Solubility design leading to high figure of merit in low-cost Ce-CoSb3 skutterudites

CoSb3-based filled skutterudite has emerged as one of the most viable candidates for thermoelectric applications in automotive industry. However, the scale-up commercialization of such materials is still a challenge due to the scarcity and cost of constituent elements. Here we study Ce, the most earth abundant and low-cost rare earth element as a single-filling element and demonstrate that, by solubility design using a phase diagram approach, the filling fraction limit (FFL) x in CexCo4Sb12 can be increased more than twice the amount reported previously (x=0.09). This ultra-high FFL (x=0.20) enables the optimization of carrier concentration such that no additional filling elements are needed to produce a state of the art n-type skutterudite material with a zT value of 1.3 at 850 K before nano-structuring. The earth abundance and low cost of Ce would potentially facilitate a widespread application of skutterudites.

T he world energy consumption has been increasing steadily and much effort is required worldwide to meet the challenging demand. Thermoelectric materials, which can convert waste heat into electricity, may help to reduce fossil fuel consumption and augment energy efficiency, and thus play an important role in the solution for the world's energy dilemma. The thermoelectric performance of materials is characterized by the dimensionless figure of merit, zT ¼ S 2 sT/k, where S is the Seebeck coefficient, s is the electrical conductivity, T is the absolute temperature and k is the total thermal conductivity.
Among various kinds of state-of-the-art thermoelectric materials, filled skutterudites distinguish themselves by allowing low thermal conductivity like a glass and high electrical conductivity like a crystal at the same time, which make them excellent thermoelectric materials according to the 'phonon glass electron crystal' concept 1 . Moreover, the intermediate temperature range (400-600°C) at which filled skutterudites have optimum thermoelectric performance makes this material a perfect candidate for automotive industry applications. Because of the heavy mass and small radius of the Yb atom compared with other fillers, Yb-CoSb 3 skutterudites have excellent thermoelectric properties (zT ¼ 1.3 at 850 K for Yb 0.3 Co 4 Sb 12 ) ref. 2 and have been selected by many automotive companies, such as General Motors, Ford and BMW, as the most promising thermoelectric material for waste heat recovery 3 . However, the deficiency of the rare earth element Yb (abundance in earth's crust 3 p.p.m.) could potentially be a problem in large-scale commercialization. Unlike Yb, Ce is the most earth abundant element of the rare earths (abundance in earth's crust 68 p.p.m.) 4 . In fact, there are huge resources of cerium because it is more abundant than other commonly known elements such as lead (14 p.p.m.), tin (2 p.p.m.), silver (0.07 p.p.m.), tellurium (0.005 p.p.m.) and gold (0.001 p.p.m.). The price of cerium is also more competitive compared with ytterbium. For large quantities, the difference is a factor of 10 (Ce; $5,000 per ton, Yb; $50,000 per ton 5 ), placing Ce in the category of other commonly used elements such as Ni.
With its larger earth abundance and fairly low cost, use of Ce would help the commercialization of n-type skutterudites for automotive industry only if the thermoelectric properties of Cedoped skutterudites can match those of Yb-doped skutterudites.
Interestingly, single-filled Ce-CoSb 3 skutterudites have been considered as unsuitable thermoelectric materials and there has yet been little report of high temperature thermoelectric properties of pure Ce-CoSb 3 skutterudites. Ce has been considered to be a good auxiliary filler in multiple-filled skutterudites, such as in (In, Ce)-CoSb 3 skutterudites (zT of 1.43 for In 0.2 Ce 0.15 Co 4 Sb 12 at 800 K) 6 or (Ba, Ce)-CoSb 3 skutterudites (zT of 1.26 for Ba 0.18 Ce 0.05 Co 4 Sb 12.02 at 850 K) 7 . Ce has not typically been considered as a single filler. This is most likely due to its reported small filling fraction limit x ¼ 0.09 in Ce x Co 4 Sb 12 (ref. 8) that would prevent Ce-containing skutterudites to achieve the optimum carrier concentration for n-type skutterudites 9 . To increase the filling fraction limit of Ce in CoSb 3 skutterudites, charge-compensational doping, such as Fe or Mn-doping has been largely applied, which can dope the material from n-type to p-type [10][11][12][13][14] .
In this study, single-filling Ce-CoSb 3 skutterudites without charge-compensational doping are prepared under equilibrium conditions and their thermoelectric properties are measured up to 850 K. The filling fraction limit of Ce is studied by solubility design using an equilibrium phase diagram approach. This approach introduces both the annealing temperature and nominal composition as variables in determining the filling fraction limit, which leads to the possibility of enhancing filling fraction of fillers thermodynamically rather than consider it as a single value. Using this phase diagram approach, a temperature-dependent solubility like the Yb in Yb-CoSb 3 sheds light on optimizing Ce-CoSb 3 , whose thermoelectric properties are limited by its low filling fraction limit 2 . With solubility design, a clear solubility enhancement with a filling fraction limit of x ¼ 0.20 is discovered at 850 K for Ce-CoSb 3 skutterudites. The surprisingly high filling fraction limit at high annealing temperatures enables the Ce-CoSb 3 skutterudites to be optimized with zT of 1.3 for Ce 0.14 Co 4 Sb 12 at 850 K, which makes it an excellent substitute for Yb-doped skutterudites for waste heat recovery applications.

Results
Optimum doping of Ce-CoSb 3 skutterudites. Unfilled CoSb 3 is an intrinsic semiconductor with carrier concentration o10 18 cm À 3 . Rare earth filler atoms in the void sites are nearly perfect n-type donors. The n-type carrier concentration is essentially determined by the number of filling atoms and the ionic charge state. In CoSb 3 a Yb filler has a valence charge þ 2 while Ce is þ 3, which is a lower oxidation state than often observed in oxides but common for Sb compounds 15 . Figure 1 demonstrates the trend of the carrier concentration versus the number of electrons per primitive cell, for either single, double or triple-filled skutterudites. To achieve high power factor of n-type skutterudites 0.4-0.6 electrons per Co 4 Sb 12 unit is required, as indicated by the red-double arrow 16 . The carrier concentration of Ce-CoSb 3 samples in the previous literature study 8 is limited by the reported low filling fraction limit (x ¼ 0.09 in Ce x Co 4 Sb 12 at 973 K), consequently these samples are far from the high-power factor region. To optimize the thermoelectric properties of Ce single-filled CoSb 3 skutterudites, higher filling fraction of Ce is needed. As we shall show later, the filling fraction limit of Ce can be as high as x ¼ 0.20 at 1,123 K through solubility design, which is not only more than twice the reported value x ¼ 0.09 but now allows for the optimization of Ce-CoSb 3 . After optimization, the four samples in this work fall in the high power factor region  refs 2,8,9,18,19,32-35. The number of electrons per primitive cell is calculated as the sum of q i *x i for partially filled (R 1 ) x1 (R 2 ) x2y (R n ) xn Co 4 Sb 12 , where q i is the effective charge state and x i is the filling fraction of the ith filler R in multiple-filled skutterudites. The solid line represents the theoretical curve calculated by using n ¼ 2x/a 3 , where x is the total number of electrons per primitive cell and a is the lattice constant of CoSb 3 . The red double arrow represents the estimated high power factor region (see discussions below) and the red dashed line represents the number of electrons per primitive cell limited by the previously thought Ce filling fraction limit 8 .
Thermoelectric properties of optimized Ce-CoSb 3 skutterudite. The thermoelectric properties can be optimized when the filling fraction x of filler R (with valence q) in R x Co 4 Sb 12 satisfies qx ¼ 0.4B0.6 (refs 9,16). From Fig. 3 we can see that when nominal compositions are in the Ce-rich three-phase regions with an annealing temperature at 1,073 and 1,123 K, the Ce actual content in skutterudite phase is about x ¼ 0.17 and 0.20, respectively. With Ce valence state being þ 3, qx for these materials would be in the optimum region. Thus, a set of samples with nominal compositions Ce x Co 4 Sb 12 (x ¼ 0.17, 0.18, 0.20 and 0.21) were prepared for thermoelectric evaluation, of which the first two samples were annealed at 1,073 K and the latter two were annealed at 1,123 K. The temperature dependence of transport properties of these samples are shown in Fig. 2. Moreover, the transport data of two Yb-doped skutterudites with doping level x ¼ 0.20 and 0.30 are also plotted for the reason of comparison 2 (Tang, Y. et al. Convergence of multivalley bands as electronic origin of high thermoelectric performance in CoSb 3 skutterudites, submitted). With Yb valence state being þ 2, qx for these two samples are right on the boundary of the optimum region.
