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Crystallization kinetics of 1Na 2 O Æ 2CaO Æ 3SiO 2 Æ glass monitored
by electrical conductivity measurements
Ana Candida M. Rodrigues
a,*
, Gilberto Tadashi Niitsu
a
, Edgar Dutra Zanotto
a
Miguel Oscar Prado
b
, Vladimir Fokin
c
a (^) Laborato´ rio de Materiais Vı´treos, Departamento de Engenharia de Materiais, Universidade Federal de Sa˜o Carlos, C.P. 676 -13565-905 Sa˜o Carlos, SP, Brazil b (^) Comisio´ n Nacional de Energı´a Ato´ mica-Centro Ato´ mico Bariloche-8400 S.C. de Bariloche (RN), Argentina c (^) S.I. Vavilov’s State Optical Institute, Babushkina 36/1, St. Petersburg 193171, Russia
Received 2 July 2006; received in revised form 18 January 2007 Available online 1 May 2007
Abstract
We investigated the kinetics of crystal nucleation, growth, and overall crystallization of a glass with composition close to the stoichi- ometric 1Na 2 O Æ 2CaO Æ 3SiO 2. The nucleation and subsequent growth of sodium-rich crystals in this glass decreases the sodium content in the glassy matrix, drastically hindering further nucleation and growth. Compositional changes of the crystals and glassy matrix at different stages of the crystallization process were determined by EDS. These compositional variations were also monitored by electrical conductivity measurements, carried out by impedance spectroscopy, in glassy, partially, and fully crystallized samples. The electrical con- ductivity of both crystalline and glassy phases decreases with the increase of the crystallized volume fraction. Starting at a crystallized volume fraction of about 0.5, the crystalline phase dominates the electrical conductivity of the sample. This behavior was corroborated by an analysis of the activation energy for conduction. We show that electrical conductivity is highly sensitive and can indicate compo- sitional shifts, changes in the spatial distribution of mobile ions in the glassy matrix. Conductivity measurements are thus a powerful tool for the investigation of complex heterogeneous systems, such as partially crystallized glasses and glass-ceramics. Ó 2007 Elsevier B.V. All rights reserved.
PACS: 72.80.Ng; 64.70.Dv
Keywords: Crystal growth; Glass-ceramics; Nucleation; Conductivity; Oxide glasses; Soda-lime-silica
- Introduction
The understanding of the properties of multiphase sys- tems is one of the challenging problems of modern materials science, and partially crystallized glasses and glass-ceramics are important multiphase systems. In most systems, the com- position of the embedded crystals differs from those of the parent glasses, which complicates the crystallization path- ways. As some of us have recently shown [1], this situation
may take place even in the case of stoichiometric glass crys- tallization, or crystallization of glasses belonging to a com- positional interval of solid solution formation, when fully crystallized samples have a single phase with the parent glass composition. The deviation of the critical nuclei’s composi- tion from that of the stable phase has been interpreted [1] as resulting from a decrease of the thermodynamic barrier for nucleation as compared with that for nuclei that have the sta- ble phase composition. This interpretation is consistent with Ostwald’s rule of stages, generalized in Ref. [2] for nucle- ation as ‘Those classes of critical clusters determine the pro- cess of the transformation, which correspond to a minimum work of critical cluster formation (as compared with all other
0022-3093/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.03.
- (^) Corresponding author. Tel.: +55 16 33518524. E-mail address: [email protected] (A.C.M. Rodrigues).
www.elsevier.com/locate/jnoncrysol
Journal of Non-Crystalline Solids 353 (2007) 2237–
possible alternative structures and compositions, which may be formed at the given thermodynamic constraints)’. Nucleation and the deterministic growth of crystals with shifted compo- sitions result in a simultaneous change of the glassy matrix composition, as shown experimentally for a series of sodium-calcium-silicate glasses belonging to the 1Na 2 O Æ 2CaO Æ 3SiO 2 (N 1 C 2 S 3 ) 1Na 2 O Æ 1CaO Æ 2SiO 2 (N 1 C 1 S 2 ) pseudo-binary line [1,3]. Such complex crystallization path- way accompanied by compositional variations in the crystals and glassy matrix, and their high sodium content make these glasses quite attractive for electrical conductivity investigations. This paper presents and discusses some relevant aspects of the crystallization kinetics of a near-stoichiometric N 1 C 2 S 3 glass from the parent to fully crystallized glass (glass-ceramic) as followed by electrical conductivity mea- surements, using impedance spectroscopy, and EDS.
- Experimental and methods
2.1. Glass and glass-ceramics preparation
A 17.0Na 2 O Æ 33.2CaO Æ 49.8SiO 2 (mol%) glass – by analysis – was prepared from sodium and calcium carbon- ates, and crushed quartz by melting in a platinum crucible at 1300–1500 °C for about 4 h and casting on massive metallic plates. To obtain samples with different crystal- lized volume fractions, a, samples of the parent glass were heat-treated at T = 690 °C for different periods of time. The a values were estimated by standard methods using optical microscopy.
