Seebeck and Figure of Merit Enhancement by Rare Earth Doping in Yb14-xRExZnSb11 (x = 0.5)

Yb14ZnSb11 has been of interest for its intermediate valency and possible Kondo designation. It is one of the few transition metal compounds of the Ca14AlSb11 structure type that show metallic behavior. While the solid solution of Yb14Mn1-xZnxSb11 shows an improvement in the high temperature figure of merit of about 10% over Yb14MnSb11, there has been no investigation of optimization of the Zn containing phase. In an effort to expand the possible high temperature p-type thermoelectric materials with this structure type, the rare earth (RE) containing solid solution Yb14-xRExZnSb11 (RE = Y, La) was investigated. The substitution of a small amount of 3+ rare earth (RE) for Yb2+ was employed as a means of optimizing Yb14MnSb11 for use as a thermoelectric material. Yb14ZnSb11 is considered an intermediate valence Kondo system where some percentage of the Yb is formally 3+ and undergoes a reduction to 2+ at ~85 K. The substitution of a 3+ RE element could either replace the Yb3+ or add to the total amount of 3+ RE and provides changes to the electronic states. RE = Y, La were chosen as they represent the two extremes in size as substitutions for Yb: a similar and much larger size RE, respectively, compared with Yb3+. The composition x = 0.5 was chosen as that is the typical amount of RE element that can be substituted into Yb14MnSb11. These two new RE containing compositions show a significant improvement in Seebeck while decreasing thermal conductivity. The addition of RE increases the melting point of Yb14ZnSb11 so that the transport data from 300 K to 1275 K can be collected. The figure of merit is increased five times over that of Yb14ZnSb11 and provides a zT ~0.7 at 1275 K.


Introduction
Compounds of the Ca 14 AlSb 11 (14-1-11) structure type have been shown to exhibit high thermoelectric figure of merit, zT, at high temperatures [1][2][3][4]. While Yb 14 MnSb 11 and Yb 14 MgSb 11 members of this group have been high achievers in this area [5,6], the more metallic Yb 14 ZnSb 11 has never been considered a good thermoelectric material because of its low Seebeck coefficient (α) and, therefore, low zT, as it scales with α 2 [7,8]. However, the low electrical resistivity that it possesses is an attractive feature, and prior work sought to tap into this by forming a solid solution of Zn with Mn, which resulted in improved zT compared with Yb 14 MnSb 11 [9]. Yb 14 ZnSb 11 has a smaller unit cell and possesses a lower decomposition temperature than those of its Mn and Mg counterparts; the latter property further dashing hopes for its use in high temperature TE devices. Yb 14 ZnSb 11 is unique amongst the members of the 14-1-11 family in that it exhibits Curie-Weiss behavior equivalent to about 0.75 Yb 3+ from 300 K to 100 K and a broad maximum in magnetic susceptibility at around 85 K that drops as temperature is lowered, followed by a sharp increase at 20 K. The fact that there is not a simple integral amount of Yb 3+ is consistent with an "intermediate valence". The broad maximum is interpreted as a fluctuation between the f 13 (3+) and f 14 (2+) electronic configurations of Yb, while the low temperature increase in susceptibility is attributed to free Yb 3+ impurities. Intermediate valence is observed in some of the rare earth elements, such as Ce, Eu, and Yb [10]. The resulting change in valence corresponds to the effective nuclear charge and then, ultimately, to a change in lattice parameters [7]. The valence fluctuation in Yb 14 ZnSb 11 is the shift from the small percentage of Yb 3+ states at high temperature to all Yb 2+ at a low temperature. A Curie-Weiss fit of the paramagnetic region above 150 K yields a µ eff of 3.8 µB, which corresponds to the presence of approximately 0.8 Yb 3+ per formula unit [7]. The existence of 0.75 Yb 3+ in this compound makes Yb 14 ZnSb 11 close to a valence precise Zintl formula, but the low resistivity and intermediate valence of Yb distinguish it from this simplistic interpretation of bonding. Recently, magnetic susceptibility measurements of the Mg compound were reported and are consistent with a similar amount of Yb 3+ , but there is no evidence for intermediate valency [11]. Yb 14 MnSb 11 contains only Yb 2+ , confirmed by X-ray photoelectron spectroscopy (XPS) and X-ray magnetic circular dichroism (XMCD) and neutron measurements [8,12]. Figure 1 shows a view of the unit cell of Yb 14 ZnSb 11 along the c axis. This compound is considered as a Zintl phase with the approximate formula of 13Yb 2+ +~1Yb 3+ +ZnSb 4 10− + Sb 3 7− + 4Sb 3− [7].
