Preparation, thermoelectric properties, and crystal structure of boron-doped Mg 2 Si single crystals

Mg 2 Si is a potential thermoelectric (TE) material that can directly convert waste energy into electricity. In expectation of improving its TE performance by increasing electron carrier concentration, the element boron (B) is doped in Mg 2 Si single crystals (SCs). Their detailed crystal structures are definitely determined by using white neutron holography and single-crystal x-ray diffraction (SC-XRD) measurements. The white neutron holography measurement proves that the doped B atom successfully substitutes for the Mg site. The SC-XRD measurement confirms the B-doping site and also reveals the presence of the defect of Si vacancy (V Si ) in the B-doped Mg 2 Si SCs. The fraction of V Si increases with increasing B-doping concentration. In the case of B-doped Mg 2 Si polycrystals (PCs), V Si is absent; this difference between the SCs and PCs can be attributed to different preparation temperatures. Regarding TE properties, the electrical conductivity, σ , and the Seebeck coefficient, S , decreases and increases, respectively, due to the decrease in the electron carrier concentration, contrary to the expectation. The power factor of the B-doped Mg 2 Si SCs evaluated from σ and S does not increase but rather decreases by the B-doping. The tendencies of these TE properties can be explained by considering that the donor effect of the B atom is canceled by the acceptor effect of V Si for the B-doped Mg 2 Si SCs. This study demonstrates that the preparation condition of Mg 2 Si should be optimized to prevent the emergence of an unexpected point defect.


I. INTRODUCTION
Thermoelectric (TE) materials have attracted attention in recent times because they can directly convert waste heat into electricity via the Seebeck effect. The performance of TEs is evaluated in terms of the dimensionless figure of merit, zT (=S 2 σT/κ), and the power factor (PF) (=S 2 σ), where S, σ, T, and κ are the Seebeck coefficient, electrical conductivity, absolute temperature, and thermal conductivity, respectively. Generally, zT > 1 or PF > 2 × 10 −3 W/K 2 m is required for practical use. Mg 2 Si is one of the promising TE materials due to its preferred characteristics such as lightweight, low cost, and low toxicity. The crystal structure is cubic (Fm3m), socalled the antifluorite structure (Fig. 1). Magnesium (Mg) and silicon (Si) atoms occupy 8c(1/4 1/4 1/4) and 4a(0 0 0) sites, respectively. In addition, a small fraction of Mg is present at the 4b(1/2 1/2 1/2) interstitial site with an occupancy of ∼1%. 1,2 This interstitial Mg (Mg i ) generates electrons, [3][4][5] and hence, Mg 2 Si is an n-type semiconductor. Because Mg 2 Si does not exhibit high zT and PF [e.g., zT = 0.05 at 860 K and PF = 4 × 10 −4 W/K 2 m at 300 K for a Mg 2 Si polycrystal (PC) 6 ], partial substitution for Mg 2 Si has been extensively performed. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] Recently, our group prepared boron (B)-doped Mg 2 Si PCs and successfully increased σ. 19 Consequently, zT and PF was about 0.68 at 850 K and 3.2 × 10 −3 W/K 2 m at 350 K, respectively, with a B-doping concentration of 0.75%. The increase in σ is due to the increase in electron carrier concentration, i.e., the doped B atom acts as an electron donor. Although the doped B atom was predicted to substitute for the Si site and generate holes, 22 another calculation assuming the presence of Mg i suggested that it was located at the interstitial site or the Mg site generating electrons. 19 In this study, we have prepared B-doped Mg 2 Si single crystals (SCs), whose σ is expected to further increase because the carrier mobility of a SC is generally higher than that of a PC. However, it should be noted that the preparation temperature of a SC is mostly higher than that of a PC. At a high preparation temperature, unexpected point defects would be generated. In the case of B-doped Mg 2 Si SCs, we found a killer defect that canceled the effect of the B atom as the electron donor, which is discussed from the results of single-crystal x-ray diffraction (SC-XRD), TE properties, and the novel technique called white neutron holography.
Atomic resolution holography is a powerful probe to directly reveal a three-dimensional local structure in the region of approximately 20 Å from a dopant atom in materials without any proper structure models. X-ray fluorescence holography and photoelectron holography are actively used in novel materials science, for example, in the investigation of dilute magnetic semiconductors, relaxor ferroelectric materials, topological insulators, and so on. [23][24][25][26][27][28][29][30] In particular, neutron holography is indispensable for novel materials science because of higher sensitivity to light elements, such as hydrogen (H), B, and oxygen (O), which play important roles in functional materials. For example, the local structures around a H atom in Al 4 Ta 3 O 13 (OH) 31

