Effect of composition on the thermal stability for Ge–In–Se intermediate compound

Journal of Alloys and Compounds 469 (2009) 427–432

Effect of composition on the thermal stability for Ge–In–Se intermediate compound E.R. Shaaban a,∗ , I.S. Yahia b , M. Fadel b a

b

Department of Physics, Al-Azahar University, Assiut 71542, Egypt Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

Received 2 January 2008; received in revised form 23 January 2008; accepted 27 January 2008 Available online 26 March 2008

Abstract The glass formation and devitrification of intermediate alloys in the Ge–In–Se system were studied by differential scanning calorimetry (DSC). A comparison of various simple quantitative methods to assess the level of stability of the glassy materials in the above-mentioned system is presented. All of these methods are based on characteristic temperatures, such as the glass transition temperature, Tg , the onset temperature of crystallization, Tc , the temperature corresponding to the maximum crystallization rate, Tp and the melting temperature, Tm . In this work, the parameter of kinetic criterion Kr (T) is added to the stability criteria. The intermediate glass formation and devitrification of Ge8 In8 Se84 proved that it is more stable than the other intermediate compositions under test because the activation energy of transition, Eg (97.2 kJ/mol) of this composition shows minimum, at its average coordination number r = 2.4. © 2008 Elsevier B.V. All rights reserved. Keywords: Chalcogenide glass; Thermal stability; Crystallization kinetics; Crystalline phase

1. Introduction Chalcogenide glasses exhibit many useful electrical properties including threshold and memory switching [1–3]. These electrical properties are influenced by the structural changes and could be related to thermally induced transitions [4,5]. In chalcogenide glassy systems, glasses exhibiting no exothermic crystallization reaction above the glass transition temperature (Tg ) show a threshold switching type [6,7]. On the other hand, glasses exhibiting an exothermic crystallization reaction above Tg exhibit a memory type of switching. Memory switches come from the boundaries of the glass-forming regions where glasses are stable and have a tendency to crystallize when heated or cooled slowly [8–10]. Glassy alloys of chalcogen elements were the initial objects of study because of their interesting semiconducting properties [11] and more recent importance in optical recording [12]. Recording materials must be stable in the amorphous state at low temperature and have a short crystallization time. Promising materials with these characteristics have been

∗

Corresponding author. Tel.: +20 882365432; fax: +20 882365432. E-mail address: esam [email protected] (E.R. Shaaban).

0925-8388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2008.01.155

recently studied [13]. Therefore, it is very important to know the glass stability and chemical durability of these types of materials. Recently, intermediate phases have been identified in chalcogenide glasses. These phases represent glass compositions where the glass-forming tendency is optimized and ideal stress-free networks exist. Phillips [14], through a constraint counting analysis and considering only short range order, demonstrated that a covalent random network structure has maximum stability at r = 2.4. It is obtained that the number based on the intuitive argument for interatomic bonds in stable glasses have three degrees of freedom. For a three-dimensional system, a topological transition at the critical value r = 2.4 is predicted at which the network changes over from a floppy (underconstrained) to a rigid (overconstrained) type. Glasses with r < 2.4 are considered underconstrained (or floppy) and those with r > 2.4 are overconstrained (rigid). In a region of optimal coordination (r ∼ 2.4), glasses have been found to behave differently from that expectation [15–19]. Glass compositions in this phase are quite stable. This is an area that has been steadily evolving [18,19]. In the present study the thermal stability of some ternary compounds of the Gex In8 Se92−x (4 ≤ x ≤ 12) type has been evaluated experimentally and correlated with the activation energies of crystallization by this kinetic criterion and compared with

