Non-isothermal crystallization kinetics of La2CaB10O19 from glass

Journal of Non-Crystalline Solids 357 (2011) 1690–1695

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Journal of Non-Crystalline Solids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l

Non-isothermal crystallization kinetics of La2CaB10O19 from glass I. Dyamant a,b, E. Korin b, J. Hormadaly a,c,⁎ a b c

Zandman Center for Thick-Film Microelectronics, Ben-Gurion University of the Negev, P. O. Box 653, Beer-Sheva 84105, Israel Department of Chemical Engineering, Ben-Gurion University of the Negev, P. O. Box 653, Beer-Sheva 84105, Israel Department of Chemistry, Ben-Gurion University of the Negev, P. O. Box 653, Beer-Sheva 84105, Israel

a r t i c l e

i n f o

Article history: Received 5 August 2010 Received in revised form 16 January 2011 Available online 4 March 2011 Keywords: Crystallization kinetics; La2CaB10O19; Avrami exponent; Differential thermal analysis; Glass crystallization

a b s t r a c t The non-isothermal crystallization kinetics of La2CaB10O19 (LCB) from a La2O3–CaO–B2O3 glass was studied. Differential thermal analysis methods were performed on three glass powders to obtain the kinetic parameters of LCB crystallization mechanism. The activation energies for overall crystallization (E), obtained by the methods of Kissinger and Ozawa, were in the range of 479–569 kJ/mol. Multiple (five) analysis methods were used to estimate the Avrami exponent (n), which could consequently be reduced into the single value of n = 3.1 ± 0.3. The growth morphology index (m) of LCB was corroborated by microscopy (optical and electron) images, which revealed a three dimensional growth. Energy dispersive spectroscopy confirmed that LCB is the crystallizing phase from the glass by an interface controlled mechanism. The parameters of the Johnson–Mehl–Avrami kinetic model for the analysis of LCB crystallization from glass were found to be n = m = 3. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Visible and ultraviolet lasers for various applications such as medical, industrial and entertainment have focused on increasing the demand for non-linear optical (NLO) crystals [1]. La2CaB10O19 (LCB) is a new crystalline phase that shows promising NLO properties with a relatively large second harmonic generation effect [2]. In addition to being nonhygroscopic and with the hardness of 6.5 Mohs [3], LCB has demonstrated potential for self-frequency-doubled lasers in which the frequency doubling function is incorporated within the active laser in a single medium [4]. LCB was found to crystallize from clear glasses within the glass forming range of the La2O3–CaO–B2O3 ternary system [5]. Recently we have investigated the characteristics of LCB crystallization from bulk glass as an alternative method for its synthesis [6]. We found that LCB crystallizes by a growth from a nuclei-site saturated glass matrix and showed that the Johnson–Mehl [7]–Avrami [8–10] (JMA) model is applicable for the non-isothermal kinetic analysis of LCB. In this paper, we report the kinetics of LCB crystallization mechanism from a glass with a stoichiometric composition of 14.3La2O3·14.3CaO·71.4B2O3 mol%. The activation energies for overall crystallization (E) of different glass powder samples, by means of non-isothermal differential thermal analysis (DTA), are discussed. Based on the obtained DTA data the kinetic parameters for

⁎ Corresponding author at: Department of Chemistry, Ben-Gurion University of the Negev, P. O. Box 653, Beer-Sheva 84105, Israel. Tel.: +972 8 646 1929; fax: +972 8 647 2846. E-mail address: [email protected] (J. Hormadaly). 0022-3093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2011.01.028

LCB crystallization are estimated by five analysis methods and microscopy measurements. The above findings serve to determine the mechanism of LCB crystallization from glass. 2. Theoretical considerations 2.1. Transformation kinetics The JMA model, Eq. (1), is generally used for the crystallization kinetics analysis by DTA methods.
 m n n x = 1−exp −gNv U t = 1−exp −ðkt Þ

ð1Þ

where x is the volume fraction crystallized, g is the crystalline phase shape factor, Nv is the number density of nuclei, U is the growth rate, m is the growth morphology index, n is the Avrami exponent and t is time. The characteristics of LCB crystallization from glass [6], which have shown nuclei site saturation, modify the JMA model by the requirement that Nv = const. and n = m. A general form of JMA with the rate constant, k, is also given in Eq. (1) where k is assumed to show an Arrhenian temperature dependence. The activation energy for overall crystallization, E, could be obtained from the relation between k and the temperature, T. Different values for m and n with their interpretations can be found elsewhere [11,12]. Another equation for evaluating the kinetic parameters is the reaction rate, which results from the derivation of Eq. (1) by time n−1 dx = nkð1−xÞ½− lnð1−xÞ n : dt

ð2Þ

I. Dyamant et al. / Journal of Non-Crystalline Solids 357 (2011) 1690–1695

2.2. Kinetic parameters from non-isothermal crystallization Non-isothermal DTA measurements are usually performed by heating the glass sample (bulk or powder) at a constant heating rate, β, until completion of the exothermal peak of crystallization. The characteristic peak temperature, TP, is used to obtain E from the wellknown plots of Kissinger [13] and Ozawa [14,15]. The established n to m dependence for this glass allows the direct interpretation of E from such plots [6]. Thus, by plotting ln(β/T2P) and ln(β) vs. 1/TP, the values for the activation energies EcK (Kissinger) and EcO (Ozawa) are obtained. The estimation of n and the related crystallization mechanism can be done on the basis of Eqs. (1) and (2). Considering that it is the first time the crystallization of LCB from glass is being studied, five different analysis methods were used. The method of Ozawa for n [15] gives a rather straightforward interpretation for non-isothermal conditions; by plotting ln[− ln(1 − x)] vs. ln(β) for a constant T a linear line with a slope value that equals to −n is obtained. The method of Augis and Bennett [17], which relays on the exothermal peak width, TP and a pre-determined E value, was used as follows:

n=

2:5·R T2 × P FWHM E

ð3Þ

where FWHM is the full width at half peak maximum, which was obtained by an integral breadth relationship of the peak area and its height. The obtained n values were assigned to nK and n O, corresponding to EcK and EcO, respectively. The methods of Šesták [18] and Piloyan [19] were also used for estimating nK and nO together with pre-determined EcK and EcO values [20]. Thus, plots of ln[−ln(1− x)] and ln(δT·T) [21] vs. 1/T (for
Šesták  and Piloyan, respectively) yield linear lines with slope value of ≅ −n RE . The δT in the Piloyan method is the instantaneous temperature difference from the DTA baseline. The x range for these methods was confined to the initial part of the exothermal peak, 0.05b x b 0.50, in accordance with the Borchardt assumption [22]. Due to the above limitations, the obtained n from both methods were considered as rough estimations. The method proposed by Pérez-Maqueda [23], for the simultaneous estimation of E (here denoted as EPM) and n, was also used. In ( ) dx = dt this method a plot of ln vs. 1/T yields a 1−1 nð1−xÞ½− lnð1−xÞ n linear line with a slope of −EPM/R, provided that a matching n is selected in advance. The required x range for this method considers end-effects only and therefore was 0.1 b x b 0.85 [23]. The matching n was obtained when a set of such plots, from various DTA scans performed with similar samples (i.e., with constant particle size and weight), converged into a single linear line. Table 1 shows the formulas of the methods which were used for the analysis of LCB crystallization from glass. 3. Experimental procedures Analytical grade H3BO3 (Bio-Lab Ltd., Israel; ≥99.5%), La2O3 (Aldrich Chem. Co., USA; ≥99.99%) and CaCO3 (Fisher Chem., USA; ≥99.0% (certified ACS)) were used for the synthesis of the La2O3–CaO–B2O3 glass with the LCB stoichiometric composition of 14.3La2O3·14.3CaO· 71.4B2O3 mol%. The La2O3 was pre-heated for 1 h at 1000 °C in order to decompose possible hydrates and carbonates to the lanthanum oxide. The batch was melted in an electric box furnace at 1200 °C, in a platinum crucible, until a homogeneous pourable melt was obtained, which was immediately quenched in water at room temperature. The obtained frit was dried in a drying furnace for 1 h at 120 °C. Then it was ground and sieved to obtain uniform powders with fractions in the desired size

