In the world of solution chemistry, mechanistic studies offer invaluable information about the reason certain reactions provide a desired result, and why others do not. [1][2][3][4][5][6] Through a combination of experimental and computational studies the rationale behind unique aspects of a reaction pathway such as site reactivity or stereoselectivity can be elucidated. 7,8 In addition to providing information about the reaction at hand, these studies can allow for the assessment of possible applications of the reaction to other systems. Because of the relatively low temperatures and selfcontained nature of the solution reactions, taking aliquots for qualitative or quantitative evaluation through the course of the reaction is easily accessible in many cases.
Unlike many reactions performed in aqueous or organic solution, solid state synthesis is often done at high temperatures with reagents that can be incredibly reactive towards an increasing number of things, including common reaction vessels (SiO2, Al2O3, etc.), as temperatures increase. Because of this, these reactions can often times be a black box where reagents are weighed, processed, and annealed to obtain a final product, but little is known about what occurs and what chemical species form before the final product is obtained. 9 Gaining an understanding of what occurs throughout this process may uncover the relationship between phases, and lead to a more guided approach to synthesis. In addition to understanding the basic pathway of a reaction, detailed studies have provided the various precursor's roles in the final morphology and purity of the product. 10 The development of temperature dependent in operando techniques using X-rays, neutrons, and electron microscopy has helped to unveil the pathways some of these reactions take, but these experiments can also be limited by the reactivity of elements towards the capillary, atmosphere, or other aspects of the experimental setup. 11 Additionally, access to equipment with capabilities to reach the desired temperature ranges can be a limiting factor. More efforts into understanding the pathways complex solid-state reactions take could unveil new synthetic approaches and a route to higher purity products and new phases. Yb14MgSb11 is a Zintl phase whose unit cell can be seen in Figure 1. This complex phase contains 8 formula units per unit cell with each formula unit containing 13 Yb +2 cations, 1 Yb +3 cation, 1 [MgSb4] -10 tetrahedron, 1 Sb3 -7 linear unit, and 4 Sb -3 anions. Yb14MgSb11 and the isostructural Yb14MnSb11 both exhibit excellent high temperature thermoelectric properties and are under consideration for implementation in radioisotope thermal electric generators for space exploration. [12][13][14][15][16][17][18] Because of the wide interest in thermoelectric modules for waste heat recovery, an efficient synthetic route to high purity phases with precise control over stoichiometry will have a significant impact on increasing the progress towards even higher efficiency materials. [19][20][21][22][23][24][25][26][27][28] In this work, a facile, accessible method for the study of reaction pathways to form the complex rare earth containing ternary phases Yb14AlSb11, Yb14MnSb11, and Yb14MgSb11 is presented. Two ytterbium antimonide binaries, Yb11Sb10 and Yb4Sb3, were investigated as reactive precursors in reactions with YbH2 and either MnSb or Mg3Sb2 for guided synthesis of high purity products. We show that Yb4Sb3 is the best reactive precursor for preparing phase pure product and speculate on why that is the case. Based on this investigation, both Yb14MgSb11 and Yb14MnSb11 are determined to be slightly Yb deficient. The effects of Yb composition on the thermoelectric figure of merit, zT, for phases of Yb14-xMnSb11 are investigated and provide insight towards increasing the highest temperature thermoelectric properties.
Quenching Studies. For reactions from the elements, Yb filings (Edgetech, 99.999%), Al filings (Alfa Aesar, 99.999%), and crushed Sb shot (5N Plus, 99.999%) were used. For reactions from the binaries, annealed binary phase powders were used. The binary powders were prepared as described below. Reactions were done with a total mass of 10 g in 65 cm 3 stainless steel ball mills with two 12.7 mm diameter balls (SPEX). They were loaded in an Ar filled glovebox under inert atmosphere (<0.5 ppm O2). Reactions were further jacketed in mylar baggies before they were removed from the glovebox and milled for three rounds of 30 minutes. The milling vials were flipped 180° after the first round and scraped with a chisel after the second. The resultant black powder was split into 10 portions, 9 of which were sealed under Ar in Nb tubes which were then further jacketed under vacuum in fused silica tubes to prevent oxidation of the refractory metal inner tube. The reactions were then placed in two box furnaces which have been programmed to the same heating rate (50 K / h) with an 8-hour offset between the two. An aliquot of the reaction was then quenched directly from the heating furnace into a large bucket of water every 100 K from 375 K to 1075 K and a final portion was left to anneal at 1075 K for 4 days. Portions of the reaction were then opened under inert atmosphere and analyzed by air-free powder X-ray diffraction to avoid oxidation of the finely divided particles or any metastable phases.
Powder X-ray Diffraction (PXRD). Samples of Yb14MSb11 (M = Mn, Mg, Al) as well as selected portions of the quenching study reactions were analyzed by powder x-ray diffraction (Bruker, Advanced Eco D8) on zero background off-axis quartz plates. A solvent smear using ethanol was used to plate samples of fully reacted Yb14MnSb11 and Yb14MgSb11. For the air-free patterns collected in the quenching study, double-sided Kapton tape (3M) or double-sided tape (Scotch TM removable double-sided tape, 3M) was used to create adhesion of the sample to the plating surface of an SiO2 zero background holder. Once a thin film of the sample was dispersed onto the adhesive, a piece of Kapton film (XRF Window Film, Spex) was placed over the sample and sealed to the doubled-sided tape underneath. If sufficient bare adhesive is exposed on all sides of the sample film, a relatively air-tight packet can be created upon placement of the top film. The resultant powder patterns were analyzed by Rietveld refinements using the Jana 2006 software package. 29 Synthesis of Binary Precursors. Polycrystalline MnSb was made in 5g batches from the melt as previously described. 30 In an Ar filled glovebox (>0.5 ppm O2), stoichiometric amounts of cleaned Mn pieces (Alfa Aesar, 99.95%) and Sb shot (5N Plus, 99.999%) were added to a BN crucible that was then heated to 1125 K for 12 hours in an evacuated fused silica ampule. After that period, magnetic, black crystallites were obtained. Due to the freshly cleaned Mn being used here, no Sb impurities were observed.
