Enhancing the Figure of Merit of Heavy‐Band Thermoelectric Materials Through Hierarchical Phonon Scattering

Hierarchical scattering is suggested as an effective strategy to enhance the figure of merit zT of heavy‐band thermoelectric materials. Heavy‐band FeNbSb half‐Heusler system with intrinsically low carrier mean free path is demonstrated as a paradigm. An enhanced zT of 1.34 is obtained at 1150 K for the Fe1.05Nb0.75Ti0.25Sb compound with intentionally designed hierarchical scattering centers.

In the past decades, thermoelectric (TE) materials have received rejuvenated interest due to their promising application in direct thermal to electric energy conversion and solid-refrigeration that could lead to signifi cant energy savings, [ 1,2 ] and also in other technological fi elds such as sensors and thermopower wave sources. [ 3,4 ] The effi ciency of a TE material is gauged by the dimensionless fi gure of merit, zT = α 2 σT /( κ e + κ L ), where α , σ , T , κ e and κ L are, respectively, the Seebeck coeffi cient, the electrical conductivity, the absolute temperature, and the electronic and lattice components of total thermal conductivity κ . [ 5 ] Large-scale application of TE technology demands the materials having high zT values, which however are diffi cult to achieve due to the interdependencies of α , σ , and κ e via the carrier concentration. [ 5 ] Besides, the decrease in κ by introducing more phonon scattering centers may concomitantly scatter the carriers leading to a decrease in σ . [ 6 ] Therefore, strategies which can decouple these parameters for synergistic optimization of electron and phonon transport are highly desirable and central theme for high zT .
Current efforts to improve zT are focused on the optimization of power factor α 2 σ through controlled doping or electron band engineering, [7][8][9][10][11] suppression in κ L by alloying or nanostructuring, [ 1,2,5,6 ] and development of new materials with intrinsically low κ L . [12][13][14][15] Heat-carrying phonons cover a broad spectrum of frequency, and the κ L is a sum of contributions from phonons of different frequencies. Thus, introducing hierarchical phonon scattering centers into the matrix, which could lead to a substantially reduced κ L , has recently been proposed to improve the TE performance of traditional PbTe-and Hence, from the view of materials cost and element abundance, Ti-doped FeNbSb system is more attractive for practical application, and further improving the zT of Ti-doped FeNbSb will greatly enhance the feasibility. Heavily doped p-type FeNb 1− x Ti x Sb with high m b * have relatively low µ of ≈15 cm 2 V −1 s −1 at 300 K, [ 31 ] implying the existence of low l c . The experimentally obtained lowest κ L for p-type FeNb 1− x Ti x Sb in the previous work is ≈2.6 Wm −1 K −1 at 1100 K, [ 31 ] higher than the calculated theoretical minimum value (≈1 Wm −1 K −1 ), indicating that further κ L suppression would be one of the main directions to improve the zT . Introducing hierarchical scattering centers into this p-type HH system may be favorable for higher zT .
In this work, it is found that the l c in the p-type FeNbSb is comparable to the lattice parameter, indicating that the carrier mobility of this system almost reaches the Ioffe-Regel limit, [ 35 ] which means that the carrier scattering has reached the highest limit and introducing more phonon scattering centers will not impair the power factor while largely suppress the κ L . By synergistically doping high content of Ti, refi ning the grain size to submicroscale, and introducing more point defects into the matrix, the κ L is largely decreased while the power factor is only slightly affected. As a result, an enhanced zT of 1.34 is obtained at 1150 K for the intentionally designed Fe 1.05 Nb 0.75 Ti 0.25 Sb HH compound. These results highlight the effi cacy of hierarchical phonon scattering in improving the performance of heavy-band TE materials.
