Crystallization kinetics of Zn2SiO4 powders prepared via polymer induced sol-gel method Vinča Institute
Bojana Milićević, Radenka M. Krsmanović, Milena Marinović-Cincović, Željka Antić, Miroslav D. Dramićanin “Vinča” Institute of Nuclear Sciences, University of Belgrade, P.O.Box 522, 11000 Belgrade, Serbia, contact:
[email protected] Zinc silicate (Zn2SiO4) has been identified as a suitable host matrix for many transition metal and rare earth dopant ions, providing excellent luminescent properties in the blue, green and red spectral zones. For Zn2SiO4 the choice of synthesis route and improvement of the working parameters is very important regarding its applications. Here zinc silicate powders were produced with polymer (PEG) assisted sol-gel synthesis [1, 2]. The resulting powders were initially fired in two ways: in conventional furnace (CF) and in microwave oven (MW), and then treated in furnace at 1453 K for 1h. With this study we aimed to determine the influence of different type of ignition (MW and CF) of zinc silicate powders on their crystallization. Samples were characterized with differential thermal analysis (DTA) using different heating rates (5, 10, 20, 40 K min-1) to study the kinetics of crystallization process. DTA is performed on the SETARAM SETSYS Evolution-1750 instrument. The powder samples, of approximately 10–15 mg, were heated in air atmosphere (air flow ϕ= 16 ml min-1) from room temperature to 1373 K.
Degree of conversion The fraction extent of reaction (or degree of conversion, α) of the sample has been obtained from the DTA curve as a function of temperature (T). The fraction extent of reaction at any temperature for crystallization was obtained as α = ST/S, where S is the total area of the exothermal curve between the temperature Ti, where the crystallization begins, and the temperature Tf, at which the crystallization is completed. ST is the area between the initial temperature and generic temperature, T, ranging between Ti and Tf. The sigmoid shape of fractional conversion curves indicates crystallization in amorphous material. The plots of α as a function of temperature at different heating rates for considered crystallization processes are shown for samples obtained under different type of ignition: a) conventional furnace and b) microwave oven.
Methods based on the variation of heating rates Kissinger and Ozawa peak methods [3, 4] are the most popular approaches for determining kinetic parameters by thermal analysis. These methods can define the overall activation energy of crystallization of amorphous material under linear heating condition by relating the dependence of the exothermic peak temperature Tp on the heating rate. Kissinger proposed that the activation energy can be determined according to the following equation:
log
Ea β AR = log − E a 2.303⋅ RTp Tp2
To define the activation energy in non-isothermal conditions Ozawa proposed this equation:
logβ = log
⎛ E ⎞ AEa − 2.315 − 0.4567⎜ a ⎟ ⎜ RT ⎟ R ⎝ p⎠
Presented graphs are related to samples treated in the: a) conventional furnace and b) microwave oven
Isoconversional (model-free) methods On the basis of dynamic DTA measurements for different heating rates, isoconversional method of Kissinger–Akahira–Sunose (KAS) [5] enables us to find Ea values over a wide range of conversions α. This model involves measuring the temperatures T corresponding to fixed values of the degree of conversion α, for different heating rates β, according to the following equation: ⎛ β ⎞ ⎞ E ⎛ A ⋅R log ⎜⎜ 2 ⎟⎟ = ln ⎜⎜ ⋅ f (α )⎟⎟ − α ⎠ RT ⎝ Eα ⎝ Tα ⎠
Flynn-Wall-Ozawa (FWO) [6] suggested this equation: ⎛ A ⋅Eα ⎞ Eα ln β = ln ⎜⎜ ⎟⎟ − 1.0518 RT ⎝ R ⋅ g (α ) ⎠
It is clear that the apparent activation energy increases as a function of α, indicating the complex process involving more than one step with different activation energies. For α value in the range of 0.3–0.7, only a small increase is observed, and the average values calculated in this α range matches well the values obtained using Kissinger and Ozawa methods.
Calculation of the Avrami exponent values Generally the value of the Avrami exponent (n) is equal to m+1, where m denotes the dimension of the crystallization growth of the nuclei formed during the heating run at constant heating rate β. In the present crystallization study, the nuclei were formed during the DTA measurements. Hence, n = m+1 for our experiments. For sample treated in MW the value of m corresponds to 2, which indicates that the growth of nuclei occurs in two dimensions, excluding the surface crystallization. On the other hand, for sample treated in CF, m = 1 indicates that the surface crystallization occured.
Average values of apparent activation energy for samples treated in: a) conventional furnace and b) microwave oven
The Avrami exponents are calculated using following equations:
β [Kmin-1]
T [K]
k [10-3 s-1]
n (CF)
β [Kmin-1]
T [K]
k [10-3 s-1]
5
1150.16
4.08
1.88
5
1151.60
3.62
10
1165.8
7.95
2.40
10
1166.30
7.05
2.41
βE a =1 k p RT p2
20
1180.39
15.51
2.31
20
1181.22
13.75
3.20
40
1195.35
30.25
2.15
40
1202.28
26.55
2.88
dα = 0.37nk p dt
n (CF) = (2.2 ± 0.2)
n (MW) 2.02
n (MW) = (2.6 ± 0.3)
Determining the dimensions of crystals The Avrami exponent (n) can be also confirmed by the method described below, proposed by Matusita et al. [7]. The fraction of crystallisation α, at the constant heating rate β, is related to the activation energy of crystallization by the equation:
dln[ − ln(1 − α)] nE a ≅ d(1/T) R The crystallization exponent n depends on the dimensionality of crystal growth. The plot of ln[−ln(1−α)] vs. 1/T gives linear fit for a fixed heating rate β. The values of nEa can be obtained from the slope. Using the value of Ea evaluated from Kissinger method under various β, the values of n are calculated and found to be in a good agreement with the previously described method for both samples.
Conclusion Calculated kinetic parameters for different conditions of ignition of Zn2SiO4 samples proved the lower values of activation energy for samples synthesized in a microwave oven. However, for both samples a fast growth of crystals is observed and values determined using two different approaches: i) comparing the rate constants (see Tables) and ii) plotting α vs. time. From obtained Avrami exponent values and kinetic parameters m we could conclude that for the sample treated in CF the surface crystallization took place, while for the sample prepared in MW the two-dimensional growth of crystals occurred, excluding the possibility of surface crystallization. [1] [2] [3] [4]
R. Krsmanović, Ž. Antić, I. Zeković, M.D. Dramićanin, J. Alloy. Compd. 480 (2009) 494–498. R.M. Krsmanović, Ž. Antić, M. Mitrić, M.D. Dramićanin, M.G. Brik, Appl. Phys. A 104 (2011) 483–492. H.E. Kissinger, Anal. Chem. 29 (1957) 1702-1706. T. Ozawa, J. Therm. Anal. Calorim. 2 (1970) 301-324.
[5] J.H. Flynn, L.A. Wall, J. Res. Natl. Bur. Stand. Sect. A 70 (1966) 487-523. [6] Akahira, T. Sunose, Res. Rep. Chiba Inst. Technel. 16 (1971) 22-31. [7] K. Matusita, S. Sakka, Phys. Chem. Glasses 20 (1979) 81-84.
Authors acknowledge the finansial support of the Ministry of Education and Science of the Republic of Serbia (projects 45020 and 172056).