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those evaluated by other criteria. The intermediate glass formation and devitrification of Ge8 In8 Se84 , which has minimum Eg (97.2 kJ/mol) at average coordination number r = 2.4 is proved that it is more stable than the other intermediate compositions. 2. Experimental The bulk glass Ge–In–Se was prepared in the conventional way [20] by melting 5N purity elements in an evacuated silica ampoule (total amount 5 gm) at 1100 K for 24 h with continuous rotation. To avoid the oxidation of the samples, the ampoules were evacuated up to 10−4 Pa. Also, the long duration of synthesis and the mechanical shaking of the ampoule in an oscillatory furnace ensured the homogeneity of the compositions being tested. The ampoule was then quenched in ice water. The elemental compositions of these glasses were checked by using energy dispersive X-ray analysis (EDAX) and the estimated average precision was about 1.0% in atomic fraction in each element. The amorphous state of the materials was checked using X-ray (Philips type 1710 with Cu as a target and Ni as a ˚ diffractometer. The absence of crystalline peaks confirms filter, λ = 1.5418 A) the glassy state of the prepared samples, see Fig. 1. The calorimetric measurements were carried out using differential scanning calorimeter (DSC) Shimadzu 50 with an accuracy of ±0.1 K. 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. 20 mg powdered samples, crimped into aluminum pans and scanned at continuous heating rates (β = 5, 10, 20, 30, and 40 K min−1 ). The value of the glass transition, Tg , the crystallization extrapolated onset, Tc and the crystallization peak, Tp , temperature were determined with accuracy ±1 K by using the microprocessor of the thermal analyzer.

3. Results and discussion In order to evaluate the level of stability of glassy system, different simple quantitative methods have been suggested. Most of these methods [21–27] are based on characteristic temperatures Tg , Tp and Tm . Fig. 2 shows the DSC thermograms of amorphous Ge4 In8 Se88 chalcogenide glass recorded at different heating rates β = 5, 10, 20, 30 and 40 K min−1 . The characteristic features of this thermogram of the considered glass are homogenous, this is confirmed by the appearance of a small single endothermic peak. This peak is attributed to the glass transition temperature range, which represents the strength or rigidity of the glass structure. Also, there is an exothermic peak

Fig. 2. (a) Typical DSC trace of Ge4 In8 Se88 , glassy alloy at different heating rates. (b) Identification of Tg , Tin , Tp and Tm for Ge4 In8 Se88 glass at heating rate β = 5 K min−1 .

originating from the amorphous–crystalline transformation. The exothermic peak has two characteristic points: the first point is the onset temperature of crystallization, Tc and the second is the peak temperature of crystallization, Tp . This figure also shows the characteristic melting temperatures Tm . Table 1 illustrates the values of Tg , Tp and Tm for the compositions Ge4 In8 Se88 (A1 ), Ge8 In8 Se84 (A2 ) and Ge12 In8 Se80 (A3 ). The glass-forming ability of the mentioned glasses studied can be estimated by using these characteristic temperatures. The first study of the glass thermal stability of various compounds was done by Sakka and Mackenzie [21], using the ratio Tg /Tm . Dietzel [22] introduced the glass criterion, T = Tc − Tg , where the onset temperature of crystallization Tc is often an important parameter to evaluate the glass-forming ability. Hruby [25] calculated the Hr as follows: Hr =

Saad and Poulain [26] obtained two criteria, weighted thermal stability H and S as follows: H =

Fig. 1. X-ray diffraction patterns for the as prepared Gex In8 Se92−x glasses.

T . Tm − T p

T Tg

and

S=

(Tp − Tc ) T . Tg

The higher values of criterion parameters reflect the greater thermal stability of the glass. In the present study the above-mentioned criteria have been applied to the alloys Gex In8 Se92−x , where x = 4 (A1 ), x = 8 (A2 ) and x = 12 (A3 ). The values of T, Hr , H and S for different composition are listed in Table 1. From Table 1, it is observed that the composition A2 (Ge8 In8 Se84 ), (which has lowest activation energy transition Eg , 97.2 kJ/mol and its coordination number r = 2.4) possess the highest values of T, Hr , H and S than the other compositions. This behavior indicates that the composition Ge8 In8 Se84 is more stable than the two other compositions. On the other hand, the formal theory of transformation kinetics can be described by the evaluation with time t and the volume

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Table 1 The values of thermal parameters of glass transition temperature Tg , onset temperature of crystallization Tc , crystallization temperature Tp and melting temperature Tm of glasses A1 , A2 and A3 with different heating rates β Glass

β

Tg (K)

Tc (K)

Tp (K)

Tm (K)

T (K)

Hr

H

S (K)

A1

5 10 20 30 40

451 459 468 475 482

542 551 561 567 572

558 569 580 590 595

652 667 683 694 701

91 92 93 92 90

0.968 0.939 0.903 0.885 0.849

0.202 0.2 0.199 0.194 0.187

3.228 3.608 3.776 4.455 4.295

A2

5 10 20 30 40

426 436 446 454 458

532 541 551 557 562

549 561 573 580 585

650 665 681 692 699

106 105 105 103 104

1.05 1.01 0.972 0.92 0.912

0.249 0.241 0.235 0.227 0.227

4.23 4.817 5.179 5.218 5.223

A3

5 10 20 30 40

461 468 476 482 486

544 553 563 569 574

559 573 583 590 595

651 666 682 693 700

83 85 87 87 88

0.902 0.914 0.879 0.845 0.838

0.18 0.182 0.183 0.18 0.181

2.701 3.632 3.655 3.79 3.802

The characteristic parameters T, Hr and S are according to the text.

fraction crystallized, χ, in terms of the rate of crystal growth, u: n    t  = 1 − exp(−I1n ) χ = 1 − exp −g (1) u dt

process. The stability criterion is defined as [32]:   −Hr Ec Kr (T ) = K0 exp RT

where g is the geometric factor, n is an exponent, which depends  t on the mechanism of transformation and I1 = 0 u dt  . By taking the derivative of Eq. (1) with respect to time and by using an Arrhenian temperature dependence for the crystal growth rate [28], the crystallization rate is obtained as   dχ −Ec = n(1 − χ)I1n−1 K0 exp = nK(1 − χ)I1n−1 (2) dt RT

where Hr is the stability factor based on characteristic temperatures. T is the temperature range between Tg and Tp . The theoretical background for the definition of the parameter Kr (T) would be based on the analysis of the relation between the parameters K(T) and Kr (T). Differentiating Eqs. (3) and (5) with respect to temperature and rewrite each parameters, results in

0

where Ec is the effective activation energy for crystal growth, R is the universal gas constant (R = 8.314472 J K−1 mol−1 ) and K is the reaction rate constant, which is depended on the temperature according to the relation:   Ec K(T ) = K0 exp − (3) RT where K0 is the frequency factor. In addition, the kinetic parameter, K(T), with Arrhenian temperature dependence, which introduced to the stability criteria. Surinach et al. [29] and Hu and Jiang [30] introduced two criterions according to the values of Tg and Tp   Ec (4a) K(Tg ) = K0 exp − RTg and

  Ec K(Tp ) = K0 exp − RTp

(4b)

Thus, the values of K(Tg ) and K(Tp ) indicate the tendency of glass to devitrify on heating. The larger their values, the greater is the tendency to devitrify. The formation of glass is a kinetic

Kr Hr Ec , = Kr T RT 2

K Ec = K T RT 2

(5)

(6)

It should be noted that the above-mentioned variation of the parameter Kr (T) is Hr times the variation in parameter K(T), which could justify the accuracy of the parameter. Just like the K(T) criteria, the smaller the values of Kr (T) are the greater thermal stability of the glass. The obvious advantage of this method is that it can evaluate the glass stability over a broad temperature range other than at only one temperature such as Tg or Tp . For the determination of the so-called activation energy of enthalpy relaxation of the glass transition, or activation energy of glass transition Eg of the investigated glass. This determination of Eg can be performed using the Kissinger formula, which is originally derived for the crystallization process and suggested to valid for glass transition [31]. This formula has the following form

 Tg2 Eg ln + const. (7) = RTg β A straight line between ln(Tg2 /β) and 1/Tg , for different composition whose slopes yield a values of Eg (see Fig. 3). The average coordination number r in a ternary compound Gex Iny Sez (x + y + z = 100) is calculated using the standard pro-

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Fig. 3. Plot of ln Tg2 /β vs. 1000/Tg of the analyzed materials.

Fig. 5. Experimental plot of ln Tp2 /β vs. 1000/Tp and straight regression lines for the different glassy alloys (β in K s−1 ).

cedures described elsewhere [19,33] as: r = xCN(Ge) + yCN(In) + zCN(Se)

(8)

Using coordination numbers (CN) of 4, 5 and 2 for Ge, In and Se, respectively, the values of r of the Gex In8 Se92−x (4 at% ≤ x ≤ 12 at%) glasses were evaluated. Fig. 4 shows both the values of the activation energy of glass transition Eg and average coordination numbers r as a function of Ge content for Gex In8 Se92−x glass. It is observed that Eg has a minimum value (97.2 kJ/mol) at r = 2.4 for glass composition Ge8 In8 Se84 (See Fig. 4). To evaluate the activation energy of crystallization Ec , it should be used the variation of Tp with β. V`azquez et al. [32] developed a Kissenger method for non-isothermal analysis of devitrification as follows:   Tp2 E Ec ln (9) + ln = β RTp RK0 Fig. 5 represents the evaluation of ln(Tp2 /β) versus 1/Tp for the different compositions. The plots were found to be straight lines. The activation energy, Ec , and frequency factor, K0 , are then evaluated by least squares fitting method. Fig. 6 shows the values of both Ec and K0 as a function of Ge content. Accord-

Fig. 4. Activation energy of transition Eg and average coordination number r in Gex In8 Se92−x glass alloys. As the predicted critical composition with x = 8 the Eg shows minimum at r = 2.4.

ing to Mehta and Kumar [34] the composition dependence of Ec has been interpreted the so-called topological models, which are based on the constraint theory [7,14,35] and on the structural dimensionality considerations [36]. In these models, the behavior of Ec with composition can be discussed in terms of the average coordination number r, which is indiscriminate of the species or valence bond. In the constraints model [7,14,35], by equating the number of operating constraints to the number of degrees of freedom, r of the most stable glass is shown to be ∼2.4. At this value of r, the glass network changes over from a floppy (underconstrained) to a rigid (overconstrained) type. Glasses with r < 2.4 are considered underconstrained (or floppy) and those with r > 2.4 are overconstrained (rigid). In a region of optimal coordination (r ∼ 2.4), glasses have been found to behave differently from that expectation. Glass compositions in this phase are quite stable. After knowing the values of E and K0 , the kinetic parameters K(T) and Kr (T) of the studied compositions were calculated by using Eqs. (3) and (5), respectively. These calculations were carried out in order to compare the stability sequence of the studied compositions from the quoted parameters with the corresponding sequence deduced from stability criteria based on

Fig. 6. The activation energy of crystalization, Ec , and frequency factor, K0 of the analyzed alloys obtained from the straight regression lines fitted to values of ln Tp2 /β vs. 1000/Tp .

E.R. Shaaban et al. / Journal of Alloys and Compounds 469 (2009) 427–432 Table 2 Kinetics parameters K(T) and Kr (T) for the alloys Glass

β

K(Tg ) (s−1 )

K(Tp ) (s−1 )

Kr (Tg ) (s−1 )

Kr (Tp ) (s−1 )

A1

5 10 20 30 40

3.032 × 10−6 5.925 × 10−6 1.225 × 10−5 2.115 × 10−5 3.594 × 10−5

0.004827 0.008803 0.016 0.026 0.033

1.034 × 10−5 5.988 × 10−5 0.0004473 0.001428 0.008205

0.013 0.057 0.286 0.774 2.713

A2

5 10 20 30 40

4.998 × 10−7 1.276 × 10−6 3.126 × 10−6 6.219 × 10−6 8.694 × 10−6

0.004748 0.009359 0.018 0.026 0.033

6.604 × 10−8 8.693 × 10−7 9.247 × 10−6 0.0001357 0.0002443

0.0009875 0.006944 0.042 0.289 0.455

A3

5 10 20 30 40

4.291 × 10−6 7.786 × 10−6 1.506 × 10−5 2.434 × 10−5 0.0000333

0.004627 0.01 0.018 0.026 0.034

0.0002113 0.0002276 0.001616 0.009044 0.015

0.115 0.163 0.814 3.27 4.994

characteristic temperatures. The values of K(T) and Kr (T) for the temperatures Tg and Tp are listed in Table 2. According to the literature [30,32], it is found that when the values of (K(Tg ) and K(Tp ) criteria) are smaller, the glassforming ability of the system become well. From Table 2, both

431

data of K(Tg ) and K(Tp ) indicate that the glass sample A2 is the most stable, and the stability orders at different heating rates are A2 > A1 > A3 . In addition, by using Eqs. (4a) and (4b), the values of Kr (Tg ) and Kr (Tp ) were calculated and given in Table 2. From this result it showed that the glass A2 is the most stable, and the orders of stability are also A2 > A1 > A3 at various heating rates. This stability result agrees with that of the K(Tg ) and K(Tp ) criteria. Fig. 7 represents the plots of Kr (T) versus T for the different glassy alloys to verify the stable order at β = 10 and 30 K min−1 . It is found that Kr (T) of A2 (Ge8 In8 Se84 ) displays the lowest values than the other two compositions, i.e. A2 is more stable than the others. 4. Conclusion The glass-forming ability of some alloys in Gex In8 Se92−x (4 ≤ x ≤ 12) system has been evaluated by using various thermal stability criteria, based on characteristic temperatures. The Kr (T) criterion has been evaluated from the glass stability of DSC data, which includes both the kinetic parameters and the critical temperatures. Therefore, it is reasonable to think that the obtained data from the quoted criterion agree satisfactorily with the values, which result from the existing criteria based on characteristic temperatures and K(T) criteria. A high value of Kr (T) means poor stability of the glass. In the present paper, the non-isothermal devitrification of three glassy alloys in the above-mentioned system has been studied at different heating rates and various temperatures. The above quoted study has verified that the Kr (T) criterion is slightly affected both by the heating rate and by the temperature, while the other criteria show a bigger variation with the heating rate. Among the glassy alloys, the intermediate glass formation and devitrification of Ge8 In8 Se84 (A2 ), which has minimum Eg (97.2 kJ/mol) at average coordination number r = 2.4 is proved more stable than the other intermediate compositions. The Kr (T) criterion of the A2 glass sample is the smallest, so this glass composition is the most stable. Finally, the stability order of these glass samples is A2 > A1 > A3 . Acknowledgment The authors are grateful to Al-Azhar University, Faculty of Science Physics Department, Assuit branch for financial support. References

Fig. 7. Plots of Kr (T) vs. T for the different glassy alloys to verify the stable order: (a) β = 10 K min−1 , and (b) β = 10 K min−1 .

[1] E.A. Davis, N.F. Mott, Electronic Processes in Non-Crystalline Materials, Clarendon, Oxford, 1979. [2] E.R. Shaaban, M.T. Dessouky, A.M. Abousehly, J. Phys.: Condens. Matter 19 (2007) 11. [3] J. Barre, et al., Phys. Rev. Lett. 94 (2005) 208701. [4] Deassy I. Novita, P. Boolchand, Phys. Rev. Lett. 98 (2007) 195501. [5] S. Chakravarty, et al., J. Phys.: Condens. Matter 17 (2005) L1. [6] R.H. Queen, R.T. Johnson, J. Non-Cryst. Solids 7 (1972) 617. [7] J.C. Phillips, M.F. Thorpe, Solid State Commun. 53 (1985) 699. [8] J.A. Savage, J. Mater. Sci. 7 (1972) 64.

432

E.R. Shaaban et al. / Journal of Alloys and Compounds 469 (2009) 427–432

[9] J. Cornet, Ann. Chem. 10 (1975) 239. [10] S.C. Moss, J.P. Deneufville, Mater. Res. Bull. 79 (1972) 423. [11] K. Tanaka, Y. Osaka, M. Sugi, S. Iizima, M. Kikuchi, J. Non-Cryst. Solids 12 (1973) 100. [12] Y. Sugiyama, R. Chiba, S. Fugimori, N. Funakoski, J. Non-Cryst. Solids 122 (1990) 83. [13] Y. Maeda, H. Andoh, I. Ikuta, M. Magai, Y. Katoh, H. Minemura, N. Tsuboi, Y. Satoh, Appl. Phys. Lett. 54 (1989) 893. [14] J.C. Phillips, J. Non-Cryst. Solids 34 (1979) 153. [15] P. Boolchand, D.G. Georgiev, M. Micoulaut, J. Optoelectron. Adv. Mater. 4 (2002) 823. [16] S. Chakravarty, D.G. Georgiev, P. Boolchand, M. Micoulaut, J. Phys.: Condens. Matter 17 (2005) L1. [17] D.G. Georgiev, P. Boolchand, M. Micoulaut, Phys. Rev. B 62 (2000) R9228. [18] P. Boolchand, G. Lucovsky, J.C. Philips, M.F. Thorpe, Philos. Mag. 85 and 32 (2005) 3823. [19] Fei Wang, S. Mamedov, P. Boolchand, B. Goodman, Meera Chandrasekhar, Phys. Rev. B 71 (2005) 174201. [20] M. Fadel, K. Sedak, Int. J. Chem. 3 (1992) 245. [21] S. Sakka, J.D. Mackenzie, J. Non-Cryst. Solids 6 (1971) 145.

[22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36]

A. Dietzel, Glasstech. Ber. 22 (1968) 41. N. Mehta, R.S. Tiwari, A. Kumar, Mater. Res. Bull. 41 (2006) 1664. D.R. Uhlmann, J. Non-Cryst. Solids 25 (1977) 43. A. Hruby, Czech. J. Phys. B 22 (1972) 1187. M. Saad, M. Poulain, Mater. Sci. Forum 19–20 (1987) 11. N. Mehta, R.S. Tiwari, A. Kumar, Eur. Phys. J. Appl. Phys. 31 (2005) 153. H. Yinnon, D.R. Uhlmann, J. Non-Cryst. Solids 54 (1983) 253. S. Surinach, M.D. Baro, M.T. Clavaguera-Mora, N. Clavaguera, J. Mater. Sci. 19 (1984) 3005. L. Hu, Z. Jiang, J. Chin. Ceram. Soc. 18 (1990) 315. H.E. Kissinger, J. Res. Nat. Bur. Stand. 57 (1956) 217. J. V`azquez, P.L. L´opez-Alemany, P. Villares, R. Jim´enez-Garay, J. Alloys Compd. 354 (2003) 153. A.F. Loffe, A.R. Regel, Prog. Semicond. 4 (1960) 239. N. Mehta, A. Kumar, J. Therm. Anal. Calorimetry 83 (2006) 669. K. Tanaka, Phys. Rev. B 39 (1989) 1270. C.H. Hurst, E.A. Davis, in: W. Brenig (Ed.), Proceedings of Fifth International Conference on Amorphous and Liquid Semiconductors, Taylor and Francis, London, 1974, p. 349.