Suppression of grain growth in nanocrystalline Bi₂Te₃ through oxide particle dispersions

Nanocrystalline thermoelectric materials can provide significant improvements in efficiency over their coarse grained counterparts.^1,2 The enhancement can be explained by a desirable increase in grain boundary phonon scattering,³ which suppresses thermal transport without adversely scattering electrons, which typically have a much smaller mean free path. The production of bulk thermoelectrics that are truly nanocrystalline (nc) with grain sizes below about 100 nm, however, is prevented by grain growth, which occurs at relatively low homologous temperatures.⁴ Grain growth presents extreme difficulties in consolidating bulk nanostructures via the powder route^5,6 and also in retaining a fine grain size during the lifetime of a thermoelectric device, which must endure extreme operating temperatures. To mitigate grain growth—and thus maximise thermoelectric performance—there is a need to engineer materials with improved thermal stability.

One promising means of retarding or suppressing grain growth is through kinetic boundary stabilization, such as by the addition of second phase particles that provide Zener pinning. The concept of adding nanoscale particles has been explored in Bi₂Te₃–based alloys, e.g., with SiC⁷ and MoS₂⁸ additions, where the corresponding grain refinement effect was explicitly demonstrated. In other material systems, the strategy of employing oxide particle additions has been validated, such as in CoSb₃-based alloys using Yb₂O₃⁹ and CeO₂,¹⁰ and in FeSi₂ alloys using Y₂O₃.¹¹ Another grain refinement method, via additions of organic surfactants during MA was demonstrated for Bi₂Te₃ composites.⁶ Surfactant evaporation was argued to result in pore formation,⁶ which could also refine the grain size by Zener pinning.

In many of the above studies, an improvement in thermoelectric performance was observed,^6,7,9,11 making it an encouraging direction for study. However, none of these articles makes a quantitative and systematic analysis of the second phase grain refinement effect. Such a description is necessary, given the need to maximize grain refinement for a given volume fraction of particles. Since the particles are essentially an inert filler, they can degrade the functional performance, and provide benefit primarily through their ability to refine the matrix nanostructure; if the fraction of particles is too great, their benefit will be eventually offset by their poor electronic transport properties. A more detailed understanding of composite microstructure and its role in structure stabilization is therefore needed.

In other engineering materials, the effect of fine second phase particles on recovery and grain growth is now relatively well understood.¹² For a good dispersion of pinning particles, a system can evolve to a static grain size following grain growth, and this grain size can be linearly related to the ratio of inclusion particle size and volume fraction, i.e., D/f, via the Zener relation.¹³ The original Zener scaling law can adequately account for general grain size trends in experiments,¹⁴ even down to the nanoscale,¹⁵ although departures from linear scaling tend to occur above volume fractions of about f = 0.05, where grain boundary curvature and particle-boundary correlation factors begin to play a role.¹⁶ 

The classical Zener relation dictates that the most effective pinning will come from the smallest particles, however, when their size is reduced appreciably into the nc regime, other annealing-related microstructural phenomena can come into play. For example, below a certain critical particle diameter—on the order of 50 nm—thermally activated grain boundary unpinning can become prevalent,¹⁷ while if the particles are sufficiently mobile, they can be dragged along by the boundary via diffusive mechanisms.¹⁸ Under certain conditions, inclusions can also promote abnormal grain growth.¹⁹ Finally, particle stimulated nucleation of recrystallization can occur near rigid pinning particles if the sample has experienced sufficient deformation, as the particles themselves are not deformed and thus tend to concentrate deformation defects in their vicinity.²⁰ This phenomenon could therefore be expected in composite materials processed via plastic deformation, such as by mechanical alloying, which is common for processing nanostructured thermoelectrics.^{1,5–7,11,21} Although these annealing processes have been comprehensively investigated in many engineering materials, we are unaware of any such investigation in nanocomposite thermoelectric materials.

