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Quantitative analysis of interstitial Mg in Mg2Si studied by single crystal X-ray diffraction
Journal of Alloys and Compounds 617 (2014) 389–392
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Quantitative analysis of interstitial Mg in Mg2Si studied by single crystal X-ray diffraction M. Kubouchi, K. Hayashi ⇑, Y. Miyazaki Department of Applied Physics, Graduate School of Engineering, Tohoku University, 6-6-05, Aramaki Aza Aoba, Aoba-ku, Sendai, Miyagi 980-8579, Japan
a r t i c l e
i n f o
Article history: Received 2 February 2014 Received in revised form 10 July 2014 Accepted 20 July 2014 Available online 29 July 2014 Keywords: Magnesium silicide Interstitial Mg Single-crystal structure refinement Thermoelectric properties
a b s t r a c t We investigate the existence of Mg at an interstitial (1/2 1/2 1/2) site of Mg-deficient Mg2Si samples, whose nominal composition is Mg2xSi (x = 0, 0.095, 0.182, 0.260, and 0.333). Single-crystal X-ray diffraction measurements indicate that the interstitial Mg (Mgi) is contained in all samples, and its occupancy is around 0.5% regardless of x. This result is supported by the Hamilton test: a hypothesis that the Mgi exists in the Mg2xSi samples is not rejected at the significant level below 0.10. On the other hand, the Mg occupancy at an (1/4 1/4 1/4) site tends to decrease with increasing x. The Seebeck coefficient and electrical conductivity of Mg2xSi is discussed in terms of the x dependence of Mgi (1/2 1/2 1/2) and Mg (1/4 1/ 4 1/4) site occupancies. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Magnesium silicide (Mg2Si) has attracted much attention as one of the promising thermoelectric materials due to the lightweight property and high natural abundance [1–18]. Mg2Si belongs to the anti-fluorite type structure wherein the 8c (1/4 1/4 1/4) and the 4a (0 0 0) sites are occupied by Mg and Si, respectively [19]. According to a first principles calculation using these structural parameters, Mg2Si became p-type [20–22]; however, Mg2Si samples that have been synthesized so far were most commonly n-type [2,13–15]. The n-type characteristic of Mg2Si was explained by assuming the existence of Mg at an interstitial site of 4b (1/2 1/ 2 1/2) for Mgi which has the lowest formation energy among the possible defects such as interstitial Si [23]. The first principles calculation predicted that Mgi leads to increase the electron carrier density. If this prediction is correct, we can prepare n-type and p-type Mg2Si by varying the amount of Mgi. Experimentally, n-type Mg-excess Mg2Si was prepared [11,12]. With increasing excess Mg, the electrical conductivity increased due to the increase of electron carrier density. However, the relation between the excess Mg and the amount of Mgi was not discussed. In this study, we evaluate the amount of Mgi in Mg2Si by using single-crystal X-ray diffraction (XRD). In addition, we prepare Mg-deficient Mg2Si samples to elucidate whether or not the amount of Mgi can be controlled.
⇑ Corresponding author. Tel./fax: +81 227957971. E-mail address: [email protected] (K. Hayashi). http://dx.doi.org/10.1016/j.jallcom.2014.07.137 0925-8388/Ó 2014 Elsevier B.V. All rights reserved.
2. Experimental The nominal composition of Mg-deficient Mg2Si was Mg2xSi (x = 0, 0.095, 0.182, 0.260 and 0.333). The starting materials, Mg2Si (2N) and Si (4N) powders, were weighted and mixed for 10 min. The polycrystalline Mg2xSi samples were synthesized by means of a spark plasma sintering (SPS) technique (SPS-511S, Fuji Electronic Industrial). The pressure and sintering temperature in the SPS process were 30 MPa and 1123 K for 10 min, respectively. The surface morphology and compositions of the samples were investigated by using a scanning electron microscope equipped with an energy-dispersive X-ray spectrometer (SEM–EDX; JEM6500F, JEOL). To characterize the crystal structure, we performed powder XRD with Cu Ka radiation (D8 ADVANCE, Bruker AXS) and single-crystal XRD with Mo Ka radiation (D8 QUEST, Bruker AXS). A simulated powder XRD pattern was calculated by means of RIETAN-FP [24]. Single-crystal structure refinement was carried out by using the least-squares calculation code JANA2006 [25]. In addition, the Seebeck coefficient and electrical conductivity of samples were measured in vacuum using an automated Seebeck tester (RZ2001i, Ozawa Science Co.).
3. Results and discussion Fig. 1 shows SEM images of the polished surface of Mg2xSi samples. The main phase was Mg2Si while there was a small amount of secondary phase of MgO for all samples. From the EDX analysis, we could not detect definite difference of Mg and Si compositions in the Mg2Si phase among the samples. With increasing x, Si secondary phase gradually increased. The SEM observations coincided with the powder XRD measurement as shown in Fig. 2a. The simulated XRD pattern of Mg2Si is also shown in the figure. Small MgO peaks were observed in all XRD patterns. The traces of Si secondary phase were found above x = 0.182. The other peaks were assigned to Mg2Si. It is noted that the 1 1 1 peak for synthesized samples was higher than that of the simulation.
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size. Fig. 2b shows the intensity ratio of the 1 1 1 peak to the 2 2 0 peak for the x = 0.333 sample as a function of grinding time. The intensity ratio decreased with grinding time, indicating that the area of the 1 1 1 plane decreased due to smaller grains; however, it was still higher than that of the simulation. Thus, the structural parameters were not refined from the powder XRD measurement. The preferred orientation of Mg2xSi grains indicates that small single crystals are easily obtained from the polycrystalline Mg2xSi samples. In fact, we could pick up Mg2Si single crystals with a typical size of 40 lm 60 lm 60 lm from fractured SPS samples. The single-crystal XRD measurement using these single crystals enabled us to refine the structural parameters. Three structures were assumed: (a) stoichiometric Mg2Si, (b) Mg-deficient Mg2Si, and (c) Mg-deficient Mg2Si with Mgi. For the Mgi site, we examined two possible cases, (1/2 1/2 1/4) and (1/2 1/2 1/2) sites, using the JANA2006 refinement program. As a result, structural parameters diverged in the case of (1/2 1/2 1/4). In addition, the ð1=2 þ Dx 1=2 þ Dy 1=2 þ DzÞ site, slightly deviated from the (1/ 2 1/2 1/2) site, was examined. It was found that the deviations, Dx; Dy, and Dz, became zero through the structural refinement. Thus, we determined that the interstitial Mg was located at the 4b (1/2 1/2 1/2) site. The evaluated wR-factor was the lowest in the third case (c) as can be seen in Fig. 3. Although it seemed that the case (c) is more preferable than the case (b), wR-factor is generally reduced with increasing the number of variable parameters. Therefore, it is necessary to confirm the significance of wR-factor reduction by using the Hamilton test [26]. Applying the Hamilton test to this study, we define a ratio of wR-factors, R, as
R¼
R0 R1
ð1Þ
where R0 and R1 are the wR factors obtained in second and third cases, respectively. The ratio R is compared to the reliability factor, Rb;nb;a , expressed by
Rb;nb;a ¼
Fig. 1. SEM images of the Mg2xSi samples. The inset in the SEM image of the x = 0.333 sample is a magnified image.
The high 1 1 1 peak was not due to the existence of Mgi, but to a cleavage characteristic of the anti-fluorite type structure such as Mg2Si. In other words, the sample could have preferred orientation to increase the intensity along the 1 1 1 peak compared with 2 2 0 peak. Since it was difficult to refine the structural parameters of Mg2Si with preferred orientation, we attempted to reduce grain
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b F b;nb;a þ 1 nb
ð2Þ
where b; n; a and F b;nb;a are the increased number of parameters, degree of freedom, significance level, and F-distribution, respectively. In this study, b is equal to 1 because one parameter, the Mgi occupancy, was added from the second case (b) to the third case (c), and n is the total number of reflections with the exception of equivalent ones. As long as R P Rb;nb;a , a hypothesis that the Mgi existed in the Mg2xSi sample is not rejected at the significance level, a. Table 1 shows the results of Hamilton test. The Rb;nb;a at the minimum a where R P Rb;nb;a is listed. Since the quality of single crystals picked up from the x = 0.260 and 0.333 samples was poor due to the existence of Si impurity, the number of n of these
Fig. 2. (a) Powder XRD patterns of the Mg2xSi samples. The simulated XRD pattern of Mg2Si is also shown. (b) Intensity ratio of the 1 1 1 peak to the 2 2 0 peak for the x = 0.333 sample and the simulation.
