials have small band gap and large value of Seebeck coefﬁcient. The tremendous advantage of these materials is that they can be easily synthesized as dense sample [14] and their efﬁciency can be enhanced via doping or by introducing defects and impurities. Another motive to reﬂect on these materials is the high value of power factor which is imperative criteria for thermoelectric applications. The Half Heusler compounds MNiSn (M ¼ Ti, Zr, Hf) with ﬁgure of merit (ZT) lying in range 0.7e1.5 are most reliable compounds [15e17]. In p-type XCoSb (X ¼ Ti, Zr, Hf) compounds, the maximum value of ZT~1.0 is obtained at 1097 K [18e20]. Recently NbFeSb Half Heusler compounds have great interest because of their high value of ZT~1.5 at 1200 K for p-type doping [21e24]. However their ZT is improved by playing with different types of doping, nanostructuring etc. The lattice thermal conductivity of TiNiSn and ZrCoSb Half Heusler compounds have been investigated with ﬁrst principle calculations and obtained results are in good agreement with available experimental data [25,26]. Recently YNiBi [27] material has been found having low thermal conductivity with very low value of ﬁgure of merit. Recently Zunger and his coworker synthesized new Half Heusler compounds (ZrNiPb and HfNiPb) with small band gaps [28]. Zunger et al. have found that these materials are semiconductor in nature. To the best of my knowledge, no theoretical and experimental works are available on these systems. The aim of this paper is to systematically investigate the electronic structure, structural properties, phonon properties and thermoelectric

298

K. Kaur, J. Kaur / Journal of Alloys and Compounds 715 (2017) 297e303

properties of these two Half Heusler compounds. The key points of this work which makes it better as compared to other theoretical works present in literature are. 1. The electronic structures and electronic thermoelectric properties have considered. 2. The analysis of the stability of these materials, a detailed description of phonon properties. 3. The thermal transport properties arising from phonon (lattice thermal conductivity) have been evaluated. 4. Lattice constants, bulk modulus (B), pressure derivative of bulk modulus (B0 ) and speciﬁc heat at constant volume of these materials have been calculated. The paper is organized as follows: in next section, computational methods are discussed; in third section the main results and discussion are elaborated. The conclusions drawn from this work are given in last section. 2. Computational methods The methodology used in this work has been explained in our earlier work [29,30]. The pseudo potential plane wave method within density functional theory as implemented in Quantum Espresso simulation package [31] was used for the computation of structural and electronic properties of these materials. In this work, Generalized Gradient Approximation (GGA) [32] with Perdew Burke- Ernzerhof (PBE) was adopted for exchange correlation functional. The plane wave cut off energy was set to be 40 Ryd and 16 16 16 k-mesh was used under MonkhorstePack scheme [33]. The convergence criteria for total energy and atomic force were set 105 Ryd and 104 Ryd/bohr, respectively. Using output and symmetry of Quantum Espresso code, we have calculated the electronic thermoelectric properties of these compounds. To ﬁnd these properties, BoltzTraP code [34] has been used which is based on constant relaxation time approximation and rigid band approximation [RBA] [35,36]. With this code thermoelectric properties are calculated with respect to the relaxation time (t). To calculate lattice thermal conductivity (kl), ShengBTE code [37] based on phonon Boltzmann transport equation (pBTE) has been used. This code is based on the second-order (harmonic) and thirdorder (anharmonic) interatomic force constants (IFCs) combined with a full solution of the pBTE and successfully predict the lattice thermal conductivity (kl) [38,39]. Quasi Harmonic approximation (QHA) [40] implemented in Quantum espresso Code [31] was used to calculate the speciﬁc heat of the lattice.

Table 1 The calculated values of lattice constants, bulk modulus (B), Pressure derivative of 0 bulk modulus (B ) and band gap of ScRhTe and ZrPtPb. Materials

Properties

Calculated

Others

ScRhTe

Lattice constant bulk modulus (B) Pressure derivative of B Band Gap (eV) Lattice constant bulk modulus (B) Pressure derivative of B Band Gap(eV)

6.335 79.3 3.96 0.43 6.537 126.01 4.61 0.83

6.350 e e 0.75 6.518 e e 1.01

ZrPtPb

By using the optimized lattice constant, we have calculated the electronic band structures along high symmetry k-points as shown in Fig. 1(a) and Fig. 2 (a). The calculated band structures indicate that both materials are direct band gap semiconductors (Fig. 1(a)) and their band gap values are shown in Table 1. In both compounds, the highest occupied valence band (HOVB) lies at t point and the lowest unoccupied conduction band (LUCB) lie at K high symmetry point. The existence of band gap in Half Heusler compounds with 18 valence electrons is explained by Galanakis et al. [42] on the basis of DMSO-d6 hybridization. The participation of d eorbitals in Half Heusler compounds is responsible for creating a band gap which is known as DMSO-d6 band gap. To analyze the contribution of different atomic orbitals, total density of states (DOS) and projected density of states (PDOS) are plotted in Figs. 1(b) and 2(b). In ScRhTe, d-states of Rh give maximum contribution in valence band region and Sc ed states contributes maximum in conduction band region. In ZrPtPb, the valence band composes with mixing of dstates of Pt, Pb s-states and Zr d-states. Pt d-states gives maximum contribution in valance band and Zr d-states gives maximum contribution in conduction band. The hybridization of DMSO-d6 orbital takes place near the Fermi level. In both the materials, the present of sharp band in conduction band indicate that these materials have high power factor in n-type composition. From the above discussion, we can say that d-electrons of elements play a major role in thermoelectric properties. To analyze the stability of these compounds, we have also calculated the phonon dispersion and phonon density of states and is depicted in Figs. 3 and 4. There is no occurrence of negative frequency, which shows that this material is thermodynamically stable. There are three atoms in primitive unit cell which give rise to the nine phonon branches including six optical modes and three acoustic modes. The calculated total phonon density of states is used to estimate the temperature dependent speciﬁc heat (Cv) of systems in a quasi eharmonic approximation. The constant evolume speciﬁc heat (Cv) is written as

3. Results and discussion

Z∞

3.1. Structural and electronic properties

Cv ðTÞ ¼ KB

The lattice parameter and bulk modulus have been calculated by computing the total energy for different volumes and ﬁtted to Murnaghan's equation of state [41].

PðVÞ ¼

B0 B00

V V0

B0

0

1

(2)

where P is the pressure, V0 is the reference volume, V is the deformed volume, B0 is the bulk modulus, and B00 is the derivative of the bulk modulus with respect to pressure. The structural parameters of relaxed ScRhTe and ZrPtPtb compounds are presented in Table 1 and our ﬁndings show close agreement with the previous works [28].

0

exp ħku B 2 FðuÞdu ħ u exp k 1 ħu kB T

2

(3)

B

where kB is Boltzmann's constant, ħ is Planck's constant, FðuÞ is the phonon density of states and T is temperature (see Fig. 5). 3.2. Thermoelectric properties The variation of Seebeck coefﬁcient of these materials with temperature and concentration is depicted in Fig. 6. In both materials, the maximum value of Seebeck Coefﬁcient is obtained for ntype doping and the optimal carrier concentration is 1020 cm3. The calculated Seebeck coefﬁcient (S), electrical conductivity (s/ t), electronic thermal conductivity (ke/t) and power factor (S2s/t)

K. Kaur, J. Kaur / Journal of Alloys and Compounds 715 (2017) 297e303

Fig. 1. (a) Band structure (b) density of states of ScRhTe.

Fig. 2. (a) Band structure (b) density of states of ZrPtPb.

Fig. 3. Phonon dispersion and phonon density of states of ScRhTe.

299

300

K. Kaur, J. Kaur / Journal of Alloys and Compounds 715 (2017) 297e303

Fig. 4. Phonon dispersion and phonon density of states of ZrPtPb.

of both materials as function of chemical potential at 1020 cm3 carrier concentration are plotted in Fig. 7 and Fig. 8. The sharp density of states near the band edge and the width of band gap are good sign for the thermoelectric properties of materials. In these materials, the calculated band structure has a sharp conduction band and ﬂat valence band which reveals that these materials have good transport properties. The large slope of density of states near the energy gap may give rise to a large Seebeck coefﬁcient [43]. Figs. 7 and 8, demonstrate the calculated thermoelectric properties of both materials at different temperatures of 300, 500, 600 and 700 K for the chemical potential (m) in the range of -2eV to 2eV. The positive value of chemical potential (m) indicates that the doping is n-type and negative value of m represents the p-type doping. The Seebeck coefﬁcient as function of chemical potential at different temperatures 300, 500, 600 and 700 K is depicted in Figs. 7(a) and 8(a). In Figs. 7(a) and 8(a), the peaks are obtained between 0.5 and 0.5 of chemical potential. The curves tend rapidly to zero outside this range. The maximum value of Seebeck coefﬁcient is

Fig. 5. Speciﬁc heat at constant volume with temperature.

