Dislocation Introduction via Domain Engineering in Mg₂Sn Single Crystal to Improve its Thermoelectric Properties

Abstract

Dislocations have increasingly become important for improving the thermoelectric properties of thermoelectric materials due to their more pronounced scattering effect on phonons than on carriers. This study combined the introduction of the dislocation cores through domain engineering with the generation of Mg vacancies (V_Mg) by controlling point defects to achieve low lattice thermal conductivity and high power factor in n‐type and p‐type Mg₂Sn single crystals (SCs). The V_Mg domain with ordered atomic arrangements allowed carrier transport with minimal scattering, while the high dislocation density at the interface effectively scattered phonons, thereby decoupling carrier‐phonon transport. This resulted in obtaining the peak zT values of 0.83(8) and 0.42(4) for n‐type and p‐type Mg₂Sn SCs, respectively. The outstanding combination of domain engineering and point defect control techniques could be a strategy for developing high‐performance thermoelectric materials.

This study proposed domain engineering and point‐defect control for developing high‐performance thermoelectric materials. Mg vacancies and dislocations introduced into Mg₂Sn single crystals enhanced thermoelectric performance through decoupling carrier‐phonon transport. The Mg vacancies formed nanoparticle‐like regions, of which the size and density were controlled. Consequently, a higher performance than polycrystalline samples was achieved for both n‐type and p‐type Mg₂Sn.

1. Introduction

Thermoelectricity presents a promising solution to the challenges posed by energy scarcity and environmental concerns since it can directly convert heat into electricity without generating supplementary emissions.^{[ 1 ]} The advancement of this field depends on enhancing the thermoelectric properties of materials. Particularly, the dimensionless figure of merit, zT, needs to be improved, defined as zT  =  S ² σT/(κ _ele+κ _bip+κ _lat), where S, σ, T, κ _ele, κ _bip, and κ _lat represent the Seebeck coefficient, electrical conductivity, absolute temperature, electrical thermal conductivity, bipolar thermal conductivity, and lattice thermal conductivity, respectively. The pursuit of enhancing zT is a paramount objective in promoting the development of thermoelectric technology. Consequently, thermoelectric materials require a high power factor (PF = S ² σ) accompanied by low thermal conductivity (κ _tot = κ _ele+κ _bip+κ _lat) to realize their full potential.

It has been well established that carrier concentration (n _H) substantially dominates material properties: S, σ, and κ _ele. Decoupling these parameters to enhance the PF through band engineering has been successful in many thermoelectric materials. On the other hand, the preparation of single crystals (SCs) to eliminate carrier grain boundary scattering has also been of increasing interest. Alternatively, κ _lat is the sole independent parameter that determines zT. Another crucial tactic for increasing zT involves minimizing κ _lat.^{[ 2 ]} The insertion of 0D point defects (PDs)^{[ 3 ]} and 2D interfaces^{[ 4 ]} are widely used to further scatter phonons, thereby effectively reducing κ _lat. Recently, it has been demonstrated that 1D dislocations efficiently decrease κ _lat. Dense dislocations have been created either at grain boundaries through liquid‐phase sintering^{[ 5 ]} and alloying or within grains through the clustering of vacancies^{[ 6 ]} or interstitials.^{[ 7 ]}

When aliovalent PDs are introduced into a material, they are often perceived as contributing carriers rather than introducing charged vacancies. However, these defects also reduce the formation energy of vacancies and may even stabilize dislocations in their vicinity. For instance, in aliovalent Na‐doped PbTe^{[ 8 ]} and Na‐doped EuMg₂Sb₂,^{[ 9 ]} a low doping level (<5%) leads to an unusual increase in dislocations. This phenomenon can be attributed to the electrostatic interaction of heterovalent PDs with charged dislocations, which serves to stabilize them. Nevertheless, this argument remains open to further investigation in the field.

Mg₂Sn has garnered considerable attention as a promising medium‐temperature thermoelectric material. It is characterized by compositions comprising abundant, inexpensive, and nontoxic elements.^{[ 10} , ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ , ^{18 ]} Efforts have been directed toward decreasing κ _lat through grain size reduction,^{[ 19} , ^{20 ]} alloying,^{[ 21} , ²² , ²³ , ^{24 ]} and introducing particles^{[ 25 ]} in polycrystals (PCs). Peak zT values (zT _peak) reported so far were 0.62 for n‐type (Sb 1% doping^{[ 13 ]}) and 0.3 for p‐type (Ag 0.5% doping^{[ 25 ]} and Li 2% doping^{[ 26 ]}). Recently, we successfully synthesized undoped and elementary‐doped Mg₂Sn SCs through the melting method.^{[ 27} , ²⁸ , ²⁹ , ³⁰ , ^{31 ]} These SCs contained Mg vacancies (V_Mg) and dislocation cores (DCs), achieving a low κ _lat. For example, the κ _lat of the undoped Mg₂Sn SC (≈4.3 W m⁻¹ K⁻¹ @ 300 K^{[ 27 ]}) was lower than that of undoped SCs reported in previous studies (≈7.3 W m⁻¹ K⁻¹ @ 300 K^{[ 32} , ^{33 ]}). In addition, the Sb‐ and Li‐doped Mg₂Sn SCs exhibited a lower κ _lat than the corresponding PCs.^{[ 28} , ^{31 ]} Furthermore, exceptionally high crystallinity of the prepared SCs realized superior carrier mobility (µ _H) compared to the corresponding PCs at equivalent n _H, leading to enhanced PF and zT.^{[ 27} , ²⁸ , ³⁰ , ^{31 ]} The zT _peak values exceeded that of PCs, reaching 0.72 for n‐type (Sb 1% doping^{[ 28 ]}) and 0.38 for p‐type (Li 2% doping^{[ 31 ]}).

In this study, we aimed to further enhance thermoelectric properties through decoupling carrier‐phonon transport by additional boron (B) doping to the Sb‐doped and Li‐doped Mg₂Sn SCs. The B single‐doping significantly decreased the κ _lat of the Mg₂Sn SC down to a minimum κ _lat (κ _min ≈0.65 W m⁻¹ K⁻¹,^{[ 34 ]} approximated through the Debye model) due to the increase in V_Mg and DCs.^{[ 29 ]} We meticulously prepared (Sb, B)‐doped Mg₂Sn SCs (Mg_{2‐ x} B _x Sn_0.99Sb_0.01 with x = 0.0025 and 0.005, denoted as (Sb 1%, B 0.25%)‐ and (Sb 1%, B 0.5%)‐doped SCs). Moreover, we prepared (Li, B)‐doped Mg₂Sn SCs (Mg_{1.98‐ x} Li_0.02B _x Sn with x = 0.0025 and 0.005, denoted as (Li 2%, B 0.25%)‐ and (Li 2%, B 0.5%)‐doped SCs). Transmission electron microscopy (TEM) revealed the emergence of various lattice defects in both the n‐type and p‐type Mg₂Sn SCs (Figure  1a). These defects have a more substantial scattering effect on phonons than on carriers. This leads to a more significant reduction of κ _lat than PF decay, ultimately improving the zT values. We conducted comprehensive investigations into their thermal and electrical transport properties to gain further insights into the implications of lattice defects in SCs. By simulating κ _lat using the Debye model, we discerned the contribution of lattice defects to the decrease in κ _lat. Eventually, we achieved noteworthy outcomes: (Sb, B)‐ and (Li, B)‐doped SCs exhibited a remarkable decrease in κ _lat, yielding peak zT values of ≈0.83(8) and ≈0.42(4), respectively. Compared with n‐type and p‐type Mg₂Sn PCs, both the (Sb, B)‐ and (Li, B)‐doped SCs exhibited the highest zT values (Figure 1b). This research significantly deepens our comprehension of the intricate mechanisms governing lattice defects. Consequently, our findings hold great potential in providing a guiding framework to understand the underpinnings of lattice defects in Mg₂ X (X = Si, Ge, Sn) and other thermoelectric materials.

Figure 1.

a) Schematic illustration of lattice defects in Mg₂Sn single crystals (SCs) and b) comparison of peak zT values between this study and Mg₂Sn from the literature.^{[ 13} , ²⁵ , ²⁶ , ²⁷ , ²⁸ , ³⁰ , ³¹ , ³⁵ , ³⁶ , ³⁷ , ³⁸ , ^{39 ]}

2. Results and Discussion

2.1. Crystal Structure

Laue X‐ray diffraction (XRD) was employed to assess the crystallinity of the (Sb, B)‐ and (Li, B)‐doped ingots. Figure S1a–d (Supporting Information) displays the Laue spots, which exhibited only one clear set of alignments. This alignment was consistent with the simulated spots of the cubic structure (Fm $\overline{3}$ m) of Mg₂Sn (Figure S1e, Supporting Information). The bulk XRD patterns of the fractured surface of the (Sb, B)‐ and (Li, B)‐doped ingots showed 111, 222, and 333 planes (Figure S1f, Supporting Information). The Laue and bulk XRD results verified that all the prepared (Sb, B)‐ and (Li, B)‐doped ingots were SCs. The phases of the (Sb, B)‐doped and (Li, B)‐doped SCs were analyzed using powder XRD, as depicted in Figure  2a. Similar XRD peaks were evident in all SCs, and they can be assigned to Mg₂Sn with the Fm $\overline{3}$ m structure, indicating the formation of single‐phase Mg₂Sn SCs.

Figure 2.

a) Powder XRD patterns, b) lattice constant, and c) fraction of Mg vacancies (V_Mg) of (Sb, B)‐ and (Li, B)‐doped SCs. d) V_Mg fraction versus lattice constant. The error bars for the lattice constant and V_Mg fraction represent standard deviation (SD), n = 3.

We used SC XRD patterns and refined the structural parameters to further analyze the crystal structure and gain crystal information about the SCs (see Table S1, Supporting Information for details). The results showed the presence of Mg vacancies and the absence of Sn vacancies, which is consistent with the results for Mg₂Sn SCs^{[ 27 ]} and PCs.^{[ 15 ]} It also corroborates the calculations of Liu et al.^{[ 40 ]} that defects on the Sn sites have high formation energy in both n‐type and p‐type Mg₂Sn, which are unlikely to occur during the crystal growth. Figure 2b shows that the lattice constant (a) of the SCs decreased after doping B. Specifically, it decreased from 6.7697(11) to 6.7634(8) Å for (Sb, B)‐doped SCs and from 6.7647(5) to 6.7628(6) Å for (Li, B)‐doped SCs. Considering neutron holography results that B dopant substituted for the Mg site of the Mg₂Sn SC,^{[ 29 ]} the smaller atomic radius of B (79.5 pm)^{[ 41 ]} compared to Mg (159.9 pm)^{[ 41 ]} might be the probable reason for this alteration. In fact, neutron holography measurements on (Sb, B)‐ and (Li, B)‐doped SCs proved that the B atom was located at the Mg site.^{[ 42 ]} The decrease in the lattice constant was more significant in the (Sb, B)‐doped SCs than in the (Li, B)‐doped SCs, which can be attributed to two reasons: 1) Sb dopant tended to cause lattice expansion, whereas Li and B dopants contributed to lattice contraction, leading to a more pronounced impact of the B dopant on the lattice of the (Sb, B)‐doped SCs; 2) While the Sb dopant entered the Sn site, Li and B dopants were incorporated into the Mg site, which may also result in different effects of the B dopant. Interestingly, we observed that the V_Mg fraction increased as the B dopant amount increased (Figure 2c). The V_Mg fraction increased from 8.9(17)% to 12.3(47)% for (Sb, B)‐doped SCs and increased from 10(2)% to 12(2)% for (Li, B)‐doped SCs. This result can be attributed to the change in the lattice constant, which exerted an augmenting chemical pressure on the Mg₂Sn lattice.^{[ 29 ]} Figure 2d summarizes a strong correlation between V_Mg and the lattice constant. As the lattice constant decreased, the V_Mg amount increased, suggesting that the increase in chemical pressure contributed to the rise in V_Mg.

2.2. Nanostructure

TEM was employed to observe the nanostructures of the (Sb 1%, B 0.25%)‐, (Sb 1%, B 0.5%)‐, (Li 2%, B 0.25%)‐, and (Li 2%, B 0.5%)‐doped SCs (Figure 3a,b; Figure S3a,b, Supporting Information, respectively). In Figure 3a,b, the striped patterns (R2 region), the so‐called Moiré pattern, were distributed in the matrix (R1 region). The R1 region in the high‐magnification TEM images (Figure 3a2[left] and 3b2[left]) exhibited a perfect atomic arrangement of the (111) and (110) surfaces, respectively, representing the SC region. Conversely, the R2 region in high‐magnification TEM images (Figure 3a3[left] and 3b3[left]) corresponds to the presence of V_Mg in the SCs (i.e., V_Mg region) based on previous studies.^{[ 28} , ^{31 ]}

Figure 3.

Low‐magnification TEM image of (a1) (Sb 1%, B 0.25%)‐doped SC and (b1) (Li 2%, B 0.25%)‐doped SC. (a2 and b2) [left] High‐magnification TEM image and [right] FFT pattern of the SC region (marked as the R1 region in a1 and b1). (a3 and b3) [left] High‐magnification TEM image and [right] FFT pattern of the V_Mg region (marked as the R2 region in a1 and b1). (a4 and b4) Filtered inverse FFT image of the R2 region using the two extra spots of the FFT pattern in a3 [right] and b3 [right]. c) [left] High‐magnification TEM image, [middle] HAADF‐STEM image, and [right] Geometric phase analysis (GPA) image of the R3 region in b1.