In this report, we present a microstructural investigation of a nanocomposite based on bismuth telluride (Bi₂Te₃) with a fine dispersion of yttria (Y₂O₃) particles. Bi₂Te₃ is selected as it is the front-running material for low temperature thermoelectric applications, and because its thermal stability in nc form was recently characterized and found insufficient for bulk materials processing operations.²² Correspondingly, Y₂O₃ was chosen on the basis of yttrium being a well-known dispersoid-former easily introduced by mechanical alloying, and yttrium is a strong oxygen scavenger relative to Bi and Te. The enhanced high temperature stability of nc Bi₂Te₃ that results from Zener pinning by such dispersoids is maintained, rather encouragingly, to temperatures near the compound melting point. Somewhat unexpectedly, at lower annealing temperatures, we find that particles tend to induce a larger final grain size in comparison to the single-phase material. This behaviour is explained in terms of existing theory for particle-stimulated nucleation of recrystallization in particle-reinforced composites.

The experimental materials were produced from powders, and their nanostructural stability was mainly evaluated in powder form after processing as well. The powders, both as-received as well as processed, were characterized by x-ray diffraction (XRD), using a PANalytical X'Pert powder diffractometer with a Cu Kα radiation source operated at 45 kV and 40 mA. Patterns were collected at a scan rate of 2° min⁻¹ over a scan range of 10°–80° 2θ. The patterns were analyzed using the Rietveld method, employing a pseudo Voigt profile function,²³ under the assumption of isotropic size and strain. Instrumental broadening was corrected for using a NIST LaB₆ sample. During the Rietveld procedure, the unit cell constants and broadening terms (both order-dependent and order-independent) were refined, allowing the volume-averaged grain size, d, microstrain, ε, and hexagonal lattice parameters, c and a to be determined. The meaning of grain size in this report is synonymous with the size of a coherent diffraction domain and is not to be confused with the particle size; powder particles were generally much larger, typically on the order of 10–100 μm.

Transmission electron microscopy (TEM) of powders was performed using a JEOL 2010 high-resolution transmission electron microscope (HRTEM) operated at an accelerating voltage of 200 kV in bright field imaging mode. TEM specimens were prepared by mixing Bi₂Te₃ powders with a fine Cu powder, followed by cold pressing into a foil. Ion milling was performed on a Fischione Model 1010 instrument, with the sample cooled to below 200 K with liquid N₂. For measurement of grain size, each identified grain was manually traced onto a transparency from which the grain diameter could be calculated.

Nanocrystalline Bi₂Te₃–Y₂O₃ composites were fabricated by mechanical alloying (MA) of elemental powders of Bi and Te with pre-synthesized Y₂O₃ nanoparticles. The Bi and Te powders (of nominal purity 99.5%, from Alpha Aesar) had maximum particle diameters of 45 and 75 μm, respectively, while the Y₂O₃ particles (from Sigma Aldrich) had a mean particle diameter < 50 nm. Fig. 1(a) shows a representative TEM image of the Y₂O₃ nanoparticles, where a number of 20 nm grains are agglomerated into a larger cluster, typical of the as-received condition. The XRD analysis as shown in Fig. 1(b) is consistent with these observations, showing an estimated grain size of 20 nm, a microstrain of 0.21%, and a body-centered cubic crystal structure with a lattice parameter of a = 1.061 nm for the as-received Y₂O₃ powders.

The powders were mechanically alloyed inside a steel vial with steel milling media, which was loaded into a SPEX 8000 shaker mill operated inside a glovebox under high purity argon. In previous reports, we showed that the alloying process occurs rapidly during the initial stages of milling²⁴ and continued treatment resulted in a minimum grain size after a specific mechanical energy dose of 32 kJ/g.²⁵ Hence, we employed this energy dose consistently to fabricate all samples in this study, which was achieved using a ball-to-powder weight ratio of 5:1 using milling media of 1.5 g, at a milling frequency of 1060 rpm for 4 h.

Composites ranging from 0.5 to 15 wt. % Y₂O₃ were fabricated. We hereafter refer to these samples as 0.5Y, 2Y, 5Y, 10Y, and 15Y, corresponding to the relevant wt. % Y₂O₃ added. Mechanical alloying of the composites occurred in a similar fashion to unreinforced Bi₂Te₃, with the final as-milled nanostructure varying little with additions of Y₂O₃. In particular, for all samples the mean grain size was estimated to be 31 ± 2 nm, with a microstrain of 0.37 ± 0.03%, and lattice parameters of a = 0.4386 ± 0.0001 nm and c = 3.044 ± 0.002 nm, and can thus be considered comparable for the purposes of analysis in this study.

During MA, the Y₂O₃ phase is not deformed significantly due to its high hardness; the estimated structural parameters of the Y₂O₃ phase via XRD remain unchanged before and after MA. The Y₂O₃ particles were generally found to be dispersed evenly, however, some agglomerated particles remained. To determine the particle size distribution of the dispersion, some milled composite powders were relaxed at 400 °C for 2 h and imaged via TEM. Fig. 2(a) shows a bright field TEM image of the powders after annealing, revealing a bi-modal dispersoid size distribution, consisting of very fine single crystal yttria particles with an average diameter of 20 nm, interspersed with large polycrystalline aggregates about 65 nm in diameter, comprising perhaps a few dozen yttria particles. Fig. 2(b) shows a particle size histogram for the yttria inclusions, taken from over 400 particle tracings, indicating an average spherical equivalent particle diameter of D = 32 nm, but a clear bimodal distribution reflective of the populations of individual particles (D ≈ 20 nm) and aggregates (D ≈ 65 nm).

For annealing treatments, powders were placed in an alumina crucible and annealed in a Mettler Toledo DSC/TGA 1 with high purity argon purge gas. The powder was heated at 10 K/min to the set point temperature, followed by air cooling. For shorter anneals, approximately 200 mg of powder was sealed within small foil packets made from 100 μm thickness stainless steel foil and immersed in a molten salt bath. After annealing, the specimens were rapidly quenched on a large copper block.

Differential scanning calorimetry (DSC) experiments were performed on powders using a TA Instruments Q100 DSC operated with a purge gas of nitrogen and a liquid nitrogen cooling system. The instrument was independently calibrated to within ±0.1 °C using an In standard. All specimens were sealed inside an aluminum pan and heated from −50 to 400 °C at 10 K/min. The irreversible stored enthalpy release was obtained by integrating the area under the curve between the linear regions either side of the exothermic region.

At the highest annealing temperatures, the grain size of the unreinforced compound grew to micrometer dimensions, which was too close to the particle size to allow accurate measurement by XRD. Therefore, to allow characterization at these temperatures, powders were consolidated prior to heat treatment. Powder compacts were made by cold pressing approximately 0.75 g of powders in a uniaxial die press, with a cylindrical tool steel die of 6 mm bore diameter, under a pressure of 750 MPa. The compacts had a relative density of 0.91 ± 0.01. After heat treatment, the microstructure was investigated by fracturing the compacts in the plane normal to the pressing direction, and imaging via scanning electron microscopy (SEM), using a JSM-6610 SEM in secondary electron imaging mode. As with the TEM micrographs, SEM grain size was measured by manually tracing grains onto a transparent film.

Fig. 3 shows the evolution in XRD patterns for the 15Y composite powders after annealing at successively higher temperatures for 2 h. A restricted section of the patterns, between 25° and 55° 2 theta, is shown for clarity. At each annealing temperature, all diffraction peaks can be indexed to the rhombohedral Bi₂Te₃ phase and the cubic Y₂O₃ phase, as labelled. The successive narrowing of the diffraction peaks at increasing temperatures is indicative of an increase in grain size and decrease in microstrain.

The evolution in stored enthalpy for the composite powders is shown in Fig. 4 alongside Bi₂Te₃. The unreinforced compound shows the broadest exotherm, beginning at 120 °C and ending at 380 °C. For the composite powders, the exotherm becomes narrower with increasing Y₂O₃ content: while the leading edge of the transient remains at about the same temperature, the tail ends significantly earlier; by about 320 °C in the case of the 15Y sample. As a result, the peak heat flow becomes more intense and is shifted to lower annealing temperatures. The total release in stored enthalpy shown at the right of each curve (normalized per unit mass of Bi₂Te₃) increases somewhat with increasing Y₂O₃ content.

The kinetics of grain size evolution for the 15Y composite and unreinforced Bi₂Te₃ are shown in Fig. 5, which plots the XRD-determined grain size as a function of annealing time at 300 °C. Unreinforced Bi₂Te₃ shows continuous grain growth, evolving to a grain size of about 150 nm after 2 h. The data-points have been fitted with a grain growth exponent of 6.5, as determined in a previous report where the kinetics of grain growth were systematically investigated.²² By contrast, the composite evolves rapidly to a grain size of about 70 nm after 2 min, where it remains in a quasi-static state for prolonged annealing times.

