Ni substitution enhanced thermoelectric properties of ZrPd1−xNixPb (x = 0,0.25,0.5,0.75,1)

Accepted Manuscript Ni substitution enhanced thermoelectric properties of ZrPd1−xNixPb Dongyang Wang, Guangtao Wang, Wenfeng Li PII:

S0925-8388(16)32838-9

DOI:

10.1016/j.jallcom.2016.09.086

Reference:

JALCOM 38920

To appear in:

Journal of Alloys and Compounds

Received Date: 28 June 2016 Revised Date:

3 September 2016

Accepted Date: 7 September 2016

Please cite this article as: D. Wang, G. Wang, W. Li, Ni substitution enhanced thermoelectric properties of ZrPd1−xNixPb, Journal of Alloys and Compounds (2016), doi: 10.1016/j.jallcom.2016.09.086. 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 Ni substitution enhanced thermoelectric properties of ZrPd1−x Nix Pb Dongyang Wang, Guangtao Wang∗ , and Wenfeng Li College of Physics and Electronic Engineering, Henan Normal University, Xinxiang, Henan 453007, People’s Republic of China (Dated: September 8, 2016)

for the new thermoelectric material in the half-Heusler compounds.

INTRODUCTION

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Based on the first-principles calculations, we systematically studied the electronic structure and thermoelectric properties of ZrPd1−x Nix Pb (x=0, 0.25, 0.5, 0.75, 1) compounds with the mBJ potential and mBJ+SOC method. By using the calculated band structures and Boltzmann transport theory, we studied the thermopower S, power factor over relaxation time S 2 σ/τ , and optimal carrier concentration for both of p- and n-type compounds. Our results indicate that all the compounds are thermodynamically stable narrow-gap semiconductors, with the band gaps ranging from 0.094 to 0.435 eV. The x = 0.25 and 0.75 compounds are direct band gap semiconductors, while the pure ones are indirect band gap semiconductors. The optimal carrier concentration and corresponding power factor (S 2 σ/τ ) for x = 0, 0.25, 0.75, and 1 compounds are very close in p-type. The Ni substitution significantly decreases the lattice thermal conductivity from 26.4 W/mK (x = 1) to 6.37 W/mK (x = 0.25) at 300 K, without reducing the S 2 σ/τ . The lower lattice thermal conductivities of ZrPd0.25 Ni0.75 Pb and ZrPd0.75 Ni0.25 Pb suggest good thermoelectric properties. The cost of the alloy can also be decreased by the Ni substitution, whose price is only about 0.2% of the Pd metal.

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Thermoelectric energy conversion is a promising and useful technology for both electric power generation from waste heat and cooling of various electronic devices. To be a good thermoelectric material, it should has a large figure of merit ZT =σS 2 T /κ, where σ, S, T , and κ are electrical conductivity, Seebeck coefficient, absolute temperature, and thermal conductivity, respectively1,2 . The desirable material should have a large power factor S 2 σ, and a low κ, which consists of a lattice component κph and an electronic component κel . However, it is difficult to find a compounds with large values of ZT , because that the σ, S and κ are coupled and dependent strongly on the detailed electronic structure, carrier concentration and crystal structure.

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Many half-Heusler alloys are narrow-gaped semiconductors and exhibit high thermopower (S ∼ -300 µV/K) at room temperature3–6 . The half-Heusler alloys M NiSn and M CoSb (M = Ti, Zr, Hf) are considered as a promising class of thermoelectric materials due to their excellent mechanical properties and high temperature stability7–10 . Recently reported half-Heusler thermoelectric material FeM Sb (M = V, Nb) has also attracted much attention due to the abundantly available constituent in the earth, the higher Seebeck coefficient (∼ -200 µVK−1 at 300 K) and the larger power factor (4.5×10−3 Wm−1 K−2 at 300 K)11–15 . The maximum ZT of p-type half-Heusler thermoelectric materials FeNb1−x Tix Sb (0.04 ≤ x ≤ 0.24) can reached 1.1 at 1100 K14 . Such high ZT inspires the investigation

* Corresponding author. E-mail addresses: [email protected]

