Control of the Thermoelectric Properties of Mg2Sn Single Crystals via Point-Defect Engineering

Mg2Sn is a potential thermoelectric (TE) material that can directly convert waste heat into electricity. In this study, Mg2Sn single-crystal ingots are prepared by melting under an Ar atmosphere. The prepared ingots contain Mg vacancies (VMg) as point defects, which results in the formation of two regions: an Mg2Sn single-crystal region without VMg (denoted as the single-crystal region) and a region containing VMg (denoted as the VMg region). The VMg region is embedded in the matrix of the single-crystal region. The interface between the VMg region and the single-crystal region is semi-coherent, which does not prevent electron carrier conduction but does increase phonon scattering. Furthermore, electron carrier concentration depends on the fraction of VMg, reflecting the acceptor characteristics of VMg. The maximum figure of merit zTmax of 1.4(1) × 10−2 is realised for the Mg2Sn single-crystal ingot by introducing VMg. These results demonstrate that the TE properties of Mg2Sn can be optimised via point-defect engineering.


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Crystallinity and composition of the Mg2Sn single-crystal ingots Figure S1a shows the bulk X-ray diffraction (XRD) measurements of the Mg2Sn singlecrystal ingots prepared under PAr = 0.6, 1.3 and 1.6 atm (described as the 0.6-, 1.3-and 1.6-atm ingots, respectively). Peaks corresponding to the 111, 222 and 333 planes appear in the XRD patterns of the fractured surface of the ingots, indicating that the ingots are actually single crystals. Figure

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Single-crystal structure refinement For single-crystal structure refinement, three structure models were used: (a) stoichiometric Mg2Sn, (b) Mg2Sn with Mg vacancies (VMg) and (c) Mg2Sn with VMg and Mg interstitial defects (Mgi). In the case of model (c), the Mgi fraction became negative or zero during structural refinement. Hence, it was concluded that Mgi does not exist in the ingots. As shown in Table S1, the evaluated wR-factor for model (b) is lower than that for model (a). To confirm the significance of the lower wR-factor, the Hamilton test 1 was performed. The ratio of VMg exist in the ingot is not rejected at the significance level, α. Table S1 lists the Rb,n-b,α values at the minimum α where R > Rb,n-b,α. It was found that α was lower than 0.006 for all ingots, indicating that the hypothesis that the crystals contain VMg should not be rejected at a significance level below 0.006. The significance level of 0.006 is low enough to conclude that the prepared Mg2Sn single-crystal ingots contain VMg. Table S1. Results and significance level obtained by Hamilton test.

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The existence of VMg in the Mg2Sn single-crystal ingots was further examined by using a difference Fourier map. Figure Table S2 lists the refined structural parameters of the prepared ingots. Sn occupancy is 100%, whereas Mg occupancy decreases with increasing PAr.
In other words, the VMg fraction increases as PAr increases.
This equation cannot be applied to materials with complex non-parabolic band structures, where L values estimated using eq. (1) deviate from calculated ones by up to 13% 6,7 . In addition, the eq.
(1) is accurate within 5% in the case that acoustic phonon scattering is dominant 5 , and for other phonon scattering mechanisms, the deviation reaches as large as 20% 5 . Mg2Sn is known as an intrinsic semiconductor with a parabolic band structure 8 . However, the dominant phonon scattering mechanism in Mg2Sn is uncertain; acoustic phonon scattering is adopted in several references [9][10][11][12] and optical phonon scattering is considered in another reference 13 . Thus, the deviation is at most 20%. Figure S5a shows the carrier thermal conductivity, κe, of the ingots estimated by using eq. (1). In spite of the large deviation, the estimated κL of the 0.6 atm ingot by subtracting κe and bipolar thermal conductivity, κbp, from total thermal conductivity is well fitted by a theoretical calculation of κL adopting nano-structural features in the 0.6 atm ingot (Fig. 6c).
This result ensures the validity of the use of eq. (1).
The κbp of the ingots is shown in Figure S5b. For the calculation of κbp, the following equation is used 9 : S-8 where Eg, p and b are the energy band gap, hole concentration, electron mobility, and mobility ratio (= μn / μp), respectively. These parameters are listed in Table S3. The equations giving the relaxation time (Umklapp process, τU 16   S-10 Table S4. Equations for the various phonon relaxation times used in the calculations.

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Comparison of κmin, PFmax, and zTmax among the Mg2Sn single crystals The κmin, PFmax and zTmax values of the Mg2Sn single-crystal ingots prepared in this study and those of the Mg2Sn single crystals reported in the literatures 13,22 are shown in Figures   S6a, S6b and S6c, respectively. The 1.6 atm ingot prepared in this study exhibited the lowest κmin.
In the literatures, the Mg2Sn single-crystal ingots were prepared under an Ar atmosphere of pressure, PAr = 0.03 atm 22  Chen et al. [13] zT max × 10 ▬2 (c)