Hydride assisted synthesis of the high temperature thermoelectric phase: Yb₁₄MgSb₁₁

High energy ball milling can be a green, energy efficient process that creates a homogeneous powder through the mechanical pulverization of metallic precursors. The product can sometimes be prepared in situ or can be reacted to form a product during an annealing step, or directly through spark plasma sintering (SPS). After milling, any one portion of the prereacted powder should have at least the elemental composition of the desired product. Often, due to the malleability of certain metals (Yb, Mg, Ca, Eu, K, etc.), sample compositions become deficient on the cation side as a consequence of materials cold welding or sticking to the surfaces of the vials. There are several different approaches to address this problem such as milling more electronegative elements before adding malleable ones, using binary precursors which are more brittle, or accounting for the loss through elemental excess.¹ 

Metal hydrides are commercially available as fine powders due to the changed nature of the bonding within the metal. With an increase in surface area and low decomposition temperatures, metal hydrides show increased reactivity allowing for lower temperature synthesis.^2,3 The use of hydrides as reactive precursors in the synthesis of thermoelectric materials has been shown to facilitate the formation of otherwise difficult to synthesize Zintl phases and clathrates.^2,4–10 The metal hydrides provide for stoichiometric reactions to products whereas the use of ductile metals requires a systematic study in stoichiometry adjusted for metal loss. The employment of malleable metals leads to homogeneity issues that depend strongly on the particle size of the starting material, time, and energy of the milling process. Hydrides, on the other hand, can be precisely massed, decompose during annealing, and the hydrogen produced could reduce any oxides present, providing a high quality, oxide-free product.

Zintl phases have shown great potential for thermoelectric applications but many with the highest zT contain Yb, Mg, or other malleable metals.^11–19 Finding an efficient route to high quality homogeneous materials that is also scalable and reproducible is important for device applications. Thermoelectric generators consist of a heat source and a series of p and n type semiconductors that are connected electrically in series and thermally in parallel. If their thermal conductivity is low and their electrical conductivity is high, a thermal gradient will be created across the material. This leads to the excitation of carriers on the hot side, which subsequently flow toward the cold side, leading to usable electricity. The efficiency at which a material performs this conversion is directly related to the unitless thermoelectric figure of merit, zT = S²σT/κ. Here, S is the Seebeck coefficient, or voltage, created per degree of temperature gradient, σ is the electrical conductivity: the inverse of resistivity (ρ), T is absolute temperature, and κ is the thermal conductivity of the material. In order to maximize efficiencies in a material, all these factors need to be optimized. However, these variables are all inter-related through carrier concentration, which makes optimization difficult.

The A₁₄MPn₁₁ family of Zintl phase materials (Fig. 1) has over 30 members (A = Yb, Eu, Ca, Sr, Ba; M = Mg, Mn, Zn, Cd, In, Al, Ga; Pn = P, As, Sb, Bi), some of which have promising thermoelectric properties.¹³ Yb₁₄MgSb₁₁ is a member of this family and has a reported zT of 1.05 at 1075 K.²⁰ Its crystal structure is defined by 13 Yb⁺², Yb⁺³, [MgSb₄]⁻¹⁰ tetrahedra, Sb₃⁻⁷ linear unit, 4 Sb⁻³. In single crystals, it has also been shown that the Yb site can accommodate about 0.2 Mg to yield Yb_13.8Mg_1.2Sb₁₁.²¹ In order to get optimal thermoelectric properties, samples with the Yb₁₄MgSb₁₁ stoichiometry and minimized side phases are desired. In this paper, we employ MgH₂ and YbH₂ as reactive precursors for the synthesis of high purity Yb₁₄MgSb₁₁ in order to provide a high quality material with efficiencies beyond a zT of 1 at high temperatures.

In an Ar filled glove box (H₂O < 1 ppm), stoichiometric amounts of elemental Yb filings (Edge Tech, 99.99%), Sb shot (5Nplus, 99.999%), and Mg chips (Strem Chemicals, 99%) were added to a 65 cm³ stainless steel ball mill with one 12.7 mm diameter stainless steel ball (Spex). Reactions were also performed with either YbH₂ (American Elements. 99.999%, purchased as Yb powder)^8,9 or MgH₂ (Alfa Aesar, 98%). Reactions were sealed under Ar in Mylar bags and milled for 3 rounds of 30 min each with scraping in between 2nd and 3rd in an Ar(g) filled glovebox. The resultant black powder was transferred to a Nb tube which was sealed at both ends under Ar and jacketed inside an evacuated quartz tube. The tube was annealed for 4 days at 800 °C after which it was removed and quenched at room temperature in air. The reactions are summarized in Table I.