II. EXPERIMENTAL PROCEDURES
Before the preparation of B-doped Mg 2 Si SCs, Mg 2 Si powder was synthesized by the solid-state reaction. Mg powder (2N5, 180 μm, Kojundo Chemical Laboratory) and Si powder (4Nup, 300 μm, Kojundo Chemical Laboratory) were weighed in the nominal composition of Mg:Si = 2:1 and was heated at 823 K for 6 h in an evacuated quartz tube. Subsequently, the synthesized Mg 2 Si powder and B powder (2 N, 45 μm pass, Kojundo Chemical Laboratory) were mixed in the nominal composition of Mg 2 Si:B = 100:x (x = 0, 0.25, 0.50, and 0.75). The mixed powder was melted at 1413 K in a quartz tube filled with an Ar gas at a pressure of 1.3 atm, followed by gradual cooling down to 1313 K for 24 h and finally to room temperature for 9 h to obtain a melted ingot. An x-ray Laue diffraction pattern, observed by using an x-ray Laue camera (RINT, Rigaku), clearly confirmed that the obtained ingot was the B-doped Mg 2 Si SC (Fig. 2).
To elucidate the B-doping site in Mg 2 Si, we adopted neutron holography measurement at the beam line 10 (BL10) of Materials and Life Science Experimental Facility (MLF) in the Japan Proton Accelerator Research Complex (J-PARC) in Tokai, Japan. The Bdoped Mg 2 Si SC with the B-doping concentration x = 0.75 was used for the measurement, whose size was 5 × 8 × 10 mm 3 . The atomic images of local atomic structures around the doped B were reconstructed using 66 holograms with different wavelengths in the range of 0.63-3.96 Å (the energy range was 5.22-206.0 meV). The details and principles of white neutron holography are also reported in Refs. 37 and 38. To characterize the crystal structure of all B-doped Mg 2 Si SCs, we performed SC-XRD with Mo Kα radiation (D8 QUEST, Bruker AXS) using a small piece of SC (typically, 30 × 60 × 70 μm 3 ) picked up from the SCs. Crystal structure refinement was carried out by using the least-squares calculation code JANA2006. 39 The measurement temperature for neutron holography and SC-XRD was set at 300 K.
Regarding the TE properties, the Seebeck coefficient, S, and electrical conductivity, σ, were measured in vacuum from 300 K to 850 K using an automated Seebeck tester (RZ2001i, Ozawa Science Co.). To evaluate the electron carrier concentration, n, and carrier mobility, μ, a Hall coefficient was measured under −50 000 Oe to 50 000 Oe magnetic fields at 300 K using the physical property measurement system (PPMS, Quantum Design). The sample size for the ARTICLE scitation.org/journal/adv TE measurements and Hall measurements was ∼3 × 3 × 9 mm 3 and ∼2.5 × 6 × 0.8 mm 3 , respectively.

III. RESULTS AND DISCUSSION
We investigated the B-doping site in the Mg 2 Si SC using white neutron holography. Figure 3(a) shows an atomic image in the [100] plane which includes the doped B atom in the Mg 2 Si SC at room temperature. Bright spots indicate the presence of some kind of atoms, not a ghost, which was periodically located around the B atom (the orange circle) set at the center of the atomic image. The distance between the B atom and the nearest neighbor atom was ∼3.18 Å, corresponding to that between the Mg sites or between the Si and interstitial sites. This means that the B atom substitutes for a specific site in the Mg 2 Si SC. Assuming that the B atom is introduced to the Mg site, Mg atoms are expected to exist in the green circles, as shown in Fig. 3(b). The observed atoms coincided with the green circles, which directly demonstrate that the B atom substitutes for the Mg site. In Fig. 3(c), the expected location of Si atoms is indicated by the red circles in case the B atom is assumed to substitute for the Si site. In the same plane, there are also interstitial sites (the yellow circles). The observed atoms can be assigned to the red and yellow circles on halves. This means that the Si and interstitial sites are occupied at the same rate; however, it is not reasonable because the occupancy of the interstitial site (only ∼1% if a small fraction of Mg exists 1,2 ) and that of the Si site (approximately 100% 1,2 ) are different in the case of the Mg 2 Si PC. The same discussion holds for the case where the B atom is assumed to substitute for the interstitial site [ Fig. 3(d)]. The observed atoms are considered to be located at the interstitial site and at the Si site whose occupancy is the same, but it is not conceivable. Thus, a possibility that the B atom substitutes for the Si or interstitial site is denied. Figure. 3(a) shows the first experimental evidence that doped B is located at the Mg site. From the white neutron holography measurement, electron carriers will increase because the B atom at the Mg site acts as an electron donor.
The B-doping site was further examined by the SC-XRD measurement using the B-doped Mg 2 Si SC with x = 0.75. We considered three situations; the B atoms are introduced to the Mg, Si, or interstitial site. As listed in Table I, the reliability factor, wR, and goodof-fitness, gof, for the case of the Mg site was the lowest among the three situations. Thus, it is concluded that the B atom substitutes for the Mg site, consistent with the result of the white neutron holography measurement. Table II lists the refined structural parameters for all B-doped Mg 2 Si SCs. The lattice parameter decreased with increasing x, supporting the successful substitution of B in the Mg 2 Si SCs. Importantly, it was found that the Si occupancy decreased with increasing x. This means that the Si vacancy (V Si ) is formed in the Bdoped Mg 2 Si SCs. In contrast, V Si was not observed for the B-doped Mg 2 Si PCs. 19 This difference is probably due to the higher preparation temperature of SCs (1413 K) than that of PCs (1123 K 19 ). As mentioned, the B atom at the Mg site introduces electrons, making the chemical potential near the conduction band minimum. In this case, V Si is an acceptor-type defect, according to a theoretical

ARTICLE
scitation.org/journal/adv calculation. 40 Thus, V Si can act like a killer defect that compensates electrons generated from the B atom.
To investigate the B-doping effect on electron concentration, we measured temperature-dependent electrical conductivity, σ, of the B-doped Mg 2 Si SCs (Fig. 4). The filled symbols are the data for the SCs. The data of B-doped Mg 2 Si PCs 19 are shown for comparison (the open symbols). In the case of PCs, σ increases by B-doping; however, the B-doping for the Mg 2 Si SC resulted in the decrease in σ.
To reveal the reason for this difference, the electron carrier concentration, n, and carrier mobility, μ, of the B-doped Mg 2 Si SCs were measured at 300 K [Figs. 5(a) and 5(b)]. In the figures, the n and evaluated μ of B-doped Mg 2 Si PCs 19 are also shown. The n of the non-doped Mg 2 Si SC was comparable with that of the non-doped Mg 2 Si PC. On the other hand, the non-doped Mg 2 Si SC exhibited ten times higher μ than the non-doped Mg 2 Si PC. This is a reason for the higher σ of the non-doped Mg 2 Si SC than the non-doped Mg 2 Si PC. With increasing x, the n increased for the case of PCs, 19 whereas it slightly decreased from 1.1 × 10 19 cm −3 (x = 0) to 8.4 × 10 18 cm −3 (x = 0.75) for the case of SCs. The decrease in n from x = 0 to x = 0.75 amounts to −24%, which is not considered to result from the change in the lattice constant induced by B-doping. The lattice constant decreased from x = 0 to x = 0.75 by −0.12%, which may rather increase n by +0.36%. Thus, an effect of the lattice constant on n and also on the TE properties can be neglected. Instead, the decrease in n can be explained by the competition between the donor-type Bdopant and the acceptor-type V Si defect in the B-doped Mg 2 Si SCs. The μ of the non-doped Mg 2 Si SC was 279 cm 2 /V s, which is in the same order with literature values. [41][42][43][44][45] The μ of the B-doped Mg 2 Si SCs and PCs both decreased with increasing x, probably due to the B-dopant and/or the V Si defect acting as a scattering center of electron carriers. Although the μ of the SCs kept a higher level in the order of 10 2 cm 2 /V s, the decrease in n resulted in the lower electrical conductivity of the B-doped Mg 2 Si SCs than the non-doped Mg 2 Si SC as well as the B-doped Mg 2 Si PC with x = 0.75.
The decrease in n for the B-doped Mg 2 Si SC is further confirmed by the measured Seebeck coefficient, S. Figure 6 shows the temperature dependence of S of the B-doped Mg 2 Si SCs (the filled symbols) together with that of B-doped Mg 2 Si PCs (the open symbols) reported in our previous study. 19 Although there is not much difference in S among the SCs and PCs, one can find that the absolute value of S decreased by B-doping in the case of the PCs. In contrast, it increased with increasing x in the case of the SCs, which is a typical behavior when n decreases.
Finally, we calculated the PF of the B-doped Mg 2 Si SCs, and plotted its temperature dependence as shown in Fig. 7    PCs. 19 Contrary to the case of the Mg 2 Si PC, B-doping deteriorated the PF of the Mg 2 Si SC, mainly reflecting the decrease in σ. The maximum PF of the non-doped Mg 2 Si SC and the B-doped Mg 2 Si SC with x = 0.75 was 2.0 × 10 −3 W/K 2 m at 348 K and 1.7 × 10 −3 W/K 2 m at 348 K, respectively, which was lower than that of the B-doped Mg 2 Si PC with x = 0.75. In this study, we attempted to enhance the TE performance of Mg 2 Si by preparing its SC in combination with B-doping. This attempt was partially successful; a higher μ was achieved for the SCs relative to the PCs, but the V Si defect was unexpectedly formed in the SCs and canceled the effect of the doped B atom as the electron donor. The concentration, N, of doped B atoms or V Si can be estimated by using the formula, because of the fact that V Si only appeared for the B-doped Mg 2 Si SCs prepared at 1413 K, not for the B-doped Mg 2 Si PCs prepared in 1123 K. To avoid the formation of V Si , the preparation temperature should be decreased in order to selectively eliminate V Si but needs to be high enough to prepare a SC. The B-doped Mg 2 Si SC without V Si is the most preferable because it should exhibit high electrical conductivity owing to high electron carrier concentration as well as high carrier mobility. The control of the preparation condition, in particular, the decrease in the preparation temperature, of the B-doped Mg 2 Si SC is underway.

