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Comments on “Kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses by DSC” by Al-Agel et al.
LETTER TO THE EDITOR Journal of Non-Crystalline Solids 358 (2012) 2931–2934
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Comment
Comments on “Kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses by DSC” by Al-Agel et al. E. Illeková ⁎ Institute of Physics, Slovak Academy of Sciences, Dúbravská 9, 845 11 Bratislava, Slovakia
a r t i c l e
i n f o
Article history: Received 1 March 2012 Received in revised form 28 May 2012 Available online 8 August 2012 Keywords: Chalcogenide glasses; Kinetics; Glass transition; Crystallization
a b s t r a c t A critical review of a recent paper by Al-Agel et al. (J. Non Cryst. Solids, 358 (2012) 564) on kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses is presented. A number of possible errors in procedures have been noticed. In particular, X-ray diffraction, Differential Scanning Calorimetry and Field Emission Scanning Electron Microscopy data may have been misinterpreted. Kinetic parameters deduced from data derived from the DSC results and using approaches developed by Kissinger, Ozawa and Matusita and others are discussed. Activation energies and Avrami exponents have been re-calculated from the experimental data presented by Al-Agel et al. © 2012 Elsevier B.V. All rights reserved.
1. Introduction We have read with interest the paper by F.A. Al-Agel et al. entitled “Kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses” [1], which belongs to a series of papers from this research group discussing the thermal stability of chalcogenide glasses. The article [1] concerns the glass transition and crystallization kinetics of two Ga10–Se–Pb glasses. The authors have used differential scanning calorimetry (DSC) in a continuous heating regime (6 heating rates, β) and have calculated the activation energy of the glass transition (ΔEg), the activation energy of crystallization (ΔEc) and the Avrami exponent (n). X-ray diffraction (XRD) was used to study the structure of the material; however, the authors did not identify any crystallized phases. The surface morphology of as-prepared and heat-treated samples was investigated by field emission scanning electron microscopy (FESEM). We have concerns about (i) the quality of experimental data and (ii) the evaluation of these data. Our postulates and procedures for the application of the kinetic models used are presented in this paper. 2. The X-ray patterns In the X-ray patterns [1], authors show two curves to be the XRD diffraction traces of two different as-prepared chalcogenide glasses, Ga10Se87Pb3 and Ga10Se84Pb6. These spectra do not show sharp diffraction peaks presenting crystalline phases. Neither they show any ⁎ Tel.: +421 2 5941 0526; fax: +421 2 5477 6085. E-mail address: [email protected]. 0022-3093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2012.06.026
broad peak (halo) which should characterize the amorphous structure and which is typical also for chalcogenide glasses [2,3]. Moreover, these two curves are entirely identical; thus they cannot represent even noise. Therefore, neither of these curves can prove the amorphous character of the samples. 3. The DSC curves For each sample, a set of six DSC plots is shown in [1] manifesting the influence of the heating rate β. On the base of these curves, the glass transition and crystallization phenomena and their kinetics ought to be evaluated. The approximately same amplitudes of the peaks on all curves demonstrate that the DSC signals were multiplied by various factors and smoothed or modified in another way. In spite of this, it is evident that the crystallization exotherms are not simple peaks; they consist of minimally two sub-peaks representing two sub-effects. Each sub-effect should be characterized by its own kinetics. Because the shape of the complex exothermic peak changes progressively increasing β, the individual kinetics of the sub-effects cannot be the same, the total maximums, characterized by the temperature Tc in [1], are only apparent and they do not represent any of the sub-effects. Also the DSC curves shown by Al-Agel et al. in Fig. 4 in [1] should qualitatively be equal to the corresponding curves in Figs. 2 and 3 in the same paper. Minimally in the case of Ga10Se84Pb6 they are not. “Enthalpies released by the samples (ΔHc)” at their crystallization are presented by Al-Agel et al. in a table, too. They, being 4000–7000 J/mg, are colossal; such values cannot represent any crystallization heat. (The biggest known by us crystallization enthalpy should be the enthalpy of crystallization of water, being approximately equal the heat of its
LETTER TO THE EDITOR 2932
E. Illeková / Journal of Non-Crystalline Solids 358 (2012) 2931–2934
fusion, ΔHc(H2O) = 333.55 J/g [4]. The enthalpies of fusion of indium and zinc, being the thermal analysis calibration standards, are ΔHc(In)= 28.45 J/g and ΔHc(Zn)= 108.37 J/g [5,6].) Also, for example, Málek documented in [7] that the enthalpies of crystallization of Ge–S chalcogenide glasses vary in the interval 23–121 J/g and the same author showed that the enthalpy of crystallization of a completely glassy chalcogenide glass should be approximately equal to the enthalpy of its subsequent melting [8].