Powdered samples of Mg3Sb2 were made in 5 g batches through ball milling of the elements followed by annealing. In an Ar filled glovebox (>0.5 ppm O2), stoichiometric ratios of Mg turnings (Strem Chemicals 99.8%) and Sb shot (5N Plus, 99.999%) were added to a 65 cm 3 stainless steel ball mill with two 12.7 mm diameter balls. The reaction was then further jacketed in a mylar baggie before being removed from the glovebox and milled for four rounds of one hour each with a 15-minute break in between cycles. After four hours of milling a major phase of Mg3Sb2 could be identified by PXRD, but small Sb and Mg impurities remained. To complete the reaction the powder was sealed under Ar in a Nb tube and then further jacketed in an evacuated fused silica ampule. It was then annealed at 975 K for 12 hours. The resultant black powder was fully indexed as pure phase Mg3Sb2 with no impurities. Both Yb11Sb10 and Yb4Sb3 were prepared by the same method of ball milling followed by annealing. In an Ar filled glovebox, Yb filings or small chunks (>3 x 3 x 3 mm) (Edge Tech, 99.999%) and crushed Sb shot (5N Plus, 99.999%) were added in stoichiometric ratios with a 10 g total mass to a 55 cm 3 tungsten carbide ball mill with two 12.7 mm diameter balls. The mill was further jacketed in mylar baggies before being removed from the glovebox and milled for three rounds of 30 minutes each. The ball mill was scraped using a chisel in the glovebox after every 30-minute cycle. This step is important to reintroduce cold welded Yb into the bulk of the reaction and help lessen the amount of the Yb deficient side phase seen in the final product. After milling, the homogenous, black powder was sealed in a Nb tube under Ar that was then further jacketed in SiO2 as described above. The reactions were then annealed at 1125 K for 12 hours. The resultant black powders could be indexed fully as a majority of the desired Yb-Sb phase with a minority impurity of the adjacent Yb deficient phase relative to the target. This minor impurity is due to Yb loss to the mill, but because the reaction can still be represented as a single point on the phase diagram, it is treated as a homogenous mixture of the two phases. To correct for the stoichiometry of the mixture, a simple weighted average using the mole fractions from Rietveld refinements can be used to find the actual composition of the obtained mixture. This calculated compositional value can be then used to balance the reaction below, eqn (1). eqn (1) Yb11-xSb10 + YbH2 + 2+x Yb + MnSb ! Yb14MnSb11 + 0.5 H2 Alternatively, one can use a three variable, three equation system of equations to balance the reaction, eqn (2), where the coefficients a, b, and c come from the three equations below that. In this approach, one equation is used to fix the Yb quantity, one is used for the Sb, and the third fixes the mole ratios of the two Yb-Sb binaries according to the results from Rietveld refinements.
Eqn (3) sets the Yb content to 14; eqn (4) sets Sb content to 11 and eqn (5) related the Yb5Sb3 content to Yb11Sb10 through the corresponding mole fraction (χ). Typical PXRD's of all binary phases are provided in Supporting Information (SI) Figures S1-5 with Rietveld refinements reported in Table S1.
Synthesis of Yb14MnSb11 and Yb14MgSb11. Yb14MnSb11 and Yb14MgSb11 were prepared by balancing the stoichiometric reactions and by utilizing the Yb-Sb and Mg-Sb or Mn-Sb binaries as described above. The reactions were balanced by one of the two methods described above. In Equations ( 1) and (2), a small amount of additional Yb is required to balance the reactions. In reactions from Yb11Sb10 the additional Yb required to balance the reaction was introduced as one equivalent of YbH2 and the rest was introduced as Yb filings. For reactions from Yb4Sb3 the entirety of the remaining Yb was introduced as YbH2. The YbH2 was originally purchased as Yb metal powder (American Elements, 99.999%) but was later identified as YbH2 by PXRD. 31,32 This is a result of the processing used to produce the powdered Yb which typically involves a hydride intermediate from which the hydrogen is removed, leaving the zero valent metal. Due to incomplete dehydrogenation, YbH2 was left as the product. In both cases, YbH2 allows for the introduction of a very high dispersity Yb source which will decompose to Yb metal and a partially reducing H2 atmosphere as the reaction is heated. 31 Due to the production of flammable hydrogen gas, the amount of YbH2 used in each reaction was kept below 1.5 mole equivalents (350 mg) in a 5 g reaction. In any reaction performed in a sealed system, the H2 gas was treated as an ideal gas to calculate possible pressures at the highest temperatures. The maximum pressure should be within the limits of the reaction vessel. Some refractory metals (Nb, Ta) are effectively transparent to small molecules like H2. In this case the fused silica tube is what is exposed to the overpressure of H2 and its volume should be considered for calculations. In an Ar filled glovebox (<0.5 ppm O2), stoichiometric amounts of the respective powders were weighed out to high accuracy and precision (± 0.0001 g) with a 5.0000 g total reaction mass. The powders were added to a 65 cm 3 stainless steel ball mill (SPEX) with two 12.7 mm balls. The sealed vials were further jacketed in a mylar baggie before being removed from the glovebox. The reactions were milled for three rounds of 30 minutes each with the milling vial being flipped 180° in the mill after the first round, and a scrape with a chisel in the glovebox after the second round. The resultant black powder was transferred to a 12.7 mm internal diameter graphite die (Cal Nano) inside the glovebox. The die was then transferred into the chamber of a Spark Plasma Sintering instrument (Dr. Lab Sinter Jr., Fuji Corp.) and the chamber was evacuated (<15 Pa). Under active vacuum, the die was heated to 873 K for 4 minutes then held for 30 minutes to perform the reaction. The progress of the reaction can be monitored by the overpressure generated from the H2 off-gassing from the powders which was observed beginning around 473 K and continues until the dwell temperature of 873 K after which chamber pressures returned to starting values. After dwelling for 30 minutes the temperature was increased to 1123 K over the course of 3 minutes and held for 20 minutes to further consolidate the sample. During the first dwell step, force was kept at 5 kN. After the increase to 1123 K, the force was increased to 6.5 kN. The resultant pellet is pure phase Yb14MSb11 (M = Mg, Mn) with a density >98% of its theoretical value. A slice of the pellet was taken and ground under inert atmosphere for analysis by PXRD as described above.
