稀有金属(英文版) 2020,39(06),659-670

Tailoring thermoelectric properties of Zr_0.43Hf_0.57NiSn half-Heusler compound by defect engineering

Krzysztof Galazka Wenjie Xie Sascha Populoh Myriam H.Aguirre Songhak Yoon Gesine Büttner Anke Weidenkaff

Institute of Plasma Physics and Laser Microfusion

Department of Materials Science,Technische Universit?t Darmstadt

Laboratory for Solid State Chemistry and Catalysis

Instituto de Nanociencia de Aragon, Universidad de Zaragoza

Departamento de Fisica de la Materia Condensada, Universidad de Zaragoza

Laboratorio de Microscopias Avanzadas, Universidad de Zaragoza

Fraunhofer Research Institution for Materials Recycling and Resource Strategies IWKS

作者简介：*Wenjie Xie,e-mail:wenjie.xie@mr.tu-darmstadt.de;*A.Weidenkaff,e-mail:anke.weidenkaff@iwks.fraunhofer.de;

收稿日期：7 October 2019

基金：financially supported by German Research Foundation Priority Programme 1386(No.WE 2803/2-2);the European Union under Marie Sklodowska-Curie Program(W. J.X.);

Tailoring thermoelectric properties of Zr_0.43Hf_0.57NiSn half-Heusler compound by defect engineering

Krzysztof Galazka Wenjie Xie Sascha Populoh Myriam H.Aguirre Songhak Yoon Gesine Büttner Anke Weidenkaff

Institute of Plasma Physics and Laser Microfusion

Department of Materials Science,Technische Universit?t Darmstadt

Laboratory for Solid State Chemistry and Catalysis

Instituto de Nanociencia de Aragon, Universidad de Zaragoza

Departamento de Fisica de la Materia Condensada, Universidad de Zaragoza

Laboratorio de Microscopias Avanzadas, Universidad de Zaragoza

Fraunhofer Research Institution for Materials Recycling and Resource Strategies IWKS

Abstract：

The thermoelectric transport properties of Zr_0.43Hf_0.57 NiSn half-Heusler compounds were investigated for samples sintered with different spark plasma sintering(SPS) periods:8,32 and 72 min.By means of scanning transmission electron microscopy with a highangular annular dark-field detector(STEM-HAADF),it was found that sintering time affected the defect concentration,namely the amount of Ni interstitial atoms,and created locally ordered inclusions of full-Heusler phase.The structural information,phase composition and electrical transport properties could be consistently explained by the assumption that Ni interstitials give rise to an impurity band situated about 100 meV below the bottom of the conduction band via a self-doping behavior.The impurity band was found to merge with the conduction band for the sample with intermediate SPS time.The effect was ascribed to the gradual dissolution of full-Heusler phase inclusions and production of interstitial Ni defects,which eventually vanished for the sample with the longest sintering time.It was demonstrated that the modification of the density of states near the edge of the conduction band and enhanced overall charge carrier concentration provided by defect engineering led to overall 26% increase in the thermoelectric figure of merit(ZT) with respect to the other samples.

Keyword：

Thermoelectric; Half-Heusler; Interstitial; Defect engineering;

Received： 7 October 2019

1 Introduction

The half-Heusler compounds based on XNiSn (X=Ti/Zr/Hf) have a high potential for thermoelectric applications [ 1] .Their thermal and electrical transport properties can be controlled by the Ti/Zr/Hf ratio and electron doping via substitution on each site [ 2, 3] .However,the properties of these compounds,even with identical composition,strongly depend on the synthesis route [ 4] .Therefore,a deep structural analysis of each sample is necessary to understand the influences of subsequent steps during the synthesis process on phase composition,structure and physical properties of the final material.

XNiSn half-Heusler compounds crystallize in a cubic crystal structure (F43m space group),where atom X occupies the 4a Wyckoff position,Sn the 4b and Ni the 4c Wyckoff positions.The 4d position is unoccupied in the half-Heusler structure,but it becomes filled in the fullHeusler compound XNi₂Sn,which is metallic [ 5] .Hence,the partial occupation of 4d position can be understood as an interstitial defect in the half-Heusler structure.It is obvious that the band structure of half-Heusler XNiSn compounds is sensitive to the occupancy of the 4d position by Ni atoms and other defects [ 6] .

The influence of defects on the density of states (DOS)in ZrNiSn shows that interstitial Ni gives rise to an impurity level within the band gap [ 7, 8] .Interstitial Ni is reported to be the most likely defect in the related compound TiNiSn [ 6] .Moreover,in compounds with intentional excess of Ni,Ni defects can form clusters of the fullHeusler phase [ 9, 10, 11] .Heusler phase nanoparticles embedded in the matrix actively contribute to transport properties and have been demonstrated to improve the figure of merit of Ti_0.5Hf_0.5CoSb_0.9Sn_0.1 due to the socalled energy filtering effect [ 12] .Even in stoichiometric compounds,some disorder in the Ni sublattice is present [ 13, 14] .Recent studies suggest that ZrNiSn_1-xSb_x and other XNiSn (X=Ti,Zr,Hf) half-Heusler compounds are arguable to be treated as highly disordered,even with only one element being situated on the X position [ 15] .Therefore,a potential way to control and improve thermoelectric properties of half-Heusler compounds is through manipulating the ordering of Ni interstitial defects on the local and global levels.

Our aim was to tailor the material properties by Ni defect engineering.Generally,the number of defects in any material can be controlled by heat treatment (for instance,annealing) for a certain amount of time.In this work,we aimed to vary the number of Ni defects in the Zr_0.43Hf_0.57NiSn bulk samples via adjusting the holding time during the spark plasma sintering (SPS) process and investigate its effects on the thermoelectric performance of Zr_0.43Hf_0.57NiSn bulk samples.We demonstrated that the transport properties of Zr_0.43Hf_0.57NiSn compounds could be tuned by simply changing the SPS time through a selfdoping mechanism by Ni interstitial defects.

2 Experimental

Samples with the nominal composition of Zr_0.43Hf_0.57NiSn were prepared by arc melting in Ar (purity 99.9999%) pure metals:Zr (Sigma Aldrich,99.95%with nominal 3%Hf),Hf (Sigma Aldrich,99.9%with nominal 3%Zr),Ni (Sigma Aldrich,>99.95%) and Sn (Sigma Aldrich,>99.99%).The samples were flipped and re-melted several times.Afterward,the ingots were crushed and hand-ground into powders in an agate mortar.The powders were sieved to select the ones with grain size between 50 and 100μm and subsequently compacted by SPS (KCE -FCT HP D 10).

The SPS compacting step played a crucial role in the synthesis process.Three holding periods at sintering temperature were adopted as t₁=8 min,t₂=32 min and t₃=72 min,and the samples are denoted as Sample 1,Sample 2 and Sample 3.The sintering time was selected to fulfill conditions t₂/t₁=2² and t₃/t₁=3²,since according to Fick’s laws,the diffusion length is proportional to the square root of time.By selecting SPS time as described above,the diffusion lengths were increased twofold and threefold,respectively.The other parameters of the SPS process were the same for all samples:5000 Pa overpressure of Ar (99.999%) atmosphere,a 100 K·min^-1 heating ramp rate up to T=1623 K and 50 MPa of applied uniaxial pressure during the sintering time [ 16] .As a result,disk-shaped pellets with about 1.5 mm in thickness and20 mm in diameter were formed.The densities of the synthesized samples were measured by Archimedes’method using ethanol as an auxiliary liquid.

The crystal structure and phase composition of the samples were assessed by powder X-ray diffraction (XRD,PANalytical X'Pert PRO).The diffractometer was equipped with a Johansson monochromator (Cu Kα₁ radiation,0.15406 nm) and an X’Celerator detector.Diffraction patterns were recorded between 20°and 140°(2θ) with an angular step interval of 0.0083°for powdered samples.The lattice parameters and strain were determined by Le Bail fitting using the program FullProf [ 17, 18] .The calculated strain corresponded to 1/4 of the strain derived from the Stokes and Wilson expression [ 19] .The Thompson-CoxHastings pseudo-Voigt function was used as a profile function,and CeO₂ (NIST SRM674b) was measured as a standard reference material to estimate the instrumentspecific contribution to the peak broadening [ 20] .

The morphologies and phase compositions of the samples were examined by scanning electron microscope(SEM,Philips ESEM-FEG XL30) with 20 kV acceleration voltage using the solid-state backscattered electron detector(BSED) and low-voltage high-contrast solid-state detector(vCD).For SEM imaging,each sample was polished(Buehler,Vibromet 2) using a 50-nm MasterPrep polishing suspension (Buehler) and finally rinsed with de-ionized water and ethanol.Energy-dispersive X-ray spectroscopy(EDX) point spectra analysis was performed to obtain the average local composition with a resolution of a few micrometers.

For transmission electron microscopy (TEM) analysis,the samples were prepared in lamella shape by a5-30 keV Ga⁺ion polishing in a focused ion beam system(FIB,Helios 600 Nanolab),preceded by the deposition of a thin Pt layer to protect the sample during the milling process.Atomic-resolution high-angular annular dark-field imaging in scanning transmission electron microscope(STEM-HAADF) was done on an FEI Titan G2(60-300 kV) equipped with a probe-aberration corrector,a monochromator and a field emission electron gun.The aberration-corrected microscope was operated at 300 keV;the local atomic composition was analyzed by using an energy-dispersive spectroscopy (EDS) detector,which allows performing experiments in scanning mode with a spatial resolution of about 0.2 nm.

The Hall resistivity (ρH) and the electrical resistivity (ρ)were measured with a physical properties measurement system (PPMS,Quantum Design) using the alternating current transport (ACT) option.The samples with approximate dimensions of 1.5 mm×1.5 mm×10.0mm were connected in a four-probe configuration by using a wire bonder (FEK Devoltec 5425) with a 20-μm-diameter Al wire to the ACT electrical interface.Measurements were taken in a He-purged,evacuated chamber in the temperature range of 10-400 K with a 10-K step size.At each temperature,the magnetic field (B) was swept from-0.7 to 0.7 T with 0.0015 T·s^-1.The Hall coefficient (R_H)was then derived as the slope of theρH(B) dependence.Afterward,the Hall mobility (μ_H) was calculated according toμ_H=R_H·ρ^-1.

The low-temperature electrical resistivity (ρ),thermal conductivity (κ) and Seebeck coefficient (α) were measured with PPMS (Quantum Design) using the thermal transport option (TTO).The same samples that were measured by PPMS-ACT were used.In the case of the TTO experiments,the samples were connected in a fourprobe configuration by using a 0.2-mm-diameter Cu wire and room-temperature-dried silver glue.Measurements were taken in high vacuum (～1×10^-2 Pa) in a continuous mode with cooling rate of 0.4 K·min^-1 in the temperature range of 400 K>T>2 K.The temperature gradient imposed on the sample was set to 1%of the current temperature.

The high-temperature electrical resistivity was determined in the temperature range of 325-1000 K with a 50-K step size by using an RZ2001i unit (Ozawa Science).Measurements were taken in Ar (99.999%) on the samples used previously for the PPMS-ACT measurements.The electrical resistivity was measured using a direct current(DC) four-point method.The corresponding Seebeck coefficient data were obtained in a steady-state method.Comparative measurements in ZEM-3 (ULVAC RIKO)were taken.In the RZ2001i unit,the applied temperature differences were in the range of 5-10 K and in the ZEM-3were in the range of 20-40 K.The measurements taken by ZEM-3 were performed in He (99.999%) atmosphere at a relative pressure of-5000 Pa.The Seebeck coefficient results obtained by the two different instruments match well with each other (within 15%).