Fig. 6 shows the grain size, d, after 2 h anneals, as a function of annealing temperature for the nanocomposites and single phase Bi₂Te₃ alloy. Grain size was determined using XRD for the composite samples, when it remained at values small enough to be credibly detected by peak broadening (generally below about 200 nm). Above 300 °C the grain size for the unreinforced samples was measured using TEM and SEM, as shown by the shading in Fig. 6. A monotonic increase in grain size is observed for all materials; however two clear regions of behavior emerge. In the low temperature region, T < 250 °C, there is relatively little grain growth for the unreinforced Bi₂Te₃ alloy, but apparently enhanced grain growth in the composite materials. For example at 180 °C, the 15Y composite and unreinforced Bi₂Te₃ alloy have d = 52 and d = 35 nm, respectively, from a common starting grain size of 31 nm. This trend is reversed at temperatures above 250 °C where grain growth in the unreinforced Bi₂Te₃ alloy becomes rampant relative to the composites; by 430 °C the 15Y and unreinforced samples reach grain sizes of about 94 nm and 2.6 μm, respectively. The grain size of the composite materials above 250 °C also clearly decreases with increasing Y₂O₃ content. For example, at the same temperature, the 0.5Y sample reaches a grain size of about 196 nm, about double that attained in the 15Y sample. At higher annealing temperatures, the grain size of the composites continues to increase mildly, however good thermal stability (<200 nm) is retained up to the melting point, while the unreinforced Bi₂Te₃ material evolves to grain sizes on the order of 5 μm.

Fig. 7 shows TEM micrographs of (a) unreinforced Bi₂Te₃, (b) 0.5Y, and (c) 5Y composites taken after annealing at 430 °C for 2 h. The observed grain sizes of the 0.5 and 5 wt. % Y₂O₃ samples are in reasonable agreement with the XRD-determined grain sizes of 196 and 126 nm, respectively. Fig. 8 shows an SEM micrograph of an unreinforced Bi₂Te₃ compact annealed at 380 °C for 2 h, from which the grain size was measured to be about 1.2 μm.

Fig. 9 shows the evolution in microstrain and lattice parameters as a function of annealing temperature, as determined via XRD. The dataset shown results from the same samples as in Fig. 6, i.e., each datapoint represents a separate 2 h anneal. The microstrain (ε), as depicted in the upper panel, continually decreases with increasing temperature. Similarly to the grain growth trends in Fig. 6, the composite powders show enhanced recovery below 250 °C, and thus lower microstrain values, but above 250 °C the reverse is true. For example the 15Y and 0Y alloys have ε = 0.06 and ε = 0.20 at 180 °C, respectively, but at 330 °C the same alloys have ε = 0.02 and ε = 0. At higher annealing temperatures still, the composites evolve towards a microstrain that is fairly constant with temperature, but that increases with increasing Y₂O₃ content. The lattice parameter evolution (c/a), as shown in the lower panel, is reflective of the point defect content of the compound, and its evolution is more complicated because it is not monotonic with annealing temperature. At temperatures below 250 °C, the c/a ratio increases from about 6.94 in the as-milled state towards the literature value c/a = 6.953.²⁶ However, above 250 °C a divergence in the lattice parameter is observed, with the unreinforced compound showing a dramatic decrease in c/a ratio, which can be attributed to decomposition of the compound. Conversely, the composite samples show an increasing c/a ratio trend at higher temperatures.

The nanostructure stabilization that we observe in bismuth telluride at conventional sintering temperatures here suggests that a bulk composite of these powders would have significantly reduced thermal conductivity, k. For example, Poudel et al.¹ showed a reduction in k between coarse grained Bi₂Te₃-based ingots and the corresponding mechanically alloyed and hot pressed material: At 373 K, k fell from 1.36 to 0.99 W/m-K.¹ For alloys with nanoparticle additions, a further reduction in k is typically observed. For example, Zhao et al.⁷ compared an unreinforced Bi₂Te₃-based alloy processed via mechanical alloying and spark plasma sintering, with a corresponding 0.5 wt.% SiC nanoparticle composite: At 373 K, k fell from 0.89 to 0.76 W/m-K. We therefore expect the composites of this study to have similarly low thermal conductivity, i.e., considerably below 1 W/m-K around room temperature, due to the increased phonon scattering at stabilized nanoscale grains, as well as the nanoparticles that pin them.

