Thermoelectric (TE) materials have attracted increasing attention because of fascinating applications in recycling industrial waste heat, cooling microelectronics and integrated circuits, and generating power using automobile exhaust heat and full-spectrum solar energy^[1]. The conversion efficiency of TE materials is determined by the dimensionless figure of merit ZT=α²σT/κ, where T, α, σ, and κ are the absolute temperature, Seebeck coefficient, electrical conductivity, and total thermal conductivity (κ=κ_E+κ_L, where κ_E is the electronic contribution and κ_L the lattice contribution), respectively. Good thermoelectric material should be the perfect combination of high power factor (α²σ) and low thermal conductivity^[2]. To improve the thermal transport properties, various phonon engineering approaches have been used to enhance phonon scattering and restrict κ_L^[3⇓-5]. To optimize the electric transport properties, a series of band structure engineering approaches have been developed to promote σ, α and/or α²σ^[6⇓-8]. However, it is extremely hard to simultaneously promote α and σ, meanwhile reduce κ because of the conflicting TE material properties.

YbAl₃ TE material has attracted considerable attention due to its potential application in Peltier cooling. As a typical heavy-fermion TE material, YbAl₃ has very high σ due to its metallic conducting behavior and considerably large α because of the hybridization of Yb4f electrons with itinerant counterparts^[9-10], and α²σ of YbAl₃ is about 3 times higher than that of Bi₂Te₃, which is one of the state-of-the-art TE materials. However, ZT of YbAl₃ is much lower than that of Bi₂Te₃ because of the high κ rooted from high σ and simple cubic crystal structure of YbAl₃^{[11⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓-24]}. Various complicated methods have been developed to synthesize YbAl₃ materials, which includes self- flux growth combined with etching and hot-pressing ^[15,19], arc melting followed by annealing and hot- pressing^[12], Bridgman growth combined with etching and hot- pressing^[11,13], arc melting combined with etching, ball milling, and pulsed electric current sintering^[16,21-22], and directly melting followed by annealing and spark plasma sintering (SPS)^[12,23-24]. All of these traditional methods not only take long time for the crystallization of YbAl₃ compound but also own multi-step processes. Especially, there are only micron- and mesoscale microstructures in YbAl₃ materials prepared in literature. These coarse microstructures only scatter phonon and decrease κ_L but have no effect on electrical transport properties. To optimize the electric transport properties of YbAl₃, various doping attempts, including doping at the Yb and Al sites and filling the Al₆ octahedral voids with external atoms, have been employed to tailor α²σ^{[17⇓⇓⇓⇓⇓⇓-24]}. Unfortunately, these attempts are not effective in suppressing κ and σ, because the major component of high κ is κ_E rather than κ_L. According to the Wiedemann-Franz law (κ_E=LσT), for YbAl₃ decreasing σ seems to be a reasonable option to lower κ_E and κ. Nevertheless, the theoretical and experimental results showed that doping at Yb and Al sites in YbAl₃ did not distinctly affect the band structure and thus did not significantly decline σ. Therefore, how to reduce σ of YbAl₃ has become an important subject to make a breakthrough in ZT. In this work, a one-step method was developed by SPS process to synthesize single-phase YbAl₃ materials. The one-step synthesis not only costs less time but also aims to form multi-scale microstructures that simultaneously scatter electrons and phonons.

The highly pure Al and Yb powders with nominal composition YbAl_3.2 were mixed in an agate mortar and then directly sintered for 10 min by SPS process (Dr Sinter, SPS-1050) under the condition of 50 MPa, 873 K and Ar atmosphere. Two samples were labeled as SPS1 and SPS2. For comparison, one sample labeled as MQA- SPS was prepared by a traditional method of melting, quenching, annealing and SPS, which took 7 d^[25]. The phase constituents of samples were determined by powder X-ray diffraction (XRD, PANalytical X’ Pert PRO) using Cu Kα radiation. The microstructures were examined by field emission scanning electron microscope (FESEM, Zeiss ULTRA-PLUS-43-13). High resolution transmission electron microscope (HRTEM) images were observed using a transmission electron microscope (JEOL-2100F). σ and α were measured with the standard four-probe method (Ulvac Riko, ZEM-3) in Ar atmosphere. κ was calculated using the equation κ=C_pλρ, where C_p is the specific heat capacity, ρ is the bulk density and λ is the thermal diffusion coefficient. λ was measured by laser flash technique (Netzsch LFA 427) in flowing Ar atmosphere. ρ was measured by Archimedes method. C_p was measued by TA Q20 differential scanning calorimeter (DSC). κ_E was calculated by the Wiedemann-Franz law(κ_E=LTσ), where the Lorentz number L has a numerical value of 1.6×10^-8 V²·K^-2 estimated by Rowe et al^[13]. κ_L was obtained by subtracting κ_E from κ based on the equation κ_L=κ-κ_E. Uncertainties are ±7% for σ and κ, and ±5% for α.

