Ternary germanide Li2ZnGe: A new candidate for high temperature thermoelectrics

Accepted Manuscript Ternary germanide Li2ZnGe: A new candidate for high temperature thermoelectrics Saleem Yousuf, Dinesh C. Gupta PII:

S0925-8388(17)34407-9

DOI:

10.1016/j.jallcom.2017.12.211

Reference:

JALCOM 44297

To appear in:

Journal of Alloys and Compounds

Received Date: 16 October 2017 Revised Date:

6 December 2017

Accepted Date: 19 December 2017

Please cite this article as: S. Yousuf, D.C. Gupta, Ternary germanide Li2ZnGe: A new candidate for high temperature thermoelectrics, Journal of Alloys and Compounds (2018), doi: 10.1016/ j.jallcom.2017.12.211. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Ternary Germanide Li2ZnGe: A New Candidate for High Temperature Thermoelectrics Saleem Yousuf and Dinesh C. Gupta* Condensed Matter Theory Group, School of Studies in Physics

RI PT

Jiwaji University, Gwalior – 474 011 (MP), INDIA Email: [email protected]*; [email protected]; Abstract

Experimentally studied F-43m structured Li2ZnGe ternary germanide is investigated theoretically by

SC

evaluating the electronic structure, thermodynamic stability and thermoelectric efficiency using the fullpotential method. The calculated lattice parameter and structural characterization agree well with the

M AN U

experimental results. The thermoelectric properties are calculated within the temperature range of 01200 K. The computed value of figure of merit is 0.40 at 1200 K and Seebeck coefficient is 150 µV/K specifying n-type nature. The electrical conductivity is high mainly due to high carrier mobility, while total thermal conductivity is moderate due to low lattice thermal conductivity. The estimated figure of

TE D

merit projects it as a potential thermoelectric material for high temperature power generation. Keywords: Ternary germanide; Electronic structure; Band structure; Thermoelectric properties; Thermodynamic properties.

EP

I. Introduction

Applications of thermoelectric materials at cryogenic as well as thermogenic temperatures has given rise

AC C

to considerable interest from the scientific community probably due to the severe exploitation of fossil fuels and an ever-increasing demand for a sustainable supply of energy [1-3]. They are envisaged with the ability to directly convert thermal and electrical energy to provide an alternative route for power generation and refrigeration. The factor establishing the efficiency of conversion is defined by dimensionless figure of merit (zT) [4-9] zT =

S 2σ T κ electronic + κ lattice

(1)

ACCEPTED MANUSCRIPT

where S is Seebeck coefficient, σ is electrical conductivity, T as temperature and κ defines the total thermal conductivity (sum of electronic (κɛ) and lattice (κL) parts). The materials for the commercial applications ought to present the zT above 1 and its enhancement is presently made through better and

RI PT

efficient techniques as quantum confinement of carriers [10]; through nano-structuring [11]; by inclusion of electron filtering [12]; application of converging electronic band valleys [13]; by adding impurities that does fostering of resonant levels inside the valence band [14]; creating point defects

making of thin-films of hetero-structured superlattice [17].

SC

through alloying [15]; by incorporating complex crystal structures like Zintl compounds [16], and

M AN U

Off these techniques, the most commercialized way of engineering thermoelectric materials is the use of narrow band gap materials such as Bi2Te3–Sb2Te3 as they stood as a gate way for best thermoelectric materials due to their values of zT >1 for near or above room temperature [18-19]. They possess the special character of enhanced power factor (PF) P = S2σ and lower thermal conductivity. The overall

TE D

performance suggest narrow-gap semiconductors or semimetals find a potential stand for applications at cryogenic as well as thermogenic temperatures. The simple setback for lower band gap is a rapid compensation between charge carriers which results in lower values of S and zT. The problem can be

EP

compensated by using the strongly correlated electronic systems, which will enable one to have large PF that will be principally electronic in origin. In this connection, a recent study on correlated FeSb2, FeSi

AC C

systems have presented high PF over the cryogenic temperature range [20]. The prominent characteristic of such systems is that they possess i) decoupled PF and κ which provides a basis in optimizing the zT by making reduction in κ ii) narrow spam of density of states close to Fermi level associates higher effective mass of charge carriers and high thermopower. This can be argued also from the following equation [21]

8 2 2 * π 23 S= π kB mDOST ( ) 3eh2 3n

(2)