All the samples show negative Seebeck coefficients throughout the whole temperature range, indicating the expected n-type semiconductor behaviour. With increasing temperature, both the electrical resistivity and the magnitude of the Seebeck coefficient increase, which is typical behaviour for heavily doped semiconductors. It has to be noted that for the Ce-doped samples, the values of electrical resistivity, seebeck coefficient and thermal conductivity all fall between the values of the two Yb-doped samples, which is in agreement with Fig. 1. k L is obtained by subtracting the electronic contribution from the total thermal conductivity using the Wiedemann-Franz law. We adopted a Lorentz number of 2.0 Â 10 À 8 V À 2 K À 2 to be consistent with previous work on skutterudites, and the lattice thermal conductivity calculated accordingly has o5% difference from the value Resistivity (mohm* cm)  Sb 12 Yb x Co 4 Sb 12 Yb x Co 4 Sb 12 ARTICLE calculated with the Lorentz number determined from a single parabolic band model 9,17 . All Ce-doped samples in this work show strongly reduced k L as compared with binary CoSb 3 with k L B10 Wm À 1 K À 1 at 300 K. As apparent from Fig. 2d, Ce is as effective in reducing lattice thermal conductivity as Yb, with both much more effective than alkali and alkaline earth element fillers. Figure 2e shows the continuously increasing zT indicative of the higher doping level than ref. 18. All Ce-CoSb 3 samples in this work have zT values higher than 1.0 at and above 750 K, with the maximum zT value in Ce-doped skutterudite samples reaching 1.3 with nominal Ce content x ¼ 0.17 and 0.18 at 850 K (with composition Ce 0.14 Co 4 Sb 12 for both samples determined from Electron Probe Micro-Analysis (EPMA)), which is 30% higher than that of previously reported literature value for Ce singlefilled skutterudites (zT ¼ 1.0 for Ce 0.11 Co 4 Sb 12 at 850 K) 18 . These zT are similar to those for single-filled skutterudites 2,19-21 , suggesting that Ce is a suitable earth abundant and low-cost replacement for other types of fillers, such as Yb, which makes the Ce single-filled skutterudites a more promising candidate for large-scale commercialization. The success of solubility design in Ce-CoSb 3 system is a good example that this is an effective strategy in the optimization of thermoelectric properties in any other ternary systems with filling elements, which allows wide applicability of this strategy. Ultra-high filling fraction limit of Ce in Ce-CoSb 3 skutterudites. The lattice expansion due to filling is an easy and effective way of characterizing the amount of fillers actually going into the void site in the skutterudite cell. Here lattice constants were derived from powder X-ray diffraction data and the actual Ce content was determined from EPMA. The lattice constant shows a simple linear dependence on the actual Ce content x in Ce x Co 4 Sb 12 , which agrees with the literature data and is consistent with Ce going into the same site across the whole range (up to x ¼ 0.20), presumably the void site. Samples annealed at higher temperatures show both higher Ce content by EPMA as well as higher lattice constants.
The partial filling of Ce in the void site increases the entropy due to the increase of disorder of the material, and thus it can be expected that the equilibrium solubility should increase measurably with temperature. While this is known theoretically 22 , the filling fraction limit is often considered to be a temperatureindependent quantity; to date, there has been no report on the temperature dependence of filling fraction limit of Ce, let alone using this to design filler solubility in skutterudites. Here we show that the Ce filling fraction limit (determined from red point in Fig. 3c) increases significantly with temperature (see Fig. 3b and Supplementary Fig. 1). It increases to about 0.197 AE 0.007 at 1,123 K and is more than twice the value reported from ref. 8 (x ¼ 0.09). This ultra-high filling fraction limit is verified using atom-probe tomography (APT) and is discussed later. This presents an opportunity for optimizing thermoelectric properties of Ce-CoSb 3 skutterudites. The filling fraction limit x ¼ 0.120 at 973 K is also 25% higher than the reported literature value x ¼ 0.09, which can be explained due to the presence of separate three-phase regions in the Ce-Co-Sb system with different Ce solubilities in Ce x Co 4 Sb 12 .    Table 1.
There are three two-phase regions and three three-phase regions near CoSb 3 . According to the phase rule, in any threephase region, there are F ¼ C-P þ 0 ¼ 3 À 3 ¼ 0 degrees of freedom where C is the number of components, P the number of phases and the 0 indicates both temperature and pressure are fixed. Thus, the compositions of the three equilibrium phases in a three-phase region are fixed and all the nominal compositions in this three-phase region will produce the same skutterudite composition with the same actual Ce content (marked as red and blue points in Fig. 3c), which are called stable skutterudite compositions in this study. This was confirmed by the EPMA measurements to be x ¼ 0.120±0.005 for the red stable composition (Ce 0.120 Co 4 Sb 12 ) and x ¼ 0.086 ± 0.007 for the blue stable composition (Ce 0.086 Co 4 Sb 12 ) at 973 K.
When the nominal composition is slightly Co rich (in addition to sufficient Ce, for example, Ce 0.5 Co 4.2 Sb 11.8, red empty triangle) the sample is in the three-phase region between CoSb 2 , Ce-CoSb 3 (ref. 23) and Ce x Co 4 Sb 12 with x ¼ 0.120±0.005 (red point). Also if the nominal composition is slightly Sb rich (for example, Ce 0.5 Co 3.9 Sb 12.1, yellow empty triangle) the sample is in the threephase region between CeSb 2 , Ce-CoSb 3 and Ce x Co 4 Sb 12 with, coincidentally, the same x ¼ 0.120±0.005 (red point) as found in the cobalt-rich three-phase region. In both cases the equilibrium Ce content in skutterudite phase will reach the same filling fraction limit x ¼ 0.120 ± 0.005 at 973 K (red point) as indicated by tie lines (red-dashed lines). Note that these three-phase regions (one with CeSb 2 , Ce-CoSb 3 and Ce x Co4Sb12; the other with CoSb 2 , Ce-CoSb 3 and CexCo4Sb12) are different from the previous phase diagram study of Ce-Co-Sb system at 400°C 23 . No similar ternary phase such as Ce-CoSb 3 is found in the Yb-Co-Sb or In-Co-Sb system, but the Ga-Co-Sb system has a ternary phase (Co 3 Ga 2 Sb 4 ) as well 24 .
However, when the nominal composition is very antimony rich, such as used by Morelli 8 the samples are in another three-phase region between Ce x Co 4 Sb 12 , CeSb 2 and liquid Sb (for example, Ce 0.2 Co 3.9 Sb 12.1 and Ce 0.15 Co 3.9 Sb 12.1, marked as green and blue empty triangles, respectively). Here the Ce content in the skutterudite phase remains constant with x ¼ 0.087 ± 0.007 (blue point) as indicated by tie lines (green-and blue-dashed lines). Note that two nominal compositions (Ce 0.10 Co 4 Sb 12.2 and Ce 0.15 Co 4 Sb 12.2 ) from ref. 8 fall into this three-phase region of Ce x Co 4 Sb 12 , CeSb 2 and liquid Sb and one (Ce 0.20 Co 4 Sb 12.2 ) falls into the two-phase region of Ce x Co 4 Sb 12 and CeSb 2 . The observance of CeSb 2 impurity phase in those samples confirms they are in a different field from that which gives the higher Ce content. The blue stable composition point coincides with the reported filling fraction limit from ref. 8, which is about 25% less of the filling fraction limit reported in this study for the same annealing temperature.
From the analysis of the temperature-dependent filling fraction limit we can also predict that the Ce content in the skutterudite phase can be controlled through the annealing temperature when the nominal composition is in one of the three-phase regions, which has proven to be a practical strategy to optimize thermoelectric performances.
APT measurements on Ce x Co 4 Sb 12 skutterudite was also performed to confirm the ultra-high filling fraction of x ¼ 0.20. APT is particularly effective at chemically and structurally characterizing materials in 3D on the nanometre length scale. It provides accurate information about atomic concentrations and can identify even the smallest nanoparticles 25 . Small nanoparticles of Yb 2 O 3 and InSb were observed in some Yb and In containing skutterudites, respectively 6,26,27 . Such small particles might go unnoticed in the Scanning Electron Microscopy (SEM) and would contribute to the EPMA signal. Here APT was used to verify the Ce content and homogeneity in the Ce x Co 4 Sb 12 majority phase for sample annealed at 1,123 K with nominal composition Ce 0.5 Co 4 Sb 12 . According to EPMA, the Ce content in the majority skutterudite phase should be x ¼ 0.20 or 1.2 at%. Figure 4a contains a 3D reconstruction of the skutterudite phase at and around a grain boundary. As can be seen in Fig. 4b, atomic concentrations were consistent and homogeneous away from the grain boundary. No nano-precipitates of Ce-rich phases were observed. Atomic concentrations were averaged over a 30 nm diameter cylinder, from 20 to 60 nm on the scale bar in Fig. 4a, and the Ce content was measured to be 1.4 ± 0.1 at%. This agrees with the values obtained by EPMA (x ¼ 0.20 corresponding to Ce content of 1.2 at %) and supports our conclusion that such a high filling fraction of Ce is indeed uniformly distributed in the skutterudite phase. A uniform accumulation of Ce at the grain boundary was also observed, accompanied by a reduction in Co. Such atomic segregation is frequently observed at grain boundaries 25 . Because of the low cost of Ce as a single filler, Ce-CoSb 3 skutterudites could have potential for scale-up commercialization in fields such as the automotive industry, if their thermoelectric performance can be optimized. Ce single-filled skutterudites in previous literature studies have been underdoped and fall out of the high power factor region due to the assumed low filling fraction limit of Ce (x ¼ 0.09). Here by conducting an equilibrium phase diagram study, we show that the filling fraction limit has a large temperature dependence and the value can reach as high as x ¼ 0.20 at 1,123 K. This is more than twice the value reported previously and thus allows to optimize Ce-CoSb 3 skutterudites. This ultra-high Ce content is confirmed by APT measurements. The optimized Ce-CoSb 3 skutterudites give a zT value of 1.3 at 850 K for Ce 0.14 Co 4 Sb 12 , which is among the highest reported zT values for single-filled skutterudites.