For the p-type FeNbSb, 20% Ti-doped FeNb 0.8 Ti 0.2 Sb has the optimal carrier concentration. [ 31 ] High content of Ti dopant not only supplies enough carriers for the optimal power factor but also creates strong mass and strain fi eld fl uctuations and electron-phonon scattering leading to great suppression in κ L . How to further reduce the κ L in FeNb 0.8 Ti 0.2 Sb? As schematically shown in Figure 1 a, the answer is to introduce hierarchical phonon scattering centers to scatter the phonons with different frequencies. The sub-microscale grain boundaries, usually targeting the low frequency phonons, can be introduced into the matrix via the ball-milling process. [ 6,36 ] In addition, more atomic-scale point defects can be created to further enhance the scattering of high-frequency phonons. Thus, by combining the submicroscale grain boundaries, atomic-scale point defects and electron-phonon interaction, hierarchical phonon scattering centers can be concurrently created in a given material, leading to a substantially reduced κ L . [ 1,37,38 ]   shows the calculated spectral lattice thermal conductivity for the so-made Ti-doped FeNbSb compounds with hierarchical phonon scattering centers (see details in Supporting Information). High content of Ti dopant in FeNbSb induces strong mass/strain fi eld fl uctuation and electronphonon interaction, which contribute to a broad frequency scattering of phonons and result in a ≈70% reduction compared to the κ L of FeNbSb. Furthermore, the introduced grain boundaries by ball milling scatter long-wavelength phonons and reduce κ L . Excess Fe, which may enter into the tetrahedral interstitial sites as excess Ni in ZrNiSn HH alloys, [ 39 ] is added into the matrix to enhance the point defect scattering of phonons. With the introduced point defects, the κ L is further suppressed resulting from the enhanced scattering of phonons with high frequencies as seen in Figure 1 b. All in all, by introducing the sub-microscale grain boundaries, atomic-scale point defects and electron-phonon interaction as hierarchical phonon scattering centers, a great reduction of ≈80% in the κ L of FeNbSb has been achieved. Coupled with the unchanged electrical properties, a signifi cantly enhanced peak zT of 1.34 have been experimentally obtained at 1150 K for the grain-refi ned Fe 1.05 Nb 0.75 Ti 0.25 Sb, as presented in Figure 1 c, which justifi es the concept that introducing hierarchical phonon scattering centers into heavy-band HH system is indeed an effective strategy to improve the zT .
The scanning electron microscopy (SEM) and transmission electron microscopy (TEM) analyses are performed to identify the microstructure features. The SEM images of the FeNb 0.8 Ti 0.2 Sb samples with different ball-milling (BM) time are displayed in Figure 2 . The average particle size of the four samples milled for 1, 4, 8, and 16 h is estimated to be about 1.6 µm, 0.8 µm, 300 nm and 200 nm, respectively. It is worth noting that, although the BM time for the sample BM-16h is largely prolonged, compared with that of sample BM-8h, the decrease in average particle size is not as obvious as that of other samples with the shorter BM times. The TEM observation of the sample BM-16h shows that the average grain size is about 140 nm (Figure 2 e,f). Figure 2 g shows the low-magnifi cation TEM image for sample Fe 1.05 Nb 0.75 Ti 0.25 Sb. The spherically shaped and unevenly distributed nanoscale precipitates can be occasionally found in the matrix. Figure 2 h gives the high-resolution TEM (HRTEM) image with an inserted fast Fourier transferred (FFT) pattern for the nanoscale precipitates. The high-angle annular dark fi eld (HAADF) STEM in combination with energy-dispersive X-ray spectroscopy (EDS) was performed to identify the composition of the nanoscale precipitates ( Figure S1, Supporting Information). The analysis shows that the nanoscale precipitates are Ti-rich, resulting from the high Ti content beyond the solubility of Ti (≈23%) in FeNbSb (see details in Supporting Information). The Ti-rich nanoscale precipitates are initially designed to enhance the scattering of middle frequency phonons. However, the results below will show they have weak effect on the electrical and thermal properties, which may result from the relatively small contents of precipitates in the matrix.
An important aspect making the hierarchical design effective in improving zT of a TE system, is the charge carrier transport cannot be signifi cantly degraded. Figure 3 a shows the temperature dependence of electrical conductivity σ for the FeNb 0.8 Ti 0.2 Sb and Fe 1+ x Nb 0.75 Ti 0.25 Sb samples. The σ of FeNb 0.8 Ti 0.2 Sb has only a slight decrease with increasing BM times, due to the trivial reduction in carrier concentration and carrier mobility (S1, Supporting Information). The carrier mean free path l c of the FeNb 0.8 Ti 0.2 Sb samples are estimated by the formula l c = (2 E F m b *) 1/2 µ / e , where the Fermi level E F was calculated by the experimental Seebeck coeffi cient, [ 19 ] and m b * was obtained from the ref. [ 31 ] . At 300 K, l c is as approximately three times large as the lattice parameter (≈5.94 Å) of FeNb 0.8 Ti 0.2 Sb materials due to the large effective mass, demonstrating that the charge carriers in this heavy-band system are almost localized. Even though the sample BM-16 h has the smallest grain size of ≈140 nm, it is still about two orders of magnitude higher than the calculated l c . As a result, the grain refi nement only has negligible effect on the carrier mobility of FeNb 0.8 Ti 0.2 Sb (Figure 2 b). By increasing Ti content to 25%, the σ of sample FeNb 0.75 Ti 0.25 Sb ( x = 0) is slightly increased, compared with that of FeNb 0.8 Ti 0.2 Sb, resulting from the increased p H (S1, Supporting Information). But the µ H of FeNb 0.75 Ti 0.25 Sb has only a trivial change compared with that of FeNb 0.8 Ti 0.2 Sb, implying that the nanoscale precipitates may have negligible effect on the charge carrier transport.