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Table 1 Analysis methods formulas and their development preliminary assumptions used for obtaining LCB crystallization kinetics parameters. Method

Formula

Preliminary assumptions

Ozawa [16]

∂ln½−lnð1−xÞ   ∂lnðβÞ T = const:



Augis and Bennett [17] Šesták [18]

n=

2:5·R FWHM

×

∂T ∂t

= −n

TP2 E



∂ln½−lnð1−xÞ  ≅−n RE  ∂ð1 = T Þ 0:05bxb0:50



Piloyan [19],[20]⁎,[21]⁎

∂ln½δT·T   ≅−n RE  ∂ð1 = T Þ 0:05bxb0:50

( ∂ln

Pérez-Maqueda [23]

)

dx =dt 1−1n

nð1−xÞ½−lnð1−xÞ ∂ð1 = T Þ

     0:05bxb0:85

=β

k∝Arrhenian E ≥25 RTP k∝Arrhenian E NN 1 RT k∝Arrhenian dx δT∝ dt

= − EPM k ∝ Arrhenian R Pre-determined n value from the range of 1–4

⁎ Modifications of the original formula.

range. Three types of powders were prepared with an average particle size of 42, 69, and 200 μm for series 1, 2 and 3, respectively. The temperature accuracy of the electric furnaces was ±2 °C. Non-isothermal DTA scans were performed with heating rates of β = 5, 10, 15, 20, 25 and 30 °C/min. The measurements were done on a TA Instruments STD 2960 apparatus in platinum crucibles with alumina powder as the reference material in an atmosphere of 100 mL/min Air flow, from which the glass transition temperature, Tg (as determined by the inflection point in the appeared endothermal step change), TP, and FWHM were obtained. The calculations of FWHM were done using peak area and peak height values that were normalized to the sample weight of each specific scan (in the range of 15–20 mg). Errors for the measured DTA temperatures and FWHM were determined from combining the systematic apparatus sensitivity with the standard deviation (SD) values, obtained from at least three measurements at β = 20 °C/min. The values of x for the kinetic analysis were obtained from the area fractions data of the exothermal peaks. Errors for x, ln[−ln(1 − x)] and β were taken as the sensitivity values of ±0.01, ±0.01 and ±0.5 °C/min, respectively. The above values were also used to calculate the errors for 1/TP, n and E. The sensitivities of ±3 s for t and ±0.1 for n were used in the calculations of the Pérez-Maqueda method. The morphology of LCB was obtained from the surface images of a heat treated bulk glass sample by means of light microscopy (transmitted; Ziess Axioplan-2) and high-resolution scanning electron microscopy (HR-SEM; Jeol JSM-7400F). The bulk glass sample was melted similarly as the frit and after casting it was annealed for 0.5 h in an electric furnace at a temperature near Tg (~670 °C [5]) and left in it to cool to room temperature. The heat treatment of the bulk glass was 1 h at 750 °C after which the sample was left to cool in the furnace. Sample preparation for HR-SEM also included an Ag coating. Additionally, energy dispersive spectroscopy (EDS) measurements were performed from selected sample regions during the HR-SEM imaging. 4. Results 4.1. Non-isothermal DTA DTA thermograms for the non-isothermal measurements of series 1–3 with β in the range of 5–30 °C/min showed only one exothermal peak in each scan, indicating the probable crystallization of a single dominant phase (Fig. 1). The Tg, TP and FWMH values from the nonisothermal DTA scans are given in Table 2. Kissinger (Fig. 2a) and

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a)

Exo.