-8.0
-8.4
ln (β/ Tg2)
4. The Kissinger approach Activation energies ΔEc and ΔEg deduced from the Kissinger equation and presented by Al-Agel et al. in [1] are false. The individual points in the ln (β/Tc2) vs 1/Tc plots and ln (β/Tg2) vs 1/Tg in [1] do not correspond to data from the table from the same paper. The correct versions of those Kissinger plots are shown in Figs. 1 and 2 in this paper. The corresponding ΔEc and ΔEg are presented in our Table 1. The Kissinger–Akahira–Sunose method (also termed the generalized Kissinger method) [9] is the isoconversion method, therefore, the degree of conversion α(Tp) must be a constant at the inspected temperature Tp, it means the same for Tc (or Tg) of each DSC curve. Al-Agel et al. did not investigate the α(T) before applying the Kissinger method. Further, to be valid, the Kissinger plots must give straight lines. In the case of the DSC measurements and temperatures Tc and Tg presented in [1], the straight lines are only averaged guides to the eyes (excepting those for Ga10Se87Pb3 and the first 5 data-points of Tc of Ga10Se87Pb6), see Figs. 1 and 2 in this paper. The changes in the slope of the Kissinger plots seem to be systematic. The errors of the calculated averaged ΔEc and ΔEg are ≫10%, see Table 1. Therefore such ΔEc and ΔEg have no scientific value.
-8.8
-9.2
-9.6
Ga10Se87Pb3 Ga10Se84Pb6
-10.0 3.04E-3
3.08E-3
3.12E-3
3.16E-3
1/Tg (K-1) Fig. 2. Corrected version of Fig. 10 from [1], plot of (β/Tg2) as a function of 1/Tg (K−1) of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses. Each full line is linear fit of the complete set of data.
versions of those Ozawa plots are shown in Figs. 3 and 4 in this paper. The corresponding ΔEc and ΔEg are presented in Table 1. Both generalized Kissinger and Flynn–Wall–Ozawa [10] methods are so called integral isoconversion methods which are applied in a continuous heating regime TðtÞ ¼ T0 þ βt
ð1Þ
where T0 and T are the initial and actual temperatures, and t is time. The common differential kinetic equation is
5. The Ozawa approach Activation energies ΔEc and ΔEg deduced by Ozawa approach in [1] are false. In addition, the Ozawa and Moynihan equations presented in [1] are inaccurate equations; see [9] and the text later. The individual points in Ozawa plots in [1] do not correspond to the data from the same paper (excepting those for ln β vs 1/Tc of Ga10Se87Pb3 and of first 5 data-points of Ga10Se87Pb6). The correct
dα ¼ f ðαÞkðTÞ dt
ð2Þ
where α is the degree of conversion, f(α) is the characteristic rate function and k(T) is the Arrhenius-type rate constant kðTÞ ¼ K0 exp
−ΔE : RT
ð3Þ
K0 and ΔE are the kinetic constants, ΔE being the activation energy and R the universal gas constant. Then the determination of ΔE is based on the separation of variables α and T in Eq. (2) and finally on the mathematically incorrect temperature integral
-8.4
-8.8
ln (β/ Tc2)
−ΔE 1 −ΔE dt ¼ ∫ exp dT: θ ¼ ∫ exp RTðtÞ β RT
ð4Þ
-9.2
The final relation between the temperature at a selected (fixed) α = const being Tα and the heating rate β, by which the Tα could be -9.6
-10.0
Table 1 Correct version of Table 2 from [1], compositional dependence of ΔEc (kJ/mol) and ΔEg (kJ/mol) of Ga10Se87Pb3 and Ga10Se84Pb6 glasses from non-isothermal DSC experiments.
Ga10Se87Pb3 Ga10Se84Pb6
Sample
-10.4 2.45E-3
2.50E-3
2.55E-3
2.60E-3
2.65E-3
2.70E-3
1 / Tc (K-1) Fig. 1. Corrected version of Fig. 8 from [1], plot of (β/Tc2) as a function of 1/Tc (K−1) of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses. Each full line is linear fit of the complete set of data. Dashed line is linear fit of the first five data-points.
Ga10Se87Pb3 Ga10Se84Pb6 a
ΔEg (kJ/mol)
ΔEc (kJ/mol)
lnβ versus 1/Tg
ln(β/Tg2) versus 1/Tg
lnβ versus 1/Tc
ln(β/Tc2) versus 1/Tc
210 ± 33 168 ± 40
215 ± 35 171 ± 43
88 ± 2 63 ± 9 49 ± 0.5a
86 ± 2 60 ± 10 45 ± 0.5a
When data from only 5 heating rates were taken except β = 5 K/min.
LETTER TO THE EDITOR E. Illeková / Journal of Non-Crystalline Solids 358 (2012) 2931–2934
[1], the mutual relations between the positions of the individual points in corresponding Kissinger and Ozawa plots (i.e. the values of their declinations from the averaging straight lines) are approximately the same, see our Figs. 1 and 3 or Figs. 2 and 4. Therefore, we suppose, that in this case the corresponding ±δΔE reflects predominantly the impropriety of the DSC data.
4.0
3.0
ln (β)
6. The Matusita approach The Kolmogorov–Johnson–Mehl–Avrami (KJMA) kinetic equation, cited and used in [1] 2.0
n αðtÞ ¼ 1− exp −ðktÞ Ga10Se87Pb3 Ga10Se84Pb6
1.0 2.50E-3
2.60E-3
2.70E-3
1 / Tc (K-1) Fig. 3. Corrected version of Fig. 9 from [1], plot of lnβ as a function of 1/Tc (K−1) of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses. Each full line is linear fit of the complete set of data. Dashed line is linear fit of the first five data-points.
reached in the sample, can be written in the form which has been generalized by Starink [9] ln
2933
β BΔE ¼− : RTα TAα
ð5Þ
A and B are numbers which depend on the applied approximation of the temperature integral (4). Thus A = 2 and B = 1 in the Kissinger approach, A = 0 and B = 1.052 in the Ozawa approach (and not B = 1 as it has been written in [1]). Starink [9] also investigated the accuracy of such integral isoconversion methods. The Doyle approximation being used in the Ozawa method has been found to be the most inaccurate of the ones considered. However, generally, the incorrectness in the measurement of the reaction kinetics (it means in the determination of α(T) from the DSC measurement) is responsible for the A principal deviations in the ln(β/Tα ) versus 1/Tα dependence, and is also responsible for the significant part of the error ±δΔE independently of A and B. In the case of the sets of values Tc and Tg from 4.0
ð6Þ
has been derived for the specific type of nucleation-and-growth kinetics (namely, it assumes constant nucleation rate and simultaneous growth of all existing crystalline grains by the constant growth rate until the impingement of two growing grains causes the cessation of their growth) by Kolmogorov, Johnson, Mehl and Avrami. When Eq. (3) has been accepted for k(T), this kinetic equation can be rewritten as ln½− lnð1−αðtÞÞ ¼ n lnK0 −
nE þ n lnt RT
ð7Þ
in the isothermal case. Also, it can be rewritten into ln½− lnð1−αðTÞÞ ¼ n lnK0 −
nE þ n lnðT−T0 Þ−n lnβ RT
ð8Þ
in the case of continuous heating. There are two ways how Eqs. (7) or (8) can be exploited to determine any kinetic parameter. (I) A set of DSC curves measured at different heating rates should be taken and one distinct temperature Tconst such that 0b α(Tconst)b 1 for all β should be chosen. Then the dependence of the individual points ln[−ln(1−αTconst(β)] versus lnβ should give a straight line the slope of which is the parameter n. (II) One DSC curve is sufficient and a single curve fitting procedure should be chosen. Then in the isothermal case, the ln[−ln(1− α(t))] versus lnt dependence should give the straight line the slope of which is n. In the case of the continuous heating regime, parameters n, and T0, at which the desired transformation starts, should be already known. Then the activation energy might be calculated, namely the {ln[−ln(1− α(T))]− nln(T − T0)} versus 1/T dependence should give the straight line which slope is nE/R. The authors in [1] utilized the first approach. However, their so called Matusita expression is not equivalent to Eq. (8) and it does not come out from the KJMA Eq. (6). Moreover, they used a false technique to construct the ln[−ln(1 − αTconst(β)] versus lnβ dependence. Taking the data-points [β;α] from the ln[− ln(1 − α)] vs ln β plot in [1], we tried to appraise the corresponding temperatures at the individual DSC curves from DSC plots for Ga10Se87Pb3 in [1]. The results of
3.5
ln (β)
3.0
2.5 Table 2 Degree of conversion (α) roughly estimated from each data-point presented in the plot of ln − [ln(1 − α)] as a function of ln β in [1] as a function of the heating rate (β), and corresponding temperature (Tconst) roughly estimated from respective DSC curve in [1].
2.0
Ga10Se87Pb3 Ga10Se84Pb6 1.5 3.04E-3
3.08E-3
3.12E-3
3.16E-3
1 / Tg (K-1) Fig. 4. Corrected version of Fig. 11 from [1], plot of lnβ as a function of 1/Tg (K−1) of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses. Each full line is linear fit of the complete set of data.
β
lnβ
ln − [ln(1 − α)]
α
Tconst (K)
5 10 15 20 25 30
1.6 2.3 2.7 3 3.2 3.4
−2.9 −1 0 0.95 1.4 1.9
0.05 0.3 0.6 0.92 0.98 1
360 380 395 420 430 450
LETTER TO THE EDITOR 2934
E. Illeková / Journal of Non-Crystalline Solids 358 (2012) 2931–2934
7. The SEM images Ga10Se87Pb3
Authors [1] state that in their FESEM images document that “there is a crystal growth during annealing of the samples”. In fact, the dimensions of the particles which are present already in the asprepared samples and which are seen in the first FESEM image in [1] have dimensions of the order > 1 μm, therefore, they probably could be the individual particles of the powdered sample. Then, the eventual growth or smoothing of the shape of those particles cannot be the growth of any individual crystalline grains; it might be due to the eventual heat-treatment induced sintering or coalescence of particles. In conclusion, it is believed that it has been shown that due to imperfect experimental results, logic failures and numerous incorrect calculations the interpretations and conclusions presented in paper [1] are of very low justification.
ln (-ln (1-α))
2
0
-2
-4
1.5
2.0
2.5
3.0
3.5
ln β Fig. 5. Approximate version of Fig. 7 from [1], plot of ln[−ln(1 − α)] as a function of lnβ of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses.
our approximate calculations are in Table 2. They show that, in the Al-Agel et. al advancement, Tconst was not constant; it increases by an undefined incorrect way. Therefore, the eventual n derived from such ln[− ln(1 − αTconst(β)] versus lnβ dependence is false. Accepting the individual DSC curves in [1], we tried to assess the correct value of n, too. We took the temperature of the maximum of the crystallization peak from the first DSC plot for Ga10Se78Pb3 [1], which has been taken at β = 5 K/min, Tc = 382 K and defined it to be Tconst = 382 K. Assuming the KJMA kinetics, α in this peak maximum should be α ~ 0.63 [11]. Thus we could obtain the first data-point for the ln [− ln(1 − αTconst(β)] versus lnβ dependence to be [β1;α1] = [5;0,63]. Further for β = 30 K/min, we assumed that the corresponding crystallization peak presented in [1] is in its onset at Tconst = 382.53 K, it means that α ~ 0.1 in that moment. Thus another data-point should be [β2;α2] = [30;0,1]. These two points should indicate the approximate ln[− ln(1 − αT = 382K(β)] versus lnβ dependence and its slope is n = 1.26, see Fig. 5. We consider this n to be more valuable than n = 2.68, the value which has been deduced by Al-Agel et al. and published in [1]. It should be added that the grain size of the glass powder used for DSC measurements (as described in the paragraph: 2. Experimental in [1]) was not indicated. The grain size is considered as extremely important factor to the value to attribute to the parameter n in the KJMA kinetic Eq. (6), as reported by Karamanov et al. [12]. Also, we found no justification for declaration of m = 2, for the investigated Ga–Se–Pb glasses.
Acknowledgments Support of the Agency of the Ministry of Education of the Slovak Republic for the Structural Funds of the EU (CEKOMAT II, ITMS 26240120020) is gratefully acknowledged. The research was supported also by the projects VEGA 2/0111/11, 2/0171/09, 2/0143/12 and APVV-0647-10. References [1] F.A. Al-Agel, Shamshad A. Khan, E.A. Al-Arfaj, A.A. Al-Ghamdi, Kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses by DSC, J. Non-Cryst. Solids 358 (2012) 564–570. [2] M.V. Chekaylo, V.O. Ukrainets, G.A. Il'chuk, Yu.P. Pavlovsky, N.A. Ukrainets, Differential thermal analysis of Ag–Ge–Se, Ge–Se charge materials in the process of their heating and Ag8GeSe6, GeSe2 compound synthesis, J. Non-Cryst. Solids 358 (2012) 321–327. [3] N. Prasad, D. Furniss, H.L. Rowe, C.A. Miller, D.H. Gregory, A.B. Seddon, First time microwave synthesis of As40Se60 chalcogenide glass, J. Non-Cryst. Solids 356 (2010) 2134–2145. [4] http://en.wikipedia.org/wiki/Properties_of_waterFeb. 29 2012. [5] I. Barin, Thermochemical data of pure substances (Part 1), 3rd ed. VCH, Weinheim, Germany, 1995. [6] Pyris Software for Windows, Copyright © 1996–2000, Perkin Elmer Instruments LLC version 3.8, http://www.perkinelmer.com/. [7] J. Málek, The glass transition and crystallization of germanium–sulphur glasses, J. Non-Cryst. Solids 107 (1989) 323–327. [8] J. Málek, J. Klikorka, Crystallization of glassy GeS2, J. Therm. Anal. 32 (1987) 1883–1893. [9] M.J. Starink, The determination of activation energy from linear heating rate experiments: a comparison of the accuracy of isoconversional methods, Thermochim. Acta 404 (2003) 163–176. [10] T. Ozawa, Estimation of activation energy by isoconversion methods, Thermochim. Acta 203 (1992) 159–165. [11] Y.Q. Gao, W. Wang, On the activation energy of crystallization in metallic glasses, J. Non-Cryst. Solids 81 (1986) 129–134. [12] A. Karamanov, I. Avramov, L. Arrizza, R. Pascoval, I. Gutzow, Variation of Avrami parameter during non-isothermal surface crystallization of glass powders with different sizes, J. Non-Cryst. Solids 358 (2012) 1486–1490.
