In situ neutron scattering study of nanoscale phase evolution in PbTe-PbS thermoelectric material Free

Thermoelectric materials can directly convert between thermal and electrical energies with energy conversion efficiencies that are related to the dimensionless figure of merit, ZT = S²σT/(κ_e + κ_L), where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature, and κ_e and κ_L are electronic and lattice (phonon) thermal conductivities, respectively.¹ One successful strategy to improve the ZT is to reduce lattice thermal conductivities by introducing structural inhomogeneities such as superlattices,^2,3 nanoinclusions,^4,5 and nanoscale grain boundaries.⁶ A series of PbTe-based thermoelectric materials with high ZTs have been discovered in the past decade, including LAST (PbTe-AgSbTe₂),⁴ PbTe-PbS,^5,7,8 PbTe-PbSnS₂,^9,10 PbTe–SrTe,¹¹ PbTe-MgTe,¹² and PbTe-GeTe.¹³ A common characteristic shared by these materials is the limited solubility of the second phase in the PbTe matrix, which in turn enables the formation of nanostructures by means of spinodal decomposition and/or nucleation and growth of precipitates.

PbTe-PbS with good thermoelectric properties was first reported by Androulakis and coworkers, who showed that a ZT of 1.5 could be achieved at 642 K in PbTe-8 mol. %PbS.⁵ Using transmission electron microscopy and scanning electron microscopy, Girard et al.⁷ observed nano-scale (c.a. 10 nm) and submicron-scale (c.a. 100 nm) second phase particles in annealed samples. However, these features could not be detected by powder x-ray diffraction (XRD) in either the quenched or the annealed conditions.⁷ A more thorough study was performed by the same group,⁸ who examined PbTe-PbS powders using in situ synchrotron x-ray diffraction during heating. In the PbTe-8%PbS material, PbS first precipitated around 498 K and then re-dissolved and disappeared at temperatures higher than 773 K.⁸ On the other hand, an isothermal hold at 500 K resulted in continuous increases of the lattice parameter of the matrix implying precipitation of the PbS second phase.

In this study, we examined the PbTe-8 mol. % PbS material system using in situ neutron diffraction and small angle neutron scattering techniques to quantify the nanostructural evolution with respect to their size and weight fraction. These results not only help us understand the behavior of the nanostructures in the PbTe-PbS system but also provide insights for the design and processing of other nanostructured thermoelectric materials.

The starting material PbTe-8%PbS was obtained from melt casting. Samples were reacted at 1323 K in vacuum-sealed ampoules and then slowly cooled to room temperature with an isothermal hold at 773 K for 10 h. Cast ingots were then ball milled in Ar filled jars to obtain powders with an average particle size of 6 μm. Detailed information regarding sample preparation can be found elsewhere.¹⁴ 

The neutron diffraction experiment was conducted using the VULCAN instrument at the Spallation Neutron Source, Oak Ridge National Laboratory (ORNL).¹⁵ The powder sample was sealed in a vanadium tube and placed in a vacuum furnace. Heating and cooling rates were kept at 3 K/min. Diffraction experiments were carried out between room temperature (∼300 K) and 663 K. Diffraction data were collected at 30 K temperature interval after an isothermal hold of at least 30 min to ensure that the sample had reached thermal equilibrium. During cooling, data collection was stopped at 393 K because the cooling rate became very slow as the furnace approached room temperature. The diffraction data were analyzed by Rietveld refinement with the GSAS (General Structure Analysis System) software.¹⁶ 

Small Angle Neutron Diffraction (SANS) measurements were performed using the general purpose-SANS (CG2) beamline of the High Flux Isotope Reactor (HFIR) at ORNL. A heating rate of 3 K/min was used. Data were collected after reaching equilibrium at each of the targeted temperatures. After being corrected for detector response, dark current, and background scattering, the SANS data were azimuthally averaged to produce an intensity versus scattering vector or I(Q) versus Q plot. The scattering vector data were placed on an absolute scale (nm⁻¹) using measurements of the direct beam.

Neutron diffraction profiles collected at different temperatures are shown in Figure 1. Prior to thermal annealing, only PbTe peaks (cubic, Fm-3m) can be identified (Figure 1(a)), although it was expected that the slow cooling and isothermal hold at 773 K during ingot processing would generate PbS nanostructures by a nucleation and growth mechanism.^5,7,8 However, it is possible that the neutron diffraction technique may not be able to detect the PbS nanostructures if the size or the number density of the nanostructures was very small. As previously mentioned, Girard and coworkers⁷ could not identify the PbS phase in annealed PbTe-8%PbS powder using x-ray diffraction, although the PbS phase was detected via transmission electron microscopy.