The thermal conductivity of half-Heusler compounds mainly comes from the lattice thermal conductivity16 . In order to decrease the lattice thermal conductivity, some efforts are made: 1. increasing the number of atoms in unit cell to strengthen the phonon scattering17,18 via complicated structure18–20 ; 2. decreasing the material dimension21 and introducing heavy atom into thermoelectric parent materials17,20,22 ; 3. introducing point defect into the material23 . All of these methods are aimed to increase scattering centers and decrease mean free path of phonons. The complicated structure with heavy elements, i.e. Hfx Zr1−x CoSb0.8 Sn0.2 (x= 0.15, 0.2, 0.25), can effectively increase the electrical conductivity and decrease the thermal conductivity, comparing with the M CoSb (M = Ti,Zr,Hf) alloys17,24,25 . New half-Heusler compound ZrNiPb was recently synthesized by Zunger et. al.26 with a small band gap 0.53 eV. They found the thermopower and power factor of ZrNiPb were -153.9 µV/K and 5.2 µW cm−2 K−1 at room temperature, which are higher than those of Zr0.5 Hf0.5 NiSn with power factor 3.0 µW cm−2 K−1 and ZT > 0.5 at 700 K27 . Guo28,29 reported the thermal conductivity of ZrNiPb as 14.5 W/mK at room temperature, which is higher than other half-Heusler compounds16 . In order to enhance the thermoelectric performance of ZrNiPb-based compounds, we systematically studied the electronic structure and thermoelectric properties of ZrPd1−x Nix Pb (x = 0, 0.25, 0.5, 0.75, 1) compounds. There are no reports on the thermoelectricity of ZrPd1−x Nix Pb, except for x = 0 and 126,28,30 . In this study, we aimed to decrease the lattice thermal conductivity by substituting Pd atom with isoelectric element Ni in the pure ZrPdPb compound.

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FIG. 1: The calculated phonon spectrum of (a) ZrPdPb, (b) ZrPd0.75 Ni0.25 Pb, (c) ZrPd0.5 Ni0.5 Pb, (d) ZrPd0.25 Ni0.75 Pb, and (e) ZrNiPb.

METHODOLOGY

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We systematically studied the electronic structure and thermoelectric properties of ZrPd1−x Nix Pb by using the first-principles calculations and Boltzmann theory. We found that the thermoelectric properties were greatly improved by Ni substitution (x = 0.25 and 0.75), which decreased the thermal conductivity without reducing the power factor over relaxation time S 2 σ/τ .

The crystal structure optimization was performed by using the Vienna Ab-initio Simulation Package (VASP)31 . The generalized gradient approximation (GGA)32 of Perdew-Burke-Ernzerhofer (PBE)33 with the project-augmented wave (PAW) method was adopted. The wave functions are expanded in plane waves with the cut off energy of 550 eV. The HellmannFeynman forces acting on atoms were relaxed to < 0.01 eV ˚ A−1 . The optimized lattice parameters are listed in Table.I, which are consistent with the experimental data reported by Zunger26 . Phonon calculations were carried

out with the frozen phonon method as implemented in the Phonopy34 package with 2×2×2 supercell.

The electronic structures of ZrPd1−x Nix Pb (x = 0, 0.25, 0.5, 0.75, 1) were calculated with the full-potential linearized augmented plane-wave (LAPW) method as implemented in the WIEN2k code35 . Tran-Blaha modified Becke-Johnson (mBJ) potential36,37 was adopted in our calculations. The spin-orbital coupling (SOC) effect was also considered for all the atoms. The temperature and doping-level dependent thermopower was calculated based on the Boltzmann transport theory within the constant scattering-time approximation (CSTA)38 by using the BoltzTraP code39 . This method has been provided to obtaining a good description of thermopower in a variety of thermoelectric materials5,40–43 .

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RESULTS AND DISCUSSION

Crystal structures and lattice thermodynamics

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FIG. 2: The calculated band structures with mBJ (red solid line) and mBJ+SOC method (green dashed line) and density of states using mBJ+SOC method for (a) ZrPdPb, (b) ZrPd0.75 Ni0.25 Pb, (c) ZrPd0.5 Ni0.5 Pb, (d) ZrPd0.25 Ni0.75 Pb, and (e) ZrNiPb. The Fermi level is at zero.

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The half-Heusler ABX alloys are ternary compounds with the LiAlSi-type structure. These compounds crystallized in the face-centered cubic structure with the space group F ¯43m (No. 216). The unit cell of ZrPdPb contains four formula unites with Zr, Pd and Pb atoms locating at the 4b (0.5,0.5,0.5), 4c (0.25,0.25,0.25) and 4a (0,0,0) Wyckoff sites, respectively. We studied the different Ni substitutions, i.e. x = 25%, 50%, 75%, and 100%. The unit cell and space group were changed due to the substitution. For x = 50%, the primitive cell of ZrPd0.5 Pd0.5 Pb contained six atoms and had a tetragonal structure with space group P ¯ 4m2 (No. 115). The relaxed lattice constants of doped and undoped compounds were summarized in Table.I, with Zunger’s results26 for comparison. For the compounds that x = 0 and 1, the optimized lattice constants were in agreement

with the experimental26 data and calculated results28,30 . The lattice constants decreased with the increasing of x, due to the smaller radium of Ni than Pd. In order to investigate the stability of the artificially substituted compounds, we evaluated the phonon dispersion based on the harmonic force constants obtained from the Phonopy package34,44 . In Fig.1, there is no imaginary frequency, which indicates the thermodynamic stability of Ni-substituted compounds. The optical phonon modes have weak dispersion, which implies that they hardly contribute to the heat transport due to their smaller group velocities. While the acoustic modes take the responsibility for the heat transport as they have strong dispersion and large group velocities. The frequency of acoustic branches in ZrNiPb and ZrPdPb could reached to 110 cm−1 . For x = 0.25, 0.5 and 0.75, the frequency of acoustic branches were lower than 75 cm−1 . The low frequency optical modes mixed with the acoustic branches, which suggests the stronger phonon-phonon scattering.

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TABLE I: Lattice parameter a, band gaps with mBJ (Eg ) and mBJ+SOC (Eg SOC ) methods, and the spin-orbital splitting energy (△ESOC ) of ZrPd1−x Nix Pb (x= 0, 0.25, 0.5, 0.75, 1). The lattice parameter and band gaps in bracket were adopted from Ref. 26. ˚) compounds a(A Eg (eV) Eg SOC (eV) △ESOC (eV)

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FIG. 3: Seebeck coefficient, S, (in µV /K) as function of carrier concentrations and temperatures for (a) ZrPdPb, (b) ZrPd0.75 Ni0.25 Pb, (c) ZrPd0.25 Ni0.75 Pb, and (d) ZrNiPb. The color lines refer to different temperature: black (300 K), red (500 K), green (700 K), and blue (900 K). The solid and dashed lines refer to the results with mBJ and mBJ+SOC methods, respectively.

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The thermal conductivity in bulk semiconductor is intrinsically limited by anharmonic phonon-phonon scattering45,46 . Such strong phonon-phonon scattering implies low thermal conductivity. The similar behavior was observed in BiCuSeO47 , where the thermal conductivity was very low at high temperature. So the lower lattice thermal conductivity will be expected in these artificially doped compounds than in ZrPdPb.

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0.6787 0.6764 0.6115 0.7009 0.7158

conduction band maximum (CBM) changes with Ni substitutions. ZrPd0.75 Ni0.25 Pb and ZrPd0.25 Ni0.75 Pb are direct band-gap semiconductors with Eg = 0.247 eV and 0.178 eV. For x = 0 and 1, they are indirect band-gap (Γ-X) semiconductors with Eg = 0.435 eV and 0.414 eV, respectively. For x = 0.5, the CBM locates at M , forming an indirect band gap of 0.094 eV, which is smaller than that of Bi2 Te3 39 . The SOC effect leads to a split between the degenerated bands around the Fermi level, but the split is too small to cause significant difference between Eg SOC and Eg . Our calculated Eg of undoped compounds were in agreement with experimental results26 . Previous reports3,36 demonstrate that the mBJ method was a good way to reproduce the band gap of semiconductor. So we used both mBJ and mBJ+SOC in this work. The SOC effect was not significant for the bands at the Fermi level, but it had a notable impact on the bands around at -0.7 eV, which was mainly derived from Pb-6p state.

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Electronic band structure

Based on the optimized stable crystal structures, we calculated the band structures with mBJ and mBJ+SOC method, as shown in Fig.2. The corresponding band gaps with (Eg SOC ) and without SOC (Eg ) and the energy splitting (△ESOC ) were summarized in Table.I. Our results indicate that all the compounds are narrow-gap semiconductors. The valence band maximum (VBM) of all compounds locates at Γ, while the position of

The results of calculated DOS with mBJ+SOC method are shown in Fig.2. The VBM is mainly derived from Zr-4d state, while the contribution from Ni/Pd/Pb is very small. The contribution to CBM is relatively complex. For x = 0 and 0.25, the CBM are mainly derived from the mixture of Zr-4d and Pd-4d states. For x = 0.75 and 1, the CBM mainly composed of hybridized Zr-4d and Ni-4d states. However, for x = 0.5, the contribution of Ni-3d and Pd-4d are smaller than that of Zr-4d state. The DOS has a sharply increase when the energy changes from -1.0 to -0.5 eV, and the slope of x = 0.25 and 0.75 around VBM are significantly larger than those of other compounds. This rapid DOS increment with energy at the Fermi level is a good indicator of large thermopower48 in p-type material. Within the rigid band model, we can easily transfer the Fermi level to this range, and then enhance the thermoelectric properties.

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Thermoelectric properties

Fig.3 shows the Seebeck coefficient (S) as a function of carrier concentration for different Ni substitution

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FIG. 4: The power factor, S 2 σ/τ , (in 1014 µW/cm−1 K−2 s−1 ) as function of carrier concentrations and temperatures for (a) ZrPdPb, (b) ZrPd0.75 Ni0.25 Pb, (c) ZrPd0.25 Ni0.75 Pb, and (d) ZrNiPb. The color lines refer to different temperatures: black (300 K), red (500 K), green (700 K), and blue (900 K). The mBJ and mBJ+SOC results are in solid and dashed lines, respectively.

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at four temperatures, 300, 500, 700, and 900 K. The difference of S between mBJ and mBJ+SOC is very small for n-type, but it is relatively large for p-type. This difference indicates that SOC has moderate influence on p-type due to the energy split in the valence band, as shown in Fig.2 around -0.7 eV. For x = 0, the Seebeck coefficient |S| decreases when the carrier concentration increases at the temperature lower than 700 K. At 900 K, |S| increases first and then decreases with carrier concentration increase, showing a peak at n = 1.63×1020 cm−3 with mBJ method and at n = 9.13×1019 cm−3 with mBJ+SOC method. The |S| peaks are caused by the bipolar effect due to the small band gap and high temperature. For x = 0.25 and 0.75, their gaps are smaller than those of x = 0 and 1, the bipolar effect is more significant in the lower carrier concentration (1020 cm−3 ) with higher temperature, i.e. T = 700 K. Comparing the calculated data with the experimental Seebeck coefficient26 S = -153.9 µV/K of ZrNiPb, we found the corresponding carrier concentration n = 1.47×1020 cm−3 (0.0089 electron per unit cell) at room temperature (in Fig.3(d)), which was lower than Guo’s28 result n = 1.57×1020 cm−3 (0.0097 electron per unit cell). The absolute value of S in p-type materials is larger than that of corresponding n-type. In Fig.4, we present the power factor over relaxation time, S 2 σ/τ , as a function of carrier concentration and temperature, with the mBJ and mBJ+SOC methods for both n- and p-type. The wide range of carrier concentra-

tion, 1019 -1022 cm−3 , allows us to find the optimal carrier concentration. At room temperature, the maximum S 2 σ/τ and corresponding carrier concentration are summarized in Table.II. The S 2 σ/τ difference between the mBJ and mBJ+SOC results is very small for n-type materials, but the difference is significant for that of p-type, which means that the SOC effect has a significant influence on p-type compounds28,30 . For x = 0.25 and 0.75, the peak value of S 2 σ/τ in p-type is larger than that of n-type, which indicates that p-type compounds have a better performance than the n-type. For x = 0, the S 2 σ/τ in n-type is very close to that in p-type at the same temperature and carrier concentration. For x = 1, with the mBJ method, the S 2 σ/τ of n-type is larger than that in p-type at the same temperature and carrier concentration, which implies that the thermoelectric properties of n-type is better than that in p-type28,30 . The optimal carrier concentration and corresponding properties of four compounds at 300 K are listed in Table.II. The x = 0.25 and 0.75 compounds exhibit good performance in p-type with optimal carrier concentration 1.76 × 1020 cm−3 (0.0466 hole/unit cell) and 1.81×1020 cm−3 (0.0452 hole/unit cell), respectively. The optimal carrier concentration and corresponding transport properties of p-type materials are very close to each other (different Ni-substitution), while the n-type compounds have a significant difference. For ZrPd0.75 Ni0.25 Pb, their optimal concentration monotonically increase from n = 1.76 × 1020 (p-type) and n = 2.11×1020 (n-type)

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TABLE II: The optimal carrier concentration n and the doping level N , corresponding thermopower S and S 2 σ/τ for ZrPd1−x Nix Pb (x = 0, 0.25, 0.75, 1) compounds at 300 K with mBJ and mBJ+SOC methods. The value in bracket is calculated with mBJ+SOC method. The unit of n, N , S 2 σ/τ , and S are 1020 cm−3 , holes (or electrons) per unit cell, 1014 µW/(cmK2 s) and µV/K, respectively.

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at 300 K to n = 8.97×1020 cm−3 (p-type) and n = 9.78×1020 cm−3 (n-type) at 900 K. While the optimal hole-concentration of ZrPd0.25 Ni0.75 Pb increases from n = 1.81×1020 at 300 K to n = 8.42×1020 cm−3 at 900 K (p-type), and the optimal electron-concentration increases from n = 9.37× 1020 to n = 1.39×1021 cm−3 (n-type).

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The lattice thermal conductivity κ is important to ZT , due to ZT = S 2 T σ/(κph + κe ). Recently, a new method49–52 to estimate the lattice thermal conductivity has been proposed by using the Debye temperature (θD ) and the Gruneision parameter (γ)53–55 : κph (T ) =

0.617 θ3 k 3 mV 1/3 × D B3 2 −2 −1 1 − 0.514γ + 0.228γ nh γ T 1

υ 2 −4υ 2 /3

S 145.4(129.5) -129.1(-133.6) 145.5(131.3) -96.5(-79.6) 137.4(123.0) -54.4(-54.2) 143.0(137.3) -138.8(-137.5)

Based on the above formula, we calculated the lattice thermal conductivity of ZrPd1−x Nix Pb (x = 0, 0.25, 0.75, 1) and presented the results in Fig.5. The lattice thermal conductivity decreases with the temperature increase. ZrNiPb has a larger lattice thermal conductivity than ZrPdPb, due to the heavier Pd atoms. At 300 K, the lattice conductivity of four compounds are 14.56, 6.37, 8.72 and 26.42 W/(mK) for x = 0, 0.25, 0.75, and 1, respectively. The κph of doped compounds are lower than that of the pure compounds, because that the Ni substitution increase the number of atoms in unit cell18–20 and the phonon scattering centers17,18,20 . Comparing x = 0.25 and 0.75 with the pure compounds of x = 0 and 1, we find that the p-type S 2 σ/τ hardly decrease with Ni substitution (see Table.II), while the lattice thermal conductivities of doped compounds decrease greatly (Fig.5). So we can expect a significant improvement of ZT in the Ni substituted compounds (x = 0.25, 0.75).

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9 Aρ 3 L t Where θD = khB [ 3nN 2 +2υ 2 ), NA is 4M π ] υm , γ = 2 ( υL t Avugadro’s constant, n is the number of atoms in unit cell, M is the mass of the unit cell, kB is Boltzmann constant, V is the volume of the unit cell and m is the average atomic mass, υL , υt , υm are longitudinal, transverse and average sound velocity, respectively.

IV.

CONCLUSION

In this work, we studied the thermodynamic stabilities, electronic structure and thermoelectric properties of ZrPd1−x Nix Pb (x = 0, 0.25, 0.5, 0.75, 1) compounds by using the first-principles calculations within improved mBJ potential and mBJ+SOC method. The phonon spectrum and band structure confirm that the three doped compounds are thermodynamically stable narrow-gap semiconductors. The Ni substitution changes the band structure from indirect band gap of pure compounds (x = 0, 1) to direct band gap of doped compounds (x = 0.25, 0.75). Based on the calculated band structure and the Boltzmann transport theory, the thermopower S and power factor over relaxation time S 2 σ/τ of both p- and n-type doped compounds were studied. Using the rigid band model, we got the optimal carrier concentrations of four compounds at 300 K. The S 2 σ/τ was calculated with the optimal carrier

ACCEPTED MANUSCRIPT concentration. According to the Slack method53–55 , we estimated the lattice thermal conductivity and confirmed the significant decrease in the doped systems. With the lower lattice thermal conductivity and higher S 2 σ/τ , the p-type ZrPd0.25 Ni0.75 Pb and ZrPd0.75 Ni0.25 Pb are expected to be good thermoelectric materials.

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for Science and Technology Innovation Talents in the Universities of Henan Province (No.2012HASTIT009, No.104200510014, and No.114100510021). This work is supported by The High Performance Computing Center (HPC) of Henan Normal University.

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Highlights: 1. ZrPd1-xNixPb are thermodynamically stable compounds 2. the phonon spectrum, band structure and thermoelectric properties of ZrPd1-xNix 3. Ni substitution decreases the lattice thermal conductivity significantly 4. ZrPd0.25Ni0.75Pb and ZrPd0.75Ni0.25Pb are good p-type thermoelectric materials