ACCEPTED MANUSCRIPT

where the symbols have their usual meanings. Narrow band gap materials are found to possess high effective mass and low mobilities, and are regarded as potential candidates for large PFs. Here in the present paper, we investigated a material candidate possessing narrow semiconducting band gap

RI PT

together with correlated-electron system. The basic theme is to investigate the effect of incorporation of heavier correlated atoms on the transport properties and its comparison with the other experimentally observed systems. In this connection, Li2ZnGe ternary germanide is investigated to explore its use for

SC

thermoelectric applications and also its electrical conductivity measurements may be filed for its use in lithium ion batteries as electrode sources. The next section II defines the various theoretical methods and

of the results along with their importance. II. Theoretical Methods and Tools

M AN U

tools used for investigating the properties followed by section III which explores the general discussion

The choice in using theoretical methods to investigate the ground state properties depends upon the

TE D

extent of correlation of the computed results with the experimental findings. The DFT method which has proven to be one of the most accurate methods for the computation of the electronic structure of solids [22-27] and has proven as a basic tool for its exactness with the experimental results [28]. It generally

EP

calculates the ground state properties at 0 K. The Perdew-Burke–Ernzerhof generalized gradient approximation (PBE-GGA) [29] under (FPLAPW) [30] method is employed for exchange-correlation

AC C

potential functional. Perfect ground state properties were analyzed through GGA and modified BeckeJohnson potential (mBJ) [31]. The mBJ method is incorporated in order to exactly calculate the experimentally observed semiconducting band structure. The mBJ method is basically designed to reproduce the shape of the exact exchange optimized effective potential (OEP) of atoms. The modified BJ potential can be expressed as BR vxMBJ ,σ ( r ) = cvx ,σ ( r ) + (3c − 2)

1

5 2tσ (r ) π 12 ρσ (r )

(3)

ACCEPTED MANUSCRIPT

Where, ρσ = ∑ iN=σ1 ψ i ,σ is the electron density, tσ = 2

1 Nσ * ∑ i =1 ∇ψ i ,σ .∇ψ i ,σ is the kinetic energy density, 2

and the first term is defined as Becke-Roussel potential [32] as

1  1  − xσ ( r ) − xσ (r )e− xσ ( r )  1 − e bσ (r )  2 

RI PT

vxBR,σ (r ) = −

(4)

originally proposed to calculate the Coulomb potential created by the exchange hole.

SC

The whole crystal space is divided into non-overlapping spheres as muffin-tin spheres and the remaining space is treated as interstitial space. Fourier series incorporated with spherical harmonic functions is

M AN U

modelled in approximating the wave functions of the muffin-tin spheres. Correct approximation in muffin-tin with accurate choice of lattice harmonics in the basis set is obtained through immense iterative steps. Further, for the perfect ground state energy Eigen-value, convergence of wave function is taken into account. Highly converged ground state energy is controlled through the proper cut-off parameter in the basis set. The selected energy threshold between the core and the valence states favors

TE D

the convergence criteria. Highly concise use of first Brillouin zone (BZ) sampling for the proper calculation of the properties was used. The convergence criteria for energy is 10-4Ry and the integrated charge difference between two successive iterations was less than 10-4/a.u3.

EP

III. Results and Discussion

AC C

The results and discussion portion is sub-divided under various headings as I. Structural Characterization and Ground State Properties

The narrow gap semiconductor Li2ZnGe is experimentally [33] observed to crystallize in cubic form with a non-centrosymmetric C1b structure with possible crystal structures shown in Fig. 1. In order to assure theoretically, we have investigated its stability in possible phases F-43m and F-m3m. The method of optimizing the ground state properties via Murnaghan’s equation of state is used to calculate the

ACCEPTED MANUSCRIPT

lattice parameter, Bulk’s modulus and its pressure derivative. The graphical variation of energy vs volume in the said structures is shown in Fig. 2 with optimized values in Table 1. The highly precise GGA and mBJ potentials are used to correctly estimate the ground state band

RI PT

structure along the high symmetry directions of BZ. The accurate semiconducting behavior was not predicted as GGA underestimates the correct band structure, so we have made use of the mBJ approximation. The band structure plot is shown in Fig. 3, where we can see that narrow semiconducting

SC

behavior is predicted correctly. The band gap value of 0.389 eV is of indirect nature as the maxima of valence band is situated at Г-point while the minima of conduction band is at X-point.

