The glass forming systems may be regarded as model systems for technical glass ceramics. Many papers on investigation of nucleation in oxide glasses are known. Table 1 shows the compound glass-forming systems, for which the temperature dependence of the steady and unsteady crystal nucleation in the bulk nucleation were studied.

As can be seen from Table 1, the greatest attention was paid by researchers to the system Li₂O-SiO₂ [1] - [68] because of its practical importance. A specific feature of the system Li₂O-SiO₂ is that, in the region of compositions from 0 to 32 mol% Li₂O, the glasses have a tendency towards the phase separation. Many authors [91] - [94] have believed that the process of phase separation of glasses into two vitreous phases favors a homogeneous crystallization of a glass with the formation of small crystals. As follows from [95] [96] , the role of the phase separation is reduced to the appearance of phase boundaries that serve as a particular catalyst of the crystallization. According to [93] ,

the crystallization of phase separated glasses cannot be referred to as catalytic. It is necessary to speak about the influence of the phase separation on a further crystallization process rather than about catalysis. Actually, a review of a number of experimental works [81] [97] - [101] demonstrates that the liquid-liquid phase separation before crystallization affects the crystal structure of glass-ceramic materials through at least three different ways.

1) The boundary between phases plays a role of an initiating agent.

2) Since, after the phase separation, the composition of a matrix or dispersed phase becomes closer to that of a crystallizing phase, the formation and growth of crystals progress more easily.

3) In one of the phases, the metastable phase precipitates and plays a role of a catalyst for the main crystalline phase.

The purpose of this work is to investigate the crystal growth and nucleation in glasses in the lithium silicate and sodium silicate systems that serve as a basis for the preparation of glass ceramic materials.

The rates of nucleation and growth of crystals and phase separated in homogeneities were studied in glasses of the analyzed compositions xLi₂O×(100 − x)SiO₂ (where x = 23.4, 26.0, 29.1 and 33.5 mol% Li₂O). Since it was established earlier that the crystal nucleation parameters are strongly affected by water [35] and bubbles formed in the course of glass synthesis [102] , the glasses were homogenized to a maximum extent under specially established temperature-time conditions of synthesis. As was previously shown, bubbles can play a role of initiators of nucleation of lithium disilicate crystals and increase a number of crystals to 20% [103] . As the water content increases, the stationary nucleation rate increases and the position of the maximum shifts toward lower temperatures [35] . In this respect, all cares were taken in order to prepare glasses homogenized to a maximum extent. Water was removed by bubbling glass melts with argon for 20 min [49] . Bubbles were removed by performing the synthesis at a high temperature. The glasses were synthesized according to the technique described in [103] . A batch was prepared from lithium carbonate (analytical grade) and dehydrated silicon dioxide (analytical grade) by mixing in a drum. The glasses were synthesized in a platinum crucible (volume, 200 ml) in a Globar-heater furnace with silicon carbide heaters (synthesis temperature, 1550˚C; synthesis time, 5 h). Heat treatments were performed in SShOL electric shaft furnaces and a gradient furnace designed at a laboratory. The temperature was maintained accurate to within ±1˚C. The results of the chemical analysis of the synthesized glasses are presented in Table 2.

X-ray powder diffraction analysis was performed on a DRON-2 diffractometer (CuK_α radiation; operating voltage 30 kV; current 20 mA; detector rotation rate, 2 deg/min). Differential thermal analysis (DTA) was carried out on a MOM derivatograph (heating rate, 10 K/min; sample weight, 1 g ; galvanometer sensitivity, 1/5; reference sample, Al₂O₃; platinum crucible). Optical microscopy investigations in transmitted and reflected light

were performed on Carl Zeiss Jenaval and Neophot 32 microscopes ( Germany ). Electron microscopy studies were carried out on an EM-125 transmission electron microscope (accelerating voltage, 75 kV). Samples were prepared using the method of celluloid-carbon replicas. The viscosity was measured by the bending method on a Klyuev viscometer. The temperature dependence data on the viscosity was processed by the least squares technique with the conventional computer program for determining the coefficients A, B, and T₀ in the approximation according to the Vogel-Fulcher-Tammann equation [104] . The nucleation and growth rates of phase separated inhomogeneities and crystals were determined by the development method: preliminary heat treatment of the glass at a low temperature T, followed by the development at a higher temperature T_dev > T bringing to sizes that can be fixed in an optical microscope. The crystal growth rate was measured by quenching the samples. The samples in the form of small glass pieces were held at a specified temperature for different times and were used to prepare polished plane parallel disks 0.5 mm thick. Crystals with a maximum size were found in the bulk of a sample, and their radius R_max was measured using the Jenaval optical microscope. The radius R_max of the phase separated droplet or crystal was taken to be equal to the average value over ten maximum radii of crystals or phase separated droplets. This requires the explanation. If some number of phase separated droplets or crystals in the shape of spheres with the same radius R are randomly distributed in the glass bulk (their number per unit volume is designated as N), certain crystals or phase separated droplets will be cut by the plane when preparing the cleavage or cross section of the sample. This holds true only for crystals or phase separated droplets with the centers located at a distance that is not larger than R from the cut plane. Therefore, all crystals or phase separated droplets with the centers located in the layer of thickness 2R leave a trace on the cut plane. It is clear that the maximum radius of the trace of the crystal or phase separated droplet will correspond to the real radius of these particles.

In the 33.5Li₂O×66.5SiO₂ glass with the composition closest to the stoichiometric composition of the lithium disilicate, excess SiO₂ is absent and, therefore, no phase separation is observed. The compositions of the glasses containing 23.4 mol% Li₂O (no. 1), 26Li₂O (no. 2), and 29.1Li₂O (no. 3) lie in the metastable phase separation region of the lithium-silicate system. The samples of glasses no. 1, no. 2, no. 3 and no. 4 were subjected to preliminary heat treatment at temperatures in the range 370˚C - 560˚C for different times. Then, they were held at a development temperature of 600˚C for 10 min. If glass no. 1, no. 2 or 3 is held at the temperature T = 600˚C for a time in the range 0 - 10 h, it remains transparent without visible opalescence in visual examination. If the glass is heat treated for t = 2 h 40 min at temperatures of 400˚C - 560˚C, it remains visually transparent and does not become opalescent. After additional heat treatment at 600˚C for 10 min, the glass acquires bright blue (yellow in transmission) going to milky opalescence. The electron microscopic images of the glasses preliminarily heat treated at temperatures in the range 400˚C - 560˚C and developed at 600˚C for 10 min are displayed in Figures 1(a)-1(c).

We counted the number of traces of particles per unit area in the electron microscopic image N_S/S₀ and determined the sizes of the maximum traces of particles R. The corresponding results for glass no. 1 are listed in Table 3.

Figure 2 presents the quantitative characteristics of the phase separation structure in glasses no. 1 and no. 2 as a function of the temperature, namely, the ratio of the number of traces to the maximum number of traces N_S/N_Smax and the ratio of the radius of the particle trace to the maximum radius R/R_max.

Here, we assume that the dependence of the number of traces of phase separated droplets per unit area of the sample surface on the heat treatment temperature (at a constant heat treatment time) obeys the same function law as the temperature dependences of the stationary nucleation rate of droplets. Strictly speaking, in order to determine the stationary nucleation rate I(T), initially, it is necessary to determine the number of droplets per unit volume of the glass by the number of traces per unit area with the use of stereological formulas. Then, it is required to determine a variation in the number of droplets per unit volume as a function of the heat treatment time. Thereafter, it is necessary to check that the nucleation rate is stationary and to determine its value. This is not a simple problem, which is complicated by the fact that the droplets in the volume of the glass can have different sizes. The obtained dependence of the number of traces on the temperature for a fixed heat treatment time can differ substantially from the dependence of the stationary nucleation rate of droplets. However, we used a simpler method to approximately evaluate the temperature dependence of the nucleation rate of droplets. Instead of the dependence I(T), we constructed the dependence N_S(T) of the number of traces of particles developed for the same specified time of development t_dev at T_dev after preliminary heat treatment for the same specified time t at all temperatures T. Since the quantities I and N_S are approximately proportional to each other, the curves I(T)/I_max and N_S(T)/N_Smax are very close to each other and, in order to evaluate the temperature of the maximum nucleation rate, it is sufficient to measure the dependence of the number traces of crystals N_S without regarding for their shape and sizes [77] [80] . It can be seen from Figure 2 that these dependences exhibit maxima. The maximum values of the number of traces and sizes correspond to temperatures of 460 and 600˚C, respectively. On the whole, the results obtained can be explained as follows. The nucleation rate of a new phase (phase separated or crystalline) I has the form [68]

where Φ* is the increment of the thermodynamic potential of the glass due to the appearance of a critical (in composition and size) inhomogeneity nucleus, Φ_A is the thermodynamic potential of diffusion jumps and transformations during the phase separation, and A is the factor that, like the quantities Φ_A and Φ*, depends on the glass composition and temperature more weakly than an exponential function. If the glass composition c₀ belongs to the bimodal region at a given temperature, the thermodynamic potential Φ* is relatively high because the inhomogeneities that do not reach some limiting concentration c₁ appear to be energetically unfavorable irrespectively of their sizes. When the glass composition belongs to the spinodal region, inhomogeneities with an arbitrarily small difference and, correspondingly, with negligible Φ* can be energetically favorable if only their size exceeds the critical size. As a consequence, there is an increase in the nucleation rate of inhomogeneities I (expression (1)). By using the notion of the concentration wave length λ introduced by Cahn, in the spinodal region, the value most rapidly increases in amplitude and, hence, the inhomogeneities with the size λ_m that is larger than the critical size λ_cr by a factor of nucleate most rapidly. The wave amplitude λ_m increases as exp(t/τ_m); in this case, the magnitude 1/τ_m can be considered not only as the measure of the nucleation rate of the amplitude but also as the measure of the nucleation rate of inhomogeneities by taking I = B/τ_m. As a result, we have (2)

where B and c are temperature independent constants and T_S is the spinodal temperature. From the condition dI/dT = 0, we find that the maximum of the rate is located at the temperature T_max satisfying the Equation (3).

, (3)

By assuming that the thermodynamic potential Φ_A does not depend on the temperature T, i.e., Φ_A = E_A, and setting Φ_A = 83 kcal/mol (activation energy of oxygen diffusion), at, Equation (3) takes the form

Under the assumption that the thermodynamic potential Φ_A is equal to the activation energy of lithium self diffusion, we obtain

Therefore, the maximum of the ratio N_S/N_Smax in Figure 2 reflects the maximum of the nucleation rate of droplets with a diameter λ = 200 - 400 Å. This reflection is rather

indirect because the number of inhomogeneities n' nucleated for the time t'

can differ significantly (and differs) from the number n of large particles growing in the course of the development. The reason is that, after the increase in the temperature to 600˚C, the inhomogeneities with the composition and size that reach critical values at 600˚C are predominantly retained and will develop. The inhomogeneities with the composition that approaches the binodal composition at the corresponding temperature during low temperature heat treatment go beyond the binodal with the increase in temperature to 600˚C and should dissolve in the glass located between inhomogeneities. A number of inhomogeneities can merge together when reaching the critical sizes for a temperature of 600˚C. This dissolution and merging of small inhomogeneities can lead to the formation of larger and stable inhomogeneities with a composition close to the binodal composition at the temperature of 600˚C.

Although the relation between the quantities n and n' is complex, the maximum of the ratio N_S/N_Smax in Figure 2 reflects the rate of nucleation and development of phase separated inhomogeneities. Then, the temperature of its left boundary can be identified with the spinodal temperature T_S and the difference between this temperature and the temperature of the maximum T_max is appropriately identified by the difference − T_max, which was estimated above as 25˚C - 60˚C. It is difficult to accurately determine the spinodal temperature. In our experiment, we determined this temperature from the appearance of pronounced phase separated droplets in the electron microscopic images. Experimental data on the determination of the spinodal are absent in the literature.

Haller et al. [105] calculated the spinodal for glasses in the lithium silicate system. A comparison of our data with those obtained in [105] leads to the following results. According to [105] , the spinodal temperature T_S amounts to approximately 600˚C for glass no. 1 (23.4 mol% Li₂O) and is in the vicinity of 500˚C for glass no. 2 (26.0 mol% Li₂O). Below 500˚C, data in [105] are absent. However, if the curve is extrapolated to 400˚C, the spinodal temperature T_S for glass no. 2 appears to be 400˚C. In our work, the maximum of the ratio N_S/N_Smax in Figure 2 lies in the temperature range 350˚C - 570˚C for glass no. 1 and ≈ 400˚C - 650˚C for glass no. 2. Therefore, the experimental and calculated data for glass no. 2 (26.0 mol% Li₂O) are in good agreement, whereas, for glass no. 1 (23.4 mol% Li₂O), the calculated value is by 200˚C higher than the experimental. For glasses no. 1 and no. 2, the difference − T_max @ 40˚C - 50˚C actually lies in this range. The maximum of the rate of nucleation and development of inhomogeneities is located at the glass transition temperature T_g.

