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Crystallization processes of Ag–Ge–Se superionic glasses
Journal of Non-Crystalline Solids 320 (2003) 151–167 www.elsevier.com/locate/jnoncrysol
Crystallization processes of Ag–Ge–Se superionic glasses M.A. Ure~ na a, M. Fontana
a,*
, B. Arcondo a, M.T. Clavaguera-Mora
b
a
b
Laboratorio de S olidos Amorfos, Facultad de Ingenierıa, Universidad de Buenos Aires, Paseo Col on 850, (1063) Buenos Aires, Argentina Grup de Fısica dels Materials I, Facultat de Ci encies, Universitat Aut onoma de Barcelona, (08193) Bellaterra, Spain Received 19 February 2002; received in revised form 4 October 2002
Abstract The interest in superionic systems has increased in recent years because of the potential application of these materials as solid electrolytes. In this field, amorphous materials present important advantages when compared to the crystalline solids: larger conductivity, isotropy and absence of grain boundaries. In this work, amorphous alloys of compositions (Ge25 Se75 )100y Agy with y ¼ 10, 15, 20 and 25 at.% have been studied. Amorphous samples in bulk were obtained from the liquid by water quenching (melt-quenching technique). The crystallization kinetics of the amorphous alloys have been studied under continuous heating and isothermal conditions by means of differential scanning calorimetry. A glass transition and two exothermic transformations were observed in all the samples. The quenched samples and the crystallization products have been characterized by X-ray diffraction. The primary crystallization of the ternary phase Ag8 GeSe6 and the secondary phase GeSe2 was observed. The glass and crystallization temperatures, the activation energy and the crystallization enthalpy are reported. The first step of the crystallization of the Ag8 GeSe6 phase in all the (Ge25 Se75 )100y Agy samples is modelled taking into account the Johnson–Mehl–Avrami–Kolmogorov theory and considering that the changes in the composition only modify the viscosity of the undercooled liquid. The transformation diagrams (TTT and THRT) are calculated and the glass forming ability is analyzed. The experimental results are discussed and correlated with the structures proposed for the glass. The present results and conclusions are also compared with those reported by other authors. 2003 Elsevier Science B.V. All rights reserved.
1. Introduction Ge–Se glasses have been widely studied due to their extended amorphization composition range [1]. The fact that bulk glasses are easily obtained makes Ge–Se an ideal system to investigate a great variety of properties and their correlation with
*
Corresponding author. E-mail address: mfontan@fi.uba.ar (M. Fontana).
structure and composition. It has been reported [2] that the electric transport in these glasses can be strongly affected by the addition of metals. GeSeAg glasses evolve from semiconductors to superionic conductors as Ag concentration is increased (r ¼ 1 104 X1 cm1 for Ag25 Se56:25 Ge18:5 glass at room temperature) [3,4]. The interest in superionic glasses has increased in recent years because of the potential application of these materials as solid electrolytes. In this field, the amorphous materials present important advantages when
0022-3093/03/$ - see front matter 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-3093(03)00022-X
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compared to the crystalline solids: larger conductivity, isotropy and absence of grain border [5]. Borisova et al. [6] studied the glass forming ability (GFA) of this ternary system by water quenching. They found that in samples with a composition Ge25 Se75 the vitreous character could be retained introducing a maximum Ag content of 30 at.%. The structure of these glasses has been studied by several authors employing different sources of radiation [3,7,8]. Several associations have been reported and also a strong medium range order that the increasing of Ag concentration weakens. Moreover, a dual chemical role of Ag has been reported [9], network glass former and network modifier behaviors. In the second class of glasses, a bimodal glass transition temperature (Tg ) is reported and attributed to a phase separation of Ag centered structures (resembling a-Ag2 Se) from the host matrix. Recently, electrical properties of (Ge25 Se75 )100y Agy glasses were investigated by impedance spectroscopy. As the concentration of silver is increased the total electrical conductivity steeply increases from 1013 to 105 X1 cm1 at about y ¼ 10 [10]. They supposed a percolation transition is happening at y . The aim of this work is to analyze the thermal stability, the crystallization kinetics and the crystallization products of bulk glasses of atomic compositions (Ge25 Se75 )100y Agy with y ¼ 10, 15, 20 and 25 using differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The dependence of the crystallization kinetics on the concentration of Ag is discussed with reference to the equilibrium phase diagram and the amorphous structure.
