A study of the crystallization kinetics in Se 68 Ge 22 Pb 10 chalcogenide glass

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1 Indian Journal of Engineering & Materials Sciences Vol. 11, December 2004, pp A study of the crystallization kinetics in Se 68 Ge 22 Pb 10 chalcogenide glass N Mehta a, P Agarwal b & A Kumar a a Department of Physics, Harcourt Butler Technological Institute, Kanpur , India b Department of Physics, DBS College, Kanpur , India Received 5 March 2004; accepted 9 September 2004 Differential scanning calorimetry (DSC) is performed at different heating rates under non-isothermal conditions to study the crystallization kinetics of Se 68 Ge 22 Pb 10 chalcogenide glass. Different kinetic parameters such as the activation energy of crystallization (E c ), the order parameter (n), the rate constant and its frequency factor have been determined. Four different non-isothermal methods Kissinger s method, Matusita-Sakka theory, Augis-Bennett approximation and Ozawa- Chen method have been used in the present study. The average value of activation energy of crystallization E c is ev. The average value of Avrami s index n is 3.61, which indicates that in the glassy Se 68 Ge 22 Pb 10, two crystallization (two- and three-dimensional growth) mechanisms are working simultaneously during its amorphous to crystalline transformation. IPC Code: Int. Cl. 7 C03C In general, chalcogenide glasses are p-type semiconductors due to the fact that the number of electrons excited above the conduction band mobility edge is smaller than the number of holes below the valence band mobility edge 1. They also contain positively and negatively charged defect states, known as valence alternation pairs 2 (VAPs) which essentially pin the Fermi level at the middle of the band gap making these materials rather insensitive to doping 3. Thus, chalcogenide glasses had long been considered to be undopable, characterized by p-type conduction only. However, in the recent past, it has been observed 4-9 that when certain heavy metallic additives like Bi and Pb are added to Se-Ge and Se-In glasses, the number of holes decreases in these systems, while the number of electrons increases. These two effects together shift the Fermi level towards the conduction band resulting in p to n transition at a particular impurity concentration. The electrical properties of these glasses have been studied by various workers 4-9 but thermal properties, especially crystallization kinetics have not been reported. The crystallization kinetics in chalcogenide glasses have been investigated by various workers using isothermal and non-isothermal methods One of the non-isothermal techniques is differential scanning calorimetry (DSC) which allows the measurement of heat released as a function of time or temperature when sample is heated at a constant rate. This technique is particularly important due to the fact that: (i) it is easy to carry out; (ii) it requires little sample preparation; (iii) it is quite sensitive and (iv) it is relatively independent of the sample geometry. Various theoretical methods have been suggested to determine activation energy of crystallization from non-isothermal DSC data. It is, therefore, interesting to use different methods for studying the crystallization kinetics using the same experimental data of a particular chalcogenide glassy alloy. With the above points of view, four different methods of analysis, Kissinger s relation 24, Matusita- Sakka theory 25,26, Augis-Bennett approximation 27 and Ozawa-Chen method 28,29 have been used to study the crystallization kinetics of an important ternary alloy Se 68 Ge 22 Pb 10 under non-isothermal condition. Theoretical The crystallization kinetics of amorphous alloys has been intensively studied using the classical Johnson-Mehl-Avrami (JMA) theoretical model in which the crystallization fraction (α) can be described as a function of time (t) according to the formula: α(t) = 1 exp [ (K t) n ] (1) where n is the Avrami index and K is the rate constant which is given by: K = K o exp ( E c /RT) (2) here E c is the activation energy of crystallization, R is the universal gas constant and K o is also a constant, which is known as frequency factor.

2 512 INDIAN J. ENG. MATER. SCI., DECEMBER 2004 Based on JMA model, different researchers have developed very diverse methods to study crystallization kinetics of various alloys. Given below are the details of four important and useful methods, which have been used in the present study: Kissinger s relation According to Kissinger 24, T c peak temperature of crystallization T c, in terms of heating rate β, can be expressed as: ln (β/t c 2 ) = E c /(R T c ) + constant (3) This equation is used to calculate the activation energy of crystallization by plotting ln β/t c 2 versus 1/T c curve. Matusita-Sakka theory The extent of crystallization (α) at a temperature T is well expressed by the expression: ln (1 α ) 1 = (C/β n ).[( n E c )/(RT)] (4) derived by Matusita and Sakka 25,26 from the classical JMA equation. For constant temperature, this equation can be written as: ln [ln (1 α) 1 ] = n ln β + constant (5) From this equation, the value of n can be calculated by plotting ln [ln (1- α) -1 ] versus ln β curves at different temperatures. Further, since the values of α are independent of β at T= T c 33, so at T = T c, the Eq. (4) takes the form: ln β = E c /(R T c ) + constant (6) This equation is used to calculate the activation energy of crystallization by plotting ln β versus 1/T c curve. Augis-Bennett approximation The activation energy of crystallization E c can also be determined by an approximation method developed by Augis and Bennett 27. The relation used by them is of the form: ln β/t c = E c /(R T c ) + ln K o (7) The activation energy of crystallization can be evaluated by this equation using the plots of ln β/t c against 1/T c. This method has an extra advantage that the intercept of ln β/t c versus 1/T c gives the value of pre-exponential factor K o of Arrhenius equation [Eq. (2)]. Ozawa-Chen method The other useful method used to evaluate the activation energy of crystallization is Ozawa-Chen 28,29 method, which is based on the following equation: ln (β/t 2 ) = E c /(R T) + constant (8) At a fixed value of the crystallized fraction α, the value of E c can be deduced from the slopes of the linear relations, when ln (β/t 2 ) is plotted against 1/T. The average of the slopes of these straight lines gives the value of activation energy of crystallization. Experimental Procedure Glassy alloy of Se 68 Ge 22 Pb 10 was prepared by quenching technique. High purity materials (5N pure) were weighed according to their atomic percentages and were sealed in a quartz ampoule under the vacuum of 10-5 Torr. The ampoule was kept inside the furnace at an appropriate temperature (where the temperature was raised at a rate of 3-4 C/min). The ampoule was rocked frequently for 10 h at the maximum temperature to make the melt homogeneous. Quenching was done in ice water and the glassy nature of alloy was checked by X-ray diffraction technique. The glass, thus prepared, was ground to make fine powder for DSC studies mg of sample was heated at a constant heating rate and the changes in heat flow with respect to an empty pan were measured. Five heating rates (5, 10, 15, 20 and 25 K/min) were chosen in the present study. Results and Discussion Figure 1 shows the DSC thermograms for ternary alloy Se 68 Ge 22 Pb 10 at five different heating rates. The values of peak crystallization temperature T c at different heating rates for ternary Se 68 Ge 22 Pb 10 alloy are given in Table 1. The crystallization kinetics is generally well characterized, when the four kinetics parameter (E c, n, K o and K) are determined. From the data of experiments at different heating rates, these parameters have been determined. Evaluation of activation energy of crystallization E c The activation energy of crystallization of the alloy has been calculated by Kissinger s relation, Matusita-

3 MEHTA et al.: CRYSTALLIZATION KINETICS IN Se 68 Ge 22 Pb 10 CHALCOGENIDE GLASS 513 Fig. 1 DSC thermograms for Se 68 Ge 22 Pb 10 alloy at different heating rates Fig. 2 Plot of ln β/t c 2 versus 10 3 /T c for Se 68 Ge 22 Pb 10 alloy Table 1 The values of peak crystallization temperature (T c ) of ternary Se 68 Ge 22 Pb 10 alloy at different heating rates Heating rate β (K/min) Peak crystallization temperature T c (K) Fig. 3 Plot of ln β versus 10 3 /T c for Se 68 Ge 22 Pb 10 alloy Sakka theory, Augis-Bennett approximation and Ozawa-Chen method. For this purpose, the plots of ln (β/t c 2 ) versus 10 3 /T c, ln β versus 10 3 /T c, ln (β/t c ) versus 10 3 /T c and ln (β/t 2 ) versus 10 3 /T c are plotted for ternary Se 68 Ge 22 Pb 10 alloy. These plots are shown in Figs 2-5 respectively. The values of E c obtained for the present sample using the above four methods are given in Table 2. Comparison of E c values obtained from Eqs (3) and (6)-(8) shows that the values are in good agreement

4 514 INDIAN J. ENG. MATER. SCI., DECEMBER 2004 with each other. This means that one can use any of the four equations to calculate the activation energy of crystallization. Evaluation of Avrami index n Figure 6 shows the variation of ln [ln(1 α) -1 ] with ln β at three constant temperatures. Using Eq. (5), the values of n have been determined from the slopes of these curves at three different temperatures. The values of Avrami index n at three different temperatures are given in Table 3. From Table 3, it is clear that n decreases with increase in temperature. It is well known that crystallization of chalcogenide glasses is associated with nucleation and growth process and the extent of crystallization α increases with increase in temperature. In other words it tends to its maximum value 1. The decreasing trend of n, therefore, shows the decrease in the nucleation rate due to nucleation saturation. The average value of n comes out to be The non-integer value of n means that two crystallization (two- and three-dimensional growth) mechanisms are working simultaneously during the amorphous to crystalline transformation of the Se 68 Ge 22 Pb 10 chalcogenide glasses. Evaluation of rate constant K and frequency factor K o Knowing the values of E c and ln K o from Eq. (7), the values of rate constant K have been determined by Eq. (2). The values of ln K at different temperatures in the crystallization region are given in Table 4 for ternary Se 68 Ge 22 Pb 10 alloy, which indicates that K increases with increase in temperature. Fig. 4 Plot of ln β/t c versus 10 3 /T c for Se 68 Ge 22 Pb 10 alloy Table 2 The values of activation energy of crystallization (E c ) of ternary Se 68 Ge 22 Pb 10 alloy calculated using different nonisothermal methods Fig. 5 Plot of ln (β/t 2 ) versus 10 3 /T c for Se 68 Ge 22 Pb 10 alloy Non-isothermal method Activation energy of crystallization E c (ev) Kissinger relation Matusita-Sakka theory Augis-Bennet approximation Ozawa-Chen method Average value Table 3 Temperature dependence of Avrami index n Temperature (K) n Fig. 6 Plots of ln [ln(1 α) 1 ] versus ln β for Se 68 Ge 22 Pb 10 alloy Table 4 Temperature dependence of rate constant K T (Kelvin) ln K

5 MEHTA et al.: CRYSTALLIZATION KINETICS IN Se 68 Ge 22 Pb 10 CHALCOGENIDE GLASS 515 Table 5 Heating rate dependence of rate constant K p β (K/min) K p (min) To obtain more information about morphology of growth, the following equation from Gao-Wang model 30 has been used: K p = (β E c )/(R T c 2 ) (9) Here, K p represents the value of rate constant K at peak crystallization temperature T c for a constant heating rate. The heating rate dependence of K p is given in Table 5. Conclusions The study of the crystallization kinetics in ternary Se 68 Ge 22 Pb 10 alloy has been studied by four different methods under non-isothermal condition. DSC technique has been used in the present study to calculate the activation energy of crystallization (E c ). It has been found that E c values obtained by four different methods Kissinger s method, Matusita- Sakka theory, Augis-Bennett approximation and Ozawa-Chen method are in good agreement with each other. Thus, one can use any of the four methods to calculate the activation energy of crystallization. The average value of activation energy of crystallization E c is ev. The average value of Avrami s index n is 3.61, which indicates that in the glassy Se 68 Ge 22 Pb 10, two crystallization (two- and threedimensional growth) mechanisms are working simultaneously during its amorphous to crystalline transformation. The value of frequency factor K o is min 1. The rate constant K increases with increase in temperature as well as with increase in heating rate. References 1 Mott N F & Davis E A, Electronic processes in noncrystalline materials, (Clarendon, Oxford) Kastner M D, Adler D & Fritzsche H, Phys Rev Lett, 37 (1976) Adler D & Yoffa E J, Phys Rev Lett, 36 (1976) Tohge N, Minami T & Tanaka M, J Non-Cryst Solids, 37 (1980) Nagel P, Ticha H, Tichy L & Triska A, J Non-Cryst Solids, (1983) Tohge N, Matsuo H & Minami T, J Non-Cryst Solids, (1987) Bhatia K L, Parthasarathy G, Gopal E S R & Sharma A K, Solid State Commun, 51 (1984) Bhatia K L, Parthasarathy G, Gosan D P & Gopal E S R, Phil Mag B, 51 (1985) L63. 9 Kohli S, Sachdeva V K, Mehra R M & Mathur P C, Phys Stat Sol (b), 209 (1998) Agarwal P, Goel S, Rai J S P & Kumar A, Phys Stat Sol (a), 127 (1991) Agrahari S K, Arora R & Kumar A, Physica B, 191 (1993) Singh A, Rai J S P & Kumar A, Adv Mater Opt Electron, 9 (1999) Acharya K V, Asokan S & Panchapagesan T S, Indian J Pure & Appl Phys, 37 (1999) Abu El-Oyoun M, J Phys D: Appl Phys, 33 (2000) Soltan A S, Physica B, 307 (2001) Khan S A, Zulfequar M & Husain M, Solid Stat Commun, 123 (2002) Abu Sehly A A, Physica B, 325 (2003) Sharma D, Shukla R K, Singh A, Nagpal A K & Kumar A, Adv Mater Opt Electron, 10 (2000) Ligero R A, Vazquez J, Villares P & Jimenez-Garay R, Thermochim Acta, 162 (1990) Moharram A H, Abu El-Oyoun M & Abu-Sehly A A, J Phys D: Appl Phys, 34 (2000) Rysava N, Spasov T & Tichy L, J Therm Anal, 32 (1987) Giridhar A & Mahadevan S, J Non-Cryst Solids, 51 (1982) Afify N, J Non-Cryst Solids, 128 (1991) Kissinger H E, Anal Chem, 29 (1957) Matusita K & Sakka S, Phys Chem Glasses, 20 (1979) Matusita K & Sakka S, Bull Inst Chem Res, Kyoto Univ, 59 (1981) Augis J A & Bennett J E, J Them Anal, 13 (1978) Ozawa T, Bull Chem Soc Japan, 38 (1965) Chen H S, J Non-Cryst Solids, 27 (1978) Johnson W A & Mehl R F, Trans Am Inst Min (Metal) Eng, 135 (1939) Avrami M, J Phys Chem, 7 (1939) Avrami M, J Phys Chem, 8 (1940) Ozawa T, J Therm Anal, 2 (1970) Gao Y Q & Wang W, J Non-Cryst Solids, 81 (1986) 129.