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Fig. 3. Final wR-factor for three structures: (a) Mg2Si, (b) Mg-deficient Mg2Si, and (c) Mg-deficient Mg2Si with Mgi.
Table 1 Results of significance level by Hamilton test. x
R0
R1
n
R
Rb;nb;a
a
0 0.095 0.182 0.260 0.333
1.60 2.48 1.43 1.68 1.65
1.47 2.25 1.34 1.60 1.56
48 48 45 29 29
1.0884 1.1022 1.0672 1.0500 1.0604
1.0883 1.0993 1.0664 1.0500 1.0602
0.005 0.003 0.018 0.100 0.073
two samples became smaller than that of the others. Nevertheless, we found that a was lower than 0.10 for all samples. The significant level of 0.10 is enough to conclude that the Mg2xSi samples contains Mgi regardless of x. Table 2 represents the occupancies of the Mg, Si, and Mgi sites of Mg2xSi samples. We set a linear constraint condition that the
thermal displacement parameter of Mgi is equal to that of Mg. The Si occupancy was almost 100% for all samples, while the occupancy of the Mg site tended to decrease with increasing x although the variation of Mg occupancy was within the standard deviation range. We found that all samples contained Mgi whose amount did not show clear x dependence. The Mgi occupancy was about 0.5%. These results indicate that it is difficult to control the Mgi occupancy, but the occupancy of the 8c Mg site may be controllable. To investigate the effect of site occupancies to thermoelectric properties, we measured the Seebeck coefficient and electrical conductivity of Mg2xSi samples as shown in Fig. 4. The x = 0.333 sample was too fragile to measure. The other samples exhibited negative Seebeck coefficient, reflecting the existence of Mgi. With increasing x, the absolute value of Seebeck coefficient increased, while the electrical conductivity decreased. The x dependences of Seebeck coefficient and electrical conductivity can be attributed to the increasing Si secondary phase and the decrease of the Mg occupancy. The latter leads to decrease the electron carrier density because the Fermi level moves from the bottom of conduction band down into the band gap [20,21]. In fact, the temperature where the Seebeck coefficient reached to the maximum value became lower with increasing x, verifying the shift of Fermi level. Thus, we believe that the 8c Mg site occupancy decreased with increasing x. It is expected that n-type and p-type Mg2Si can be prepared by changing the 8c Mg site occupancy. We note in passing that the Mg-deficient Mg2Si was prepared by using Mg2Si and Si in this study. This preparation method led to the conclusion that only 8c Mg site occupancy was controllable. There is another method to prepare the Mg-deficient Mg2Si, e.g., using Mg and Si as starting materials, which may enable us to control 4b Mgi as well as 8c Mg site occupancies. Since the Mgi introduces the electron carriers to Mg2Si, the increase (decrease) of Mgi amount will improve the n-type (p-type) thermoelectric
Table 2 Occupancies of 8c (1/4 1/4 1/4) for Mg, 4a (0 0 0) for Si and 4b (1/2 1/2 1/2) for Mgi sites of the Mg2xSi samples. The unit of thermal displacement parameters U iso , is pm2. x
Mg occupancy (%)
Si occupancy (%)
Mgi (%)
Lattice parameter (Å)
0
99.9 (5) U iso ¼ 117 99.6 (8) U iso ¼ 119 99.5 (4) U iso ¼ 107 99.7 (8) U iso ¼ 117 98.9 (6) U iso ¼ 114
99.9 (5) U iso ¼ 85 99.9 (4) U iso ¼ 94 99.9 (5) U iso ¼ 79 99.9 (4) U iso ¼ 88 99.9 (4) U iso ¼ 89
0.54 (22) U iso ¼ 117a 0.92 (31) U iso ¼ 119a 0.39 (19) U iso ¼ 107a 0.44 (29) U iso ¼ 117a 0.47 (28) U iso ¼ 114a
6.3521 (7)
0.095 0.182 0.260 0.333 a
ð2Þ ð4Þ ð2Þ ð4Þ ð4Þ
ð3Þ ð4Þ ð2Þ ð5Þ ð4Þ
We set a linear constraint condition that the thermal displacement parameter of Mgi is equal to that of Mg.
