Influence of Phase Separation and Spinodal Decomposition on

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Influence of Phase Separation and Spinodal Decomposition on Microstructure of Mg2Si1−xSnx Alloys

Andrey Sizov,*,† Hazel Reardon,‡ Bo B. Iversen,‡ Paul Erhart,§ and Anders E. C. Palmqvist† †

Department of Chemistry and Chemical Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark § Department of Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden ‡

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S Supporting Information *

ABSTRACT: Mg2Si1−xSnx alloys with nominal values of x [0.03:0.18] were synthesized at 780 °C by solid-state reaction from Mg2Si and Mg2Sn and subsequently annealed at either 680 or 580 °C. Their microstructure was investigated by X-ray diffraction using the Rietveld method. Depending on the treatment temperature and the nominal composition, the solid solutions split into different Si- and/or Sn-rich Mg2Si1−xSnx phases. Traces of spinodal decomposition were observed for the samples with a low Sn content independent of treatment temperature due to the limited diffusion kinetics when entering the miscibility gap. A similar effect was observed when applying a higher cooling rate to the samples with higher Sn concentration. In this case, the samples experience thermodynamic spinodal decomposition being located in the spinodal region sufficiently long time at higher temperatures. Samples treated in the miscibility gap showed an agreement of the Si-rich binodal line with calculated phase diagrams. However, the Sn-rich binodal line stays undefined, perhaps due to grain boundary pinning of diffusing atoms. The study elucidates the possibility of tailoring the microstructure of magnesium silicide-stannide alloys utilizing merely judiciously designed heat treatment protocols. A particular attention is brought to spinodal decomposition, which has the potential to reduce the lattice thermal conductivity.

1. INTRODUCTION

A similar approach can in principle be realized in the Mg2Si−Mg2Sn system. Because the lattice mismatch between Si-rich and Sn-rich phases is less than 6%, it is expected that nearly coherent (endotaxial) interphases between these phases can be formed. Moreover, the significant difference in atomic masses between Si and Sn as well as atomic disorder induce scattering of phonons. In addition, the thermal transport can be suppressed and the power factor enhanced by utilizing quantum confinement effects.10,11 To illustrate this, the scattering of phonons increases if the thickness of the alternating phases (in socalled superlattices) is less than the mean free path of phonons, i.e., in the order of 1−100 nm.12 Because the manufacturing of superlattice materials is restricted to components of small size, spinodal decomposition can instead be utilized to achieve a similar effect in bulk materials.13,14 An alloy decomposes spinodally in the area of a miscibility gap, where the second derivative of the free energy vs composition (calculated for each temperature) is negative; if the second derivative is positive, decomposition should follow the mechanism of nucleation and growth. While the microstructure formed during nucleation and growth consists of “islands” of one phase in a matrix of another, spinodal

In the scientific field of thermoelectricity, Mg2Si1−xSnx alloys attract attention as abundant and low-cost materials. In addition, they are nontoxic, oxygen resistant at temperatures up to 350−400 °C,1 possess good mechanical properties, and have low density. They show fairly high dimensionless figure of merit zT = S2σ/(λl + λe), where S is the Seebeck coefficient, σ is the electrical conductivity, λl and λe are the lattice and electrical components of the thermal conductivity, respectively. For instance, zT values up to 1.4 have been reported, e.g., Bior Sb-doped Mg2Si0.4Sn0.62,3 and Mg2Si0.3Sn0.665Bi0.035.4 It was argued that these high zT values were obtained due to the unusual microstructures (Sn-rich clusters in a Mg2Si matrix), which were formed on cooling from a single-phase region to a miscibility gap. However, the formation of the clusters was not fully understood due to both an uncertainty in the available phase diagrams5−7 and a lack of information about diffusion kinetics of Si and Sn atoms in Mg2Si1−xSnx alloys. As was demonstrated by Biswas et al.8 on a PbTe-SrTe system, endotaxial precipitations (clusters) and atomic mass fluctuations impede the propagation of heat, while leaving charge carrier mobilities almost unaffected. This results in the reduction of the lattice component of the thermal conductivity while keeping the thermoelectric power factor (S2σ) virtually unimpeded.9 © XXXX American Chemical Society

Received: January 3, 2019 Revised: June 22, 2019

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DOI: 10.1021/acs.cgd.9b00013 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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samples were ground and diffraction measurements were carried out on a Bruker D8 with Cu Kα radiation (using a Si single crystal monochromator). The measurements were performed at room temperature in normal air atmosphere. Data were analyzed using the Rietveld method by TOPASAcademic v.5 software (Bruker). The Rietveld refinement was carried out based on the antifluorite structure of Mg2Si1−xSnx, with the space group Fm3m (with Mg at 8c (1/4, 1/4, 1/4) and Si/Sn sharing 4a (0, 0, 0) sites). Relatively small amounts of free Si and Sn were identified in certain samples with space groups Fm3m and I41/amd, respectively. An instrument contribution of the D8 diffractometer to the peak profiling was corrected. A simple axial model (fitted to a Gaussian function) was utilized to describe the peaks. The background was subtracted utilizing a fifth-order polynomial fitting. The background, unit cell, scale factor, temperature factor, and peak profile parameters were refined, while the atomic position parameters were held fixed. Refinement of occupancy factors for Si and Sn in Sn-rich Mg2Si1−xSnx yields unphysical results, perhaps due to weak data or inhomogeneity of the samples, or local atomic ordering on the nanoscale. Therefore, the occupancy factor for tin, occ(Sn), was calculated according to the Vegard’s law,17 i.e., from the interpolation between the unit cell parameters of pure Mg2Si (PDF 00-035-0773) and Mg2Sn (PDF 00007-0274) phases. The occupancy factor for Si in Mg2Si1−xSnx was set to 1 − occ(Sn).

decomposition allows the formation of continuous endotaxial lamellae-like clusters with an alternation period in the nanometer size range.15 Utilizing spinodal decomposition in materials production is therefore an interesting approach to manufacturing advanced thermoelectric materials. However, such fine microstructure could be unstable during extended thermal cycling at elevated temperatures. The stability of the microstructure can be increased by reducing operational temperature of the device or by utilizing a pinning effect of certain dopants.16 The phase separation phenomena in Mg2Si1−xSnx alloys is not yet fully understood. This study aims at analyzing the conditions required to achieve microstructures of interest for thermoelectric applications. Of particular attention are conditions that promote controlled phase separation and spinodal decomposition of these alloys.

2. EXPERIMENTAL SECTION 2.1. Sample Preparation. Five different Mg2Si1−xSnx alloys with nominal values of x = 0.03, 0.06, 0.08, 0.13, and 0.18 were synthesized by solid-state reaction from in-house made Mg2Si and Mg2Sn by mixing the two phases in stoichiometric amounts. Mg2Si and Mg2Sn were prepared via direct solid-state reaction from the constituent metals, Mg (Aldrich, 99.9%), Si (Aldrich, 99.95%), and Sn (Alfa Aesar, 99.9%). All components were ball milled (Retsch) at 15 Hz for 60 min before heat treatments using a single ball and container of zirconia; the particle size distribution (in wt %) after milling was approx 12%, 28%, 35%, and 25% for 160−80, 80−50, 50−20, and −20 μm, respectively. The powder mixtures were loaded into alumina crucibles and reacted in a tube furnace in an Ar atmosphere with 10% H2, first at 780 °C for 600 min for homogenization in the assumed single-phase region, and then either at 680 °C for 1200 min or at 580 °C for 2400 min (Figure 1) for annealing. The dwelling times were chosen based on the prestudy presented in Figures S1 and S2 in the Supporting Information. The cooling rate was approximately 7 K/ min. The samples used for studying the effect of cooling rates on the microstructure were sintered in a spark plasma sintering (SPS) apparatus (Dr. Sinter, model SPS-5.40MK-IV). Some of these samples were subjected to high cooling rates (approximately 140 K/min) in the SPS apparatus directly after sintering. 2.2. Structural Characterization and Analysis. The crystal structure of the samples was investigated by powder XRD. The

3. RESULTS AND DISCUSSION The goal of this study is to correlate the influence of heat treatment protocols with the composition of Mg2Si1−xSnx alloys. Because the position of the binodal curve in the available phase diagrams5−7 differs, a set of experiments (black squares in the phase diagram plotted in Figure 1) was conducted with the aim to cover the possible single-phase region and miscibility gap in the Si-rich region. Depending on in which region the samples are treated, it is expected to result in different compositions and microstructures, which are formed either via spinodal decomposition or by phase separation via the mechanism of nucleation and growth. The samples were kept at the selected temperatures for a sufficiently long time to bring the system into thermodynamic equilibrium. Thus, for samples inside the miscibility gap, the compositions of the formed phases are expected to follow the binodal curve in both the Si- and Sn-rich regions of the phase diagram. 3.1. Composition after Heat Treatment at 680 °C. The XRD patterns of the powder samples, which were homogenized at 780 °C and then slowly cooled to 680 °C and kept there for 1200 min, are presented in Figure 2a. A small amount of free Si was observed in all diffraction patterns, while free Sn was only observed in the patterns of Mg2Si0.87Sn0.13 and Mg2Si0.82Sn0.18 (Table 1). The presence of free Si and Sn could be due to evaporation of Mg during the heat treatment. No Sn-rich phase was found in the samples Mg2Si0.97Sn0.03, Mg2Si0.94Sn0.06, and Mg2Si0.92Sn0.08, which confirms that these samples fall in the single-phase region. This contrasts with samples Mg2Si0.87Sn0.13 and Mg2Si0.82Sn0.18, which appear to have been treated in the miscibility gap and show the presence of both Si-rich and Sn-rich phases. A closer examination of the individual XRD peaks, as shown in the magnification of the (220) peaks in Figure 2b, reveals that the three samples with lowest Sn content all contain a couple of Si-rich phases with slightly different elemental compositions, although the Rietveld analysis failed to resolve the second phase in the Mg2Si0.92Sn0.08 sample. In contrast, the sample with the highest Sn amount, Mg2Si0.82Sn0.18, showed two Sn-rich phases of slightly different elemental compositions.

Figure 1. Existing quasibinary phase diagram Mg2Si−Mg2Sn5−7 and indicators of the samples synthesized in the current article. Blue solid curve shows approximately shape of the spinodal region according to Viennois et al.7 B

DOI: 10.1021/acs.cgd.9b00013 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Figure 2. XRD patterns of the Si-rich samples homogenized at 780 °C and then treated at 680 °C: (a) 2θ = 20−50° (red and blue vertical dashed lines represent positions of the reflections of pure Mg2Sn and Mg2Si, respectively); (b) magnification of the (220) reflection.

When x exceeds 0.08, only a single solid solution of the Sirich phase is present, and the Sn-rich phase can also be observed; the amount of the Sn-rich phase grows with increasing x. At first sight, it seems that both samples Mg2Si0.87Sn0.13 and Mg2Si0.82Sn0.18 were treated in the miscibility gap at 680 °C. However, if this is true, compositions of the Sn-rich phases in these samples should be the same as in the case of the samples treated at 580 °C, which formed the Sn-rich phases of same compositions (cf. next section). Therefore, we suggest that the sample Mg2Si0.82Sn0.18 was treated inside the miscibility gap at 680 °C, while the sample Mg2Si0.87Sn0.13 was still located in the single-phase region at 680 °C and underwent phase separation on cooling. This statement can also be confirmed by the fact that Mg2Si0.82Sn0.18 contains two Sn-rich phases instead of a single Sn-rich phase, which was formed in Mg2Si0.87Sn0.13. Because Mg2Si0.82Sn0.18 was treated in the miscibility gap, one Sn-rich phase appeared while treating the sample at 680 °C and another Sn-rich phase could be formed on cooling, similarly to Mg2Si0.87Sn0.13. The slow cooling rate applied to the samples allows to suggest that the phase separation followed the mechanism of nucleation and growth in both cases. The overall amount of tin was estimated by summarizing the estimated tin amount in each respective phase. As it can be seen in Table 1, the analysis shows slightly higher overall Sn amounts for all samples. Regarding Mg2Si0.87Sn0.13 and Mg2Si0.82Sn0.18, a higher deviation in the overall Sn amount from the nominal value might be due to strain in the Si- and Sn-rich phases because these samples underwent a complex phase separation on cooling. The broadening of the Sn-rich reflections could also stem from the small size of the precipitates formed on cooling. Alternatively, more Sn-rich phases could be present in each sample, however, adding additional phases into the Rietveld refinement does not improve the matching of the overall Sn amount with the nominal value. Thus, it is possible to vary the microstructure of Mg2Si1−xSnx alloys by changing their composition, i.e., from the spinodal decomposition (when x ≤ 0.08) to the phase separation via nucleation and growth (when 0.13 ≤ x ≤ 0.18) at a temperature of 680 °C using a slow cooling rate. 3.2. Composition after Heat Treatment at 580 °C. By analyzing XRD diffraction data presented in Figure 3a, it was found that the samples treated at 580 °C form different

Table 1. Summary of Results from Rietveld Refinement of Mg2Si1−xSnx Alloys treated at 680 °C nominal composition

phases composition

phase amount (mol %)

overall Sn amount (at. %)

Mg2Si0.97Sn0.03

Mg2Si0.987Sn0.013 Mg2Si0.944Sn0.056 Si

29.6 66.0 4.4

4.1

Mg2Si0.94Sn0.06

Mg2Si0.977Sn0.023 Mg2Si0.926Sn0.074 Si

11.2 84.9 3.9

6.5

Mg2Si0.92Sn0.08

Mg2Si0.911Sn0.089a Si

93.1 6.9

8.5

Mg2Si0.87Sn0.13

Mg2Si0.888Sn0.112 Mg2Si0.150Sn0.850 Si Sn

87.0 6.9 5.2 0.8

16.4

Mg2Si0.82Sn0.18

Mg2Si0.880Sn0.120 Mg2Si0.095Sn0.905 Mg2Si0.227Sn0.763 Si Sn

80.7 8.8 0.8 8.5 1.1

19.4

a The second Si-rich phase of sample Mg2Si0.92Sn0.08 was not possible to refine. Lattice parameters and Rwp factors are presented in Table S1 of Supporting Information.

The amount of the Si-rich phase with a higher Si content decreases with increasing x in Mg2Si1−xSnx (Table 1), whereas the amount of Sn in this phase also slightly increases with x. When x equals 0.08, the Si-rich phase with a higher Si content is barely visible and the Rietveld analysis fails to converge. The presence of two Si-rich phases with similar compositions in the samples with 0.03 ≤ x ≤ 0.08 indicates traces of spinodal decomposition, as also observed by Kim et al.14 This decomposition can be explained by the rapid demixing of the single solid solutions, which enter the miscibility gap region at lower temperatures, at which Sn and Si atoms have lower mobility. Hence, the atoms cannot diffuse long distances to form nuclei of the Sn-rich phase, which is why the materials decompose spinodally instead. C

DOI: 10.1021/acs.cgd.9b00013 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Figure 3. XRD patterns of the Si-rich samples homogenized at 780 °C and then treated at 580 °C: (a) 2θ = 20−50° (red and blue vertical dashed lines represent positions of the reflections of pure Mg2Sn and Mg2Si, respectively); (b) magnification of the (220) reflection.

phases in the samples treated at 680 °C. This could be explained by the increased dwelling time or a higher content of free Si, which could influence the demixing process.14 For the sample Mg2Si0.92Sn0.08, the treatment at 580 °C results in small amounts of two Sn-rich phases in contrast to when the sample was treated at 680 °C. The Sn-rich phases can barely be observed in the enlarged section of reflection (220) depicted in Figure 3b. This phenomenon is also accompanied by the decrease in the right shoulder of the Sirich peak. This can be explained by phase separation switching from the spinodal mechanism to the mechanism of nucleation and growth when lowering the treatment temperature from 680 to 580 °C. The composition of the primary Sn-rich phase (at ∼38.4°) in Mg2Si0.92Sn0.08 is approximately Mg2Si0.33Sn0.67, and it does not change with increasing x. Moreover, because the amount of this phase increases with x, one can deduce that the samples with 0.08 ≤ x ≤ 0.18 were treated in the miscibility gap at 580 °C. The presence of the secondary Snrich phase (at ∼37.8°) of minor quantities in the samples with 0.08 ≤ x ≤ 0.18 could be a result of additional phase separation on cooling from 580 °C. The phase separation according to the mechanism of nucleation and growth in the samples with 0.08 ≤ x ≤ 0.18 is expected due to the slow cooling rate from the single-phase region to 580 °C. Overall Sn contents in the samples are also slightly higher than the nominal composition. However, it matches well for Mg2Si0.87Sn0.13 and Mg2Si0.82Sn0.18 treated at 580 °C. Taking into account the reduction of diffusion kinetics at lower annealing temperature, these samples probably do not undergo additional phase separation on cooling, and hence the Sn amounts in these samples can be correctly estimated with the Rietveld refinement. Thus, the reduced treatment temperature (from 680 to 580 °C) brings Mg2Si0.87Sn0.13 and Mg2Si0.92Sn0.08 to the miscibility gap (most likely to the binodal region because these points should be located close to the single phase region in the phase diagram), resulting in the samples demixing differently and forming different microstructures at the two different temperatures. The sample Mg2Si0.82Sn0.18 obtains different elemental composition of the Sn-rich phase formed at 580 °C compared to 680 °C due to the change in solubility limits of Si- and Snrich phases with temperature.

microstructures than the samples treated at 680 °C. Free Si is still present in all samples, and this amount does neither change with the decreased treatment temperature nor with the increased dwelling time. Interestingly, no free Sn phase was found in the samples, which, in fact, could be an effect of either the changed temperature or dwelling time. The compositions of the Si-rich phases in the samples with x ≤ 0.06 treated at 580 °C are identical to the compositions of the phases formed in the samples treated at 680 °C (Tables 1 and 2), which indicates that they were also treated in the single-phase region at 580 °C and also formed spinodal microstructures. However, the amounts of Si-rich phases in the samples treated at 580 °C differ from the amounts of these Table 2. Summary of Results from Rietveld Refinement of Mg2Si1−xSnx Alloys Treated at 580 °Ca nominal composition

phase composition

phase amount (mol %)

overall Sn amount (at. %)

Mg2Si0.97Sn0.03

Mg2Si0.988Sn0.012 Mg2Si0.958Sn0.062 Si

41.8 48.9 9.2

3.5

Mg2Si0.94Sn0.06

Mg2Si0.975Sn0.025 Mg2Si0.927Sn0.073 Si

8.7 87.6 3.7

6.6

Mg2Si0.92Sn0.08

Mg2Si0.917Sn0.083 Mg2Si0.331Sn0.669 Mg2Si0.169Sn0.831 Si

93.2 0.8 0.4 5.6

8.6

Mg2Si0.87Sn0.13

Mg2Si0.922Sn0.078 Mg2Si0.328Sn0.672 Mg2Si0.110Sn0.890 Si

85.0 9.1 0.4 5.5

13.1

Mg2Si0.82Sn0.18

Mg2Si0.901Sn0.099 Mg2Si0.331Sn0.669 Mg2Si0.108Sn0.892 Si

81.4 14.9 0.2 3.6

18.2

a

Lattice parameters and Rwp factors are presented in Table S2 of Supporting Information. D

DOI: 10.1021/acs.cgd.9b00013 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Figure 4. Available phase diagrams5−7 of Mg2Si−Mg2Sn and formed phases in the samples of the current work, which were treated inside the miscibility gap, i.e., Mg2Si0.92Sn0.08, Mg2Si0.87Sn0.13, and Mg2Si0.82Sn0.18. Gray solid oval encloses the starting point for these samples. Black solid and blue solid curves show binodal and spinodal lines according to Viennois et al.7 Gray dashed oval encloses secondary Sn-rich phases of a minor quantity.

3.3. Establishment of the Binodal Curve Position. The position of the binodal curve is important to establish to enable designing heat treatment protocols to achieve desired microstructures.15 For instance, the binodal curve is utilized to determine the spinodal curve, below which clusters of another phase may grow. Furthermore, the spinodal decomposition may occur if the single solid solution quickly passes the binodal region so that the clusters of other phases cannot be formed. Because the dwelling time at 680 and 580 °C was chosen to bring the samples into thermodynamic equilibrium, it is possible, to a certain extent, to estimate the position of the binodal curve. In addition, the use of low energy ball milling when preparing the samples, the homogenization at a temperature close to the solidus line, as well as the long treatment time employed are all factors that contribute to allowing us to consider that the binodal line should be based merely on chemical equilibrium (without elastic contribution coming from the strain between Sn- and Si-rich phases, which suppresses the miscibility gap18). However, a low cooling rate might distort the results because an additional phase separation could occur on cooling. Compositions of the analyzed phases in the samples of the current work, which were treated inside the miscibility gap, are marked in Figure 4. The samples treated inside the binodal region, as discussed in previous sections, i.e., with 0.08 ≤ x ≤ 0.18, tend to form Sirich phases along the binodal curve calculated by Viennois et al.7 A slight mismatch of the acquired Si-rich phases with the proposed solubility limit of Sn at 680 °C is possibly caused by the additional phase separation on cooling. By comparing XRD results presented in Figure 2 and 3, the binodal curve in the Si-rich region can also be assessed by looking at transitions: (a) between temperatures 680 and 580 °C at x(Sn) = 0.08; b) between Sn atomic fractions 0.18 and 0.13 at 680 °C. Because the sample Mg2Si0.92Sn0.08 spinodally decomposes at 680 °C but forms a very small amount of the Sn-rich phase at 580 °C, it is suggested that the binodal curve passes slightly above 580 °C at x(Sn) = 0.08. Unlike the samples with higher x, Mg2Si0.92Sn0.08 treated at 680 °C could not form Sn-rich phases on cooling. This, apparently, due to insufficient time spent in the binodal region at the temper-

atures, where the mobility of atoms was still high enough to allow diffusion at relatively long distances. In addition, because the samples Mg2Si0.87Sn0.13 and Mg2Si0.82Sn0.18 treated at 680 °C form an Sn-rich phase of different compositions (unlike the samples with the same initial compositions treated at 580 °C), it is expected that the binodal curve in the Si-rich area passes at the temperature 680 °C at x(Sn) slightly higher than 0.13. Thus, these findings are also close to the Si-rich binodal curve suggested by Viennois et al.7 Contradictory to the Si-rich phases, the formed Sn-rich phases deviate greatly from the binodal curve presented by Viennois et al.7 and other references.5,6 This could potentially come from the utilized Vegard’s law when calculating compositions of the phases, however, a good match of the overall Sn amounts for most of the samples with their nominal composition suggests that the linear approximation is fairly accurate. Another apparent contradiction is that the Sn content in the Sn-rich phases is higher in the sample treated at 580 °C compared to those treated at 680 °C. This is unphysical, because the solubility limit should increase with temperature. This might, however, be explained by different diffusion rates of Sn at 580 and 680 °C as well as by different pinning effects provided by the grain/powder-particle boundaries at these temperatures. Thus, performing the same treatment for a sintered (bulk) sample with the initial composition Mg2Si0.87Sn0.13 (Figure S2, Supporting Information), one can find that the Sn-rich phase contains a lower amount of Si by approximately 6 at. % (Figure 4) than in the powder sample, however the compositions of the Si-rich phases match well. Further reduction of the Si content in the Sn-rich phase is not observed with increasing dwelling time, according to the XRD patterns in Figure S2, Supporting Information (where the reflections corresponded to the Sn-rich phase do not shift after 1200 and 2400 min treatment at 580 °C, respectively). Because the bulk sample also contains grain boundaries, the same pinning effect (but less pronounced due to the decreased interface area of the sintered sample) might also prevent further reduction of a Si content in the Sn-rich phase. Another possible explanation might be the presence of free Si, which could distort the regions in the phase diagram or provide additional pinning. E

DOI: 10.1021/acs.cgd.9b00013 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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The formation of the Sn-rich phase can be explained as follows. The increase in cooling rate reduces the time in which a single solid solution spends in the binodal region, hence the nucleation is suppressed. Moreover, because the cooling also continues in the spinodal region, the diffusion kinetics of the system reduces quickly, which limits the spinodal decomposition as well so that the single phase starts splitting but “freezes” before the thermodynamic equilibrium is achieved. However, because cooling occurs exponentially with time, the sample spends more time in the spinodal region than in the binodal region, therefore a minor amount of the Sn-rich phase is formed and, most likely, according to the mechanism of spinodal decomposition. The slowly cooled samples form the Sn-rich phases in higher amounts due to sufficient time spent in the binodal region and, most likely, according to the mechanism of nucleation and growth. Different shapes and positions of the peaks of the Snrich reflections depicted in Figure 5 represent different formed microstructures, expected to give different thermoelectric properties. Thus, a judicious choice of cooling rate is a way to create a microstructure of interest in magnesium silicide-stannide alloys due to the presence of a miscibility gap in the quasibinary phase diagram Mg2Si−Mg2Sn. As demonstrated here, utilizing certain cooling rates allows formation of spinodal microstructures in Si-rich Mg2Si1−xSnx.

