Continuously Enhanced Structural Disorder To Suppress the Lattice

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Functional Inorganic Materials and Devices

Continuously enhanced structural disorder to suppress the lattice thermal conductivity of ZrNiSn-based half-Heusler alloys by multielement and multisite alloying with very low Hf content Bo Gong, Yu Li, Fusheng Liu, Jiaxu Zhu, Xiao Wang, WeiQin Ao, Chaohua Zhang, Junqin Li, Heping Xie, and Tie-Jun Zhu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b00648 • Publication Date (Web): 18 Mar 2019 Downloaded from http://pubs.acs.org on March 19, 2019

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ACS Applied Materials & Interfaces

Continuously enhanced structural disorder to suppress the lattice thermal conductivity of ZrNiSn-based half-Heusler alloys by multielement and multisite alloying with very low Hf content Bo Gong

a, ‡ ,

Yu Li

a, ‡

, Fusheng Liu

a,*,

Jiaxu Zhu a, Xiao Wang a, Weiqin Ao a, Chaohua

Zhang a, Junqin Li a, Heping Xie a, Tiejun Zhu b, *

a

College of Materials Science and Engineering, Institute of Deep Underground Sciences and

Green Energy, Shenzhen University, and Shenzhen Key Laboratory of Special Functional Materials, Shenzhen, 518060, P.R. China

b

State Key Laboratory of Silicon Materials and School of Materials Science and Engineering,

Zhejiang University, Hangzhou 310027, China

KEYWORDS: half-Heusler alloys; ZrNiSn; thermoelectric; multielement; lattice thermal conductivity.

*

Corresponding Authors: [email protected] (F. S. Liu), [email protected] (T. J. Zhu)

‡ These authors contributed equally to this work

1

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ABSTRACT: ZrNiSn-based half-Heusler (HH) alloys are considered very promising thermoelectric (TE) materials at intermediate and high temperatures due to their favorable intrinsic electrical properties, but they are also limited by their inherent high thermal conductivities. Numerous works have focused on reducing their thermal conductivities, especially their lattice thermal conductivities. A multielement (Ti, Hf, Nb, V, and Sb) and multisite alloying strategy for simultaneously improving the electrical properties and greatly reducing the lattice thermal conductivity of ZrNiSn-based HH TE materials is reported in this work. The continuous enhancement in structural disorder is the main factor in dramatically suppressing the lattice thermal conductivity of the materials. The use of suitable dopants also optimizes the electrical properties of the material, which is also an indispensable aspect in achieving high ZT values. As a consequence, a lowest lattice thermal conductivity κl = 0.99 W/m/K and a highest ZT ~ 1.2 were obtained for Zr0.95M0.05Ni1.04Sn0.99Sb0.01 (M = Ti0.25Hf0.25V0.25Nb0.25) refined by a ball-milling process. The calculated conversion efficiency (ƞ) of the same sample from room temperature to 873 K was close to 12%. In addition, compared with that used in other studies, the amount of Hf used in this study was greatly reduced, which means a reduction in cost. All of the findings in this study make the commercialization of ZrNiSn-based TE materials more competitive.

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1. Introduction The energy crisis is an important issue that cannot be ignored in today's society. In addition to finding new clean energy sources to replace traditional oil, coal, and other sources, the recycling of waste energy is a very promising way to address the problem. Thermoelectric materials (TE) can directly convert thermal energy into electric energy and are therefore a candidate for waste heat utilization; thus, these materials have attracted much attention1-4. The properties of TE materials are typically characterized by a dimensionless figure of merit 𝑍𝑇 = 𝑆2𝜎𝑇/𝜅, where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature and κ is the total thermal conductivity; moreover, κ = κl + κc, where κl and κc are the lattice thermal conductivity and carrier thermal conductivity, respectively5-6. In general, the lattice thermal conductivity accounts for the main part of the total thermal conductivity. A high ZT requires a high power factor (𝑆2𝜎) and low thermal conductivity (𝜅), which has provided ideas for improving the performance of TE materials7. It is known that the S, σ, and κc of materials are intercoupled via the carrier concentration8, while κl is a relatively independent parameter. Therefore, optimized TE performances can be obtained by regulating both the electrical and thermal properties of materials. The general ‘phonon-glass electron-crystal’ concept, band engineering, heavy doping alloying and nanostructuring are several successful design strategies for improving the TE figure of merit and have been applied in many systems9-11. As a medium- and high-temperature TE material, half-Heusler (HH) alloys have received much attention in recent years due to their nontoxicity, high thermal stability, excellent mechanical strength, and, most importantly, excellent electrical properties1, 11-12. They have a 3