Fig. 4. Temperature dependence of (a) Seebeck coefficient and (b) electrical conductivity of the Mg2xSi samples.
6.3516 (36) 6.3538 (7) 6.3512 (14) 6.3475 (8)
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performance due to the increase (decrease) of electron carriers. The preparation of Mg-excess or Mg-deficient Mg2Si from Mg and Si raw materials in combination with doping is underway.
Japan, and Industry, and Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.
4. Conclusions
References
We investigate the existence of Mgi in Mg2Si by preparing polycrystalline Mg2xSi in the nominal composition, i.e, the Mg-deficient Mg2Si samples, using an SPS technique. The SEM–EDX observation indicates that the main phase is Mg2Si for all samples. The MgO and Si secondary phases are slightly contained. These results are consistent with the powder XRD measurement. In the powder XRD patterns, we find that the 1 1 1 peak is higher than the 2 2 0 peak due to the preferred orientation of Mg2xSi grains in the Mg2xSi polycrystalline samples. Taking advantage of the preferred orientation, we succeed in picking up small single crystals of Mg2xSi from the fractured SPS samples. Using these single crystals, the single-crystal XRD measurement is performed to refine structural parameters. As a result, we found that all samples contain about 0.5% Mgi regardless of x, an indication of difficulty in controlling the Mgi occupancy. On the other hand, the occupancy of the Mg site tends to decrease with increasing x. Reflecting the x dependence of the Mg site occupancy, the Seebeck coefficient increases and the electrical conductivity decreases as a function of x. In other words, the decrease of the Mg site occupancy leads to decrease the electron carrier density. Therefore, we expect that controlling the electron carrier density as well as doping is the key to improve the thermoelectric performance of n-type and p-type Mg2Si. Acknowledgements The authors appreciate Prof. T. Kajitani for discussion on the single-crystal structure refinement. M.K. is grateful to Mr. T. Miyazaki of Instrumental Analysis Group at Tohoku University for the SEM–EDX measurements. This work was partly supported by the Supporting Industry project of Ministry of Economy, Trade of
[1] V.K. Zaitsev, M.I. Fedorov, E.A. Gurieva, I.S. Eremin, P.P. Konstantinov, A.Y. Samunin, M.V. Vedernikov, Phys. Rev. B. 74 (2006) 045207. [2] J. Tani, H. Kido, Intermetallics 15 (2007) 1202. [3] T. Niwa, Y. Todaka, T. Masuda, T. Kawai, M. Umemoto, Mater. Trans. 50 (2009) 1725. [4] M. Yang, W. Luo, Q. Shen, H. Jiang, L. Zhang, Adv. Mater. Res. 66 (2009) 17. [5] K. Mars, H. Ihou-Mouko, G. Pont, J. Tobola, H. Scherrer, J. Electr. Mater. 38 (2009) 1360. [6] T. Sakamoto, T. Iida, S. Kurosaki, K. Yano, H. Taguchi, K. Nishio, Y. Kogo, Y. Takanashi, J. Electr. Mater. 39 (2010) 1708. [7] W. Liu, X. Tang, J. Sharp, J. Phys. D: Appl. Phys. 43 (2010) 085406. [8] Y. Isoda, S. Tada, T. Nagai, H. Fijiu, Y. Shinohara, Mater. Trans. 51 (2010) 868. [9] W. Luo, M. Yang, F. Chen, Q. Shen, H. Jiang, L. Zhang, Mater. Trans. 51 (2010) 288. [10] H. Ihou-Mouko, C. Mercier, J. Tobola, G. Pont, H. Scherrer, J. Alloys Comp. 509 (2011) 6503. [11] W. Liu, X. Tang, H. Li, J. Sharp, X. Zhou, C. Uher, Chem. Mater. 23 (2011) 5256. [12] Z. Du, T. Zhu, Y. Chen, J. He, H. Gao, G. Jiang, T.M. Tritt, X. Zhao, J. Mater. Chem. 22 (2012) 6838. [13] S. You, K. Park, I. Kim, S. Choi, W. Seo, S. Kim, J. Electr. Mater. 41 (2012) 1675. [14] Y. Hayatsu, T. Iida, T. Sakamoto, S. Kurosaki, K. Nishio, Y. Kogo, Y. Takanashi, J. Solid State Chem. 193 (2012) 161. [15] G. Jiang, L. Chen, J. He, H. Gao, Z. Du, X. Zhao, T.M. Tritt, T. Zhu, Intermetallics 32 (2013) 312. [16] T. Nemoto, T. Iida, J. Sato, T. Sakamoto, N. Hirayama, T. Nakajima, Y. Takanashi, J. Electr. Mater. 