0.25

30 °C/min

series 3

0.15

-10.4

25 °C/min 20 °C/min 15 °C/min

0.20 0.10

10 °C/min 5 °C/min

0.05

Series 1 Series 2 Series 3

-10.8 2

Tg

ln ( /T P )

0.30

0.00

-11.2 -11.6 -12.0

0.45

Exo.

-12.4

0.40

series 2

30 °C/min

0.35

-12.8 90

0.30

92

0.20

b)

15 °C/min

0.15 Tg

0.10

93

94

95

4.0

10 °C/min

0.05

96

1/T P×105 (K-1)

20 °C/min

0.25

Series 1 Series 2 Series 3

3.5

5 °C/min

0.00

3.0

ln ( )

0.35

91

25 °C/min

Exo.

0.30

30 °C/min

series 1

2.0

25 °C/min 20 °C/min

0.25 0.20

2.5

1.5

15 °C/min

0.15 Tg

0.10

10 °C/min

1.0 90

91

5 °C/min

0.05

92

93

94 5

95

96

-1

1/T P×10 (K )

0.00 600

650

700

750

800

850

900

Temperature (°°C) Fig. 1. Non-isothermal DTA thermograms for series 1–3 heated in the range of β = 5– 30 °C/min.

Ozawa (Fig. 2b) plots gave EcK and EcO values for series 1–3, respectively, which are also given in Table 2. 4.2. Avrami exponent Figs. 3–5 present data for series 3 only and Fig. 6 includes the data for series 1–3. Table 3 summarizes the obtained n and EPM for series 1– 3 from the various analysis methods of the non-isothermal DTA. 4.2.1. The Ozawa method Fig. 3 shows plots of ln[−ln(1 − x)] vs. ln(β) for series 3. Similar plots (not given) were constructed for series 1 and 2 also. The obtained n by the Ozawa method (mean ± SD) for series 1, 2 and 3 are: 3.4 ± 0.4, 3.4 ± 0.3 and 3.6 ± 0.3 (Table 3), respectively.

Fig. 2. a) Kissinger and b) Ozawa plots for series 1–3. Calculated errors for ln(β/T2P) and ln(β) are ±0.1. E for each series was calculated (Table 1) from the slope values of the linear regression lines (solid), with Pearson correlation coefficient values (r2) in the range of 0.998–0.999.

4.2.2. The Šesták method Fig. 4 shows plots of ln[−ln(1 − x)] vs. 1/T, for the values obtained from the non-isothermal DTA scans of series 3. Similar plots (not given) were also constructed for series 1 and 2. The obtained nK by the Šesták method (mean ± SD) for series 1, 2 and 3 are: 3.2 ± 0.3, 3.1 ± 0.5 and 3.2 ± 0.5 (Table 3), respectively. Similarly, the nO values (mean ± SD) for series 1, 2 and 3 are: 3.1 ± 0.3, 3.0 ± 0.5 and 3.1 ± 0.5 (Table 3), respectively. 4.2.3. The Piloyan method Fig. 5 shows plots of ln(δT·T) vs. 1/T, for the values obtained from the non-isothermal DTA scans of series 3. Similar plots (not given) were also constructed for series 1 and 2. Originally the Piloyan method was developed with ln(δT) vs. 1/T [19]. However, it was found that ln(δT·T) vs. 1/T [21] provided plots with higher correlation coefficients. The obtained nK by the Piloyan method (mean± SD) for series 1, 2 and 3 are:

Table 2 Non-isothermal DTA values of Tg, Tp and FWHM and the values for EcK and EcO from the Kissinger and the Ozawa plots (Fig. 2), respectively, for series 1–3. Calculated errors are given in parentheses. β (°C × min)

