Structural distortion dependence of thermoelectric properties in CoFeZrSi Heusler material

Journal Pre-proof Structural distortion dependence of thermoelectric properties in CoFeZrSi Heusler material A. Birsan PII:

S0925-8388(19)34738-3

DOI:

https://doi.org/10.1016/j.jallcom.2019.153492

Reference:

JALCOM 153492

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Journal of Alloys and Compounds

Received Date: 7 October 2019 Revised Date:

18 December 2019

Accepted Date: 20 December 2019

Please cite this article as: A. Birsan, Structural distortion dependence of thermoelectric properties in CoFeZrSi Heusler material, Journal of Alloys and Compounds (2020), doi: https://doi.org/10.1016/ j.jallcom.2019.153492. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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. © 2019 Published by Elsevier B.V.

Credit author statement This study was designed, analyzed and written by A.B.

Structural distortion dependence of thermoelectric properties in CoFeZrSi Heusler material A. Birsana a National

Institute of Materials Physics, P.O. box MG-7,Bucharest-Magurele, Ilfov, 077125, Romania.

Abstract The effect of potential tetragonal and triclinic distortions of the energetic favorable cubic crystalline structure in CoFeZrSi Heusler compound, was investigated, using semiclassic Boltzmann theory on the thermoelectric functionalities. Chemical potential dependence of the conductivity integral σ/τ for relaxed cubic and tetragonal structures confirms p-type thermoelectric characteristics. When triclinic deformation is investigated, the electrical conductivity response indicates that the material’s ability to conduct electric current decreases. The calculated Seebeck coefficients exhibit positive values for the crystalline structures whose angles are equal to 90o (cubic and tetragonal), over the 300-1200K temperature range. The figures of merit ZT, for relaxed cubic and tetragonal structures, at optimum unit cell volume or higher, present around room temperature, promising features as a potential thermoelectric material (i.e. ZT = 0.94 for 350K in optimum cubic structure). Keywords: quaternary Heusler compounds, interfacial distortions, thermoelectric properties

1. INTRODUCTION Direct converting the waste heat generated by industrial furnace, engines or gas pipes into electricity via the Seebeck effect, actively counteract global warming, as one of the clean energy conversion techniques, that can significantly reduce the CO2 emissions and the fossil-fuel consumption. The efficiency of thermoelectric converters for power generation depends strongly on carrier concentration and electronic structure [1]. Therefore, relentless efforts have been focused on discovery new and promising materials, such are Heusler compounds [2, 3, 4, 5, 6, 7] or Zintls [8], with characteristics enabling convenient combinations of large Seebeck coefficient, high electrical conductivity and low thermal conductivity to enhance energy conversion efficiency which depends on compounds’ dimensionless figure-of-merit (ZT).

Email address: [email protected] (A. Birsan)

Preprint submitted to Elsevier

December 25, 2019

State-of the art thermoelectric converters, generally developed on the Edisonian trial and error approach, present a combination of expensive elementary constituents and low efficiency values, which is time-consuming and economic inefficient. As a result, the theoretical studies could provide valuable guidance for a more efficient rational approaches, to balance the cost and reliability in identifying new promising materials with thermoelectric performance, that may be experimentally identified as stable. Heusler materials recently attracted the technological interest as potential thermoelectric compounds, due to their unique physical properties: at the Fermi energy, the minority spin density of Heusler systems vanishes, while the majority spin density displays electronic states, a property referred in literature as half-metallic ferromagnetism (HMF) [9], that imply a high spin polarization. Moreover, the possibility to optimize the thermoelectric properties by individually doping of each one of the three fcc sublattices, turned out to be a great advantage in favor of detailed investigation of the Heusler compounds. K¨ ubler et al [10] reported from theoretical calculations that Co2 -based Heusler compounds exhibit exceptional transport properties and the first principle calculations were confirmed experimentally, as in Co2 T iAl case [11]. The list of promising materials for thermoelectric applications is long and the compounds were designed to tailor the energy band gap from one spin channel, to be located around the Fermi level [12, 13, 14, 15, 16, 17, 18, 19, 20] Nevertheless, the thermoelectric effect in two-dimensional (2D) materials is attracting a wide appeal, due to the anticipated superiority of converting heat energy to useful electricity comparing with their bulk counterparts. Additionally, in 2D materials the degree of disorder observed is remarkably low for as cast samples [11], this interesting feature being useful in thin film devices, where high annealing temperatures are not allowed. However, in contrast to the bulk structures that generally exhibit high symmetry crystalline configurations, 2D structures may have crystalline configuration, whose symmetry decreases due to distortions and stresses. In order to substantially reduce the experimental efforts required to identify the influence of symmetry decrease (from cubic to tetragonal/triclinic structure) on the target thermoelectric functionalities in CoFeZrSi Heusler compound, (reported by Kanbe et all [21]), theoretical investigation were performed on the typical thermoelectric parameters : electrical conductivities, electronic thermal conductivities, Seebeck coefficients and figures of merit. 2. METHOD OF CALCULATION Theoretical investigations on CoFeZrSi quaternary Heusler compound were performed within the Density Functional Theory framework, using the Full Potential Linearized Augmented Plane Wave (FPLAPW) method, as implemented in Wien2k code [22] with the exchange and correlation interactions described by the Perdew-Burke-Ernzehof (PBE) functional [23, 24]. The technical details regarding first principle calculations have been reported in Ref. [25]. The calculated bandstructure were the starting point for investigations of thermoelectric 2