M AN U

For understanding the hybridization and extent of occupation of bands around the Fermi level, we have investigated the total and partial density of states (DOS) as shown in Fig. 4. The total density of states shows negligible DOS around the Fermi level with an extent or peak of bands up to 4 eV. While applying the mBJ potential, shifting as well as widening of bands occurs around the Fermi level to

TE D

accurately estimate the band gap. On analyzing the partial density of states (PDOS) in Fig. 5, the main peaks around the Fermi level mainly originate from the contribution of Zn-s and Ge-p orbitals. The hybridization among these atomic orbitals is mainly responsible for the occupation and character of

EP

bonding in the crystal structure.

Different density of states in Li, Zn and Ge are the result of hybridization between Li-2s, Zn-4s and Ge-

AC C

4p electrons. Strength of hybridization is mainly influenced by chemical nature as well as the surrounding environment of the near ligand. Here we have shown the electron charge density plot in Fig. 6, to correctly understand the nature of bonding and interactions among these constituents. The two Liatoms share negligible amount of charge and show ionic nature of bonding with Zn and Ge. Significant amount of charge occurs between Zn and Ge giving rise to covalent bonding, while in Zn-Li and Ge-Li charge mainly presides on the higher valent atom and show ionic bonding.

ACCEPTED MANUSCRIPT

II.

RI PT

Table 1: Calculated lattice parameter, band gap by the specified approximations. Lattice constant a0 Method Expt. a0 (Ǻ) Band Gap (eV) (Ǻ) 0.185 GGA 6.14 6.12[27] 0.393 mBJ Transport properties

In order to estimate the thermoelectric performance of Li2ZnGe, Boltzmann transport theory is used. It makes use of the electronic structure. The basic theory of calculation of the semiclassical approach of

SC

Boltzmann transport theory presides under the constant relaxation time approximation. As we define, in

M AN U

general, the electric current of carriers as J = e∑ f kr vkr r k

(5)

Here, the symbols have their usual meanings, where f kr is the population of the quantum state labelled r with k and vkr the group velocity associated to that state defined as

1 ∂ε kr r h ∂k

TE D

vkr =

(6)

There are various mechanisms by which distribution function can change like external fields (such as

EP

electric and magnetic fields or a temperature gradient), diffusion and scattering of the carriers by phonons, impurities etc. in the crystal lattice. The solution of the Boltzmann equation gives the

∂f kr

AC C

r population of the state k which has an interplay between all the above mentioned mechanisms uur   ∂f r  e  ur 1 + vkr .∇ rr f kr +  E + vkr × H  .∇ kr f kr =  k  ∂t h c   ∂t  scatt .

(7)

When there are no external fields, the solution of the above equation is given by Fermi distribution function f 0 ( ε kr ) and by the method of linearization using the constant relaxation time approximation, the solution becomes as

ACCEPTED MANUSCRIPT

ur  ∂f  f kr = f0 ( ε kr ) + e  − 0  τkr vkr E  ∂ε 

(8)

where τ being the relaxation time.

 ∂f 0  r r σ = e2 ∑ − v τ r  ∂ε  k k k 

For simplicity we define the transport distribution as

SC

Ξ=∑ vkr τkr r

RI PT

Now, we define the conductivity tensor by using the above equation as

k

(9)

(10)

M AN U

The other transport coefficients are defined using the transport distribution function as

S=

e  ∂f  Ξ (ε)  − 0  (ε − µ ) d ε ∫ Tσ  ∂ε 

κ=

1  ∂f  Ξ (ε )  − 0  ( ε − µ ) 2 d ε ∫ T  ∂ε 

TE D

 ∂f  σ = e 2 ∫ Ξ (ε )  − 0  d ε  ∂ε 

(11)

(12)

(13)

respectively.

EP

Where, σ, S and κ define the electrical conductivity, Seebeck coefficient and thermal conductivity

The calculation of various transport properties is based on the assumption of constant scattering

AC C

approximation, which drops out of the expression for calculating Seebeck coefficient, or in general we need not to consider it for its calculation. Under general conditions, it comes out to be a good approximation as long as the scattering time does not vary in an energy scale of kBT. Thermoelectric properties are largely affected by the band structure, so we tried to correctly estimate the band structure by using both GGA and mBJ calculation schemes. As GGA overestimates the band structure and mBJ method was used to predict the band structure of the compound. The calculated band gap through both

ACCEPTED MANUSCRIPT

the schemes is enlisted in Table 1. Moreover, the predicted band gap is in agreement with the previous results [34]. In order to study the temperature effects, we have calculated the thermopower (S(T)), electrical conductivity (σ), thermal conductivity (κ) and figure of merit (zT).