After being annealed at 663 K in a vacuum, several small peaks emerged in the neutron diffraction profiles at 1.72 Å, 2.10 Å, and 2.98 Å (Figure 1(b)), which correspond to the (311), (220), and (200) planes of the PbS phase (cubic, Fm-3m) respectively. These PbS peaks first appeared around 480 K upon heating and remained visible after the specimen was heated to 663 K and then cooled to 393 K (Figure 1(c)). Using synchrotron x-ray diffraction, Girard et al.⁸ also observed the in situ formation of PbS when annealing the PbTe-8%PbS sample. However, Girard et al.⁸ did not report x-ray diffraction data during cooling. Results of the current neutron diffraction study showed that PbS formed during annealing remained detectable after cooling to 393 K. It is also worth noting that after heat treatment, the widths of the PbTe peaks (Figure 1(c)) were reduced, which could be a result of annealing of defects (e.g., dislocations) during the heat treatment.

The lattice parameter of the matrix phase (PbTe rich), a_Matrix, was determined as a function of temperature using Rietveld refinement. Figure 1(d) shows the fitting results to the experimental data of the as-milled powder prior to heating using the Rietveld refinement, where all peaks are attributed to the PbTe phase. As shown in Figure 2(a), before annealing, a_Matrix = 6.425 ± 0.003 Å, which is smaller than the lattice parameter of the pure PbTe at 300 K (a_PbTe = 6.462 Å).¹⁷ Assuming the matrix phase is an ideal solid solution between PbTe and PbS (a_PbS = 5.936 Å),¹⁸ Vegard's law predicts a molar fraction of PbS in the matrix phase of approximately 7 mol. % (supplementary material, Figure S1), which is slightly smaller than the nominal molar ratio of PbS in PbTe-8 mol. % PbS.

With the temperature being increased, a_Matrix initially increased linearly. The dotted line in Figure 2(a) represents a linear fit to the low temperature data during heating, and its extrapolation to higher temperatures (Figure 2(a)) indicates the predicted behavior of a_Matrix at elevated temperatures if no phase separation had occurred (that is, the lattice parameter changed by thermal expansion effects only). However, a_Matrix rapidly increased at approximately 480 K, which corresponded to the onset temperature of PbS precipitation (Figure 1(c)), indicating that (in addition to thermal expansion effects) the lattice parameter of the matrix increased due to the precipitation of the PbS nanostructure. Since a_PbS is smaller than a_PbTe, when PbS precipitates out of the matrix, a_Matrix should increase. Above 570 K, the difference between the measured data and the dotted line (thermally induced lattice expansion only) decreased (Figure 2(a)), which is consistent with the onset of re-dissolution of PbS into the matrix. Using in situ x-ray diffraction, Girard et al.⁸ also discovered the re-dissolution of the PbS phase and noted that the PbS peaks completely disappeared above 773 K.⁸ 

During cooling, a_Matrix initially followed the heating curve and then decreased linearly below 570 K (Figure 2(a)). Although the data collection was stopped at 393 K, it is expected that a_Matrix would decrease linearly to room temperature following the dashed line in Figure 2(a). At room temperature, a_Matrix is projected to be about 6.450 Å, corresponding to a composition of PbTe-2 mol. %PbS (supplementary material, Figure S1). The coefficient of thermal expansion (CTE) of the linear portion of the cooling curve was 2.19 ± 0.03 × 10⁻⁵/K, which is similar to the CTE values reported by Ni et al.¹⁴ For bulk samples with the same composition, Ni and co-workers¹⁴ used thermomechanical analysis and found CTE values varied between 2.14 × 10⁻⁵/K and 2.19 × 10⁻⁵/K for the temperature interval between room temperature and 773 K. For powder samples, high temperature x-ray diffraction (XRD) work by Ni et al.¹⁴ yielded CTE values of 2.09 × 10⁻⁵/K to 2.17 × 10⁻⁵/K between room temperature and 663 K. Thus, the CTE values in the literature¹⁴ determined by both thermomechanical analysis and high temperature XRD agree relatively well with CTE values found in this study. For comparison purposes, the temperature dependent lattice parameter of pure PbTe is also plotted as the solid line in Figure 2(a) using the CTE of pure PbTe at 300 K (2.04 × 10⁻⁵/K).¹⁹ 

Based on the Vegard's law, the compositional change of the matrix phase during annealing is illustrated in Figure 2(b). During heating, the molar fraction of the PbS dissolved in the matrix initially slowly decreased with increasing temperature, while the rate of decrease accelerated above 480 K. The concentration of dissolved PbS in the matrix was a minimum at 570 K and increased upon further heating. During cooling, the concentration of the dissolved PbS in the matrix initially decreased and then slightly increased below 500 K (Figure 2(b)).