system. The crystalline compound GeSe2 has a congruent melt point at 742 C and the compound Ag2 Se, at 897 C. On Ag2 Se–GeSe2 pseudobinary system the ternary compound Ag8 GeSe6 forms and melts congruently at 902 C. The Ag8 GeSe6 exists in at least three modifications: c-Ag8 GeSe6 a fcc structure from 902 to 48 C, b0 -Ag8 GeSe6 with orthorhombic structure from 48 to )4 C and, a0 Ag8 GeSe6 is stable below )4 C. The Ag8 GeSe6 separates two eutectics on the pseudobinary Ag2 Se–GeSe2 . The eutectic e1 : GeSe2 –Ag8 GeSe6 is located at 29 at.% Ag and 560 C. The eutectic e2 Ag2 Se–Ag8 GeSe6 occurs at 59 at.% Ag and 810 C (see Fig. 1). The pseudobinary section Ag8 GeSe6 –Se subdivides the partial ternary system Ag2 Se–GeSe2 –Se. A monotectic reaction, L1 () Ag8 GeSe6 + L2 , occurs at 700 C with L1 containing 50 at.% Se and L2 96 at.% Se. This reaction falls in temperature within the ternary and closures the region of the liquid immiscibility at a critical tie line L1 / L2 () Ag8 GeSe6 at 520 C. The eutectic separation e1 is shown by a monovariant curve descending from the eutectic towards the Se corner. In the projection of the liquidus, the monovariant
1.1. Background about the Ag–Ge–Se system 1.1.1. The Ag–Ge–Se equilibrium system The equilibrium phase diagram of the Ag–Ge– Se system was compilated and evaluated by Prince [11]. The Ag2 Se–GeSe2 pseudobinary system allows the invariant equilibria in the ternary system to be considered as resulting from the two partial ternary systems Ag2 Se–GeSe2 –Se and Ag2 Se– GeSe2 –Ge–Ag. All samples compositions studied in this work are included in the first partial ternary
Fig. 1. Liquidus surface of the AgGeSe ternary system in the Se rich corner. Ag10, Ag15, Ag20 and Ag25 are the compositions of the studied samples.
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curve intersects the liquid immiscibility gap at a composition 29 at.% Ag, 15 at.% Ge and 56 at.% Se (L3 ), showing the presence of the ternary monotectic reaction, L3 ! L4 + Ag8 GeSe6 + GeSe2 at 400 C (see Fig. 1). The solidification in the Ag8 GeSe6 –GeSe2 –Se system ends with a eutectic reaction in the Se rich corner at 217 C. All samples compositions studied in this work are at the homogeneous liquid region and at the GeSe2 primary crystallization field (see Fig. 1). 1.1.2. The Ag–Ge–Se glass Network former compounds are covalent alloys such as oxides (or chalcogenides) of silicon, boron, phosphorus, germanium, etc. They generally have a relevant glass-forming tendency. The crystalline structure consists of chains of tetrahedrons or triangles. However, a certain dispersion of valence angles and bond lengths appears in the vitreous phase and only short-range order (SRO) is conserved. Intermediate range order (IRO) appears to be maintained in certain cases and the glass then consists of clusters [12]. The GeSe system is an example of this kind of glasses. Network modifiers are compounds with a marked ionic feature and include in particular the oxides and chalcogenides of alkalis, alkaline earths and silver ions. They do not form glasses alone, but can easily react with a former and become incorporated in its network. The chemical reaction that results from the interaction can take the form of the breaking of chalcogenide bonds that connect two former cations and leads to the creation of ionic bonds. It is difficult to specify the precise environment of the modifier cation [12]. The structure of AgGeSe glasses is not yet fully determined, however, the basic framework of this structure is based on the Gey Se100y glassy network. There are many structural investigations on glassy Gey Se100y . All the reports indicate that the SRO in the GeSe2 glass is due to Ge(Se1=2 )4 tetrahedra [13,14]. However, the interconnection of the tetrahedra has given rise to many controversies; for example, assessing the proportion of edgeshared to corner-shared tetrahedra [15,16]. When the atomic composition moves towards the Se corner, the homopolar bond contribution to SRO
153
increases, i.e.: Se-rich Gey Se100y glasses contain Se-chains (homopolar bond Se–Se) which are cross-linked with the Ge(Se1=2 )4 tetrahedra [13,14]. This result supports the idea that the formation of these binary glasses is controlled by a chemically ordered process [17]. For y ¼ 20, 33 and 40 there is evidence for some of the tetrahedra being in an edge-shared configuration. The number of edgeshared tetrahedra in these glasses increases with increasing Ge content [13]. It was also established that a well-defined IRO exists in Gex Se100x glasses. The Ôpre-peakÕ or the first sharp diffraction peak (FSDP) in the structure 1 [13]. factor SðqÞ is around 1.0 A The GeSeAg glass is likely to share many structure and transport characteristic with the (network former)–(network modifier) family of glasses. In this glass, Ge is termed the network forming cation, Ag the mobile cation and Se the anion [8]. The previous work in the (Ge25 Se75 )75 Ag25 glass indicates that Ge remains tetrahedrally coordinated by Se, as it is in Gey Se100y glasses. The first . The network