RI PT

As shown in Fig. 7 (a), the S(T) becomes sizable above 300 K with a negative sign. Huge absolute maximum value |Smax| is observed around 1200 K and is found to be strongly dependent on band structure. The variation of thermopower with chemical potential shown in Fig. 7 (b) lights up that up to

SC

a slight span above or below the Fermi level, maximum values can be attained. We have attained this maximum value above the Fermi level with n-type carrier. Effect of the correlated electron assumes a

M AN U

heavy charge-carrier effective mass with large non parabolicity of bands around Fermi level that defends the enhanced thermopower. Similarly, the extended nature of 3d bands of Zn lead to hybridization with the conduction band that accounts for opening of the narrow gap and formation of the narrow band at the gap edges.

TE D

We have estimated the electrical conductivity as shown in Fig. 7 (c). As the temperature increases, an exponential increasing trend can be seen, which may trigger its thermoelectric efficiency and is found to increase from 3.45×104 (Ωm)-1 at 300 K to 5.45×104 (Ωm)-1 at 1200 K. In addition to better

EP

thermoelectric efficiency, the present material may prove as a potential candidate for electrode material in lithium ion batteries as similar ranges of σ are observed in electrode materials [35-36].

AC C

In order to study the thermal conductivity, which contains contribution from both electrons as well as lattice, we have make use of Slack’s method [37-38] which gives accurate approximation of the lattice thermal conductivity and is evaluated as M θ Dδ 3

κL = A

2 3

γn T

(14)

ACCEPTED MANUSCRIPT

where M is average mass, θD is Debye temperature, δ is volume per atom, γ is Grüneisen parameter, n is the number of atoms in the primitive cell, T is an absolute temperature. The constant A is defined as the collection of physical constants determined as: 5.720 × 0.847 ×107   0.514   0.228   2 1 −   +  2    γ   γ 

RI PT

A(γ ) =

(15)

SC

The variation of total thermal conductivity is shown in Fig. 7 (d), where the electronic thermal conductivity increases with temperature, while the lattice part decreases with increase in temperature. In

M AN U

case of electronic thermal conductivity, as the temperature increases from 300 K to 1200 K, exponential increase occurs from 0.28 W/mK to 3.67 W/mK. In case of lattice thermal conductivity, there is decrease from 2.37 W/mK at 300 K to 0.30 W/mK, and it is very small as compared to traditional Heusler alloys [39-40]. The capability of showing lower lattice thermal conductivity may stand it as a potential candidate for thermoelectrics.

TE D

In order to comment on the performance of the material, we also figure out its PF (P) defined as S2σ shown graphically in Fig. 7 (e). The P shows a linearly increasing trend with temperature and increase

EP

from 1.10×10-4 W/K2m at 300 K which reaches to 12.89×10-4 W/K2m at 1200 K. The PF indicates that the correlated electrons play an important role in optimizing the thermoelectric response without

AC C

degrading the electrical conductivity. Similarly, the lower lattice thermal conductivity has come out enormously diminished and make its stand as a potential candidate for thermoelectrics. Similarly, the techniques of nano inclusion and thin film growth for such compounds may empower the better phonon scatters by the grain boundaries which can help in enhance the thermoelectric performance of such materials. The calculated transport coefficients are now used to estimate the thermoelectric efficiency through zT measurement. The variation of zT is shown in Fig. 7 (f), which shows linearly increasing trend with

ACCEPTED MANUSCRIPT

temperature. The room temperature value is estimated as 0.025 and goes on increasing to 0.40 at 1200 K. The increasing trend may prove it a candidate for high temperature thermoelectric applications. In order to check the thermodynamic stability, we also report the specific heat (CP) which is a key factor

RI PT

for linking thermodynamic properties with microscopic structure. The variation of specific heat gives us the idea about the extent of energy stored by the structure. Here, the variation of CP with temperature is shown in Fig. 8. At lower temperatures, CP varies exponentially and follows the Debye model

SC

[C(T)∝T3] up to 300 K which on higher temperatures show a monotonous increase and then remain constant and follows the Dulong-Petit law. We have also noted that CP shows a decreasing trend with

nearly found similar with Bi2Te3 [41-42].