The lattice parameter of the second phase, a_Second, was plotted in Figure 2(c). At room temperature, a_Second = 5.942± 0.001 Å, which is greater than the pure PbS (5.936 Å)¹⁸ and corresponds to a composition of PbS-1.2%PbTe (supplementary material, Figure S1). All data collected during heating and cooling in this study follow the same linear trend with a CTE of 2.35 ± 0.04 × 10⁻⁵/K, implying that the second phase remained stable after precipitation. Figure 2(c) also shows the thermal expansion behavior of the pure PbS as estimated using the room temperature lattice parameter and the room temperature CTE value of 2.01 × 10⁻⁵/K for pure PbS.²⁰ 

Using Rietveld refinement, the observable weight fraction of the matrix phase was also obtained. As shown in Figure 2(d), the weight fraction of the matrix phase started to decrease at 480 K, reached its minimum around 570 K, and then slightly increased upon further heating. During cooling, the weight fraction of the matrix continued to decrease, which is estimated to be 98 wt. % at room temperature (Figure 2(d)). The weight fraction of the second phase was obtained by subtracting the weight fraction of the matrix phase from 100%. The weight fraction of the detectable second phase was estimated to be approximately 2 wt. % after cooling to room temperature (Figure 2(d)). It is important to note that amorphous and nanocrystalline (with crystallites ≲5 nm) phases are extremely difficult to account for by Rietveld analysis of diffraction data.

The evolution of the PbS nanostructure is of practical interest since it may be related to the thermoelectric performance of this material. Androulakis and coworkers⁵ found that the PbTe-8%PbS material possessed very low lattice thermal conductivity, which could be attributed to the nanostructure-induced phonon scattering between the PbTe-rich matrix and the PbS nanoinclusions. At room temperature, the lattice thermal conductivity of PbTe-8%PbS was approximately 0.4 W/m K, which is 72% lower than that of the pure PbTe. With the temperature being increased from room temperature to approximately 480 K, the lattice thermal conductivity slightly decreased to ∼0.3 W/m K, which then showed a slight increase upon further heating. At 670 K, the lattice thermal conductivity was approximately 0.5 W/m K.⁵ Although Androulakis et al.⁵ did not provide detailed explanation, we suspect that the increase in the lattice thermal conductivity above 480 K is related to the redissolution of PbS nanostructures due to decreased phonon scattering at the PbTe matrix/PbS nanostructure interface.

In the work by Girard and coworkers,⁷ the electrical conductivity of the PbTe-8%PbS material was found to generally decrease with increasing temperature between 300 K and 670 K. During the initial heating cycle, the electrical conductivity plateaued between 400 K and 500 K. Girard and coworkers⁷ attributed this behavior to a rapid increase in the carrier concentration in the same temperature range as a result of formation of the PbS precipitates in the same temperature range.⁷ In contrast, no plateau was observed during the second heating/cooling cycle; instead, the electrical conductivity decreased monotonically with increasing temperature. In contrast, the lattice thermal conductivity rapidly decreased during the first heating cycle between room temperature and ∼500 K, followed by a slight increase between 500 K and 670 K.⁷ This phenomenon was not explained⁷ but may be related to the redissolution of the PbS nanostructures into the matrix.

While neutron diffraction provides useful information on the composition and weight fraction of the second phase, in situ SANS can help one to understand the size evolution of the nanostructures. Figure 3(a) shows the scattering intensity I(Q) as a function of the scattering vector, Q, at different annealing temperatures. Two regions can be identified in the I(Q) versus Q plots: Region A in the low-Q range corresponds to structures with a relatively large size and Region B in the high-Q range corresponds to smaller features.