Methods
Sample preparation. High-purity elements Co (99.95%, slug), Sb (99.9999%, shot) and Ce (99.9%, rod) purchased from Alfa Aesar were used as raw materials. The samples were sealed in carbon-coated fused silica tubes under vacuum. The silica tubes were heated slowly up to 1,373 K in 12 h, held at this temperature for 12 h and then quenched in water to room temperature. Samples were then annealed at temperatures ranging from 973 to 1,123 K for 7 days. The resulting ingots were hand ground into fine powders and consolidated by rapid hot pressing at 973 K for 1 h under a pressure of about 60 MPa, yielding fully dense bulk samples. High density (498% of the theoretical density of CoSb 3 ) was achieved in all hot-pressed samples. Hot-pressed samples were sealed in fused tubes under vacuum for further annealing at the same annealing temperatures as before for 7 days again to erase the temperature effect of the hot pressing process before thermoelectric properties were measured 2 . Impurity phases were identified with X-ray diffraction and confirmed with SEM analysis in the same way as described in previous work 2, 28,29 .
Thermoelectric property measurements. Electrical transport properties, including electrical conductivity (s) and Seebeck coefficient (S), were measured using the ZEM-3 (ULVAC.) apparatus under a helium atmosphere from 300 to 850 K. Thermal conductivity (k) was calculated using k ¼ dD T C P , with the thermal diffusivity D T measured along the cross-plane direction by the laser flash method (Netzsch LFA 457) under argon flow with the Cowan model plus pulse correction. The density of the samples was measured using the geometrical method. The specific heat capacity C P was determined using the Dulong-Petit law C P ¼ 3k B per atom throughout the temperature range 300-850 K. The in-plane Hall coefficient (R H ) was measured using the Van der Pauw method in a magnetic field up to 2 T 30 . Hall carrier concentration (n) was then estimated to be equal to 1/R H e, where e is the elementary charge. The Hall carrier mobility (m n ) was calculated according to the relation m n ¼ R H s. The estimated measurement uncertainties are listed as follows: 5% for electrical resistivity, 7% for seebeck coefficient, 5% for thermal diffusivity and 1% for density. The data precision (reproducibility) is smaller than the accuracy (see Supplementary Fig. 5), leading to zT values within the range of ±0.2.
Atomic probe topographic measurement. APT experiments were conducted on a Cameca LEAP-4000X Si equipped with a picosecond ultaviolet laser (wavelength 355 nm). Microtip samples of the nominal composition Ce 0.5 Co 4 Sb 12 were prepared using a dual-beam focused-ion beam microscope (FEI Helios Nanolab) equipped with a micromanipulator (similar to the lift-out method) 31 . Microtips with a diameter of B100 nm were fabricated to contain a grain boundary and the last step of the tip sharpening process utilized a low voltage and current (5 kV, 16 pA) Ga þ ion beam to minimized Ga implantation in the sample (Ga content of the region analysed was o0.01 at%). The sample was maintained at 30 K and a laser energy of 10 pJ pulse À 1 was used at a pulse rate of 250 Hz with a target evaporation rate of 0.5% atom pulse À 1 . The primary ions detected were Co 2 þ , Co þ , Ce 3 þ , Ce 2 þ , Sb 3 þ , Sb 2 þ and Sb þ . Very small amounts of Sb 2 þ and CoCe þ , Ga þ and O 2 þ were also detected. Ions were detected using a twodimensional microchannel plate detector with a detector efficiency of 50%. This detection efficiency is the same for all ions evaporated. The data collected were analysed and a three-dimensional reconstruction was created using the programme IVAS v.3.6.6.