Conclusion

M AN U

increasing pressure. The room temperature value of CP at 0 GPa comes out as 93.3 J/mol K and is

We have investigated the structural, electronic and thermoelectric properties of ternary germanide

TE D

Li2ZnGe by the first-principles calculation method. The calculated lattice parameter agrees well with the experimental value. The F-43m space group is estimated to be ground state structural phase with lattice parameter of 6.14 Ǻ. The thermoelectric properties are investigated with a temperature range of 0-1200

EP

K. The absolute thermopower value of 151.35 at 1200 K was obtained with moderate lattice thermal conductivity. Further, the zT measurement of 0.40 at higher temperatures may stand it as a potential

AC C

candidate for high temperature power generation applications.

References [1] [2] [3] [4]

J.F Li, W.S. Liu, L.D. Zhao, M. Zhou, High-performance nanostructured thermoelectric materials, NPG Asia Mater. 2 (2010) 152. T.T. Terry, Thermoelectric materials, phenomena, and applications: A bird's eye view, MRS Bull. 31 (2006) 188. G.J. Snyder, E.S. Toberer, Complex thermoelectric materials, Nat. Mater. 7 (2008) 105. T.M. Bhat and D.C. Gupta, Robust thermoelectric performance and high spin polarisation in CoMnTiAl and FeMnTiAl compounds, RSC. Adv. 6 (2016) 80302.

ACCEPTED MANUSCRIPT

[11]

[12]

[13] [14]

[15] [16] [17] [18]

[19] [20] [21] [22] [23]

[24]

RI PT

[10]

SC

[9]

M AN U

[8]

TE D

[7]

EP

[6]

S.A. Khandy D.C. Gupta, Structural, elastic and thermo-electronic properties of paramagnetic perovskite PbTaO3, RSC Adv. 6 (2016) 48009. . S.A. Khandy and D.C. Gupta, Investigation of structural, magneto‐electronic, and thermoelectric response of ductile SnAlO3 from high‐throughput DFT calculations, Int. J. Qua. Chem. DOI: 10.1002/qua.25351 (2017). T. M. Bhat and D.C. Gupta, Transport, structural and mechanical properties of quaternary FeVTiAl alloy, J. Elec. Mater. 45 (2016) 6012. D.C. Gupta and I.H. Bhat, Investigation of electronic structure, magnetic and transport properties of half-metallic Mn2CuSi and Mn2ZnSi Heusler alloys, J. Magn. Magn. Mater. 374 (2015) 209. S. Yousuf and D.C. Gupta, Thermoelectric and mechanical properties of gapless Zr2MnAl compound, Indian J. Phys. 91 (2017) 33. L.D. Hicks, M.S. Dresselhaus, Effect of quantum-well structures on the thermoelectric figure of merit, Phys. Rev. B 47 (1993) 12727. J.R. Sootsman, H. Kong, C. Uher, J.J. D’Angelo, C.I. Wu, T.P. Hogan, T. Caillat, M.G. Kanatzidis, Large enhancements in the thermoelectric power factor of bulk PbTe at high temperature by synergistic nanostructuring, Angew. Chem. Int. Ed. 47 (2008) 8618. J.M.O. Zide, D. Vashaee, Z.X. Bian, G. Zeng, J.E. Bowers, A. Shakouri, A.C. Gossard, Demonstration of electron filtering to increase the Seebeck coefficient in In0.53 Ga0.47 As⁄In0.53 Ga0.28 Al0.19As superlattices, Phys. Rev. B 74 (2006) 205335. A. Banik, U.S. Shenoy, S. Anand, U.V. Waghmare, K. Biswas, Mg alloying in SnTe facilitates valence band convergence and optimizes thermoelectric properties, Chem. Mater. 27 (2015) 581. Q. Zhang, B. Liao, Y. Lan, K. Lukas, W. Liu, K. Esfarjani, C. Opeil, D. Broido, G. Chen, Z. Ren, High thermoelectric performance by resonant dopant indium in nanostructured SnTe, Proc. Natl. Acad. Sci. 110 (2013) 13261. P. Carruthers, Theory of thermal conductivity of solids at low temperatures, Rev. Mod. Phys. 33 (1961) 92. E.S. Toberer, A.F. May, G.J. Snyder, Zintl chemistry for designing high efficiency thermoelectric materials, Chem. Mater. 22 (2010) 624. R. Venkatasubramanian, E. Siivola, T. Colpitts, B. O’Quinn, Thin-film thermoelectric devices with high room-temperature figures of merit, Nature 413 (2001) 597. R. Venkatasubramanian, T. Colpitts, E. Watko, M. Lamvik, N. E1-Masry, MOCVD of Bi2Te3, Sb2Te3 and their superlattice structures for thin-film thermoelectric applications, J. Crystal Growth 170 (1997) 817. T.C. Harman, P. Taylor, M.P. Walsh, and B.E. LaForge, Quantum dot superlattice thermoelectric materials and devices, Science 297 (2002) 2229. P. Sun, N. Oeschler, S. Johnsen, Bo B. Iversen, and F. Steglich, Huge thermoelectric power factor: FeSb2 versus FeAs2 and RuSb2, Appl. Phys. Express 2 (2009) 091102. S. Yousuf, D.C. Gupta, Investigation of electronic, magnetic and thermoelectric properties of Zr2NiZ (Z = Al, Ga) ferromagnets, Mat. Chem. Physics 192 (2017) 33. D.C. Gupta and I.H. Bhat, A first-principles study of RuMn2Si: Magnetic, electronic and mechanical properties, J. Allo Compd. 557 (2013) 292. M. Chauhan and D. C. Gupta, Structural, electronic, mechanical and thermo-physical properties of TMN (TM= Ti, Zr and Hf) under high pressures: A first-principle study, Int. J. Refract. Met. Hard Mater. 42 (2014) 77. D.C. Gupta, S. Ghosh, Pressure-and Temperature-Dependent Study of Heusler Alloys Cu2MGa (M= Cr and V), J. Elec. Mater. 46 (2017) 2185.