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crystal structure of the MgAgAs type with a space group of F-43m, and itʼs represented by the general formula ABX. Based on the Zintl–Klemm concept, the valence electron rule for ABX half-Heusler compounds can be rationalized. As a result, half-Heusler compounds can be described as An+ (BX)

n−.

Many of the same bonding and doping principles developed for

Zintl compounds are helpful in explaining and understanding the structure and bonding in HH compounds13. Because of the cubic structure of HH alloys and their abundantly available constituent elements, one can optimize the performance of the system over a wide range of properties14-15. The n-type ANiSn (A = Ti, Zr or Hf)-based HH alloys have been most widely studied due to their high S and good σ; unfortunately, their intrinsic high thermal conductivity limits their TE performance and commercial applications. A series of methods have been adopted to improve the TE performance of the ANiSn-based n-type HH alloys. For instance, the carrier concentration and Fermi level can be optimized by doping with adjacent elements such as Sb or Bi for Sn16-20. The heavy doping of A with Hf, Ti and Zr can significantly reduce the lattice thermal conductivity due to the introduced mass and stress fluctuations21-22. The experimental results in the literature have demonstrated that Hf is an element that effectively reduces the lattice thermal conductivity of materials but is also a very expensive raw material22-23. The reduction in grain size to enhance the boundary scattering of phonons and the segregation of full-Heusler (FH) ANi2Sn phases in Ni-rich ANi1+zSn compositions have also been reported24. A new way to significantly reduce the lattice thermal conductivity of p-type NbFeSb-based HH materials, namely, by introducing high-entropy effects, was discussed in our earlier work25. In this work, we applied a strategy for optimizing the TE performance of n-type 4


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ZrNiSn-based HH alloys by means of solid solutions with multiple elements and multisite alloying with multiple elements (Ti, Hf, Nb, V) at the Zr sites, Sb at the Sn sites and Ni self-doping. This method continuously increases the structural disorder of the materials to enhance phonon scattering and greatly suppresses the lattice thermal conductivity. As adjacent periodic elements Nb and V to Zr and Sb to Sn provide additional electrons, the conductivity of the sample is significantly improved, while the carrier mobility is not significantly affected26. A lowest lattice thermal conductivity κl < 1 W/m/K and highest ZT ~ 1.2 were obtained for Zr0.95M0.05Ni1.04Sn0.99Sb0.01 (M = Ti0.25Hf0.25V0.25Nb0.25) refined by a ball-milling process at 873 K. It is assumed that when the legs of a TE device are made of the optimized material and when the conditions are a hot end temperature that reaches 873 K and a cold end temperature of room temperature, the calculated conversion efficiency (ƞ) of the material is close to 12%. These results effectively illustrate the successful application of the multielement and multisite alloying strategy to the ZrNiSn-based HH system and make the material more promising for future commercial applications in medium- to high-temperature use environments.