properties, based on semi-classical Boltzmann equations, as implemented in the BoltzTraP code [26] . 3. RESULTS AND DISCUSSIONS The electronic structures and magnetic properties of CoFeZrSi Heusler compound, investigated via self-consistent procedure, having the cubic structure (reported as the energetic most favorable one) and the tetragonal / triclinic distortions were published in our previous study [25]. The result regarding the electronic configuration of CoFeZrSi, with F-43m symmetry and Si(4a) Fe(4c) Zr(4b) Co(4d) atomic arrangement along the unit cell diagonal, presents halfmetallic properties and a calculated total magnetic moment of 1 µB /f.u. at ˙ )[25]. After tetragonal deformations, the optimized lattice parameter (5.97 A half-metallic properties and total magnetic moment reported for cubic structure, are preserved, despite the increase/decrease of unit cell volume or c/a ratio change. The triclinic distortion changes the half-metallic character into a metallic one and the total magnetic moment significantly increases up to 3.25 ˙ , α = β = 900 , γ = 890 . µB /f.u. for the unit cell with a=b=c=5.97 A Based on our previous published results, the transport properties were calculated via the BoltzTraP code [26] implemented using the semi-classical, Boltzmann transport equations, for the cubic configuration and tetragonal/triclinic distortions of the unit cell, not only for increase/decrease of unit cell volume but also for c/a ratio change. Therefore, the deformations were analyzed as result of which, the unit cell passes from the cubic structure, either into the tetragonal one (by modifying the c/a ratio with −4% respectively 2% as well as increasing/decreasing the volume (+4% /−4%) ) or in the triclinic one (for which, in addition to the modifications used in the investigation of the tetragonal structure, the angle γ has been reduced with one degree). The matrix of the thermoelectric coefficients: the electrical conductivities, the electronic part of the thermal conductivities and the Seebeck coefficients calculated in the relaxation time approximation, from Boltzmann transport equations, are given by the formulas [26, 27, 28]: ∫ ∞ ∂f (E, µ, T ) σij = −e2 τk vi (k)vj (k)ρ(E) dE (1) ∂E 0 ∫ 1 ∞ ∂f (E, µ.T ) κ0ij = − dE (2) τk vi (k)vj (k)ρ(E)(E − µ)2 T 0 ∂E ∫ ∂f (E, µ, T ) vij e ∞ τk vi (k)vj (k)ρ(E)(E − µ) Sij = ; vij = − dE (3) σij T 0 ∂E where ρ(E) is the density of states, e is the electron charge, µ is the chemical potential and f (E, µ, T ) is the Fermi-Dirac distribution. The dimensionless figure-of-merit (ZT) of a thermoelectric material is defined as ZT = σS 2 T /(κele + κlat ); where σ is the electrical conductivity, S is the Seebeck coefficient, T is the absolute temperature, κele is the electronic 3

3

Cubic

Cubic

optimum volume

optimum volume

350K 700K

vol + 4 %

1050K

2

(10

20

/

ms)

4

1

0 -0.1

0.0

0.1

-0.1

0.0

0.1 Ry

Ry

Figure 1: Chemical potential dependence of the electrical conductivity integral σ/τ for cubic structure, left panel at 350K, right panel at optimum volume.