In order to compare more rigorously the theory with the experiment, it is necessary to know the spinodal temperature T_S. This temperature was evaluated as follows. Quenched glasses no. 1 and no. 2 (without low temperature heat treatments) were held in the gradient furnace at temperatures in the range 300˚C - 800˚C for 2 h. This led to the appearance of the opalescent band along the sample length, which was stable with respect to a further increase in the holding time. This band had a higher intensity in the central part and weaker intensities toward higher and lower temperatures up to its complete visual disappearance. The temperature of the upper edge of the visible opalescence (770˚C for glass no. 1) coincided with the phase separation temperature T_l (770˚C for glass no. 1) determined as the temperature of the disappearance of the visible opalescence after the opalescent part of the rod was displaced in the range of temperatures a priori higher than T_l. The analysis of the electron microscopic images demonstrates that, in going from the high temperature edge of the band to the low temperature edge, the number of particle traces per unit area (or the relative area occupied by particle traces) increases linearly. Initially, this process goes slowly and then accelerates. It is clear because the nucleation rate is minimum in the vicinity of the phase separation temperature T_l and increases as the spinodal temperature T_S is approached as a result of the decrease in the thermodynamic potential Φ* in expression (1). When the traces of inhomogeneities begin to cover a larger part of the replica area and to merge together, the increase in the relative area S/S₀ occupied by particles at is retarded sharply. The temperature of this kink in the curve S/S₀ is naturally identified by the spinodal temperature T_S corresponding to the beginning of fast nucleation of inhomogeneities occupying the volume of the glass. This temperature almost absolutely coincides with the low temperature edge of the visible opalescence. The temperature width of the opalescent band ΔT_op corresponds to the difference T_l − T_S @ ΔT_op.

The nucleation of the lithium disilicate was observed in all glasses. The dependences of the number of developed crystals n in the nucleation temperature range 400˚C - 520˚C (development at 600˚C for 10 min) were used to determine the stationary nucleation rate and the nonstationary nucleation time at each specific temperature. The induction period t_ind decreases monotonically with an increase in the temperature. The temperature dependence of the induction period t_ind(T) allows us to determine the activation energies for nucleation of lithium disilicate crystals E_τ from the formula E_τ = Rdlnt_ind/d(1/T). The corresponding activation energies are equal to 129, 128, 127 and 126 kcal/mol for glasses no. 1 - no. 4, respectively. The temperature dependences of the stationary nucleation rate of lithium disilicate crystals I_st(T) for the glass with the stoichiometric lithium disilicate composition and glasses with displaced compositions are shown in Figure 6. It can be seen from this figure that the nucleation rate of lithium disilicate crystals I_st(T_max) at the maximum decreases from 160 to 60 mm⁻³∙min⁻¹; in this case, the position of the maximum T_max is shifted toward higher temperatures by 12˚C. This relatively small change in the quantity I_st(T_max) can be explained by the fact that the glasses with displaced compositions correspond to the phase separation region in the Li₂O-SiO₂ system, so that the nucleation of the lithium disilicate occurs in phase separated inhomogeneities with the composition that is displaced toward the lithium disilicate composition and depends weakly on the temperature. The shift in the maximum T_max by 12˚C can be explained by the increases in the viscosity and the glass transition temperature of the melt in the phase separated (matrix) region [106] [107] enriched by SiO₂ as compared to the lithium disilicate composition, which provides an increase in the temperature T_max according to the relationship for the maximum of the nucleation rate

, , , (6)

where T_melt is the melting temperature and the enthalpy H_A, activation entropy S_A, and the nucleation barrier correspond to T = T_max. It can be seen from Figure 6 that the temperature T_max of the maximum nucleation rate of lithium disilicate crystals for all the compositions under investigation is close to the glass transition temperature T_g. The closeness of the temperatures T_max and T_g for the glass of the stoichiometric compositions and the glasses with displaced compositions can be explained as follows. The

relative displacements of structural units that are necessary for crystal nucleation and occur through the breaking and switching of chemical bonds become sufficiently fast with an increase in the temperature beginning from the glass transition point T_g. The presence of the viscosity determined by the free activation energy Φ_η = Φ_A leads to a shift in the maximum of the stationary nucleation rate I_st(T) according to relationship (6) toward higher temperatures (T_max = T_g = 2/3T_melt) as compared to its position T_max = 1/3T_melt that would be observed at H = 0.

Before proceeding to the discussion of the results of the experiment on the determination of the growth rate of lithium disilicate crystals in glasses no. 1 - no. 3, let us consider the main notions used when determining the crystal growth. The crystal growth occurs as a result of accidental attachments and detachments of structural units from the surface of a supercritical nucleus (the supercritical nucleus is a nucleus with the size exceeding a critical size). The growth of the super-critical nucleus is thermodynamically favorable because this is accompanied by a decrease in the free energy of the system ΔΦ. The linear growth rate of the nucleus is determined by the equation

where l is the thickness of the monomolecular layer growing on the crystal for some time interval, equal to the linear size of the structural unit), and β₊ and β₋ are the probabilities of attachment and detachment of one structural unit from the crystal surface per unit time:

, (8)

Here, τ₀ is the time of the order of the period of vibrations of atoms in a chemical bond, whose switching provides the transition of the structural unit to the ordered state of the crystal structure of the nucleus; ΔΦ is the change in the free energy of the system; and a is the linear size of the structural unit. Substitution of these expressions into formula (7) gives

(9),

where is the difference between the free energies of the glass and nucleus per unit volume of the nucleus and r* is the radius of the critical nucleus. It follows from this relationship that the growth rate of the critical nucleus is equal to zero. Since the critical nucleus is in an unstable equilibrium state, both the increase and decrease in its size is accompanied by a decrease in the difference and is equally probable. With an increase in the size of the supercritical nucleus, the growth rate increases and becomes constant when the nucleus radius is larger than the critical radius ().

Now, we consider the temperature dependence of the stationary growth rate. Under the assumption that, where q is the specific heat capacity, we have

According to expression (10), the growth rate is equal to zero at T → 0 and T → T_melt. At some temperature (), the growth rate is maximum. This temperature can be evaluated. We assume that and substitute into expression (10). After the differentiation with respect to the temperature, we obtain

From the extremum condition, we find that

The quantity kT_melt/H_A in formula (12) usually does not exceed 1/10. Therefore, the temperature of the maximum growth rate is close to the melting temperature, and it is very difficult to experimentally determine this temperature. This inference is very important for experimenters.

Thus, we have investigated the kinetics of phase separation in three lithium silicate glasses containing 23.4, 26.0 and 29.1 mol% Li₂O with the compositions lying in the phase separation region in the Li₂O-SiO₂ system. It has been found that the temperature dependences of the ratio of the number of traces to the maximum number of traces N_S/N_Smax and the ratio of the radius of the particle trace to the maximum radius R/R_max exhibit maxima. The crystal nucleation rate has been studied in glasses with the compositions displaced from the stoichiometric lithium disilicate composition toward an increase in the SiO₂ content. The following features have been revealed.

1) The absolute values of the crystal nucleation rate in glasses with the lower content Li₂O than that in the glass with the stoichiometric lithium disilicate composition vary insignificantly.

2) The position of the temperature maximum of the nucleation rate for the glass with the lower lithium oxide content is shifted on the temperature scale by 12˚C. This relatively small change in the quantities I_st(T_max) and T_max is explained by the fact that the glasses with the displaced composition correspond to the phase separation region in

the Li₂O-SiO₂ system, so that the lithium disilicate in glasses with displaced composition nucleates in phase separated inhomogeneities with compositions that are displaced toward the lithium disilicate composition and depend weakly on the temperature.

Variations in the crystal growth rate have been investigated as a function of the temperature and time of heat treatment. It has been shown that the temperature dependences of the crystal growth rate tend to an extremum. It has been found that the crystal growth rate depends substantially on the heat treatment time for phase separated glasses and that the growth rate is constant for the glass with the stoichiometric lithium disilicate composition. The dependence of the crystal growth rate on the heat treatment time in phase separated glasses exhibits a damped oscillatory behavior, which is explained by the depletion of the building material for crystals and the necessity of some time for its supply. Therefore, the performed investigations allow us to draw the following conclusion. Unlike the universally accepted opinion, the phase separation not only does not facilitate the conditions for the formation and growth of crystals but, in some cases (see, for example, the dependences of the crystal growth rate on the time of low-temperature heat treatment), even retards the crystal growth process. The data obtained on the nucleation and growth of crystals help to find optimum compositions and temperature-time conditions for the preparation of many glass-ceramic nanomaterials in lithium silicate system, including photostructured materials.

Sycheva, G.A. (2016) Crystal Growth and Nucleation in Glasses in the Lithium Silicate System. Jour- nal of Crystallization Process and Tech- nology, 6, 29-55. http://dx.doi.org/10.4236/jcpt.2016.64004