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Continuous compositional changes of crystal and liquid
during crystallization of a sodium calcium silicate glass
V.M. Fokin
a,*
, E.D. Zanotto
b
a (^) S.I. Vavilov’s State Optical Institute, ul. Babushkina 36/1, St. Petersburg 192131, Russia b (^) Vitreous Materials Laboratory, Federal University of Sa˜o Carlos, 13565-905 Sa˜o Carlos, SP, Brazil
Received 17 September 2006; received in revised form 20 December 2006
Abstract
This paper deals with a systematic study of crystal nucleation and growth kinetics in a 14.6Na 2 O–34.0CaO–51.4SiO 2 mol% glass, which is close to the CaO Æ SiO 2 –Na 2 O Æ SiO 2 pseudo-binary section, just left of the stoichiometric Na 2 O Æ 2CaO Æ 3SiO 2 (N 1 C 2 S 3 ) com- pound. We show that crystallization begins with nucleation of a Na (^) 4+2xCa (^4) x[Si 6 O 18 ] (0 < x < 1) solid solution that is enriched in sodium as compared with both parent glass and the N 1 C 2 S 3 compound; while a fully crystallized sample is composed only by a solid solution that is stable at very high temperatures, but is metastable in the temperatures under investigation. We thus confirm a continuous composi- tional change of the crystals during the course of crystallization. Ó 2007 Elsevier B.V. All rights reserved.
PACS: 64.70.Kb; 64.60.Qb
Keywords: Crystallization; Crystal growth; Glass ceramics; Nucleation
- Introduction
The thermodynamic barrier for nucleation or the work for critical nucleus formation, W* , to a great extent deter- mines the nucleation rate in supercooled liquids. For this reason, to use any nucleation theory one must first define the composition, structure and thermodynamic properties of the critical nucleus to evaluate W*. This task, and espe- cially its experimental solution, is not trivial due to the extremely small critical nucleus sizes (only a few nanome- ters) at the deep undercoolings needed to attain detectable homogeneous nucleation in typical glass forming liquids. This is one of the reasons why the newly evolving macro- phase (predicted by the respective equilibrium phase dia- gram) is commonly used as a reference to describe the properties of the critical nucleus. This approach is consis- tent with assumptions of the classical nucleation theory
(CNT) employing Gibbs’ description of heterogeneous sys- tems. However, a maximum thermodynamic driving force, i.e. that of the stable phase, is not a necessary condition to attain the minimum value of the thermodynamic barrier and maximum nucleation rate, because W* is a combina- tion of the thermodynamic driving force, DGV , for crystal- lization and the specific surface energy, rc/l , of the nucleus/ liquid interface:
W
r^3 c=l DG^2 V
: ð 1 Þ
Particularly, preferred nucleation of the phase having the lowest thermodynamic barrier rather than other thermody- namically possible phases is the basis of the kinetic argu- mentation of Ostwald’s rule of stages, according to which any system prefers to reach intermediate stages having the closest free energy difference to the initial state [1]. Thus, some serious problems that often arise during quantita- tive analyses of nucleation data in the framework of CNT (e.g. see [2]) could be caused, at least in part, by the
0022-3093/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.04.
- (^) Corresponding author. Tel.: +7 812 355 30 38. E-mail address: [email protected] (V.M. Fokin). URL: www.lamav.ufscar.br (E.D. Zanotto).
www.elsevier.com/locate/jnoncrysol
Journal of Non-Crystalline Solids 353 (2007) 2459–
erroneous employment of DGV for crystallization of the sta- ble macro-phase for the critical nuclei using the specific sur- face energy as a fitting parameter. Indeed, in the last decade, indirect and direct experimental evidences appeared point- ing out to the difference between the critical (and near critical) nuclei, and the corresponding stable macro-phase. Some of these evidences are listed below:
(a) A strong discrepancy between the time-lags for nucle- ation estimated from crystal nucleation and growth kinetics [3,4] in lithium silicate glasses with composi- tions between di- and metasilicate. (b) Discrepancy between the rc/l estimated from the nucleation rate, and from the effect of dissolution of sub-critical nuclei as the temperature increases [5]. This problem could be avoided by assuming that the thermodynamic driving force is smaller than that for macro-phase crystallization. (c) Crystallization of sodium–calcium silicate glasses (in particular of the stoichiometric composition Na 2 O Æ 2CaO Æ 3SiO 2 ) by nucleation of solid solutions whose composition continuously varies during the phase transformation [6,7] approaching the composition of the stable phase only in the end. (d) A remarkable size-dependence of the cluster composi- tion has also been observed during primary crystalli- zation of NiP particles in a hypoeutectic Ni–P amorphous alloy [8]. In this case, the compositional evolution was completed when the clusters attained about 10 nm. (e) Variation of (micron size) crystal compositions with the degree of undercooling was found recently in CaO–Al 2 O 3 –SiO 2 glasses [9] where it was demon- strated, that equilibrium crystals form near the liqui- dus, while disordered and non-stoichiometric phases precipitate near the glass transition temperature. This finding corroborates the statement that ‘metastable crystalline phases commonly precipitate in the initial stage of low-temperature crystallization of multicom- ponent glasses’ made in Ref. [10]. (f) A size-dependence of the crystal composition has also been detected for crystals formed on the surface of a cordierite glass [11].
The above mentioned results are still not numerous. This situation is due to the fact that most authors do not pay attention to the exact composition of the crystalline phases that precipitate in undercooled liquids, especially in the ini- tial stages of phase transformation. However, one can expect that the compositional and structural evolution of the crys- talline phase during phase transformation is a general fea- ture. Therefore, the search and study of such phenomenon are of great interest from both theoretical and practical points of view since they may help one to find out a realistic approach for the nucleation process in glasses. In particular, from these evidences it became clear that the choice of stoi- chiometric glass compositions as model systems does not
guarantee that the crystal nuclei will have the same compo- sition as the parent glass, i.e. the condition needed to treat the studied system as ‘one-component’ (or stoichiometric) is not necessarily fulfilled in this way. This paper presents additional experimental evidence for a continuous evolution of the crystal composition during nucleation and growth in a sodium–calcium silicate glass, extending the composition interval studied earlier and described in Refs. [12,13]. In addition, existing crystal nucleation rates are analyzed and compared with our own as a function of glass composition and reduced glass transition temperature.
- Materials and methods
We employed sodium and calcium carbonates, and amorphous silicon dioxide of analytical grade for the glass synthesis. The melt was cast on a massive steel plate after about 2 h at 1450 °C in a platinum crucible. The glass com- position by analysis (14.6Na 2 O–34.0CaO–51.4SiO 2 mol%) is close to the pseudo-binary meta silicate section CaO Æ SiO 2 –Na 2 O Æ SiO 2 and lies just left of the stoichiometric compound Na 2 O Æ 2CaO Æ 3SiO 2 , while the compositions of the glasses studied in Refs. [12,13] are between the com- pounds Na 2 O Æ 2CaO Æ 3SiO 2 (N 1 C 2 S 3 ) and Na 2 O Æ CaO Æ 2SiO 2 (N 1 C 1 S 2 ), Fig. 1. To evaluate the number of crystals per unit volume, N(t), nucleated at a given temperature versus heat treat- ment time we employed the well-known Tammann or so- called ‘development’ method (see e.g. [5]). Then, N(t) data were fitted into Collins’s/Kashchiev’s equation (2) [15,16] N ðtÞ Ists
t s
p^2 6
X^1
m¼ 1
ð 1 Þm m^2
exp m^2 t s
ð 2 Þ
to estimate the time-lag for nucleation, s, and the steady- state value of the nucleation rate, Ist , as fitting parameters. For sufficiently long times, this expression can be approximated by N (^) VðtÞ ¼ Istðt tindÞ; ð 3 Þ where
tind ¼
p^2 6
s: ð 4 Þ
Moreover, to obtain quantitative information about nucleation kinetics in the advanced stages of phase trans- formation the overall crystallization kinetics were analyzed with the JMAK equation: aðtÞ ¼ 1 exp f Kt ng; ð 5 Þ where a is the volume fraction transformed, n is the so- called Avrami coefficient, which can be estimated from the slope of a ln(ln(1a(t)) versus ln(t)) plot. In the case of three-dimensional growth, the Avrami coefficient can be written as n ¼ j þ 3 m; ð 6 Þ where j and m characterize the evolution of the crystal number (N tj) and size (D tm) with time.
strongly exceed the period investigated by the ‘development’ method (see Fig. 2). An Avrami plot is shown in Fig. 4(b). The crystal growth kinetics at the same temperature (610 °C) is shown in Fig. 5 in normal (a) and logarithmic (b) coordinates. Fig. 6 shows the increase of crystal size at T = 710 °C for different crystal number densities. Since the nucleation rates are very small at T = 710 °C, prelimin- ary nucleation heat treatments were performed to change the crystal number density. In all cases the crystal size dis- tributions were close to monodisperse. Lines represent approximations via the equation D = At m.
3.3. Thermal analysis and reversible polymorphous transition
DSC heating and cooling curves are shown in Fig. 7. After crystallization from the liquid state the crystalline
phase undergoes a reversible (exothermic) polymorphic transition at a temperature Tpm (well below the glass tran- sition temperature). Fig. 8 presents Tpm taken from DSC heating-curves of partly crystallized samples versus volume fraction of crystalline phase.
3.4. The ‘courtyard’ phenomenon
Fig. 9 shows micrographs of glass samples subjected to a long single-stage treatment (a) at Tn (close to Tmax), and to a triple treatment (b): first for a short time (30 min) at Tn to nucleate an appropriate number of crystals, then at Tgr Tmax to grow them, and finally again at Tn for the same time as for the samples shown in Fig. 9(a). Thus this third treatment differs from the single-stage treatment only by the presence of previously formed large crystals.
3.5. EDS results
Fig. 10 shows a scanning electron microscopy (SEM) micrograph of crystals in a glass sample subjected to the
580 600 620 640
1E
1E
I^ st , m
-3s
T, oC
580 oC
0.00112 0.00114 0.
7
8
9
10
11
12
13
620 600
ln(t
ind , s)
1/T, K -
Fig. 3. Temperature dependencies of the steady-state nucleation rate (a) and induction period for nucleation (b).
0 4000 8000 12000 16000
α
t, min
7 10
0
1
ln(-ln(1-
α))
ln(t, min) 8 9
Fig. 4. Kinetics of overall crystallization at T = 610 °C (a) and the respective Avrami plot (b). The lines were obtained by least-squares linear fits.
same triple treatment as the sample shown in Fig. 9(b). The line at the bottom shows the change of sodium content in arbitrary units (estimated via EDS) along the section
shown in the top line. The relative content of sodium in the glassy matrix and crystalline phase is shown by a dot map in Fig. 11(b). This figure refers to a partly crystallized glass sample (Fig. 11(a)) having a thermal history similar to that of the sample shown in Fig. 9(b), with exception of the second heat treatment.
- Discussion
The present results can be separated into two groups. The first one refers to nucleation at the early stages. In this case, when the crystallized volume fraction is very small, the possible difference between the crystal and liquid com- positions does not have a remarkable influence on the glassy matrix composition. This situation is realized at low temperatures, typically at or below Tg (where crystal growth rates are very slow); or for short time intervals of
0 4000 8000 12000 16000
0
4
8
12
16
D, m
μ
t, min
8.0 8.5 9.0 9.5 10.
ln(D,m
μ)
ln(t, min)
Fig. 5. Diameter of the largest crystals as a function of heat treatment time at T = 610 °C in linear (a) and logarithmic (b) coordinates. The lines were obtained by least-squares linear fits.
0 50 100 150 200 250 300
0
40
80
120
160
D, m
μ
t, min
1 2 3
Fig. 6. Crystal diameters versus heat treatment time at T = 710 °C for different crystal number densities N = 250 (1), 1200 (2) and 4400 mm^3 (3). The lines were fit to D = Atm.
0 200 400 600 800 1000 1200 1400
-4 0
-2 0
0
20
exo
Tpm
Tg
T, º^ C Fig. 7. Heating and cooling DSC curves: with cooling and heating rates jqj = 10 grad/min. The weight of the monolithic sample was about 40 mg.
0.0 0.2 0.4 0.6 0.8 1.
450
460
470
480
490
500
T pm
,^ º^ C
α Fig. 8. Temperature of reversible polymorphic transition taken from heating DSC curves versus volume fraction crystallized at T = 706 °C. The dashed line is a linear fit.
the Imax(Tgr ) dependence, which clearly demonstrates a strong correlation between Imax and Tgr , that has been discussed in detail in Ref. [18]. This correlation indicates that with the increase of Tgr the kinetic inhi- bition of nucleation proceeds at higher temperatures corresponding to a higher thermodynamic barrier for nucleation (owing to the lower values of the ther- modynamic driving force). Such correlation is much more pronounced when the nucleation rates refers to the same or similar crystal phases, since the ther- modynamic barrier also depends on the melting enthalpy, the difference between the heat capacities of melt and crystal, and surface energy. This is the case shown in Fig. 12(b) where all nucleation rates refer to solid solutions based on the N 1 C 2 S 3 struc- ture. It should be stressed that the nucleation rates
shown in Fig. 12 (obtained by the ‘development’ method) refer to a stage when the crystals have about critical size and hence a is still negligible. (ii) A significant prolongation of the heat treatment time, even at the lowest temperatures, allows one to study the overall crystallization kinetics. The kinetics of overall crystallization at T = 610 °C is shown in Fig. 4. The N(t) plot at this temperature for relatively short times is presented in Fig. 2. The respective Avrami plot (Fig. 4(b)) can be separated into two parts – before and after 6765 min, see the Avrami coefficients listed in Table 1. Crystal growth in the indicated time intervals (Fig. 5(b)) can be described as D t m, where m is shown in Table 1. This table also includes the values of j estimated via Eq. (6). As follows from Table 1, for times below 6765 min the overall crystallization kinetics (n 4) correspond to nucleation and growth with constant rates. For t > 6765 min the overall crystallization kinetics is controlled only by crystal growth, since the values of n and m reduce up to about 1 and 0.3, respectively. This means that at 6765 min the nucleation process is practically terminated (j 1).
It is natural to assume that suppression of nucleation is caused by the exhaustion of sodium in the glassy matrix due to the compositional difference between the parent glass and growing crystals, as it was the case for glasses with compositions between N 1 C 2 S 3 and N 1 C 1 S 2 [7] in which sodium-rich solid solution crystals nucleated. In con- trast to the latter case, however, in the glass here investi- gated (see Fig. 1) the formation of the stable phase N 1 C 2 S 3 as well as of sodium-rich solid solution crystals has to lead to sodium depletion causing a change in the crystallization kinetics. The change of the polymorphic transition temperature Tpm (Fig. 8) evidences the variation of the crystal composition during the course of crystalliza- tion. This change allows us to conclude that the starting crystal (critical nucleus) composition is not equal to N 1 C 2 S 3. Indeed according to the Tpm (Na 2 O) dependence shown in Fig. 13, the initial crystal composition has about 18 mol% Na 2 O (36 mol% Na 2 OSiO 2 ) just right hand side of the N 1 C 2 S 3 compound in the phase diagram, and is thus remarkably different from that of the parent glass, which has 14.6 mol% Na 2 O. Similar results were obtained for a glass with 13.8 mol% Na 2 O, for which we plotted the dependence of Tpm on the volume fraction crystallized (see Fig. 14). An estimate of
Table 1 Avrami exponent, n, crystal growth exponent m, D tm, crystal number exponent j, N tj t (min) na^ m j <6765 4.2 ± 0.3 1.1 ± 0.1 1
6765 1.2 ± 0.1 0.3 ± 0.1 1 a (^) n = 3m + j.
14 16 18 20 22 24
9
10
11
12
13
14
N 1 C 2 S 3 [11][10]
log( I
max
, m
-3s
-1)
log( I
max
, m
-3s
-1)
Na 2 O, mole %
0.52 0.53 0.54 0.55 0.
9
10
11
12
13
14
T (^) gr
[11] [10]
Fig. 12. Maximum steady-state nucleation rate in sodium–calcium metasilicate glasses versus sodium oxide content (a) and reduced glass transition temperature (b).
the critical nuclei composition via variation of Tpm was also performed for a glass with 17 mol% Na 2 O. Fig. 15 shows the sodium content in the critical nuclei estimated by extrapolation of the Tpm(a) plots to a = 0, and by EDS measurements, previously performed by us [20], ver- sus sodium content in the parent glasses. The data obtained via Tpm agree within the error limits with EDS measure- ments. One should recall that the parent glass and a fully crystallized sample were used in Ref. [20] as standards. According to Fig. 15 crystallization begins with nucleation
of solid solution crystals enriched in sodium as compared to the stoichiometric composition N 1 C 2 S 3 and the parent glass compositions. It is true for glasses with composition just left of N 1 C 2 S 3 and from the N 1 C 2 S 3 –N 1 C 1 S 2 interval that leads to solid solution formation. As we have shown early, in the case of glasses of the N 1 C 2 S 3 –N 1 C 1 S 2 interval, during crystallization the composition of the solid solution crystals reach that of the parent glass, i.e. at relatively low crystallization temperature the system arrives to its equilib- rium corresponding to its phase diagram. Another situation is verified for glasses just left of N 1 C 2 S 3. An X-ray analysis of fully crystallized materials with 14.6 mol% Na 2 O treated at 607 °C did not reveal any CaO Æ SiO 2. But according to the equilibrium phase diagram (Fig. 1) about 4 vol.% of this phase should form at some late stage. To confirm this result we crystallized at 650 °C the glasses with 13.8 and 12.4 mol% Na 2 O (up to 100 and 98.6 vol.% crystalline phase), increasing in such a way the expected volume fraction of CaO Æ SiO 2 up to 6% and 10%, respectively. However the new X-ray analysis did not reveal again any CaO Æ SiO 2 crystal phase. This result means that the crystalline phase is sodium depleted solid solution. The continued slow increase of the Tpm of crystals containing less than 16.6 mol% sodium oxide (Fig. 13) also gives indirect evidence for formation of a solid solution since, if the stoichiometric phase N 1 C 2 S 3 precipitated the value of Tpm would not vary. According to the phase dia- gram (Fig. 1), a sodium depleted solid solution is stable at temperatures higher than about 1050 °C and thus should decay at temperatures as low as 607 and 650 °C into N 1 C 2 S 3 and CaO Æ SiO 2. However this decomposition could be suppressed by kinetic reasons. Thus glasses with compositions just left of N 1 C 2 S 3 , fully crystallized at low temperatures are composed by solid solutions, which are metastable with respect to N 1 C 2 S 3. It should be noted that
12 14 16 18 20 22
320
360
400
440
480
520
T pm
,^ º
C
Na 2 O, mol%
1 2 3 4 5
N 1 C 2 S (^3)
Fig. 13. Temperature of reversible polymorphic transition taken from DSC (1, 2) versus sodium oxide content at CSiO 2 close to 50 mol%. 1, 3 – heating and 2 – cooling with rate 10°/min. Dashed and doted lines are linear fits of experimental data (for glasses containing more than 16.6 mol% sodium oxide). 3 – data taken from Ref. [19].
Tpm
,^ º
C
0 10 20 30 40 50 60 70 80 90 100
380
400
420
440
460
480
500
Crystallized volume fraction, %
Fig. 14. Tpm of crystals versus volume fraction crystallized at T = 650 °C of a glass with composition 13.8Na 2 O–35.4CaO–50.8SiO 2 (mol%) by analysis. The dashed line is a linear fit of the experimental points with exception of the data corresponding to a = 100%.
Na
O, mol% 2
Na 2 O, mol%
13 14 15 16 17 18 19 20 21 22 23 24 25
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
N 1 C 1 S 2 N 1 C 2 S 3
Fig. 15. Sodium oxide content in the critical nuclei versus sodium oxide in the parent glasses. Estimate by EDS (1) [20] and Tpm measurements (2). The solid line corresponds to the case when the compositions of the critical nuclei are equal to those of the respective parent glasses.
Thus the explication given in [9] of the compositional deviation of critical nuclei observed in sodium calcium metasilicate glasses [7], which keeps also at initial stage of crystal growth, as result of kinetics due to high diffusivity of sodium as compared with that of calcium conflicts the theoretical results. Also, as was shown in [29] for N 1 C 2 S 3 glass, the effective diffusion coefficient estimated from crys- tal growth rates is closer to that of Ca than to Na. More- over in the crystallized glasses with composition just right of N 1 C 1 S 2 from N 1 C 1 S 2 –N 2 C 1 S 3 interval only N 1 C 1 S 2 crys- tals were detected [30] whereas according to [9] one could expect the formation of N 2 C 1 S 3 crystals as the first phase.
- Conclusions
We demonstrated a well-defined correlation between the maximum nucleation rate of solid solutions Na (^) 4+2xCa (^4) x- [Si 6 O 18 ] and the reduced glass transition temperature for glasses with compositions close to the meta silicate CaO Æ SiO 2 –Na 2 O Æ SiO 2 pseudo-binary section corroborating the tendency observed in previous studies with other compositions. We have shown that crystallization of a glass with com- position close to the CaO Æ SiO 2 –Na 2 O Æ SiO 2 pseudo-bin- ary section, being just left of Na 2 O Æ 2CaO Æ 3SiO 2 , does not start with nucleation of the stable crystalline phases CaO Æ SiO 2 (CS) or Na 2 O Æ 2CaO Æ 3SiO 2 (NC 2 S 3 ), as one expects from the equilibrium phase diagram, but instead it starts with a Na (^) 4+2xCa 4 x[Si 6 O 18 ] (0 < x < 1) solid solu- tion that is noticeably enriched in sodium as compared to N 1 C 2 S 3. During crystallization the average composition of this solid solution changes, and in the fully crystallized sample arrives at that of the parent glass. This solid solu- tion is stable at temperatures higher than 1050 °C, but is metastable at the used temperatures. We thus confirm a continuous compositional change of the crystals during the course of crystallization, starting from the very early (nucleation) stage, an effect which has not been given proper attention in the past.
Acknowledgments
We express our appreciation of the funding provided by the Brazilian agency FAPESP, and our indebtedness to Dr A.A. Cabral for DSC measurements.
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