For the samples treated in the miscibility gap, a minor amount of a secondary Sn-rich phase can be found (gray dashed oval in Figure 4). This minor Sn-rich phase has a lower Si content than the primary Sn-rich phase at 580 °C, while it has higher Si content than the primary phase at 680 °C. This can be also explained by the pinning effect, which could dominate at lower temperatures, whereas diffusion through grain/particle boundaries is higher at higher temperatures. Thus, the results in the experiments of the current work render the binodal curve in the Si-rich area, in agreement with earlier results by Viennois et al.7 However, the binodal curve in the Sn-rich area still needs further experimental investigations. 3.4. Effect of Cooling on the Microstructure. Varying the cooling rate is another effective way to influence the microstructure. Depending on the cooling rate, when a single solid solution enters the miscibility gap, it can either remain as a single phase or decompose spinodally or via the mechanism of nucleation and growth. Thus, this section is aimed to show how the cooling rate influences the microstructure of magnesium silicide-stannide alloys for the example of Mg2Si0.87Sn0.13. All samples presented below were sintered in SPS at 780 °C and kept at the same temperature for 10 h and subsequently exposed to different cooling rates. Their XRD patterns are presented in Figure 5.

4. CONCLUSIONS It was demonstrated that various microstructures can be formed in Si-rich magnesium silicide-stannide alloys depending on their nominal compositions, heat treatment, as well as cooling rates. The spinodal microstructure is favorable for x(Sn) < 0.08 due to low diffusion kinetics, when the samples enter the miscibility gap. The same applies to the samples with x(Sn) > 0.08 (relying on the phase diagrams down to x(Sn) ∼ 0.20) if the cooling rate is sufficient to quickly overcome the binodal region, where the formation of nuclei of Sn-rich clusters is favorable. The results show good agreement with the binodal curve in the Si-rich region calculated by Viennois et al.,7 however, the Sn-rich region is not yet fully explored due to the pinning effect. To acquire more detailed information about this region, Sn-rich samples have to be examined. Nevertheless, the pinning effect could be also employed to create complex microstructures, expected to be beneficial for thermoelectric applications.

Figure 5. XRD data of the sample Mg2Si0.87Sn0.13, which experienced different cooling rates: quick cooling 780 °C − RT with initial rate ∼140 K/min (black), slow linear cooling 780 °C − 400 °C with ∼2 K/min (red), slow exponential cooling 780 °C − RT with initial rate ∼2 K/min (blue), and slow exponential cooling 580 °C − RT (magenta).

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ASSOCIATED CONTENT

S Supporting Information *

In the inset of Figure 5 showing the (111) reflection, it is possible to see that the quickly cooled sample (black pattern) has two overlapping peaks at ∼24.1°, which represent two Sirich phases with similar compositions, whereas the slowly cooled samples (magenta, blue, and red patterns) have only one peak corresponding to a single Si-rich phase. Hence, quick cooling provides a similar effect as if the samples passed the binodal curve at the temperature of low kinetics, e.g., as it was observed for Mg2Si0.97Sn0.03 and Mg2Si0.94Sn0.06. However, unlike these samples, Mg2Si0.87Sn0.13 also forms a minor amount of the Sn-rich phase, which is most likely also a result of spinodal decomposition. This Sn-rich phase cannot be residual, because its amount does not decrease with increasing dwelling time at 780 °C (Figure S1, Supporting Information).

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.9b00013.

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Homogenization of Mg2Si0.87Sn0.13 at 780 °C; phase separation in Mg2Si0.87Sn0.13 at 580 °C; extended summary of results from Rietveld refinement of Mg2Si1−xSnx alloys treated at 680 °C; extended summary of results from Rietveld refinement of Mg2Si1−xSnx alloys treated at 580 °C (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. F

DOI: 10.1021/acs.cgd.9b00013 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Andrey Sizov: 0000-0003-2826-8423 Bo B. Iversen: 0000-0002-4632-1024 Paul Erhart: 0000-0002-2516-6061 Anders E. C. Palmqvist: 0000-0002-7579-3936 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge project funding from Hot Disk AB and the Swedish Energy Agency (Energimyndigheten, project 38340-1). The project is also supported by the Danish Innovation Foundation funded Center for Thermoelectric Energy Conversion, and Danish National Research Foundation (DNRF93) through the Center for Materials Crystallography. In addition, Drs. Daniel Lindroth and Richard Heijl are acknowledged for carrying out some initial work on the topic presented in this article.

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DOI: 10.1021/acs.cgd.9b00013 Cryst. Growth Des. XXXX, XXX, XXX−XXX