The composition of polycrystalline samples was analyzed by powder X-ray diffraction (PXRD) using a Bruker D8 Eco Advanced with Cu K_α radiation (λ = 1.54 Å) and a Ni filter to remove Cu K_β. Diffraction experiments were performed using a zero background off-axis quartz plate at room temperature. Diffraction patterns were analyzed by Rietveld refinement using the JANA 2006 software package.²² Samples were consolidated into pellets using spark plasma sintering (SPS, Dr. Sinter Lab Jr., Fuji Corp.). Powders were loaded under an inert atmosphere into a graphite die with an inner diameter of 12.7 mm, a height of 30 mm, and a 30 mm outer diameter with a hole for thermocouple placement for temperature measurement. The die was heated to 800 °C under dynamic vacuum, and the force was increased from 2 to 7 kN as the sample began to sinter. Resultant pellet densities were greater than 90% of theoretical crystallographic density for those synthesized with YbH₂ and greater than 94% for those with MgH₂. Thermal diffusivity was measured on densified pellets using Laser Flash Analysis (Netzsch LFA 475 Microflash) under Ar(g) flow. The Seebeck coefficient and resistivity measurements were collected at UC Davis on a Linseis LSR-3 using a 4-probe method with 8 mm probe spacing and a 50 °C thermal gradient. Densified pellets were shaped into 1 × 1 × 10 mm³ rectangular prisms for this measurement. Resistivity and Hall carrier concentrations were measured at the Jet Propulsion Laboratory (JPL) using the Van der Pauw method with a current of 100 mA and a 1.0 T magnet on a specialized high temperature instrument.²³ Seebeck coefficients were measured also at JPL using a custom instrument, which uses the light pipe method with tungsten-niobium thermocouples under high vacuum.²⁴ Elemental analysis was performed using electron probe microanalysis (EPMA) (Cameca SX-100) utilizing backscattered electron mode and x-ray elemental mapping using MgO, Sb, and a Yb₁₄MgSb₁₁ single crystal as standards.

Bulk polycrystalline samples of Yb₁₄MgSb₁₁ were synthesized by the reaction of stoichiometric amounts of the powders employing YbH₂ (YBH) as described above over 4 days at 800 °C, lower than what has been previously reported for the same compound. A large (1.5) excess of Mg was required in order to avoid the formation of a common side phase, Yb₁₁Sb₁₀, in this reaction. The resultant product provided diffraction patterns that were well refined by Rietveld refinement and were indexed fully as the tetragonal phase pure compound, Yb₁₄MgSb₁₁ (Rp: 6.78, wRp: 8.92; see the supplementary material)_. The unit cells of samples prepared with YbH₂ are a = 16.6159(1) Å, c = 22.2539(1) Å, and V = 6144.1(1) ų. The lattice parameters are consistent with those previously reported for single crystals [a = 16.625(1) Å, c = 22.24(1) Å, V = 6147(1) ų] but larger than those reported for polycrystalline [a = 16.602(1) Å, c = 22.233(1) Å, V = 6128(1) ų].²⁰ After densification by SPS, small amounts (less than 5% by mass) of Yb₁₁Sb₁₀ can become evident due to the vaporization of Mg and the crystallization of amorphous side phases (Rp: 5.95, wRp: 7.85). However, crystalline impurities are not evident in the samples prepared with YbH₂, presumably due to the large magnesium excess (50%) employed in the synthesis.

Bulk polycrystalline samples of Yb₁₄MgSb₁₁ were also synthesized employing MgH₂ (MGH) as described above over 4 days at 800 °C. Due to the increased surface area and reactivity of MgH₂, a smaller excess was required to synthesize phase pure materials at lower temperatures. The resultant product provided diffraction patterns that were well refined by Rietveld refinement and could be fully indexed and refined with a slight (0.5%) Yb₂O₃ impurity (Rp: 7.45, wRp:9.67). The unit cells of samples prepared with MgH₂ were a = 16.6081(1) Å, c = 22.2436(1) Å, and V = 6135.5(1) ų (Fig. 2). Those synthesized with MgH₂ show a slight reduction in all parameters and are consistent with those previously reported for polycrystalline samples. After densification by SPS, small amounts (less than 5% by mass) of Yb₁₁Sb₁₀ became evident in the powder pattern of the sample prepared with MgH₂ (Rp: 7.36, wRp: 9.37). Although some impurities may have significant effects on the material properties, Yb₁₁Sb₁₀ is reported to have a small Seebeck coefficient and low resistivity at temperatures relevant for Yb₁₄MgSb₁₁.^20,25 It has also been reported as present in some of the best samples of Yb₁₄MnSb₁₁ with minimal impact on the thermoelectric properties.^11,14 At low mass percent, the contribution due to the Yb₁₁Sb₁₀ impurity is considered negligible. Patterns of milled, annealed, and SPSed powders can be found in the supplementary material.