AC C

[5]

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

[25] A.H. Reshak, Electronic structure and transport properties of Ba2Cd2Pn3(Pn = As and Sb): An efficient materials for energy conversion, J. Alloy Compd. 670 (2016) 1. [26] A.H. Reshak, Transport properties of Co-based Heusler compounds Co2VAl and Co2VGa: spinpolarized DFT+U, RSC Adv. 6 (2016) 54001 [27] A.H. Reshak, Thermoelectric properties of highly-mismatched alloys of GaNxAs1−x from first-to second-principles methods: energy conversion, RSC Adv. 6 (2016) 72286. [28] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Techn. Universität Wien, Austria), ISBN 3-9501031-1-2, 2001. [29] J.P. Perdew, K. Burke and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865. [30] K. Schwarz, P. Blaha and G.K.H. Madsen, Electronic structure calculations of solids using the WIEN2k package for material sciences, Comput. Phys. Commun. 147 (2002) 71. [31] F. Tran and P. Blaha Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential, Phys. Rev. Lett. 102 (2009) 226401. [32] A.D. Becke, M.R. Roussel, Exchange holes in inhomogeneous systems: A coordinate-space model, Phys. Rev. A 39 (1989) 3761. [33] L.L.-Orio, M. Tillard and C. Belin, Synthesis, crystal and electronic structure of Li8Zn2Ge3, a compound displaying an open layered anionic network, Solid State Sciences 8 (2006) 208. [34] F. Kalarasse, L. Kalarasse, B. Bennecer, A. Mellouki, Elastic and electronic properties of Li2ZnGe, Comput. Mater. Science 47 (2010) 869. [35] F. Sauvage, J.M. Tarascon and E. Baudrin, In situ measurements of Li ion battery electrode material conductivity:  Application to LixCoO2 and conversion reactions, J. Phys. Chem. C 111 (2007) 9624-9630. [36] M. Parka, X. Zhanga, M. Chunga, G.B. Less, A.M. Sastrya, A review of conduction phenomena in Li-ion batteries, J. Power Sources 195 (2010) 7904. [37] Z.Y. Jiao, T.X. Wang, S.H. Ma, Phase stability, mechanical properties and lattice thermal conductivity of ceramic material (Nb1−xTix)4AlC3 solid solutions, J. Alloy Compd. 687 (2016) 47. [38] S. Yousuf and D.C. Gupta, Temperature and pressure dependent structural and thermo-physical properties of quaternary CoVTiAl alloy, J. Phys. Chem. Solids 108 (2017) 109. [39] S. Yousuf and D.C. Gupta, Insight into electronic, mechanical and transport properties of quaternary CoVTiAl: Spin-polarized DFT+ U approach, Mater. Sci. Eng. B 221 (2017) 73. [40] S. Singh and R. Kumar, Ab-initio calculations of elastic constants and thermodynamic properties of LuAuPb and YAuPb half-heusler compounds, J. Alloy Compd. 722 (2017) 544. [41] E.S. Itskevich, The heat capacity of bismuth telluride at low temperatures, Soviet Physics JETP 11 (1960) 2. [42] N.P. Gorbachuk, A.S. Bolgar, V.R. Sidorko and L.V. Goncharuk, Heat capacity and enthalpy of Bi2Si3 and Bi2Te3 in the temperature range 58-1012 K, Powder Metall. Met. Ceram 43 (2004) 5.