IV. CONCLUSIONS
We have prepared B-doped Mg 2 Si single crystals (SCs) and investigated the effect of B-doping on their crystal structures and thermoelectric (TE) properties. White neutron holography and single-crystal x-ray diffraction (SC-XRD) measurements reveal that the doped B atom substitutes for the Mg site in Mg 2 Si SC together with the formation of Si vacancy (V Si ). It is expected that the B atom  19 This difference between the B-doped Mg 2 Si SCs and PCs is probably due to the preparation temperature. With a higher preparation temperature of the SCs, the formation of V Si is evident.
Regarding the TE properties, the electrical conductivity, σ, of the non-doped Mg 2 Si SC is higher than that of the non-doped Mg 2 Si PC, 19 and this can be seen as a result of their difference in carrier mobility. Opposite to the expectation that B-doping increases σ, electron carrier concentration, n, of the Mg 2 Si SC decreases with increasing x, which can be explained by considering that the V Si defect acts as a killer defect against the doped B atom. In other words, electron carriers generated from the B atom are compensated by the acceptor-type V Si defect. Due to the decrease in n, the absolute value of the Seebeck coefficient of the Mg 2 Si SC slightly increases by Bdoping. Consequently, the power factor, PF, of the Mg 2 Si SC is not enhanced by B-doping. The maximum PF among the SCs is 2.0 × 10 −3 W/K 2 m at 348 K for the non-doped Mg 2 Si SC, which is higher than that of the non-doped Mg 2 Si PC but is lower than that of the B-doped Mg 2 Si PC with x = 0.75.
This study demonstrates that some kind of point defect is unintentionally formed in Mg 2 Si depending on its preparation condition, in particular, on the preparation temperature. White neutron holography and SC-XRD measurements are useful in determining the detailed crystal structure such as dopant sites and point defects in Mg 2 Si. An optimized preparation condition to control the dopant site and point defects can be revealed by using these measurements, and the enhancement of the TE performance of the B-doped Mg 2 Si SC will be realized in the future.

DATA AVAILABILITY
The data that supports the findings of this study are available within this article.