42 (2013) 2192. [17] W. Liu, K. Yin, X. Su, H. Li, Y. Yan, X. Tang, C. Uher, Intermetallics 32 (2013) 352. [18] T. Kajitani, M. Kubouchi, S. Kikuchi, K. Hayashi, T. Ueno, Y. Miyazaki, K. Yubuta, J. Electr. Mater. 42 (2013) 1855. [19] Y. Noda, H. Kon, Y. Furukawa, N. Otsuka, I.A. Nishida, K. Masumoto, Mater. Trans, JIM 33 (1992) 845. [20] Y. Imai, A. Watanabe, M. Mukaida, J. Alloys Comp. 358 (2003) 257. [21] J. Tobola, S. Kaprzyk, H. Scherrer, J. Electr. Mater. 39 (2010) 2064. [22] H. Wang, W. Chu, H. Jin, Comp. Mater. Sci. 60 (2012) 224. [23] A. Kato, T. Yagi, N. Fukusako, J. Phys.: Condens. Matter 21 (2009) 205801. [24] F. Izumi, K. Momma, Solid State Phenom. 130 (2007) 15. [25] V. Petricek, M. Dusek, L. Palatinus, JANA2006, The Crystallographic Computing System, Institute of Physics, Praha, 2006. [26] W.C. Hamilton, Acta Crystallogr. 18 (1965) 502.
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Quantitative analysis of interstitial Mg in Mg2Si studied by single crystal X-ray diffraction M. Kubouchi, K. Hayashi ⇑, Y. Miyazaki Department of Applied Physics, Graduate School of Engineering, Tohoku University, 6-6-05, Aramaki Aza Aoba, Aoba-ku, Sendai, Miyagi 980-8579, Japan
a r t i c l e
i n f o
Article history: Received 2 February 2014 Received in revised form 10 July 2014 Accepted 20 July 2014 Available online 29 July 2014 Keywords: Magnesium silicide Interstitial Mg Single-crystal structure refinement Thermoelectric properties
a b s t r a c t We investigate the existence of Mg at an interstitial (1/2 1/2 1/2) site of Mg-deficient Mg2Si samples, whose nominal composition is Mg2xSi (x = 0, 0.095, 0.182, 0.260, and 0.333). Single-crystal X-ray diffraction measurements indicate that the interstitial Mg (Mgi) is contained in all samples, and its occupancy is around 0.5% regardless of x. This result is supported by the Hamilton test: a hypothesis that the Mgi exists in the Mg2xSi samples is not rejected at the significant level below 0.10. On the other hand, the Mg occupancy at an (1/4 1/4 1/4) site tends to decrease with increasing x. The Seebeck coefficient and electrical conductivity of Mg2xSi is discussed in terms of the x dependence of Mgi (1/2 1/2 1/2) and Mg (1/4 1/ 4 1/4) site occupancies. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Magnesium silicide (Mg2Si) has attracted much attention as one of the promising thermoelectric materials due to the lightweight property and high natural abundance [1–18]. Mg2Si belongs to the anti-fluorite type structure wherein the 8c (1/4 1/4 1/4) and the 4a (0 0 0) sites are occupied by Mg and Si, respectively [19]. According to a first principles calculation using these structural parameters, Mg2Si became p-type [20–22]; however, Mg2Si samples that have been synthesized so far were most commonly n-type [2,13–15]. The n-type characteristic of Mg2Si was explained by assuming the existence of Mg at an interstitial site of 4b (1/2 1/ 2 1/2) for Mgi which has the lowest formation energy among the possible defects such as interstitial Si [23]. The first principles calculation predicted that Mgi leads to increase the electron carrier density. If this prediction is correct, we can prepare n-type and p-type Mg2Si by varying the amount of Mgi. Experimentally, n-type Mg-excess Mg2Si was prepared [11,12]. With increasing excess Mg, the electrical conductivity increased due to the increase of electron carrier density. However, the relation between the excess Mg and the amount of Mgi was not discussed. In this study, we evaluate the amount of Mgi in Mg2Si by using single-crystal X-ray diffraction (XRD). In addition, we prepare Mg-deficient Mg2Si samples to elucidate whether or not the amount of Mgi can be controlled.