There are four Yb crystallographic sites in the structure, but there is no direct evidence from the structure concerning site preference for the Yb 3+ cation, although Yb 14 ZnSb 11 does have the smallest lattice parameters within this family of compounds. While the valence precise Zintl phase of Yb 14  that drops as temperature is lowered, followed by a sharp increase at 20 K. The fact that there is not a simple integral amount of Yb 3+ is consistent with an "intermediate valence". The broad maximum is interpreted as a fluctuation between the f 13 (3+) and f 14 (2+) electronic configurations of Yb, while the low temperature increase in susceptibility is attributed to free Yb 3+ impurities. Intermediate valence is observed in some of the rare earth elements, such as Ce, Eu, and Yb [10]. The resulting change in valence corresponds to the effective nuclear charge and then, ultimately, to a change in lattice parameters [7]. The valence fluctuation in Yb14ZnSb11 is the shift from the small percentage of Yb 3+ states at high temperature to all Yb 2+ at a low temperature. A Curie-Weiss fit of the paramagnetic region above 150 K yields a µeff of 3.8 µB, which corresponds to the presence of approximately 0.8 Yb 3+ per formula unit [7]. The existence of 0.75 Yb 3+ in this compound makes Yb14ZnSb11 close to a valence precise Zintl formula, but the low resistivity and intermediate valence of Yb distinguish it from this simplistic interpretation of bonding. Recently, magnetic susceptibility measurements of the Mg compound were reported and are consistent with a similar amount of Yb 3+ , but there is no evidence for intermediate valency [11]. Yb14MnSb11 contains only Yb 2+ , confirmed by X-ray photoelectron spectroscopy (XPS) and X-ray magnetic circular dichroism (XMCD) and neutron measurements [8,12]. Figure 1 shows a view of the unit cell of Yb14ZnSb11 along the c axis. This compound is considered as a Zintl phase with the approximate formula of 13Yb 2+ + ~1Yb 3+ +ZnSb4 10− + Sb3 7− + 4Sb 3− [7]. There are four Yb crystallographic sites in the structure, but there is no direct evidence from the structure concerning site preference for the Yb 3+ cation, although Yb14ZnSb11 does have the smallest lattice parameters within this family of compounds. While the valence precise Zintl phase of Yb14AlSb11 has been shown to have semiconducting electrical transport properties, Yb14ZnSb11 shows the lowest resistance of compounds of this structure type published to date. The crystal structures of Yb14ZnSb11 and Ca14ZnSb11 were reported with defects or interstitial atoms; Yb14ZnSb11 contains a slight deficiency on the Zn site and Ca14ZnSb11 is purported to contain interstitial Sb [8,13]. The low resistance of Yb14ZnSb11 is attributed to either the intermediate valence of Yb or to the defects in the structure [7]. In Yb14MnSb11, the substitution of 3+ rare earth (RE) cations for Yb cations in small amounts (x < 0.5) has been successful in improving zT and, in addition, has been shown in some cases to decrease the high temperature sublimation (as is the case for RE = La) [14]. A slight reduction in carrier In Yb 14 MnSb 11 , the substitution of 3+ rare earth (RE) cations for Yb cations in small amounts (x < 0.5) has been successful in improving zT and, in addition, has been shown in some cases to decrease the high temperature sublimation (as is the case for RE = La) [14]. A slight reduction in carrier concentration from the substitution of the RE helps to boost α and, in turn, zT. In all attempts, no more than x~0.7 was found to incorporate into the structure of single crystals of Yb 14-x RE x MnSb 11 solution grown in Sn flux [14][15][16][17]. The isostructural Ca 14-x RE x MnSb 11 grown in Pb flux is reported to exhibit a limit of x = 1 [18]. It is not clear if the differences in substitution for the two different parent phases, Yb 14 MnSb 11 versus Ca 14 MnSb 11 , is due to the different flux employed or electronic and size effects.
In an effort to further expand our investigation of the effect of RE 3+ on the transport properties of this structure type, the solid solution, Yb 14-x RE x ZnSb 11 (RE = Y and La), was investigated. The solid solutions were made via a stoichiometric metallurgical approach and the samples condensed into fully dense pellets for measurement. Seebeck, electrical and thermal transport, and Hall measurements are reported.