2.2. Crystallization kinetics
To calculate the steady-state nucleation rate, Ist , and time lag for nucleation, s, for a given temperature, T, the number density of nucleated crystals, N, versus heat treat- ment time, t, at T was obtained by the ‘development’ method [3]. These data were fitted to the Collins–Kash- chiev Eq. (1) to estimate Ist and s as fit parameters [4].
N ðtÞ ¼ Ists
t s
p^2 6
X^1
m¼ 1
ð 1 Þm m^2 exp m^2
t s
: ð 1 Þ
The kinetics of overall crystallization were analyzed by the Avrami equation [4]
aðtÞ ¼ 1 expfKt ng; ð 2 Þ
where K is a parameter that comprises the crystal nucle- ation rate (or the crystal number density) and the growth rate, n is the Avrami coefficient, which in the case of the three-dimensional growth can be approximately written as
n ¼ k þ 3 m: ð 3 Þ
k and m are exponents of t in the formulas N tk^ and D t m^ describing the variations of the crystal number (N) and size (D) with time [3].
2.3. Estimates of the crystals and glassy matrix compositions
The average compositions of the crystals were analyzed by EDS using a fully crystallized sample as a standard. The composition of the glassy matrix was then calculated based on the parent glass and crystal compositions taking into account the values of a.
2.3.1. Impedance spectroscopy Electrical conductivity measurements were carried out by impedance spectroscopy, which employs alternating current with variable frequency. The main feature of this method, which is widely employed in investigations of semiconductors and ionic conductors, is that it allows for the separation of electrical phenomena having different time constants, e.g., electrode and bulk properties [5]. Impedance data of a homogeneous ionic conducting glass, can be represented by a so-called Nyquist diagram (x-axis: the real part of the impedance; y-axis: the negative of the imaginary part of impedance), which is commonly a semi-circle followed by a characteristic spike of electrode polarization due to ionic conduction. The sample’s resis- tance (R) is read at the intersection of the semi-circle with the x-axis at low frequencies. The electrical conductivity, r, can thus easily be calculated employing:
r ¼
R
L
S
; ð 4 Þ
where L is the sample’s thickness and S the electrode sur- face area. Before taking the measurements, to ensure that only bulk properties would be investigated, the crystallized sur- face layer was eliminated by polishing. Platinum electrodes were then sputtered onto the samples’ surfaces to ensure the necessary electrical contact. Measurements were taken in a two-electrode configuration cell, in dry air, using an impedance analyzer HP 4192A, which allows the frequency to vary from a 5 Hz to 13 MHz. The measurements were done in the 250–600 °C temperature range.
- Results
3.1. Crystallization kinetics and EDS data
Figs. 1 and 2 show a typical kinetic curve, N(t), and the temperature dependencies of the steady-state nucleation rate, Ist , and time lag, s, for nucleation, respectively. The overall crystallization was studied at T = 690 °C, which exceeds the temperature corresponding to the maximum nucleation rate Tmax ffi 593 °C (see Fig. 2) by about 100 °C, and hence corresponds mainly to growth of ‘ather- mal’ crystals, i.e. crystals nucleated during cooling of the melt and heating of the glass up to the temperature under study. T = 690 °C was also used to prepare samples with different crystallized volume fractions. Fig. 3 shows a and the diameter of the crystals, that is equal to the largest
matrix. At first sight, the conductivity of the partially crys- tallized samples, rpcs, up to a 0.54 is mainly determined
by the glassy matrix, since its conductivity is close to the conductivity of the pure glass with sodium content similar
0 20 40 60 80
0
20
40
60
80
b
D,
μ m
0 20 40 60 80 100 120
1.0 a
α
t, min t, min
2.0 2.5 3.0 3.5 4.0 4.
0
1
c
n=2.73+0.
n=1.82+0.
ln(-ln(1-
α))
ln(t,min) ln(t,min)
1.5 2.0 2.5 3.0 3.5 4.0 4.
d
m=0.88+0.
m=0.62+0.
ln(D,
μ m)
Fig. 3. Volume fraction crystallized (a, c) and diameter of largest crystals (b, d) versus time of heat treatment at T = 690 °C in normal (a, b), Avrami’s (c), and logarithmic (d) coordinates.
0.0 0.2 0.4 0.6 0.8 1.
10
12
14
16
18
CCa
in parent glass
C
Na^
in parent glass
CNa(in glassy matrix)
CNa(in cryst.)
CCa (in cryst.)
C, at %
α
Fig. 4. Average composition, C, of the crystalline phase (points), measured by EDS, and glassy matrix, calculated from the crystallized volume fraction and the parent glass composition, versus volume crystallized at T = 690 °C.