The most unexpected effect of particle additions to the structural evolution of nanocrystalline Bi₂Te₃ is the crossover in degree of structural disorder at a temperature of about 250 °C. Below this temperature, the dispersoids apparently lead to greater recovery (less microstrain and lattice distortion), and more rapid grain growth. Above this temperature, they apparently retard grain growth. In what follows, we discuss these two regimes in turn, beginning with the higher temperature one. We then make some recommendations for potential improvements in processing of these nanocomposites based on the mechanisms of structural evolution discerned from this analysis.

The behavior seen in the high temperature regime above about 250 °C is in line with expectations for structure stabilization by Zener pinning, as described in the Introduction: the unreinforced compound exhibits runaway grain growth from the nanoscale to the microscale, while the yttria reinforced materials stabilize at fine nanoscale grain sizes. The original and most widely accepted model for the limiting grain size that is reached during thermal annealing of a material containing fine particles is given by the generalized Zener equation¹³ 

where D and f are the average diameter and volume fraction of the particles, respectively, and α is a geometric constant that was originally assumed to be α = 2/3, although analysis of experimental data¹⁴ suggests it could be significantly lower. The form of this equation is valid for low particle volume fractions where boundaries are assumed macroscopically planar.

In the case of a high-volume fraction of particles, however, boundaries no longer remain planar and particle-boundary correlation factors are expected to play a role. Under these conditions, an alternative form for the grain size limit is suggested

where β is a geometric constant. Many authors have discussed this type of relationship, and Hillert suggests that β = 1.8.¹⁶ Since the above quantities, d_Z and d_ZC, scale differently with f, the grain size limit is given by the larger of either Eq. (1) or Eq. (2). Thus, a gradual transition from uncorrelated pinning (Eq. (1)) to correlated pinning (Eq. (2)) is expected to occur at some intermediate volume fraction between f = 0.01 and f = 0.1.^16,27,28

Fig. 10 shows the above limiting grain size models as a function of particle volume fraction, for assumed geometric constants of α = 0.17 and β = 2, according to Ref. 14. Such an analysis yields a transition from uncorrelated to correlated pinning at about f = 0.025. Datapoints from a variety of unrelated experimental studies are shown, alongside the new data from this study, which are shown as closed symbols—from the XRD measured grain sizes at the maximum annealing temperature (530 °C). A good agreement with Eq. (2) is observed, indicating approximate f ^−1/3 grain size scaling, which suggests that particle correlation effects are prevalent in the composites. The data points can be best-fitted to Eq. (2) with a geometric constant of β = 1.6, which is close to the value of β = 1.8 as proposed by Hillert.¹⁶ 

At temperatures between about 400–500 °C, the limiting grain size in Fig. 6 appears to increase slowly with increasing temperature. The continued grain growth at higher temperatures could be due to thermal activation of boundary unpinning. This process is suggested by Gore et al.¹⁷ to become important for very small pinning particle sizes and high temperatures. The authors evaluated the tendency for thermally activated unpinning in an Fe alloy, and suggested that thermally activated unpinning could play a role below a particle diameter of about D = 50 nm, which is on the order of the particle sizes in this study. It is therefore possible that some grain boundaries will have a low enough energy to preferentially unpin from the smallest particles, leading to a slight increase in grain size with increasing temperature.

The enhanced grain growth and recovery in the composite materials at low annealing temperatures is suggestive of particle stimulated nucleation (PSN) of recrystallization, which is known to evoke exactly those two effects in other particulate reinforced systems, e.g., FCC metals,^20,29 but also intermetallic compounds such as Fe₃Al.³⁰ The underlying physics of PSN pertains to the localization of deformation defects around rigid reinforcement particles in materials that have experienced deformation. In our specimens the deformation of the MA process might reasonably be expected to cause such local defect accumulation, as the yttria particles are indeed rigid as compared to the much softer and more compliant Bi₂Te₃ matrix phase; the accommodation of plastic mismatch during MA would require defects to accumulate locally around the dispersoids. Evidence for such excess defect accumulation around particles is shown by the increasing stored enthalpy values per unit of Bi₂Te₃ phase with increasing particle contents, as shown in Fig. 4. With excess defect energy near particles, relaxation processes can give way to outright recrystallization there. Additionally, the shape of a DSC exotherm for a recrystallization process is much narrower than for simple grain growth,³¹ therefore the fact that this enthalpy release becomes increasingly narrow in the composites with higher volume fractions is also suggestive of a transition from gradual relaxation and grain growth kinetics, to more punctuated recrystallization kinetics.