obtained at 300 K. which means that this material has good thermoelectric performance. The maximum value of Seebeck coefﬁcient decreases with increase in temperature. ScRhTe and ZrPtPb materials are n-type semiconductors and provide better thermoelectric performance. Figs. 7(b) and 8(b) show the variation of electrical conductivity per second with chemical potential and temperature. The electrical conductivity per second exhibits similar behavior at all temperatures. The value of electrical conductivity per second increases with increase in chemical potential at all temperatures. The increase in carrier concentration increases the mobility which increases the conductivity. The value of electrical conductivity with respect to relaxation time is high for positive chemical potential as compared to negative value of m, from which we can say that n-type composition has high electrical conductivity than p-type composition. The value of electrical conductivity per second is zero in 0.25 to 0.25 range of chemical potential. But beyond this range the value increases. Figs. 7 (c) and 8 (c) shows the variation of electronic thermal conductivity per second with chemical potential (m) and temperature. These plots also show that the electronic thermal conductivity increases with chemical potential and temperature. The value of electronic thermal conductivity per second is large for positive chemical potential than negative chemical potential. The variation of power factor (S2 s) with chemical potential at different temperatures are depicted in Figs. 7 (d) and 8 (d). The power factor reﬂects the performance the thermoelectric materials. The maximum value of power factor 4.95 1011 W/msK2 (ScRhTe) and 6.73 1011 W/msK2 (ZrPtPb) are observed for n-type doping at 700 K in both materials. Total thermal conductivity is sum of electronic (ke) and lattice thermal conductivity (kl). The variations of lattice thermal conductivity with temperature of both materials are plotted in Fig. 9. This plot revealed that the lattice thermal conductivity decreases with increase in temperature. The lattice thermal conductivity shows 1/T dependence. At room temperature, the lattice thermal conductivity of both materials is 8.35 W/mK (ScRhTe) and 7.97 W/ mK (ZrPtPb) respectively. We compared our calculated results with other well know Half Heusler compounds like ZrNiPb (14.5 W/mK) [44], TiNiSn (7.6 W/mK) [25] and HfNiSn (6.7e10 W/mK) [44]. It gives good agreement with other well known Half Heusler compounds.

K. Kaur, J. Kaur / Journal of Alloys and Compounds 715 (2017) 297e303

301

Fig. 6. Variation of Seebeck coefﬁcient (a) ScRhTe (b) ZrPtPb at different concentration (cm3) and temperature.

Fig. 7. The variation of (a) Seebeck Coefﬁcient (b) electrical conductivity (c) electronic thermal conductivity (d) power factor with chemical potential (m) at different temperature in ScRhTe.

302

K. Kaur, J. Kaur / Journal of Alloys and Compounds 715 (2017) 297e303

Fig. 8. The variation of (a) Seebeck Coefﬁcient (b) electrical conductivity (c) electronic thermal conductivity (d) power factor with chemical potential (m) at different temperature in ZrPtPb.

4. Conclusion In summary, the structural, electronic, phonon and thermoelectric properties of ScRhTe and ZrPtPb are calculated using ﬁrst principle calculations and Boltzmann transport theory. It is found that these materials are direct band gap semiconductors. The phonon dispersion relation and phonon density show that these materials are thermodynamically stable because there is no negative frequency. The maximum value of thermo power of both materials is obtained at 1020 cm3. The Seebeck coefﬁcient, electrical conductivity per second, electronic thermal conductivity per second and power factor with chemical potential at different temperatures are also calculated. These materials have high power factor for n-type doping. The lattice thermal conductivity of both materials is also obtained with variation of temperature. The lattice thermal conductivity decreases with increase in temperature. We can say that these materials are good for thermoelectric application. The structural, electronic, thermoelectric and phonon properties of these materials are studied ﬁrst time in this work. Fig. 9. The calculated lattice thermal conductivity of ScRhTe and ZrPtPb with temperature.