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Comment
Comments on “Kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses by DSC” by Al-Agel et al. E. Illeková ⁎ Institute of Physics, Slovak Academy of Sciences, Dúbravská 9, 845 11 Bratislava, Slovakia
a r t i c l e
i n f o
Article history: Received 1 March 2012 Received in revised form 28 May 2012 Available online 8 August 2012 Keywords: Chalcogenide glasses; Kinetics; Glass transition; Crystallization
a b s t r a c t A critical review of a recent paper by Al-Agel et al. (J. Non Cryst. Solids, 358 (2012) 564) on kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses is presented. A number of possible errors in procedures have been noticed. In particular, X-ray diffraction, Differential Scanning Calorimetry and Field Emission Scanning Electron Microscopy data may have been misinterpreted. Kinetic parameters deduced from data derived from the DSC results and using approaches developed by Kissinger, Ozawa and Matusita and others are discussed. Activation energies and Avrami exponents have been re-calculated from the experimental data presented by Al-Agel et al. © 2012 Elsevier B.V. All rights reserved.
1. Introduction We have read with interest the paper by F.A. Al-Agel et al. entitled “Kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses” [1], which belongs to a series of papers from this research group discussing the thermal stability of chalcogenide glasses. The article [1] concerns the glass transition and crystallization kinetics of two Ga10–Se–Pb glasses. The authors have used differential scanning calorimetry (DSC) in a continuous heating regime (6 heating rates, β) and have calculated the activation energy of the glass transition (ΔEg), the activation energy of crystallization (ΔEc) and the Avrami exponent (n). X-ray diffraction (XRD) was used to study the structure of the material; however, the authors did not identify any crystallized phases. The surface morphology of as-prepared and heat-treated samples was investigated by field emission scanning electron microscopy (FESEM). We have concerns about (i) the quality of experimental data and (ii) the evaluation of these data. Our postulates and procedures for the application of the kinetic models used are presented in this paper. 2. The X-ray patterns In the X-ray patterns [1], authors show two curves to be the XRD diffraction traces of two different as-prepared chalcogenide glasses, Ga10Se87Pb3 and Ga10Se84Pb6. These spectra do not show sharp diffraction peaks presenting crystalline phases. Neither they show any ⁎ Tel.: +421 2 5941 0526; fax: +421 2 5477 6085. E-mail address: [email protected]. 0022-3093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2012.06.026
broad peak (halo) which should characterize the amorphous structure and which is typical also for chalcogenide glasses [2,3]. Moreover, these two curves are entirely identical; thus they cannot represent even noise. Therefore, neither of these curves can prove the amorphous character of the samples. 3. The DSC curves For each sample, a set of six DSC plots is shown in [1] manifesting the influence of the heating rate β. On the base of these curves, the glass transition and crystallization phenomena and their kinetics ought to be evaluated. The approximately same amplitudes of the peaks on all curves demonstrate that the DSC signals were multiplied by various factors and smoothed or modified in another way. In spite of this, it is evident that the crystallization exotherms are not simple peaks; they consist of minimally two sub-peaks representing two sub-effects. Each sub-effect should be characterized by its own kinetics. Because the shape of the complex exothermic peak changes progressively increasing β, the individual kinetics of the sub-effects cannot be the same, the total maximums, characterized by the temperature Tc in [1], are only apparent and they do not represent any of the sub-effects. Also the DSC curves shown by Al-Agel et al. in Fig. 4 in [1] should qualitatively be equal to the corresponding curves in Figs. 2 and 3 in the same paper. Minimally in the case of Ga10Se84Pb6 they are not. “Enthalpies released by the samples (ΔHc)” at their crystallization are presented by Al-Agel et al. in a table, too. They, being 4000–7000 J/mg, are colossal; such values cannot represent any crystallization heat. (The biggest known by us crystallization enthalpy should be the enthalpy of crystallization of water, being approximately equal the heat of its
LETTER TO THE EDITOR 2932
E. Illeková / Journal of Non-Crystalline Solids 358 (2012) 2931–2934
fusion, ΔHc(H2O) = 333.55 J/g [4]. The enthalpies of fusion of indium and zinc, being the thermal analysis calibration standards, are ΔHc(In)= 28.45 J/g and ΔHc(Zn)= 108.37 J/g [5,6].) Also, for example, Málek documented in [7] that the enthalpies of crystallization of Ge–S chalcogenide glasses vary in the interval 23–121 J/g and the same author showed that the enthalpy of crystallization of a completely glassy chalcogenide glass should be approximately equal to the enthalpy of its subsequent melting [8].
-8.0
-8.4
ln (β/ Tg2)
4. The Kissinger approach Activation energies ΔEc and ΔEg deduced from the Kissinger equation and presented by Al-Agel et al. in [1] are false. The individual points in the ln (β/Tc2) vs 1/Tc plots and ln (β/Tg2) vs 1/Tg in [1] do not correspond to data from the table from the same paper. The correct versions of those Kissinger plots are shown in Figs. 1 and 2 in this paper. The corresponding ΔEc and ΔEg are presented in our Table 1. The Kissinger–Akahira–Sunose method (also termed the generalized Kissinger method) [9] is the isoconversion method, therefore, the degree of conversion α(Tp) must be a constant at the inspected temperature Tp, it means the same for Tc (or Tg) of each DSC curve. Al-Agel et al. did not investigate the α(T) before applying the Kissinger method. Further, to be valid, the Kissinger plots must give straight lines. In the case of the DSC measurements and temperatures Tc and Tg presented in [1], the straight lines are only averaged guides to the eyes (excepting those for Ga10Se87Pb3 and the first 5 data-points of Tc of Ga10Se87Pb6), see Figs. 1 and 2 in this paper. The changes in the slope of the Kissinger plots seem to be systematic. The errors of the calculated averaged ΔEc and ΔEg are ≫10%, see Table 1. Therefore such ΔEc and ΔEg have no scientific value.
-8.8
-9.2
-9.6
Ga10Se87Pb3 Ga10Se84Pb6
-10.0 3.04E-3
3.08E-3
3.12E-3
3.16E-3
1/Tg (K-1) Fig. 2. Corrected version of Fig. 10 from [1], plot of (β/Tg2) as a function of 1/Tg (K−1) of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses. Each full line is linear fit of the complete set of data.
versions of those Ozawa plots are shown in Figs. 3 and 4 in this paper. The corresponding ΔEc and ΔEg are presented in Table 1. Both generalized Kissinger and Flynn–Wall–Ozawa [10] methods are so called integral isoconversion methods which are applied in a continuous heating regime TðtÞ ¼ T0 þ βt
ð1Þ
where T0 and T are the initial and actual temperatures, and t is time. The common differential kinetic equation is
5. The Ozawa approach Activation energies ΔEc and ΔEg deduced by Ozawa approach in [1] are false. In addition, the Ozawa and Moynihan equations presented in [1] are inaccurate equations; see [9] and the text later. The individual points in Ozawa plots in [1] do not correspond to the data from the same paper (excepting those for ln β vs 1/Tc of Ga10Se87Pb3 and of first 5 data-points of Ga10Se87Pb6). The correct
dα ¼ f ðαÞkðTÞ dt
ð2Þ
where α is the degree of conversion, f(α) is the characteristic rate function and k(T) is the Arrhenius-type rate constant kðTÞ ¼ K0 exp
−ΔE : RT
ð3Þ
K0 and ΔE are the kinetic constants, ΔE being the activation energy and R the universal gas constant. Then the determination of ΔE is based on the separation of variables α and T in Eq. (2) and finally on the mathematically incorrect temperature integral
-8.4
-8.8
ln (β/ Tc2)
−ΔE 1 −ΔE dt ¼ ∫ exp dT: θ ¼ ∫ exp RTðtÞ β RT
ð4Þ
-9.2
The final relation between the temperature at a selected (fixed) α = const being Tα and the heating rate β, by which the Tα could be -9.6
-10.0
Table 1 Correct version of Table 2 from [1], compositional dependence of ΔEc (kJ/mol) and ΔEg (kJ/mol) of Ga10Se87Pb3 and Ga10Se84Pb6 glasses from non-isothermal DSC experiments.
Ga10Se87Pb3 Ga10Se84Pb6
Sample
-10.4 2.45E-3
2.50E-3
2.55E-3
2.60E-3
2.65E-3
2.70E-3
1 / Tc (K-1) Fig. 1. Corrected version of Fig. 8 from [1], plot of (β/Tc2) as a function of 1/Tc (K−1) of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses. Each full line is linear fit of the complete set of data. Dashed line is linear fit of the first five data-points.
Ga10Se87Pb3 Ga10Se84Pb6 a
ΔEg (kJ/mol)
ΔEc (kJ/mol)
lnβ versus 1/Tg
ln(β/Tg2) versus 1/Tg
lnβ versus 1/Tc
ln(β/Tc2) versus 1/Tc
210 ± 33 168 ± 40
215 ± 35 171 ± 43
88 ± 2 63 ± 9 49 ± 0.5a
86 ± 2 60 ± 10 45 ± 0.5a
When data from only 5 heating rates were taken except β = 5 K/min.
LETTER TO THE EDITOR E. Illeková / Journal of Non-Crystalline Solids 358 (2012) 2931–2934
[1], the mutual relations between the positions of the individual points in corresponding Kissinger and Ozawa plots (i.e. the values of their declinations from the averaging straight lines) are approximately the same, see our Figs. 1 and 3 or Figs. 2 and 4. Therefore, we suppose, that in this case the corresponding ±δΔE reflects predominantly the impropriety of the DSC data.
4.0
3.0
ln (β)
6. The Matusita approach The Kolmogorov–Johnson–Mehl–Avrami (KJMA) kinetic equation, cited and used in [1] 2.0
n αðtÞ ¼ 1− exp −ðktÞ Ga10Se87Pb3 Ga10Se84Pb6
1.0 2.50E-3
2.60E-3
2.70E-3
1 / Tc (K-1) Fig. 3. Corrected version of Fig. 9 from [1], plot of lnβ as a function of 1/Tc (K−1) of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses. Each full line is linear fit of the complete set of data. Dashed line is linear fit of the first five data-points.
reached in the sample, can be written in the form which has been generalized by Starink [9] ln
2933
β BΔE ¼− : RTα TAα
ð5Þ
A and B are numbers which depend on the applied approximation of the temperature integral (4). Thus A = 2 and B = 1 in the Kissinger approach, A = 0 and B = 1.052 in the Ozawa approach (and not B = 1 as it has been written in [1]). Starink [9] also investigated the accuracy of such integral isoconversion methods. The Doyle approximation being used in the Ozawa method has been found to be the most inaccurate of the ones considered. However, generally, the incorrectness in the measurement of the reaction kinetics (it means in the determination of α(T) from the DSC measurement) is responsible for the A principal deviations in the ln(β/Tα ) versus 1/Tα dependence, and is also responsible for the significant part of the error ±δΔE independently of A and B. In the case of the sets of values Tc and Tg from 4.0
ð6Þ
has been derived for the specific type of nucleation-and-growth kinetics (namely, it assumes constant nucleation rate and simultaneous growth of all existing crystalline grains by the constant growth rate until the impingement of two growing grains causes the cessation of their growth) by Kolmogorov, Johnson, Mehl and Avrami. When Eq. (3) has been accepted for k(T), this kinetic equation can be rewritten as ln½− lnð1−αðtÞÞ ¼ n lnK0 −
nE þ n lnt RT
ð7Þ
in the isothermal case. Also, it can be rewritten into ln½− lnð1−αðTÞÞ ¼ n lnK0 −
nE þ n lnðT−T0 Þ−n lnβ RT
ð8Þ
in the case of continuous heating. There are two ways how Eqs. (7) or (8) can be exploited to determine any kinetic parameter. (I) A set of DSC curves measured at different heating rates should be taken and one distinct temperature Tconst such that 0b α(Tconst)b 1 for all β should be chosen. Then the dependence of the individual points ln[−ln(1−αTconst(β)] versus lnβ should give a straight line the slope of which is the parameter n. (II) One DSC curve is sufficient and a single curve fitting procedure should be chosen. Then in the isothermal case, the ln[−ln(1− α(t))] versus lnt dependence should give the straight line the slope of which is n. In the case of the continuous heating regime, parameters n, and T0, at which the desired transformation starts, should be already known. Then the activation energy might be calculated, namely the {ln[−ln(1− α(T))]− nln(T − T0)} versus 1/T dependence should give the straight line which slope is nE/R. The authors in [1] utilized the first approach. However, their so called Matusita expression is not equivalent to Eq. (8) and it does not come out from the KJMA Eq. (6). Moreover, they used a false technique to construct the ln[−ln(1 − αTconst(β)] versus lnβ dependence. Taking the data-points [β;α] from the ln[− ln(1 − α)] vs ln β plot in [1], we tried to appraise the corresponding temperatures at the individual DSC curves from DSC plots for Ga10Se87Pb3 in [1]. The results of
3.5
ln (β)
3.0
2.5 Table 2 Degree of conversion (α) roughly estimated from each data-point presented in the plot of ln − [ln(1 − α)] as a function of ln β in [1] as a function of the heating rate (β), and corresponding temperature (Tconst) roughly estimated from respective DSC curve in [1].
2.0
Ga10Se87Pb3 Ga10Se84Pb6 1.5 3.04E-3
3.08E-3
3.12E-3
3.16E-3
1 / Tg (K-1) Fig. 4. Corrected version of Fig. 11 from [1], plot of lnβ as a function of 1/Tg (K−1) of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses. Each full line is linear fit of the complete set of data.
β
lnβ
ln − [ln(1 − α)]
α
Tconst (K)
5 10 15 20 25 30
1.6 2.3 2.7 3 3.2 3.4
−2.9 −1 0 0.95 1.4 1.9
0.05 0.3 0.6 0.92 0.98 1
360 380 395 420 430 450
LETTER TO THE EDITOR 2934
E. Illeková / Journal of Non-Crystalline Solids 358 (2012) 2931–2934
7. The SEM images Ga10Se87Pb3
Authors [1] state that in their FESEM images document that “there is a crystal growth during annealing of the samples”. In fact, the dimensions of the particles which are present already in the asprepared samples and which are seen in the first FESEM image in [1] have dimensions of the order > 1 μm, therefore, they probably could be the individual particles of the powdered sample. Then, the eventual growth or smoothing of the shape of those particles cannot be the growth of any individual crystalline grains; it might be due to the eventual heat-treatment induced sintering or coalescence of particles. In conclusion, it is believed that it has been shown that due to imperfect experimental results, logic failures and numerous incorrect calculations the interpretations and conclusions presented in paper [1] are of very low justification.
ln (-ln (1-α))
2
0
-2
-4
1.5
2.0
2.5
3.0
3.5
ln β Fig. 5. Approximate version of Fig. 7 from [1], plot of ln[−ln(1 − α)] as a function of lnβ of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses.
our approximate calculations are in Table 2. They show that, in the Al-Agel et. al advancement, Tconst was not constant; it increases by an undefined incorrect way. Therefore, the eventual n derived from such ln[− ln(1 − αTconst(β)] versus lnβ dependence is false. Accepting the individual DSC curves in [1], we tried to assess the correct value of n, too. We took the temperature of the maximum of the crystallization peak from the first DSC plot for Ga10Se78Pb3 [1], which has been taken at β = 5 K/min, Tc = 382 K and defined it to be Tconst = 382 K. Assuming the KJMA kinetics, α in this peak maximum should be α ~ 0.63 [11]. Thus we could obtain the first data-point for the ln [− ln(1 − αTconst(β)] versus lnβ dependence to be [β1;α1] = [5;0,63]. Further for β = 30 K/min, we assumed that the corresponding crystallization peak presented in [1] is in its onset at Tconst = 382.53 K, it means that α ~ 0.1 in that moment. Thus another data-point should be [β2;α2] = [30;0,1]. These two points should indicate the approximate ln[− ln(1 − αT = 382K(β)] versus lnβ dependence and its slope is n = 1.26, see Fig. 5. We consider this n to be more valuable than n = 2.68, the value which has been deduced by Al-Agel et al. and published in [1]. It should be added that the grain size of the glass powder used for DSC measurements (as described in the paragraph: 2. Experimental in [1]) was not indicated. The grain size is considered as extremely important factor to the value to attribute to the parameter n in the KJMA kinetic Eq. (6), as reported by Karamanov et al. [12]. Also, we found no justification for declaration of m = 2, for the investigated Ga–Se–Pb glasses.
Acknowledgments Support of the Agency of the Ministry of Education of the Slovak Republic for the Structural Funds of the EU (CEKOMAT II, ITMS 26240120020) is gratefully acknowledged. The research was supported also by the projects VEGA 2/0111/11, 2/0171/09, 2/0143/12 and APVV-0647-10. References [1] F.A. Al-Agel, Shamshad A. Khan, E.A. Al-Arfaj, A.A. Al-Ghamdi, Kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses by DSC, J. Non-Cryst. Solids 358 (2012) 564–570. [2] M.V. Chekaylo, V.O. Ukrainets, G.A. Il'chuk, Yu.P. Pavlovsky, N.A. Ukrainets, Differential thermal analysis of Ag–Ge–Se, Ge–Se charge materials in the process of their heating and Ag8GeSe6, GeSe2 compound synthesis, J. Non-Cryst. Solids 358 (2012) 321–327. [3] N. Prasad, D. Furniss, H.L. Rowe, C.A. Miller, D.H. Gregory, A.B. Seddon, First time microwave synthesis of As40Se60 chalcogenide glass, J. Non-Cryst. Solids 356 (2010) 2134–2145. [4] http://en.wikipedia.org/wiki/Properties_of_waterFeb. 29 2012. [5] I. Barin, Thermochemical data of pure substances (Part 1), 3rd ed. VCH, Weinheim, Germany, 1995. [6] Pyris Software for Windows, Copyright © 1996–2000, Perkin Elmer Instruments LLC version 3.8, http://www.perkinelmer.com/. [7] J. Málek, The glass transition and crystallization of germanium–sulphur glasses, J. Non-Cryst. Solids 107 (1989) 323–327. [8] J. Málek, J. Klikorka, Crystallization of glassy GeS2, J. Therm. Anal. 32 (1987) 1883–1893. [9] M.J. Starink, The determination of activation energy from linear heating rate experiments: a comparison of the accuracy of isoconversional methods, Thermochim. Acta 404 (2003) 163–176. [10] T. Ozawa, Estimation of activation energy by isoconversion methods, Thermochim. Acta 203 (1992) 159–165. [11] Y.Q. Gao, W. Wang, On the activation energy of crystallization in metallic glasses, J. Non-Cryst. Solids 81 (1986) 129–134. [12] A. Karamanov, I. Avramov, L. Arrizza, R. Pascoval, I. Gutzow, Variation of Avrami parameter during non-isothermal surface crystallization of glass powders with different sizes, J. Non-Cryst. Solids 358 (2012) 1486–1490.