The observation of PSN in a nanocomposite material is generally unexpected due to the decreasing tendency for PSN as the size of the rigid particle is reduced. This trend has been explored systematically, e.g., in pure cold worked aluminium.²⁰ However, the large amount of enthalpy that can be stored as chemical defects within the grain interior of intermetallic compounds, such as Bi₂Te₃,²² could mean this phenomenon is more prevalent in compounds than in cold worked metals.

In order to assess the likelihood of PSN, we can use the analysis of Humphreys,^20,32 who considered the balance of recrystallization driving pressure from stored enthalpy within the grain interior, E_stored, acting against the retarding pressure of the curved boundary of a new nucleus forming, 4γ/d, where γ is the grain boundary energy. Humphreys further assumed that the forming recrystallization nucleus is of the same size as the reinforcement particle on which it is forming, D.^12,20,32 By equating the two forces acting on the boundary, the critical particle size above which PSN is given as^12,20,32

In the present experiments, as shown in Fig. 2, there is not a single rigid particle size, but rather a bimodal distribution of D. The effect of a bimodal particle size distribution is two-fold, since the largest particles provide favorable sites to nucleate recrystallized grains according to Eq. (3), but the smaller particles may offer Zener pinning points for a forming recrystallization nucleus. The recrystallization behavior of a bimodal particle size distribution has been previously studied in detail, e.g., in the Al-Mn system,³³ and Eq. (3) can be modified to incorporate the effects described above¹² 

where D_min is the diameter of the smaller pinning particles. Thus as the size of the finest particles decreases, the Zener pinning force increases, and the critical particle size for PSN also increases.

The driving force for recrystallization can be calculated by subtracting the grain boundary enthalpy from the total stored enthalpy³¹ 

where g is a geometric factor accounting for the grain shape, which is estimated to be 1.3 ± 0.2,³¹ and V is the molar volume. The grain boundary energy for an average relaxed boundary in Bi₂Te₃ was recently measured via calorimetry to be γ = 0.26 J/m².²² The average stored enthalpy in the composite powders is 6.7 J/g (as shown in Fig. 4), from which E_stored is calculated to be 2.8 J/g or 2.2 × 10⁷ J/m³.

In the limit of the smallest volume fraction used in this study, i.e., about f = 0.01, D_crit is calculated using Eq. (4) to be 48 nm. We note that this is the same as the D_crit value that is returned from Eq. (3), which is also 48 nm. In the limit of the largest volume fractions (f = 0.21), D_crit increases to about 76 nm. These values are all significantly larger than the mean diameter of the single crystal yttria dispersoids used in this study shown in Fig. 2(a) and quantified to be of an average size D_min = 20 nm in Fig. 2(b). This suggests that the single crystal particles are unlikely to be sites for PSN. However the agglomerated particles that were quantified to be of an average size D_max = 65 nm in Fig. 2(b), are quite well in line with D_crit across the range of volume fractions studied, which suggests that the agglomerated particles could serve as nucleation sites for recrystallizing grains.

This analysis helps to rationalize why PSN is observed in the present nanocomposite system where it is normally not expected; while nanoscale (d < 100 nm) dispersions are usually associated with a decreasing tendency for PSN,^20,29,32 the increased stored enthalpy from chemical defects²² and the presence of large dispersoid agglomerates work together to provide sufficient driving force for PSN to occur in nc Bi₂Te₃. This analysis also suggests that the agglomeration of particles during processing would be desirable to eliminate. A finer and more uniform particle dispersion could provide an enhanced Zener pinning pressure, and remove the nucleation sites for PSN—leading to a finer microstructure. In what follows we explore a potential processing route towards such a uniform dispersion.

In addition to the tendency for particle agglomeration, the Y₂O₃ nanoparticles used in this study are expensive and require complicated and time intensive manufacturing steps. For example, the sol-gel method involves: (i) mixing of chemical precursors, typically metal salts; (ii) precipitation to form a gel; (iii) rinsing gel to remove salts; (iv) drying to obtain powders; (v) calcination of powders; and (vi) grinding or some other process operations.³⁴ Therefore, commercial production of oxide dispersions during MA, such as for Ni, Fe, and Al alloys, is typically achieved via in-situ oxidation.³⁵ 

To validate the concept of in-situ production of oxide particles, Bi₂Te₃–Y₂O₃ composites were made by internal oxidation. Fig. 11 shows the structural evolution during this procedure for a 15Y sample. First, the intermetallic Bi₂Te₃ was made by milling Bi and Te powders for 4 h. Next, Y powders were added to the formed compound, resulting in a composite of Bi₂Te_3−x and YTe₂ after a further 4 h of milling. Finally, water was added to displace Te from the YTe₂, forming a fine dispersion of Y₂O₃ particles, and returning Te to the matrix to regain proper stoichiometry in the Bi₂Te₃ phase.

The stability of the 15Y in-situ powders is compared in Fig. 12 to material made via the ex-situ incorporation of yttria nanoparticles described in Secs. III and IV, at the same nominal chemistry. The grain size, microstrain, and lattice c/a ratio are reported in the upper, middle, and lower panels. The grain size of the in-situ material shows improved thermal stability as displayed by a grain size of 56 nm when annealed at 530 °C, compared to 115 nm for the conventional 15Y powders. The improved thermal stability of the in-situ alloy is probably due to its having a smaller particle size; the estimated mean domain size of the Y₂O₃ phase from the XRD analysis was 3 nm, in comparison to about 20 nm in the commercial nanoparticles. It should be noted that the lattice parameters of the in-situ composite are highly distorted in the as-milled condition—as seen from the very low c/a ratio—which is likely due to remaining O and Y impurity atoms in the lattice. However upon annealing, the lattice parameters return to the literature value of Bi₂Te₃.

Another interesting point is the minor grain growth at temperatures below 250 °C, where the conventional composites showed enhanced grain growth over the unreinforced compound (cf. Fig. 6). At 180 °C, the grain size of the in-situ alloy grew by only 2 nm, compared to 21 nm in the case of the conventional composite. This result suggests that PSN was successfully suppressed in the in-situ alloy, not only because of the finer particle size of the dispersed yttria, but also because of the lack of large agglomerates that act as nucleation sites for PSN. The estimated dispersoid size of 3 nm is far below the critical particle diameters predicted by Eqs. (3) and (4).

The effect of a fine dispersion of nanoscale Y₂O₃ particles on the microstructural stability of nanocrystalline Bi₂Te₃ was investigated, across various particle volume fractions. The particles imparted an acceleration of grain growth at temperatures below about 250 °C, which transitioned to inhibition of grain growth at temperatures above this.

In the high temperature region, the composites retained increasingly finer grain structures than the unreinforced Bi₂Te₃ compound. The stabilization effect was retained up to near the compound melting point. Grain size appeared to scale with volume fraction according to an f ^−1/3 law, with a geometric constant of β = 1.6 for the highest annealing temperature, in agreement with existing theoretical and experimental data in the high volume fraction regime. These data support the use of Zener pinning to stabilize fine nanostructures in nanostructured thermoelectric compounds.

The acceleration of grain growth in composite materials at low temperatures was explained on the basis of particle-stimulated nucleation of recrystallization. By considering the competing driving forces for boundary migration in the case of the unreinforced compound and composite materials, recrystallization was shown to be thermodynamically favorable around the largest agglomerated particles but not the smallest, isolated ones. The analysis also suggested that control of the processing parameters to ensure well-dispersed, very fine nanoparticles below about ∼40–50 nm, would avoid particle-stimulated recrystallization, leading to finer and more homogeneous nanostructure. Our preliminary experiments using internal oxidation of yttria support this interpretation and also demonstrate a viable pathway to the production of such materials.

This material was based upon work supported as part of the Solid State Solar Thermal Energy Conversion (S3TEC) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001299.