2. Experimental Section High-purity Zr (99.99%), Ti (99.99%), Hf (99.99%), Nb (99.98%), V (99.9%), Ni (99.99%), Sn (99.99%), and Sb (99.97%) raw materials were used to synthesize the samples. To prevent the volatilization of Sb, Sb and low-melting-point Sn were first smelted into alloy ingots using a high-frequency melting apparatus. The alloy ingot and other materials were further subjected to arc-melting under an argon atmosphere according to a certain chemical formula. To ensure homogeneity, the ingots were remelted 4 times. The obtained alloy ingot was then 5



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sealed in a quartz tube and vacuumed and annealed at 1173 K for 168 hours. The powder obtained by manual grinding and filtering through a 250 mesh screen was sintered by spark plasma sintering (SPS) at 1323 K under a pressure of 60 MPa in a vacuum for 12 min. Mechanical milling was carried out with an oscillation frequency of 20 MHz for 20 min, and the powder was then sintered under the same conditions. The as-sintered samples, for which the relative density was found to be ~ 95%, were cut to a suitable size and subjected to TE measurements. The experimental process is divided into the following four steps. First, the Zr position is doped with multielement M (Ti0.25Hf0.25V0.25Nb0.25) to find the optimized doping amount a of Zr1-aMaNiSn. Second, on the basis of the optimization, Sb is doped at the Sn site, and the optimized doping amount b of Sb is confirmed. Third, Ni is self-doped with Zr1-aMaNiSn1-bSbb as a matrix. Finally, the grains are refined by a ball-milling process to further optimize the material properties. The phase structures of the powders and sintered samples were studied by X-ray diffraction (XRD) on a Bruker® D8 Advance SS/18 kW diffractometer with Cu Kɑ radiation. The lattice parameters were derived from Rietveld refinements using Topas® 3.1 software. The microstructures were inspected by scanning electron microscopy (SEM, Hitachi® SU-70, Japan) coupled with energy-dispersive X-ray spectroscopy (EDS) and transmission electron microscopy (TEM, JEOL 2010 F, 300 kV), and the compositions of the samples were detected by electron probe microanalysis (EPMA, EPMA-1720, Japan) with a relative error below 2%. The electrical transport was probed through electric conductivity and Seebeck coefficient measurements using a ZEM-2 apparatus. The Hall effect was measured by a Quantum Design® physical property measurement system (PPMS) in a magnetic field up 6


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to ± 5 T. The carrier concentration and mobility were calculated by the equations 𝑛𝐻 = 1

𝑒𝑅𝐻 and 𝜇𝐻 = 𝑅𝐻𝜎, respectively. The overall measurement errors for the resistivity and

the Seebeck coefficient were ± 2% and ± 3%, respectively. The thermal conductivity κ was calculated by the equation к = αρCP, where the thermal diffusivity α was measured by a Netzsch® LFA 467 laser flash apparatus, the isobaric heat capacity CP was measured by a Netzsch® apparatus, and the density ρ was measured by the Archimedes method (the overall measurement error was ± 4%). Finally, the ZT parameter was calculated according to relation (1) (the overall measurement errors were ± 12%, the sum of all contributions).

3. Results and discussion 3.1 Phase and microstructure analysis A series of samples were prepared to analyze their phases, microstructures, and TE properties. The names and nominal compositions of the samples are listed in Table 1, and the ratio of the actual density to the theoretical density of all sintered samples is greater than 96%. Table 1. Physical properties of the samples, including nominal composition, carrier concentration and mobility, relative density and Lorentz constant, at 300 K. M = (Ti0.25Hf0.25V0.25Nb0.25). ‘bm’ represents the

ball-milling process. Name

Composition

n (1020 cm-3)

Relative μ (cm2/VS)

density (%)

L ( × 10-8 WΩK-2, 300K)

1-ZrNiSn

ZrNiSn

0.70(5)

13.6(5)

96.1

1.68

2-M0.05

Zr0.95M0.05NiSn

7.30(5)

13.3(5)

98.6

1.87

3-Sb0.01

Zr0.95M0.05NiSn0.99Sb0.01

10.0(5)

16.8(5)