thermal conductivity, defined as the heat current produced per unit of temperature gradient when the electrical current is zero and κlat is the lattice part of the thermal conductivity [1]. The movement of electrons from high temperature regions to low temperature regions causes the appearance of an electric current. Materials with good thermoelectric properties exhibit high values of electrical conductivity. The variation of the ratio between the electrical conductivity and the relaxation time was calculated as a function of chemical potential not only for the cubic , energetically optimum structure, when its volume decreases / increases by −4%, respectively +4% but also for the structures obtained from the tetragonal and triclinic deformations described above. Fig 1 shows the dependence by the variation of ratio between the electrical conductivity and the relaxation time of the chemical potential, at the temperature of 350K (left panel) for CoFeZrSi, having cubic crystalline structure. One can see the occurrence of two maximum peaks, one in the p-type region and the other in the n-type region. The maximum values calculated at 350K, in the p-type region, are 2.79x1020 Ω/ms (-0.054Ry), and 2.44x1020 Ω/ms (0.049Ry) respectively, being higher than those obtained in the n-type region, 1.75x1020 Ω/ms (+ 0.061Ry), 1.65x1020 Ω/ms (+ 0.056Ry) which confirms that the material has p-type thermoelectric characteristics, for cubic structure, having optimum volume or a volume increased with +4% respectively. When the temperature is increased from 350K to 1050K the amplitudes of maximum peaks decrease in both sides of Fermi level, however the material continue to exhibit p-type behavior(see Fig 1-right panel). Similar dependence of chemical potential by the variation of ration between electrical conductivity and relation time was recently reported also in p-type thermoelectric spin gapless semiconductors from Heusler family [12] Following the tetragonal deformation, the half-metallic characteristics of the CoFeZrSi compound are maintained [25] and the electrical conductivity presents a result similar to the cubic structure for the entire temperature range. As a result of changing the γ angle values, when the crystalline structure

4

/ Wms)

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Triclinic

optimum volume

a=b, c/a=1.02

vol +4%

1.2

/

(10

1.8

0.6

-0.1

0.0 0

0.1

(Ry)

4

Tetragonal

350 K

a=b, c/a=0.96

700K

vol=+ 4%

1050 K

2

(10

15

W/ mKs)

Figure 2: Chemical potential dependence of the electrical conductivity integral σ/τ for triclinic distorted structure.

0 -0.1

0.0

(Ry)

0.1

Figure 3: The electronic thermal conductivity and relaxation time ratio, as function of chemical potential, for tetragonal crystalline structure

changes, becoming triclinic, the electrical conductivity response is nonzero at the Fermi level and the half-metallic properties disappear, a situation illustrated in Fig 2 for a ratio of c / a = 1.02 and a variation of the optimum cell volume of −4% respectively +4%, values obtained at 350K. In general, the characteristics of CoFeZrSi as thermoelectric material, regarding the high electrical conductivity for the cubic or tetragonal crystalline structure, are similar to the other Heusler compounds analyzed in the literature [11, 12, 13, 16, 17, 18, 19, 20]. The only disadvantage of this material is the relatively high electronic thermal conductivity, which increases with temperature for both crystalline structures whose angles are equal to 90o . In Fig 3 was illustrated the increases with the temperature (300K, 700K and 1050K respectively) of the ratio between the electronic thermal conductivity and relaxation time, as function of chemical potential ( µ0 being associated to Fermi energy) for tetragonal structure characterized by a=b and c/a=0.96 for a volume with +4% higher than the optimum volume. The variation of the Seebeck coefficient for the cubic structure was analyzed according to its volume variation. In the case of a −4% decrease of optimum

5

0 S ( V/K)

S ( V/K)

900

600

-100 -200 vol -4%

-300 350

700

300

1050

T(K)

Cubic optimum volume vol +4%

350

700

1050

T (K)

Figure 4: The Seebeck coefficient as function of temperature, for cubic crystalline structure

S( V/K)

S ( V/K)

600

S( V/K)

0

900

-200 -400

350

300

0

700

350

1050

optimum volume

vol +4%

vol +4%

700

T(K)

1050

c/a=1.02

optimum volume

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700

T(K)

T(K)

c/a=0.96

vol -4% 0 -6

vol -4%

-600

6

350

1050

700

1050

T(K)

