Materials Science and Engineering A 434 (2006) 166–170
Thermal stability and grain growth behavior of nanocrystalline Mg2Si
L. Wang, X.Y. Qin ∗ , W. Xiong, L. Chen, M.G. Kong
Key Laboratory of Materials Physics, Institute of Solid State Physics Academia Sinica, 230031 Hefei, PR China
Received 5 January 2006; received in revised form 26 June 2006; accepted 26 June 2006
Abstract
Thermal stability and grain growth behavior of nanocrystalline Mg2 Si (nano-Mg2 Si), prepared by using mechanically activated solid-state
reaction plus hot-pressing in vacuum, were investigated by the method of in situ high-temperature X-ray diffraction. The result indicates that the
evolution of grain size d with isothermal-annealing time t for nano-Mg2 Si can be well described by the formula d − d0 = ct1/n with grain growth
exponent n = 6, 5 and 4 at 700, 800 and 900 ◦ C, respectively, indicating that nano-Mg2 Si has a good thermal stability. Simultaneously, an Arrhenius
plot of rate constant c against the reciprocal of T yields a straight line, from which an activation energy of 112 ± 1 kJ/mol is derived for the grain
growth of nano-Mg2 Si.
© 2006 Elsevier B.V. All rights reserved.
Keywords: Nanocrystalline materials; Intermetallic compounds; Grain growth; Mg2 Si
1. Introduction
2. Experimental procedures
The ordered intermetallic Mg2 Si has emerged as a suitable
candidate material for structure application because of its low
density (1.99 g/cm3 ), high compression strength (1640 MPa),
high melting point (1358 K) and great Young’s modulus
(120 GPa). However, the poor room temperature ductility and
low toughness of Mg2 Si are its major shortcomings. It is brittle from room temperature up to 450 ◦ C (the temperature of
ductile to brittle transition) [1]. Previous investigations showed
that the mechanical properties of Mg2 Si could be improved
by refining the grains [2–4], and several studies were focused
on fabrication of nanocrystalline Mg2 Si (nano-Mg2 Si) [5–7].
There are many investigations on thermal stability and grain
growth behavior of various nanocrystalline materials including
pure metals [8], oxides [9], compounds, and composites [10].
However, investigations on thermal stability of bulk nanocrystalline intermetallics, such as nano-Mg2 Si, are still wanting. In
this work, thermal stability and grain growth of nano-Mg2 Si,
fabricated by using the method of mechanically activated solidstate reaction plus hot-pressing in vacuum, were investigated by
in situ high-temperature X-ray diffraction (HT-XRD).
The nano-Mg2 Si compact was prepared by mechanically
activated solid-state reaction [6] and hot-pressing (HPing) in
vacuum. At first, Mg and Si powders (both are 99% pure
(100 mesh)) were blended. Then ball milling was carried out in
a planetary ball mill in Ar (5 N pure) atmosphere at room temperature. The ball-to-powder weight ratio is 50:1. After milled
for 25 h, the as-milled powders were sealed in a tungsten carbide die with internal diameter of 13 mm, and hot-pressed in
vacuum at 400 ◦ C for 1 h under the pressure of 1.5 GPa. Then a
Mg2 Si compact with a relative density of 91.5% was obtained.
The average grain size of the Mg2 Si compact was determined
(by XRD) to be 30 nm.
Three disk-shaped specimens with dimension of Ø13 mm ×
(∼)1 mm were cut from the compact for HT-XRD experiments. Isothermal annealing and in situ HT-XRD measurements
were carried out (using Cu K␣ radiation) on the diffractometer
(PW3373) equipped with a high-vacuum chamber (background
pressure in the chamber <1.2 × 10−2 Pa). The average grain
size of Mg2 Si and its evolution during isothermal annealing
were determined by line-broadening of (1 1 1) reflection peak
of Mg2 Si using Scherrer formula [11]. A small angular step of
0.02◦ (2Θ) and a fixed counting time of 20 s were utilized to measure the intensity of (1 1 1) reflection peak. The heating rate from
room temperature to the desired temperatures was 15 ◦ C/min.
After the desired temperatures were reached, the specimens were
∗
Corresponding author. Tel.: +86 551 5592750; fax: +86 551 5591434.
E-mail address: [email protected] (X.Y. Qin).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.msea.2006.06.130
L. Wang et al. / Materials Science and Engineering A 434 (2006) 166–170
167
then kept isothermally. The XRD data were collected at the time
intervals of 8.95, 8.06 and 6.73 min during isothermal annealing
at 700, 800 and 900 ◦ C, respectively. The temperature fluctuation was controlled within ±1 ◦ C. The density of specimens
was measured, based on the Archimedes principle, within an
accuracy of ±0.2%. The fractography was performed by using
a field-emission scanning microscope (FE-SEM, Sirion 200).
3. Results
Fig. 1 shows room temperature X-ray diffraction patterns
for the as-prepared specimen (Fig. 1a) and those annealed
isothermally at different temperatures in HT-XRD experiments
(Fig. 1b–d). One can see that only Mg2 Si phase is observed in the
as-prepared specimen. However, upon annealing a small quantity of MgO appeared, as indicated in the figure. The observed
MgO phase is, therefore, deduced to originate from oxidation of
the specimens during annealing, presumably due to trace oxygen
present in the vacuum chamber of the X-ray diffractometer.
The average grain sizes of nano-Mg2 Si as a function of time
in isothermal annealing at different temperatures are shown in
Fig. 2. One can see that the grain size of nano-Mg2 Si increases
rapidly to about 63 nm after annealing at 900 ◦ C for 4.14 h. In
contrast, it increases only to about 43 nm after annealing at
800 ◦ C for 4.68 h. Specially, the grain growth of nano-Mg2 Si
occurs much slowly at 700 ◦ C; after annealing at this temper-
Fig. 2. Variations of grain size of the nano-Mg2 Si with the time of isothermal
annealing at 700 ◦ C (a), 800 ◦ C (b), and 900 ◦ C (c). The solid lines are the best
fits of the experimental data to formula (1).
ature for ∼3 h it increases to only ∼40 nm and then it seems
to level off as annealing proceeds further (<5.22 h). This result
indicates that nanostructured Mg2 Si displays a good thermal
stability, at least, at (or below) 700 ◦ C. To confirm the XRD
results, FE-SEM observations on the fracture surfaces of the
nano-Mg2 Si samples were performed. As a typical example,
Fig. 3 shows grain morphology for the specimen annealed at
900 ◦ C for 4.14 h. One can see that most of Mg2 Si grains are
round shaped with average diameter around 60–70 nm, which is
in good agreement with the XRD measurement.
The relationship between average grain size and isothermalannealing time can be expressed in the form [12,13]:
d − d0 = ct 1/n
(1)
or
1
ln(d − d0 ) =
ln(t) + ln(c)
n
(1 )
where d0 is the initial grain size (in isothermal annealing), d the
grain size after annealing for time t, c the rate constant at a given
Fig. 1. Room-temperature XRD patterns for an as-prepared specimen (a), and
those isothermally annealed at 700 ◦ C for 5.22 h (b), at 800 ◦ C for 4.68 h (c),
and at 900 ◦ C for 4.14 h (d).
Fig. 3. Micrograph of the fracture surface observed by using FE-SEM for the
specimen annealed at 900 ◦ C for 4.14 h.
168
L. Wang et al. / Materials Science and Engineering A 434 (2006) 166–170
Fig. 4. Plot of ln(d − d0 ) vs. ln(t). The solid line is linear fit of the experimental
data to formula (1 ).
Fig. 5. Plot of ln(c) against 1000/T.
temperature, and n is the grain growth exponent. Formula (1 )
indicates that there is a linear relation between ln(d − d0 ) and
ln(t) with a slope being equal to 1/n. Fig. 4 shows the plots of
ln(d − d0 ) versus ln(t). The best fitting of the data to formula
(1 ) yields the growth exponent n to be 6 at 700 ◦ C (0.72Tm ,
here Tm is melting point of Mg2 Si), 5 at 800 ◦ C (0.79Tm ) and
4 at 900 ◦ C (0.86Tm ). Therefore, the grain growth kinetics of
nano-Mg2 Si can be expressed as d − d0 = c1 t1/6 , d − d0 = c2 t1/5
and d − d0 = c3 t1/4 at 700, 800 and 900 ◦ C, respectively.
Moreover, the rate constant c in formula (1) depends on temperature in an Arrhenius form so that it can be written as:
Q
c = c0 exp −
(2)
RT
or
Q
+ ln(c0 )
ln(c) = −
RT
Fig. 6. Plot of ln (G) vs. 1000/T.
(2 )
where c0 is the pre-exponential factor, R the gas constant, Q
the activation energy for grain growth, and T is the isothermalannealing temperature. Hence, the activation energy Q for grain
growth can be derived from the rate constant c obtained at different isothermal-annealing temperatures. Fig. 5 shows the plot
of ln(c) versus 1/T. One can see that a good linear relation exists
between ln(c) and 1/T. By best (linear) fit of the data to formula
(2 ), we obtain Q = 112 ± 1 kJ/mol.
Alternatively, the activation energy for grain growth Q can
also be estimated by measuring the rate of grain growth G that
is obtained by the average grain size after annealing at different
temperatures for a fixed period. The growth rate G also obeys
the Arrhenius relationship as [12]:
ln(G) = ln(G0 ) −
Q
RT
(3)
where G0 is a constant. For this purpose, the data of average
grain sizes were taken from isochronal annealing at different
temperatures for about 70 min, and thus the rate of grain growth
G was obtained. Fig. 6 shows the plot of ln(G) versus 1/T. The
activation energy determined by fitting to formula (3) is found
to be 127 ± 2 kJ/mol, which is close to the activation energy
derived from rate constant c as given above.
4. Discussions
At present, there are no exact thermodynamics data available concerning grain growth and/or diffusion in conventional
coarse-grained Mg2 Si or nano-Mg2 Si, which can be used to
compare with our obtained results. Previous work showed that
grain growth of nano-Fe exhibited the same trend as that of
conventional coarse-grained Fe with n decreasing toward 2 as
T/Tm increases to ∼0.6 [14]. In contrast, the growth exponent
n obtained here for nano-Mg2 Si is 6, 5, and 4 at homologous
temperature T/Tm = 0.72, 0.79 and 0.86, respectively. This result
indicates that nano-Mg2 Si displays high resistance against grain
growth as compared to nano-Fe or conventional coarse-grained
Fe. One of the important factors that may contribute to high thermal stability of nano-Mg2 Si would be associated with chemical
L. Wang et al. / Materials Science and Engineering A 434 (2006) 166–170
169
growth of nano-Mg2 Si is unlikely to be dominated by conventional lattice-diffusion of Mg (or Si) in Mg2 Si. Considering the
fact that nano-Mg2 Si consists of nanometer-sized grains and
has a large volume fraction of grain boundaries, grain growth
through atom diffusion in these boundaries is expected much
easier than that through conventional lattice diffusion, and the
energy barriers involved is expected to be substantially lower
for the former than for the latter. In other words, grain boundary
diffusion would play a very important role in the grain growth
process of nano-Mg2 Si, which would explain why the obtained
activation energy for the grain growth of nano-Mg2 Si is relatively small (112 kJ/mol). In fact, grain growth relating to grain
boundary diffusion was reported previously in many nanocrystalline materials [19–23].
Fig. 7. Variation of relative density of nano-Mg2 Si () and porosity in nanoMg2 Si (䊉) with isothermal-annealing temperature (the corresponding annealing
time at 700, 800 and 900 ◦ C is 5.22, 4.68 and 4.14 h, respectively).
ordering [15]. Since Mg2 Si is ordered intermetallics with strong
chemical bonds (covalent bond mixed with ionic bond [16])
between Mg and Si atoms, any grain boundary migration must
involve both vacancy (Mg or/and Si) formation and bond cracking between Mg and Si. The mobility of Mg (or Si) can only
be realized in terms of corresponding vacancies of its own type,
which should retard grain growth process.
Another factor inhibiting grain growth of nano-Mg2 Si may
be related to the porosity in our specimens. The relative density
of the specimens in as-prepared state is 91.4%, which means
that there is 8.6% porosity in the specimens. Although experiments revealed that sintering (or densification) process occurred
during annealing process (see Fig. 7), the amount of porosity
only decreased from 8.6% in as-prepared state to 6.8% upon
annealing at 900 ◦ C for 4.14 h. This indicates that a great amount
of porosity accompanies the grain growth process throughout,
which should inhibit the migration of grain boundaries of nanoMg2 Si through pore drag, as was shown previously in nano-TiO2
[17]. In addition, as mentioned above, a small quantity of MgO
formed during the annealing process. In fact, prolonged ball
milling and then HPing (even if performed in vacuum) will
inevitably introduce considerable amount of oxygen into grain
boundaries (although it was not detected in our X-ray data).
Clearly, this oxygen and the formed MgO phase would play an
important role in prohibiting the grain growth of nano-Mg2 Si.