Synthesis
Samples of Yb 13.5 RE 0.5 ZnSb 11 were synthesized by combining Yb filings, Sb shot, Zn shot (100% excess), and RE filings with a total mass of 8 g in a SPEX 55ml tungsten carbide canister with one large and two small tungsten carbide balls. Work was performed in an argon filled drybox and both RE and Yb were brushed with a designated wire brush prior to filing to remove any oxide on the surface. Samples were milled using a SPEX 8000M mixer mill (SPEX, 65 Liberty Street, Metuchen, NJ, USA) for a total of 1 h and 30 min, with 15 min of rest time between 30 min milling intervals, and a scrape down inside the drybox after 1 h of milling time. Samples were sealed in 13 cm long Nb tubes, arc melted shut under Ar, and sealed in quartz under vacuum. The samples were annealed for 96 h at 900 • C in a box furnace. Zn was used in 100% excess in an effort to prevent formation of Yb 11 Sb 10 . Samples made with a stoichiometric amount of Zn contained this side phase as 20% or larger composition, indicating some loss of Zn during the ball milling or annealing stage.

Consolidation of Powder
Annealed powder samples were made into dense pellets for measurement via a spark plasma sintering (SPS) Dr. Sinter Lab SPS-211LX unit (Fuji Electric Industrial Co., Ltd, 6-2-22 Fujimi, Tsurugashima, Saitama, Japan). In an argon drybox, the annealed powder was ground in an agate mortar and pestle and passed through a 200 mesh stainless steel sieve and loaded between multiple thin graphite foil spacers in a 12.7 mm inner diameter high-density graphite die. Sintering was performed under dynamic vacuum and with a starting sample pressure of 20 MPa. The temperature was ramped from 20 • C to 750 • C over four minutes, then to 800 • C in one minute to avoid temperature overshoot. The pressure was slowly and steadily increased to 63 MPa during the temperature range 700-800 • C (about 1.5 min). Then, 800 • C and 63 MPa were held constant for 15 min, after which the sintering process was ended, and pressure/temperature released. Pressed pellets were typically 2 g in size and were cut circumferentially into two disks using a Buehler diamond saw to allow for one to be pulverized for use in characterization via powder X-ray diffraction. The other pellet was saved for properties measurements. The pellet densities obtained through this sintering profile were greater than 96% of the theoretical densities for each compound.

Electron Microprobe Analysis and Wavelength Dispersive Spectroscopy
After measurement of TE properties, small pieces of pellets were mounted in epoxy and polished using grits sizes down to 0.01 µm. Care was taken to prevent oxidation of these polished sample pucks and, after preparation, they were stored under dynamic vacuum and transported triple-bagged in argon atmosphere. Prior to their measurement, the pucks were carbon coated to prevent charging. Samples were analyzed using a Cameca SX100 electron microprobe (CAMECA Instruments, Inc., 5470 Nobel Drive, Madison, WI, USA) with five wavelength dispersive X-ray spectrometers, operated at 15 kV accelerating potential and beam current of 20 nA. A polished single crystal of Yb 14 MnSb 11 was used as wavelength dispersive X-ray spectroscopy (WDS) standard for Yb. Zn and Sb metal, LaPO 4 , and yttrium aluminum garnet (YAG) crystals were used as WDS standards for Zn and Sb, La and Y, respectively. The composition of each sample was determined by calculating the average and standard deviation of 15 data points of the main phase and 5 data points of the side phase randomly spaced through the sample.

Powder X-Ray Diffraction
Powder X-ray diffraction (PXRD) data were collected on each sample after furnace annealing and after consolidation in the SPS. Samples were ground into a fine powder by mortar and pestle in an Ar drybox and plated with ethanol to obtain a uniform, thin spread onto a zero background holder on a Bruker D8 Advance Eco Diffractometer (BRUKER AXS, Inc., 5465 East Cheryl Parkway, Madison, WI, USA) operated at 40 kV and 25 mA utilizing Ni filtered Cu Kα radiation with the knife-edge attachment. Data were collected from 20 • to 80 • 2θ with a step size of 0.19 • at 1.5 s. Data were converted from .raw to .gsas using powdll and analyzed via Rietveld refinement using General Structure Analysis System, GSAS-II [19,20]. The GSAS-II instrument parameter file used in refinement was generated from a similarly-prepared LaB 6 standard. Lattice parameters of the RE phases were obtained from refinement of a 14-1-11 phase modelled from published Crystallographic Information File (CIF) of Yb 14 ZnSb 11 .