The thermal conductivity was calculated fromк=Ddc_p using the experimental results for thermal diffusivity (D),density (d) and specific heat under constant pressure (c_p).The thermal diffusivity was measured with a laser flash apparatus (Micro Flash LFA 457,Netzsch) on squareshaped,graphite-coated samples with 10 mm in side length.Measurements were taken in Ar (99.999%) in the temperature range of 323-1023 K with a 50-K step.The c_p of the samples was measured by differential scanning calorimetry (DSC,Netzsch Pegasus 404C) in the temperature range of 400-1033 K during heating with10 K·min^-1.The experiments were performed in50 ml·min^-1 Ar (99.999%) flow by using Pt crucibles with an Al₂O₃ lining to prevent alloying between the crucible and the sample.A sapphire disk was used as reference material,and c_p was calculated by using the ratio method.

Thermal conductivity,electrical resistance and Seebeck coefficient values were used to calculate the dimensionless figure of merit:ZT=α²T/(ρк).The uncertainty of each measurement was calculated according to the exact differential method based on the systematic errors of the measured values and the double statistical standard deviation,where available.

3 Results and discussion

3.1 Crystal structure and phase composition

The diffraction patterns of the synthesized samples are presented in Fig.1.For each sample,the main phase belongs to the cubic F43m space group symmetry,which is a characteristic for half-Heusler materials.Each main phase reflection exhibits a low-angle shoulder with lower intensity (inset in Fig.1).It indicates the presence of another phase with Heusler or half-Heusler structure,but with a slightly larger unit cell.The intensities of the shoulder reflections evidence a non-negligible amount of the secondary phase for Samples 1 and 2,but a much lower amount for Sample 3.Sample 3 can be considered as the purest and ordered from the crystallographic point of view.The lattice parameters for the main phase (a_main) and the expanded phase (a_exp) obtained from Le Bail fitting are listed in the inset table in Fig.1.

Fig.1 XRD patterns of Zr_0.43Hf_0.57NiSn samples;inset patterns presenting (220) reflection showing a shoulder on the low-angle side,indicating a secondary phase with a larger unit cell;inset table being lattice and strain parameters (corresponding reflection positions of main and expanded phases being indicated by ticks on top of inset patterns;calculated expected position of (220) reflection for Zr_0.43Hf_0.57NiSn being indicated by a black vertical line)

All obtained a_main values are close to the reported experimental values for a similar composition (values found in Refs. [ 21, 22, 23] for Zr_0.5Hf_0.5NiSn are 0.61082,0.6099,0.60951 nm).Thea_main values for Samples 1 and 3are in a good agreement with the expected value of0.6096 nm (see the black vertical line in the inset in Fig.1)calculated from Vegard’s law by using the end-composition lattice parameters for ZrNiSn and HfNiSn [ 24] .The lattice parameters a_main and a_exp exhibit the same trend with the SPS process time:they increase for Sample 2 and decrease for Sample 3.It will be shown that electrical transport properties also show this nonlinear trend.

The phase with larger lattice parameter can be explained with various origins like local non-stoichiometry and/or micro-strains.And one of the plausible explanations considered is the existence of Ni interstitials [ 4] .The assigned phase cannot correspond to a solid solution between ZrNiSn and HfNiSn,as for all samples a_exp is larger than a_zrNiSn=0.6113 nm and incorporating Hf in the structure should result in a shrinkage of the lattice parameter [ 16] .On the other hand,the Heusler phase Zr_0.43Hf_0.57Ni₂Sn has a much larger lattice parameter of 0.6251 nm,as calculated from Vegard’s law based on the experimental values for ZrNi₂Sn and HfNi₂Sn compounds [ 16] .It should be also noted that the calculated lattice strain for the shoulder phase (inset table in Fig.1) is much larger for aexp than for a_main.It cannot be excluded that the expanded phase is a certain amount of small inclusions of full-Heusler phase,as its reflections are very broad.

According to the calculated structure factor,the reflection intensity ratio of (200)-(220) is inversely proportional to the amount of full-Heusler phase,and the presence of the full-Heusler phase can be recognized from the (200) to(220) intensity ratio.The relative intensities ratio of (200)-(220) is 0.42,0.51 and 0.61 for Samples 1,2 and 3,respectively,which indicates that the amount of locally ordered full-Heusler inclusions diminishes with SPS time increasing.A strong evidence is that the (220) intensity ratio of the expanded phase to the main phase diminishes from 0.20 for Sample 1,through 0.12 for Sample 2 to 0.09for Sample 3.Intensity ratio comparison cannot be a measure of quantitative analysis of all the XRD data sets even with the identical measurement conditions and sample preparation;this finding can be a hint that the expanded phase is decreasing with SPS time increasing.

Fig.2 SEM-BSED images of Zr_0.43Hf_0.57NiSn samples in×500(left) and×1500 (right) magnification (local composition estimated from EDX point spectra):a Sample 1,b Sample 2 and c Sample 3

In SEM images presented in Fig.2,it is not possible to detect any inclusions of full-Heusler phases (>10μm) by means of EDX point spectra.The only secondary phases confirmed by EDX analysis are Sn,a compound with composition close to (ZrHf)5Sn₃ and Ni₃Sn₄;their corresponding XRD reflections are very weak,thus not visible in the scale selected for diffractograms in Fig.1.It is expected that the secondary phases do not affect the transport properties directly due to their spatial isolation and a similar amount in all samples.

SEM images show the granular microstructure of the samples.The contrast between the grains of the main phase is due to their different orientations.By averaging the results of a number of SEM-EDX spectra (more than 20),it was possible to estimate the composition of the main phase.The results normalized to (Zr+Hf) contents are presented in Table 1.

The average composition of each sample shows a constant Zr/Hf/Sn ratio.The Ni/Sn ratio is greater than 1,suggesting either Sn deficiency or Ni excess.Ni excess in stoichiometric compounds was reported several times in the literature for ZrNiSn or Zr_0.5Hf_0.5NiSn,where it was ascribed to Ni interstitials [ 11, 25] .On average,the Zr/Hf/Sn ratio is constant for all samples,which allows relating the transport properties to the variation in the Ni content.A large standard deviation of the Ni content originates from the co-existence of previously observed main and expanded phases and their random intermixing.This will be discussed in the following section in accordance with TEM results.No correlation was found between EDX-measured

Table 1 Estimated elemental composition and standard deviation obtained statistically from SEM-EDX results (values for each sample being normalized to (Zr+Hf) content) average Ni contents and the gray contrast of different grains in the SEM images.

Although the initially selected powder grain size was50-100μm,it can be seen from SEM images that during the SPS process,the samples underwent partial recrystallization which resulted in smaller grains.The advance of the recrystallization process appears to be proportional to the SPS time:for Sample 1 only a few grains fragmented into pieces with about 20μm in size are visible while in Sample 3 almost only grains with size of about 10μm are presented.The recrystallization is in line with the previous observation on the vanishing of the full-Heusler inclusions concluded from XRD results.

The samples with different SPS process periods were analyzed by atomic-resolution STEM-HAADF.Figure 3a shows a coherent full-Heusler inclusion in the half-Heusler matrix in Sample 1.Owing to the Z-contrast of HAADF which indicates the atoms with a different atomic numbers,it is possible to distinguish the full-Heusler and halfHeusler phases.The different colors arise from the degree of occupation of the lattice sites.Both phases localized in well-resolved,different areas show a slight mismatch detectable by the splitting of the diffraction planes (002),as seen from the fast Fourier transform (FFT) of the whole image in the inset in Fig.3a.A detailed analysis is shown in Fig.3b,c.Figure 3b shows the full-Heusler alloy with every atomic position filled:Zr,Hf,Ni,Sn.The green color represents Ni occupying 4c and 4d Wyckoff positions,and the blue color corresponds to Ni vacancies.In Fig.3c,green still represents the Ni positions,but it is intercalated with vacancies (blue).The imperfections of Ni occupancy are detected by local EDS in situ STEM (see supplementary information) with high spatial resolution of aberrationcorrected TEM.

The variation of Ni composition was investigated on different length scales from 1000 to 15 nm.It changes from28 at%for Sample 1 through 22.6 at%for Sample2-18 at%for Sample 2.It agrees with the previous conclusion on the degree of the atomic ordering of the sample:longer annealing leads to enhanced atomic order.It also corresponds to a more homogeneous matrix and less fullHeusler inclusions in the half-Heusler matrix,as observed from XRD data.In Sample 2,the combination of disordered Ni interstitials and full-Heusler structure inclusion is beneficial for TE properties discussed in the next section.

3.2 Electrical transport properties

Figure 4 presents the results of the electrical resistivity measurements.In Fig.4a,the Arrhenius plots for all three samples are presented.The results acquired by different techniques (ACT and TTO) agree very well with each other,within the experimental error (below 2%).It shows that all samples are in the intrinsic regime of the electrical conduction at high temperatures and extrinsic regime at low temperatures.From the position of the low-temperature plateau,it can be concluded that Sample 2 has the highest concentration of impurities,whereas Sample 3 has the lowest [ 26] .Here“impurities”can simply be understood as atoms different from the matrix that can supply charge carriers to the electrical current conduction mechanism.The crossover temperatures are 180,290 and 150 K for the Samples 1,2 and 3,respectively.Sample 3 exhibits the lowest crossover temperature among all.

Fig.3 High-resolution STEM-HAADF image of Sample 1 a showing coherent intergrowth of half-Heusler and full-Heusler phase (inset being FFT pattern showing a slight mismatch detectable in diffraction planes (002) due to Ni occupancy);b,c enlarged phase regions (color code indicating atoms with different atomic number (Z) due to Z-contrast of HAADF detector,yellow-orange region representing full-Heusler and blue half-Heusler phase

Fig.4 a Arrhenius plot and b temperature derivative of electrical resistivity (dρ/dT) for Zr_0.43Hf_0.57NiSn samples (inset in a presenting high-temperature electrical conductivity data and model fitted according to Eq.(1);open symbols representing data measured by PPMS-ACT and Ozawa RZ2001i;small,filled symbols measured by PPMS-TTO;the solid lines being spline-connected dρ/dT derivatives calculated numerically from results obtained by PPMS-TTO and RZ2001i;error bars in a being smaller than symbol sizes and left away for sake of clarity)

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Table 2 Summary of fitted parameters for high-temperature electri-cal resistivity of three samples

At high temperatures,Sample 2 exhibits a remarkably higher electrical conductivity than Samples 2 and 3 (inset in Fig.4a).This observation is in line with the conclusion on the contribution of impurity carriers to the electrical conduction as concluded from the low-temperature resistivity data.The electrical conductivity (ρ) follows the equation:

where the first term corresponds to activation of the charge carriers over the band gap (AE₀) and the second term describes activation of the charge carriers from the impurity level placed at AE₁ below the bottom of the conduction band (all examined compounds are n-type semiconductors);k_B is the Boltzmann constant;andσ₀ andσ₁ are preexponential factors.The most plausible explanation for the presence of impurity levels in the compounds is Ni interstitial defects in the half-Heusler matrix,which act as donors [ 6] .In this context,the term“impurity”refers to an interstitial Ni defect rather than to a foreign atom or to a locally ordered full-Heusler phase inclusion.The fullHeusler phase is expected to have metallic properties [ 5] .However,as long as there is no percolation effect,it should have negligible influence on the electrical conductivity of the material [ 27, 28] .The results of the fit of Eq.(1) are presented in Table 2 and depicted in the inset in Fig.4a.

The parameters for Samples 1 and 2 indicate that the band gap of the Zr_0.43Hf_0.57NiSn compound is about340 meV.This is higher than the reported experimental result for similar Zr_0.5Hf_0.5NiSn (240 meV),however,close to the one for Hf_0.75Zr_0.25NiSn_0.99Sb_0.01(～360 meV) and to the theoretically calculated value(430 meV) [ 29, 30, 31] .Arguably,the discrepancy of band gap values of similar ZrNiSn-related compounds obtained by the experiment and the theoretical prediction is a wellknown issue [ 30] .Here,similarly as in our previous work,we state that ignoring the contribution of the impurity band can underestimate the band gap value [ 4] .The influence of impurities on the band gap value was already discussed,and our findings strongly support the previous literature [ 30] .It is remarkable that the onset of intrinsic conduction in each model corresponds to the level of ordering in the sample:the lower limit of the electrical resistivity fit is shifted to low temperatures for the least-defective S ample 3(T ranges in Table 2).

The narrowing of the band gap in Sample 2 could be attributed to the presence of Zr-Sn antisite defects [ 5, 32, 33] .However,it is not likely that the amount of antisite defects would show a non-monotonous behavior as a function of time,but it is expected that upon a prolonged annealing,the degree of ordering is enhanced [ 2, 33] .A more plausible explanation is that the impurity level merges with the conduction band in Sample 2 as in a heavily doped semiconductor [ 34, 35] .If the energy of the impurity level (E₁) is subtracted from E₀ for Sample 1 or 2,then the result is fairly close to the band gap for Sample 2.

By analyzing the dρ/dT dependency presented in Fig.4b,it is found that for Samples 1 and 2 at low temperatures,there is a regime where dρ/dT>0,meaning metallic-like conduction behavior.This can be explained by the conduction within the impurity level.In other words,the impurity level is a narrow band allowing for conduction with activation energy much smaller thanΔE₁.For ZrNiSn-related compounds,it was found that at low impurity concentrations,the low-temperature conduction is attributed to variable range hopping [ 4, 36, 37] .However,for high impurity concentrations,the conduction mechanism can be more complicated since the impurity band broadens and overlaps with the conduction band,leading to metallic behavior [ 34, 38] .This is explicitly observable for Sample 2 at T<130 K.A local maximum in dρ/dT at about 30 K is visible for Sample 1 and even for Sample 3,although it exhibits semiconducting properties (dρ/dT<0)in the whole T range.The same position of the local maximum in dρ/dT for each sample is physically meaningful:it is caused by the same kind of defect.The temperature of 30 K corresponds to 2.59 meV,which can be understood as the activation energy for conduction in the impurity band.

The impurity band connected with Ni defects can be further discussed in the scope of Hall measurements.Figure 5 a presents the Hall constant (R_H) for the examined Zr_0.43Hf_0.57NiSn half-Heusler samples which exhibits a non-monotonous dependence on T.The position of the maximum of-R_H(T)(note the inverted scale) depends on the sample and is correlated with the amount of impurities;it is shifted to lower temperatures for less defected samples [ 38] .Analogically to the case of mixed conduction,with the existence of an impurity band characterized by mobility(μ_e,imp) and carrier concentration (n_imp),the Hall coefficient at low temperatures can be expressed as:

where n andμ_e are the charge carrier concentration in the conduction band and their mobility,respectively [ 39] ;_the parameter b_imp=μ_e/μ_e,imp denotes the mobility ratio,e is the elementary charge,and r_H is the Hall factor,a constant which is in order of 1,depending on the involved charge carrier scattering processes [ 40] .At low temperatures,the excitation of carriers over the band gap is negligible and the charge neutrality relationship can be written as:

where is the number of impurities which are neutral.This means that from the total N_imp of donor impurities in the sample, still contains electrons,which can take part in the impurity band conduction,so .The rest impurities are ionized so that their electrons are excited to the conduction band and contribute to in-band charge carrier concentration (n).Calculation of-R_H is possible by using the charge neutrality relationship in Eq.(3) and expressions for n and n_imp from semiconductor theory to find the reduced Fermi levelη_F=E_F/(k_BT),where E_F is the position of Fermi level relative to the bottom of the conduction band.In this work,numerical calculations were performed using the following expressions:

where N_C=2(2π·m_C^*k_BT)^1.5/h³ is the effective density of states with m_C^*being the electron effective mass in the conduction band,ηF is the reduce Fermi energy,and h is the Planck constant,F_1/2(η_F) is the Fermi-Dirac integral of order 1/2 with Gamma functionΓ(3/2)=π^1/2/2,g is the spin degeneracy,andη_imp=E_imp/(k_BT) is the reduced impurity energy with E_imp being the impurity activation energy relative to the bottom of the conduction band [ 34, 38] .Altogether,the following equation is derived:

Equation (6) was solved under the following assumptions:m_C^*=3m_e,where me is the mass of electron,b_imp=50(the shape of the observed-R_H(T) dependency is a direct consequence of large difference betweenμ_e,imp andμ_e),and E_imp=100 meV (indicated by findings for E₁ presented in Table 2) [ 2, 4, 39, 41, 42] .The gray lines in Fig.5a were calculated from the model by using different impurity concentrations Nimp.

For Sample 2,the Hall coefficient model agrees with the measurement data very well,allowing for estimating the amount of Ni interstitial defects as N_imp=2.6×10²⁰ cm^-3.For Sample I with a lower amount of impurities,Nmp can be estimated as5.0×10¹⁹ cm^-3.For Sample 3,a rough agreement with the predicted behavior allows estimating a lower limit for N_imp from the value at the extreme as 4.0×10¹⁸ cm^-3.These values correlate with the Hall charge carrier concentrations.For instance,at room temperature,|1/(RHe)|equals 1.3×10¹⁹,4.4×10¹⁹ and 6.5×10¹⁸ cm^-3 for Samples 1,2 and 3,respectively.Differences between the data and the model in the positions of the extremes in case of Samples 1 and 3 suggest that they differ not only in N_imp,but also in other parameters,which were fixed during the modeling [ 43] .

The behavior of the Hall mobility (μ_H) is presented in Fig.5b.It is expected that there are at least two concurrent electron scattering processes,as the shape of theμ_H(T)dependency is non-monotonous.According to Matthiessen’s rule,a simple model describingμ_H(T) can be constructed as:

where A and B are constants;r and p are fitting parameters [ 44] .It is expected that in the high-temperature region,the dominant scattering process is the alloy scattering,so p=-0.5 [ 42, 45] .With this constraint,the free fit of the remaining parameters results in r values of 3.7 for Sample1,2.6 for Sample 2 and 2.3 for Sample 3.These are much larger than the expected value of r=1.5 for impurity scattering [ 45, 46] .Although there is currently no explanation of such a high exponent,similar observations(r=3.5) were reported for the other materials with identified impurity band conduction [ 38, 47] .The unexpectedly steep slope ofμ_H(T) for the investigated Zr_0.43Hf_0.57NiSn compounds is situated in the vicinity of the Hall coefficient extreme,as in the previous research. [ 4] .

Fig.5 a Hall coefficient measurement with a theoretical model and b Hall mobility data with an experimental fit for Zr_0.43Hf_0.57NiSn samples

Fig.6 a Seebeck coefficient and b thermal conductivity of Zr_0.43Hf_a.57NiSn samples (Inset presenting a correlation between previously derived parameter (N_imp) and values of minimum of Seebeck coefficient and maximum of thermal conductivity;in b a theoretical T^-1 dependency ofкfor Umklapp scattering being recalled)

3.3 Thermoelectric performance

The Seebeck coefficient and the thermal conductivity of Zr_0.43Hf_0.57NiSn samples are presented in Fig.6a,b,respectively.The general behavior is consistent with the predictions of the non-degenerate semiconductor theory,where the Seebeck coefficient is inversely proportional to the logarithm of charge carrier concentration,which is affected by the amount of intrinsic impurities like lattice defects [ 48] .In this case,it is quite straightforward that Sample 3 with the highest ordering (the longest SPS process time and the lowest number of impurities) exhibits the highest Seebeck coefficient,as it can be seen in the inset in Fig.6a.Also,the position of the extremum of the Seebeck coefficient is correlated to the estimated number of impurities (N_imp).Since the occurrence of an extremum in Seebeck coefficient is related to the onset of excitation of the minority charge carriers,it can be concluded that there is a direct influence of N_imp on the position of the Fermi level [ 49] .A large amount of impurities in Sample 1 and even higher in Sample 2 act as doping and shift the extremum of Seebeck coefficient to higher temperatures [ 4] .

Fig.7 Dimensionless figure of merit of Zr_0.43Hf_0.57NiSn samples

Fig.8 A sketch of DOS of synthesized samples together with key physical parameters (distances representing energy differences drawn in same scale)

The thermal conductivity presented in Fig.6b shows that the dominant phonon scattering mechanism at high temperatures above 100 K is through Umklapp processes characterized by T^-1 dependency (gray line in Fig.6b) [ 50] .Besides,the low-temperature peak at 30 K,almost no difference in the thermal conductivity of the samples is observed as at high temperatures,high energy phonons are less scattered by lattice imperfections.The low-temperatureкpeak is known to be a signature of crystalline order in the sample:the higher the peak is,the better the lattice is [ 50] .The highest peak can be observed for Sample 3,the smallest for Sample 2,which supports the previous findings on the amount of Ni interstitials,as demonstrated in the inset in Fig.6b.At the temperatures higher than approximately 700 K,the trend changes as the electronic contribution to the thermal conductivity starts to be significant.

The resulting high-temperature data for the dimensionless figure of merit (ZT) of the samples are presented in Fig.7.It can be seen from Fig.7 that Samples 1 and 3show almost no difference in ZT.The higher Seebeck coefficient for Sample 3 is compensated by its higher electrical resistivity.Regardless of the differences in microstructure and the impurity concentration,the final thermoelectric performance appears to be almost the same.

In the case of Sample 2,the maximum ZT value is increased to about 0.9 between 700 and 800 K,and it increases by 26%compared to the maximum ZT of Samples 1 and 3.This improvement can be unambiguously attributed to a high N_imp compared to that of the other samples which leads to self-doping effect.This is due to a high number of interstitial Ni defects accommodated in the half-Heusler matrix.At high temperatures,the samples undergo recrystallization to a certain degree proportional to the SPS time and full-Heusler phase inclusions are dissolved.This process produces many single interstitial Ni defects for Sample 2,and further longer time sintering eventually diminishes their number for Sample 3.Interstitial Ni atoms play the role of electron donors.An analogical improvement of ZT can be achieved in ZrNiSn by Sb doping [ 15] .It is most likely that the high concentration of defects causes the impurity band to merge with the bottom of the conduction band,changing the density of states.A sketch of the idea of the influence of the number of impurities and the position of the impurity level on the band structure summarizing the acquired information is presented in Fig.8.It is clearly seen that varying sintering periods during SPS process can be used as a simple and effective method to control the crystallinity and thermoelectric properties of Zr_0.43Hf_0.57NiSn half-Heusler compounds by defect engineering.There is still room to improve the achieved parameters by controlling the interplay between full-Heusler phase cluster size and phonon and electron scattering processes,for example,by facilitating the energy filtering effect.