However, for the Fe 1+ x Nb 0.75 Ti 0.25 Sb samples with excess Fe, the σ has an obvious reduction with increasing Fe content, especially near room temperature (Figure 3 a). For sample x = 0, the σ approximately follows a temperature dependence of T −1.5 while the σ of sample x = 0.08 approaches the T −1.0 dependence, indicating that Fe excess may enhance the alloying scattering of carriers. Hall measurement shows that both the decreased hole concentration and mobility ( Figure S2 and S1, Supporting Information) lead to the decreased σ . Excess Fe may enter into the interstitial tetrahedral sites of the crystal structure to supply electrons, and make the hole concentration decrease. This phenomenon is similar to the scenario happened in another HH compound Ni 1+ y ZrSn, in which excess Ni had been proven to enter into the interstitial tetrahedral sites and generate electrons. [ 28,39 ] At high temperatures the σ decrease with increasing Fe content for Fe 1+ x Nb 0.75 Ti 0.25 Sb tends to be slower (Figure 3 a), due to the slower decrease in high temperature µ H . As shown in Figure 3 b, the room temperature µ H of sample x = 0.08 has a ≈30% reduction compared with that of x = 0, but only ≈17% reduction at 500 K and almost unchanged at 900 K. By the Ioffe-Regel criterion that the lowest distance for metallic conduction is close to lattice constant, the minimum electrical conductivity σ min and the minimum carrier mobility µ min can be roughly estimated using the formulas [ 35 ] : σ min = 0.33 e 2 p 2/3 a / ប and µ min = σ min / p , where e , p , a and ប are the unit charge, carrier concentration, lattice parameter, and the reduced Planck constant, respectively. The calculated σ min and µ min of Fe 1+ x Nb 0.75 Ti 0.25 Sb samples are displayed in Figure 3 a,b, which suggests that at high temperatures this system is approaching the Ioffe-Regel limit and thus excess Fe will not notably enhance the carrier scattering and reduce the µ H . Figure 3 c shows that the Seebeck coeffi cient α of the FeNb 0.8 Ti 0.2 Sb and Fe 1+ x Nb 0.75 Ti 0.25 Sb samples display an increasing trend with temperature, which is typical behavior for degenerate semiconductors. The slight increase in α with increasing Fe content can be observed, corresponding to the decreased hole concentration ( Figure S2, Supporting Information). The above analysis shows that the grain refi nement only has negligible effects on carrier transport of p-type heavy-band FeNbSb system due to the intrinsically low carrier mean free path. This phenomenon is rarely observed in traditional TE materials. Fe excess leads to a weak µ H decrease at low temperatures, but almost has no effect at high temperatures. As a  result, the introduced hierarchical phonon scattering centers have negligible effects on carrier transport of p-type FeNbSb system and therefore the power factor α 2 σ is almost unchanged in the whole temperature range, as shown in Figure 3 d.
The effect of hierarchical phonon scattering centers on thermal conductivity of p-type FeNbSb is displayed in Figure 4 . The lattice thermal conductivity κ L is obtained by subtracting the electronic component κ e from the total κ and κ e is calculated via κ e = LσT , where L is the Lorenz number and can be calculated under the SPB approximation. [ 25 ] As expected, the κ of the FeNb 0.8 Ti 0.2 Sb samples decreases with increasing BM time, ≈17% reduction at room temperature for sample BM-16h, compared with that of sample BM-1h (Figure 4 a), which results from the both reduced κ e (Figure 4 b) and κ L (Figure 4 c). For FeNb 0.75 Ti 0.25 Sb ( x = 0), although Ti-rich nanoscale precipitates exist in the matrix, the κ L of the sample has only a slight change compared with that of FeNb 0.8 Ti 0.2 Sb (BM-8h), indicating that the introduced Ti-rich nanoscale precipitates have a relatively weak effect on the κ L , which may be due to the relatively small contents of precipitates in the matrix.
An obvious decrease in κ is found for the Fe 1+ x Nb 0.75 Ti 0.25 Sb samples with increasing Fe content (Figure 4 a). For example, ≈30% reduction at room temperature is observed for x = 0.05, compared with x = 0. At low temperature, a large decrease in κ e (Figure 4 b) with increasing Fe content is the dominated reason for the large κ decrease. At high temperatures, the decrease in κ e with increasing Fe content tends to be slower, consistent with the change of σ in Figure 3 a. The κ L obviously decreases with increasing Fe content as shown in Figure S3 (Supporting Information), mainly resulting from the additionally enhanced point defect scattering of phonons. The κ L of x = 0.08 is ≈6% higher than that of x = 0.05, which may result from the uncertain measurement of thermal conductivity and estimation of Lorenz parameter, or Fe precipitation.
In short, the introduced hierarchical phonon scattering centers indeed signifi cantly enhance the phonon scattering and decrease κ L in p-type FeNbSb. As a result, the zT of the samples is obviously enhanced. The maximum zT of ≈1.34 is obtained at 1150 K for the grain-refi ned Fe 1.05 Nb 0.75 Ti 0.25 Sb (Figure 4 d), ≈30% higher than that of FeNb 0.8 Ti 0.2 Sb with the shortest BM time. Considering that Ti is much cheaper and more abundant than Hf, the Ti-doped Fe 1.05 Nb 0.75 Ti 0.25 Sb system should be great promising for large-scale power generation application.
In summary, hierarchical phonon scattering is suggest to be effective in reducing the lattice thermal conductivity and enhancing the fi gure of merit of heavy-band TE materials, and p-type heavy-band FeNbSb half-Heusler system with intrinsically low carrier mean free path is demonstrated as a paradigm in this work. By combining the sub-microscale grain boundaries, atomic-scale point defects and electron-phonon interaction, hierarchical phonon scattering centers are concurrently introduced into the p-type Ti-doped FeNbSb, which have almost negligible effect on the carrier transport but contribute to a great reduction in the lattice thermal conductivity. Therefore, a high zT of 1. 34 [ 35 ] www.MaterialsViews.com www.advancedscience.com Adv. Sci. 2016, 3, 1600035 hierarchical scattering centers. These results highlight the efficacy of hierarchical phonon scattering in improving the performance of heavy-band TE system.

Experimental Section
Methods : The ingots with nominal composition FeNb 0.8 Ti 0.2 Sb and Fe 1+ x Nb 0.75 Ti 0.25 Sb ( x = 0-0.08) were prepared by levitation melting of stoichiometric amount of Fe (piece, 99.97%), Nb (foil, 99.8%), Ti (rod, 99.99%) and Sb (block, 99.999%) under an argon atmosphere for 3 min and then remelted three times to ensure homogeneity. The ingots with nominal composition FeNb 0.8 Ti 0.2 Sb were subjected to a mechanical ballmilling (BM) process (Mixer Mill MM200, Retsch) from 1 to 16 h under argon protection to obtain the powders with different sizes. The ingots with nominal composition Fe 1+ x Nb 0.75 Ti 0.25 Sb were subjected to a BM process for 8 h. The obtained powders were loaded into the graphite die and compacted by spark plasma sintering (SPS-1050, Sumitomo Coal Mining Co.) at 1123 K for 10 min under 65 MPa in vacuum. The as-sintered samples, of which the relative densities were found to be ≈95%, were annealed at 1023 K for 2 d.
Characterization : Phase structures of the samples were investigated by X-ray diffraction (XRD) on a RigakuD/MAX-2550PC diffractometer using Cu Kα radiation ( λ 0 = 1.5406 Å). The diffraction peaks of all samples could be indexed to a single-phase half-Heusler structure and no obvious impurities exist in the samples. The chemical compositions (S1, Supporting Information) were checked by electron probe microanalysis (EPMA, JEOL, JXA-8100). The XRD patterns of the BMed FeNb 0.8 Ti 0.2 Sb and Fe 1+ x Nb 0.75 Ti 0.25 Sb samples show a single phase that can be indexed to the HH phase with a cubic MgAgAs-type crystal structure ( Figure S4, Supporting Information). The freshly fractured surfaces of the samples were observed by scanning electron microscopy (SEM) to show the particle size. Transmission electron microscopy (TEM, JEOL JEM-3000F) was also performed to observe the possible nanostructures.
Measurements : The room temperature Hall coeffi cients were measured using a Mini Cryogen Free Measurement System (Cryogenic Limited, UK). The carrier concentration p H was calculated by p H = 1/ eR H , where e is the unit charge and R H is the Hall coeffi cient. The estimated error of Hall coeffi cient is within ±10%. The carriers mobility µ H was calculated by µ H = σR H . The Seebeck coeffi cient and electrical conductivity from 300-1150 K were measured on a commercial Linseis LSR-3 system using a differential voltage/temperature technique and a DC four-probe method. The accuracy is ±5% and ±3%, respectively. The thermal conductivity κ was calculated by using κ = DρC p , where ρ is the sample density estimated by the Archimedes method and. The thermal diffusivity D and specifi c heat C p were measured by a laser fl ash method on Netzsch LFA457 instrument with a Pyroceram standard. The accuracy is ±3% and ±5%, respectively. The combined uncertainty for determining zT is less than 20%. The thermal stability of the samples was checked through the high-temperature annealing treatment at 1023 K ( Figure S5, Supporting Information). Only negligible change in TE properties was found with increased annealing time up to 10 d, indicating the good thermal stability for the samples with hierarchical phonon scattering centers.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.