Electrical Resistivity, Hall Effect, and Seebeck Coefficient
The electrical resistivity (ρ) and Hall coefficient were measured simultaneously from 300 K to 1275 K on a home-built instrument under dynamic vacuum. Resistivity was measured via the van der Pauw technique using a current of 100 mA; Hall was measured under a forward and reverse magnetic field of about 7500 G. The carrier concentration (n) was calculated from n = 1/R H e, where R H is the measured Hall coefficient and e the elementary charge. The hall factor was assumed to be 1 [21]. The Seebeck coefficient (α) was measured using a home-built instrument with graphite heater using W/Nb thermocouples and the temperature differential generated by light pulse. The resultant resistivity and Seebeck data from the heating up measurements were each fitted to a six-order polynomial function for the calculation of zT.

Thermal Conductivity
Thermal diffusivity (D t ) data were collected from 300 K to 1275 K using a Netzsch LFA-457 laser flash unit (Netzsch Instruments North America, 129 Middlesex Turnpike Burlington, MA, USA). Then, 12.7 mm diameter pellet samples were polished to obtain parallel top and bottom surfaces and overall thickness less than 1.2 mm, and were then coated in graphite. The measurement was performed under dynamic vacuum and with three data points per temperature step. The Cowan + pulse correction fit of the detected signal was employed through the Netzsch software to obtain values of thermal diffusivity, which were then averaged for each temperature step. Thermal conductivity was calculated via κ = D t × ρ × Cp, where ρ = density and Cp = heat capacity as a function of temperature [21]. Room-temperature density was measured geometrically and high-temperature density was estimated using thermal expansion data from previous study on Yb 14 MnSb 11 [22]. The previously reported experimentally-determined Cp values for Yb 14 MnSb 11 were used as an estimate for these compounds correcting for mass [23].

Results
The two compounds, Yb 13.5 RE 0.5 ZnSb 11 (RE = Y, La), were prepared with excess Zn in order to prevent the formation of the unwanted side phase Yb 11 Sb 10 . We have shown in previous publications that the highest temperature properties of compounds of this structure type are compromised once Yb 11 Sb 10 forms [24]. Synthesis of phase pure Yb 14 MgSb 11 requires 20% excess Mg; this requirement is attributed to the high vapor pressure of Mg at the reaction temperature. Zn has a slightly higher vapor pressure than that of Mg at the reaction and sintering temperatures, highlighting the need for excess [25]. The samples were prepared by balling the elements, sealing the fine powder into niobium tubes, and heat treating at 900°C. The product was then pressed into a dense pellet via spark plasma sintering (SPS).
Yttrium and lanthanum rare earth elements were chosen for this study because of their sizes. Y 3+ (0.900 Å) is closest in size to Yb 3+ (0.868 Å), while La 3+ (1.032 Å) represents the largest of the 3+ RE cations [26]. As previously mentioned, there are four crystallographic sites for the Yb cation in Yb 14 ZnSb 11 coordinated by antimony with various sized polyhedral volumes. The site specificity of various rare earth elements has been shown to be correlated with size in studies of Yb 14-x RE x MnSb 11 . Early RE cations with larger ionic radius, such as La, were shown to preferentially substitute on the Yb2 and Yb4 sites, while RE of smaller ionic radius such as Y substitutes on all of the Yb sites [15,16]. While it is expected that carrier concentration plays the largest role in controlling the transport properties, the RE site selectivity has been indicated as important for subtle differences in thermoelectric properties across the series, Yb 14-x RE x MnSb 11 [2,27].