Elemental Analysis. The sample composition was analyzed by Z contrast using scanning electron microscopy (SEM, Thermo Fisher Quattro ESEM). Elemental distribution and total content were analyzed by energy dispersive spectroscopy (EDS, Bruker Quantax) using Yb14MgSb11 and Yb14MnSb11 single crystals as elemental standards.
Hall Measurements and Van Der Paw Resistivity. 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. 33 High Temperature 2-Probe Measurements of the Seebeck Coefficient. The Seebeck coefficients were measured at JPL using a custom instrument which uses the light pipe method with tungstenniobium thermocouples under high vacuum. 34 High Temperature 4-Probe Measurement of the Seebeck Coefficient and Resistivity. The Seebeck coefficient and electrical resistivity were measured on a portion of the sample after measurement at JPL. The sample was shaped into a bar (approx. 10 x 1 x 3 mm) and polished, so all sides were parallel. The Seebeck coefficient and the electrical resistivity were measured with an off-axis 4probe arrangement using a Linseis LSR-3 instrument with Pt/Rh thermocouples interleaved with carbon film strips on the bar to prevent any reactions. The measurement was performed under static He atmosphere after 3 prior pump/purge cycles (Pmin < 20 mTorr) and heated in a high temperature IR furnace. A polished Zr ribbon was placed inside the susceptor to act as an oxygen sponge, protecting the sample integrity. The ribbon became blackened and brittle upon completion of the measurement. Thermal Conductivity. Thermal diffusivity was measured on densified pellets using Laser Flash Analysis on a Netzsch LFA 475 Microflash under Ar flow. The fully densified pellet was sliced into a thin disk (>1.5 mm) and polished until a uniform level surface was achieved on both sides. The density of this disk was measured using the Archimedes method with toluene as the liquid. Heat capacity of Yb14MgSb11 was estimated using the molecular weight of the Yb14MgSb11 analog relative to Yb14MnSb11, where Cp(Yb14MgSb11) = Cp(Yb14MnSb11) x MM(Yb14MgSb11) / MM(Yb14MnSb11). 17,18,31 Here, MM is the molar mass of the respective compounds. The coefficient of thermal expansion for Yb14MnSb11 was used to estimate the temperature dependence of the density. 17,18 These were all combined to give the total thermal conductivity according to the equation:. 𝜅 = D x Cp x d (D = measured diffusivity; Cp = heat capacity adjusted for molar mass; d = the temperature-adjusted density from Yb14MnSb11). 15
The Formation of Yb14AlSb11 from the Elements. To investigate the mechanism by which Yb14MSb11 (M = Al, Mn, Mg) compounds form, a quenching study of the chemical reaction to form Yb14AlSb11 from the elements was performed. Figure 2 shows the resulting PXRD as a function of temperature. The Al analog was chosen because it has the least amount of peak overlap with many of the binary phases in this region of phase space. The milled powder before heat treatment is shown at the bottom of the experimental patterns which are ordered according to the indicated temperature with a reaction heating rate of 50 K per hour. The milled powder does not contain any reflections which are identifiable as the starting elements but is best matched with Yb4Sb3 and Yb11Sb10, suggesting that it is a mixture of the two Yb-Sb binary phases. As temperature increases, the reflections associated with these two phases become more intense, indicating that the phases become more crystalline. At 600 °C new reflections, which can be attributed to the ternary Yb14AlSb11 phase, can be seen around 31° 2q. After that point, the ternary phase continues to form and becomes more crystalline as the reflections from the binaries dissipate. The final product after 4 days at 800 °C shows a majority Yb14AlSb11 phase with a minor Yb11Sb10 impurity. The progression of this reaction can be understood through the principle of collision theory, which states that for two bodies to react, they need to collide with enough energy and in the correct orientation. Similarly, diffusion theory could be used to explain phase formation as diffusion can be described as the random movement of particles through space, usually due to a concentration gradient. In both cases an Arrhenius equation can be applied to explain chemical reactions. Figure 3 provides a schematic to show that the elemental reaction to produce a ternary phase initially consists of segregated particles of each element. The only region for a reaction to occur is at the interface of two of these particles. Ball milling of the elements inputs physical energy into the reaction. [35][36][37] Because the reaction is starting with elementally segregated particles, a maximum of two elements can exist at the interface of any two particles. This means that, at least initially, only binary phases can result at the interfaces of particles. Because the rates of collision between Yb and Sb particles are going to reflect the overall composition of the mixture, it would be expected that the phases forming would reflect that as well. Here the two binaries Yb4Sb3 and Yb11Sb10 are the result because Yb14AlSb11 resides between those two phases on a Yb-Sb binary diagram when not considering Al. Due to the low molar concentration of Al in this reaction, the rate of Al-Sb collisions, and in turn contribution to the formation of products, is near negligible. After milling, the mixture likely consists of small crystalline domains of binary phases along with unreacted amorphous regions. During annealing some of these small unreacted regions can react if the proper stoichiometry of elements is present locally. As temperature increases, these binary particles begin to increase in crystallinity and the interfaces between particles increase their complexity. What was once mainly interfaces of Yb and Sb is now interfaces of Yb-Sb binaries and particles of Al or Al-Sb. This interface now has all the elements required for the formation of the ternary phase. As temperature increases the possibility of collisions leading to the formation of the desired phase also increases, which is indeed what was observed at the higher temperature range in the study above.
Figure 3. A schematic illustrating the interfaces of elemental grains for a reaction from the elements, A, B, C to form the ternary phase ABC. Each box is representative of a single particle/grain, one of which is highlighted in yellow for clarity.
One approach used for the synthesis of complex ternary phases is to avoid the formation of these binary intermediates altogether. [38][39][40][41][42] By depositing the elements into a thin, ordered film the diffusion path length of all the elements can be minimized. As this ordered amorphous film is then annealed, the layers react and directly form the desired ternary product with very high purity. Because each layer of the amorphous film is thin and the elements are layered in a specific order, there is effective control over the collisions at each interface. This approach is quite effective as it allows for the targeting of metastable phases which may not be as thermodynamically favorable as binary phases in the same region of phase space. Because Yb14MnSb11 is the most thermodynamically favorable phase within its region of phase space (Yb-Mn-Sb), it was investigated to determine whether those binary intermediates could be embraced rather than avoided to effectively lower diffusion path lengths and improve the overall purity of the product.
The Formation of Yb14MnSb11 from Yb11Sb10, MnSb, Yb and YbH2. To investigate the possible reaction pathways polycrystalline Yb11Sb10 was prepared. Yb14MnSb11 was chosen as the synthetic target because of its excellent properties as a thermoelectric material in comparison to the Al analog. [15][16][17]30,43,44 Figure 4 shows the PXRD of high energy milled powder and after annealing of the constituents, Yb11Sb10, MnSb, Yb, and YbH2, to make Yb14MnSb11. After milling, the reactants have gone from their crystalline forms to something more amorphous. The major reflections of Yb11Sb10 heavily overlap but can be identified as the broad peak observed between 30° to 33° 2q. As the reaction heats to 400 °C, the peaks attributed to Yb11Sb10 become more crystalline in nature. At 500 °C reflections that can be attributed to the targeted Yb14MnSb11 begin to appear with intensities above the Yb11Sb10 reflections. The majority of the desired Yb14MnSb11 phase has formed 100 °C after the initial reflections appear. As the temperature is increased to 800 °C Yb14MnSb11 continues to become more crystalline, and the reflections attributed to the binary phases fade away. After 4 days at 800 °C the majority Yb14MnSb11 phase has formed with only minor impurities of Yb2O3 and Yb11Sb10. Taking a closer look at the diffraction patterns, the main diffraction peaks for Yb2O3 cannot be indexed in any pattern below 700 °C. This suggests that the oxide originates from a high temperature reaction possibly between unreacted Yb metal and the native oxide present on the interior of the Nb tubes. If this oxide was sourced from the Yb metal used, the oxide should be identifiable at lower temperatures. If this oxidation was due to significant amounts of oxygen gas present in the reaction vessel the oxidation of Yb metal would likely also happen at lower temperatures than what is shown here. Therefore, a likely hypothesis is that the thermite-style reaction between Yb and Nb2O5 has a sizeable activation energy which is why the oxide is not observed until higher temperatures. [45][46][47] The formation of Yb14MnSb11 from Yb4Sb3, MnSb, and YbH2. In a similar fashion to the study described above, polycrystalline Yb4Sb3 was prepared and the temperature study of the reaction to form Yb14MnSb11 is provided in Figure 5. Yb4Sb3 is the other Yb-Sb binary originally identified in the reaction from the elements for Yb14AlSb11. After milling Yb4Sb3, MnSb, and YbH2, the powder can be described as a mixture of amorphous material with very small crystalline domains much like what was observed in the reactions from Yb11Sb10. SEM micrographs (shown in SI Figure S6) show a mixture of particle sizes ranging from around 40 microns down to nanometer scale. Although there were larger sized particles, these contained several fractures, splitting them into smaller crystalline domains (Figure 6 a)). Unlike Yb11Sb10, which crystallizes in a tetragonal space group and has many reflections, Yb4Sb3 crystallizes in a cubic space group which lends to a simpler diffraction pattern with two main reflections around 30° and 36° 2q. Because of this simplicity, reflections from YbH2 were also able to be indexed in the milled powder, as shown in Figure 6 b), confirming that it does not decompose during the milling process. As the reaction is heated, the reflections from Yb4Sb3 become more intense and crystalline. Small reflections from the ternary phase Yb14MnSb11 can be identified around 33° 2θ as low as 300 °C, but at 600 °C there is a drastic transformation from the mixture of binary phases to the targeted ternary phase. The Yb14MnSb11 continues to grow in crystallinity as the temperature increases to 800 °C. After 4 days at that temperature, the resultant product is pure phase Yb14MnSb11 with only a minor (~ 1 %) Yb2O3 impurity. Much like the reaction from Yb11Sb10, this oxide does not appear until elevated temperatures are reached, suggesting a high temperature reaction between Yb metal and an oxide containing species like the Nb2O5 native oxide that forms on the surface of the niobium tubes. The differences in product purity between the three reaction studies described above can be understood through the lens of elemental distribution and loss. In the reaction from the elements, the resultant product was a mixture of Yb11Sb10 and Yb14AlSb11. In relation to Yb14AlSb11, the binary, Yb11Sb10, is Yb deficient with respect to the Yb-Sb relative atomic amounts. This suggests that the undesired Yb11Sb10 side phase is a result of Yb deficiencies within the reaction mixture and that it is the result of Yb loss to the mill. This loss is hard to avoid in elemental synthesis due to the sticky nature of Yb metal and brings the overall reaction to a Yb deficient state. This deficient reaction then progresses by the reaction shown below.
14-x Yb + Al + 11 Sb ! Yb14AlSb11 + Yb11Sb10 + Al
In the case of the reaction from Yb11Sb10 to form Yb14MnSb11, the resultant product was a mixture of Yb11Sb10, Yb2O3, and the desired Yb14MnSb11 phase. Here, there are both the Yb deficient phase Yb11Sb10 and the Yb rich phase Yb2O3. The final mixture of these two phases with Yb14MnSb11, along with the formation of Yb2O3 at elevated temperatures, suggests that the reaction mixture was not homogenous. If the reaction consisted of small Yb rich and deficient regions, the deficient regions would progress by a similar reaction as outlined above. The Yb rich regions react to fully form Yb14MnSb11, due to a more favorable enthalpy of formation (ΔHYb11Sb10 = -1.035 eV, ΔHYb14MnSb11 = -1.052 eV), with residual unreacted Yb metal, as indicated in the reaction shown below. Yb metal is extremely susceptible to oxidation at high temperatures and therefore oxidizes and is identified as Yb2O3, indicated in parentheses below.
Finally, Yb14MnSb11 was made in very high purity through a reaction from Yb4Sb3 with only a minor oxide impurity. This implicates the possibility of native Yb defects being present in the Yb14MnSb11 that is being formed. 2/3 Yb + 10/3 Yb4Sb3 + MnSb ! Yb14-xMnSb11 + x Yb (Yb2O3) Figure 7 illustrates the interfaces of particles/grains of the two binary phases A2C and B2C to form the ternary phase ABC. Because this model reaction consists solely of binary particles/grains, the distribution of C within A and B is on an atomic level. As the binary phases employed are further from the desired target and more additional reactants are required, the elemental distribution with that reaction is more like that of reactions from the elements (Figure 3). Therefore, the reason the reactions from Yb11Sb10 and Yb4Sb3 do not lead to the same products (Yb14MnSb11 with Yb11Sb10 and Yb2O3 vs Yb14MnSb11 with Yb2O3) is attributed to the relative ratios of elements within the binary phases employed. The reaction employing Yb11Sb10 requires more additional Yb to balance. This introduces more segregated regions of Yb in the initial reaction and increases the probability of inhomogeneous regions of Yb and results in the corresponding impurities (Yb2O3 and Yb11Sb10) in the final product. This is not the case for Yb4Sb3 as the starting reagent, which results in a higher purity of the final product Yb14MnSb11 with about 1% Yb2O3. Although not as ideal as the ABC case presented in the model, Yb4Sb3 requires significantly less additional Yb to balance the reaction and is as close to the model as the phase diagrams allow. The ideal reaction is one in which both the number of elemental reactants and the total number of reactants are minimized. Reactions to form Yb14MgSb11 and Yb14MnSb11 from the Binaries. Figure 8 shows the PXRD patterns of Yb14MgSb11 (red, top) and Yb14MnSb11 (blue, bottom) synthesized from Yb4Sb3, YbH2, and either MnSb or Mg3Sb2 through ball milling followed by direct reaction through spark plasma sintering. Reference patterns for both structures are shown in black below the experimental patterns. 18,44 Yb14MnSb11 prepared from Yb4Sb3, YbH2, and MnSb has lattice parameters of a = 16.628(2) Å, c = 22.046(2) Å, and V = 6096.0(4) Å 3 , consistent with those previously reported for polycrystalline samples at room temperature. 17 The lattice parameters of Yb14MgSb11 refine to a = 16.623(1) Å, c = 22.259(1) Å, and V = 6150.9(8) Å 3 , slightly larger than what has previously been reported in both single crystals and polycrystalline samples which range from V = 6128(1) -6147(1) Å 3 . 18,31,48,49 In both cases the high purity of the sample is immediately evident and there is no indication of the presence of Yb11Sb10 or residual Yb4Sb3. However, a small Yb2O3 impurity was observed (1.08(6) wt% for Mn and 1.16(3) wt% for Mg) in both samples of Yb14MSb11 (M = Mg, Mn). The absence of Yb11Sb10 in either sample supports the hypothesis that Yb14MSb11 is slightly Yb deficient. Because these reactions are performed using oxide-free reagents (SI, Figures S1-5) in low oxygen atmospheres (< 0.5 ppm O2), the source of the oxygen is likely from an external source. Oxygen has been shown to strongly chemisorb to the surface of graphite, [50][51][52][53] and therefore could come from the graphite die during the SPS processing. These C-O species do not desorb until temperatures above 1253 K, 52 but unreacted Yb could react with these species to form Yb2O3 at temperatures below that, much like in the Nb2O5 case. In the reaction employing the binary phase Yb11Sb10 to form Yb14MnSb11, Yb2O3, Yb11Sb10, an Yb-rich phase and an Yb-deficient phase were identified by PXRD as the impurities. A Mn containing phase is also required to balance the reaction, but the amount would be too small to be detectable. This is also observed when making Yb14MgSb11 from Yb11Sb10 (SI, Figure S7). This is attributed to inhomogeneities of the starting reagents in the reaction mixture. However, in the reactions to form Yb14MnSb11 and Yb14MgSb11 from Yb4Sb3, only Yb2O3 is present among the final products, with a notable lack of Yb11Sb10 or other Yb-deficient Sb containing phases to balance the reaction. This suggests that the Yb14MnSb11 phase is Yb deficient as the stoichiometric reaction leaves unconsumed Yb, but apparently without accompanying Sb.
Yb14-xMnSb11 Defect Study. To investigate the possibility that Yb14MSb11 phases are inherently Yb deficient, samples of Yb14-xMnSb11 were prepared employing YbH2, MnSb, and Yb4Sb3 as binary precursors. The Yb content of the reaction was adjusted by changing equation 3 to be equal to the desired Yb content and then the 3-variable system of equations was re-solved based off the purity of the Yb4Sb3 being used for that reaction. Figure 9 a) shows the PXRD patterns of Yb14-xMnSb11 (x = 0, 0.02, 0.05) in comparison to the calculated pattern shown in black. All three samples show very high purity Yb14MnSb11. The pattern at the top of the plot is on stoichiometry for Yb, and those below that have systematically reduced Yb content. The powder diffraction pattern of the x = 0 sample refines with a 1.08(6) wt% Yb2O3 impurity present. As the Yb content of the reaction was reduced to 13.98 (x = 0.02), the refined oxide impurity in the PXRD pattern reduced to 0.76(6) wt%. At 13.95 (x = 0.05), the oxide impurity can no longer be refined. At 13.92 (x = 0.08) reflections from the Yb deficient phase, Yb11Sb10, are identified (SI, Figure S8). Figure 9 b) shows the highest intensity peak of Yb2O3 observed in these patterns. As the Yb content of the reaction is reduced, the intensity of this peak decreases until only the intensity of a peak related to the Yb14MnSb11 phase is present. The apparent oxide impurity was systematically reduced through reduction of Yb content within the reaction. This further supports the hypothesis that the Yb2O3 observed in these reactions forms due to Yb-richness, either locally or overall. The systematic reduction in Yb content was further confirmed through energy dispersive spectroscopy (SI, Figures S9 -S12). Although the lattice parameters of the main Yb14-xMnSb11 phase (a = 16.6293(9) Å, c = 22.0458(9) Å, V = 6096.5(4) Å 3 ) do not change, it is likely there are minor differences in defects within the samples. It has been shown in other materials that synthesis in a region of apparent elemental richness can influence the defects present in the main phase. [54][55][56] A summary of the reactions and their products can be found in table 1. Thermal Conductivity and Electrical Transport of Yb14MgSb11 and Yb14-xMnSb11. The thermal conductivity of the stoichiometric samples, Yb14MgSb11 and Yb14MnSb11, are shown in Figure 10 a). The Yb14MgSb11 sample shows a lower thermal conductivity compared with the Mn analog across the entire temperature range. Although the thermal conductivity is higher than what was previously reported for Yb14MgSb11, 18,31 it can be attributed to differences in the electronic contribution. The thermal conductivity of the stoichiometric sample of Yb14MnSb11 is comparable to that previously reported. 17 The "S-shaped" thermal conductivity seen here in both cases is indicative of the multiband transport which has been previously identified in these materials. 48 The Yb deficient series, Yb14-xMnSb11 (x = 0.02, 0.05) are also provided in Figure 9a. Yb13.98MnSb11 (x = 0.02) shows a nearly identical thermal conductivity to the stoichiometric compound until the highest temperatures which is shown in the inset. At 1073 K, the data deviates with a thermal conductivity of 7.70 mW cm -1 K -1 and provides a consistently higher thermal conductivity, reaching a maximum of 8.71 mW cm -1 K -1 at 1273 K. The more deficient structure, Yb13.95MnSb11 (x = 0.05) shows an overall lower thermal conductivity, starting at 7.78 mW cm -1 K -1 at 327 K, increasing to 8.39 mW cm -1 K -1 at 574 K and then decreasing to a minimum of 7.46 mW cm -1 K -1 at 1073 K. Following the typical temperature dependence for this structure type, the thermal conductivity above 1073 K increases to 8.56 mW cm -1 K -1 at 1273 K. The thermal conductivity of the x = 0.05 sample fits closely what has been reported for single crystals samples. 17,44 What is most noticeable in this series is the distinctly different slope of the stoichiometric sample after the onset of bipolar conductance in comparison to both Yb deficient samples, shown in the inset of Figure 9a. This suggests that a slight excess in Yb may play a role in the manipulation of transport properties at the highest temperatures.
The electrical resistivity as a function of temperature for all samples are shown in Figure 10 b). Consistent with the higher thermal conductivity, Yb14MgSb11 exhibits a lower electrical resistivity than previously published. 18,31 This is likely due to the reduction of Mg employed compared to previously published reactions (typically 20% excess) thereby reducing unreacted Mg at grain boundaries, which has previously been shown to have negative effects on the electrical resistivity. 31 The electrical resistivity of Yb14MgSb11 is 2.35 mΩ•cm at 294 K and increases to a maximum of 7.41 mΩ•cm at 1250 K. The Yb14-xMnSb11 series of samples all start at the same approximate value at room temperature. The resistivity of Yb14-xMnSb11 series at 294 K are 1.92 mΩ•cm, 1.91 mΩ•cm, and 2.04 mΩ•cm, for x = 0.00, 0.02, 0.05, respectively. As temperature increases, x = 0.00 shows the lowest resistivity, with x = 0.02 above that, and x = 0.05 the highest. By 800 K this ordering is noticeable with the resistivities of 3.78 mΩ•cm, 3.92 mΩ•cm and 4.19 mΩ•cm, for the x = 0.00, 0.02, and 0.05, respectively. At 1175 K, the resistivities of the two Ybdeficient samples begin to bend over due to bipolar conduction. Notably, the x = 0.00 shows a less drastic change in slope and the resistivity continues upwards until the final temperature is reached. The high temperature behavior can be seen in the enlarged view shown as an inset in Figure 9b. The electrical resistivity of all samples within the Yb14-xMnSb11 series fit well with what has previously been reported for samples of this material, with those having the highest performance showing the same high temperature behavior as the stoichiometric (x = 0.00) sample. 17,44 The Hall carrier concentration versus temperature is shown in Figure 10 c). The carrier concentration of Yb14MgSb11 starts below that of the Mn analog at 6.74 x 10 20 h + cm -3 at 294 K, higher than what has previously been reported (5.37 x 10 20 h + cm -3 ). 31 The carrier concertation stays relatively level with increasing temperature until around 900 K. At that point, there is an increase in carrier concentration to a maximum of 4.56 x 10 21 h + cm -3 at 1250 K. The increase in carrier concentration at the highest temperature can be attributed to the onset of bipolar conductance. For the Yb14-xMnSb11 series, the carrier concentration at 294 K begins at 1.48 x 10 21 h + cm -3 , 1.15 x 10 21 h + cm -3 , and 1.09 x 10 21 h + cm -3 , for x = 0.00, 0.02, 0.05, respectively. All three samples converge to approximately 9 x 10 20 h + cm -3 by 400 K. The carrier concentrations of the three samples are in close agreement until 700 K, where they begin to deviate and by 800 K the difference is significant. Yb14MnSb11 shows a higher carrier concentration of 1.14 x 10 21 h + cm -3 at 807 K in comparison to Yb13.98MnSb11 (7.19 x 10 20 h + cm -3 ) and Yb13.95MnSb11 (8.04 x 10 20 h + cm -3 ). This trend holds true as the temperature increases with x = 0.00 having the highest carrier concentration, x = 0.05 having a lower carrier concentration, and x = 0.02 being close to that, but lower. Around 1000 K there is a noticeable increase in the carrier concentrations of all three samples which is attributed to the onset of bipolar conduction. The samples of Yb14-xMnSb11 all have the same carrier concentration as what has previously been reported of 9 x 10 20 h + cm -3 at 400 K. 17 The noticeable difference in temperature dependent carrier concentration seen in the Yb14MnSb11 in comparison to the deficient samples may be a result of the apparent Yb richness and its influence on defects within the main phase.