Figure 5: The Seebeck coefficient as function of temperature, for tetragonal crystalline structure

unit cell volume, under the influence of an isostatic pressure of 7.54 GPa, the Seebeck coefficient has the characteristic properties of a half-metallic material with n-type conduction, at a temperature of 350K, the Seebeck coefficient having a value of -228.79 µV /K, decreasing so that the value of -37µV /K is reached at 1050K temperature (Fig 4, inset). However, when the energetically favorable cubic structure was considered, for which the calculated formation entropy was minimal, the Seebeck coefficient presents exclusively positive values (i.e. 480 µV /K at 700K when a=b=c=5.97 ˚ A and α = β = γ = 900 ) over the entire temperature range of 300-1200K, similar as for CoFeMnSb [4] and higher than that reported for some other Heusler compounds [5], proving on the basis of our previously published results [25] to be a p-type half-metal Heusler compound. At high temperature, CoFeZrSi material exhibits values of Seebeck coefficient around 300 µV /K alike recently reported half-Heusler with rare-earth p-type NbFeSb [6]. This characteristic of the material is maintained even when the crystalline lattice relaxes, remaining cubic, but the volume of the elementary cell increasing to +4% (see Fig 4) In the case of tetragonal deformations in which the volume of elementary cell is kept equal to that of the optimum energy cell or is increased by +4%,

6

20

Triclinic

0

c/a=0.96

-7

0

c/a=0.96 c/a=1

-20

c/a=1.02

Triclinic vol +4%

optimum volume

S ( V/K)

vol -4 %

S ( V/K)

S ( V/K)

7

6

Triclinic

0

-6

-12

c/a=0.96

c/a=1.02

c/a=1.02

-18 350

700

1050

350

T(K)

700

1050

T(K)

Figure 6: The Seebeck coefficient as function of temperature, for triclinic crystalline structure

the Seebeck coefficient has values comparable to those obtained for the cubic structure. When the unit cell volume decreases by −4% (Fig 5 insets) and the c / a ratio is subunit (0.96), the material presents n-type half-metallic properties, with negative values of the Seebeck coefficient in the temperature range 3001200K. If the structure is tetragonal with c / a = 1.02, at a volume of −4% of the optimum volume, the Seebeck coefficient has very low values (+4.27 µV /K at 350K and -5.36 µV /K at 1050K) and a transition from the p-type to the n-type character occurs, which demonstrates the instability of transport properties of CoFeZrSi compound, when an isostatic pressure is applied to optimum tetragonal crystalline structure. Fig 6 shows the variation of the Seebeck coefficient for triclinic crystalline structure obtained from the tetragonal structure by decreasing with a degree the γ angle; this being the angle between a and b, so that the base turns from cube to rhombus. The decreases/increases of the elementary cell volume by −4% / +4% were taken into account and the change of the ratio c/a (0.96, respectively 1.02), where a = b. The modifications applied to the elementary cell lead to the vanish of the half-metallic properties of the compound [25], the material having magnetic properties specific to metals. The values of the Seebeck coefficient also decrease significantly, being closer to those of most metals. In addition, the presence of metastable transport properties is noted, the material having the tendency to pass from a compound with thermoelectric characteristics of p-type to those of a n-type with increasing temperature if the c/a ratio is over unitary. (1.02) The efficiency of a thermoelectric material can be evaluated by the thermoelectric figure of merit parameter ZT = S 2 σT /κte where S, σ, T and κte are the Seebeck coefficient, the electrical conductivity, the absolute temperature and the electronic thermal conductivity respectively. As can be seen in Fig 7, the efficiency to conduct electric curent of the studied material is high at 350K, being equal to 0.94. These results are significant especially because the non-doped material CoFeZrSi has a figure of merit parameter comparable to the values obtained experimentally for p-type materials such as ZT=0.7 at 973K for T iF e0.6 N i0.4 Sb [7] In addition, as the structure becomes more and 7

350

700

1050

T(K)

Cubic optim volume

0.9

vol +4%

0.04

vol -4%

0.02

0.3

0.00 350

700

ZT

ZT

0.6

1050

T(K)

0.0 350

700

1050

T(K)

Figure 7: The thermoelectric figure of merit as function of temperature, for cubic crystalline structure

ZT

c/a=1.02

0.2 0.1

vol -4%

-0.1 350

0.5

0.0

vol -4%

0.002 0.001

0.0

1.0

ZT

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c/a=0.96 ZT

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700

0.000

1050

350

optimum volume

optimum volume

vol +4%

vol +4%

350

700

T(K)

