Crystallisation Kinetics of a β-Spodumene-Based Glass Ceramic

1 Unidade Acadêmica de Ciências, Engenharias e Tecnologias (UNACET), Universidade do Extremo Sul Catarinense (UNESC), 88806-000 Criciúma, SC, Brazil 2 Group of Ceramic and Glass Materials (CERMAT), Department of Mechanical Engineering (EMC), Federal University of Santa Catarina (UFSC), 88040-900 Florianópolis, SC, Brazil 3 Department of Materials Science, Institute of Glass and Ceramics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany


Introduction
A considerable effort has been spent to obtain high-performance glass ceramics for several potential applications in the medical, automotive, and telecommunication fields [1].Low-temperature cofired ceramics (LTCCs) have created good perspectives for those applications, with special attention to the glass ceramic materials [2,3].LZSA glass ceramics (Li 2 O-ZrO 2 -SiO 2 -Al 2 O 3 ) have been studied because of their beneficial thermal, mechanical, and thermal properties [4], among other interesting features.Moreover, laminated LZSA bodies crystallized at 850 • C/30 min have demonstrated to exhibit a low dielectric constant of 8.61 ± 0.84 at 1 MHz (room temperature) [5].Furthermore, their relatively low temperatures of sintering [6] make β-spodumene-based glass ceramics (LZSA) a potential candidate for obtaining multilayered structures processed by LOM technology (Laminated Objects Manufacturing) [7].However, the low sintering temperature is also accomplished by low crystallization temperature in this system, especially for very fine powders and low heating rates.In order to control thermal treatment for obtaining optimized properties, it is necessary to determine the kinetics parameters of crystallization for this glass ceramic system.
Isothermal crystallization kinetics of glass ceramic systems commonly refers to the following well-established Johnson-Mehl-Avrami equation [8]: where x is the volume fraction crystallized at a given temperature and time t, n is the Avrami parameter related to the nucleation and crystal growth mechanisms, and k is the reaction rate constant related to the apparent activation energy for crystallization, E c .Nonisothermal conditions have been more largely widespread in the crystallization studies of amorphous materials [3,[9][10][11][12][13][14][15], despite the scepticism of Shaaban [16].According to Shaaban [16], Kissinger plot and Ozawa plot cannot be directly used for crystallization of amorphous materials, because crystallization is advanced by the nucleation and crystal growth process instead of by nth order reaction.However, most of work reported in the literature used DTA or DSC to determine the kinetics parameters E c and n.Measurements using dilatometer were also applied in some cases [17,18].Those methods, which assume that deflection from the baseline is proportional to the instantaneous reaction rate, require a uniform temperature of the sample independently of the heating rate.This is obtained employing small samples and low heating rates during heat treatments [9].
The aim of this work is to present the results of an investigation about the crystallization kinetics of a β-spodumene-(LiAl [Si 2 O 6 ]) based LZSA glass ceramic composition by means of Nonisothermal method.

Samples Preparation.
A β-spodumene-based glass ceramic composition with interesting chemical, thermal, and electrical (dielectric constant) properties [4,5] was selected and prepared from suitable amounts of Li 2 CO 3 , ZrSiO 4 , SiO 2 , and LiAl[Si 2 O 6 ] (spodumene, Colorminas Colorifício e Minerac ¸ão, Crici úma, Brazil).The powders were mixed and melted at 1550 ± 3 • C for 2 h in a gas furnace using a mullite crucible.The melt was poured into deionized water and the quenched frit powder was remelted at 1550 ± 2 • C for 2 h in an electric furnace (Nabertherm LHT 02/17 LBR, Nabertherm, Lilienthal, Germany) using an alumina crucible to finally obtain a homogeneous viscous liquid.Chemical analysis is shown in Table 1.A small amount of the obtained melt was poured into a graphite crucible, transferred to an annealing furnace (Linn High Therm LM 421.27,Linn High Therm, Eschenfelden, Germany) and held at 570 • C for 1 h to obtain small monoliths (50 mm × 5 mm × 4 mm) that were used to determine the glass transition temperature (T g ) by beam-bending test (Beam-Bending Viscosimeter, Bähr Thermoanalyse VIS 401, Hüllhorst, Germany) applying a constant heating rate of 10

Determination of the Predominant Crystallization Mechanism.
The method of Thakur and Thiagarajan [19] was used to determine the nucleating efficiency, in which the variation in onset of crystallization, ΔT x , with particle size was monitored in a differential scanning calorimeter (DSC 404C, Netzsch, Selb, Germany; alumina crucibles, dry air).A constant heating rate of 10 • C•min −1 was applied to determine the predominant crystallization mechanism.Moreover, a small monolith sample (5 mm × 4 mm × 4 mm) was polishing to eliminate apparent surface defects and subsequently heat-treated at 875 • C for 2 h (10 • C•min −1 ).

Identification of the Crystalline Phases Formed.
Hightemperature X-ray diffraction (HT-XRD) patterns were recorded (Siemens D500, Siemens AG, Mannheim, Germany) from powdered samples.Monochromated Cu Kα1 radiation was applied at a voltage of 30 kV and a current of 30 mA.   30, 60, and 120 min were applied.After heat treatment, each sample was transversally cut.Morphology, crystal formation, and crystalline growth from surface towards to the centre of the monoliths were analysed by scanning electronic microscopy (SEM, Philips XL 30, Eindhoven, The Netherlands).

Determination of the Activation Energy for Structural
Relaxation.The activation energy for structural relaxation was determined for the investigated composition by means of the method of Moynihan et al. [20] Small monoliths (20 mm × 5 mm × 4 mm) were analyzed to determine the glass transition temperature (T g ) according to DIN 52324 (Bestimmung der Transformationstemperatur) with a horizontal dilatometer (DIL 402C, Netzsch, Selb, Germany; dry air).However, the last heating run to determine T g was performed at 5, 10, 15, and 20 • C•min −1 heating rates.

Results and Discussion
Some basic properties of the selected glass are summarized in Table 2. Taking into account this glass presents T g of 580 • C (Figure 1), determined by beam-bending test, and sintering in glasses occurs by viscous flow, densification would be expected to start around T g .In fact, Figure 2 shows that sintering started at about 600 • C and maximum shrinkage was achieved at 800-850 • C.This result compares very favorably with relative density data, Figure 3.By means of optimized heat treatment (30 min at 700 • C and 10 min at 850 • C), a low-porosity (3.2%), low-CET (2.38 × 10 −6• C −1 ), and low-dielectric constant (9.97 ± 0.84) material was obtained.

Crystallization and Particle
Size.According to previous work [4], very fine powders of β-spodumene-based glass ceramics show crystallization on the surface rather than in the bulk because of very high specific surface area.Figure 4 shows DSC of two LSZA glass powders differing in size: powder a is of small grain size (d 50 ∼ 2.34 μm) and exhibits a pronounced exothermic peak centered at approximately 790  during heating; powder b has a significantly larger particle size (d 50 ∼ 500-700 μm) and a small peak at approximately 840 • C. Thus, with decreasing particle size, the temperature of the exothermic peak maximum was shifted to lower temperatures.From the magnitude of the peak temperature shift with the particle size, ΔT x , it was concluded that surface crystallization should dominate over volume crystallization when ΔT x > 20 • C whereas volumetric crystallization was expected to prevail for ΔT x <10 • C [19].Since for the LSZA glass ΔT x ∼ 50 • C for the two grain sizes studied surface crystallization is concluded to dominate devitrification which is in good agreement with previous work for similar glasses [4].Thus, the results confirm a distinct particle size effect on the  crystallization of β-LiAl[Si 2 O 6 ] which for small particle sizes will be dominated mainly by surface crystallization.Hence, for larger particle size, crystallization rate will be slower and volumetric crystallization will increase at a given heating rate [14].

Crystalline Phase Composition.
HT-XRD patterns recorded on a powdered sample in the temperature range of 650-950 • C are shown in Figure 5.Additional powder samples were prepared and heat-treated at 650, 670, 685, 700, and 725 • C for 10 min in order to obtain new XRD patterns as shown in Figure 6.At room temperature the material is essentially vitreous except for traces of zirconia (monoclinic ZrO 2 , m-ZrO 2 ) (Figure 5).Due to the limited cooling rate and small solubility, precipitation of m-ZrO 2 may have occurred even during quenching.Crystallization of β-spodumene solid solution (Li 0−6 Al 0−6 Si 2−4 O 6 , ICCD card no.21-503; LiAlSi 3 O 8 , ICCD card no.15-27) was found to commence at approximately 670 • C (Figure 6).A pronounced acceleration was observed at temperatures above 725 • C. The peak maxima occurred at 800 • C which coincides with the results of DTA measurements.Above 750 • C zircon (ZrSiO 4 , ICCD card no.6-266) crystallized as the second major phase with maxima reached at 900 • C (Figure 5).[14][15][16][21][22][23].Based on the variation in peak crystallization temperature (T p ) with heating rate (α = dT/dt) the apparent activation energy for crystallization, E c , was derived from Matusita and Sakka's [22] modification of the Kissinger [21] equation:

Crystallization Kinetics. DTA and DSC have widely been used to evaluate Nonisothermal crystallization kinetics
where n and m are numerical factors related to the crystallization mechanism [12], R is the gas constant, and C is a constant.For the case when crystallization is dominated by three-dimensional crystal growth, n = m = 3, and for predominantly surface crystallization, n = m = 1.A plot of

Heating rates
ln (T 2 p /α n ) against 1/T p should give a straight line with slope (E c /R).The value of the Avrami parameter n was evaluated from a common method developed by Augis and Bennett [23]: where Δw is the full width of the DTA exothermic peak at the half maximum and E c was calculated from (2).Avrami parameter n was found to be in the range of 1.0 and 1.2 and can be adjusted to a value of 1, confirming that the glass shows crystallization by surface mechanism.Then, one can consider n = m = 1 [9], taking into account that crystallization at different heating rates occurs on a fixed number of nuclei, and (3) can be reduced to the Kissinger equation [20].Typical DTA scans of glasses subjected to different heating rates from 5 • C/min to 20 • C/min are shown in Figure 7, while T p values are summarized in Table 3.The peak temperature T p of the exothermic peak associated with crystallization of β-spodumene ss increased from 755 • C to 799 • C with increasing heating rate.However, the exothermic event related to zircon crystallization is not well defined, although it was clearly recorded in the XRD patterns.
Apparent activation energy for crystallization plot is given in Figure 8.The linearity of the curve obtained for these plots suggests that a fixed number of nuclei were achieved in the crystallization [24].Taking n = m = 1 values of E c ∼ 274 kJ/mol and n ∼ 1.2 were derived.Hu et al. [25] reported E c values of 415 kJ•mol −1 for crystallization of β-quartz ss and β-spodumene crystalline phases, whilst Lee et al. [24] measured 285 kJ•mol −1 for crystallization of βeucryptite (β-LiAl [SiO 4 ]).
The area under the exothermic peak can provide information about the evolution of the crystallization process.Considering the area under the exothermic peak (DTA scan) for each temperature that is proportional to the volumetric fraction of crystals (X), the crystallization progress by DTA scans with different heating rates was also evaluated (Figure 9).For each heating rate, the curves assumed typical sigmoidal shape.Crystallization started at approximately 700 • C independently on all the heating rate but finished at higher temperatures as the heating rate was increased.The incubation time (τ), that is, the time necessary for βspodumene ss crystalline phase development, increases with heating rate increasing.Thus, the improvement of densification could be achieved at 20 • C•min −1 heating rate.LZSA glass ceramic.Distinct differences in morphology and distribution of crystalline precipitations are related to different stages of the crystallization process.At the beginning of the crystallization process, columnar crystals of β-spodumene ss with a typical grain size of ∼ 4 μm form that preferentially grow perpendicular from the surface (Figure 10(b)).This one-dimensional growth pattern is in agreement with Avrami parameter obtained (n ∼ 1.2).With increasing crystallization time at 875 • C, however, crystallites tend to form spherical particles with grain sizes of 1 μm (Figure 10(c)).According to the DTA data and XRD patterns, the second front of crystalline growing should be related to the formation of zircon in the presence of βspodumene ss .

Determination of the Activation Energy of Structural
Relaxation.The activation energy of structural relaxation, E relax , can be related to the activation energy of viscous flow.
The value for E relax should give an indication of the sintering ability of a glass powder system [26].The activation energy of structural relaxation was calculated according to the relation of Moynihan et al. [20]: Values of glass transition temperature, T g , for the different heating rates were 589 • C (α = 5 • C/min), 600 • C (10 • C/min), and 607 • C (15 • C/min).The activation energy of structural relaxation derived from these data attained a value of E relax ∼ 386 kJ/mol which significantly is higher than the activation energy for crystallization.
Regarding the powdered glass features (composition, mean particle size, and thermal properties), processing characteristics (temperatures and heating rates), and the final properties of the obtained glass ceramic, some properties were improved such as porosity, despite the small temperature range for sintering, and CTE.However, the control of crystallization (temperature and time) can be used to create a three-layered structure with specific thickness of each layer from glass monoliths.An internal, thinner layer mostly formed by crystals of β-spodumene ss and an external, coarser layer formed by crystals of β-spodumene ss and zircon could create residual stress in order to exhibit increased apparent fracture toughness and energy absorption.

Conclusions
Taking into account some interesting thermal and dielectric properties, a selected β-spodumene-based glass ceramic composition (16.9Li 2 O•5.0ZrO 2 •65.1SiO 2 •8.6Al 2 O 3 ) was used for crystallization kinetics investigation by means of Nonisothermal method.The crystallization mechanism was found to be predominantly surface crystallization when the particle size is small.Two crystallization fronts regarding the crystalline phases formed, β-spodumene ss and zircon, were identified starting at approximately 670 • C and 700 • C, respectively.The morphology of the microstructures showed a columnar structure for the former and a globular for the second one.Apparent activation energy for crystallization E c was found to be in the range 274 kJ/mol with an Avrami parameter n of 1 that is compared very favorably with SEM observations.At 850 • C/10 min, a low-porosity (3.2%), low-CTE (2.38 × 10 −6• C −1 ), low-dielectric constant (9.97 ± 0.84) material was obtained.Moreover, the dielectric loss at 1 MHz was <0.3%.A value of 386 kJ•mol −1 was obtained for the activation energy of structural relaxation E relax , in which its value is significantly higher than the activation energy for crystallization, hindering densification of material.

Figure 2 :Figure 3 :
Figure 2: Linear shrinkage versus temperature of the selected glass.

=Figure 8 :
Figure 8: Apparent activation energy for crystallization plot for the selected glass based on (2) with n = m = 1.

Figure 9 :
Figure 9: Measurement of the crystallization progress from normalization and integration of the DTA scans.

3. 4 .
Microstructure.Figure10shows SEM micrographs of the microstructures observed in the parent and crystallized

Table 1 :
Chemical composition of LZSA parent glass.
• C•min −1 .Thermal expansion was measured with a horizontal dilatometer (DIL 402C, the ratio between apparent and theoretical densities of the heat-treated samples.Dielectric constant measurements were carried out according to DIN 53 482/VDE 0303 in a HP Dielectric Test Fixture (16451B, Hewlett Packard, Waldhausen, Germany) at room temperature applying a frequency of 1 MHz.The samples were discs of 20 mm × 1.2 mm heat-treated at 850 • C for 10 min.

Table 2 :
Properties of the investigated LZSA glass ceramic (sintered at 850 • C for 10 min).
× 4 mm) were prepared from the transparent glass samples.Some of them were cut in small pieces of 5 mm × 4 mm × 4 mm which were used for investigating the crystal growth under different heat treatment conditions in an electrically heated furnace (LM 421.27,Linn High Therm, Eschenfelden, Germany).Temperatures of 700, 750, 775, 800, 825, 850, 875, and 900 • C and swelling times of 15, Figure 5: HT-XRD patterns recorded on a powdered sample in the specified temperatures: S: β-LiAl[Si 2 O 6 ]-ss; ZS: ZrSiO 4 ; Z: ZrO 2 .

Table 3 :
Onset temperature for each heating rate investigated.