SC

RI PT

ACCEPTED MANUSCRIPT

M AN U

(a)

(b)

Fig. 1: Crystal structure of Li2ZnGe in (a) F-43m space group (b) F-m3m space group.

-7820.592

F-43m F-m3m

TE D

-7820.594

EP

-7820.598

-7820.600

AC C

Energy (Ry)

-7820.596

-7820.602

-7820.604

340

360

380

400

420

440

Volume (a.u)3 Fig. 2: Structural optimization in possible structural phases of Li2ZnGe.

460

ACCEPTED MANUSCRIPT

GGA

M AN U

SC

RI PT

mBJ

Fig. 3: Band structure plot of Li2ZnGe in GGA and mBJ approximations. The Fermi level is set at zero value.

TE D

GGA mbj

Fermi level (Ef)

4

AC C

EP

Density of states (states/ev per unit cell)

6

2

0 -10

-5

0

Energy (eV)

5

Fig. 4: Total density of states of Li2ZnGe plot in GGA and mBJ calculations.

10

ACCEPTED MANUSCRIPT 1.0

0.08

Li (i) s-mbj Li (ii) s-mbj

Ge (s)-mbj Ge (p)-mbj

0.8 0.06

0.4

0.02

0.2

0.00

0.0 -2.5

0.0

2.5

5.0

-10

0

Energy (eV)

5

Zn-(s) mBJ Zn-(p) mBJ Zn-(D-eg) mBJ

1.2

1.0

M AN U

Zn-(D-t2g) mBJ

0.8

0.6

0.4

TE D

0.2

0.0

-5

SC

Energy (eV)

Density of states/eV

-10

-5

0

5

Energy (eV)

Fig. 5: Partial density of states around the Fermi level depicting the type of contribution to the band structure.

EP

-5.0

RI PT

DOS/eV

0.04

AC C

DOS/eV

0.6

Fig. 6: Calculated electronic charge densities (in Å-3) of Li2ZnGe in (110) plane.

10

ACCEPTED MANUSCRIPT 150

-160 100

-120

S ( µ V/K)

-100 -80 -60 -40

50

0

-50

RI PT

Seebeck Coefficient (S) µ V/K

-140

-100

-20

Fermi level

-150

0 200

400

600

800

1000

1200

-1.02

T (K) (a) 25

M AN U κ (W/mK)

5.0

4.5

3.5 200

400

600

T (K)

(c)

0.34

0.68

1.02

20

κL

15

κε κTotal

(b)

10

800

1000

0 200

1200

8

6

800

1000

1200

(d) 0.35 0.30 0.25

zT

10

600

0.40

AC C

12

400

T (K)

EP

14

2

0.00

5

4.0

TE D

4

-1

σ (10 (Ω m) )

5.5

-4

-0.34

E-Ef (eV)

6.0

Power factor (×10 W/K m)

-0.68

SC

0

0.20 0.15

4 0.10

2

0.05

0

0.00

0

200

400

600

Temperature (K)

(e)

800

1000

1200

200

400

600

T (K)

(f)

800

1000

1200

ACCEPTED MANUSCRIPT Fig. 7: Variation of various transport coefficient with temperature for Li2ZnGe.

120

Dulong-Petit limit 100

RI PT

0 GPa 5 GPa 10 GPa

SC

60

40

20

0 0

100

M AN U

CP (J/mol.K)

80

200

300

400

500

600

T (K)

AC C

EP

TE D

Fig. 8: The Calculated heat capacity per atom at constant pressure of Li2ZnGe compound.

ACCEPTED MANUSCRIPT

The main highlights of our research findings are

AC C

EP

TE D

M AN U

SC

RI PT


Pure Semiconducting nature at the Fermi level.
Possibly efficient high temperature thermoelectric material.
It is thermodynamically stable.