Electron microprobe X-ray maps of the dense pellets ( Figure 2) show that the samples have a good distribution of the elements and that there is excess Zn at the grain boundaries. Figure S1 shows the microprobe backscatter electron images of Yb 13.5 Y 0.5 ZnSb 11 and Yb 13.5 La 0.5 ZnSb 11 . Wavelength dispersive X-ray spectroscopy of the samples show two phases: a main phase (Yb 13.5 RE 0.5 ZnSb 11 ) and side phase (Yb 1.95 RE 0.0.5 Zn 0.8 Sb 2) , tabulated in Table 1. While the main phase was loaded as Yb 13.5 RE 0.5 ZnSb 11 , the analysis shows that when RE = Y, the amount incorporated is slightly less. Whereas for RE = La, it is in good agreement, and the Zn is slightly deficient in both samples, giving rise to the stoichiometries Yb 13.7 Y 0.35 Zn 0.85 Sb 11 and Yb 13.7 La 0.48 Zn 0.91 Sb 11 . The WDS data were normalized to 11 Sb and while that provides a slightly high Yb + RE content, it is within error consistent with the stoichiometry of 14-1-11, with deficiencies of Zn. Table 1. Wavelength dispersive X-ray spectroscopy (WDS) stoichiometry from pelleted samples from an average of 15 data points (main phase) and an average of 5 points (side phase). RE-rare earth. excess [25]. The samples were prepared by balling the elements, sealing the fine powder into niobium tubes, and heat treating at 900 ℃. The product was then pressed into a dense pellet via spark plasma sintering (SPS). Yttrium and lanthanum rare earth elements were chosen for this study because of their sizes. Y 3+ (0.900 Å) is closest in size to Yb 3+ (0.868 Å), while La 3+ (1.032 Å) represents the largest of the 3+ RE cations [26]. As previously mentioned, there are four crystallographic sites for the Yb cation in Yb14ZnSb11 coordinated by antimony with various sized polyhedral volumes. The site specificity of various rare earth elements has been shown to be correlated with size in studies of Yb14-xRExMnSb11. Early RE cations with larger ionic radius, such as La, were shown to preferentially substitute on the Yb2 and Yb4 sites, while RE of smaller ionic radius such as Y substitutes on all of the Yb sites [15,16]. While it is expected that carrier concentration plays the largest role in controlling the transport properties, the RE site selectivity has been indicated as important for subtle differences in thermoelectric properties across the series, Yb14-xRExMnSb11 [2,27].

As Loaded
Electron microprobe X-ray maps of the dense pellets ( Figure 2) show that the samples have a good distribution of the elements and that there is excess Zn at the grain boundaries. Wavelength dispersive X-ray spectroscopy of the samples show two phases: a main phase (Yb13.5RE0.5ZnSb11) and side phase (Yb1.95RE0.0.5Zn0.8Sb2), tabulated in Table 1. While the main phase was loaded as Yb13.5RE0.5ZnSb11, the analysis shows that when RE = Y, the amount incorporated is slightly less. Whereas for RE = La, it is in good agreement, and the Zn is slightly deficient in both samples, giving rise to the stoichiometries Yb13.7Y0.35Zn0.85Sb11 and Yb13.7La0.48Zn0.91Sb11. The WDS data were normalized to 11 Sb and while that provides a slightly high Yb + RE content, it is within error consistent with the stoichiometry of 14-1-11, with deficiencies of Zn. Table 1. Wavelength dispersive X-ray spectroscopy (WDS) stoichiometry from pelleted samples from an average of 15 data points (main phase) and an average of 5 points (side phase). RE-rare earth.   The WDS of the side phase provides a formula that is consistent as a solid solution of RE and 'Yb 2 ZnSb 2 ' with slight deficiency of Zn. The phase Yb 2 ZnSb 2 is as of yet unreported, and the obvious possible analog, Ca 2 ZnSb 2 , is also not a reported phase. Rietveld refinement of powder X-ray diffraction data for each of these samples included the phases Yb 14 ZnSb 11 and Yb 2 O 3 ; small unidentified peaks were present after refinement attributed to this side phase. There are reports of the Eu 2 ZnSb 2 and Sr 2 ZnSb 2 phase that crystallize in the P6 3 /mmc space group [28]. Attempts to unambiguously identify these peaks with the appropriately scaled lattice parameters of known 2-1-2 structure types