Glass transition and crystallization kinetics of Sb14.5As 29.5Se53.5Te2.5 amorphous solid

Article abstract of DOI:10.1002/pssa.200521189

The crystallization kinetics of the quaternary Sb_14.5As _29.5Se_53.5Te_2.5 glassy alloy was studied under non-isothermal conditions. The method was applied to the experimental data obtained by differential scanning

Full text of DOI:10.1002/pssa.200521189

Original
Paper
phys. stat. sol. (a) 203, No. 5, 837–843 (2006) / DOI 10.1002/pssa.200521189
Glass transition and crystallization kinetics
of Sb As Se Te amorphous solid
14.5
29.5
53.5
2.5
1 *, 2
A. A. Othman , K. A. Aly , and A. M. Abousehly
2
1
Physics Department, Assiut University, Assiut, Egypt
2
Physics Department, Al-Azhar University, Assiut, Egypt
Received 1 August 2005, revised 5 February 2006, accepted 15 February 2006
Published online 24 March 2006
PACS 61.10.Nz, 61.43.Fs, 64.70.Pf, 65.60.+a
The crystallization kinetics of the quaternary Sb As Se Te glassy alloy was studied under non-
14.5
29.5
53.5
2.5
isothermal conditions. The method was applied to the experimental data obtained by differential scanning
calorimetry (DSC), using continuous-heating techniques. In addition, two approaches are used to analyze
the dependence of glass transition temperature (Tg) on the heating rate (β). One is empirical linear rela-
2
tionship between (Tg) and ln (β). The other approach is the use of straight line ln (T /b) vs. 1/Tg for eva-
g
luation of the activation energy for glass transition. The phases at which the alloy crystallizes after the
thermal process have been identified by X-ray diffraction. The diffractogram of the transformed material
shows the presence of some crystallites of As, SbTe, AsSb, As Se , Sb Se and AsSe Te in the residual
2
3
2
3
5
5
amorphous matrix.
© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction
An understanding of the kinetics of crystallization in glasses is important for the manufacturing of glass-
ceramics and in preventing devitrification. Nucleation and growth rates are sometimes measured directly in
the microscope [1] but this method could not be applied to glasses in which nucleation and crystallization
occurred in times below 1 h. Differential scanning calorimetry (DSC) is valuable for the quantitative study
of crystallization in different glassy systems. The study of crystallization kinetics has been widely discussed
in the literature [2–8]. Different methods were proposed to get crystallization kinetics from the exothermic
peaks of the (DSC) curves under non-isothermal conditions. Theoretical models [9–11] proposed for the
crystallization process under non-isothermal conditions were applied to calculate crystallization kinetics.
In this work, the glass transition and the crystallization kinetics were studied using DSC with continu-
ous heating of the sample at various uniform heating rates. The characteristic temperatures T , T , and T
g
c
p
as well as the activation energy of glass transition and the activation energy for crystallization, E and E ,
g c
respectively were determined for Sb As Se Te glassy alloy. Finally, the crystalline phases corre-
14.5 29.5 53.5 2.5
sponding to the crystallization process were identified by X-ray diffraction (XRD) measurements.
2 Experimental details
The semiconducting Sb As Se Te glassy alloy was prepared from their components of 99.999%
14.5 29.5 53.5 2.5
high purity. The proper amount for each material was weighed, and then the weighed materials were
introduced into cleaned silica tubes. To avoid the oxidation of the samples the tube was evacuated to
1.33 × 10–3 Pascal, then put into a furnace at around 1250 K for 24 h. During the course of heating the
*
Corresponding author: e-mail: kamalaly2001@yahoo.com, Phone: +02 86 2325647
© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

838
A. A. Othman et al.: Glass transition and crystallization kinetics
Fig. 1 DSC traces for powdered Sb As Se Te
2.5
14.5
29.5
53.5
–1
chalcogenide glass at heating rate 5 K min . The
TP
hatched area shows AT. The area between Ti and T.
Tg
Tc
T
Ti
Tf
350
400
450
500
550
600
T (K)
ampoule was shaken several times to maintain their uniformity. Finally, the ampoule was quenched into
ice cooled water to avoid crystallization.
The amorphous state of the material was confirmed by a diffractometric X-ray scan (Philips diffrac-
tometer 1710) using Cu as target and Ni as filter (λ = 1.542 Å). Energy dispersive X-ray spectroscopy
(Link analytical EDS) was used to measure the elemental composition and indicates that the investigated
composition is correct up to 0.2 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 cali-
brated, for each heating rate, using the well-known melting temperatures and melting enthalpies of zinc
and indium supplied with the instrument [12]. 20 mg powdered samples, crimped into aluminum pans and
scanned at continuous heating rates (β = 2.5, 5, 10, 15, 20, 25 and 30 K min–1). The value of the glass
transition temperature, T , the crystallization extrapolated onset, T and the crystallization peak tempera-
g
c
ture, T , were determined with accuracy 1 K by using the microprocessor of the thermal analyzer.
p
The fraction, χ, crystallized at a given temperature, T, is given by χ = A /A, where A is the total area of
T
the exotherm between the temperature, T , where crystallization is just beginning and temperature, T ,
i f
where the crystallization is completed, A is the area between T and T, as shown in Fig. 1.
T i
3 Results and discussion
The DSC curve for Sb As Se Te quaternary glass obtained at a heating rate of 5 K min–1 as
14.5
29.5
53.5
2.5
shown in Fig. 1. The glass transition temperature, T = 450.56 2 K, the extrapolated onset crystalliza-
g
tion temperature, T = 515.8 2.2 K, and the peak temperature of crystallization, T = 539.29 2.5 K.
c p
This DSC trace shows the typical glass crystal transformation. The DSC Data at different heating rates,
β, shows that, the characteristic temperatures T , T , and T increase with increasing β, a property which
g
c
p
has been reported in the Ref. [13].
3.1 Glass transition
Two approaches are used to analyze the dependence of glass transition temperature on the heating rate.
The first is the empirical relationship of the form
T = A + B ln β ,
g
(1)
where A and B are constants for a given glass composition [14]. The results shown in Fig. 2 indicate the
validity of Eq. (1) for the Sb As Se Te glassy alloy. The empirical relationship for this glass can
14.5
29.5
53.5
2.5
be written in the form
T = 441.26 + 5.61 ln β ,
g
(2)
where a straight regression line has been fitted to the experimental data.
© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.pss-a.com

Original
Paper
phys. stat. sol. (a) 203, No. 5 (2006)
839
Fig. 2 Glass transition temperature versus ln (β) (β in
–1
KS ) of Sb As Se Te glass.
14.5
29.5
53.5
2.5
460
456
452
448
444
0.6
1.2
1.8
2.4
3.0
3.6
ln
β
The other approach is the dependence of the glass transition temperature on the heating rate, β, by
using Kissinger’s formula [15] in the form [16, 17]
2
ln (T /β ) = -E /RT + const. ,
(3)
g
g
g
2
a straight line between ln (T /β ) and 1/T , whose slope yields a value of E and where the subscript g
g
g
g
denotes magnitude values corresponding to the glass transition temperature.
2
Given that the variation of ln (T ) with β is negligibly small compared with the variation of ln (β ), it
g
is possible to write [14, 18]
ln (β ) = -E /RT + const.
(4)
Figure 3 shows plots of ln (T /β ), curve (a), and ln (β ), curve (b), versus 1/T for the
g
g
2
g
g
Sb As Se Te semiconductor glass, displaying the linearity of the used equations. The obtained
14.5 29.5 53.5 2.5
values of the glass transition activation energy E are 293.98 kJ/mol (a) and 300.32 kJ/mol (b), respec-
g
tively. The average value of E is 297.1 4 kJ/mol.
g
3.5
3.0
2.5
2.0
1.5
1.0
0.5
11.4
10.8
10.2
9.6
b
a
9.0
2
Fig. 3 (online colour at: www. pss-a.com) a) ln (T /β )
g
vs. 1/T , b) ln (β ) vs. 1/T for Sb As Se Te glass.
2.5
g
g
14.5
29.5
53.5
8.4
2.16 2.18 2.20 2.22 2.24
1000/Tg K-1
www.pss-a.com
© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

840
A. A. Othman et al.: Glass transition and crystallization kinetics
12.0
-9.0
-9.6
5.5
5.0
11.5
b
4.5
11.0
4.0
a
-10.2
-10.8
-11.4
10.5
10.0
9.5
3.5
3.0
2.5
2.0
1.5
9.0
1.70
1.75
1.80
1.85
1.90
1.95
1.80 1.84 1.88 1.92 1.96
1000/Tc K-1
1000/Tp K-1
2
2
Fig. 5 (online colour at: www.pss-a.com) a) ln (T /β ) vs.
Fig. 4 (online colour at: www.pss-a.com) ln (b/T )
c
p
vs. 1/T for Sb As Se Te glass.
c
1000/T , b) ln (T /β ) vs. 1000/T for Sb As Se Te
2.5
14.5
29.5
53.5
2.5
p
p
p
14.5
29.5
53.5
glass.
3.2 Crystallization
By using Kissinger’s formula [15] for the evaluation of the activation energy of glass transition, E , for
g
homogeneous crystallization with spherical nuclei, it has been shown that [16, 19] the dependence of T
c
on b is given by
2
ln (β /T ) = -E /RT + const. ,
c
(5)
c
c
2
where T is the onset temperature of crystallization. The relationship between ln(β /T )and 1/T is shown
c c
c
in Fig. 4. The calculated value of E was found to be equal to 132.03 kJ/mol.
c
For the evaluation of activation energy for crystallization (E ) from the variation of T with β Bansal
c p
et al. [1] developed a method for nonisothermal analysis of devitrification as follows:
2
ln (T /β ) = -E /RT + ln (E /R) - ln K ,
(6)
p
c
p
c
0
2
where K is the frequency factor. The plot of ln (T /β ) vs. 1/T is shown in Fig. 5(a). From the linear
0
p
p
dependence E was found to be equal 121.41 kJ/mol. Furthermore, from the intercept of this linear rela-
c
tion the frequency factor K = 6.636 × 108 s–1. The relation between ln (T /β ) vs. 1/T is shown in
Fig. 5(b) according to the following relation [16, 20]
0
p
p
ln (T /β ) = - E /RT - ln K ,
(7)
p
c
p
0
from the linear dependence, E was found to be equal to 123.69 kJ/mol and the frequency factor
c
K = 1.02 × 109 s–1.
The area under the DSC curve is directly proportional to the total amount of alloy crystallized. The
0
ratio between the coordinates and the total area of the peak gives the corresponding crystallization rates,
which make it is possible plot the curves of the exothermal peaks Fig. 6. It is observed that, the (dx/dt)
p
values increases as well as the heating rate, a property which has been widely discussed in the Ref. [9,
21]. In order to form a large number of nuclei the material was reheated up to 470 K (a temperature
slightly higher than T ) for 1 h. It was ascertained by X-ray diffraction that, there is no crystalline peaks
g
were detected after the nucleation treatment.
© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.pss-a.com

Original
Paper
phys. stat. sol. (a) 203, No. 5 (2006)
841
4.0
3.2
β=30
β=25
2.4
b
β
=20
1.6
a
0.8
β
=15
β
=10
0.0
-0.8
-1.6
β=5
β
=2.5
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
520
540
560
580
ln
β
T(K)
Fig. 6 Crystallization rate versus temperature
of the exothermal peaks at different heating
rates.
Fig. 7 (online colour at: www.pss-a.com) Varia-
tion of ln [–ln (1 – x)] with logarithm of heating rate
–1
(β in KS ), a) as quenched glass 560 K, and b) re-
heating glass 548 K.
For non-isothermal crystallization, the volume fraction χ of crystals precipitated in a glass heated at a
uniform rate β is related to E by the expression [22, 23]
c
ln [-ln (1 - χ)] = -n ln β -1.052(mE /RT) + const.
c
(8)
where m and n are numerical factors depending on the mechanism of nucleation and growth. The plots of
ln [–ln (1 – x)] versus ln β at different specific temperatures have been drawn, both for the as-quenched
glass and the reheated glass. 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. Figure 6 shows the relation between ln [–ln (1 – x)]
and ln β for as-quenched glass at fixed temperature 560 K and reheated glass at 548 K. According to
Eq. (8), the slopes of these lines give the n-values, and it was found that, n = 2.27 for the as-quenched
glass and n = 1.96 for the reheated glass. Allowing for experimental error, both values are close to 2.
Rate K/min
2.5
5
1.6
10
15
20
25
30
1.2
0.8
0.4
0.0
Fig. 8 (online colour at: www.pss-a.com) ln [–ln (1 – x)] versus
1/T plots calculated from the exothermic peaks at different heat-
-0.4
ing rates for Sb As Se Te glass.
53.5
14.5
29.5
2.5
1.70
1.75
1.80
1.85
1.90
1000/T K-1
www.pss-a.com
© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

842
A. A. Othman et al.: Glass transition and crystallization kinetics
4.2
3.6
3.0
2.4
1.8
1.2
Fig. 9 (online colour at: www.pss-a.com) a) ln [β /
(T - T )] vs. 1000/T , b) ln (β) vs. 1000/Tp for
Sb As Se Te glass.
p
0
p
-3.0
-3.6
-4.2
-4.8
-5.4
-6.0
14.5
29.5
53.5
2.5
a
b
1.72 1.76 1.80 1.84 1.88 1.92
1000/Tp K-1
This indicates that a large number of nuclei already exists in the material, therefore m = n = 2, that is, the
crystal particles grow one-dimensionally.
On the other hand, Fig. 8 shows the plots of ln [–ln (1 – x)] versus 1/T for different heating rates (2.5
up to 30 K min–1). From the slopes of these linear relations, the average value of the crystallization acti-
vation energy is 130.98 kJ/mol.
Finally, the crystallization activation energy, E , can be deduced using the formula suggested by Augis
c
and Bennett [24] as follows
ln [β /(T - T )] = ln K - E /RT .
c
(9)
p
0
0
p
When ln [β /(T - T )] is plotted versus 1/T a straight line is obtained whose slope is E /R as shown in
p
c
p
0
Fig. 9(a). The value of E for Sb
c
As Se
29.5
Te glass calculated by using this method is
53.623 2.5
14.625
125.72 kJ/mol. For T ꢀ T , the slope of the linear relation between ln(β) versus 1/T yields also the
p
o
p
crystallization activation energy, E , Fig. 9(b). The calculated value of E by using this assumption is
c c
130.5 kJ/mol.
4 Identification of the crystalline phases
Taking into account the crystallization exothermal peaks shown by the glassy alloy Sb As Se Te it
14.5 30 53.5 2.5
is recommended to try to identify the possible phases that crystallize during the thermal treatment ap-
plied to the samples by means of XRD. For this purpose, in Fig. 10(a) shows the absence of the peaks
which are characteristic of the crystalline phases for the as quenched glass. The diffractogram of the
transformed material after the crystallization process (Fig. 10(b)) suggests the presence of some crystal-
As
SbTe
AsSb
As Se
Sb22Se33
AsSe.5Te.5
*
*
b
a
Fig. 10 Diffractogram of Sb As Se Te glass a)
53.5
14.5
29.5
2.5
as prepared b) after thermal treatment (annealing at T
p
for 2 h).
10
20
30
40
50
60
© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.pss-a.com

Original
Paper
phys. stat. sol. (a) 203, No. 5 (2006)
843
lites of As, SbTe, AsSb, As Se , Sb Se and AsSe Te indicated with d and I, respectively, while there
2 3 2 3 5
5
remains also a residual amorphous phase.
5 Conclusions
(1) Two approaches were used to analyze the glass transition. One is the linear dependence of the
glass transition temperature T on the logarithm of the heating rateβ . The other is the linear relationship
g
2
between ln(T /β ) and 1/T .
g
g
(2) The numerical factors, n and m depend on the mechanism of nucleation, growth, and the dimen-
sionality of the crystal. 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 value of the kinetic exponent (n = 2) for the as quenched glass is
consistent with the mechanism of volume nucleation with one dimensional growth.
(3) Finally, the identification of the crystalline phases reveals the existence of some crystallites of As,
SbTe, AsSb, As Se , Sb Se and AsSe Te dispersed in the remaining amorphous matrix.
2
3
2
3
5
5
References
[1] N. P. Bansal, R. H. Doremus, A. J. Bruce, and C. T. Moynihan, J. Am. Ceram. Soc. 66, 233 (1983).
[2] Z. G. Ivanova and E. Cernoskova, Thermochimica Acta 411, 177–180 (2004).
[3] K. F. Kelton, Crystal Nucleation in Liquids and Glasses, Solid State Phys., Vol. 45 (Academic Press, New
York, 1991).
[4] N. Clavaguera, J. Non-Cryst. Solids 162, 40 (1993).
[5] S. A. Khan, M. Zulfequar, and M. Husain, J. Phys. Chem. Solids 123, 463–468 (2002).
[6] J. Vazquez, P. L. Lopez-Alemany, P. Villares, and R. Jimenez-Garay, J. Phys. Chem. Solids 61, 493 (2000).
[7] H. Yinnon and D. R. Uhlmann, J. Non-Cryst. Solids 54, 253 (1983).
[8] A. H. Moharram and M. S. Rasheedy, phys. stat. sol. (a) 169, 33 (1998).
[9] P. L. Lopez-Alemany, J. Vazquez, P. Villares, and R. Jimenez-Garay, J. Alloys Compd. 285, 185–193 (1999).
[10] K. Matusita and S. Sakka, Phys. Chem. Glasses 20, 81 (1979).
[11] H. E. Kissinger, Anal. Chem. 29, 1702 (1957).
[12] G. W. H. Höhne, W. Hemminger, and H.-J. Flammershiem, Differential Scanning Calorimetry (Springer-
Verlag, Berlin, Heidelberg, 1996).
[13] J. Vazquez, P. L. Lopez-Alemany, P. Villares, and R. Jimenez-Garay, Mater. Chem. Phys. 57, 162 (1998).
[14] A. A. Othman, K. Tahon, and M. A. Osman, Physica B 311, 356 (2002).
[15] H. E. Kissinger, J. Res. Natl. Bur. Stand. 57, 217 (1956).
[16] H. S. Chen, J. Non-Cryst. Solids 27, 257 (1978).
[17] J. Vazquez, C. Wagner, P. Villares, R. Jimenez Garay,J. Non-Cryst. Solids 235–237, 548–553 (1998).
[18] S. Mahadevan, A. Giridhar, and A. K. Singh, J. Non-Cryst. Solids 88, 11 (1986).
[19] J. E. Shelby, J. Non-Cryst Solids 34, 111 (1979).
[20] T. Ozawa, Bull. Chem. Soc. Jpn. 38, 1881 (1965).
[21] Yi Qun Gao, W. Wang, F. Q. Zheng, and X. Liu, J. Non-Cryst. Solids 81, 135 (1986).
[22] N. Afify, Physica B 179, 48 (1992).
[23] K. Matusita, T. Komatsu, and R. Yokota, J. Mater. Sci. 19, 291 (1984).
[24] J. A. Augis and J. E. Bennett, J. Therm. Anal. 13, 283 (1978).
www.pss-a.com
© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim