Quantitative analysis of interstitial Mg in Mg2Si

Journal of Alloys and Compounds 617 (2014) 389–392
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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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M. Kubouchi et al. / Journal of Alloys and Compounds 617 (2014) 389–392
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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M. Kubouchi et al. / Journal of Alloys and Compounds 617 (2014) 389–392
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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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
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preferred orientation, we succeed in picking up small single crystals of Mg2xSi from the fractured SPS samples. Using these single
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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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