Pieces of densified pellet were set in epoxy and analyzed by electron probe microanalysis (EPMA). Samples appear to be phase pure with no evident regions of impurity, see Figs. 3 (YBH) and 4 (MGH). Some deviation from uniform counts in the elemental maps corresponds to topographical inconsistencies. These inconsistencies are attributed to surface roughness: providing a surface that is not in the proper orientation with relation to the electron beam and detector, leading to improper elemental X-ray mapping at those points. However, for YBH, there are high Mg counts apparent in the Mg elemental map that are not related to the topographical inconsistencies indicated by the red spots in Fig. 3(d). This suggests that Mg is present, presumably at the grain boundary in this sample. Porosity of the sample is also evident (low counts in the elemental mapping) consistent with lowered density observed for this sample. The porosity may be attributed to the relative thermal stability of YbH₂. The kinetics of hydride decomposition are not reported for YbH₂ and it is possible that some residual subhydride was still present before SPS consolidation (although not evident via PXRD), giving rise to more porosity. It is also possible that the additional Mg present contributes to porosity if it sublimes during the SPS densification.

Elemental analysis (Table II) shows deficiency in Yb and Sb and an excess in Mg for the YBH sample. Although this could suggest Mg incorporation into the Yb sites, the unit cell volume from PXRD does not match that of those found in the single crystal study of Yb_13.85Mg_1.15Sb₁₁ (V = 6079 ų).²¹ When the data are reanalyzed by forcing Yb stoichiometry to be 14, Sb content returns to that expected, and the Mg content becomes slightly less than what was originally loaded [1.3(2)]. The elemental mapping and elemental analysis support the idea that there is Mg at the grain boundaries of this sample.

The overall composition of the sample synthesized using MgH₂ (MGH) is shown to be stoichiometric with low standard deviation in the magnesium composition (Table II). Figure 4 shows some topography, but overall the elemental maps are much more uniform. Starting with a powered reagent of the low stoichiometry element for this compound leads to a more homogeneous product through better dispersion. Indeed, better dispersion lowers the solid state diffusion path length of Mg atoms, increasing reactivity, and hence requiring less elemental excess.³ 

Hall mobility and carrier concentration of the two samples were measured up to 1273 K (see the supplementary material). For Yb₁₄MgSb₁₁ synthesized using YbH₂, carrier concentrations ranged from 5.7 × 10²⁰ to 1.5 × 10²¹ cm⁻³ and mobilities from 2.3 to 0.5 cm² V⁻¹ S⁻¹. The carrier concentration at 300 K is in agreement with what has previously been reported.²⁰ The lower mobility of the YbH₂ is most likely due to the presence of Mg at the grain boundaries. The sample synthesized using MgH₂ showed similar carrier concentrations ranging from 5.3 × 10²⁰ to 1.3 × 10²¹ cm⁻³ and higher mobilities from 4.7 to 0.7 cm² V⁻¹ S⁻¹. The lower mobility of the samples synthesized using YbH₂ could be due to the presence of excess Mg at grain boundaries, which is avoided in MgH₂ samples due to improved dispersity and reaction kinetics.

Thermoelectric properties are shown in Fig. 5. Thermal diffusivity was measured on densified pellets. The thermal conductivity was then calculated using κ = C_pρD, where κ is the thermal conductivity, C_p is the specific heat capacity, ρ is the density, and D is the thermal diffusivity. Thermal conductivity consists of two parts: a lattice component (κ_l) which is the contribution due to the material's structure and an electrical component (κ_e) which considers the thermal energy transferred by charge carriers. This leads to the equation κ = κ_l+ κ_e. The sample synthesized with YbH₂ (YBH) has a slightly lowered thermal conductivity (6.13 mW cm⁻¹ K⁻¹), which may be due to the lower density of this sample along with the increased electrical resistivity, lowering both the lattice and the electronic contributions of thermal conductivity. With low density samples, there is an increased percent of void space present in the sample. These voids lead to increased phonon scattering and lower lattice thermal conductivity. Yb₁₄MgSb₁₁ synthesized using MgH₂ (MGH) had a thermal conductivity comparable to that previously published (6.719 and 6.68 mW cm⁻¹ K⁻¹ at 1075 K, respectively).²⁰ Because both samples have comparable densities, their thermal conductivity are expected to be similar.