employing the elements Yb, Zn, and Sb were unsuccessful. Figure 3 contains a zoomed-in overlay of the PXRD data from Yb 13.5 RE 0.5 ZnSb 11 , with the unidentified peaks marked. Unit cell parameters of Yb 13.5 RE 0.5 ZnSb 11 obtained from the refinement are listed in Table 2. Representative PXRD data are provided in Figure S2. Because the two pellets show similar amounts of this unknown phase and the majority of the phase is the Yb 13.5 RE 0.5 ZnSb 11 , measurements of the thermoelectric and transport properties will provide some insight into the effects of the RE solid solution. The WDS of the side phase provides a formula that is consistent as a solid solution of RE and 'Yb2ZnSb2' with slight deficiency of Zn. The phase Yb2ZnSb2 is as of yet unreported, and the obvious possible analog, Ca2ZnSb2, is also not a reported phase. Rietveld refinement of powder X-ray diffraction data for each of these samples included the phases Yb14ZnSb11 and Yb2O3; small unidentified peaks were present after refinement attributed to this side phase. There are reports of the Eu2ZnSb2 and Sr2ZnSb2 phase that crystallize in the P63/mmc space group [28]. Attempts to unambiguously identify these peaks with the appropriately scaled lattice parameters of known 2-1-2 structure types employing the elements Yb, Zn, and Sb were unsuccessful. Figure 3 contains a zoomed-in overlay of the PXRD data from Yb13.5RE0.5ZnSb11, with the unidentified peaks marked. Unit cell parameters of Yb13.5RE0.5ZnSb11 obtained from the refinement are listed in Table 2. Because the two pellets show similar amounts of this unknown phase and the majority of the phase is the Yb13.5RE0.5ZnSb11, measurements of the thermoelectric and transport properties will provide some insight into the effects of the RE solid solution. Figure 3. Powder X-ray diffraction (PXRD) patterns of Yb13.5Y0.5ZnSb11 (filled in blue) and Yb13.5La0.5ZnSb11 (filled in red) from 28° to 37° 2θ. Unidentified peaks in each pattern are marked by asterisks in respective colors. Table 2. Lattice parameters as determined by refinement of powder X-ray diffraction (PXRD) data using GSAS II.

As Loaded a (Å) c (Å) V (Å 3 ) wR (Overall) RF 2 /RF (14-1-11 Phase)
Yb13.5Y0.5ZnSb11 16.5939(4) 21.9309 (7) Figure 4 contains the plots of the electrical resistivity, Seebeck, and thermal conductivity of the samples. As mentioned previously, Yb14ZnSb11 has low electrical resistivity, similar to that seen in many intermediate Yb valence compounds, and magnetic susceptibility is consistent with the presence of about 0.75 Yb 3+ [7]. This mixture of Yb 2+ and Yb 3+ can be more exotic and can be described as an intermediate valence state. Yb containing intermetallics can show this effect when the nearly Figure 3. Powder X-ray diffraction (PXRD) patterns of Yb 13.5 Y 0.5 ZnSb 11 (filled in blue) and Yb 13.5 La 0.5 ZnSb 11 (filled in red) from 28 • to 37 • 2θ. Unidentified peaks in each pattern are marked by asterisks in respective colors. Table 2. Lattice parameters as determined by refinement of powder X-ray diffraction (PXRD) data using GSAS II.

As Loaded a (Å) c (Å) V (Å 3 ) wR (Overall) RF 2 /RF (14-1-11 Phase)
Yb 13.5 Y 0.5 ZnSb 11 16.5939(4) 21.9309 (7) 6038.9(3) 20.812% 14.122%/9.616% Yb 13.5 La 0.5 ZnSb 11 16.6412(4) 21.9188 (6) 6070.0(3) 19.914% 12.328%/8.316% Figure 4 contains the plots of the electrical resistivity, Seebeck, and thermal conductivity of the samples. Both heating and cooling data sets for resistivity and Seebeck are provided in Figures S3  and S4. As mentioned previously, Yb 14 ZnSb 11 has low electrical resistivity, similar to that seen in many intermediate Yb valence compounds, and magnetic susceptibility is consistent with the presence of about 0.75 Yb 3+ [7]. This mixture of Yb 2+ and Yb 3+ can be more exotic and can be described as an intermediate valence state. Yb containing intermetallics can show this effect when the nearly degenerate 4 f 13 and 4f 14 electron levels are close to the s-d band, favoring an intermediate valence state. Rare earth ions in this state fluctuate between two 4f electronic configurations competing for stability. With doping, the