Fast Fourier transform (FFT) patterns were obtained to analyze the V_Mg region, SC region, and their interfaces. The FFT pattern from the SC region (Figure 3a2[right] and 3b2[right]) displayed a set of diffraction spots, indicating the alignment of atoms in this region, corresponding to the cubic structure from the [111] direction for (Sb, B)‐doped SC and the [110] direction for (Li, B)‐doped SC. The FFT pattern for the V_Mg region (Figure 3a3[right] and 3b3[right]) showed two sets of spots: bright and dark. The bright spots were similar to the diffraction spots observed in the SC region, while the dark spots were from the V_Mg region (V_Mg spots). The V_Mg spots were close to the Mg₂Sn spots due to the smaller lattice constant of the V_Mg region than that of the SC region, indicating the same lattice structure with only lattice distortions. For a clearer view of the lattice, the inverse FFT (IFFT) image from a set of additional V_Mg spots (Figure 3a3[right] and 3b3[right], yellow arrow) is shown in Figure 3a4,b4. DCs (marked in red) were located at the interface between the V_Mg region and SC region due to lattice mismatch, which is widely observed in other thermoelectric materials such as (Sb, Bi)₂Te₃,^{[ 43 ]} PbTe,^{[ 44 ]} PbSe,^{[ 45 ]} Mg₂Si,^{[ 46 ]} and Mg₂Sn.^{[ 27} , ²⁸ , ²⁹ , ³⁰ , ^{31 ]} Figure 3b5 and 3b6 show high‐magnification TEM and atomic‐resolution high‐angle annular dark‐field scanning TEM (HAADF‐STEM) images of the R3 region in Figure 3b. The black area in the R3 region in the TEM image (Figure 3b1) was bright in the HAADF‐STEM image (Figure 3b5). This black area was the Sn‐rich nanoprecipitate (NP), also observed in Li‐doped SCs.^{[ 31 ]} The FFT pattern from the R4 region displayed a set of diffraction spots (Figure 3b6), indicating the same crystal structure for the Sn‐rich NPs and SC region. A geometric phase analysis (GPA) image in Figure 3b7 indicates that no high‐strain center was observed around the interface between the Sn‐rich NP and the SC region.

The density of DCs (N _DC) is calculated by dividing the number of DCs by the area in the IFFT images. It is generally believed that the introduction of vacancies promotes dislocation formation. As shown in Figure  4a, the N _DC increased with the B doping content; from 1.0 × 10¹⁶ m⁻² (Sb 2%‐doped SC) to 4.2 × 10¹⁶ m⁻² ((Sb 2%, B 0.25%)‐doped SC) and from 3.3 × 10¹⁶ m⁻² (Li 2%‐doped SC) to 6.8 × 10¹⁶ m⁻² ((Li 2%, B 0.25%)‐doped SC). The increase in N _DC is attributable to the increase in the V_Mg fraction. However, this scenario does not fully explain the B‐doping effect. Figure 4b,c respectively show the average size and density of the V_Mg regions in the undoped, B‐doped, (Sb, B)‐doped, and (Li, B)‐doped SCs. With the increase in the B dopant content, the average size decreased, whereas the density increased. The decrease in average size was smaller than the increase in density, leading to an overall increase in N _DC. The formation process of the V_Mg regions is illustrated in Figure 4d. During melting at low cooling rates, V_Mg is sufficiently mobile to form V_Mg regions. DCs are then formed at the interface between the V_Mg region and the SC region. If charged dopants (B atoms herein) are introduced into Mg₂Sn SCs, V_Mg ²⁻‐B³⁺ complex PDs are formed.^{[ 25 ]} Thus, the aggregation of V_Mg is repelled, decreasing the average size of the V_Mg regions. On the other hand, the B dopants apply chemical pressure to Mg₂Sn SCs, thereby increasing the V_Mg fraction and density of the V_Mg regions.

Figure 4.

a) Dislocation density N _DC, b) average size of the V_Mg regions, and c) density of the V_Mg regions for undoped,^{[ 27 ]} Sb‐doped,^{[ 28 ]} B‐doped,^{[ 29 ]} Li‐doped,^{[ 31 ]} (Sb, B)‐doped, and (Li, B)‐doped SCs. d) Schematic illustration of the formation of dislocations.

2.3. Electronic Transport Properties

Figure  5a,b depict the dependence of the absolute Seebeck coefficient (S) of the (Sb, B)‐ and (Li, B)‐doped SCs on temperature, respectively. The (Sb, B)‐doped SCs showed n‐type conduction with electrons as the majority charge carriers, while the (Li, B)‐doped SCs exhibited p‐type conduction with holes as the majority charge carriers. It was observed that the |S| of (Sb, B)‐doped SCs was higher than that of (Li, B)‐doped SCs in the entire temperature ranges; thus, (Sb, B)‐doped SCs may have higher electrical properties than (Li, B)‐doped SCs. Looking across the entire temperature range, as the B content increased from 0% to 0.5%, the |S| of (Sb, B)‐doped SCs slightly increased from |−95(3)| µV K⁻¹ to |−97(3)| µV K⁻¹, whereas that of (Li, B)‐doped SCs decreased. The change in |S| reflects the variation in n _H, which can be understood based on the behavior of V_Mg and the B dopant. As mentioned earlier, V_Mg acted as an acceptor and B dopant acted as a donor in Mg₂Sn. Since the change in V_Mg was greater than that of the B dopant (≈1% V_Mg with 0.25% B), the result was a decrease in the electron carrier concentration and an increase in the hole carrier concentration for (Sb, B)‐ and (Li, B)‐doped SCs, respectively. Additionally, as the temperature increased, the |S| of the (Sb, B)‐doped SCs increased across all temperatures. The |S| of the (Li, B)‐doped SCs initially increased and then slightly decreased. The decrease in |S| at high temperatures was caused by the inverse sign of S contributed by the thermal excitation of minority carriers, known as the bipolar effect. Moreover, the increase in the majority carrier concentration helped to suppress this effect.

Figure 5.

a,b) Temperature dependence of the Seebeck coefficient S and (c, d) Pisarenko plot using |S| and carrier concentration n _H at 300 K for (Sb, B)‐ and (Li, B)‐doped SCs. The error bars represent SD, n = 3.

The carrier transport behavior and characteristics of the (Sb, B)‐ and (Li, B)‐doped SCs were analyzed using the Pisarenko relation, which evaluates the scattering factor (r) and effective mass (m ^*) of carriers. The Pisarenko relation is given by Equation (1):

$$\left|S\right|=\left[\frac{8{\pi }^{2/3}{k}_{\mathrm{B}}^2\left(r+3/2\right)}{3^{5/3}e{h}^2}\right]\left(\frac{m^{\ast }}{{n_{\mathrm{H}}}^{2/3}}\right)T$$ (1)

where k _B is the Boltzmann constant, r the scattering parameter (e.g., r  =   − 1/2 for acoustic phonon scattering, 0 for neutral impurity scattering, 3/2 for ionized impurity scattering, etc.), h the Planck's constant, and e the carrier charge. In Figure 5c,d, the Pisarenko plot displays the dependence of the |S| versus the n _H, with different curves representing specific m* and r conditions. The scattering mechanism for Sb 1%‐doped and Li 2%‐doped SCs was acoustic phonon scattering, with r taken as − 1/2. The m ^* of the n‐type SCs was higher than that of the p‐type SCs, which was in good agreement with the literature data (Table S2, Supporting Information). This difference in m* resulted in better electrical properties of the n‐type SCs. After B doping, no change in the scattering factor was observed for both (Sb, B)‐ and (Li, B)‐doped SCs, indicating that there were no additional scattering mechanisms. According to previous studies,^{[ 28} , ^{31 ]} the addition of small amounts of dopants and the increase in the amount of V_Mg have little effect on the scattering factor. More importantly, dense dislocations have no significant impact on m ^*.

Figure  6a,b present the dependence of electrical conductivity (σ) on temperature for (Sb, B)‐ and (Li, B)‐doped SCs, respectively. All SCs exhibited degenerate semiconductor behavior. Comparing the two types of SCs, the σ of (Sb, B)‐doped SCs was slightly higher than that of (Li, B)‐doped SCs. The σ at 300 K of (Sb, B)‐ and (Li, B)‐doped SCs dropped by ≈10%, specifically, decreasing from 4.12(8) × 10³ S cm⁻¹ for the Sb 1%‐doped SC to 3.48(7) × 10³ S cm⁻¹ for the (Sb 1%, B 0.5%)‐doped SC. The decrease in σ was attributed to the changes in n _H and µ _H (Figure 6c,d). The carriers received the combined action of PDs and dislocations. For the carrier concentration, V_Mg contributed holes and B contributed electrons, and every 0.25% increase in the B content increased V_Mg by 1%. The result was a decrease in the electron concentration for (Sb, B)‐doped SCs and an increase in the hole concentration for (Li, B)‐doped SCs. As the B content increased, the µ _H decreased; however, both (Sb, B)‐doped and (Li, B)‐doped SCs exhibited higher µ _H than Mg₂Sn‐based PCs.^{[ 13} , ²⁵ , ²⁶ , ²⁷ , ²⁸ , ³⁰ , ³¹ , ³⁵ , ³⁶ , ³⁷ , ³⁸ , ^{39 ]}

Figure 6.

a,b) Electrical conductivity σ and c,d) relationship between the carrier mobility, µ _H, and carrier concentration, n _H, at 300 K for (Sb, B)‐ and (Li, B)‐doped SCs. The error bars represent SD, n = 1.

Figure  7a,b show the temperature‐dependent PF of the (Sb, B)‐doped and (Li, B)‐doped SCs, respectively. The PF as well as S and σ did not show significant change during the heating and cooling cycles, supporting the chemical stability of the SCs. The PF of the (Sb 1%, B 0.25%)‐doped SC (≈4.8(2)  mW K⁻² m⁻¹) was 6% lower than that of the Sb 1%‐doped SC (≈5.1(3)  mW K⁻² m⁻¹). The PF of the (Li 2%, B 0.25%)‐doped SC (≈1.89(9) mW K⁻² m⁻¹) was 18% lower than that of the Li 2%‐doped SC (≈2.3(1) mW K⁻² m⁻¹). It is worth noting that despite the decrease in PF values, the PF_max of the (Sb 1%, B 0.25%)‐ and (Li 2%, B 0.25%)‐doped SCs was significantly higher than that of undoped SC^{[ 26 ]} (0.11 mW K⁻² m⁻¹) and B‐doped SC^{[ 28 ]} (0.10 mW K⁻² m⁻¹). The PF_max of the (Sb 1%, B 0.25%)‐ and (Li 2%, B 0.25%)‐doped SCs was respectively ≈48 times and ≈19 times higher than that of the B‐doped SC, which verifies the successful co‐doping. Moreover, the PF of the (Sb 1%, B 0.5%)‐ and (Li 2%, B 0.25%)‐doped SCs was still maintained at a high level compared to other Mg₂Sn PCs.^{[ 13} , ²⁶ , ³⁶ , ^{38 ]}

Figure 7.

Power factor PF of a) (Sb, B)‐ and b) (Li, B)‐doped SCs as a function of temperature. The error bars represent SD, n = 3.

2.4. Thermal Transport Properties

The κ _tot (=  κ _ele + κ _bip + κ _lat) of the (Sb, B)‐doped SCs (open symbols) and (Li, B)‐doped SCs (filled symbols) is shown in Figure  8a,b, respectively. The κ _tot of the (Sb, B)‐ and (Li, B)‐doped SCs decreased as the B content x increased. Especially, the κ _tot value of the (Sb 1%, B 0.5%)‐ and (Li 2%, B 0.25%)‐doped SCs was ≈33% and ≈20% lower than that of the Sb 1%‐ and Li 2%‐doped SCs, respectively. The electrical thermal conductivity (κ _ele), bipolar thermal conductivity (κ _bip), and lattice thermal conductivity (κ _lat) were calculated separately to better understand the effect of B doping on the thermal transport properties. The κ _ele was estimated using the Wiedemann–Franz law (see Figure S3, Supporting Information), which showed a trend similar to σ, decreasing somewhat to compensate for the deterioration in thermoelectric performance caused by the decrease in σ. The κ _bip of the (Sb, B)‐doped SCs was lower than that of the (Li, B)‐doped SCs (Figure S4, Supporting Information). The κ _bip behaved opposite to the trend of carrier variation because the increase in n _H favored the suppression of the bipolar effect. The κ _lat of the (Sb, B)‐ and (Li, B)‐doped SCs was evaluated using κ _lat = κ _tot−κ _ele−κ _bip and is shown in Figure 8c,d, respectively. Similar to the case of B‐doped SCs,^{[ 29 ]} we found that the B dopant significantly contributed to the decrease in κ _lat due to the increase in the V_Mg fraction and N _DC. Compared with Sb 1%‐doped SC, a lower κ _lat was achieved for (Sb, B)‐doped SCs. A lower κ _lat was observed for (Li, B)‐doped SCs than Li 2%‐doped SC. It should be noted that the Li 2%‐ and (Li, B)‐doped SCs showed an abrupt decrease in κ _lat above 600 K. According to a study on the effect of Ag₂Te NPs in PbTe,^{[ 47 ]} small NPs (< 2 × 10⁻⁸ m) decreased κ _lat near room temperature, whereas large NPs (1 × 10⁻⁷ −2 × 10⁻⁷ m) reduced κ _lat at higher temperatures. Herein, the Sn‐rich NPs in the SCs prepared in this study had different sizes (Figure S2c, Supporting Information). Thus, the decrease in κ _lat above 600 K is attributable to large NPs in these SCs.

Figure 8.

Temperature dependence of total thermal conductivity κ _tot of a) (Sb, B)‐ and b) (Li, B)‐doped SCs. Temperature dependence of lattice thermal conductivity κ _lat of c) (Sb, B)‐ and d) (Li, B)‐doped SCs. The error bars represent SD, n = 3.

The Debye model combined with TEM observations was used to estimate the contribution of the Umklapp process (UP) and various defects, including PDs, DCs, and NPs, to the κ _lat. Figure  9a shows the measured κ _lat at 300 K as a function of the evaluated disorder parameter, Γ (Equations S16–S18, Supporting Information) of (Sb, B)‐doped SCs. The Γ‐dependent calculated κ _lat curves with different N _DC are also shown. They fitted well with the measured κ _lat values, indicating that the V_Mg and DCs dominated the phonon scattering in the (Sb, B)‐doped SCs. The spectral lattice thermal conductivity κ _s was calculated to analyze the effect of various defects on the phonon frequency. Figure 9b,c show that PDs (V_Mg) and DCs scattered phonons at high and mid frequencies, respectively, in both (Sb 1%, B 0.25%)‐ and (Li 2%, B 0.25%)‐doped SCs. The Sn‐rich NPs additionally scattered phonons at low frequencies in the (Li 2%, B 0.25%)‐doped SC. The temperature‐dependent calculated κ _lat of the (Li 2%, B 0.25%)‐doped SC is shown in Figure S5 (Supporting Information). The κ _lat curves from top to bottom represent the calculated κ _lat adopting the effects of UP (black), UP+PD (green), UP+PD+DC (brown), and UP+PD+DC+NP (blue). The κ _lat calculated considering all scattering processes (UP+PD+DC+NP) well matched the measured κ _lat, further supporting that the PDs, DCs, and NPs contributed to the κ _lat reduction of the (Li 2%, B 0.25%)‐doped SC.