96.1

1.99

4-Ni1.04

Zr0.95M0.05Ni1.04Sn0.99Sb0.01

5.80(5)

23.8(5)

97.7

1.95

5-bm-Ni1.04

Zr0.95M0.05Ni1.04Sn0.99Sb0.01

5.58(5)

22.6(5)

98.0

1.94

M = (Ti0.25Hf0.25Nb0.25V0.25), ‘bm’: the balii-milling process

As shown in Fig. 1 a, the powder XRD patterns taken from the ingots of ZrNiSn-based HH alloys after SPS could be well indexed to the cubic MgAgAs-type crystal structure and a 7



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negligible Sn phase between 30 and 40°, consistent with previous reports27-28. As shown in Fig. S 1 (Supporting Information), for the multielement M-doped Zr position, when the doping amount a is greater than 0.15, the sample begins to show significant phase separation, which has previously been reported in the Hf- and Ti-doped (Hf, Zr, Ti) NiSn system29-31. As the doping amount increases, the lattice constant of the sample gradually decreases. The average atomic radius of M is 1.33 Å, which is smaller than the Zr atomic radius of 1.45 Å. Therefore, the doping of M elements at the Zr site will reduce the cell size. Fig. 1 b shows the lattice constants of the optimized samples at each step. The lattice constant (a) of the M-optimized sample is smaller than that of the matrix sample ZrNiSn because the average radius of the dopant atoms is smaller than the atomic radius of Zr. The ionic radius of tetracoordinated Sb was determined to be 0.75 Å, and the ionic radius of tetracoordinated Sn was 0.55 Å. Therefore, when an Sb atom is introduced into the crystal lattice, the lattice constant of the sample starts to increase. All samples maintained the crystal structure of the HH alloys. A, B and X represent the elemental compositions of the three types of lattice positions of the HH structure (Fig. 1 b): the A position (0, 0, 0) is generally a neighboring element of Zr, the B position (1/4, 1/4, 1/4) is usually Ni, and the X position (1/2, 1/2, 1/2) is generally occupied by Sn or Sb.

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Figure 1. (a) XRD patterns for ZrNiSn, M0.05 (M=Ti0.25Hf0.25V0.25Nb0.25), Sb0.01, Ni1.04 and bm-Ni1.04; (b) lattice parameter and crystal structure of each sample (inline pattern). A typical cross-sectional SEM image of the bm-Ni1.04 sample is presented in Fig. 2 a. Clear grains and grain boundaries were observed. The SEM image of the same sample after a polishing and etching process is shown in Fig. 2 b, and the grain distribution of the sample is counted (Fig. 2 c), indicating that the average grain size was approximately 11.0 μm, as determined by software (IPP) analysis. Several typical TEM images of the bm-Ni1.04 sample after sintering are presented in Fig. 2 d ~ f. The grain size of the sample is on the order of microns (Fig. 2 d); the high-resolution TEM image in Fig. 2 e shows a lattice in which the FH phase is distributed in the lattice of the HH matrix, the red solid line frame is a lattice of the FH phase, and the interplanar spacing is approximately 0.263 nm, which is larger than the interplanar spacing of the HH phase, similar to reports in previous studies32. Distortion of the crystal lattice was also observed (Fig. 2 f). The dispersed FH alloy phase, lattice distortion and grain refinement can enhance phonon scattering, and the decrease in the thermal conductivity of the lattice could be partly attributed to these factors.

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Figure 2. Microstructure analysis of the bm-Ni1.04 sample after SPS. (a) Cross-sectional SEM image of the bm-Ni1.04 sample; (b) SEM image after metallographic corrosion; (c) grain size distribution; (d) TEM image; (e) and (f) high-resolution TEM image.