hybridization strength of the f -electrons with the conduction electrons can change, resulting in a change in the effective mass and thereby the associated transport properties [29,30]. The electrical resistivity of Yb 13.5 RE 0.5 ZnSb 11 shows a significant increase at temperatures above 500 K over Yb 14 ZnSb 11 for both samples. In the Zintl electron counting scenario, RE 3+ adds one electron to the p-type Yb 14 ZnSb 11 and is thus expected to reduce the carrier concentration and thereby the electrical resistivity. Consistent with the slightly higher amount of RE in the sample, the RE = La sample shows a slightly higher resistivity value. Consistent with the electrical resistivity, the thermal conductivities of the samples are reduced from that of Yb 14 ZnSb 11 . Lattice thermal conductivity is provided in Figure S5. This is attributed to both the loss of electrical conduction at a high temperature and, from point defect scattering, of the solid solution. There is a decrease in thermal conductivity even at 300 K compared with Yb 14 ZnSb 11 . The Seebeck coefficient shows a remarkable increase over that of Yb 14 ZnSb 11 for the entire temperature range, with the RE = La sample showing a slightly higher Seebeck at the highest temperatures, consistent with the slightly larger amount of RE cation. This suggests that the effect of the RE 3+ is to change the hybridization of Yb/RE, thereby leading to a change in bands that are important for the high temperature behavior.    Figure 5 shows the Hall mobility and Hall carrier concentration of the RE solid solutions. The RE element was substituted with the goal of reducing the carrier concentration and making this compound a better thermoelectric material. The carrier concentrations of both RE samples are lower than that of Yb 14 ZnSb 11 , which shows conductive electrical resistivity at low temperatures and presumably has a high carrier concentration. Typically, for transition metal containing compounds with the formula Yb 14 MSb 11 , where Yb is considered to be all Yb 2+ and M = M 2+ , the carrier concentration is equivalent to one hole in the unit cell volume. Therefore, the addition of an RE 3+ cation provides one additional electron to reduce the p-type carrier concentration. In this example, considering the effect of the RE 3+ cation is complicated because this compound has both Yb 2+ and Yb 3+ at room temperature. If the Y 3+ or La 3+ cation does not simply substitute for Yb 3+ in Yb 14 ZnSb 11 and instead substitutes for Yb 2+ , it would contribute an extra 0.5 electron per formula unit (or 0.35 in the case of Y). Calculating the carrier concentration, it would contribute approximately 6.6 × 10 20 carriers/cm 3 . This would indicate that at room temperature, the carrier concentration of Yb 14 ZnSb 11 should be 1.3 × 10 21 cm −3 , a value close to the highest room temperature concentrations obtained for Yb 14 MnSb 11 , which is much less metallic than Yb 14 ZnSb 11 . In a similar system, Yb 14-x La x MnSb 11 (x = 0.4, 0.7) was found to have a reduction in room temperature carrier concentration from that of Yb 14 MnSb 11 (1.1 to 1.3 × 10 21 cm −3 ), which closely corresponded with the amount of La added, 6 × 10 20 cm −3 and 4 × 10 20 cm −3 for 0.4 La and 0.7 La, respectively [14,17]. Therefore, these results suggest that RE 3+ is substituting for Yb 3+ in Yb 14 ZnSb 11 and that once the Yb 3+ is no longer a species in the structure, the metallic conduction is no longer viable. Because neither Y nor La have filled f electrons, it is possible that a hybridized band from Yb 3+ is responsible for the low electrical conduction in Yb 14 ZnSb 11 . Considering the reductions in carrier concentrations from the Y 3+ and La 3+ substitutions, the large increase in Seebeck is consistent.  [14,17]. Therefore, these results suggest that RE 3+ is substituting for Yb 3+ in Yb14ZnSb11 and that once the Yb 3+ is no longer a species in the structure, the metallic conduction is no longer viable. Because neither Y nor La have filled f electrons, it is possible that a hybridized band from Yb 3+ is responsible for the low electrical conduction in Yb14ZnSb11.