700

1050

T(K)

T(K)

350

1050

700

1050

T(K)

Figure 8: The thermoelectric figure of merit as function of temperature, for tetragonal crystalline structures

more relaxed and the volume increases with +4%, without modifying its energetic favorable crystalline structure (cubic), the thermoelectric efficiency of the material characterized by the figure of merit ZT, is improved. When tetragonal deformation is considered (see Fig 8 ) the figure of merit for relaxed volumes (optimized and vol=+4 %) is still high at temperatures up to 600K, afterwards, decreasing sharper for optimum volume. However, for a confined volume (as vol=-4 %) when the material exhibited negative Seebeck coefficients, having n-type characteristics, the figures of merit are insignificant for both c/a ratio. Triclinic distortion destroys not only half metallic properties [25] but also the thermoelectric features are lost. Consequently, the preservation of 90o angles at the interface with other layer or with substrate is mandatory to obtain a material with half-metallic and thermoelectric characteristics. 4. Conclusions Self-consistent investigations on cubic structure, the energetic favorable one, and on tetragonal / triclinic distortions, which may appear in experimental 8

condition, at the interface between the deposited layer of CoFeZrSi Heusler material and substrate or other layer, due to lattice mismatch, provide information regarding thermoelectric characteristics. In cubic structure, the material exhibits p-type thermoelectric characteristics for relaxed unit cell (optimum or with a volume increased with +4 % ) and ntype thermoelectric features when the structure is isostatic confined with -4% under a pressure of 7.54GPa. The tetragonal distortion doesn’t significantly change the thermoelectric properties observed for cubic structure, except that when the c/a ratio increased with +2%, and the volume of unit cell in confined with -4%, the Seebeck coefficient decreases significantly at values typical for metal materials, and show a transition from p-type thermoelectric material to n-type, as the temperature increases. Triclinic deformation, based on the decrease with one degree of γ angle (the angle located between a and b lattice parameters ) destroys the thermoelectric features observed for the crystalline structures whose whole angles are equal to 90o , leading to the conclusion that the thermoelectric characteristics of an Heulser material may be destroyed by the lattice mismatch, occurring at the interface between thin layers. 5. ACKNOWLEDGMENTS The author would like to thank Dr. P. Palade for computational support and Prof Dr. V. Kuncser for helpful discussions. The author acknowledge the financial support provided by the Romanian National Authority for Scientific Research through the Core Program PN21N, PN-III-P1-1.2-PCCDI-2017-0871. [1] J. He, and T. M.Tritt, Science 357 (2017) eaak9997 [2] Jun Mao, Jiawei Zhou, Hangtian Zhu, Zihang Liu, Hao Zhang, Ran He, Gang Chen, and Zhifeng Ren. Chem. Mater. 2017, 29, 867-872. [3] W.Ren, H.Zhu, J.Mao, L.You, S.Song, T.Tong, J. Bao, J. Luo, Z.Wang, Z.Ren, Adv. Funct. Mater. 5 (2019) 1900166 [4] S.C. Lee Enamullah, J. Alloys Compd. 742 (2018) 903 [5] T.M. Bhat, D.C. Gupta, RSC Adv. 6 (2016) 80302 [6] J.Zhou, H. Zhu, T.-H. Liu, Q. Song, R.He, J. Mao, Z.Liu, W.Ren, B.Liao, D.J. Singh, Z.Ren, G.Chen, Nat. Commun. 9 (2018) 1721 [7] Z. Liu, S. Guo, Y. Wu, J. Mao, Q. Zhu, H. Zhu, Y. Pei, J. Sui, Y. Zhang, Z. Ren Adv. Funct. Mater., 29 (2019) 1905044 [8] Ting Zhou, Jun Mao, Jing Jiang, Shaowei Song, Hangtian Zhu, Qing Zhu, Qinyong Zhang, Wuyang Ren, Zhiming Wang, Chao Wang and Zhifeng Ren. J. Mater. Chem. C, 7 (2019), 434-440. 9

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• • • •

The thermoelectric properties of CoFeZrSi were theoretically investigated. Evidence for p-type half-metallic Heusler compound in cubic structure was provided. Estimated 480µV/K at 700K when a=b=c=5.97Å and α=β=γ=90°. Estimated ZT=0.94 in optimum cubic structure at 350K

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: