Journal of Alloys and Compounds Glass transition and crystallization

Journal of Alloys and Compounds 491 (2010) 85–91

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Glass transition and crystallization kinetics of Inx (Se0.75 Te0.25 )100−x chalcogenide glasses A.M. Abd Elnaeim a,∗ , K.A. Aly a , N. Afify b , A.M. Abousehlly a a b

Department of Physics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut 71542, Egypt Department of Physics, Faculty of Science, Assuit University, Assuit, Egypt

a r t i c l e

i n f o

Article history: Received 4 July 2009 Received in revised form 16 October 2009 Accepted 19 October 2009 Available online 5 November 2009 Keywords: Glassy alloy Non-isothermal process Heating rate Glass transition temperature Crystallization kinetics Crystalline phases

a b s t r a c t The results of differential scanning calorimetry (DSC) under non-isothermal conditions of the chalcogenide Inx (Se0.75 Te0.25 )100−x (where 0 ≤ x ≤ 10 at.%) glasses are reported and discussed. The dependence of the characteristic temperatures “glass transition temperature (Tg ), the crystallization onset temperature (Tc ) and the crystallization peak temperature (Tp ) on the heating rate (˛) utilized in the determination of the activation energy for the glass transition (Eg ), the activation energy for crystallization (Ec ) and the Avrami’s exponent (n). The composition dependence of the Tg , Eg , and Ec were discussed in terms of the chemical bond approach, the average heats of atomization (Hs ) and the cohesive energy (CE). The diffractogram of the transformed material shows the presence of some crystallites of Se–Te and In–Se in the residual amorphous matrix. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Chalcogenide semiconducting glasses have particular interest due to their wide range of applications as solid state devices both in scientific and technological fields. Se–In and Se–Te binary alloys have got several advantages over pure and amorphous Se [1,2]. The binary In–Se glassy alloys have drawn great attention because of their potential use in solar cells [3,4]. Amorphous Se–Te alloys have greater hardness, higher crystallization temperature, higher photosensitivity and smaller ageing effects than pure Se [1]. As these glasses have poor thermomechanical properties, in order to enlarge their domain of applications, it is necessary to increase their softening temperature and mechanical strength. The addition of a third element (In) which has a large electro-negativity difference with Se and Te, expands the glass forming area and also creates compositional and configurational disorder in the system, and also is found to modify the structure and thus the electrical and thermal properties of the Se–Te system [5–10]. There are number of papers [11–16] found in the literature deal the effect of addition of In into Se–Te glasses on the physical prop-

∗ Corresponding author. E-mail addresses: [email protected] (A.M. Abd Elnaeim), [email protected] (K.A. Aly). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.10.237

erties such as electrical-, photoelectrical-properties and thermal analysis. The thermal analysis of these alloys is important from an application point of view. The present work study in detail the effect of the additions of In content at the expense of Se and Te content on the glass transition, crystallization kinetics and the Avrami’s exponent for different compositions of Inx (Se75 Te25 )100−x (x = 0, 2, 4, 6, 8 and 10 at.%) chalcogenide glasses. 2. Theoretical background The theoretical bases for interpreting DTA or DSC results is provided by the formula theory of transformation kinetics as the volume fraction () crystallized in time (t) by using the Johnson, Mehl and Avrami’s equation [17] n

= 1 − exp [−(kt) ]

(1)

where k is defined as the effective (overall) reaction rate, which is usually assumed to have an Arrhenian temperature dependence. k = k0 exp

−E RT

(2)

where E is the effective activation energy describing the overall crystallization process, n is the growth (Avrami) exponent and K0 the rate constant, depend on the operating nucleation and growth modes [18,19].

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A.M. Abd Elnaeim et al. / Journal of Alloys and Compounds 491 (2010) 85–91

2.1. Afify method [20]

The time integral in Eq. (8) is transformed to temperature integral yielding

To determine the effective activation energy for crystallization, Ec , under isothermal or non-isothermal conditions, Eq. (1) can be written as n

ln(1 − ) = −(kt)

(3)

the important condition in this method is at = 0.63205 where ln(1 − ) = −1. This condition has been discussed in early work [21]. The advantage of this condition is that the results at k0.63 are independent of the value of n, contrary to Avrami’s method, which is dependent on the value of n. Eq. (3) at = 0.63205, gives 1 = (k0.63 t0.63 )

n

(4)

i.e. k0.63 =

1 t0.63

(5)

I(T ) =

K0 ˛

T

exp T0

−E dT¯ RT¯

(11)

which is represented by several approximate analytical expressions [24–27] by the sum of the alternating series e−y¯ (−1)k (k + 1)! y¯ 2 y¯ k k=∞

¯ = S(y)

(12)

k=0

where y¯ = E/RT¯ . Considering that, in this type of series the error produced is this less than the first term neglected and bearing in mind that, in most crystallization reactions y¯ = E/RT¯ 1, it possible to use only the two first terms of this series and the error introduced is not greater than 1%. By assuming that, T 2 (1 − 2RT /E)exp(−E/RT ) ¯ T02 (1 − 2RT0 /E)exp(−E/RT 0) Eq. (11) becomes

The value of the effective overall reaction rate at = 0.63205, (k0.63 ), can be determined from Eq. (5), i.e. from the inverse of the time at = 0.63205, (1/t0.63 ). The values of = 0.63205, t0.63 has been determined using the partial area technique [22] described in the experimental techniques. The effective overall reaction rate at = 0.63205 (k0.63 ) can be written as

considering the assumptions used to get Eq. (13) and taking the logarithm of the quoted equation leads to an expression that in the range of values of y = E/RT, 25 ≤ y ≤ 55, can be fitted very satisfactorily by a linear approximation (an additional assumption) yielding [28]

k0.63 = k0 exp

ln[e−y y−2 (1 − 2y−1 )] ∼ = −5.304 − 1.052y

−E

(6)

R T0.63

I = K0 E(˛R)−1 e−y y−2 (1 − 2y−1 )

ln[−ln(1 − )] = n ln(k) + n ln(t)

(7)

At constant temperature (k is constant), the relation between ln[−ln(1 − )] and ln(t) gives the reaction order, n. In the isothermal condition, the above graph is carried out from one thermogram, but in the case of non-isothermal condition, the graph is carried out, at constant temperature, from different thermograms, i.e. different heating rates.

I = K0 E(˛R)−1 exp(−5.304 − 1.052y)

2.2. Bansal’s method In a non-isothermal DSC experiment the rate constant K, changes continually with time due to the change of the temperature and Eq. (1) can be rewritten in the form [23]

n

t

= 1 − exp(−I n )

K[T (t¯ )]dt¯

(8)

0

Deriving Eq. (8) with respect to time, the crystallization rate is obtained as ˙ = nK(1 − )I n−1

(9)

The maximum rate of crystallization occurs at the peak of the exotherm at time tp and temperature Tp [17], the differentiation of Eq. (9) with respect to time yields ¨ = nKp (I n )p − (n − 1)Kp −

˛EIp RTp2

=0

(10)

(15)

where the above-mentioned approximation might introduce 5.8% error in the value of e−y y−2 (1 − 2 y−1 ) in the worst cases. Substituting (y = E/RT) and (K = K0 exp(−E/RT)) into Eq. (15) gives I = RT 2 K(˛E)−1 (1 − 2RT /E)

(16)

if it is assumed that T T0 so that, y0 can be taken as infinity, the last expression of the integral I is Ip =

1 − 2RT 1/n p

(17)

nE

Substituting I into Eq. (10) and taking the logarithmic form

ln

(t) = 1 − exp −

(14)

Substituting into Eq. (13)

where Ec can be determined from the slope of ln(k0.63 ) vs. 1/T0.63 graphs, obtained from different thermograms. In the isothermal condition, the thermograms are carried out at different temperatures, but in case of non-isothermal condition, the thermograms are carried out at different heating rates. To determine the reaction order, n, Eq. (3) can be written as

(13)

Tp2

+ ln

˛

K R 0 E

−

E ≈ RTp

2RT p

E

1−

1 n2

(18)

note that, Eq. (18) reduces to the Kissinger’s expression [29] for the case of n = 1 as one might have anticipated since this corresponds to the homogeneous reaction case. Thus, it can be seen that, the Kissinger’s method is appropriate for the analysis not only for homogeneous reactions, but also for the analysis of heterogeneous reactions which are described by the JMA equation in the isothermal experiments [17]. The approximation in Eq. (18) RHS = 0 yielding,

ln

Tp2 ˛

=

−Ec − ln RTp

K R 0 E

(19)

where the quoted approximation might introduce a 3% error in the value of E/R in the worst cases. Finally, it should be noted that, the term (−2RT/E) in Eq. (16) is negligible in comparison to the unity, since in most crystallization reactions E/RT 25 [17]. Therefore, Eq. (16) may be rewritten I = RT 2 K(˛E)−1

(20)


87

Substituting I into Eq. (9) gives ˙ p =

n(0.37˛Ec )

(21)

RTp2

That makes it possible to calculate kinetic exponent n. Then it is easy to deduce the formula of the growth mode parameter, m [18,30] by defining an extended volume of transformed material and assuming spatially random nucleation [31,32] the crystallized volume fraction can be rewritten = 1 − exp(ext )

(22)

Here ext represents the ‘extended’ volume fraction (i.e., the one which the crystallites would occupy in the absence of interaction or overlap). The evolution with time, t, of the fraction, ext , in terms of the nucleation frequency (per unit volume), IV , and the crystal growth rate u, is described as

ext (t) = g

t

IV () 0

m

t

u(t)dt

d

(23)

where g is a geometric factor, is the time in which an individual region is nucleated, and m is an exponent which depends on the dimensionality of the crystal growth. An overview of the value of m that occurs for different types of reaction has been given in the literature [30,33]. For interface controlled growth, m assumes the values 1, 2 and 3 for one-, two- and three-dimensional growth, respectively. For diffusion-controlled growth, m assumes the values 1/2, 1 and 3/2 for the respective dimensionalities of growth [34]. The usual analytical methods, proposed in the literature for analyzing the transformation kinetics, assume that the reaction rate constant can be defined by Arrhenian temperature dependence. In order for this condition to hold, the present work assumes that, the crystal growth rate, u, has an Arrhenian temperature dependence, and over the temperature range where the thermoanalytical measurements are carried out, the nucleation rate is either constant or negligible (i.e., the condition of site saturation). From this point of view, the crystallization rate is obtained by deriving the volume fraction crystallized with respect to time, yielding [35,36]

d dt

−(n−1)

p

= k˛

(1 − p )exp

−mE RTp

(24)

The maximum crystallization rate is found by making d2 /dt2 = 0, thus obtaining the relationship

d dt

p

=

mE˛(1 − p ) RTp2

(25)

Eqs. (24) and (25) have been deduced taking a sufficiently limited range of temperature (such as the range of crystallization peaks in DSC experiments) so that the fraction, 1/T2 , can be considered practically constant, and designating with the subscript, p, the magnitudes corresponding to the maximum crystallization rate. For studying the crystallization kinetics for glasses when the nuclei formed during the heating at constant rate, ˛, are dominant, the kinetic exponent, n, is equal to m + 1 and when nuclei formed during any previous heat treatment prior to thermal analysis are dominant, n is equal to m [37,38]. 3. Experimental details Different compositions of bulk Inx (Se0.75 Te0.25 )100−x (where x = 0, 2, 4, 6, 8 and 10 at.%) chalcogenide glasses were prepared from their components of high purity (99.999%) by the usual melt quenching technique. The elements were heated together in an evacuated silica ampoule up to 750 K, and then the ampoule temperature kept constant for about 20 h. During the course of heating, the ampoule was shaken several times to maintain the uniformity of the melt. Finally, the ampoule was quenched into ice cooled water to avoid crystallization. The amorphous nature of the bulk ingots was checked using a Philips X-ray diffractometer (1710). Energy dispersive X-ray spectroscopy (Link analytical EDS)

Fig. 1. DSC traces for powdered Se75 Te25 chalcogenide glass recorded at heating rate 5 K min−1 . The hatched area shows AT , the area between Ti and T.

was used to measure the elemental composition and indicates that the investigated composition is correct up to ±0.4 at.%. The calorimetric measurements were carried out using differential scanning calorimeter Shimadzu 50 with an accuracy of 0.1 K, keeping a constant flow of nitrogen to extract the gases generated during the crystallization reactions, which, is a characteristic of chalcogenide materials. The calorimeter was calibrated, for each heating rate, using the well-known melting temperatures and melting enthalpies of zinc and indium supplied with the instrument [39,40]. 15 mg powdered samples, crimped into aluminium pans and scanned at continuous heating rates (˛ = 2.5, 5, 10, 20 and 40 K min−1 ). The value of the glass transition temperature, Tg , the crystallization extrapolated onset, Tc , and the crystallization peak temperature, Tp , were determined with accuracy ±1 K by using the microprocessor of the thermal analyzer. The fraction, , crystallized at a given temperature, T, is given by = AT /A, where A is the total area of the exotherm between the temperature, Ti , where crystallization is just beginning and temperature, Tf , where the crystallization is completed, AT is the area between Ti and T, as shown in Fig. 1.

4. Results and discussion Fig. 2 shows a set of DSC thermogram for different compositions of the Inx (Se0.75 Te0.25 )100−x (where x = 0, 2, 4, 6, 8 and 10 at.%) glasses recorded at heating rates 10 K/min. this figure shows that, both of the characteristic temperatures, Tg , Tc and Tp increases with the increasing indium content. 4.1. Glass transition Two approaches were used to analyze the dependence of glass transition temperature on the heating rate (˛). The first is the empirical relationship that can be written in the following form Tg = A + B ln(˛)

(26)

where A and B are constants for a given glass composition [41]. The A and B values for different compositions are listed in Table 1. The results shown in Fig. 3 indicate the validity of Eq. (26) for the Inx (Se0.75 Te0.25 )100−x glasses. The second approach is the dependence of the glass transition temperature on the heating rate, ˇ, for this purpose Eq. (19) [29] can be written in the form

ln

Tg2 ˛

=

Eg + const. RTg

(27)

A straight line between ln(Tg2 /˛) and 1/Tg , whose slope yields a value of Eg as shown in Fig. 4, Given that, the variation of ln(Tg2 )

88


Fig. 4. ln(Tg2 /˛) vs. 1/Tg for Inx (Se0.75 Te0.25 )100−x (where x = 0, 2, 4, 6, 8 and 10 at.%) chalcogenide glasses.

Fig. 2. DSC curves for powdered Inx (Se0.75 Te0.25 )100−x (where x = 0, 2, 4, 6, 8 and 10 at.%) chalcogenide glasses recorded at heating rate 10 K min−1 .

Fig. 3. Glass transition temperature Tg vs. ln(˛) for Inx (Se0.75 Te0.25 )100−x (where x = 0, 2, 4, 6, 8 and 10 at.%) chalcogenide glasses.

with ˇ is negligibly small compared with the variation of ln(˛), it is possible to write [41,38] ln(˛) = −

Eg + const. RTg

(28)

The plots of ln(˛) vs. 1/Tg for different compositions of Inx (Se0.75 Te0.25 )100−x chalcogenide glasses are represented in Fig. 5. The obtained values of the glass transition activation energy Eg are listed in Table 1.

Fig. 5. ln(˛) vs. 1/Tg for Inx (Se0.75 Te0.25 )100−x (where x = 0, 2, 4, 6, 8 and 10 at.%) chalcogenide glasses.

The deduced values of Eg lie within the observed values for chalcogenide glasses [38,42,43]. The observed increase of Eg with increasing Te content resulted in an apparent increase of Tg with increasing In content. Therefore, the rigidity of Inx (Se0.75 Te0.25 )100−x glasses increases with increasing In content. The glass transition temperature is known to depend on several independent parameters such as the band gap, bond energy, effective molecular weight, the type and fraction of various structural units formed, cohesive energy, the average heats of atomization and the average coordination number [44–46].

Table 1 The A and B constants according to Losaka formula Eq. (26), The activation energy of glass transition, Eg , deduced by Eqs. (27) and (28) and it is average value Eg , the cohesive energy and the average heats of atomization of different compositions for Inx (Se0.75 Te0.25 )100−x (x = 0, 2, 4, 6, 8 and 10 at.%) glasses. In at.%

A (Eq. (26))

B (Eq. (26))

Eg (Eq. (27)) (kcal mol−1 )

Eg (Eq. (26)) (kcal mol−1 )

Eg (kcal mol−1 )

CE (kcal atom−1 )

Hs (kcal g atom−1 )

0 2 4 6 8 10

324.09 328.22 331.06 336.61 338.96 342.81

6.23 5.44 5.02 4.69 4.51 4.28

30.00 35.83 39.78 44.31 47.00 49.54

31.25 37.10 41.06 45.62 48.31 50.87

30.625 36.465 40.42 44.965 47.655 50.205

44.12 45.17 46.23 47.29 48.34 49.40

28.60 28.78 28.84 28.96 29.08 29.14


89

The bond energies D(A − B) for hetero-nuclear bonds have been calculated by using the empirical relation proposed by Pauling [47] as D(A–B) = [D(A–A) · D(B–B)]1/2 + 30(A –B )2

(29)

where D(A − A) and D(B − B) are the energies of the homonuclear bonds (in units kcal mol−1 ) [48], A and B are the electro-negativity values for the involved atoms [49]. Bonds are formed in the sequence of decreasing bond energy until the available valence of atoms is satisfied [50]. In the present compositions, the In–Se bonds with the highest possible energy (54.321 kcal mol−1 ) are expected to occur first followed by the Se–Te bonds (44.19 kcal mol−1 ) to saturate all available valence of Se. There are still unsatisfied as which must be satisfied by Se–Se defect homo-polar bonds. Based on the chemical bond approach, the bond energies are assumed to be additive. Thus, the cohesive energies were estimated by summing the bond energies over all the bonds expected in the material. Calculated values of the cohesive energies for all compositions are presented in Table 1. These results indicate that, the cohesive energies of these glasses show an increase with increasing the In content. According to Pauling [51], the heat of atomization Hs (A − B), at standard temperature and pressure of a binary semiconductor formed from atoms A and B, is the sum of the heat of formation H and the average of the heats of atomization HsA and HsB that corresponds to, the average non-polar bond energy of the two atoms Hs (A − B) = H +

1 A (H + HsB ) 2 s

Fig. 6. The plots of ln(k0.63 ) vs. 1000/T0.63 for Inx (Se0.75 Te0.25 )100−x (where x = 0, 2, 4, 6, 8 and 10 at.%) chalcogenide glasses.

(30)

The first term in Eq. (30) is proportional to the square of the difference between the electro negativities A and B of the two atomsH˛(A − B )2 This idea can be extended to quaternary semiconductor compounds according to Sadagopan and Gotos [52]. In most cases, the heat of formation of chalcogenide glasses is unknown. In the few materials for which it is known, its value does not exceed 10% of the heat of atomization and therefore can be neglected [53,54]. Hence, Hs (A − B) is given quite well by Hs (A − B) =

1 A (H + HsB ) 2 s

(31)

The obtained results of the heats of atomization of Inx (Se0.75 Te0.25 )100−x (x = 0, 2, 4, 6, 8 and 10 at.%) glasses are listed in Table 1, using the values of Hs for In, Se, and Te given here [52]. 4.2. Crystallization For the evaluation of activation energy for crystallization (Ec ) one can use Eq. (6) by plotting ln(k0.63 ) vs. 1/T0.63 for Inx (Se0.75 Te0.25 )100−x (x = 0, 2, 4, 6, 8 and 10 at.%) glasses as shown in Fig. 6. the obtained values of the activation energy of crystallization Ec according to Eq. (6) are listed in Table 2. Further more Eq. (7) can be used for the determination of the Avrami’s exponent, n. Fig. 7 represents the plots of ln[−ln(1 − )] vs. ln(t) at different heating rates for Se0.75 Te0.25 glass as an example.

Fig. 7. The plots of ln[−ln(1 − )] vs. ln(t) at different heating rates for Se0.75 Te0.25 glass.

Also, from the dependence of the crystallization peak of temperature, Tp , on the heating rate, ˇ, one can use Eq. (19) [29] in order to deduce the values of the activation energy of crystallization. The plots of ln[Tp2 /˛] vs. 1/Tp for Inx (Se0.75 Te0.25 )100−x (x = 0, 2, 4, 6, 8 and 10 at.%) glasses are shown in Fig. 8. The area under DSC curve is directly proportional to the total amount of the alloy crystallized. The ratio between the ordinates and the total area of the peak gives the corresponding crystallization rates, which make it possible, to plot the curves of the exothermal peaks represented in Fig. 9 for Se75 Te25 as a comparative example. It may be observed that, the (d/dt)p values increases

Table 2 The activation energy of crystallization, Ec , according to Eqs. (6) and (14) and the numerical factors n and m for different compositions for Inx (Se0.75 Te0.25 )100−x (x = 0, 2, 4, 6, 8 and 10 at.%) glasses. In at.%

Ec (Eq. (6)) (kcal mol−1 )

Ec (Eq. (19)) (kcal mol−1 )

n (Eq. (7))

n (Eq. (21))

m (Eq. (25))

0 2 4 6 8 10

20.10 23.52 25.11 26.93 27.85 29.07

20.62 21.78 24.42 25.58 28.32 29.66

2.77 2.65 2.64 2.63 2.61 2.56

2.78 2.64 2.64 2.63 2.61 2.56

1.63 1.64 1.55 1.54 1.54 1.50

90


Fig. 8. The plots of ln[Tp2 /˛] vs. 1/Tp for Inx (Se0.75 Te0.25 )100−x (x = 0, 2, 4, 6, 8 and 10 at.%) glasses.

as well as the heating rate increases, a property which has been widely discussed in the literature [55]. With the aim of the correct applying of the preceding theory, the materials were reheated up to a temperature slightly higher than Tg for 1 h in order to form a large number of nuclei. It was ascertained by X-ray diffraction that, there is some crystalline peaks were detected after the nucleation treatment. The diffractogram of the transformed material after heat treatment (Figs. 10 and 11) suggests the presence of some crystallites of SeTe and InSe indicated with d and I, respectively, while there remain also a residual amorphous phase. From the experimental data, It has been observed that, the correlation coefficients of the corresponding straight regression lines show a maximum value for a given temperature, which was considered as the most adequate one for the calculation of parameter n by using Eq. (21). It was found that, the n value for the as-quenched glass differs than that for the reheated glass. This indicates that, there is no nuclei exist already in the material, and therefore n = m + 1 for all glasses under study. In addition, n = m + 1 for as-quenched glass containing no nuclei while n = m for a glass containing a sufficiently large number of nuclei. The kinetic parameters were deduced based on the mechanism of crystallization. The

Fig. 10. X-ray diffraction pattern for Se0.75 Te0.25 glass (a) as prepared glass, (b) annealed glass at 370 K for 1 h. (c) Annealed glass at 370 K for 2 h.

Fig. 11. X-ray diffraction pattern for In10 (Se0.75 Te0.25 )90 glass (a) as prepared glass, (b) annealed glass at 380 K for 1 h. (c) Annealed glass at 380 K for 2 h.

value of the kinetic exponent, n are found decreases from 3 to 2 with the addition of the In content at the expense of Se or Te content. The value of the kinetic exponent (n = 2) for the as-quenched glass is consistent with the mechanism of volume nucleation with one dimensional growth and the value of the kinetic exponent (n = 3) is consistent with the mechanism of volume nucleation with two dimensional growth. Finally it was worth mentioned that, the calculated values for the m parameter according to Eq. (25) also indicates that, n = m for all glasses under study. Furthermore Afify’s method successfully applies for the determination of the activation energy of crystallization and the kinetic exponent, n. 5. Conclusion The addition of In at the expense in Se or Te of Inx (Se0.75 Te0.25 )100−x (x = 0, 2, 4, 6, 8 and 10 at.%) glasses result in:

Fig. 9. Crystallization rate vs. temperature of the exothermal peaks at different heating rates for Se0.75 Te0.25 glass.

(1) The increase of characteristic temperatures (Tg , Tc , and Tp ) with increasing In content leads to the increase of both the activation energy of glass transition, Eg , and crystallization, Ec . The obtained results well discussed in terms of the chemical bond approach, the average heats of atomization and the cohesive energy CE. Afify’s method successfully applied for the determination of the activation energy of crystallization, Ec , and the kinetic exponent, n.


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