5 10 15 20 25 30 EcK (± 1; kJ/mol) EcO (± 1; kJ/mol)

Series 1

Series 2

Series 3

Tg (± 0.3; °C)

TP (± 1; °C)

FWHM (± 0.5; °C)

Tg (± 0.4; °C)

TP (± 1; °C)

FWHM (± 0.5; °C)

Tg (± 0.4; °C)

TP (± 1; °C)

FWHM (± 0.8; °C)

664.8 669.8 671.5 673.3 674.8 674.7 551 569

777 788 794 800 804 806

10.7 12.3 12.8 13.6 13.9 14.1

666.4 669.0 670.5 672.3 673.7 674.8 509 526

779 790 797 803 807 811

12.1 12.3 12.9 13.6 13.7 13.3

664.0 669.5 670.6 672.5 673.6 673.9 479 497

798 812 820 826 830 835

14.0 15.0 15.0 16.0 19.1 18.6

I. Dyamant et al. / Journal of Non-Crystalline Solids 357 (2011) 1690–1695

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2 799 °C 801 °C 803 °C 807 °C 809 °C

ln [-ln (1-x )]

0 -2 -4 -6 -8 1.5

2

2.5

3

3.5

ln ( ) Fig. 3. Plots of the Ozawa method from constant temperatures in DTA scans with β = 5– 30 °C/min, for series 3. Calculated error is ± 0.01 for ln[− ln(1 − x)]. Slopes of linear regression lines (solid) gave n = 3.4 ± 0.4 (SD), with Pearson correlation coefficient values (r2) in the range of 0.994–0.999.

Fig. 6. Plots of the Pérez-Maqueda method from DTA scans with β = 5–30 °C/min, for series 1–3. Calculated error is ± 0.2 for the ordinate. Insets are matching n values that gave linear regression lines (solid) to obtain EPM (Table 3), with Pearson correlation coefficient values (r2) in the range of 0.995–0.997.

0 5 °C/min 10 °C/min 15 °C/min 20 °C/min 25 °C/min 30 °C/min

ln [-ln (1-x )]

-0.5 -1

Bennett method (mean ± SD) for series 1, 2 and 3 are: 3.4 ± 0.3, 3.6 ± 0.1 and 3.3 ± 0.3 (Table 2), respectively. Similarly, the values of nO (mean ± SD) for series 1, 2 and 3 are: 3.3 ± 0.3, 3.5 ± 0.1 and 3.2 ± 0.3 (Table 3), respectively.

-1.5

4.2.5. The Pérez–Maqueda method (

-2 -2.5 89.5

Fig. 6 shows plots of ln

90

90.5

91

91.5

92

92.5

93

5

-1

93.5

94

94.5

95

95.5

1/T ×10 (K ) Fig. 4. Plots of the Šesták method from DTA scans with β = 5–30 °C/min for series 3. Calculated error is ± 0.01 for ln[− ln(1−x)]. Slopes of linear regression lines (solid) were used to obtain nK and nO (Table 2), with Pearson correlation coefficient values (r2) in the range of 0.999–1.000.

)

dx = dt

vs. 1/T, obtained 1−1 nð1−xÞ½− lnð1−xÞ n from the non-isothermal DTA scans of series 1–3. Insets in Fig. 6 are the pre-assumed matching n values, which gave a converged linear line for the set of DTA scans of each series. The matching n and resultant EPM by the Pérez-Maqueda method, for series 1, 2 and 3 are: 3.2 and 514 kJ/mol, 3.2 and 495 kJ/mol, and 3.0 and 408 kJ/mol (Table 3), respectively. 4.3. Morphology index

2.6 ± 0.2, 2.5 ± 0.3 and 2.4 ± 0.2 (Table 3), respectively. Similarly, the nO values (mean ± SD) for series 1, 2 and 3 are: 2.3 ± 0.2, 2.3 ± 0.3 and 2.3 ± 0.2 (Table 3), respectively. 4.2.4. The Augis and Bennett method Table 3 gives the obtained nK and nO from the relationship in Eq. (3), for series 1–3. FWHM and corresponding E values were taken from the DTA scans data (Table 2). The obtained nK by the Augis and

9

8

ln ( T ·T )

Table 3 The Avrami exponent and calculated errors from different analysis methods: n, nK and nO (obtained with EcK and EcO (Table 2), respectively). EPM is activation energy values of the Pérez-Maqueda method.

