High Temperature Transport Properties of Yb and In Double-Filled p-Type Skutterudites

Yb and In double-filled and Fe substituted polycrystalline p-type skutterudite antimonides were synthesized by direct reaction of high-purity elements, followed by solid-state annealing and densification by hot pressing. The stoichiometry and filling fraction were determined by both Rietveld refinement of the X-ray diffraction data and energy dispersive spectroscopic analyses. The transport properties were measured between 300 K and 830 K, and basically indicate that the resistivity and Seebeck coefficient both increase with increasing temperature. In both specimens, the thermal conductivity decreased with increasing temperature up to approximately 700 K, where the onset of bipolar conduction was observed. A maximum ZT value of 0.6 at 760 K was obtained for the Yb0.39In0.018Co2.4Fe1.6Sb12 specimen.


Introduction
Thermoelectric materials research is of current significant interest for improving device performance in order to efficiently convert waste heat into electrical power [1].Thermoelectric device improvement would result in an expanded array of potential applications, including automobile applications [2].The efficiency of a thermoelectric material is given by the dimensionless figure of merit ZT = S 2 T/ρ κ, where S is the Seebeck coefficient, T is the absolute temperature, ρ is the resistivity, and κ is the thermal conductivity.The larger both the average and the peak ZT value are, the better the thermoelectric properties of a material.Both n-type and p-type materials are required in a thermoelectric device; the efficiency of the device is characterized by the combination of both materials' thermoelectric properties.
Skutterudites have been studied extensively-not only due to their encouraging thermoelectric performance at intermediate temperatures, but also due to their good mechanical properties [3][4][5][6].Optimization of p-type skutterudites is difficult due to the relatively small effective mass of holes compared to the effective mass of electrons in these materials [4]; therefore, the optimum carrier concentration of n-type skutterudites is larger than that of p-type, leading to a larger power factor (S 2 σ, where σ is electrical conductivity) [7].It is well documented that the twelve Sb atoms in the skutterudite crystal structure form relatively large icosahedral cages [1,3,8]; thus, reduction of the lattice thermal conductivity, κ L , can be achieved by fractional filling of these cages with rare-earth, alkali-earth, or alkali-metal atoms, since these cage-fillers result in the scattering of lattice phonons [3,8].Yb filling has been shown to be a good filler candidate for skutterudites because of its large mass and small ionic radius, which results in strong phonon scattering.Furthermore, in skutterudites Yb has been shown to have an intermediate valence state (+2~+3), demanding less charge compensation for p-type materials [9].The thermoelectric properties of n-type (Yb, In) double-filled skutterudite antimonides have been previously reported with a maximum ZT of 0.97 [10].The pursuit of p-type materials is also needed; herein we investigate similar double filling in p-type skutterudites in order to determine their potential for thermoelectric applications.

Experimental
The high-purity elements were weighed and loaded into silica crucibles in a N 2 environment inside a glove box to minimize exposure to air.Yb chunks (99.9%,Ames Labs), In foil (99.9975%,Alfa Aesar), Co powder (99.998%,Alfa Aesar), Fe powder (99.998%,Alfa Aesar), and crushed Sb chunks (99.5%, Alfa Aesar) were reacted in the nominal compositions Yb 0.4 In 0.02 Co 3 FeSb 12 and Yb 0.8 In 0.02 Co 2.5 Fe 1.5 Sb 12 for this study, which were chosen based off of previous studies of Yb single-filled Fe substituted skutterudites [11,12].The specimens were sealed in a quartz tube under vacuum and reacted in a furnace at 1173 K for 48 h.The tube was removed and allowed to cool to room temperature in air before the specimens were ground into fine powders in a N 2 glove box and cold pressed into pellets.These pellets were again sealed under vacuum in a quartz tube and annealed at 973 K for 7 days.This grinding and annealing process was repeated once more to further encourage homogeneity.The specimens were then finely ground and sieved (325 mesh) before being loaded into a graphite die inside the glove box for hot pressing.The hot pressing conditions for densification were performed under constant N 2 flow at 923 K and 120 MPa for 3 h, resulting in high-density polycrystalline skutterudites as measured by the Archimedes method.
Analyses of the homogeneity and stoichiometry of the specimens were performed by Rietveld refinement of the powder X-ray diffraction (XRD) data using a Bruker D8 Focus Diffractometer in Bragg-Brentano geometry with Cu Kα radiation and a graphite monochromator, and energy dispersive spectroscopy (EDS) using an Oxford INCA X-Sight 7852 equipped scanning electron microscope (SEM, JEOL, JSM-6390LV).The densified pellets were cut with a wire saw for high-temperature transport measurements.A rectangular parallelepiped (2 × 2 × 5 mm 3 ) was used for four-probe ρ and S measurements on a ULVAC ZEM-2 system.Thermal diffusivity measurements on a thin disk were performed by the laser flash method on a NETZSCH LFA 457 system, under constant Ar flow.The experimental uncertainties in both these measurements were 5-10%.Heat capacity measurements were performed using a NETZSCH DSC 404C system.Separate pieces of the specimens were also used for room-temperature Hall measurements and air stability tests.Air stability tests indicated that the specimens began to oxidize and degrade at 673 K, similar to that of previously reported skutterudites [13,14].

Structural Characterization
Rietveld refinement profiles from the powder XRD data are shown in Figure 1, displaying calculated and observed data and the difference between them.Table 1 indicates the refinement results.The crystal structures were refined with space group Im3 (#204), and the initial atomic positions were based on data from previously reported Yb filled skutterudites [11,12].The filler Yb atoms at the 2a site occupy less than the nominal composition, due in part to a trace amount of Yb 2 O 3 (observed in profiles at 29.7 • ) and to steric effects [11,12,15,16].The Co-to-Fe ratios are extremely close to the nominal compositions.The lattice parameters are 9.0661 Å and 9.0877 Å for Yb 0.13 In 0.02 Co 3 FeSb 12 and Yb 0.39 In 0.02 Co 2.4 Fe 1.6 Sb 12 , respectively, with an increase in lattice parameter with Yb and In filling fractions and Co-to-Fe ratio, in agreement with previously reported data.Furthermore, the Yb filling fraction increases from 33% to 49% with increased Fe substitution, similarly reported for Gd and (Ba, Yb) filled skutterudites [10][11][12][13][14][15][16][17].Elemental mapping from EDS data shows an even dispersion of elements for both specimens, indicating good homogeneity of the specimens, and corroborate our refinement results.

Transport Properties
Figure 2a,b show temperature-dependent (300-800 K) S and ρ data, respectively.The Yb 0.13 In 0.02 Co 3 FeSb 12 specimen exhibits a metallic-like temperature dependence with ρ increasing with temperature, although these values saturate to 1.6 mΩ cm −1 at 650 K.The ρ values for Yb 0.39 In 0.02 Co 2.4 Fe 1.6 Sb 12 do not exhibit as strong a temperature dependence in the measured temperature range.The S values for both specimens increase with increasing temperature and peak at 700 K, with values of 140 µV/K and 160 µV/K for Yb 0. 13  In the single parabolic band model, S and p are given by [18] and where the plus and minus signs in Equation ( 1) are for holes (+) and electrons (−), η is the reduced Fermi energy (=E F /k B T, where E F is the Fermi energy, k B is the Boltzmann constant, and T is absolute temperature), Fr is the Fermi integral of order r, and r is the exponent of the energy dependence of the electron mean free path.r = 0 for scattering from acoustic phonons (lattice vibrations) and r = 2 for ionized impurity scattering. and where the plus and minus signs in Equation ( 1) are for holes (+) and electrons (−), η is the reduced Fermi energy (=EF/kBT, where EF is the Fermi energy, kB is the Boltzmann constant, and T is absolute temperature), Fr is the Fermi integral of order r, and r is the exponent of the energy dependence of the electron mean free path.r = 0 for scattering from acoustic phonons (lattice vibrations) and r = 2 for ionized impurity scattering.In our estimate for effective mass, m*, the intermediate value of r = 1 is used.Using our room-temperature S and p values, we estimate m* to be 0.7me for Yb0.13In0.02Co3FeSb12and 1.4me for Yb0.39In0.02Co2.4Fe1.6Sb12.These values are much smaller than that for YbxFe3.5Ni0.5Sb12compositions, but are similar to Yb0.5Fe1.5Co2.5Sb12and Ca0.17Ce0.05Fe1.47Co2.53Sb12which have a comparable Co-to-Fe content [19][20][21].Figure 2c shows κ data calculated from thermal diffusivity and heat capacity measurements using the equation κ = D•d•Cp, where D is measured density, d is measured thermal diffusivity, and Cp is measured heat capacity. Figure 3 shows κL as calculated using the Wiedmann-Franz relation, where κE = L0T/ρ (L0 being the Lorenz number taken to be 2.45 × 10 −8 V 2 K −2 ).These κ values are smaller compared to those of previously reported (Yb, In) and (Ba, In) double-filled n-type skutterudites, as well as that of (Ce, Nd) double-filled p-type skutterudites [10,22,23].An increase in κ and κL is observed above 700 K, which can be attributed to bipolar diffusion.The contribution of bipolar diffusion, κB, is given by κB = σeσh(Sh-Se) 2 T/σe + σh, where σe is the electron conduction, σh is the hole conduction, Sh is the hole Seebeck coefficient, and Se is the electron Seebeck coefficient [1].An Figure 2c shows κ data calculated from thermal diffusivity and heat capacity measurements using the equation κ = D•d•C p , where D is measured density, d is measured thermal diffusivity, and C p is measured heat capacity. Figure 3 shows κ L as calculated using the Wiedmann-Franz relation, where κ E = L 0 T/ρ (L 0 being the Lorenz number taken to be 2.45 × 10 −8 V 2 K −2 ).These κ values are smaller compared to those of previously reported (Yb, In) and (Ba, In) double-filled n-type skutterudites, as well as that of (Ce, Nd) double-filled p-type skutterudites [10,22,23].An increase in κ and κ L is observed above 700 K, which can be attributed to bipolar diffusion.The contribution of bipolar diffusion, κ B , is given by κ B = σ e σ h (S h -S e ) 2 T/σ e + σ h , where σ e is the electron conduction, σ h is the hole conduction, S h is the hole Seebeck coefficient, and S e is the electron Seebeck coefficient [1].An estimation of κ B can be made from the high-temperature data using κ L = 3.5(k B /h) 3 where h is Planck's constant, M is the average mass per atom, V is the average atomic volume, θ D is the Debye temperature, and γ is the Grüneisen parameter.It is clear that Umklapp scattering dominates κ L above θ D [1].Therefore, the inset to Figure 3 illustrates the procedure of using a fit κ L ~T−1 to estimate κ B for the Yb 0.13 In 0.02 Co 3 FeSb 12 specimen, resulting in proportions of 53%, 33%, and 14% for κ E , κ L , and κ B , respectively.The estimations for the Yb 0.39 In 0.02 Co 2.4 Fe 1.6 Sb 12 specimen were done with the same method, and gave values of 48%, 44%, and 8% for κ E , κ L , and κ B , respectively.These κ B values are higher than that of single-filled Yb compositions, possibly due to the additional low-lying donor states with In filling [3,10].An increase in Fe content resulted in a near 50% reduction in κ B [11].
Crystals 2017, 7, 256 5 of 7 estimation of κB can be made from the high-temperature data using κL = 3.5(kB/h) 3 (MV 1/3 θD 3 /γ 2 T), where h is Planck's constant, M is the average mass per atom, V is the average atomic volume, θD is the Debye temperature, and γ is the Grüneisen parameter.It is clear that Umklapp scattering dominates κL above θD [1].Therefore, the inset to Figure 3 illustrates the procedure of using a fit κL ~ T −1 to estimate κB for the Yb0.13In0.02Co3FeSb12specimen, resulting in proportions of 53%, 33%, and 14% for κE, κL, and κB, respectively.The estimations for the Yb0.39In0.02Co2.4Fe1.6Sb12specimen were done with the same method, and gave values of 48%, 44%, and 8% for κE, κL, and κB, respectively.These κB values are higher than that of single-filled Yb compositions, possibly due to the additional low-lying donor states with In filling [3,10].An increase in Fe content resulted in a near 50% reduction in κB [11].Figure 4 shows the ZT values for both specimens.These values have been calculated from the measured data, and both specimens show increasing ZT with increasing temperature, with a maximum value of 0.6 at 760 K for the Yb0.39In0.02Co2.4Fe1.6Sb12specimen.This maximum ZT value is lower than that of the n-type (Yb, In) double-filled skutterudite but greater than (Ce, Yb) doublefilled p-type skutterudites with comparable filling fraction and Co-to-Fe ratio [10,21].However, other reported p-type (Ce, Yb) double-filled skutterudites with greater filling fraction and Fe substitution exhibit a larger ZT (=0.87) [24].Figure 4 shows the ZT values for both specimens.These values have been calculated from the measured data, and both specimens show increasing ZT with increasing temperature, with a maximum value of 0.6 at 760 K for the Yb 0.39 In 0.02 Co 2.4 Fe 1.6 Sb 12 specimen.This maximum ZT value is lower than that of the n-type (Yb, In) double-filled skutterudite but greater than (Ce, Yb) double-filled p-type skutterudites with comparable filling fraction and Co-to-Fe ratio [10,21].However, other reported p-type (Ce, Yb) double-filled skutterudites with greater filling fraction and Fe substitution exhibit a larger ZT (=0.87) [24].