Resistivity and the Seebeck coefficient of Yb₁₄MgSb₁₁ synthesized with YbH₂ (YBH) were measured by the off axis 4-probe method. This sample showed a relatively high resistivity (8.7 mΩ cm at 900 K), which rolls over before reaching peak temperatures. This high resistivity is attributed to Mg's presence at the grain boundaries. It is possible that the metallic boundary from Mg leads to bending of the Yb₁₄MgSb₁₁ bands and an increase in resistivity. There is no evidence for sample decomposition or melting after measurement. The Seebeck coefficient of YBH is similar to that of those synthesized with elemental reagents or MgH₂ (MGH). Both the Seebeck coefficient and electrical resistivity of the sample bend over around 900 K. This coincides closely with the melting point of elemental Mg and may suggest the presence of Mg at grain boundaries.

The electrical resistivity and the Seebeck coefficient of Yb₁₄MgSb₁₁ synthesized with MgH₂ (MGH) were also measured by the off axis 4-probe method. Resistivity of the sample measured by this technique was similar to what was previously published (8.4 and 8.2 mΩ cm, respectively). The Seebeck coefficient measured by the 4-probe method was 251 μV/K at 1075 K, higher than that previously reported. This difference in the Seebeck coefficient at higher temperatures could be attributed to possible cold finger effect.¹ Overall, the properties measured at UC Davis resulted in a calculated zT of 1.19 at 1075 K. Because of these promising results, Yb₁₄MgSb₁₁ made with MgH₂ (MGH) was measured up to higher temperatures (1273 K) at JPL. In comparison to samples synthesized with elemental reagents, MGH exhibited significantly reduced resistivity, peaking at 7.39 mΩ cm at 1275 K. Because of the higher surface area and increased dispersity of the hydride, it is more reactive during annealing, leading to less elemental Mg at grain boundaries. Additionally, the hydrogen rich environment during annealing reduces any minor oxides present. As a result of the reduced electrical resistivity, the Seebeck coefficient of MGH is reduced but still reaches peak values of 232 μV/K before rolling over at 1200 K. The turnover temperature in the Seebeck coefficient correlates with the beginning of the turnover in the resistivity. This suggests that the turnover in electronic properties is due to bipolar conduction at high temperatures. Due to the presence of the Yb⁺³, Yb₁₄MgSb₁₁ is closer to a full charge compensated Zintl phase. This leads to a smaller bandgap in comparison to Yb₁₄MnSb₁₁. This Seebeck coefficient and temperature correspond to a bandgap of 0.56 eV by the Goldsmid-Sharp equation.^1,26 This agrees well with the previously determined value of 0.6 eV determined by computational methods.²⁰ Overall, the reduction in electrical resistivity overcomes the small drop in the Seebeck coefficient to give samples synthesized using MgH₂ (MGH) a peak zT of 1.26 at 1200 K. The differences in properties between what was measured at UC Davis and JPL can be attributed to a combination of the cold finger effect, which can result in exaggerated Seebeck coefficient values and slight differences in sample composition between two halves of the same consolidated sample.¹ 

Metal hydrides have proven to be highly effective as reactive precursors for malleable or low atomic percent metals. Due to the increase in surface area and better dispersity within the milled powder, there is an increase in reactivity, allowing for lower temperature synthesis, which requires less energy. Additionally, the increase in reactivity of MgH₂ compared with YbH₂ leads to a pure product with less Mg at grain boundaries. Samples of Yb₁₄MgSb₁₁ prepared with MgH₂ showed increased thermoelectric efficiencies, reaching a peak zT of 1.26 at 1200 K, which is comparable to efficiencies reported by Grebenkemper et al. and the ATEC project for Yb₁₄MnSb₁₁.^14,19

See the supplementary material for powder diffraction patterns, carrier concentration and Hall mobility as a function of temperature and a plot of Power Factor.

We would like to thank Nicholas Botto for EPMA and the NEUP for funding. Part of this work was performed at the California Institute of Technology/Jet Propulsion Laboratory under contract with the National Aeronautics and Space Administration. This work was supported by the NASA Science Missions Directorate under the Radioisotope Power Systems Program. G. Cerretti's research at Jet Propulsion Laboratory was supported by an appointment to the NASA Postdoctoral Program, administered by Universities Space Research Association under contract with NASA.