3.2 Thermoelectric Properties The sample carrier concentration (n) and mobility (μ) are shown in Table 1. The carrier concentration of the pure ZrNiSn sample is approximately 7 × 1019 cm-3, which is similar to a result reported in the literature33. This concentration increases after multielement alloying. The incorporation of Nb and V increases the carrier concentration of the material because they provide extra electrons. The carrier concentration of the M0.05 sample is 7 × 1020 cm-3, which is approximately 10 times higher than that of the pure sample. On this basis, the Sn-doped Sb further increases the carrier concentration of the material, reaching 1 × 1021 cm-3. The carrier concentration of the bm-Ni1.04 sample reaches the optimal range of the system9, which is partly due to the FH alloy phase generated after the introduction of excess Ni, along with the scattering of some of the low-energy carriers. This phenomenon is commonly referred to as the energy filtering effect. ZrNiSn-based solid solutions exhibit a low deformation potential and a low alloy scattering potential26, which are beneficial for maintaining a relatively high 10


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carrier mobility (μ) (Table 1). As a result, compared with the carrier mobility of the pure sample, which was 12 cm2/VS, the carrier mobility of the multielement alloyed M0.05 sample did not significantly decrease, and that of the Ni1.04 sample increased to 24 cm2/VS because the embedded FH phase forms a barrier at the interface with the matrix due to the offset of its conduction band minimum34. The slight decrease in bm-Ni1.04 is due to grain refinement after the ball-milling process. Fig. 3 shows the temperature-dependent electric properties of ZrNiSn-based HH alloys prepared by the SPS method. The resistivity of the sample after multielement alloying is much lower than that of the matrix sample, and the resistivity of the sample increases with temperature, showing metal-like conduction characteristics. The room temperature resistivity of ZrNiSn is 4.6 × 10-5 Ωm, and it drops to 3.7 × 10-6 Ωm for the bm-Ni1.04 sample. The optimization of the conductivity is mainly because Nb, V, and Sb provide additional free electrons (majority carriers in the n-type semiconductor) for the material. By applying Mottʼs formula for a degenerate semiconductor, at a temperature below the Debye temperature, the Seebeck coefficient is calculated by the relation 𝑆 =

8𝜋2𝜅𝐵𝑇

2

∗ 𝜋3 2 𝑚 3𝑛 , 3𝑒ℎ

where kB is the Boltzmann

constant, e is the electron charge, h is the Planck constant, and m* is the density of states effective mass of carriers35. This formula shows that S decreases as n increases, as observed in Fig. 3b. Fortunately, the alloyed sample still retains a large Seebeck coefficient at 873 K (inset of Fig. 3 b). Based on this relationship, the Pisarenko plot at 300 K is fitted to better understand the relationship between S and multielement alloying (Fig. 3 c). The observed increase in m* with alloying is also consistent with previously reported studies, and varying m* does not allow the fitting of all the data with a single parabolic curve, suggesting a 11



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modified band structure32. The results obtained herein show that multielement alloying significantly changes the electronic band structure close to the Fermi level by moving to a higher position on the Fermi level conduction band, similar to some reports in the literature32, 36-37.

It was also found that the Ni1.04 and bm-Ni1.04 samples appeared on the same fitting

curve, indicating that the ball-milling process employed in this study did not affect the band structure of the sample. Fig. 3 d shows the temperature dependence of the power factor (PF=S2/ρ). Because of the gradually decreasing resistivity and the high Seebeck coefficient maintained at high temperatures, the power factor of the sample is increased significantly. The bm-Ni1.04 sample achieved a maximum power factor of 5210 μW/m/K2, which is approximately 76% greater than the value of 3200 μW/m/K2 for ZrNiSn over the entire measurement temperature range. The carrier concentration of bm-Ni1.04 was optimized to 5.58 × 1020 cm-3, reaching the desired concentration range9.