Fig. 1 displays XRD patterns of SPS1, SPS2 and MQA-SPS samples. All diffraction peaks can be indexed to YbAl₃ (JCPDS 65-0957), indicating that three samples are composed of single-phase YbAl₃. The result demonstrates that single-phase YbAl₃ materials can be directly synthesized with Yb and Al raw powders through one- step SPS process. FESEM images (Fig. 2) show the obvious difference in microstructures between SPSn and MQA-SPS samples on the micron scale. Like the majority of YbAl₃ materials prepared by traditional processes, MQA-SPS exhibits mesoscopic-scale microstructures that are composed of micrometer-sized crystals, as shown in Fig. 2(a). However, besides mesoscopic-scale microstructures, there are a large number of grain boundaries, nanocrystals and nano-pores in SPSn, as shown in Fig. 2(b-d).

In order to further characterize various microstructures in SPSn, the HRTEM images were investigated. The results were shown in Fig. 3 as exampled by SPS1. The insets are inversed fast Fourier transferred (IFFT) images of the marked regions. It can be seen that SPSn are composed of nanocrystals, strip-like noncrystal, and various dislocations. YbAl₃ nanocrystals with 5-20 nm in diameter reveal different diffraction contrast as shown in Fig. 3(a), indicating that these nanocrystals have different crystal orientation. The strip-like noncrystal with several nanometers in width occurs in big YbAl₃ perfect crystals as shown in Fig. 3(b), being attributed to the synergistic effects of the fast synthesis and pressure. Various atomic-scale defects are induced and accumulated in YbAl₃ nanocrystals as shown in Fig. 3(c, d), which are distorted arrays (left inset in Fig. 3(c)), edge dislocations (right inset in Fig. 3(c) and left inset in Fig. 3(d)), faults occurring at distorted layer interfaces (right inset in Fig. 3(d)), and small-angle grain boundaries (marked with yellow lines in Fig. 3(d)). Therefore, these multi-scale microstructures in SPSn samples span from the atomic scale, nanometer sizes, to mesoscale.

The temperature dependences of electrical conductivity, Seebeck coefficient for SPS1, SPS2, and MQA- SPS in the temperature range of 300-500 K are shown in Fig. 4. The inset in Fig. 4(b) displays the temperature dependence of power factor. All samples have negative α over the whole temperature range, implying n-type conduction. σ of all samples gradually reduced as temperature increasing in the range of 300-500 K owing to the enhanced scattering of carriers and phonons on crystal lattice^[26]. It is worth noting that σ of SPSn samples significantly descends as compared to that of MQA-SPS sample, which can be reasonably explained with enhanced electron scattering induced by YbAl₃ nanocrystals with 5-20 nm in diameter, nanoscale strip-like noncrystal and various atomic-scale distortions. As shown in Fig. 4(b), the absolute values of α for SPSn samples are higher than that of MQA-SPS, which attributes to the decline of σ. The highest α of SPS samples reaches about -85 μV∙K^-1 at 300 K which is much higher than that of other intermetallic compounds and close to the data reported by Rowe^[11]. Compared with MQA-SPS, σ of SPSn samples at 300 K are decreased by 15% and α value of SPSn samples at 300 K are increased by 8%. As a result, the α²σ values of two SPSn samples are higher than that of MQA-SPS, showing that the electric transport properties of YbAl₃ materials prepared by one-step method are better than those of YbAl₃ materials synthesized by traditional method.

These temperature dependences of electrical transport properties undoubtedly reveal that the multi-scale microstructures in the heavy-fermion YbAl₃ play beneficial roles in decreasing σ. It is necessary to explain why the multi-scale microstructures are so important for σ of YbAl₃ materials. The theoretical studies about the heavy- fermion YbAl₃ based on the first-principle calculation and Boltzmann transport theory showed that the nanostructures with less than 30 nm in size could strongly scatter the electrons and cause the substantial decline in σ of YbAl₃, the calculated σ and κ_E of YbAl₃ effectively decreased at 300 K when the mean free path was less than 30 nm^[27]. The theoretical discovery has been confirmed by our previous experimental result^[28]. Therefore, the remarkable decline in σ of SPSn samples is firmly ascribed to the nanocrystals with 5-20 nm in diameter, nanoscale strip-like noncrystal and various atomic-scale distortions scattering electrons.

Fig. 5 displays the temperature dependences of (a) thermal conductivity, (b) carrier thermal conductivity, (c) lattice thermal conductivity, and (d) ZT of all samples. κ of all samples ascended with increasing temperature in the range of 300-500 K, exhibiting metallic heat conduction behavior. κ of SPS1 and SPS2 are far less than those of MQA-SPS, indicating that the multi-scale microstructures in SPS1 and SPS2 can significantly reduce κ. As shown in Fig. 5(a, b), κ and κ_E of SPS1 and SPS2 at 300 K significantly fell from 19.7 and 14.8 W·K^-1·m^-1 for MQA-SPS to 13.4 and 10.8 W·K^-1·m^-1, decreased by 32% and 27%, respectively. The significant decline in κ_E values of SPS1 and SPS2 are attributed to the contribution of the reduced σ. Meanwhile, it is worth noting that κ_L values of SPSn samples are much lower than that of MQA-SPS in the range 300-500 K, decreased by 47% at 300 K. The remarkable reduction in κ_L of SPSn samples is attributed to the broad-frequency phonon scattering induced by the multi-scale microstructures (Fig. 3), indicating that κ_L of YbAl₃ materials substantially descends through various microstructures rather than doping or filling. The similar phenomenon that κ_L effectively decreased with multi-scale microstructures was reported by some important TE materials such as hierarchical architectures in PbTe^[3], micro- and nanopores in CoSb₃^[4], and multi-scale microstructures in Bi₂Te₃^[29]. Therefore, the multi-scale microstructures through one-step SPS method can simultaneously decrease κ_E and κ_L, resulting in lower κ of YbAl₃ TE materials.

ZT values were calculated according to the measured α, σ and κ in the range of 300-500 K, and the results were shown in Fig. 5(d). It is worth noting that ZT values of SPS1 and SPS2 are much larger than that of MQA- SPS. The maximum ZT reached 0.35 at 300 K for SPS2, increased by 49% as compared with MQA-SPS. Meanwhile, the maximum ZT outperforms all undoped YbAl₃ materials reported by other groups^[11,13,20], suggesting that the multi-microstructures from one-step synthesis process can substantially improve the TE properties of YbAl₃ materials. The remarkable decline in σ and κ plays a key role in enhancing ZT values for SPSn samples. The decreased σ results in significant rise of α, and the electric property of YbAl₃ materials is enhanced through the compromise between σ and α. In addition, the enhanced electron and phonon scattering reduces κ_E and κ_L, respectively. As a result, SPSn samples fabricated by one-step SPS process display very low κ.

In summary, a one-step SPS method was developed to synthesize YbAl₃ materials. The results from XRD, FESEM and HRTEM confirm that single-phase YbAl₃ materials with multi-scale microstructures spanning from atomic scale, nanometer sizes, to mesoscale was directly formed in 10 min from Yb and Al elements with this method. It is found that the nanocrystals with 5-20 nm in diameter, nanoscale strip-like noncrystal and various atomic-scale distortions effectively scatter electrons and significantly reduce σ and κ_E, while other hierarchical microstructures spanning from nanometer size to mesoscale can strongly scatter phonons and remarkably decrease κ_L. As a result, σ, κ, κ_L and κ_E at 300 K for SPSn samples descended by 15%, 32%, 47% and 27%, as compared with MQA-SPS. Meanwhile, α and ZT ascended by 8% and 49%, respectively. The maximum ZT is about 0.35 at 300 K. This work demonstrated that the multi-scale microstructures obtained through one-step SPS method can simultaneously optimize all TE parameters of heavy-fermion YbAl₃ materials.