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Phase transformation and crystallization kinetics of Te67.5Ga2.5As30 amorphous alloy
Physica B 410 (2013) 53–56
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Phase transformation and crystallization kinetics of Te67.5Ga2.5As30 amorphous alloy Mostafa I. Abd-Elrahman n, Mohmmed M. Hafiz Physics Department, Faculty of Science, Assiut University, Assiut 71516, Egypt
a r t i c l e i n f o
abstract
Article history: Received 29 September 2012 Received in revised form 24 October 2012 Accepted 25 October 2012 Available online 2 November 2012
The amorphous to crystalline transformation in Te67.5Ga2.5As30 occurs under non-isothermal conditions. The crystallization parameters of this amorphous material are estimated using differential scanning calorimetery (DSC). The activation energy of crystallization (Ec) and the frequency factor (K0) are calculated to be 113.167 1.5 kJ/mol and 1.04 1010 7 31.70 s 1, respectively. The crystallization mechanism is found to be one-dimensional growth mechanism as indicated from the estimated Avrami exponent value. X-ray investigations confirm the amorphous phase and crystalline state for the asprepared and annealed samples, respectively. The crystallized grain sizes of nanoscale are calculated from the XRD peaks. & 2012 Elsevier B.V. All rights reserved.
Keywords: Chalcogenides Differential scanning calorimetery Phase transition X-ray diffraction
1. Introduction Chalcogenide materials having the property of amorphous to crystalline transformation have received much attention. This is because of their applications in the filed of solid electronics, particularly for memory switching [1,2]. These materials can be reversibly switched between the amorphous and crystalline states and thus they have applications in rewritable optical recording [3–5]. The crystallization process can be induced by calorimetric measurements which are isothermal and non-isothermal methods. In the isothermal method, the sample is brought to a temperature above the glass transition temperature and the heat produced during the crystallization process at a constant temperature is recorded as a function of time. In the non-isothermal method, the sample is heated at a fixed heating rate (a) and the heat produced is recorded as a function of temperature or time. Tellurite-based chalcogenides are a subject for intensive studies because they have high refractive index, infrared transmission and high photosensitivity [6–8]. Gallium has been chosen as an additive material to the As–Te system because it has a low melting point (301 K) and a very high boiling point (2676 K). Gallium can readily be alloyed with most metals and has been used as a component of low melting alloys [9]. Crystallization kinetics can be described by three kinetic parameters; the activation energy for crystallization (Ec), the
n
Corresponding author. Tel.: þ20 1092808520; fax: þ20 882342708. E-mail address: [email protected] (M.I. Abd-Elrahman).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.10.021
Avrami exponent (n) which reflects the characteristics of nucleation and the growth process and the frequency factor (K0). The aim of this work is to obtain the crystallization kinetics parameters of Te67.5Ga2.5As30 amorphous. Also, we shed more light on some aspects of the crystallization mechanism.
2. Experimental Bulk Te–Ga–As materials were prepared using the well known melt-quench technique. In this technique, high purity (99.999%) Te, Ga and As (from Aldirch Co., UK) in atomic proportions were weighed into a quartz glass ampoule (12 mm diameter). The content of ampoule (15 g) was sealed in a vacuum of 10 4 Torr and heated in a rotating furnace at around 1200 K for 24 h. The ampoule was then quenched in ice-cold water. The powdered samples were prepared by grinding of the resulting bulk alloy sample in a mortar. The thermal behavior was investigated using a DU Pont 1090 differential scanning calorimeter (DSC). The temperature and energy calibrations of the instrument are performed using the well-known melting temperature and melting enthalpy of highpurity indium supplied with the instrument. The calorimetric sensitivity was 10 mW/cm and the temperature precision was 70.1 K. In order to identify the crystallization phases in the DSC thermograms, X-ray investigation of the as-prepared and the annealed powder was performed using a Philips Diffractometer 1710 with Ni filtered CuKa source (l ¼0.145 nm). The composition of the as-prepared Te67.5Ga2.5As30 bulk was investigated using energy dispersive spectroscopy (EDS). The crystallization
54
M.I. Abd-Elrahman, M.M. Hafiz / Physica B 410 (2013) 53–56
thermograms were recorded as the temperature of the sample was increased at uniform rate. Typically, 20 mg of the sample in powdered form was sealed in standard aluminum pans and the temperature was scanned over a range from room temperature to 500 1C at uniform heating rate, a, ranging from 5 to 35 1C/min. The values of the crystallization onset, the crystallization peak and the melting temperatures were determined with an accuracy of 70.1 K. A best fit for the results was calculated by the leastsquare method. The arithmetic mean value as well as the standard deviation was obtained for the activation energies.
3. Results and discussion
Thermal characteristics of the composition were investigated by DSC analyses. In order to evaluate the thermal stability of a chalcogenide against the crystallization, the common stability criterion of DT¼Tc–Tg [10] and the weight stability criterion of Hw ¼ DT/Tg [11] have been used. In the present case, stability criterion can be modified to meet the thermal stability of a crystallized system against melting. However in this case, the value of DT can be suggested in terms of the difference between Tm and Tp. The higher value of DT corresponds the greater thermal stability. As a is increased from 5 to 35 1C/min, the DT value is decreased from 189 to 164 1C. Therefore, the thermal stability against melting is controlled by the heating rate. 3.2. Crystallization kinetics
3.1. Thermal analysis Typical DSC traces of Te67.5Ga2.5As30 chalcogenide at different heating rates (a) are shown in Fig. 1. Three characteristic events were resolved in the DSC thermograms. At a ¼5 1C/min, the first event is the onset of crystallization at temperature Tc, at T¼156 1C, the second one is an exothermic formation at T¼159 1C corresponding to the peak temperature of crystallization transition Tp, and the other event is the recurrence of an endothermic peak at T ¼348 1C corresponding the melting peak temperature Tm. Table 1 shows changes of the positions of these peaks toward higher temperatures with increasing heating rate. From the table, both Tc and Tp are considerably increased while the Tm is slightly changed as increasing a.
Generally, the dependence of Tp on the heating rate, a, could be discussed using two approaches which are Kissinger and Augis & Bennet formulas [12,13]. These approaches have often been used to calculate the crystallization kinetic parameters such as the activation energy of the crystallization transition, Ec, and the frequency factor, K0 (s 1). The later relates to the probability of effective crystallization process for the activated complex. The dependence of Tp on a is given by the following equations [12,13]: a Ec 1 þlnK 0 ð1Þ ¼ ln Tp R Tp ln
!
a T 2p
Ec 1 ¼ þ constant, R Tp
ð2Þ
where R is the gas constant. Based on Eq. (1), plotting ln(a/Tp) versus (1/Tp) gives a linear relation. The experimental points show a good fit with Eq. (1), as shown in Fig. 2. The obtained value of Ec is 113.1671.5 kJ/mol. The value of Ec calculated from Eq. (2) is 109.4371.5 kJ/mol which is close to that calculated from Eq. (1). This confidence of calculated values of Ec confirms the validity of both approaches. The rate factor K0 is evaluated from the intercept value of plot of Eq. (1) to be 1.04 1010 731.70 s 1. The value of K0 relates to the shape factor of the growing grain, the atomic vibration frequency and the magnitude of atomic movement. High K0 values imply the possibility of high transformation rate; however, the evaluation of reaction rate should take into account other parameters such as Ec and n altogether. The order of crystallization reaction (Avrami index, n) was appropriated in a model for non-isothermal crystallization in which the crystallized fraction (x) can be described as a function
Exo
o
35 C/min.
o
25 C/min.
ΔQ o
15 C/min.
-1
o
5 C/min.
-8
200
300
Temp. [oC] Fig. 1. Typical DSC traces of Te67.5Ga2.5As30 amorphous at different heating rates.
Table 1 Crystallization and melting temperatures, Avrami index and enthalpy of crystallization of Te67.5Ga2.5As30 amorphous at different heating rates.
a (1C/min) 5 15 25 35
Tc (1C) 156 166 175 179
Tp (1C) 159 170 180 186
Tm (1C) 348 349 350 350
Tm Tp (1C) 189 179 170 164
Index n 0.76 1.20 1.26 1.12
-2 -10 -3 -12 -4
DHc (kJ/kg) 14.11 41.16 42.90 15.73
2.20
2.24
2.28
2.32
ln(α / T2) [min-1oC-1]
100
ln(α / T) [min-1]
Endo
-14
1000/T [K-1] Fig. 2. Plots of ln a=T p and ln a=T 2p versus 1=T p for activation energy of crystallization of Te67.5Ga2.5As30 amorphous.
M.I. Abd-Elrahman, M.M. Hafiz / Physica B 410 (2013) 53–56
Intensity(a. u.)
EXO
ΔQ
152
Tc
Base line of crystallization
156 a
160
Temp. [oC]
55
(b) (a)
164
10
168
20
Fig. 3. Shape analysis of crystallization peak for Te67.5Ga2.5As30 amorphous at heating rate of 5 oC/min.
30
40
50
60
70
80
2 θ (degrees)
b
Fig. 4. X-ray diffraction pattern for (a) as-prepared Te67.5Ga2.5As30 amorphous and (b) after annealing at 170 1C for 1 h.
those at lower heating rates leading to a decrease in the value of of heating rate according to the following formula [14]: ln½lnð1xÞ ¼ n lna1:052mEc =RT þ constant,
DHc. ð3Þ
where m and n are constants that depend on the mechanism of the growth and the dimensionality of the crystal. If the formation of the nuclei is dominant during the heating at constant rate, n is equal to (m þ1). If the nuclei are predominantly formed during any previous heat treatment prior to the thermal analysis, n is equal to m [15]. The index n can be obtained from the DSC curves using the method suggested by Kissinger [12]. Fig. 3 shows the analysis of the shape of the crystallization peak by which the exponent, n, can be written in the form [12] n ¼ 1:26
a1=2 b
,
ð4Þ
where a and b are depicted in Fig. 3. The value of n is calculated for each heating rate and presented in Table 1. As a is increased, the value of n increases up to a ¼ 25 1C/min and then decreases. It has been reported that the crystallization mechanisms are categorized according to the value of reaction order n [16]. During the crystallization process, a decreasing kinetic exponent implies a diminishing nucleation rate or growth dimensionality along with the reaction. Taking into account diffusion limited processes, n o1.5 indicates that the amorphous–crystallization transformation proceeds with one-dimensional growth. The enthalpy as a thermodynamic parameter increases when one mole of a substance is transformed into its crystalline state at constant pressure. The change in enthalpy (DHc) of the crystallization of Te67.5Ga2.5As30 amorphous is driven by the reduction of its free energy when it becomes crystalline. Like most solid-state transformations, crystallization is a heterogeneous transformation governed by thermally activated nucleation and growth steps. The value of DHc of the investigated chalcogenide was obtained from the computer program involved in the DSC apparatus and is listed in Table 1. It has been found to behave like the order of crystallization reaction, n. That is DHc increases as a is increased and then decreases for a ¼35 1C/min. This could be attributed to the relationship between the heat of crystallization and the intermolecular forces, which decrease on increasing the heating rate and then the exothermic heat due to the crystallization process increases. At higher heating rate, the saturation of nucleation sites reaches early in comparison with
3.3. X-ray diffraction analysis Fig. 4a shows the X-ray diffraction structure of the as-prepared Te67.5Ga2.5As30 composition. As presented in the figure, the amorphous state of the composition is proved. As 2y of the scanning range increases, diffraction intensity has only some fluctuations with the instrumental background line. There are no sharp peaks and crystalline phases observed in the measured spectra by X-ray diffraction investigation, showing the typical amorphous state of the synthesized composition. This means the as-prepared sample has no nuclei formed during the sample preparation. This result is very important as it concerns understanding of the mechanism of the crystallization as discussed in the previous section. X-ray examination of the sample annealed at 170 1C for 1 h shown in Fig. 4b indicates the existence of crystalline peaks. The crystalline phases at different 2y of the annealed sample are in good agreement with those recorded in the crystalline phase [17,18]. Indexing is carried out by comparing the diffractogram with the ASTM data. The obtained Miller indices and values of d are given in Table 2. The average crystallite size (D) is calculated using the Scherer formula from the full-width at half-maximum (FWHM): D¼
0:94l b cosy
ð5Þ
where l is wavelength of the X-ray used, b is the FWHM and y is half of the angle between the incident and the scattered X-ray beams. The grain sizes are calculated from the diffraction peaks and are collected in Table 2. The XRD pattern of the annealed powder shows that the sample is crystallized in preferential orientations indicated with strong peaks. These orientations are along (0 0 3) plane corresponding to the As2Te3 phase and (3 1 1), (2 0 4) and (6 0 3) planes corresponding to the GaTe phase. Generally, the GaTe and As2Te3 phases are found to be dominant phases in the crystallization state. 4. Conclusion Using the result of the thermal analysis, the crystallization parameters, Ec, K0 and n, of the Te67.5Ga2.5As30 amorphous can be
56
M.I. Abd-Elrahman, M.M. Hafiz / Physica B 410 (2013) 53–56
Table 2 Calculated particle size (D) and standard ASTM values for interplanar distances (d) and hkl values for the bulk of Te67.5Ga2.5As30 annealed at 170 1C. 2y (deg.)
˚ d spacing (A)
(h k l)
D (nm)
Phase
2y (deg.)
˚ d spacing (A)
(h k l)
D (nm)
Phase
20.82 22.74 24.25 25.90 27.18 29.32 31.84 35.08 38.44 39.54 40.14 40.96 43.09 44.77 45.40 46.75 49.41 51.04 51.74
4.228 3.894 3.675 3.437 3.278 3.033 2.800 2.578 2.341 2.264 2.242 2.202 2.095 2.020 1.998 1.940 1.845 1.790 1.763
( 4 0 1) (2 0 2) (4 0 1) ( 2 0 3) (0 0 3) (3 1 1) (2 0 0) (0 0 4) (2 0 4) (2 0 4) ( 5 1 3) ( 1 1 4) ( 1 1 4) ( 4 0 5) (6 0 3) ( 2 0 5) ( 3 1 5) ( 4 0 5) (7 1 1)
15.19 31.04 32.06 27.06 23.61 17.56 30.20 10.15 9.57 24.11 38.62 40.13 24.53 14.08 25.01 17.20 22.69 26.07 20.29
Ga Te As2 Te3 Ga Te Ga Te As2 Te3 Ga Te As Ga Ga Te Ga Te As2 Te3 Ga Te Ga Te As2 Te3 Ga Te Ga Te As2 Te3 Ga Te As2 Te3 As2 Te3
52.41 53.22 54.47 55.80 56.63 61.30 62.71 63.40 64.36 65.67 67.67 69.01 70.08 71.83 72.92 73.37 74.14 76.71 78.82
1.741 1.715 1.689 1.645 1.623 1.508 1.476 1.464 1.445 1.420 1.382 1.359 1.340 1.313 1.297 1.289 1.278 1.243 1.213
( 2 2 3) ( 10 0 2) ( 2 2 3) ( 7 1 3) (2 0 6) ( 8 0 4) (2 8 2) (8 2 0) ( 9 1 2) ( 8 2 3) (9 1 2) ( 12 0 4) (10 0 2) ( 2 0 8) (5 1 6) (0 0 8) ( 8 2 5) ( 5 1 7) (11 1 1)
39.56 20.69 17.76 32.86 38.83 19.23 26.57 31.90 24.41 28.40 23.92 26.24 18.65 18.44 33.97 35.83 27.98 27.37 31.15
Ga Te Ga Te As2 Te3 As2 Te3 Ga Te As2 Te3 Ga Te Ga Te As2 Te3 Ga Te As2 Te3 Ga Te As2 Te3 Ga Te As2 Te3 Ga Te Ga Te As2 Te3 As2 Te3
determined. Both approaches used to evaluate the activation energy of the crystallization, Ec, are valid to discuss the amorphous–crystalline transformation. Based on the evaluated value of the reaction of crystallization order, n, and the results of X-ray diffraction, the crystallization mechanism of the Te67.5Ga2.5As30 amorphous is found to be one-dimensional growth. References [1] S. Kumar, D. Singh, S. Shandhu, R. Thangaraj, Appl. Surf. Sci. 258 (2012) 7406. [2] P. Kumar, S.N. Yannopoulos, T.S. Sathiaraj, R. Thangaraj, Mater. Chem. Phys. 135 (2012) 68. [3] N. Yamada, MRS Bull. (1996) 48. [4] H.J. Borg, R. van Woudenberg, J. Magn. Magn. Mater. 193 (1999) 521.
[5] M. Ahmad, R. Thangaraj, Physica B 404 (2009) 1553. [6] G. Upender, S. Bharadwaj, A.M. Awasthi, Mater. Chem. Phys. 118 (2009) 298. [7] A.A. Bahishti, M.A. Majeed Khan, B.S. Patel, J. Non-Cryst. Solids 355 (2009) 2314. [8] D. Singh, S. Kumar, R. Thangaraj, J. Non-Cryst. Solids 358 (2012) 2826. [9] Zishan H. Khan, M. Zulfequar, M. Manzer Malik, M. Husain, Mater. Sci. Technol. 13 (1997) 484. [10] J. Hruby, J. Phys. B 22 (1972) 89. [11] M. Saad, M. Poulain, Mater. Sci. Forum 19 (1987) 18. [12] H.E. Kissinger, Anal. Chem. 29 (1957) 1702. [13] J.A. Augis, J.E. Bennett, J. Electrochem. Soc. 125 (1978) 330. [14] N. Rysava, T. Spasov, L. Tichy, J. Therm. Anal. 32 (1987) 1015. [15] K. Matusita, T. Konatsu, R. Yokota, J. Mater. Sci. 19 (1984) 291. [16] N. Ohshima, J. Appl. Phys. 79 (1996) 8357. [17] T. Karakostas, J.G. Antonopoulos, S. Kokko, G.L. Bleris, N.A. Economou, Phys. Status Solidi A 59 (1980) K17. [18] H. Arabi, A. Pourghazi, F. Ahmadian, Z. Nourbakhsh, Physica B 373 (16) (2006) 22.
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Phase transformation and crystallization kinetics of Te67.5Ga2.5As30 amorphous alloy Mostafa I. Abd-Elrahman n, Mohmmed M. Hafiz Physics Department, Faculty of Science, Assiut University, Assiut 71516, Egypt
a r t i c l e i n f o
abstract
Article history: Received 29 September 2012 Received in revised form 24 October 2012 Accepted 25 October 2012 Available online 2 November 2012
The amorphous to crystalline transformation in Te67.5Ga2.5As30 occurs under non-isothermal conditions. The crystallization parameters of this amorphous material are estimated using differential scanning calorimetery (DSC). The activation energy of crystallization (Ec) and the frequency factor (K0) are calculated to be 113.167 1.5 kJ/mol and 1.04 1010 7 31.70 s 1, respectively. The crystallization mechanism is found to be one-dimensional growth mechanism as indicated from the estimated Avrami exponent value. X-ray investigations confirm the amorphous phase and crystalline state for the asprepared and annealed samples, respectively. The crystallized grain sizes of nanoscale are calculated from the XRD peaks. & 2012 Elsevier B.V. All rights reserved.
Keywords: Chalcogenides Differential scanning calorimetery Phase transition X-ray diffraction
1. Introduction Chalcogenide materials having the property of amorphous to crystalline transformation have received much attention. This is because of their applications in the filed of solid electronics, particularly for memory switching [1,2]. These materials can be reversibly switched between the amorphous and crystalline states and thus they have applications in rewritable optical recording [3–5]. The crystallization process can be induced by calorimetric measurements which are isothermal and non-isothermal methods. In the isothermal method, the sample is brought to a temperature above the glass transition temperature and the heat produced during the crystallization process at a constant temperature is recorded as a function of time. In the non-isothermal method, the sample is heated at a fixed heating rate (a) and the heat produced is recorded as a function of temperature or time. Tellurite-based chalcogenides are a subject for intensive studies because they have high refractive index, infrared transmission and high photosensitivity [6–8]. Gallium has been chosen as an additive material to the As–Te system because it has a low melting point (301 K) and a very high boiling point (2676 K). Gallium can readily be alloyed with most metals and has been used as a component of low melting alloys [9]. Crystallization kinetics can be described by three kinetic parameters; the activation energy for crystallization (Ec), the
n
Corresponding author. Tel.: þ20 1092808520; fax: þ20 882342708. E-mail address: [email protected] (M.I. Abd-Elrahman).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.10.021
Avrami exponent (n) which reflects the characteristics of nucleation and the growth process and the frequency factor (K0). The aim of this work is to obtain the crystallization kinetics parameters of Te67.5Ga2.5As30 amorphous. Also, we shed more light on some aspects of the crystallization mechanism.
2. Experimental Bulk Te–Ga–As materials were prepared using the well known melt-quench technique. In this technique, high purity (99.999%) Te, Ga and As (from Aldirch Co., UK) in atomic proportions were weighed into a quartz glass ampoule (12 mm diameter). The content of ampoule (15 g) was sealed in a vacuum of 10 4 Torr and heated in a rotating furnace at around 1200 K for 24 h. The ampoule was then quenched in ice-cold water. The powdered samples were prepared by grinding of the resulting bulk alloy sample in a mortar. The thermal behavior was investigated using a DU Pont 1090 differential scanning calorimeter (DSC). The temperature and energy calibrations of the instrument are performed using the well-known melting temperature and melting enthalpy of highpurity indium supplied with the instrument. The calorimetric sensitivity was 10 mW/cm and the temperature precision was 70.1 K. In order to identify the crystallization phases in the DSC thermograms, X-ray investigation of the as-prepared and the annealed powder was performed using a Philips Diffractometer 1710 with Ni filtered CuKa source (l ¼0.145 nm). The composition of the as-prepared Te67.5Ga2.5As30 bulk was investigated using energy dispersive spectroscopy (EDS). The crystallization
54
M.I. Abd-Elrahman, M.M. Hafiz / Physica B 410 (2013) 53–56
thermograms were recorded as the temperature of the sample was increased at uniform rate. Typically, 20 mg of the sample in powdered form was sealed in standard aluminum pans and the temperature was scanned over a range from room temperature to 500 1C at uniform heating rate, a, ranging from 5 to 35 1C/min. The values of the crystallization onset, the crystallization peak and the melting temperatures were determined with an accuracy of 70.1 K. A best fit for the results was calculated by the leastsquare method. The arithmetic mean value as well as the standard deviation was obtained for the activation energies.
3. Results and discussion
Thermal characteristics of the composition were investigated by DSC analyses. In order to evaluate the thermal stability of a chalcogenide against the crystallization, the common stability criterion of DT¼Tc–Tg [10] and the weight stability criterion of Hw ¼ DT/Tg [11] have been used. In the present case, stability criterion can be modified to meet the thermal stability of a crystallized system against melting. However in this case, the value of DT can be suggested in terms of the difference between Tm and Tp. The higher value of DT corresponds the greater thermal stability. As a is increased from 5 to 35 1C/min, the DT value is decreased from 189 to 164 1C. Therefore, the thermal stability against melting is controlled by the heating rate. 3.2. Crystallization kinetics
3.1. Thermal analysis Typical DSC traces of Te67.5Ga2.5As30 chalcogenide at different heating rates (a) are shown in Fig. 1. Three characteristic events were resolved in the DSC thermograms. At a ¼5 1C/min, the first event is the onset of crystallization at temperature Tc, at T¼156 1C, the second one is an exothermic formation at T¼159 1C corresponding to the peak temperature of crystallization transition Tp, and the other event is the recurrence of an endothermic peak at T ¼348 1C corresponding the melting peak temperature Tm. Table 1 shows changes of the positions of these peaks toward higher temperatures with increasing heating rate. From the table, both Tc and Tp are considerably increased while the Tm is slightly changed as increasing a.
Generally, the dependence of Tp on the heating rate, a, could be discussed using two approaches which are Kissinger and Augis & Bennet formulas [12,13]. These approaches have often been used to calculate the crystallization kinetic parameters such as the activation energy of the crystallization transition, Ec, and the frequency factor, K0 (s 1). The later relates to the probability of effective crystallization process for the activated complex. The dependence of Tp on a is given by the following equations [12,13]: a Ec 1 þlnK 0 ð1Þ ¼ ln Tp R Tp ln
!
a T 2p
Ec 1 ¼ þ constant, R Tp
ð2Þ
where R is the gas constant. Based on Eq. (1), plotting ln(a/Tp) versus (1/Tp) gives a linear relation. The experimental points show a good fit with Eq. (1), as shown in Fig. 2. The obtained value of Ec is 113.1671.5 kJ/mol. The value of Ec calculated from Eq. (2) is 109.4371.5 kJ/mol which is close to that calculated from Eq. (1). This confidence of calculated values of Ec confirms the validity of both approaches. The rate factor K0 is evaluated from the intercept value of plot of Eq. (1) to be 1.04 1010 731.70 s 1. The value of K0 relates to the shape factor of the growing grain, the atomic vibration frequency and the magnitude of atomic movement. High K0 values imply the possibility of high transformation rate; however, the evaluation of reaction rate should take into account other parameters such as Ec and n altogether. The order of crystallization reaction (Avrami index, n) was appropriated in a model for non-isothermal crystallization in which the crystallized fraction (x) can be described as a function
Exo
o
35 C/min.
o
25 C/min.
ΔQ o
15 C/min.
-1
o
5 C/min.
-8
200
300
Temp. [oC] Fig. 1. Typical DSC traces of Te67.5Ga2.5As30 amorphous at different heating rates.
Table 1 Crystallization and melting temperatures, Avrami index and enthalpy of crystallization of Te67.5Ga2.5As30 amorphous at different heating rates.
a (1C/min) 5 15 25 35
Tc (1C) 156 166 175 179
Tp (1C) 159 170 180 186
Tm (1C) 348 349 350 350
Tm Tp (1C) 189 179 170 164
Index n 0.76 1.20 1.26 1.12
-2 -10 -3 -12 -4
DHc (kJ/kg) 14.11 41.16 42.90 15.73
2.20
2.24
2.28
2.32
ln(α / T2) [min-1oC-1]
100
ln(α / T) [min-1]
Endo
-14
1000/T [K-1] Fig. 2. Plots of ln a=T p and ln a=T 2p versus 1=T p for activation energy of crystallization of Te67.5Ga2.5As30 amorphous.
M.I. Abd-Elrahman, M.M. Hafiz / Physica B 410 (2013) 53–56
Intensity(a. u.)
EXO
ΔQ
152
Tc
Base line of crystallization
156 a
160
Temp. [oC]
55
(b) (a)
164
10
168
20
Fig. 3. Shape analysis of crystallization peak for Te67.5Ga2.5As30 amorphous at heating rate of 5 oC/min.
30
40
50
60
70
80
2 θ (degrees)
b
Fig. 4. X-ray diffraction pattern for (a) as-prepared Te67.5Ga2.5As30 amorphous and (b) after annealing at 170 1C for 1 h.
those at lower heating rates leading to a decrease in the value of of heating rate according to the following formula [14]: ln½lnð1xÞ ¼ n lna1:052mEc =RT þ constant,
DHc. ð3Þ
where m and n are constants that depend on the mechanism of the growth and the dimensionality of the crystal. If the formation of the nuclei is dominant during the heating at constant rate, n is equal to (m þ1). If the nuclei are predominantly formed during any previous heat treatment prior to the thermal analysis, n is equal to m [15]. The index n can be obtained from the DSC curves using the method suggested by Kissinger [12]. Fig. 3 shows the analysis of the shape of the crystallization peak by which the exponent, n, can be written in the form [12] n ¼ 1:26
a1=2 b
,
ð4Þ
where a and b are depicted in Fig. 3. The value of n is calculated for each heating rate and presented in Table 1. As a is increased, the value of n increases up to a ¼ 25 1C/min and then decreases. It has been reported that the crystallization mechanisms are categorized according to the value of reaction order n [16]. During the crystallization process, a decreasing kinetic exponent implies a diminishing nucleation rate or growth dimensionality along with the reaction. Taking into account diffusion limited processes, n o1.5 indicates that the amorphous–crystallization transformation proceeds with one-dimensional growth. The enthalpy as a thermodynamic parameter increases when one mole of a substance is transformed into its crystalline state at constant pressure. The change in enthalpy (DHc) of the crystallization of Te67.5Ga2.5As30 amorphous is driven by the reduction of its free energy when it becomes crystalline. Like most solid-state transformations, crystallization is a heterogeneous transformation governed by thermally activated nucleation and growth steps. The value of DHc of the investigated chalcogenide was obtained from the computer program involved in the DSC apparatus and is listed in Table 1. It has been found to behave like the order of crystallization reaction, n. That is DHc increases as a is increased and then decreases for a ¼35 1C/min. This could be attributed to the relationship between the heat of crystallization and the intermolecular forces, which decrease on increasing the heating rate and then the exothermic heat due to the crystallization process increases. At higher heating rate, the saturation of nucleation sites reaches early in comparison with
3.3. X-ray diffraction analysis Fig. 4a shows the X-ray diffraction structure of the as-prepared Te67.5Ga2.5As30 composition. As presented in the figure, the amorphous state of the composition is proved. As 2y of the scanning range increases, diffraction intensity has only some fluctuations with the instrumental background line. There are no sharp peaks and crystalline phases observed in the measured spectra by X-ray diffraction investigation, showing the typical amorphous state of the synthesized composition. This means the as-prepared sample has no nuclei formed during the sample preparation. This result is very important as it concerns understanding of the mechanism of the crystallization as discussed in the previous section. X-ray examination of the sample annealed at 170 1C for 1 h shown in Fig. 4b indicates the existence of crystalline peaks. The crystalline phases at different 2y of the annealed sample are in good agreement with those recorded in the crystalline phase [17,18]. Indexing is carried out by comparing the diffractogram with the ASTM data. The obtained Miller indices and values of d are given in Table 2. The average crystallite size (D) is calculated using the Scherer formula from the full-width at half-maximum (FWHM): D¼
0:94l b cosy
ð5Þ
where l is wavelength of the X-ray used, b is the FWHM and y is half of the angle between the incident and the scattered X-ray beams. The grain sizes are calculated from the diffraction peaks and are collected in Table 2. The XRD pattern of the annealed powder shows that the sample is crystallized in preferential orientations indicated with strong peaks. These orientations are along (0 0 3) plane corresponding to the As2Te3 phase and (3 1 1), (2 0 4) and (6 0 3) planes corresponding to the GaTe phase. Generally, the GaTe and As2Te3 phases are found to be dominant phases in the crystallization state. 4. Conclusion Using the result of the thermal analysis, the crystallization parameters, Ec, K0 and n, of the Te67.5Ga2.5As30 amorphous can be
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M.I. Abd-Elrahman, M.M. Hafiz / Physica B 410 (2013) 53–56
Table 2 Calculated particle size (D) and standard ASTM values for interplanar distances (d) and hkl values for the bulk of Te67.5Ga2.5As30 annealed at 170 1C. 2y (deg.)
˚ d spacing (A)
(h k l)
D (nm)
Phase
2y (deg.)
˚ d spacing (A)
(h k l)
D (nm)
Phase
20.82 22.74 24.25 25.90 27.18 29.32 31.84 35.08 38.44 39.54 40.14 40.96 43.09 44.77 45.40 46.75 49.41 51.04 51.74
4.228 3.894 3.675 3.437 3.278 3.033 2.800 2.578 2.341 2.264 2.242 2.202 2.095 2.020 1.998 1.940 1.845 1.790 1.763
( 4 0 1) (2 0 2) (4 0 1) ( 2 0 3) (0 0 3) (3 1 1) (2 0 0) (0 0 4) (2 0 4) (2 0 4) ( 5 1 3) ( 1 1 4) ( 1 1 4) ( 4 0 5) (6 0 3) ( 2 0 5) ( 3 1 5) ( 4 0 5) (7 1 1)
15.19 31.04 32.06 27.06 23.61 17.56 30.20 10.15 9.57 24.11 38.62 40.13 24.53 14.08 25.01 17.20 22.69 26.07 20.29
Ga Te As2 Te3 Ga Te Ga Te As2 Te3 Ga Te As Ga Ga Te Ga Te As2 Te3 Ga Te Ga Te As2 Te3 Ga Te Ga Te As2 Te3 Ga Te As2 Te3 As2 Te3
52.41 53.22 54.47 55.80 56.63 61.30 62.71 63.40 64.36 65.67 67.67 69.01 70.08 71.83 72.92 73.37 74.14 76.71 78.82
1.741 1.715 1.689 1.645 1.623 1.508 1.476 1.464 1.445 1.420 1.382 1.359 1.340 1.313 1.297 1.289 1.278 1.243 1.213
( 2 2 3) ( 10 0 2) ( 2 2 3) ( 7 1 3) (2 0 6) ( 8 0 4) (2 8 2) (8 2 0) ( 9 1 2) ( 8 2 3) (9 1 2) ( 12 0 4) (10 0 2) ( 2 0 8) (5 1 6) (0 0 8) ( 8 2 5) ( 5 1 7) (11 1 1)
39.56 20.69 17.76 32.86 38.83 19.23 26.57 31.90 24.41 28.40 23.92 26.24 18.65 18.44 33.97 35.83 27.98 27.37 31.15
Ga Te Ga Te As2 Te3 As2 Te3 Ga Te As2 Te3 Ga Te Ga Te As2 Te3 Ga Te As2 Te3 Ga Te As2 Te3 Ga Te As2 Te3 Ga Te Ga Te As2 Te3 As2 Te3
determined. Both approaches used to evaluate the activation energy of the crystallization, Ec, are valid to discuss the amorphous–crystalline transformation. Based on the evaluated value of the reaction of crystallization order, n, and the results of X-ray diffraction, the crystallization mechanism of the Te67.5Ga2.5As30 amorphous is found to be one-dimensional growth. References [1] S. Kumar, D. Singh, S. Shandhu, R. Thangaraj, Appl. Surf. Sci. 258 (2012) 7406. [2] P. Kumar, S.N. Yannopoulos, T.S. Sathiaraj, R. Thangaraj, Mater. Chem. Phys. 135 (2012) 68. [3] N. Yamada, MRS Bull. (1996) 48. [4] H.J. Borg, R. van Woudenberg, J. Magn. Magn. Mater. 193 (1999) 521.
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