12


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Figure 3. Electrical properties of each sample as a function of temperature. (a) Resistivity; (b) Seebeck coefficient; (c) Pisarenko plot of sample at 300 K; (d) power factor (PF). The thermal conductivity of the crystal is obtained by considering the lattice thermal motion system as a "phonon-gas", analogous to the direct thermal conductivity of the gas. It is typically limited by phonon-phonon scattering, point defect scattering (alloying scattering), electron-phonon scattering and boundary scattering. Fig. 4 shows the gradual optimization of the thermal conductivity and its relationship with the temperature. As shown in Fig. 4 a, the alloyed samples have a lower total thermal conductivity than ZrNiSn near room temperature. In the high-temperature range, the total thermal conductivities of samples M0.05 and Sb0.01 are higher than that of the matrix sample, and the total thermal conductivities of the Ni1.04 and bm-Ni1.04 samples are lower than that of the matrix sample. Among the samples tested, the bm-Ni1.04 sample achieved the lowest total thermal conductivity of 3.76 W/m/K at 873 K. To better understand the optimization process of the thermal conductivity of the material, the electronic thermal conductivity (κe) of the sample is calculated via the Wiedemann-Franz law (Fig. S 3), 𝜅𝑒 = 𝐿𝑇/𝜌, which shows that the electron thermal conductivity is directly related to the carrier concentration. The Lorentz constant (L) is calculated by the equation 𝐿 = 1.5 + exp ( ― ‫ ׀𝑆׀‬116)

× 10-8 WΩK-2

. The relationship of the Lorentz constant

38-39

13



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calculation results for other samples with the temperature is shown in Fig. S2. The calculation of the electronic thermal conductivity shows that the part of the total thermal conductivity of the sample increasing in the high-temperature region comes from the contribution of the electronic thermal conductivity (𝜅𝑒). The lattice thermal conductivity is obtained by subtracting the electronic thermal conductivity from the total thermal conductivity (Fig. 4 b), and it is the main contributor to the total thermal conductivity. Therefore, lowering the lattice thermal conductivity is key to ensuring that the material maintains a low total thermal conductivity, which is also essential for optimizing the TE properties of the material. When the multielement M-doped Zr lattice position, mass (atomic mass difference) and stress fluctuations (atomic size difference) are introduced, the lattice thermal conductivity of the alloyed sample decreases (the red line); on this basis, the M0.05 sample is used as the substrate, and the Sb-doped Sn position is selected. Due to the difference in ionic radius between Sb and Sn, when atoms with different sizes replace some of the original atoms, further lattice distortion occurs inside the material. The crystal structure of the sample is more disordered, which enhances the phonon scattering and reduces the lattice thermal conductivity (blue line). Similarly, with the optimized Sb sample as the matrix, an excessive amount of Ni was introduced at the Ni lattice position for self-doping. The FH alloy phase that formed in the matrix effectively reduces the lattice thermal conductivity of the material; this drastic reduction in thermal conductivity can be ascribed to efficient phonon scattering at multiple length-scale grain and phase boundaries31. The ‘disorder’ inside the material can also be considered enhanced. Grain refinement is a commonly used means of reducing lattice thermal conductivity40. The ball-milled Ni1.04 sample is simultaneously prepared; the refined grains 14


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generate more grain boundaries and enhance the phonon scattering. The lattice thermal conductivity (κl) of an alloy is given by a mathematical model developed by Callaway based on the Boltzmann distribution41: 𝑘𝑏

𝜅𝑙 = 2𝜋2𝜐

𝑘𝑏𝑇 3

( )

𝑠

ћ

𝜃𝐷

∫0𝑡

𝑥4𝑒𝑥 𝜏𝑝 ―1(𝑒𝑥 ― 1)

(1)

𝑑𝑥

2

1

𝜏𝑝 =

― 𝜃𝐷 4

3

2

a𝜔 + 𝑏𝑇 𝜔 𝑒

(2) 𝑇

+

𝜐 𝑙

According to the above model, the lattice thermal conductivity of a material is closely related to the phonon relaxation time (𝜏), where 𝜐𝑠 is the speed of sound in the material, 𝜃𝐷 is the Debye temperature, 𝜔 is the phonon frequency, l is the grain size, and a and b are constants. 𝜏𝑝