K. Kaur, J. Kaur / Journal of Alloys and Compounds 715 (2017) 297e303

Acknowledgement The author, Kulwinder Kaur, thanks the Council of a Scientiﬁc and Industrial Research (CSIR), India for providing fellowship. References [1] W.S. Liu, Q. Zhang, Y. Lan, S. Chen, X. Yan, Q. Zhang, H. Wang, D. Wang, G. Chen, Z. Ren, Adv. Energy Mater. 1 (2011) 577. [2] D.K. Ko, Y. Kang, C.B. Murray, Nano Lett. 11 (2011) 2841. [3] M. Zebarjadi, G. Joshi, G. Zhu, B. Yu, A. Minnich, Y. Lan, X. Wang, M. Dresselhaus, Z. Ren, G. Chen, Nano Lett. 11 (2011) 2225. [4] B. Yu, M. Zebarjadi, H. Wang, K. Lukas, H. Wang, D. Wang, C. Opeil, M. Dresselhaus, G. Chen, Z. Ren, Nano Lett. 12 (2012) 2077. [5] D.Y. Chung, T.H. Hogan, P. Brazis, M. Rocci-Lane, C. Kannewurf, M. Bastae, C. Uher, M.G. Kanatzidis, Science 287 (2000) 1024. [6] R.T. Littleton IV, Terry M. Tritt, J.W. Kolis, D.R. Ketchum, Phys. Rev. B 60 (1999) 13453. [7] G.S. Nolas, M. Kaeser, T.M. Tritt, Appl. Phys. Lett. 77 (2000) 1855. [8] B.C. Sales, D. Mandrus, R.K. Williams, Science 272 (1996) 1325. [9] T. Graf, C. Felser, S.S. Parkin, Prog. Solid State Chem. 39 (2011) 1. [10] J.R. Sootsman, D.Y. Chung, M.G. Kanatzidis, Ange-wandte Chem. Int. Ed. 48 (2009) 8616. [11] M. Schwall, B. Balke, Appl. Phys. Lett. 98 (2011) 042106. [12] S. Chen, Z. Ren, Mater. Today 16 (2013) 387. [13] J. Yang, H. Li, T. Wu, W. Zhang, L. Chen, J. Yang, Adv. Funct. Mater. 18 (2008) 2880. [14] G.S. Nolas, J. Poon, M. Kanatzidis, MRS Bull. Volume 31 (March 2006). [15] Q. Shen, L. Chen, T. Goto, et al., Appl. Phys. Lett. 79 (2001) 4165. [16] S. Sakurada, N. Shutoh, Appl. Phys. Lett. 86 (2005) 082105. [17] Cui Yu, Tie-Jun Zhu, Rui-Zhi Shi, et al., Acta Mater. 57 (2009) 2757. [18] X. Yan, W. Liu, S. Chen, H. Wang, Q. Zhang, G. Chen, Z. Ren, Adv. Energy Mater. 3 (2013) 1195. [19] E. Rausch, B. Balke, S. Ouardi, C. Felser, Phys. Chem. Chem. Phys. 16 (2014) 25258. [20] R. He, H.S. Kim, Y. Lan, D. Wang, S. Chen, Z. Ren, RSC Adv. 4 (9) (2014) 64711.

303

[21] C. Fu, T. Zhu, Y. Pei, H. Xie, H. Wang, G.J. Snyder, Y. Liu, Y. Liu, X. Zhao, Adv. Energy Mater. 4 (2014) 1400600. [22] C. Fu, T. Zhu, Y. Liu, H. Xie, X. Zhao, Energy Environ. Sci. 8 (2015) 216. [23] G. Joshi, R. He, M. Engber, G. Samsonidze, T. Pantha, E. Dahal, K. Dahal, J. Yang, Y.C. Lan, B. Kozinsky, Z.F. Ren, Energy Environ. Sci. 7 (2014) 4070. [24] E. Dahal, K. Dahal, J. Yang, Y. Lan, B. Kozinsky, Z. Ren, Energy Environ. Sci. 7 (2014) 4070. [25] G. Ding, G.Y. Gao, K.L. Yao, J. Phys. D Appl. Phys. 48 (2015) 235302. [26] J. Shiomi, K. Esfarjani, G. Chen, Phys. Rev. B 84 (2011) 104302. [27] Shanming Li, Huaizhou Zhao, Dandan Li, et al., J. Appl. Phys. 117 (2015) 205101. [28] R. Gautier, X. Zhang, L. Hu, L. Yu, A. Zunger, Nat. Chem. 7 (2015) 308. [29] K. Kaur, R. Kumar, Chin. Phys. B 5 (2016) 056401. [30] K. Kaur, S. Dhiman, R. Kumar, Phys. Lett. A 381 (2017) 339. [31] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A.D. Corso, Gironcoli S de, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, J. Phys. Cond. Matter 21 (2009) 395502. [32] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3864. [33] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [34] G.K. Madsen, D.J. Singh, Comput. Phys. Commun. 175 (2006) 67. [35] T.J. Scheidemantel, C. Ambrosch-Draxl, T. Thonhauser, J.V. Badding, J.O. Sofo, Phys. Rev. B 68 (2003) 125210. [36] L. Jodin, J. Tobola, P. Pecheur, H. Scherrer, S. Kaprzyk, Phys. Rev. B 70 (2004) 184207. [37] W. Li, J. Carrete, N.A. Katcho, N. Mingo, Comput. Phys. Commun. 185 (2014) 1747. [38] J. Ma, W. Li, X. Luo, Appl. Phys. Lett. 105 (2014) 082103. [39] J. Carrete, N. Mingo, S. Curtarolo, Appl. Phys. Lett. 105 (2014) 101907. [40] Stefano Baroni, Theor. Comput. Methods Min. Phys. 71 (2010) 39. [41] F.D. Murnaghan, Proc. Natl. Acad. Sci. U. S. A. 30 (1944) 244. [42] I. Galanakis, P.H. Dederichs, N. Papanikolaou, Phys. Rev. B 66 (2002) 174429. [43] M. Onoue, F. Ishii, T. Oguchi, J. Phys. Soc. Jpn. 77 (2008) 054706. [44] S.D. Guo, RSC Adv. 6 (2016) 47953.