⇑ Corresponding author. Tel./fax: +81 227957971. E-mail address: [email protected] (K. Hayashi). http://dx.doi.org/10.1016/j.jallcom.2014.07.137 0925-8388/Ó 2014 Elsevier B.V. All rights reserved.
2. Experimental The nominal composition of Mg-deficient Mg2Si was Mg2xSi (x = 0, 0.095, 0.182, 0.260 and 0.333). The starting materials, Mg2Si (2N) and Si (4N) powders, were weighted and mixed for 10 min. The polycrystalline Mg2xSi samples were synthesized by means of a spark plasma sintering (SPS) technique (SPS-511S, Fuji Electronic Industrial). The pressure and sintering temperature in the SPS process were 30 MPa and 1123 K for 10 min, respectively. The surface morphology and compositions of the samples were investigated by using a scanning electron microscope equipped with an energy-dispersive X-ray spectrometer (SEM–EDX; JEM6500F, JEOL). To characterize the crystal structure, we performed powder XRD with Cu Ka radiation (D8 ADVANCE, Bruker AXS) and single-crystal XRD with Mo Ka radiation (D8 QUEST, Bruker AXS). A simulated powder XRD pattern was calculated by means of RIETAN-FP [24]. Single-crystal structure refinement was carried out by using the least-squares calculation code JANA2006 [25]. In addition, the Seebeck coefficient and electrical conductivity of samples were measured in vacuum using an automated Seebeck tester (RZ2001i, Ozawa Science Co.).
3. Results and discussion Fig. 1 shows SEM images of the polished surface of Mg2xSi samples. The main phase was Mg2Si while there was a small amount of secondary phase of MgO for all samples. From the EDX analysis, we could not detect definite difference of Mg and Si compositions in the Mg2Si phase among the samples. With increasing x, Si secondary phase gradually increased. The SEM observations coincided with the powder XRD measurement as shown in Fig. 2a. The simulated XRD pattern of Mg2Si is also shown in the figure. Small MgO peaks were observed in all XRD patterns. The traces of Si secondary phase were found above x = 0.182. The other peaks were assigned to Mg2Si. It is noted that the 1 1 1 peak for synthesized samples was higher than that of the simulation.
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size. Fig. 2b shows the intensity ratio of the 1 1 1 peak to the 2 2 0 peak for the x = 0.333 sample as a function of grinding time. The intensity ratio decreased with grinding time, indicating that the area of the 1 1 1 plane decreased due to smaller grains; however, it was still higher than that of the simulation. Thus, the structural parameters were not refined from the powder XRD measurement. The preferred orientation of Mg2xSi grains indicates that small single crystals are easily obtained from the polycrystalline Mg2xSi samples. In fact, we could pick up Mg2Si single crystals with a typical size of 40 lm 60 lm 60 lm from fractured SPS samples. The single-crystal XRD measurement using these single crystals enabled us to refine the structural parameters. Three structures were assumed: (a) stoichiometric Mg2Si, (b) Mg-deficient Mg2Si, and (c) Mg-deficient Mg2Si with Mgi. For the Mgi site, we examined two possible cases, (1/2 1/2 1/4) and (1/2 1/2 1/2) sites, using the JANA2006 refinement program. As a result, structural parameters diverged in the case of (1/2 1/2 1/4). In addition, the ð1=2 þ Dx 1=2 þ Dy 1=2 þ DzÞ site, slightly deviated from the (1/ 2 1/2 1/2) site, was examined. It was found that the deviations, Dx; Dy, and Dz, became zero through the structural refinement. Thus, we determined that the interstitial Mg was located at the 4b (1/2 1/2 1/2) site. The evaluated wR-factor was the lowest in the third case (c) as can be seen in Fig. 3. Although it seemed that the case (c) is more preferable than the case (b), wR-factor is generally reduced with increasing the number of variable parameters. Therefore, it is necessary to confirm the significance of wR-factor reduction by using the Hamilton test [26]. Applying the Hamilton test to this study, we define a ratio of wR-factors, R, as
R¼
R0 R1
ð1Þ
where R0 and R1 are the wR factors obtained in second and third cases, respectively. The ratio R is compared to the reliability factor, Rb;nb;a , expressed by
Rb;nb;a ¼
Fig. 1. SEM images of the Mg2xSi samples. The inset in the SEM image of the x = 0.333 sample is a magnified image.