―1

4

3

2

consists of three parts: isotope scattering (a𝜔 ), the Umklapp process (𝑏𝑇 𝜔 𝑒

― 𝜃𝐷 𝑇

)

𝜐

and boundary scattering ( 𝑙 ). According to the calculation results for Zr0.5Hf0.5NiSn0.985Sb0.015 obtained by Liu et al.9, the decrease in the relaxation time is an important factor leading to the decrease in the thermal conductivity of materials. In our work, the continuous structural disorder enhancement promotes various types of phonon scattering, which significantly reduces the phonon relaxation time of the material and ultimately reduces the lattice thermal conductivity. A typical alloying scattering behavior κl

~

T

-1/2

was observed for all the

ZrNiSn-based samples. Throughout the alloying process, the internal structural disorder of the sample is continuously enhanced, the phonon scattering is gradually intensified, and the lattice thermal conductivity of the sample is effectively suppressed (Fig. 4 c). Among the samples tested, bm-Ni1.04 exhibited the lowest lattice thermal conductivity κl-min = 0.99 W/m/K at 873 K, which is approximately 74% lower than that of ZrNiSn. Compared with the methods reported in the literature for this system, the method proposed in this work has obtained an ultralow lattice thermal conductivity that is the closest to the theoretical minimum (Fig. 4 d)9, 15



16, 21, 30, 33, 36, 42-44.

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The bm-Ni1.04 sample shows a much faster decrease in the lattice thermal

conductivity with increasing temperature, which is mainly due to the following reasons. Firstly, the incorporation of Nb, V and Sb increases the carrier concentration of ZrNiSn and effectively suppresses the bipolar thermal conductivity of the material, so the lattice thermal conductivity of the sample decreases with increasing temperature throughout the test temperature interval. Secondly, the multielement and multisite alloying introduces a large number of point defects thus greatly enhances phonon scattering, so that the phonon scattering mechanism in the sample is dominated by alloy scattering(point defect scattering); that is, the temperature-dependent relationship is κl ~ T -0.5 and is also shown in Figure 4b. More details of the experimental results can be found in the supporting information material.

Figure 4. Thermal performance as a function of temperature. (a) Total thermal conductivity (κ); (b) lattice thermal conductivity (κl); (c) κl at 300, 600, and 900 K for the different alloying 16


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samples; (d) comparison of lattice thermal conductivity between sample bm-Ni1.04 and samples reported in the literature.

3.3 Thermoelectric Figure of Merit and Efficiency The material TE figure of merit ZT is a direct manifestation of the TE properties of the material, and the conversion efficiency (ƞ) of a TE device is determined by the average ZT and the temperature at both ends of the material. Fig. 5 a shows the ZT of the samples as a function of the temperature. As the alloying step progresses, the ZT of the sample increases, and the highest ZT value of the bm-Ni1.04 sample over the entire measurement temperature range reaches approximately 1.2, which is 2.5 times that of ZrNiSn, mainly because alloying greatly increases the conductivity of the sample while maintaining a large Seebeck coefficient at high temperatures. Most importantly, multielement and multisite alloying combined with the ball-milling process continuously increases the internal disorder of the material, so the lattice thermal conductivity of the material is greatly suppressed. Ultimately, the high power factor and low thermal conductivity give the material an optimized ZT. For the ZrNiSn system, the medium- to high-temperature range is the optimum temperature range for applications, so the average ZT value in the 600-900 K temperature range is also an important factor reflecting performance. Obviously, the average ZT of the alloyed samples is also gradually increasing (Fig. 5b). The efficiency (η) of a TE material is given by45 𝑇𝑐

ƞ 𝑐 = 𝑇ℎ ― 𝑇𝑐

[

1 + 𝑍𝑇𝑎𝑣𝑒 ―

𝑇ℎ

]

𝑇𝐶

1 + 𝑍𝑇𝑎𝑣𝑒 + 1

, where Th and Tc represent the temperatures of the hot and

cold ends of the device, respectively. Assuming that the optimized material is used for the legs of a TE device, the hot end temperature is 873 K, and the cold end is room temperature, 17



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the calculated conversion efficiency (ƞ) is shown in Fig. 5 c. The average ZT used in the conversion efficiency calculation formula is a value for the interval from room temperature to 873 K. Ultimately, the conversion efficiency of bm-Ni1.04 exceeded 11%, which was nearly 50% higher than that of ZrNiSn. For commercial applications, the performance and cost of the material need to be balanced to make them more competitive. Fig. 5 d provides a brief comparison of the results described in some literature reports1, 17, 42-43, 46 with the experimental results in this paper based on the amount of Hf used. In the sample composition herein, the molar ratio of Hf is 1.25%, which is lower than the amount used in the literature. An increased conversion efficiency and cost control will make this material more promising in the mediumand high-temperature range.

Figure 5. TE figure of merit. (a) ZT value of each sample as a function of the temperature; (b) average ZT value for the 600K to 873K temperature range; (c) average ZT value of the 18


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sample from room temperature to 873 K and the corresponding calculated efficiency (ƞ); (d) maximum ZT value of the sample corresponding to the Hf content.

4. Conclusions In summary, ZrNiSn-based HH compounds with an HH main phase and small amounts of tin and FH alloy phases are successfully synthesized by levitation melting and the SPS method. Due to the cubic crystal structure and various potential alloying elements of ZrNiSn-based HH alloys, multielement alloying at the Zr position successfully introduces mass and stress fluctuations, and Sb doping at the Sn site further enhances the lattice distortion. On this basis, Ni self-doping introduces a nano-FH alloy phase into the main phase, and the continuously enhanced structural disorder strengthens the phonon scattering and greatly suppresses the lattice thermal conductivity. The introduction of Nb, V, and Sb significantly increased the carrier concentration of the sample, while the appearance of the FH alloy phase scattered some of the low-energy carriers so that the carrier concentration of the sample was optimized to the appropriate range. Ultimately, the power factor is optimized. As a result, the lowest κl decreased to 0.99 W/m/K, and the ZT value at 823 K reaches ~ 1.2 for n-type Zr0.95M0.05Ni1.04Sn0.99Sb0.01 (M = (Ti0.25Hf0.25V0.25Nb0.25)). The average ZTave value was ~ 0.96 from 600-873 K, and the conversion efficiency η was ~12% from 300 to 823 K. Last but not least, a reduction in the amount of Hf used reduces the cost of material preparation. The present findings demonstrate an effective means of regulating the TE properties of ZrNiSn-based HH alloys via a multielement and multisite alloying strategy.

Acknowledgements This work was supported by the National Natural Science Foundation of China (Nos: 19



Page 20 of 26

51701126 and 51571144) and a Shenzhen Science and Technology Research Grant (Nos. JCYJ20150827155136104).

Conflicts of Interest There is no conflict of interest in this work.

Supporting Information XRD patterns of Zr1-xMxNiSn (M = (Ti0.25Hf0.25Nb0.25 V0.25)) samples; Calculation of the Lorentz constant of the sample; Electronic thermal conductivity of Zr1-xMxNiSn and Zr0.95 M0.05NiSn1-ySby

samples; Thermoelectric properties as a function of the temperature of

Zr1-aMaNiSn, Zr0.95 M0.05NiSn1-bSbb and Zr0.05 M0.05Ni1+cSn0.99Sb0.01 samples; Crystal structure involved in this paper; Thermal diffusion coefficient and Cp; EPMA compostions.

20


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Graphical Abstract


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Continuously Enhanced Structural Disorder To Suppress the Lattice

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