Conclusions
The structural and high-temperature transport properties of p-type (Yb, In) double-filled skutterudites were investigated.We observed an increase in both ρ and S for Yb0.39In0.02Co2.4Fe1.6Sb12,whereas κ was less for the specimen with lower Yb content.Above 700 K, both specimens exhibited a fairly large κB contribution that significantly increased κ above this temperature, although κB decreased with increasing Fe content.Both specimens exhibited the largest ZT values at 750 K.The performance of these p-type skutterudites may be enhanced by a further increase in overall filling fractions of (Yb, In), corresponding to an increase in Fe content.

Conclusions
The structural and high-temperature transport properties of p-type (Yb, In) double-filled skutterudites were investigated.We observed an increase in both ρ and S for Yb 0.39 In 0.02 Co 2.4 Fe 1.6 Sb 12 , whereas κ was less for the specimen with lower Yb content.Above 700 K, both specimens exhibited a fairly large κ B contribution that significantly increased κ above this temperature, although κ B decreased with increasing Fe content.Both specimens exhibited the largest ZT values at 750 K.The performance of these p-type skutterudites may be enhanced by a further increase in overall filling fractions of (Yb, In), corresponding to an increase in Fe content.

Figure 3 .
Figure 3. Temperature-dependent κ L for Yb 0.13 In 0.02 Co 3 FeSb 12 (circle) and Yb 0.39 In 0.02 Co 2.4 Fe 1.6 Sb 12 (triangle).The inset illustrates the method used to estimate κ B for both specimens, with Yb 0.13 In 0.02 Co 3 FeSb 12 shown here, where the solid line is the T −1 dependence between 400 K and 700 K.
0.13 In 0.02 Co 3 FeSb 12 and 1.4m e for Yb 0.39 In 0.02 Co 2.4 Fe 1.6 Sb 12 .These values are much smaller than that for Yb x Fe 3.5 Ni 0.5 Sb 12 compositions, but are similar to Yb 0.5 Fe 1.5 Co 2.5 Sb 12 and Ca 0.17 Ce 0.05 Fe 1.47 Co 2.53 Sb 12 which have a comparable Co-to-Fe content [19-21].
In our estimate for effective mass, m*, the intermediate value of r = 1 is used.Using our room-temperature S and p values, we estimate m* to be 0.7m e for Yb