4 Conclusion

The Zr_0.43Hf_0.57NiSn half-Heusler compounds were synthesized by arc melting followed by SPS.Three samples with different SPS process periods were investigated.The sintering time was found to affect the defect concentration,namely the amount of Ni interstitial atoms occupying the4d Wyckoff positions.The presence of these structural defects,clearly visible by STEM-HAADF,is corroborated by XRD results as a high-angle shoulder in the halfHeusler diffraction patterns.Defects act as dopants giving rise to an impurity level within the band gap.Low-temperature electrical resistivity and the Hall measurement confirm that in the examined samples,the defect concentration is high enough to allow for electrical conduction within the impurity level and it behaves as an impurity band.Whereas Sample 3 with the longest SPS time(72 min) was found the most ordered one,Sample 2 with SPS time of 32 min was found to have the largest amount of Ni defects.This fact was connected to the process of recrystallization and dissolution of full-Heusler inclusions present at a high degree in originally synthesized samples.For Sample 2,the impurity band was found to merge with the conduction band,as concluded from a smaller value of the band gap and metallic conductivity at low temperatures.Owing to the modified density of states near the bottom of the conduction band and higher charge carrier concentration for Sample 2,the thermoelectric figure of merit (ZT) was increased.The transport properties of Zr_0.43Hf_0.57NiSn and related half-Heusler compounds can be tuned by simply changing the SPS time through selfdoping mechanism by Ni interstitial defects.

参考文献

[1] Xie W,Weidenkaff A,Tang X,Zhang Q,Poon J,Tritt TM.Recent advances in nanostructured thermoelectric half-Heusler compounds.Nanomaterials.2012;2(4):379.

[2] Uher C,Yang J,Hu S,Morelli D,Meisner G.Transport properties of pure and doped MNiSn(M=Zr,Hf).Phys Rev B.1999;59(13):8615.

[3] Shen Q,Chen L,Goto T,Hirai T,Yang J,Meisner G,Uher C.Effects of partial substitution of Ni by Pd on the thermoelectric properties of ZrNiSn-based half-Heusler compounds.Appl Phys Lett.2001;79(25):4165.

[4] Galazka K,Populoh S,Xie W,Yoon S,Saucke G,Hulliger J,Weidenkaff A.Improved thermoelectric performance of(Zr_(0.3)Hf_(0.7))NiSn half-Heusler compounds by Ta substitution.J Appl Phys.2014;115(18):183704.

[5] Ogut S,Rabe K.Band gap and stability in the ternary intermetallic compounds NiSnM(M=Ti,Zr,Hf):a first-principles study.Phys Rev B.1995;51(16):10443.

[6] Colinet C,Jund P,Tedenac J.NiTiSn a material of technological interest:ab initio calculations of phase stability and defects.Intermetallics.2014;46:103.

[7] Miyazaki H,Nakano T,Inukai M,Soda K,Izumi Y,Muro T,Kim J,Takata M,Matsunami M,Kimura S,Nishino Y.Electronic and local crystal structures of the ZrNiSn Half-Heusler thermoelectric material.Mater Trans.2014;55(8):1209.

[8] Do D,Mahanti S,Pulikkotil J.Electronic structure of Zr-Ni-Sn systems:role of clustering and nanostructures in half-Heusler and Heusler limits.J Phys Condens Mater.2014;26(27):275501.

[9] Chai Y,Kimura Y.Nanosized precipitates in half-Heusler TiNiSn alloy.Appl Phys Lett.2012;100(3):033114.

[10] Chai Y,Kimura Y.Microstructure evolution of nanoprecipitates in half-Heusler TiNiSn alloys.Acta Mater.2013;61(18):6684.

[11] Chai Y,Yoshioka K,Kimura Y.Intrinsic point defects in thermoelectric half-Heusler alloys.Scr Mater.2014;83:13.

[12] Sahoo P,Liu Y,Makongo J,Su X,Kim S,Takas N,Chi H,Uher C,Pan X,Poudeu P.Enhancing thermopower and hole mobility in bulk p-type half-Heuslers using full-Heusler nanostructures.Nanoscale.2013;5(19):9419.

[13] Xie H,Mi J,Hu L,Lock N,Chirstensen M,Fu C,Iversen B,Zhao X,Zhu T.Interrelation between atomic switching disorder and thermoelectric properties of ZrNiSn half-Heusler compounds.CrystEngComm.2012;14(13):4467.

[14] Morimura T,Hasaka M.ALCHEMI for coexistent Heusler and half-Heusler phases in TiNi_(1.5)Sn.Ultramicroscopy.2006;106(7):553.

[15] Xie H,Wang H,Fu C,Liu Y,Snyder G,Zhao X,Zhu T.The intrinsic disorder related alloy scattering in ZrNiSn half-Heusler thermoelectric materials.Sci Rep.2014;4:6888.

[16] Zhou M,Chen L,Feng C,Wang D,Li J.Moderate-temperature thermoelectric properties of TiCoSb-based half-Heusler compounds Ti_(1-x)Ta_xCoSb.J Appl Phys.2007;101(11):113714.

[17] Le Bail A,Duroy H,Fourquet J.Ab-initio structure determination of LiSbWO_6 by X-ray powder diffraction.Mater Res Bull.1988;23(3):447.