The high 1 1 1 peak was not due to the existence of Mgi, but to a cleavage characteristic of the anti-fluorite type structure such as Mg2Si. In other words, the sample could have preferred orientation to increase the intensity along the 1 1 1 peak compared with 2 2 0 peak. Since it was difficult to refine the structural parameters of Mg2Si with preferred orientation, we attempted to reduce grain
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b F b;nb;a þ 1 nb
ð2Þ
where b; n; a and F b;nb;a are the increased number of parameters, degree of freedom, significance level, and F-distribution, respectively. In this study, b is equal to 1 because one parameter, the Mgi occupancy, was added from the second case (b) to the third case (c), and n is the total number of reflections with the exception of equivalent ones. As long as R P Rb;nb;a , a hypothesis that the Mgi existed in the Mg2xSi sample is not rejected at the significance level, a. Table 1 shows the results of Hamilton test. The Rb;nb;a at the minimum a where R P Rb;nb;a is listed. Since the quality of single crystals picked up from the x = 0.260 and 0.333 samples was poor due to the existence of Si impurity, the number of n of these
Fig. 2. (a) Powder XRD patterns of the Mg2xSi samples. The simulated XRD pattern of Mg2Si is also shown. (b) Intensity ratio of the 1 1 1 peak to the 2 2 0 peak for the x = 0.333 sample and the simulation.
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Fig. 3. Final wR-factor for three structures: (a) Mg2Si, (b) Mg-deficient Mg2Si, and (c) Mg-deficient Mg2Si with Mgi.
Table 1 Results of significance level by Hamilton test. x
R0
R1
n
R
Rb;nb;a
a
0 0.095 0.182 0.260 0.333
1.60 2.48 1.43 1.68 1.65
1.47 2.25 1.34 1.60 1.56
48 48 45 29 29
1.0884 1.1022 1.0672 1.0500 1.0604
1.0883 1.0993 1.0664 1.0500 1.0602
0.005 0.003 0.018 0.100 0.073
two samples became smaller than that of the others. Nevertheless, we found that a was lower than 0.10 for all samples. The significant level of 0.10 is enough to conclude that the Mg2xSi samples contains Mgi regardless of x. Table 2 represents the occupancies of the Mg, Si, and Mgi sites of Mg2xSi samples. We set a linear constraint condition that the
thermal displacement parameter of Mgi is equal to that of Mg. The Si occupancy was almost 100% for all samples, while the occupancy of the Mg site tended to decrease with increasing x although the variation of Mg occupancy was within the standard deviation range. We found that all samples contained Mgi whose amount did not show clear x dependence. The Mgi occupancy was about 0.5%. These results indicate that it is difficult to control the Mgi occupancy, but the occupancy of the 8c Mg site may be controllable. To investigate the effect of site occupancies to thermoelectric properties, we measured the Seebeck coefficient and electrical conductivity of Mg2xSi samples as shown in Fig. 4. The x = 0.333 sample was too fragile to measure. The other samples exhibited negative Seebeck coefficient, reflecting the existence of Mgi. With increasing x, the absolute value of Seebeck coefficient increased, while the electrical conductivity decreased. The x dependences of Seebeck coefficient and electrical conductivity can be attributed to the increasing Si secondary phase and the decrease of the Mg occupancy. The latter leads to decrease the electron carrier density because the Fermi level moves from the bottom of conduction band down into the band gap [20,21]. In fact, the temperature where the Seebeck coefficient reached to the maximum value became lower with increasing x, verifying the shift of Fermi level. Thus, we believe that the 8c Mg site occupancy decreased with increasing x. It is expected that n-type and p-type Mg2Si can be prepared by changing the 8c Mg site occupancy. We note in passing that the Mg-deficient Mg2Si was prepared by using Mg2Si and Si in this study. This preparation method led to the conclusion that only 8c Mg site occupancy was controllable. There is another method to prepare the Mg-deficient Mg2Si, e.g., using Mg and Si as starting materials, which may enable us to control 4b Mgi as well as 8c Mg site occupancies. Since the Mgi introduces the electron carriers to Mg2Si, the increase (decrease) of Mgi amount will improve the n-type (p-type) thermoelectric
Table 2 Occupancies of 8c (1/4 1/4 1/4) for Mg, 4a (0 0 0) for Si and 4b (1/2 1/2 1/2) for Mgi sites of the Mg2xSi samples. The unit of thermal displacement parameters U iso , is pm2. x
Mg occupancy (%)
Si occupancy (%)
Mgi (%)
Lattice parameter (Å)
0
99.9 (5) U iso ¼ 117 99.6 (8) U iso ¼ 119 99.5 (4) U iso ¼ 107 99.7 (8) U iso ¼ 117 98.9 (6) U iso ¼ 114
99.9 (5) U iso ¼ 85 99.9 (4) U iso ¼ 94 99.9 (5) U iso ¼ 79 99.9 (4) U iso ¼ 88 99.9 (4) U iso ¼ 89
0.54 (22) U iso ¼ 117a 0.92 (31) U iso ¼ 119a 0.39 (19) U iso ¼ 107a 0.44 (29) U iso ¼ 117a 0.47 (28) U iso ¼ 114a
6.3521 (7)
0.095 0.182 0.260 0.333 a
ð2Þ ð4Þ ð2Þ ð4Þ ð4Þ
ð3Þ ð4Þ ð2Þ ð5Þ ð4Þ
We set a linear constraint condition that the thermal displacement parameter of Mgi is equal to that of Mg.
Fig. 4. Temperature dependence of (a) Seebeck coefficient and (b) electrical conductivity of the Mg2xSi samples.
6.3516 (36) 6.3538 (7) 6.3512 (14) 6.3475 (8)
392
M. Kubouchi et al. / Journal of Alloys and Compounds 617 (2014) 389–392
performance due to the increase (decrease) of electron carriers. The preparation of Mg-excess or Mg-deficient Mg2Si from Mg and Si raw materials in combination with doping is underway.
Japan, and Industry, and Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.
4. Conclusions
References
We investigate the existence of Mgi in Mg2Si by preparing polycrystalline Mg2xSi in the nominal composition, i.e, the Mg-deficient Mg2Si samples, using an SPS technique. The SEM–EDX observation indicates that the main phase is Mg2Si for all samples. The MgO and Si secondary phases are slightly contained. These results are consistent with the powder XRD measurement. In the powder XRD patterns, we find that the 1 1 1 peak is higher than the 2 2 0 peak due to the preferred orientation of Mg2xSi grains in the Mg2xSi polycrystalline samples. Taking advantage of the preferred orientation, we succeed in picking up small single crystals of Mg2xSi from the fractured SPS samples. Using these single crystals, the single-crystal XRD measurement is performed to refine structural parameters. As a result, we found that all samples contain about 0.5% Mgi regardless of x, an indication of difficulty in controlling the Mgi occupancy. On the other hand, the occupancy of the Mg site tends to decrease with increasing x. Reflecting the x dependence of the Mg site occupancy, the Seebeck coefficient increases and the electrical conductivity decreases as a function of x. In other words, the decrease of the Mg site occupancy leads to decrease the electron carrier density. Therefore, we expect that controlling the electron carrier density as well as doping is the key to improve the thermoelectric performance of n-type and p-type Mg2Si. Acknowledgements The authors appreciate Prof. T. Kajitani for discussion on the single-crystal structure refinement. M.K. is grateful to Mr. T. Miyazaki of Instrumental Analysis Group at Tohoku University for the SEM–EDX measurements. This work was partly supported by the Supporting Industry project of Ministry of Economy, Trade of
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