Since there are no literature data concerning activation
energies for both grain growth and diffusion in conventional
coarse-grained Mg2 Si, one has difficulty to judge grain growth
mechanism of nano-Mg2 Si from the obtained activation energy
(112 kJ/mol) here. However, in view of analogy in crystallographic structure (the diamond structure of Si is similar to the
anti-fluorite structure of Mg2 Si to some extent) and bond nature
(covalent) between silicon and Mg2 Si, a comparison of the corresponding thermodynamic data of silicon with activation energy
for grain growth of nano-Mg2 Si would give some clue to understanding its grain growth process. Since the activation energy
for self lattice-diffusion of Si is about 347 kJ/mol [18], the small
activation energy (112 kJ/mol) obtained here suggests that grain
5. Conclusions
Thermal stability and grain growth behavior of nanocrystalline Mg2 Si (grain size d = ∼30 nm), prepared by using
mechanically activated solid-state reaction plus vacuum hotpressing were investigated by the method of in situ hightemperature x-ray diffraction. The results indicate that grain
growth behavior of nanocrystalline Mg2 Si can be described by
the formula d − d0 = ct1/n , with n = 4, 5 and 6 at 700, 800 and
900 ◦ C, respectively. Simultaneously, the activation energy for
grain growth is determined to be 112 ± 1 kJ/mol.
Acknowledgments
The authors thank Prof. Q.P. Kong for his helpful discussions
in the revision of this work. The Financial support by National
Natural Science Foundation of China (No. 50371081) is gratefully acknowledged.
References
[1] J.M. Mu˜noz-Palos, M.D.C. Cristina, P. Adeva, Mater. Trans. JIM 37 (1996)
1602–1606.
[2] G. Frommeyer, S. Beer, K. Oldenburg, Z. Metallkd. 85 (1994) 372–376.
[3] L.F. Mondolfo, Aluminum Alloys-Structures and Properties, ButterWorths,
London–Boston, 1976.
[4] L. Wang, X.Y. Qin, W. Xiong, X.G. Zhu, J. Zhang, HZ. Dong, Mater. Chem.
& Phys., submitted for publication.
[5] L. Lu, M.O. Lai, M.L. Hoe, Nanostruct. Mater. 10 (1998) 551–563.
[6] L. Wang, X.Y. Qin, Scripta Mater. 49 (2003) 243–248.
[7] G.H. Li, Q.P. Kong, Scripta Metal. Mater. 32 (1995) 1435–1440.
[8] H. Gleiter, Prog. Mater. Sci. 33 (1989) 223–315.
[9] C. Suryanarayana, Int. Mater. Rev. 40 (1995) 41–46.
[10] K. Lu, Mater. Sci. Eng. R 16 (1996) 161–221.
[11] H.P. Klug, X-ray Diffraction Procedures, Jones Wiley & Sons, New York,
1962.
[12] M.C. Iordache, S.H. Whang, Z. Jiao, Z.M. Wang, Nanostruct. Mater. 11
(1999) 1343–1349.
[13] L.Z. Zhou, J.T. Guo, Scripta Mater. 40 (1999) 139–144.
[14] T.R. Malow, C.C. Koch, Acta Mater. 45 (1997) 2177–2186.
[15] C. Bansa, Z. Gao, B. Fullz, Nanostruct. Mater. 5 (1995) 327–336.
[16] M.T. Hutchings, T.W.D. Farley, M.A. Hackett, W. Hayes, S. Hull, U.
Steigenberger, Solid State Ionics 28–30 (1988) 1208–1216.
[17] H. Hahn, J. Logas, R.S. Averback, J. Mater. Res. 5 (1990) 609–614.
[18] H. Siethoff, W. Schr¨oter, Phil. Magn. 37 (1978) 711–721.
170
L. Wang et al. / Materials Science and Engineering A 434 (2006) 166–170
[19] B. G¨unther, A. Kumpmann, H.D. Kunze, Scripta Metal. Mater. 27 (1992)
833–838.
[20] P. Knauth, C.P. Gas, Scripta Metal. Mater. 28 (1993) 325–330.
[21] S. Kawanishi, K. Isonishi, K. Okazaki, Trans. Mater. JIM 34 (1993)
49–58.
[22] Y.K. Huang, A.A. Menovsky, FR.Boer de, Nanostruct. Mater. 2 (1993)
587–595.
[23] J. Ecker, J.C. Holzer, C.E. Krill, W.L. Johnson, J. Mater. Res. 7 (1992)
2962–2971.