Figure 9.

a) Relationship between the κ _lat at 300 K and disorder parameter, Γ, for (Sb, B)‐doped SCs. The dotted curves are κ _lat calculated at 300 K with different N _DC. Frequency‐dependent accumulative reduction in κ _lat (κ _s) of b) (Sb 1%, B 0.25%)‐ and c) (Li 2%, B 0.25%)‐doped SCs, considering the phonon scattering by UP, PD, DC, and NP.

2.5. Quality Factor and Dimensionless Figure of Merit

The temperature‐dependent weighted mobility (µ _w) of the (Sb, B)‐doped SCs (open symbols) and the (Li, B)‐doped SCs (filled symbols) is analyzed using Equation (2):^{[ 48 ]}

$$\begin{array}{ccc}\hfill {\mu }_{\mathrm{w}}& =& 331\left(\frac{1}{\rho }\right){\left(\frac{T}{300}\right)}^{-\frac{3}{2}}\hfill \\ & & \left[\frac{\exp \left[\frac{\left|S\right|}{k_{\mathrm{B}}/e}-2\right]}{1+\exp \left[-5\left(\frac{\left|S\right|}{k_{\mathrm{B}}/e}-1\right)\right]}+\frac{\frac{3}{{\pi }^2}\frac{\left|S\right|}{k_{\mathrm{B}}/e}}{1+\exp \left[5\left(\frac{\left|S\right|}{k_{\mathrm{B}}/e}-1\right)\right]}\right]\hfill \end{array}$$ (2)

Here, ρ is the electrical resistivity measured in mΩ∙cm, and k _B/e = 86.3 µV K⁻¹. Figure  10a shows that the µ _w of the (Sb, B)‐ and (Li, B)‐doped SCs decreased with the increase in the B content. The higher µ _w for the (Sb, B)‐doped SCs compared to the (Li, B)‐doped SCs explains the superior electrical properties of n‐type Mg₂Sn. Despite the reduction in µ _w due to the introduction of B dopant, the µ _w values remained higher than those of Li 2%‐doped Mg₂Sn PC^{[ 26 ]} and Na 7%‐doped Mg₂Sn PC^{[ 39 ]} without dense dislocations. This result demonstrates the advantage of excellent crystallinity in the SCs and the less influence of dislocations on carriers than PCs. Thus, the analysis of µ _w provides further evidence of the electrical superiority of the Mg₂Sn SCs over Mg₂Sn PCs despite the slight reduction in µ _w with B doping. To comprehensively understand the role of B in Mg₂Sn, the quality factor B _Q is appraised using Equation (3):^{[ 49 ]}

$$B_{\mathrm{Q}}=9\frac{{\mu }_{\mathrm{w}}}{{\kappa }_{\mathrm{lat}}}{\left(\frac{T}{300}\right)}^{5/2}$$ (3)

Figure 10.

Temperature dependence of a) weighted mobility µ _w and b) quality factor B _Q of (Sb, B)‐doped SCs (open symbols) and (Li, B)‐doped SCs (filled symbols). c,d) zT values of (Sb, B)‐ and (Li, B)‐doped SCs. The error bars represent SD, n = 3.

The increase in B _Q of the (Sb 1%, B 0.25%)‐ and (Li 2%, B 0.25%)‐doped SCs (Figure 10b) demonstrates the enhanced electrical and thermal properties resulting from the addition of B.

The zT values of the (Sb, B)‐doped SCs were higher than that of the Sb 1%‐doped SC at high temperatures (>500 K) (Figure 10c). Specifically, the (Sb 1%, B 0.25%)‐doped SC exhibited the peak zT value (zT _peak) of ≈0.83(8) at 650 K, which was ≈15% higher than that of the Sb1%‐doped SC. For the (Li, B)‐doped SCs, the zT _peak was found to be 0.42(4) for the (Li 2%, B 0.25%)‐doped SC (Figure 10d), which was 11% higher than that of the Li 2%‐doped SC. The high zT values were realized for the (Sb 1%, B 0.25%)‐ and (Li 2%, B 0.25%)‐doped SCs due to the high µ _H and low κ _lat. This highlights the importance of defect engineering in Mg₂Sn SCs in enhancing thermoelectric performance.

3. Conclusion

This study successfully demonstrated the enhancement of thermoelectric characteristics of n‐ and p‐type Mg₂Sn SCs by introducing B as a dopant to engineer defects. Adding B increased the chemical pressure in the Mg₂Sn lattice, thereby increasing V_Mg and dislocations. These lattice defects, along with their effects on the precipitation of the Sn‐rich phase in the p‐type Mg₂Sn SCs, led to a decrease in carrier mobility and electrical conductivity, ultimately enhancing thermoelectric performance. The peak zT values obtained for both the n‐ and p‐type Mg₂Sn SCs were higher than those recently reported for Mg₂Sn materials and were close to those of Mg₂Sn‐based solid solutions. This research provides valuable insights into how defects can be engineered to improve the thermoelectric properties of Mg₂ X (X = Si, Ge, Sn) materials. This study also contributes to understanding the role of defects and their impact on carrier transport and phonon scattering. It provides a guide for enhancing the thermoelectric performance of Mg₂Sn and other materials.

4. Experimental Section

Sample Preparation

Mg_{2‐ x} B _x Sn_0.99Sb_0.01 and Mg_{1.98‐ x} Li_0.02B _x Sn SCs (x = 0, 0.0025, and 0.005) were prepared using the melting method.^{[ 27} , ²⁸ , ^{30 ]} Mg grains (4N, Mitsuwa Chemicals Co., Ltd. ≈Φ4 mm × L4 mm), Sn powder (4N, Kojundo Chemical Lab., 63 µm pass), Sb powder (5N, Kojundo Chemical Lab., 150 µm), Li rod (3N, Sigma‐Aldrich Co. Ltd., ≈Φ12.7 mm), and B (2N, Kojundo Chemical Lab., 45 µm pass) were weighed according to the stoichiometric ratio. The weighed materials were loaded into a BN‐coated alumina crucible in a glove box filled with an Ar atmosphere and an oxygen concentration of less than 0.1 ppm. The alumina crucible was then loaded into a quartz tube, vacuumed to ≈10⁻⁶ Pa after three gas washes, and then charged with Ar gas at a pressure of 0.16 MPa. Here, the role of Ar gas was to provide physical pressure during the synthesis process.^{[ 27 ]} The sealed quartz tubes were placed in a vertical furnace where the furnace was first heated to 1123 K, then cooled to 1023 K at a rate of 2 K h⁻¹, and finally to room temperature within 9 h. The prepared ingot size was ≈Φ10 mm × L20 mm, and the test area was from 2 to 7 mm from the bottom.

Sample Characterization

The crystalline surfaces were characterized using powder XRD (D8 ADVANCE, Bruker) and Laue XRD (RINT, Rigaku). The lattice constants and V_Mg amounts were obtained using single‐crystal XRD (SC XRD; D8 QUEST, Bruker) characterization combined with refinement. This structural refinement is difficult to achieve using powder XRD patterns due to the high orientations of the powder XRD peaks.^{[ 10} , ^{11 ]} Small SCs were selected by crushing the ingots and refined using jana2006^{[ 50 ]} (see, Supporting Information for details). An atomic‐resolution analytical electron microscope (JEM‐ARM200F, JEOL) was used to carry out TEM, scanning TEM (STEM), and atomic‐resolution high‐angle annular dark‐field STEM (HAADF‐STEM) observations. All XRD measurements, as well as TEM and energy‐dispersive X‐ray spectroscopy (EDS) observations, were performed at room temperature.

The Mg_{2‐ x} B _x Sn_0.99Sb_0.01 and Mg_{1.98‐ x} Li_0.02B _x Sn SCs were subjected to measurement of S and σ values using an automated thermoelectric tester (RZ2001i, Ozawa Science Co. Ltd.) under a vacuum from 300 to 700 K. The Hall coefficient R _H was determined at room temperature by sweeping a magnetic field from −5.0 to 5.0 T using a device for measuring physical parameters (PPMS, Quantum Design). The Hall carrier concentration n _H was calculated as n _H = |1/(eR _H)|, and the Hall carrier mobility µ _H was determined using the formula µ _H = σR _H. The typical sample size used for the S and σ measurements was 2.5 × 2.5 × 8 mm³, and that for the Hall measurements was 2.5 × 6 × 0.8 mm³. The total thermal conductivity κ _tot was calculated using the relation κ _tot = ρ _s DC _p, where ρ _s, D, and C _p are the mass density, thermal diffusivity, and specific heat capacity, respectively. The measured mass density ρ _s = m/V, where m is the mass and V is the volume, is shown in Table S4. The ρ _s values obtained in this study were lower than that of a Mg₂Sn single crystal without V_Mg (3.59 g cm^{−3 [ 51 ]}), verifying the presence of V_Mg in the prepared SCs. From the SC‐XRD refinements, ρ _s was also evaluated using the refined lattice constant and site occupancies (Table S1, Supporting Information). The difference between the measured and evaluated ρ _s may be related to nanostructures: the V_Mg was confined in the V_Mg regions, thereby compressing the lattice relative to the SC regions.^{[ 28 ]} The D and C _p of the samples were measured from 300 to 700 K under a vacuum using a laser flash apparatus (TC‐7000, ULVAC‐RIKO). The sample size for the D and C _p measurements was typically ≈Φ10 mm × L2 mm.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Huang Z., Hayashi K., Saito W., et al. “Dislocation Introduction via Domain Engineering in Mg₂Sn Single Crystal to Improve its Thermoelectric Properties.” Small Methods 9, no. 9 (2025): 2500385. 10.1002/smtd.202500385

Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.