Considering the reductions in carrier concentrations from the Y 3+ and La 3+ substitutions, the large increase in Seebeck is consistent.  Figure 6 shows the zT for the Yb13.5RE0.5ZnSb11 (RE = Y, La) compounds compared with the zT of Yb14ZnSb11. The properties of Yb14ZnSb11 were only measured up to 900 K because of the stability of the compound. With the addition of the RE, the Yb13.5RE0.5ZnSb11 (RE = Y, La) compounds are stable to 1275 K. This is a side benefit of RE 3+ incorporation that has been also noted for Yb14MnSb11, where the melting point is increased and sublimation vapor pressure is decreased depending upon the identification and amount of rare earth ion incorporation [31].  Figure 6 shows the zT for the Yb 13.5 RE 0.5 ZnSb 11 (RE = Y, La) compounds compared with the zT of Yb 14 ZnSb 11 . The properties of Yb 14 ZnSb 11 were only measured up to 900 K because of the stability of the compound. With the addition of the RE, the Yb 13.5 RE 0.5 ZnSb 11 (RE = Y, La) compounds are stable to 1275 K. This is a side benefit of RE 3+ incorporation that has been also noted for Yb 14 MnSb 11 , where the melting point is increased and sublimation vapor pressure is decreased depending upon the identification and amount of rare earth ion incorporation [31]. Figure 7 contains Pisarenko plots at 400 K, 800 K, and 1200 K that were generated using a single parabolic band (SPB) model. The parameters used to generate these plots are provided in Table 3. The effective mass values generated for this model at 1200 K for both RE = La, Y are significantly larger than those generated at 400 and 800 K. These parameters indicate that modelling Yb 13.5 RE 0.5 ZnSb 11 as a single parabolic band is insufficient and that the band(s) change from light to heavy with temperature [32]. This is supported by the reduction in carrier concentration that these samples exhibit with only a small donation of 0.5 or less extra edensity per formula unit. These plots suggest that the carrier concentration could be further reduced to obtain peak zT.
Materials 2019, 12, x FOR PEER REVIEW 10 of 13 Figure 6. Calculated zT for the Yb13.5RE0.5ZnSb11 (RE = Y, La) compounds compared with that of Yb14ZnSb11 (data from the work of [9]). Figure 7 contains Pisarenko plots at 400 K, 800 K, and 1200 K that were generated using a single parabolic band (SPB) model. The parameters used to generate these plots are provided in Table 3. The effective mass values generated for this model at 1200 K for both RE = La, Y are significantly larger than those generated at 400 and 800 K. These parameters indicate that modelling Yb13.5RE0.5ZnSb11 as a single parabolic band is insufficient and that the band(s) change from light to heavy with temperature [32]. This is supported by the reduction in carrier concentration that these samples exhibit with only a small donation of 0.5 or less extra edensity per formula unit. These plots suggest that the carrier concentration could be further reduced to obtain peak zT.    Figure 7 contains Pisarenko plots at 400 K, 800 K, and 1200 K that were generated using a single parabolic band (SPB) model. The parameters used to generate these plots are provided in Table 3. The effective mass values generated for this model at 1200 K for both RE = La, Y are significantly larger than those generated at 400 and 800 K. These parameters indicate that modelling Yb13.5RE0.5ZnSb11 as a single parabolic band is insufficient and that the band(s) change from light to heavy with temperature [32]. This is supported by the reduction in carrier concentration that these samples exhibit with only a small donation of 0.5 or less extra edensity per formula unit. These plots suggest that the carrier concentration could be further reduced to obtain peak zT.

Conclusions
The addition of the rare earths, Y and La, to the Yb 14 ZnSb 11 system has a profound but complex effect on the carrier concentration and presumably the density of states (DOS) as a function of temperature. The large improvement in zT observed in the Yb 13.5 RE 0.5 ZnSb 11 (RE = Y, La) samples over Yb 14 ZnSb 11 is unexpected because these RE 3+ ions are simply replacing Yb 3+ . These remarkable results suggest that better modeling/theoretical understanding of complex systems is important to further advance the field. Renewed interest in the nuanced system of Yb 14 ZnSb 11 may lead to a more complete understanding of the electronic and structural factors affecting the 14-1-11 compounds and aid in the future design of optimized materials. Further improvement to the zT of these compounds might be achieved by reducing carrier concentration further by means of increasing x or by substitution of Ca on the Yb site or Al on the Zn site. Yb 14-x Ca x MnSb 11 and Yb 14 Mn 1-x Al x Sb 11 solid solutions show reduced carrier concentration with increasing x and higher zT's than Yb 14 MnSb 11 . While x has been shown to be limited in the case of Yb 14-x RE x MnSb 11 to x~0.5, it might be possible to increase x to 1 for the Zn 14-1-11 phase, as is the case for Ca 14-x RE x MnSb 11 . Overall, these results for Yb 13.5 RE 0.5 ZnSb 11 (RE = Y, La) suggest that there is significant room for improvement of zT with new compositions of this structure type.