[18] Rodriguez-Carvajal J.Recent advances in magnetic structure determination by neutron powder diffraction.Phys B.1993;192(1-2):55.

[19] Stokes A,Wilson A.The diffraction of X rays by distorted crystal aggregates—Ⅰ.Proc Phys Soc Lond.1944;56(3):174.

[20] Thompson P,Cox D,Hastings J.Rietveld refinement of Debye-Scherrer synchrotron X-ray data from Al_2O_3.J Appl Crystallogr.1987;20(2):79.

[21] Schwall M,Balke B.Niobium substitution in Zr_(0.5)Hf_(0.5)NiSn based Heusler compounds for high power factors.Appl Phys Lett.2011;98(4):042106.

[22] Shutoh N,Sakurada S.Thermoelectric properties of the Ti_x(Zr_(0.5)Hf_(0.5))_(1-x)NiSn half-Heusler compounds.J Alloy Compd.2005;389(1):204.

[23] Hohl H,Ramirez A,Kaefer W,Fess K,Thurner C,Kloc C,Bucher E.A new class of materials with Promising thermoelectric properties:MNiSn(M=Ti,Zr,Hf).MRS Proc.1997;478:109.

[24] Jeitschko W.Transition metal stannides with MgAgAs and MnCu_2Al type structure.Met Trans.1970;1(11):3159.

[25] Yu C,Xie H,Fu C,Zhu T,Zhao X.High performance halfHeusler thermoelectric materials with refined grains and nanoscale precipitates.J Mater Res.2012;27(19):2457.

[26] Fritzsche H.Resistivity and hall coefficient of antimony-doped germanium at low temperatures.J Phys Chem Solids.1958;6(1):69.

[27] Bergman DJ.Electrical transport properties near a classical conductivity or percolation threshold.Phys A.1989;157(1):72.

[28] Dai U,Palevski A,Deutscher G.Hall effect in a three-dimensional percolation system.Phys Rev B.1987;36(1):790.

[29] Cook B,Meisner G,Yang J,Uher C.High temperature thermoelectric properties of MNiSn(M=Zr,Hf).In:Proceedings of eighteenth international conference on thermoelectrics,Baltimore,IEEE;1999,64.

[30] Schmitt J,Gibbs Z,Snyder G,Felser C.Resolving the true band gap of ZrNiSn half-Heusler thermoelectric materials.Mater Horiz.2015;2(1):68.

[31] Zou D,Xie S,Liu Y,Lin J,Li J.Electronic structure and thermoelectric properties of half-Heusler Zr_(0.5)Hf_(0.5)NiSn by first-principles calculations.J Appl Phys.2013;113(19):193705.

[32] Graf T,Felser C,Parkin S.Simple rules for the understanding of Heusler compounds.Prog Solid State Chem.2011;39(1):1.

[33] Qiu P,Yang J,Huang X,Chen X,Chen L.Effect of antisite defects on band structure and thermoelectric performance of ZrNiSn half-Heusler alloys.Appl Phys Lett.2010;96(15):152105.

[34] Blakemore J.Semiconductor statistics.New York:Dover Publications,Inc.;1987.1.

[35] Hazama H,Asahi R,Matsubara M,Takeuchi T.Study of electronic structure and defect formation in Ti_(1-x)Ni_(1+x)Sn HalfHeusler alloys.J Electro Mater.2010;39(9):1549.

[36] Aliev F,Brandt N,Moshchalkov V,Kozyrkov V,Skolozdra R,Belogorokhov A.Gap at the Fermi level in the intermetallic vacancy system RBiSn(R=Ti,Zr,Hf).Z Phys B Condens Matter.1989;75(2):167.

[37] Arushanov E,Kaefer W,Fess K,Kloc C,Friemelt K,Bucher E.Transport properties of n-ZrNiSn single crystals.Phys Status Solidi A.2000;177(2):511.

[38] Conwell E.Impurity band conduction in germanium and silicon.Phys Rev.1956;103(1):51.

[39] Hung C.Theory of resistivity and hall effect at very low temperatures.Phys Rev.1950;79(4):727.

[40] Putley EH.The Hall effect and related phenomena.London:Butterworth&Co.;1960.1.

[41] Simonson J,Wu D,Xie W,Tritt T,Poon S.Introduction of resonant states and enhancement of thermoelectric properties in half-Heusler alloys.Phys Rev B.2011;83(23):235211.

[42] Xie H,Wang H,Pei Y,Fu C,Liu X,Snyder G,Zhao X,Zhu T.Beneficial contribution of alloy disorder to electron and phonon transport in half-heusler thermoelectric materials.Adv Funct Mater.2013;23(41):5123.

[43] Mott N,Twose W.The theory of impurity conduction.Adv Phys.1961;10(38):107.

[44] Matthiessen A,Vogt C.On the influence of temperature on the electric conducting-power of alloy.Philos Trans R Soc.1864;154:167.

[45] Nolas G,Sharp J,Goldsmid H.Thermoelectrics:basic principles and new materials developments.Berlin:Springer;2001.1.

[46] Conwell E,Weisskopf V.Theory of impurity scattering in semiconductors.Phys Rev.1950;77(3):388.

[47] Fritzsche H,Lark-Horovitz K.Electrical properties of p-type indium antimonide at low temperatures.Phys Rev.1955;99(2):400.

[48] Ioffe A.Fizika Poluprovodnikov.Moscow:Publishing House of USSR;1957.1.

[49] Goldsmid H,Sharp J.Estimation of the thermal band gap of a semiconductor from seebeck measurements.J Electro Mater.1999;28(7):869.

[50] Tritt T.Thermal conductivity:theory,properties,and applications.New York:Kluwer Academic/Plenum Publishers;2004.1.