0 200 400 600 800 1000 1200 1400
0
50
exo
T (^) pm
T (^) g
T, o^ C Fig. 5. DSC heating and cooling curves (heating and cooling rate of 10 °C/min) for a glass composition 17.0Na 2 O Æ 33.2CaO Æ 49.8SiO 2 (mol%).
to that of glassy matrix (Fig. 9). However, according to Fig. 4, the crystals contain much more sodium than the respective glassy matrix, for all values of the crystallized volume fraction. As a result, the electrical conductivity of the crystals (rcr ) approaches that of the glassy matrix (rgm). Since during phase transformation the sodium con- tent in the glassy matrix decreases faster than in crystalline phase, the electrical conductivity of the crystals becomes higher than that of the respective glassy matrix. For exam- ple, according to Fig. 4, for a 0.3 the sodium content in crystalline and glassy phases ðCcrNa 16 :15at:%; CgNam 11 :15 at:%Þ corresponds at T = 395 °C to log(rcr ) 5. and log(rgm ) 5.70 respectively, while for a 0.54 the conductivity of the crystalline phase (log(rcr ) 5.54) exceeds that of the glassy matrix (log(rgm) 6.47) by about one order of magnitude due to the higher difference in sodium content between crystals ðCcrNa 15 :49 at:%Þ and glassy matrix ðCgNam 9 :32 at:%Þ. Hence we may assume that, beginning with a 0.54, the electrical conductivity of the sample is dominated by the crystalline phase.
To improve this analysis of the electrical conductivity of partially crystallized samples, rpcs , we calculated the respective activation energy for all samples. Such data are plotted in Fig. 10 versus sodium content, which refers, in the case of partly crystallized glasses, to the conductivity of the glassy matrix. Although the conductivity of the sam- ple with a 0.54, rpcs , is close to the conductivity rgm of a glass having the same sodium content as the glassy matrix (Fig. 9), its activation energy is higher and close to that of the sodium-enriched crystals (Fig. 10). This tendency becomes apparent at a 0.30. Thus, the comparison between the values of activation energy of partially crystal- lized samples, glasses, and crystals corroborate the above assumption that the electrical conductivity of partially crystallized glasses, beginning with a 0.54, is dominated by the crystals. This conclusion is reinforced by a weak inflection in the Arrhenius plot of a sample with a 0. (Fig. 6), which is attributed to the reversible polymorphic transition in the crystalline phase. The decrease in activa- tion energy for conduction with the increasing of alkaline
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.
-8.
-7.
-7.
-6.
-6.
-5.
-5.
-4.
-4.
-3.
-3.
crystal
glass
600 500 400 300 OC
log (
σ,
Ω
-1cm
-1 )
1000/T, K-
cryst. glass α = 0.
1.3 1.4 1.
log (σ, Ω
cm
-1 )
1000/T, K-
Fig. 6. Arrhenius plot of electrical conductivity of glass, partially crystallized glass, and poly-crystal.
Fig. 7. SEM of the glass cross-sections treated at T = 690 °C for 17 (a) and 50 (b) min. Fractions of the crystallized volume are about 0.1 (a) and 0.54 (b). The bar has a length of 50 lm. The photo’s height is equal to the thickness of the plates used for electrical conductivity measurement.
1.1 1. 2 1 .3 1.4 1.5 1. 6 1 .7 1.8 1.
600 500 400 300 O^ C
log (
σ,
Ω
-1cm
-1)
1000/T,K -
Na 2 O 9.82 mol%
Fig. 8. Arrhenius plot of electrical conductivity of glasses with different sodium oxide content.
nounced decrease in the electrical conductivity of the partially crystallized sample observed during a long heat treatment at T = 400 °C, as compared with the behavior of the pure glass (see Fig. 12).
- Conclusions
Electrical conductivity measurements of partially crys- tallized samples corroborated EDS evidence for variations in the composition of both glassy phase and crystals during crystallization of a glass with composition close to the stoi- chiometric 1Na 2 O Æ 2CaO Æ 3SiO 2. In this particular case, electrical conductivity was dominated by the glassy phase up to a 0.30, and by the crystals from a 0.54. These findings were confirmed by an analysis of the electrical con- ductivity of glasses and crystals having the same sodium contents as the partially crystallized samples, and were fur- ther substantiated by an analysis of activation energy. For samples with higher crystallinities, Arrhenius plots showed a kink due to a crystal phase transition, confirming that the crystals dominate the electrical conductivity.
Thus, electrical conductivity is a very sensitive property that can indicate changes in the glassy matrix and crystals compositions, and in the spatial distribution of chemical elements. Hence, electrical conductivity measurements could contribute to investigations of complex heteroge- neous systems, such as partially crystallized glasses.
References
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[6] I. Maki, T. Sugimura, J. Ceram. Assoc. Jpn. 75 (1968) 144. [7] G.H. Frischat, H.L. Oel, Glastech. Ber. 39 (1966) 50. [8] O.L. Anderson, D.A. Stuart, J. Am. Ceram. Soc. 37 (12) (1954) 573. [9] E.N. Soboleva, N.S. Yuritsyn, V.L. Ugolkov, Glass Phys. Chem. 30 (2004) 481.
