Journal of the Korean Physical Society, Vol. 46, No. 1, January 2005, pp. 155∼158
Isothermal Observation of Phase Transformation in Amorphous (Li0.9 Na0.1 )2 B4 O7 S. J. Kim, H. W. Choi, J. E. Kim, M. Kim, J. K. Lee, H. W. Park, D. G. Kang and Y. S. Yang∗ School of Nano Science and Technology, RCDAMP, Department of Physics, Pusan National University, Busan 609-735 (Received 5 August 2004) Isothermal in-situ optical studies on the kinetics of crystal growth in amorphous (Li0.9 Na0.1 )2 B4 O7 have been performed. It is observed that the crystal grows linearly with time at various temperatures. The typical growth rate is 0.17 µm/s at 512 ◦ C with a growth activation energy of 3.6 eV. The Avrami exponent that concerns the crystallization mechanism is obtained by isothermal differential scanning calorimetry (DSC) measurements. The Avrami exponent value of 3.3 indicates that the system is in interface-controlled growth with decreasing nucleation rate. The crystallization activation energies obtained by isothermal optical and DSC measurements agree well with each other. We have also performed non-isothermal DSC measurements on amorphous (Li1−x Nax )2 B4 O7 and have observed a mixed alkali effect. PACS numbers: 61.43.Fs, 81.10.Jt, 64.70.Kb, 05.70.Fh Keywords: Isothermal, In-situ observation, Activation energy, Phase transition, Glass
II. EXPERIMENTS
I. INTRODUCTION
Li2 B4 O7 and Na2 B4 O7 powders were mixed in N2 atmosphere to prevent reaction with water. After 2hour mixing, the powder was melted in a Pt crucible and was held for an hour at 1000 ◦ C, before cooling to room temperature. The prepared glass sample was transparent, with 1-mm thickness. The glasses were identified by X-ray diffraction and DSC (DSC3100, Mac Science, Japan) measurements. To observe the thermal characteristics during crystallization, we performed nonisothermal DSC measurements with a heating rate of 2 ◦ C/min from room temperature to 600 ◦ C. The isothermal DSC measurements were performed to study the crystallization mechanism and growth method at 490, 495, 500, 505, and 510 ◦ C. The crystallization processes were observed isothermally by using a high-resolution microscope with a CCD camera in the heating stage. The sample was heated to the desired temperatures of 502, 507, and 512 ◦ C with a heating rate of 100 ◦ C/min, and morphology changes were measured.
Li2 B4 O7 (LBO) crystal is a non-ferroelectric and piezoelectric material. At room temperature, it shows tetragonal symmetry 4mm with a = b = 9.447 ˚ A, c = 10.286 ˚ A, and has a polar axis along the crystallographic c axis. LBO crystal is a commonly used material in surface acoustic wave substrate, non-linear devices for frequency conversion in the ultraviolet region, and piezoelectric actuators [1–4]. LBO glass and glass-ceramics have wide potential interest due to advantages over their crystalline counterparts and they are considered to be one of the materials for solid-state battery application with fast ionic conduction [5]. If a glass incorporates two different alkali ions, the transport mechanisms associated with the cation mobility such as the electrical conductivity and the viscosity are pronouncedly nonlinear. This effect, known as the mixed mobile alkali ion effect, has been discussed in terms of many different models [6–13]. As a preliminary study of a mixed alkali effect in future, we mixed LBO with Na2 B4 O7 (NBO), where NBO has a triclinic structure with a = 8.646 ˚ A, b = 10.506 ˚ A, c = 6.572 ˚ A, α = 94.95◦ , β = 90.93◦ , γ = 93.18◦ , with a mole ratio LBO : NBO = 9 : 1, and performed isothermal optical and differential scanning calorimetry (DSC) measurements.
∗ E-mail:
III. RESULTS AND DISCUSSION Figure 1 shows non-isothermal DSC curves of (Li1−x Nax )2 B4 O7 glasses, measured with a heating rate of 2 ◦ C/min. The important point to be emphasized is that not all properties of mixed alkali glasses show
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Journal of the Korean Physical Society, Vol. 46, No. 1, January 2005
large departures from additivity or linearity. Usually, those properties associated with cation movement such as electrical conductivity, internal friction and viscosity show distinctive departures from additivity. In Figure 1, a non linear behavior in the glass transition temperature Tg appears. In general, atomic mobility drastically changes when a system approaches Tg from glass [14– 17]. Additive non-linearity also appears at the change of the DSC exothermic peak temperature with the addition of Na content. These phenomena clearly show that the system is in the Li-Na mixed alkali effect, with a relevant parameter of viscosity. Figure 2 shows the DSC exothermic heat flow for the (Li0.9 Na0.1 )2 B4 O7 glass as a function of time at 490, 495, 500, 505, and 510 ◦ C. The time to reach a fixed crystalline volume fraction, as a function of temperature, follows the empirical Equation t = t0 exp(E/kT ),
Fig. 2. Isothermal DSC curves as a function of time for (Li0.9 Na0.1 )2 B4 O7 glass at 490, 495, 500, 505 and 510 ◦ C.
(1)
where t0 is the time constant, E is the activation energy, and k is the Boltzmann constant. As can be seen in the figure, the exothermic peak exists in a narrow time interval as temperature increases, caused by the increase of reaction rate, but the exothermic peak area that is proportional to the transformed crystalline volume fraction remains the same for different temperatures.
Fig. 3. Transformed crystalline volume fraction at a given temperature is plotted as a function of time for (Li0.9 Na0.1 )2 B4 O7 glass. The slopes are the Avrami parameters, with an average value of n = 3.3.
Figure 3 shows a plot to calculate the Avrami parameter that concerns the crystallization mechanism from the relation of the fixed transformed crystalline volume fraction and duration at different temperatures. The Avrami parameter can be obtained from the equation known as the JMA (Johson-Mehl-Avrami) relationship [18]: x = 1 − exp(−btn ),
Fig. 1. DSC curves of (Li1−x Nax )2 B4 O7 glasses with a heating rate of 2 ◦ C/min.
(2)
where x is the crystal volume fraction, b is the prefactor, and n is the Avrami exponent. The average value n = 3.3 from the slope in Figure 3 indicates that the crystallization mechanism is in interface-controlled growth with a decreasing nucleation rate [19]. Figure 4 shows a plot to calculate crystallization activation energy from the relation of the fixed transformed crystalline volume fraction and duration at different temperatures by using Equation (1). In previous work on the isothermal in-situ optical measurements for a pure LBO sample, we obtained E = 3.3 eV [20]. The activation energy E = 3.7 eV in this work is distinctly larger
Isothermal Observation of Phase Transformation in· · · – S. J. Kim et al.
Fig. 4. The time required for the transformed crystalline volume fraction to be 50 % is plotted at each experimental temperature for (Li0.9 Na0.1 )2 B4 O7 glass. The slope is the activation energy.
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Fig. 6. Annealing time dependence of (Li0.9 Na0.1 )2 B4 O7 crystal size at 512 ◦ C. The slope is ∼ 1.0, indicating that crystals grow linearly with time.
Fig. 7. (Li0.9 Na0.1 )2 B4 O7 crystal growth rate as a function of inverse temperature in glass. The straight line shows that the growth mechanism follows the Arrhenius law with a growth activation energy of 3.6 eV.
Fig. 5. In-situ optical microscope morphologies. Crystal growth processes of (Li0.9 Na0.1 )2 B4 O7 glass are shown as a function of time at 512 ◦ C.
than the previously reported value. We think that this is caused by the mixed alkali effect, because there can be a potential-barrier change by the mutual interaction of alkali ions. The in-situ optical morphology patterns of a selected area at temperature 512 ◦ C are shown in Figure 5. In this measurement, we searched the different areas of the sample and traced a small crystal and continued to observe until the crystals impinged on each other. The traced square-like crystal located on the left side of the figure grows gradually with increasing duration. Because the purpose of the measurement is only for crystal growth, we arbitrarily choose an initial time. The size of the
crystal is ∼ 35 µm at the initial time and reaches ∼ 100 µm after 900 s. Figure 6 shows a log-log plot of crystal size against annealing time at 502, 507, and 512 ◦ C. This plot is intended to derive a crystal growth mechanism from the relationship that crystal size r is proportional to the annealing time as r ∼ tm . The growth mechanism is calculated from the slope of the radius-time plot. The growth mechanism can be divided into two categories: diffusioncontrolled growth with m = 0.5, and interface-controlled growth with m = 1 [18]. The straight line with the slope m = 1, by a least-square fit to the experimental data, indicates that the growth mechanism is the interfacecontrolled one. Figure 7 shows the activation energy of crystal growth, calculated from the crystal sizes appearing in Figure 5 at different temperatures. The relationship between the growth rate and the activation energy of crystal growth obeys an Arrhenius law r = r◦ exp(- E/kT), where the
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activation energy E is the energy barrier for molecules or atoms to jump across the interface to expand outward. The growth rate at 512 ◦ C is 0.17 µm/s. The activation energy of crystal growth calculated by using the above equation is 3.6 eV, and this result agrees well with the value obtained from the isothermal DSC measurements.
IV. CONCLUSIONS We performed DSC and optical measurements for Li2 B4 O7 and Na2 B4 O7 mixed glasses. The nonisothermal DSC measurements of the various mole ratios show that there are mixed alkali effects. The isothermal optical measurements show that amorphous (Li0.9 N0.1 )2 B4 O7 crystallizes through interfacecontrolled growth with decreasing nucleation rate. It is also found that the activation energy of 3.6 eV for the crystal growth from the DSC measurements agrees well with the results of the isothermal optical measurements.
ACKNOWLEDGMENTS This study was financially supported by Pusan National University in the program, Post-Doc 2004.
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