5 °C/min 10 °C/min 15 °C/min 20 °C/min 25 °C/min 30 °C/min

8.5

7.5

Method

7 6.5 6 5.5 90.5

91

91.5

92

92.5

93 5

93.5

94

94.5

Light microscopy (transmitted) of the glass bulk sample heated for 1 h at 750 °C and left to cool in the furnace (view of the surface), showed a uniform crystalline phase with typical lengths of 31 ± 1 (SD) μm and polygonal morphology (Fig. 7). The HR-SEM image for this heat-treated sample is shown in Fig. 8. The uniform phase reveals a regular hexagon shape with an inner star-like pattern (Fig. 8). EDS analysis from characteristic morphologies observed in the sample

95

-1

1/T ×10 (K ) Fig. 5. Plots of the Piloyan method from DTA scans with β = 5–30 °C/min for series 3. Calculated error is ±0.1 for ln(δT·T). Slopes of linear regression lines (solid) were used to obtain nK and nO (Table 2), with Pearson correlation coefficient values (r2) in the range of 0.985–0.993.

Ozawa n Šesták nK nO Piloyan nK nO Augis and Bennett nK nO Pérez-Maqueda n EPM (kJ/mol) Average n

Series 1

Series 2

Series 3

3.4 ± 0.4

3.4 ± 0.3

3.6 ± 0.3

3.2 ± 0.3 3.1 ± 0.3

3.1 ± 0.5 2.9 ± 0.5

3.2 ± 0.5 3.1 ± 0.5

2.6 ± 0.2 2.5 ± 0.2

2.4 ± 0.3 2.3 ± 0.3

2.4 ± 0.2 2.3 ± 0.2

3.4 ± 0.3 3.3 ± 0.3

3.6 ± 0.1 3.5 ± 0.1

3.3 ± 0.3 3.2 ± 0.3

3.2 514 3.1 ± 0.4

3.2 495 3.1 ± 0.5

3.0 408 3.0 ± 0.5

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Fig. 7. Transmitted light microscopy image of the bulk glass sample heated for 1 h at 750 °C and left to cool in the furnace showing crystalline phases three typical lengths of 30.5, 31.5 and 33.2 μm. View of the original heat treated surface. ×500.

(numbers in Fig. 8) indicated that the original LCB stoichiometric ratio of 2:1 for atomic La:Ca was not changed in all the selected regions. 5. Discussion As can be seen from Fig. 1 and Table 2 the characteristic temperatures Tg and TP and FWHM rose as β was increased. Thermal transitions that are measured during the non-isothermal DTA scan are expected to occur at higher temperatures as β is increased. In addition, an increased heating rate stabilizes the glass structure at higher temperatures and thus yields a higher Tg value [24]. However, the Tg of series 1–3 remained relatively constant (within ±2 °C) at each β (Table 2), which is likely to occur with powders made from the same batch. At a particular β the TP was increased as the powder particle size was increased (Table 2). In general, when the total amount of nuclei (surface and/or bulk) in a glass sample is increased (e.g., finer powder)

the crystallization temperatures are shifted towards the lower values [25]. Consequently, the slopes in the Kissinger and Ozawa plots (Fig. 2) are increased for the finer powders [26], thus yielding higher EcK and EcO values (Table 2), respectively. In agreement to the above are the values of E = 398–417 kJ/mol [6] that were obtained for the crystallization of LCB from glass bulk samples of the same composition. Moreover, the difference in TP between bulk [6] and powder samples (Table 2) remains relatively constant at all heating rates, meaning that the nuclei amount in the glass samples was not affected by changes in β [27]. Thus, it appears that the powder samples were nucleated as quenched (i.e., prior the DTA scans), which is in agreement with the findings of site-saturated matrix for the LCB glass [6]. The plots in Figs. 3–6 gave correlated linear lines for the estimation of n as expected. Additional data of series 1–3 (not given in Figs. 3–5) showed similar linear relations. The nK and nO of the Piloyan method are lower than those obtained by other methods (Table 3). Considering its' limited x range and rather low correlation coefficient values (Fig. 5), the appeared decrease in n might be not real. It can be seen that each analysis method in Table 3 gave constant n values for series 1–3 within the error ranges. Thus, the crystallization mechanism does not change in the 42–200 μm range of powder particle size measured. Calculations of the Ozawa method done with bulk glass samples' data in [6] gave n = 3.2 ± 0.4 (SD), which is in excellent agreement with the obtained results of series 1–3 (Table 3). Therefore, the values of the Avrami exponent in Table 3 could be reduced for series 1–3 to the value of n = 3.1 ± 0.3 (SD). The obtained EPM values (Table 3) show a similar decrease with increasing powder particle size as was observed for EcK and EcO (Table 2). However, the values obtained for them in Table 3 are lower than those obtained from the methods of Kissinger and Ozawa (Table 2). Considering that a 15–20% error is expected in kinetic data evaluations [19,28], the obtained E in Tables 2 and 3 are both in agreement. The determination that n = m for LCB crystallization from bulk glass [6] as well as the results of n (Table 3), both imply that the mechanism involves a three dimensional and interface controlled growth, which is related to m = 3 [11,12]. The light microscopy image of the heat-treated sample shows a polygonal and uniform phase (Fig. 7), which could be related to a three dimensional growth. The HR-SEM image for this heat-treated sample shows finer details of the LCB phase, where regular and uniform hexagons were detected with a defined glass–crystal interface (Fig. 8). The finding of a uniform phase is also in agreement with the single exothermal peaks of overall crystallization shown in Fig. 1.

Fig. 8. HR-SEM image of the bulk glass sample heated for 1 h at 750 °C and left to cool in the furnace. Numbers are the regions analyzed by EDS: left — 1. crystalline phase, 2. glass matrix; × 1500 and right — 1. inner pattern, 2. flat crystalline region; × 6000.

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In addition, the EDS analysis from regions in Fig. 8 did not detect any compositional change either between LCB and the glass matrix or within the patterns of crystalline LCB. Therefore, it is suggested that the inherent structural anisotropy of LCB [29,30] might contribute to the formation of the observed inner star-like pattern (Fig. 8). Thus, the obtained morphologies in Figs. 7 and 8 agree with the determination that m = 3 could be related to the mechanism of LCB crystallization from glass. The crystallization kinetics of LCB from glass is characterized by a three dimensional and interface controlled growth and from a nuclei site-saturated matrix, which fit the relationship of n = m = 3. 6. Conclusions Non-isothermal crystallization kinetics of LCB from glass was investigated. It was confirmed by glass powder samples that LCB crystallizes from a nuclei site-saturated matrix. Different analysis methods for estimating the Avrami exponent gave similar results for the powder samples and can be reduced to a single value. The observed morphology in a heat-treated bulk sample showed that the LCB crystallization mechanism involves a three dimensional and interface controlled growth. The JMA kinetic parameters for LCB crystallization from glass were found to be n = m = 3. Acknowledgments The authors wish to thank Mr. Dan Hirschler and Ms. Mariana Dov, Zandman Center for Thick-Film Microelectronics, for their technical support in the preparation of the glasses.

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