Kinetic Analysis for Non-isothermal Decomposition of Unirradiated and γ-Irradiated Indium Acetyl Acetonate

Kinetic studies for the non-isothermal decomposition of un-irradiated and γ-irradiated indium acetyl acetonate In(acac) 3 with 10 kGy total γ-ray dose were carried out in static air. The results showed that the decomposition proceeds in one major step in the temperature range of 150-250 °C with the formation of In 2 O 3 as solid residue. The non-isothermal data for un-irradiated and γ-irradiated In(acac) 3 were analysed using linear Flynn-WallOzawa (FWO) and nonlinear Vyazovkin (VYZ) iso-conversional methods. The results of application of these free models on the investigated data showed a systematic dependence of E a on α indicating a simple decomposition process. No significant changes were observed in both decomposition behaviour and (Eα-α) dependency between unirradiated and γ-irradiated In(acac) 3 . Calcination of In(acac) 3 at 400 °C for 5 hours led to the formation of In 2 O 3 monodispersed nanoparticles. X-ray diffraction, FTIR and SEM techniques were employed for characterization of the synthesised nanoparticles. This is the first attempt to prepare In 2 O 3 nanoparticles by solid state thermal decomposition of In(acac) 3 .


Introduction
Thermal treatment of inorganic substances has a great synthetic potential as it may turn simple compounds into advanced materials, such as ceramics, catalysts, and glasses and could reproducibly lead in most cases to metal or metal oxide nanoparticles displaying a very narrow size distribution 1,2 .Many recent studies on the thermal decomposition of inorganic solids have include measurements on samples that were exposed to radiation prior to heating with the aim to investigate the effect of ionizing radiation on the kinetics and thermal decomposition behaviour of inorganic compounds 3,4 .Indium acetylacetonate is a suitable metal-organic compound for preparation of In 2 O 3 which has many applications in optoelectronics device such as solar cells and liquid crystal display 5 .Moreover it is an important material in the gas sensor fields.No previous studies are available up to now on the thermal decomposition kinetics of both un-irradiated and γ-irradiated In(acac) 3 [6,7]   .
In the present work, the thermal decomposition behaviour of un-irradiated and γ-irradiated In(acac) 3 was investigated in air with the aim to: a) examine the kinetics of non-isothermal decomposition of both un-irradiated and γ-irradiated In(acac) 3 using model free isoconversional approach; b) clarify the effects of γirradiation on the thermal decomposition behaviour; and c) finally to follow the chemical composition of the solid residues obtained at different temperature and attempting to prepare In 2 O 3 at nanoscale by thermal decomposition of indium acetylacetonate.

Experimental
Indium acetylacetonate was obtained commercially from Aldrich Ltd and used without further purification.Samples were dried in a desiccator before analysis.For thermal experiments a thermogravimetric analyzer was used (TGA-7, Perkin Elmer ® ).The amount of the sample was kept at 10 ± 0.1 mg.Under dynamic (nonisothermal conditions) four linear heating rates (5, 10, 15, 20 °C/min) were applied.For irradiation, sample were encapsulated under vacuum in glass vials and exposed to successively increasing doses of radiation at constant intensity using a Co-60 γ-ray cell 220 (Nordion INT-INC, Ontario, Canada) at a dose rate of 10 4 Gy/h.
The fraction decomposed or the extent of conversion, α was calculated as (Equation 1) where M o , M, M f are the initial, actual and final sample masses respectively.The infrared spectra were recorded as a KBr pellets using a Perkin Elmer 1000 FT-IR spectrophotometer, XRD was carried out on a Siemens D 5000 X-ray diffractometer (Cu Kα, λ =1.5418 Å).Theory: a single step process for solid state decomposition has the following kinetics equation (Equation 2) where α is the extent of conversation, K (T) is a temperature dependent reaction rate constant and f(α) the kinetics dependent model function.The Arrhenius equation generally expresses the explicit temperature dependency of the rate constant (Equation 3) The A, E and f(α) are called the kinetic triplet that can characterise a unique decomposition reaction.Under non-isothermal conditions in which a sample is heated at a constant rate, the explicit time dependence in Equation 2 is eliminated through the trivial transformation (Equation 4) where β = dT/dt is the heating rate.Upon integration, Equation 2gives Equations 5, 6 and 7 where P(x) is the exponential integral for x = E a /RT.The temperature integral I (Eα, T) has no analytical solution but many approximations.The linear iso conversional integral method has been suggested independently by Flynn and Wall and Ozawa use Dolyle's approximation of P(x) [8] .This method is based on the Equation 8( ) Thus for α = const.The plot ln β versus (1/T) obtained from thermograms recorded at several heating rates should be a straight line, the slope of which can be used to evaluate the apparent activation energy E α .
A nonlinear iso-conversional method has been developed by Vyazovekin that avoids inaccuracies associated with analytical approximation of the temperature integral 7 , for a set of n experiments carried out at a different heating rates, the activation energy can be determined at any particular value of α by fi nding the value of E a for which this objective function Ω is minimised, where (Equations 9 and 10) (10) We have developed a mathematical program to evaluate the temperature integral and the result have been compared with Cai et al. 8 approximation where (Equation 11)

Results and Discussion
Figure 1 shows typical TG/DTA curves for un-irradiated In(acac) 3 in static air.The TG curve showed that the decomposition of In(acac) 3 proceed in one major step in the temperature range of 150-250 °C with the formation of In 2 O 3 as a solid residue according to the following Equation 12.
2 In(acac) 3 → In 2 O 3 + volatiles (12) The acetylacetonate ligand was found as the major gaseous product below 300 °C.At a temperature higher than 400 °C the ligand decomposed mainly to CO, CO 2 , and H 2 O.The main decomposition step in the TG curve of In(acac) 3 was accompanied by an endothermic peak at ≈ 180 °C.The TG curve showed a weight gain in the temperature range of 300-350 °C accompanied by two overlapped exothermic peaks due to the formation of In 2 O 3 followed by the crystallization of the oxide product.Another weight gain was detected in the TG curve of In(acac) 3 in the temperature range of 900-1000 °C and could be attributed to the formation of more non stoichiometric complex oxides.Similar observation has been made for several metal acetylacetonates earlier 9 .TG/DTA curves of γ-irradiated In(acac) 3 with 10 2 KGy total γ -ray dose show almost the same decomposition behaviour as for un-irradiated ones, except that the temperature range of the decomposition was shifted to lower value (130-230 °C) in case of γ-irradiated sample.TG/DTA curves for γ-irradiated In(acac) 3 with 10 2 kGy total γ ray dose showed almost the same behaviour for the decomposition of un-irradiated sample.The dynamic data for both un-irradiated and γ-irradiated In(acac) 3 with 10 2 kGy total γ-ray dose are shown in Figure 2. The application of both linear (FWZ) and non-linear (VYZ) model free isoconversional methods, to the non isothermal decomposition data for both unirradiated and γ-irradiated In(acac) 3 with 10 2 kGy total γ ray dose permits a determination of E α as a function of α and results are shown in Figure 3.The results of the application of these two model free on the investigated data in general showed a symmetric dependence of E a on α indicating a simple decomposition process with almost the same estimated values of E a using both linear (FWO) and non-linear (VYZ) methods.E a is ≈ 140 kJmol -1 and 120 kJmol -1 at the start of decomposition, then reach a minimum of a 80 kJmol -1 at the end of the decomposition for both un-irradiated and γ-irradiated samples.The relative lower E a value obtained at the start of decomposition for γ-irradiated sample could be attributed to the formation of additional decomposition centres created by trapped electrons and holes in the host lattice.

IR, XRD and SEM measurements
Figure 4 show IR spectra of both un-irradiated and γ irradiated In(acac) 3 .Both spectra display the characteristic bands assigned to various vibration modes of acetylacetonate functional groups.Neither disappearance nor appearance of new bands was recorded in the IR spectrum of γ-irradiated In(acac) 3 with 10 2 kGy total γ ray dose, but a decrease in the intensity of most characteristic bands was recorded as a results of γ-irradiation.The band assigned to ν In-O bond around 660 cm -1 was more affected by irradiation than any other band in the spectrum.The decreased in the intensity of this band could be attributed to bond scission and degradation caused by γ irradiation.IR bands for In(acac) 3 and their assignments are listed in Table 1.

Figure 2 .
Figure 2. Thermogravimetric data showing the extent of unirradiated In(acac) 3 conversion during nonisothermal decomposition.The heating rate of each experiment (in °C/min) is indicated by each curve.

Figure 6 .
Figure 6.SEM showing the formation of circular nanoparticles of In 2 O 3 .

Table 1 .
IR bands of In(acac) 3 and their assignments: