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

In this study, n-type Pd-doped ZrCo1-xPdxBi (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 ZrCo1-xPdxBi samples were analyzed and discussed. The results showed that the electrical properties of ZrCo1-xPdxBi, including electrical conductivity and the Seebeck coefficient, increase due to the substitution of Pd on Co site. The lattice thermal conductivity of ZrCo1-xPdxBi is markedly decreased because of the Pd/Co substitution. A minimum κL of 5.0 W/mK for ZrCo0.91Pd0.09Bi is achieved at 800 K. The figure of merit of ZrCo1-xPdxBi 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 ZrCo0.97Pd0.03Bi half-Heusler compound at 800 K.


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.

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.  [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 ZrCo1-xPdxBi half-Heusler alloys were synthesized by arc-melting and rapid hot-pressing sintering. Thermoelectric properties of Pd-doped ZrCo1-xPdxBi half-Heusler alloys were measured and discussed. To our knowledge, this is the first report on the study about the ZrCo1-xPdxBi half-Heusler compound. We hoped that the Pd/Co substitution could enhance the S 2 σ and decrease the κL and then boost the figure of merit.

Experimental Procedures
The ingots with nominal composition ZrCo1-xPdxBi (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 ZrCo1-xPdxBi 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 ZrCo1-xPdxBi 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 ZrCo1-xPdxBi samples were measured by Archimedes method. The constituent phases and microstructure of ZrCo1-xPdxBi 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 ZrCo1-xPdxBi 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 ZrCo1-xPdxBi was calculated using κ = DρCp, where D is thermal diffusion coefficient, ρ is the density, and Cp 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 (RH) measurements of ZrCo1-xPdxBi 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 (µH) were calculated based on the Hall coefficient according to n = 1/(eRH) and µH = RHσ, respectively, where e is the electron charge.

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.

Results and Discussion
The XRD diagrams of the sintered bulk ZrCo1-xPdxBi 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 ZrCo1-xPdxBi (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 ZrCo1-xPdxBi samples were calculated and are listed in Table 1; high relative densities can ensure the measurement of thermoelectric properties.

Results and Discussion
The XRD diagrams of the sintered bulk ZrCo1-xPdxBi 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 ZrCo1-xPdxBi (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 ZrCo1-xPdxBi 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 4 displays the SEM image and the elemental distribution of the sintered ZrCo0.97Pd0.03Bi 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 ZrCo0.97Pd0.03Bi 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 ZrCo0.97Pd0.03Bi half-Heusler samples is about 15 µm, just as shown in Figure 5. The variation of σ for ZrCo1-xPdxBi 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 ZrCo1-xPdxBi 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 ZrCo1-xPdxBi samples increases with the Pd-doping content rising. As Pd can donate more electrons than Co, the n of ZrCo1-xPdxBi 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 ZrCo0.91Pd0.09Bi sample increases to 5.25 × 10 20 cm −3 .    Figure 4 displays the SEM image and the elemental distribution of the sintered ZrCo0.97Pd0.03Bi 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 ZrCo0.97Pd0.03Bi 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 ZrCo0.97Pd0.03Bi half-Heusler samples is about 15 µm, just as shown in Figure 5. The variation of σ for ZrCo1-xPdxBi 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 ZrCo1-xPdxBi 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 ZrCo1-xPdxBi samples increases with the Pd-doping content rising. As Pd can donate more electrons than Co, the n of ZrCo1-xPdxBi 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 ZrCo0.91Pd0.09Bi sample increases to 5.25 × 10 20 cm −3 .   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]: where h, k 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 7 shows the variation of S for ZrCo1-xPdxBi HH samples. All ZrCo1-xPdxBi samples have negative S and display the n-type conduction. The absolute value of S for ZrCo1-xPdxBi samples first increases and then decreases with the Pd-doping content rising. The S of ZrCo0.97Pd0.03Bi reaches a maximum of −191 µV/K at 800 K. In addition, the linear increase of S with rising temperature indicates that the ZrCo1-xPdxBi 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 ZrCo1-xPdxBi samples which were derived by the relation (1)-(3) based on the single parabolic band (SPB) model [21]:   Figure 7 shows the variation of S for ZrCo1-xPdxBi HH samples. All ZrCo1-xPdxBi samples have negative S and display the n-type conduction. The absolute value of S for ZrCo1-xPdxBi samples first increases and then decreases with the Pd-doping content rising. The S of ZrCo0.97Pd0.03Bi reaches a maximum of −191 µV/K at 800 K. In addition, the linear increase of S with rising temperature indicates that the ZrCo1-xPdxBi 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 ZrCo1-xPdxBi samples which were derived by the relation (1)-(3) based on the single parabolic band (SPB) model [21]:  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].    Figure 10 shows the variation of κ for ZrCo1-xPdxBi half-Heusler compounds within the whole measurement range. It can be observed that the κ of all ZrCo1-xPdxBi samples decreases with the temperature rising over the entire measured temperature due to the umklapp process. In addition, no bipolar effect is found in ZrCo1-xPdxBi samples. The κ of ZrCo1-xPdxBi samples decreases with the Pd-doping content rising which should be mainly due to the reduced κL, just as shown in Figure 11.    Figure 10 shows the variation of κ for ZrCo1-xPdxBi half-Heusler compounds within the whole measurement range. It can be observed that the κ of all ZrCo1-xPdxBi samples decreases with the temperature rising over the entire measured temperature due to the umklapp process. In addition, no bipolar effect is found in ZrCo1-xPdxBi samples. The κ of ZrCo1-xPdxBi samples decreases with the Pd-doping content rising which should be mainly due to the reduced κL, just as shown in Figure 11.    Figure 10 shows the variation of κ for ZrCo1-xPdxBi half-Heusler compounds within the whole measurement range. It can be observed that the κ of all ZrCo1-xPdxBi samples decreases with the temperature rising over the entire measured temperature due to the umklapp process. In addition, no bipolar effect is found in ZrCo1-xPdxBi samples. The κ of ZrCo1-xPdxBi samples decreases with the Pd-doping content rising which should be mainly due to the reduced κL, just as shown in Figure 11. = � � � ( + 7/2) +5/2 ( ) ( + 3/2) +1/2 ( ) − � ( + 5/2) +3/2 ( ) ( + 3/2) +1/2 ( ) � �.
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 ZrCo1-xPdxBi half-Heusler compounds is lower than that of pristine ZrCoBi and in the range of (1.8-2.1) × 10 −8 WΩ/K 2 . Figure 11. The variation of lattice thermal conductivity for ZrCo1-xPdxBi samples. As shown in Figure 11, the κL of ZrCo1-xPdxBi 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 ZrCo1-xPdxBi 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 κL of ZrCo1-xPdxBi samples decreases evidently. Generally, the lattice thermal conductivity can be estimated according to the relationship κL = 1/3CVlV, where l is the mean free path of phonon, CV is the heat capacity per unit volume and V is the average sound velocity. It is assumed the CV and V are constant. Then, the κL 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 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.  As shown in Figure 11, the κL of ZrCo1-xPdxBi 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 ZrCo1-xPdxBi 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 κL of ZrCo1-xPdxBi samples decreases evidently. Generally, the lattice thermal conductivity can be estimated according to the relationship κL = 1/3CVlV, where l is the mean free path of phonon, CV is the heat capacity per unit volume and V is the average sound velocity. It is assumed the CV and V are constant. Then, the κL 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

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.