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https://doi.org/10.3390/ma11050728

Article

Synthesis and Thermoelectric Properties of Pd-Doped ZrCoBi Half-Heusler Compounds

School of Materials Science and Engineering, University of Jinan, Jinan 250022, China

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Author to whom correspondence should be addressed.

Received: 9 April 2018 / Accepted: 3 May 2018 / Published: 4 May 2018

## Abstract

**:**

In this study, n-type Pd-doped ZrCo

_{1-x}Pd_{x}Bi (x = 0, 0.03, 0.06, 0.09) half-Heusler samples were prepared by arc-melting and rapid hot-pressing sintering. The thermoelectric properties of ZrCo_{1-x}Pd_{x}Bi samples were analyzed and discussed. The results showed that the electrical properties of ZrCo_{1-x}Pd_{x}Bi, including electrical conductivity and the Seebeck coefficient, increase due to the substitution of Pd on Co site. The lattice thermal conductivity of ZrCo_{1-x}Pd_{x}Bi is markedly decreased because of the Pd/Co substitution. A minimum κ_{L}of 5.0 W/mK for ZrCo_{0.91}Pd_{0.09}Bi is achieved at 800 K. The figure of merit of ZrCo_{1-x}Pd_{x}Bi is boosted due to the depressed lattice thermal conductivity and the improved power factor. The highest value of figure of merit reaches 0.23 for ZrCo_{0.97}Pd_{0.03}Bi half-Heusler compound at 800 K.Keywords:

ZrCoBi; half-Heusler; Pd/Co substitution; thermoelectrics## 1. Introduction

Due to the large-scale utilization of fossil fuel energy, humans are facing a worldwide energy crisis and environmental problem. Developing reliable and renewable energy technology is becoming an inevitable choice for mankind in the 21st century to deal with the energy crisis and achieve sustainable economic development. Thermoelectric materials have huge potential and broad prospects in the application of solid-state cooling, heat pump and waste heat recovery because they can realize direct conversion between electricity and heat. Generally, the efficiency of thermoelectric materials is determined by the dimensionless figure-of-merit, ZT = σS

^{2}T/(κ_{e}+κ_{L}), where σ is the electrical conductivity, S is the Seebeck coefficient, σS^{2}is the power factor (PF), κ_{e}and κ_{L}are the respective electronic thermal conductivity and lattice thermal conductivity of total thermal conductivity κ [1,2,3]. The ZT of thermoelectric material can be enhanced by increasing the power factor and/or by decreasing the thermal conductivity. However, the complex interdependency of S, σ, and κ_{e}makes it difficult to boost the figure of merit by independently adjusting a parameter. Many advances in ZT of thermoelectric materials have been obtained by all-scale phono scattering, point defect, nanocomposite, the carrier concentration optimization and band engineering, et al. [4,5,6].Half-Heusler (HH) compounds with cubic MgAgAs structure (F-43m) have been extensively studied due to their promising properties such as high mechanical strength and reliability, non-toxicity et al. HH compounds with 18 valence electrons per unit cell such as (Hf, Ti, Zr)CoSb and(Hf, Zr, Ti)NiS, exhibit unusual thermoelectric performance due to the sharp slope of their density of states (DOS) near Fermi level and narrow gap [7,8,9]. One of the key issues of HH compounds is the relatively high κ

_{L}. Many efforts focusing on the decrease of κ have been performed in order to enhance the ZT of HH alloys. The substitution of each site in cubic MgAgAs structure is a useful approach to enhance the thermoelectric properties of HH alloys because the position of Fermi energy can be adjusted and the κ_{L}can be decreased by alloy scattering. Tang et al. found interstitial Ni atoms in TiNiSn can scatter the phonons markedly and decrease the κ_{L}, which results in the enhancement of ZT for Ni-rich TiNiSn compounds [10]. Huang et al. reported that Sn substitution leads to a doubled S and decreases the κ_{e}of NbCoSb_{1-x}Sn_{x}; thus, a maximal figure of merit of 0.54 is obtained [11]. Uher et al. and Rausch et al. reported that the mass disorder in the (Ti, Zr, Hf)-site lattice can result in extra phonon scattering, therefore decreasing the κ of (Hf, Zr, Ti)CoSb and (Hf, Zr)NiSn [12,13]. A good deal of data about the thermoelectric properties of n-type (Hf, Zr, Ti)CoSb and (Hf, Zr, Ti)NiSn [14,15,16] have been reported. However, there is little information about n-type ZrCoBi compounds.In this work, the n-type Pd-doped ZrCo

_{1-x}Pd_{x}Bi half-Heusler alloys were synthesized by arc-melting and rapid hot-pressing sintering. Thermoelectric properties of Pd-doped ZrCo_{1-x}Pd_{x}Bi half-Heusler alloys were measured and discussed. To our knowledge, this is the first report on the study about the ZrCo_{1-x}Pd_{x}Bi half-Heusler compound. We hoped that the Pd/Co substitution could enhance the S^{2}σ and decrease the κ_{L}and then boost the figure of merit.## 2. Experimental Procedures

The ingots with nominal composition ZrCo

_{1-x}Pd_{x}Bi (x = 0, 0.03, 0.06, 0.09) were synthesized by arc-melting stoichiometric amounts of Bi (rod, 99.98%), Pd (granule, 99.999%), Co (granule, 99.999%), and Zr (slug, 99.98%) under an argon atmosphere. Then, the resultant ingots were ground into fine powders in agate mortar. After pulverizing in agate mortar, the powder of ZrCo_{1-x}Pd_{x}Bi was ball-milled in in a planetary ball milling machine using zirconia balls at 180 rpm for 10 h. Then the resulting powder was sieved using a 400-mesh sieve before hot consolidation. The average size of the obtained ZrCo_{1-x}Pd_{x}Bi powder was about 3.5 µm, as shown in Figure 1. The pulverized powders were consolidated by a rapid hot-press sintering process at 1323 K under the axial pressure of 65 MPa for 8 min in vacuum. The rapid hot-pressing sintering process was carried out in self-made equipment. The heating rate of rapid hot-pressing sintering is about 100 °C/min. The densities (ρ) of sintered ZrCo_{1-x}Pd_{x}Bi samples were measured by Archimedes method. The constituent phases and microstructure of ZrCo_{1-x}Pd_{x}Bi were characterized by X-ray diffraction (XRD, Siemens D5000, Bruker, Billerica, MA, USA) and field-emission scanning electron microscopy (FE-SEM, JXA-8200, JEOL, Tokyo, Japan), respectively. The electrical transport property of ZrCo_{1-x}Pd_{x}Bi samples including Seebeck coefficient (S) and electrical conductivity (σ) was measured by ZEM-3 instrument (ULVAC-RIKO, Yokohama, Japan) in helium. The total thermal conductivity of ZrCo_{1-x}Pd_{x}Bi was calculated using κ = DρC_{p}, where D is thermal diffusion coefficient, ρ is the density, and C_{p}is the specific heat capacity. D was obtained using the laser flash method (ULVAC-RIKO, TC7000) under argon. The specific heat capacity was determined using a differential scanning calorimetry (Perkin-Elmer, Waltham, MA, USA). The Hall coefficient (R_{H}) measurements of ZrCo_{1-x}Pd_{x}Bi samples at room temperature were carried out by a Hall effect system in vacuum under a varied magnetic field ranging from −0.5 T to +0.5 T. The carrier concentration (n) and Hall mobility (µ_{H}) were calculated based on the Hall coefficient according to n = 1/(eR_{H}) and µ_{H}= R_{H}σ, respectively, where e is the electron charge.## 3. Results and Discussion

The XRD diagrams of the sintered bulk ZrCo

_{1-x}Pd_{x}Bi samples are shown in Figure 2. All major diffraction peaks could be identified and indexed as the half-Heusler ZrCoBi phase (JCPDS 51-1255) without impurity phase under the detecting limit of XRD. The calculated lattice constant of ZrCoBi is 0.6174 nm, which is consistent with the previous report [17]. As shown in Figure 3, the calculated lattice constant of ZrCo_{1-x}Pd_{x}Bi (x = 0, 0.03, 0.0.06, 0.0.09) samples gradually increases with the Pd-doping content increasing, which is attributed to the bigger atom radius of Pd than Co. The lattice constant and error evaluation were calculated according to the references [18,19,20]. The relative densities of ZrCo_{1-x}Pd_{x}Bi samples were calculated and are listed in Table 1, high relative densities can ensure the measurement of thermoelectric properties.Figure 4 displays the SEM image and the elemental distribution of the sintered ZrCo

_{0.97}Pd_{0.03}Bi HH compound. It can be clearly noted from the images that all elements were distributed homogeneously and no evident other phase or crack existed, suggesting the ZrCo_{0.97}Pd_{0.03}Bi HH sample is the single phase that is in agreement with the XRD results. In addition, the fractural SEM showed that the grain size of sintered bulk ZrCo_{0.97}Pd_{0.03}Bi half-Heusler samples is about 15 µm, just as shown in Figure 5. The variation of σ for ZrCo_{1-x}Pd_{x}Bi HH compounds is present in Figure 6. The ZrCoBi sample exhibits a typical semiconductor behavior and has the lowest σ value over the entire measurement range. However, the σ of Pd-doped ZrCo_{1-x}Pd_{x}Bi HH compounds shows the semi-metal behavior within the measured temperature range. Compared with the σ of pristine ZrCoBi sample, the σ of Pd-doped ZrCo_{1-x}Pd_{x}Bi samples increases with the Pd-doping content rising. As Pd can donate more electrons than Co, the n of ZrCo_{1-x}Pd_{x}Bi samples is high than that of pristine ZrCoBi sample which results in the higher σ, just as shown in Table 1. For instance, the n of ZrCo_{0.91}Pd_{0.09}Bi sample increases to 5.25 × 10^{20}cm^{−3}.Figure 7 shows the variation of S for ZrCo
where h, k

_{1-x}Pd_{x}Bi HH samples. All ZrCo_{1-x}Pd_{x}Bi samples have negative S and display the n-type conduction. The absolute value of S for ZrCo_{1-x}Pd_{x}Bi samples first increases and then decreases with the Pd-doping content rising. The S of ZrCo_{0.97}Pd_{0.03}Bi reaches a maximum of −191 µV/K at 800 K. In addition, the linear increase of S with rising temperature indicates that the ZrCo_{1-x}Pd_{x}Bi samples have single band conduction behavior. The Pd-doping could influence the band structure, which maybe increases the DOS near the Fermi level leading to the increase of S. Figure 8 shows the Pisarenko plots at 300 K of ZrCo_{1-x}Pd_{x}Bi samples which were derived by the relation (1)–(3) based on the single parabolic band (SPB) model [21]:
$$LS=\pm \frac{{k}_{B}}{e}\left[\xi -\frac{\left(r+5/2\right){F}_{r+3/2}\left(\xi \right)}{\left(r+3/2\right){F}_{r+1/2}\left(\xi \right)}\right],$$

$${F}_{n}\left(\xi \right)={{\displaystyle \int}}_{0}^{\infty}\frac{{x}^{n}}{1+{e}^{x-\xi}}dx,$$

$$n=4\mathsf{\pi}{\left(\frac{2{m}^{\ast}{k}_{B}T}{{h}^{2}}\right)}^{3/2}\times {F}_{1/2}\left(\xi \right),$$

_{B}, r, m^{∗}, and ξ are Planck’s constant, Boltzmann constant, scattering factor, the DOS effective mass and the reduced Fermi energy, respectively. The DOS effective mass of Pd-doped ZrCo_{1-x}Pd_{x}Bi samples was about 4.4m_{0}, which is higher than that of pristine ZrCoBi (2.9m_{0}). Therefore, the S of Pd-doped ZrCo_{1-x}Pd_{x}Bi samples is enhanced. According to the σ and S, the PF of ZrCo_{1-x}Pd_{x}Bi compounds are calculated in Figure 9. It can be seen that the PF of ZrCo_{1-x}Pd_{x}Bi compounds is markedly improved. The power factor of ZrCo_{0.97}Pd_{0.03}Bi reaches 21 μW·K^{−2}·cm^{−1}at 800 K, which is much higher than that of pristine ZrCoBi.Figure 10 shows the variation of κ for ZrCo

_{1-x}Pd_{x}Bi half-Heusler compounds within the whole measurement range. It can be observed that the κ of all ZrCo_{1-x}Pd_{x}Bi samples decreases with the temperature rising over the entire measured temperature due to the umklapp process. In addition, no bipolar effect is found in ZrCo_{1-x}Pd_{x}Bi samples. The κ of ZrCo_{1-x}Pd_{x}Bi samples decreases with the Pd-doping content rising which should be mainly due to the reduced κ_{L}, just as shown in Figure 11. Generally, the κ_{L}can be obtained by directly extracting the κ_{e}from the total κ and κ_{e}can be estimated from the Wiedemann–Franz relation, κ_{e}= LσT, where L is the Lorenz number. L can be estimated by the respective S using the SPB model according to the relation (1)–(4) [22].
$$L={\left(\frac{{k}_{B}}{e}\right)}^{2}\left[\frac{\left(r+7/2\right){F}_{r+5/2}\left(\xi \right)}{\left(r+3/2\right){F}_{r+1/2}\left(\xi \right)}-{\left(\frac{\left(r+5/2\right){F}_{r+3/2}\left(\xi \right)}{\left(r+3/2\right){F}_{r+1/2}\left(\xi \right)}\right)}^{2}\right].$$

The calculated Lorenz number at room temperature of pristine ZrCoBi half-Heusler is about 2.3 × 10

^{−8}WΩ/K^{2}and with the temperature increasing, the Lorenz number decreases. However, the calculated Lorenz number of Pd-doped ZrCo_{1-x}Pd_{x}Bi half-Heusler compounds is lower than that of pristine ZrCoBi and in the range of (1.8–2.1) × 10^{−8}WΩ/K^{2}.As shown in Figure 11, the κ

_{L}of ZrCo_{1-x}Pd_{x}Bi samples is markedly depressed because of the Pd/Co substitution. As the atom radius and mass of Pd are larger than those of Co, the Pd/Co substitution in the ZrCo_{1-x}Pd_{x}Bi samples could result in plenty of defect centers due to the strain field fluctuation (the differences of atom radius and interatomic coupling force) and the mass fluctuation (mass difference), which enhanced the phonon scattering [23]. Therefore, the κ_{L}of ZrCo_{1-x}Pd_{x}Bi samples decreases evidently. Generally, the lattice thermal conductivity can be estimated according to the relationship κ_{L}= 1/3C_{V}lV, where l is the mean free path of phonon, C_{V}is the heat capacity per unit volume and V is the average sound velocity. It is assumed the C_{V}and V are constant. Then, the κ_{L}is determined by the mean free path l. The phonon scattering in materials usually has four mechanisms including phonon–phonon scattering (l∝T^{−}^{1}), point-defect scattering, grain boundary scattering (l∝grain size), and electron–phonon scattering (l∝T^{−}^{2}). The point-defect scattering is related with the mass and size disorder introduced by atomic substitution. At high temperature (above the Debye temperature), grain boundary scattering and electron–phonon scattering can be ignored without changing any physical trend. It can be noted that the κ_{L}of pristine ZrCoBi follows a T^{−1}relationship below 473 K and the temperature-dependence of T^{−0.5}above 473 K, indicating that the phonon–phonon scattering mechanism and the mixed scattering mechanism are the dominant scatterings, respectively. With the Pd-doping concentration rising, the κ_{L}of ZrCo_{1-x}Pd_{x}Bi samples deviates the T^{−1}and displays a lower slope which follows the T^{−0.5}behavior approximately, indicating the extra point defect scattering due to the Pd/Co substitution makes a large contribution to the phonon scattering [24,25]. The κ_{L}decreases from 15.4 W/mK for pristine ZrCoBi to 9.2 W/mK for ZrCo_{0.91}Pd_{0.09}Bi at room temperature and a minimum κ_{L}of 5.0 W/mK for ZrCo_{0.91}Pd_{0.09}Bi is obtained at 800 K. Figure 12 shows the temperature-dependent of ZT of ZrCo_{1-x}Pd_{x}Bi half-Heusler compounds. The ZT of pristine ZrCoBi half-Heusler is very low and almost has no change with the increase of temperature. Compared with the ZT of pristine of ZrCoBi half-Heusler, the ZT of Pd-doped ZrCo_{1-x}Pd_{x}Bi half-Heusler compounds at room temperature is evidently enhanced and is about 0.02. Moreover, the ZT values of Pd-doped ZrCo_{1-x}Pd_{x}Bi half-Heusler compounds increase with increasing temperature. Because of the improved power factor and the depressed κ_{L}by the Pd/Co substitution, the thermoelectric performance of ZrCo_{1-x}Pd_{x}Bi half-Heusler is boosted and the maximum figure of merit reaches 0.23 for ZrCo_{0.97}Pd_{0.03}Bi half-Heusler sample at 800 K.## 4. Conclusions

The n-type Pd-doped ZrCo

_{1-x}Pd_{x}Bi half-Heusler compounds were prepared by arc-melting and rapid hot-pressing sintering. By substituting Pd on Co sites, the power factor of ZrCo_{1-x}Pd_{x}Bi is obviously improved due to the increase in electrical conductivity and Seebeck coefficient. The lattice thermal conductivity of ZrCo_{1-x}Pd_{x}Bi is greatly decreased because of the Pd/Co substitution. A minimum κ_{L}of 5.0 W/mK for ZrCo_{0.91}Pd_{0.09}Bi is obtained at 800 K. The thermoelectric performance ZrCo_{1-x}Pd_{x}Bi half-Heusler is boosted due to the depressed lattice thermal conductivity and the improved power factor. The maximum figure of merit reaches 0.23 for ZrCo_{0.97}Pd_{0.03}Bi half-Heusler sample at 800 K.## Author Contributions

All authors participated in the experiments and data discussion. D.Z. designed the experiments and wrote the manuscript. L.B. synthesized the ZrCoBi samples and Y.W. is responsible for the measurement of electrical properties. M.Z. carried out the measurement of thermal conductivity.

## Funding

This research was funded by the National Natural Science Foundations of China grant number [51772132] and [51471076].

## Acknowledgments

The authors would like to acknowledge the financial supports from the National Natural Science Foundations of China (No. 51772132 and No. 51471076). The authors would also like to thank Yanzhong Pei (Tongji University) for the help of partly thermoelectric measurement and the useful discussion.

## Conflicts of Interest

The authors declare no conflicts of interest.

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**Figure 4.**Backscattered electron SEM and elemental distribution of ZrCo

_{0.97}Pd

_{0.03}Bi HH samples.

**Figure 8.**Carrier concentration dependence of Seebeck coefficient (Pisarenko) plots for ZrCo

_{1-x}Pd

_{x}Bi.

x | Relative Density | S (μV/K) | μ_{H} (cm^{2}·V^{−1}·s^{−1}) | σ (Ω^{−1}·cm^{−1}) | κ_{L} (W·m^{−1}·K^{−1}) | n (10^{20} cm^{−3}) |
---|---|---|---|---|---|---|

0 | 98.1% | −47.7 | 1.37 | 67.6 | 16.2 | 3.09 |

0.03 | 98.6% | −96.4 | 9.94 | 762.8 | 14.2 | 4.80 |

0.06 | 97.9% | −87.5 | 10.1 | 807.2 | 12.7 | 4.97 |

0.09 | 98.8% | −80.9 | 10.3 | 867.7 | 10.3 | 5.25 |

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