For all data collected in this study, scattering in Region B (Figure 3(b)) increased with increasing annealing temperature. At 600 K, a scattering “shoulder” appeared, which moved towards the low-Q region with increasing temperature. In this case, the position of the scattering shoulder is inversely proportional to the size of the structure. The increase in scattering intensity, the formation of the scattering shoulder, and the shift of the scattering shoulder to the low-Q region all imply that annealing resulted in increased structural inhomogeneity in the sample.²¹ On the other hand, the scattering in Region A decreased only slightly with increasing temperature without significant change in position of the inflection point (Guinier region), and thus the thermal annealing did not significantly affect the size of the larger structures.

The existence of two types of structures with different length scales (Figure 3(a)) led to the selection of the Guinier-Porod model²² to analyze the neutron data. Two different radii of gyration, i.e., R_g1 and R_g2 where R_g1 > R_g2, were used in the analysis. The sum of two Guinier-Porod model functions (GP1 and GP2) were used to fit the SANS curves at different annealing temperatures (see supplementary material, Figure S2 and Table S1 for fitted curves and fitting parameters). Figures 3(c) and 3(d) depict Rg₁ and Rg₂ as a function of the annealing temperature. Rg₁, which models the radius of gyration of the larger nanostructure (roughly on the order of 100 nm), was relatively stable during the annealing experiment. Scanning electron microscopic (SEM) examination of the as-milled powder sample showed a number of particles on the order of 100 nm with a composition similar to the matrix (supplementary material, Figures S3(a) and S3(b)). These particles were likely small powder particles generated by the ball milling process. On the other hand, there also exist a very small number of nanoinclusions on the order of 100 nm that have a different composition from the matrix and may be PbS-rich second phase particles (supplementary material, Figures S3(c) and S3(d)). In either case, the SANS data indicated that the size of these nanoscale features was not significantly affected by the thermal annealing. In contrast to the insensitivity of the R_g1 value to thermal annealing, the size of the smaller nanostructures, Rg₂, enlarged significantly during the annealing process, namely, from approximately 5 nm before heat treatment to around 25 nm following an annealing at 650 K. No further change in the scattering intensity was detected during cooling; thus, the size and amount of the nanostructures remained relatively unchanged in Region B, the high-Q range corresponding to the smaller nanostructures.

For the as-milled powder without thermal annealing, the SANS and SEM results indicated that the PbS nanostructures were either very small (<5 nm, Figure 3(d)) or very few (only a very small number of PbS inclusions on the order of 100 nm could be seen). The low number density of nanoinclusions makes them extremely difficult to detect by bulk diffraction techniques. After annealing, the size of the smaller PbS nanostructures increased by a factor of five, i.e., from 5 nm to 25 nm (Figure 3(d)), implying a two orders of magnitude increase in volume fraction, which rendered the nanoparticles visible via neutron diffraction. Meanwhile, the weight fraction of the second phase increased from undetectable to approximately 2 wt. % after annealing.

In summary, the size, composition, and weight fraction of nanophases, as well as the thermal evolution of these properties, are important information to understand the behavior of nanostructured thermoelectric materials, especially at temperatures relevant to their in-service conditions. This study utilized in situ neutron diffraction and small angle scattering techniques to examine the nanophases in the PbTe-8%PbS thermoelectric material between room temperature and 663 K. The temperature-induced nanostructural evolution is illustrated in Figure 4, namely, below 500 K, the population of the small nanoinclusions (∼5 nm) remains stable while between 500 K and 600 K, the number of nanoinclusions increased with limited growth in size. Above 600 K, the size of the nanoinclusions grows significantly while the number density of nanoinclusions decreased. After the heat treatment, the size of PbS nanostructures grew to approximately 25 nm, which accounts for ∼2% of the total material weight.

One of the advantages of neutron scattering over other in situ techniques such as high-temperature TEM and x-ray diffraction is the ability to examine bulk samples,²³ enabling simultaneous measurements of the evolution of phases and nanostructures as well as changes in the temperature-dependent thermoelectric properties. Future work will be directed towards this type of experiment aiming to obtain correlated information on focus on the correlation between structural evolution and transport property changes for PbTe-PbS and other nanostructured thermoelectric materials.

See supplementary material for details of the Guinier-Porod fitting and SEM micrographs of the nanoparticles and nanoinclusions.

The authors acknowledge the financial support from Temple University faculty start-up fund and the Department of Energy, “Revolutionary Materials for Solid State Energy Conversion Center,” an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0001054. Research conducted at ORNL's Spallation Neutron Source and High Flux Isotope Reactor was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. The authors also thank Dr. Dong Ma and Ms. Hui Yang of Oak Ridge National Laboratory for their technical assistance.