The Hall mobility (Figure 10 d)) of Yb14MgSb11 starts at 4.0 cm 2 V -1 s -1 at 294 K, then increases to 4.48 cm 2 V -1 s -1 at 352 K. After that, the mobility steadily decreases to 0.175 cm 2 V -1 s -1 at 1250 K. The Hall mobility of Yb14MnSb11 starts at 2.20 cm 2 V -1 s -1 at room temperature. In comparison, the two deficient samples both show higher room temperature carrier mobilities of 2.84 cm 2 V -1 s - 1 and 2.82 cm 2 V -1 s -1 for x = 0.02, 0.05, respectively. The mobility of these samples remains relatively unchanged until 550 K where there is a drastic decrease in the carrier mobility of all samples as they trend downwards towards 0.5 cm 2 V -1 s -1 at 1273 K. The trends in mobility agree with those seen in the higher temperature region of the carrier concentration. The sample with the highest carrier concentration (x = 0.00) has the lowest mobility, and that with the lowest carrier concentration (x = 0.02) has the highest. The carrier mobilities of Yb14MgSb11 are slightly lower than what was previously reported which is expected with the higher carrier concentrations seen in this sample (4.48 vs 4.70 cm 2 V -1 s -1 ). 31 The carrier mobilities of the Yb14-xMnSb11 series are comparable to what has previously been reported for single crystal and polycrystalline samples with the two deficient samples showing mobilities closer to that of the single crystal results. 57,58 Seebeck Coefficients. Figure 11 a) shows the Seebeck coefficients as a function of temperature for all samples. The Mg analog shows a systematically higher Seebeck coefficient which steadily increases with temperature, reaching a maximum of 231.49 μV K -1 at 1181 K before decreasing due to the onset of bipolar conduction. 18,31,48 The Yb14-xMnSb11 stoichiometric sample begins at a value of 44.83 μV K -1 at 313 K and steadily increases to a maximum of 221.29 μV K -1 at 1250 K, after which there is a bend over due to the onset of bipolar conduction. The x = 0.02 sample, Yb13.98MnSb11, shows a higher Seebeck coefficient of 48 μV K -1 at 312 K, but as temperature increases, it reaches a lower peak of 214.65 μV K -1 at 1212 K after which the Seebeck coefficient bends over. The most Yb deficient x = 0.05 sample, Yb13.95MnSb11, starts between the other two samples at 46.74 μV K -1 at 321 K. As temperature increases, the Seebeck coefficient of this sample also increases, but only reaches a maximum of 212.50 μV K -1 at 1214 K. After that point, the data bends over due to bipolar conduction. The inset in Figure 10a shows the Seebeck coefficients at the highest temperatures. In this temperature range, the ordering of the Seebeck coefficients follows the Yb deficiency with x = 0.00 having the highest Seebeck coefficient and x = 0.05 having the lowest. The maximum Seebeck coefficient of Yb14MgSb11 is comparable to the 232 μV K -1 previously reported. 31 The values for Yb14-xMnSb11 agree with what has previously been reported, with the stoichiometric sample having maximum values that match the highest efficiency samples. 17 Using the Goldsmid-Sharp method for estimating band gap, the band gaps of Yb14MgSb11 and Yb14MnSb11 were both estimated to be about 0.55 eV. 59 This is close to what has been previously calculated from experimental and computational methods. 17,18,31,48,55 The Seebeck coefficients of the stoichiometric Yb14MgSb11 and Yb14MnSb11 were also measured using a commercially available Linseis LSR-3 employing an off axis 4-probe orientation (SI, Figure S14). This measurement configuration is much more accessible to a wider range of laboratories and commercial settings. Although this method is employed by many research laboratories, it is known that the 4-probe method provides systematically larger Seebeck coefficients due to a phenomena known as the "cold finger" effect. 25,60 There is a tendency to underestimate the actual thermal gradient, and in turn overestimate the Seebeck coefficient (ΔV/ΔT) due to heat flow being directed into the probes and away from the surface of the sample. The room temperature Seebeck coefficients of both samples are comparable to those measured by the 2-probe method. This trend holds true until 700 K. At that point, both 4 probe measurements begin to show systematically larger Seebeck coefficients which deviate further with temperature from the 2-probe measurements. By 900 K the sample of Yb14MgSb11 has a Seebeck coefficient of 213 μV K -1 versus 192 μV K -1 for the 4-probe versus the 2-probe method. The stoichiometric sample of Yb14MnSb11 shows similar deviations, reaching 190 μV K -1 at 900 K by the 4-probe method and 175 μV K -1 by the 2-probe method. The sample of Yb14MgSb11 provides a maximum of 276 μV K -1 at 1272 K and Yb14MnSb11 reaches 256 μV K -1 at 1225 K. These Seebeck coefficients are 19% and 16% larger than the maximums measured by the 2-probe method.
A Pisarenko plot of the Yb14-xMnSb11 series (Figure 11 b)) at 900 K shows the variation in effective mass between the two non-stoichiometric samples and the stoichiometric Yb14MnSb11 at temperatures above where the difference in carrier concentration was observed. The x = 0.00 sample in the Ybn14-xMnSb11 series was calculated to have an effective mass of 5.24 m0 whereas x = 0.02 and 0.05 showed 3.05 m0 and 3.42 m0, respectively, at 900 K. There is the clear trend of increasing effective mass with increasing carrier concentration. This is consistent with the electronic structure and modeling of the multiband transport of Yb14MnSb11 and the Yb14Mg1-xAlxSb11 series. 48 As carrier concentration is increased to 1 x 10 21 h + cm -3 and beyond, the Fermi level is pushed deeper into the valence band. As the Fermi-Dirac distribution and in turn selection functions broaden, this deeper Fermi level allows for more selection from a pocket of heavy, degenerate bands located between N-P before the onset of bipolar conduction.
Unitless Thermoelectric Figure of Merit, zT. The overall thermal to electric conversion performance of thermoelectric materials is judged by the unitless thermoelectric figure of merit, zT = S 2 T/ρκ, where S is the Seebeck coefficient, T is the absolute temperature, ρ is the electrical resistivity, and κ is the thermal conductivity. Figure 11 c) shows the calculated zT for Yb14MgSb11 and Yb14-xMnSb11. The sample of Yb14MgSb11 reaches a peak zT of 1.28 at 1175 K. This is slightly higher than the previous best for this material of 1.26 and brings the Mg analog even closer to the highest reported values for Yb14MnSb11 (1.35 at 1273 K). 17,31 Although peak efficiencies are lower, the average zT of this sample from 875 to 1275K is 1.15, which is slightly higher than the one of the best sample of Yb14MnSb11 (1.07). 17 This is important when considering a material for implementation into a thermoelectric generator where the individual legs operate within a large temperature range. The calculated figure of merit for Yb14-xMnSb11 starts at a maximum of 1.24 at 1275 K for x = 0.00. The Yb-deficient samples both show lower peak zT of 1.16 and 1.12 for x = 0.02 and 0.05, respectively, at 1225 K. The efficiencies calculated for the stoichiometric sample of Yb14-xMnSb11 match the best previously reported values for polycrystalline samples measured by the same method and the sample which showed no impurities by PXRD (x = 0.05) shows performances closer to what has been previously reported for single crystal samples. 17,44 The figure of merit was also calculated using the Seebeck coefficients and electrical resistivities measured by the off axis 4-probe method (SI, Figure S13-S15). Yb14MgSb11 has a calculated zT of 1.83 at 1275 K and Yb14MnSb11 provides 1.71 at 1275 K. Both of these are the highest reported zT for their respective phases and are competitive with some of the highest reported efficiencies for any high temperature materials measured by this method with the peak efficiencies coming at a higher temperature range than that of high performing half Heusler phases. [61][62][63][64][65][66][67][68][69] It is likely the efficiencies measured by the 4-probe method are somewhat exaggerated due to the cold finer effect, but these values allow for more direct comparison to other materials measured by the 4-probe method. A systematic study of Yb14-xMnSb11 has shown that synthesis in a region of apparent elemental excess can lead to improved properties. It is known that the impurities found at grain boundaries in polycrystalline samples can influence the minor defects present in the main phase. [54][55][56]70 These results suggest further exploration of this phase space through phase boundary mapping could lead to the realization of further improved properties and a better understanding of defects and the effects of impurities within these complex systems. 54,56,70,71
The advancement of thermoelectric materials depends on the quality of materials and in terms of device fabrication, high reproducibility and fidelity in preparing samples of a particular composition with optimal properties. While Zintl phases have found many successes in thermoelectrics, compositions of the stoichiometry Yb14MSb11 and other complex structures are difficult to prepare for reasons articulated in the beginning of the discussion. A better understanding of the reaction paths leading to the formation of Yb14MSb11 (M = Al, Mn) was obtained through thorough quenching studies paired with PXRD. These studies revealed Yb11Sb10 and Yb4Sb3 as binary intermediates which were investigated for use as precursors in reactions with with YbH2 and MnSb or Mg3Sb2. An improved synthetic route is shown to allow for efficient synthesis of stoichiometric and extremely high purity products. Through this synthesis a sample of Yb14MgSb11 was produced which exhibited material leading efficiencies of zT = 1.28 at 1175 K. The slight improvement to overall zT increased the zTavg of Yb14MgSb11 in the temperature window 875 to 1275K from 1.10 to 1.15, making this phase competitive with Yb14MnSb11 (1.07). 17,31,72 The increase in average zT is important when considering these materials for incorporation into high temperature thermoelectric generators, such as a Radioisotope Thermoelectric Generator (RTG). The impact of experimental method in acquiring the Seebeck coefficient was also investigated and showed that while the commercial 4-probe experimental setup provides reliable electrical resistivity, the Seebeck coefficients are exaggerated due to a coldfinger effect at high temperatures. However, instruments using this orientation are commercially available and accessible to a wider range of users making it a useful tool in the study of thermoelectric materials. The method used in the measurement of high temperature Seebeck coefficients should always be considered when comparing data, and the 4-probe measurements presented herein allow for more direct comparison to other materials which have been measured by this method.
This synthetic route provides a high degree of stoichiometric control which was used to adjust the Yb content of reactions. The employment of binary phases was used to investigate the source of the small Yb2O3 impurity found for Yb14MSb11. Based on the reduction of Yb2O3 in the final samples, the actual composition is slightly Yb deficient with the stoichiometry of Yb13.95MnSb11. Through the reduction of the apparent oxide impurity, the thermoelectric properties of Yb14-xMnSb11 resulted in systematically lower zT. This suggests that the excess Yb plays a role in obtaining a composition with good high temperature transport properties in the case of the M = Mn analog and warrants further exploration through phase boundary mapping. Through this synthetic approach, a high degree of stoichiometric control is obtained, which allows for accurate mapping of the phase space and provides a roadmap for the realization of optimal compositions for high thermoelectric performance in these phases. In addition to the Yb14MnSb11 region of phase space, this binary addition approach could be applied to explore other difficult ternary systems with a high degree of precision.
Supporting Information. Additional X-ray diffraction patterns, scanning electron micrographs, energy dispersive spectroscopy results, 4-probe thermoelectric measurements, and heating/ cooling curves from thermoelectric measurements can be found in the Supporting Information (PDF). This material is free of charge and available at http://pubs.acs.org.