forming neighbour distance is 2.38 A character of Ge is apparently unchanged [3,7,8]. In the case of the Ag, the position of the first-neigh agrees with Ag–Se distances bour at 2.62–2.68 A found in Ag8 GeSe6 and Ag2 Se crystalline compounds [3,8]. Also the SRO in (Ge25 Se75 )100-y Agy glasses (y ¼ 0–25) was examined by XRD using Mo(Ka) radiation at room temperature [7]. The 1 , shows a systematic FSDP, located at q 1 A increase in intensity with decreasing Ag concentration revealing a substantial decrease of the IRO [3,7]. The coordination numbers and the bond lengths of the correlation GeSe, SeSe, SeAg, and AgAg as a function of composition were determined from the radial distribution function [7] and are reproduced in Table 1. Some studies propose that the (Ge25 Se75 )75 Ag25 glass is homogeneous [3,8]. However, in a recent study, ternary (Gez Se100z )100y Agy bulk glasses in the Se-rich region (z < 33:3) are reported to be intrinsically phase separated into an Ag2 Se-rich glass and a residual Get Se100t (t > z at y 6¼ 0) with Ag acting as a network modifier [10]. They observed bimodal glass transition temperatures. In contrast, Ge-rich glasses (z > 40) are homogeneous, wherein
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Table 1 The coordination numbers and the bond lengths of the correlation GeSe, SeSe, SeAg, and AgAg ) ) x Correlation Distance ( 0.05 A Width (A
Coordination numbers ( 0.1)
0
GeSe and SeSe (1st neighbours) SeSe (2nd neighbours)
2.36 3.87
0.37 0.84
2.5 11.5 0.4
10
GeSe and SeSe (1st neighbours) AgSe AgAg SeSe (2nd neighbours)
2.37 2.67 3.05 3.85
0.35 0.28 0.22 0.78
2.2 0.4 0.25 11.0 0.4
15
GeSe and SeSe (1st neighbours) AgSe AgAg SeSe (2nd neighbours)
2.37 2.67 3.05 3.89
0.35 0.31 0.31 0.80
2.05 0.65 0.35 11.0 0.4
20
GeSe and SeSe (1st neighbours) AgSe AgAg SeSe (2nd neighbours)
2.39 2.67 3.05 3.88
0.34 0.30 0.32 0.76
1.7 1.05 0.7 10.7 0.4
25
GeSe and SeSe (1st neighbours) AgSe AgAg SeSe (2nd neighbours)
2.39 2.67 3.06 3.90
0.38 0.37 0.37 0.73
1.55 1.3 0.85 10.0 0.4
They were determined from the radial distribution function study of the glasses (Ge25 Se75 )100x Agx [7].
Ag acts as a network former, replacing available Ge sites of the backbone to be 3-fold coordinated to Se. 2. Experimental procedure Samples with compositions (Ge0:25 Se0:75 )90 Ag10 (Ag10), (Ge0:25 Se0:75 )85 Ag15 (Ag15), (Ge0:25 Se0:75 )80 Ag20 (Ag20) and (Ge0:25 Se0:75 )75 Ag25 (Ag25) (see Fig. 1) were synthesized from liquid mixtures of elemental Ge, Se (99.99% purity) and Ag (99.9% purity). Stoichiometric proportions of the reactants were loaded into 10 mm diameter quartz tubes. The loaded tubes were evacuated to 3 105 mbar and sealed. The batches were heated in a furnace at 910 C for 8 h. Melts were rapidly quenched by immersing the ampoules into an ice–water bath. Amorphous bulk samples, stable in air and with a greyish and shiny appearance, were obtained. 2.1. DSC experiment The thermal analysis was carried out in a differential scanning calorimeter under dynamic
Ar atmosphere. Previous DSC experiments showed a dependence with the sample grain size. In order to reduce this effect, bulk samples were milled with agate mortar and the grain size was ranging between 25 and 50 lm using a set of sieves. Another factor involved during the heating is the temperature gradients developed between the furnace and the sample, and within the sample itself. The magnitude of the temperature gradients increases with increasing mass [18]. Therefore we performed the DSC experiments employing always the same (low) mass. All powder samples weighting 5.00 0.05 mg were sealed in aluminum pans. Continuous heating experiments were performed at scan rates b ¼ 10, 20, 40 and 80 K min1 . Isothermal experiments were carried out at several temperatures (Ag10: 548, 553, 558 and 563 K, Ag15: 548, 553, 558 and 563; Ag20: 548, 553, 558, 563 and 568 K and Ag25: 553, 558, 563, 568, 573 and 578 K) and the measurement temperatures were attained heating the amorphous samples from room temperature to the annealing temperature at a rate of 80 K min1 .
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2.2. XRD experiment
ENDO
Ag10
Ag15
Ag20
Ag25 EXO
The rapidly quenched samples and their crystallization products were analyzed by XRD using monochromatized Cu(Ka) radiation. The crystallization processes of the amorphous sample Ag15 were registered by XRD during the annealing at several temperatures (398–773 K). In order to identify the crystallized phases occurring under both DSC regimes, XRD experiments were carried out at room temperature. For continuous heating regime, the samples were annealed at a heating rate of 20 K/min up to different temperatures and then they were rapidly cooled to room temperature at a rate of 200 K/min in order to retain the structure obtained. For isothermal regimen, the samples were annealed for 2 h at several temperatures and cooled to room temperature at a rate of 200 K/min.
-1 -1
0.1 JK g
3. Results and discussion 3.1. DSC curves Fig. 2 shows the calorimetric evolution of the as-quenched specimens under a continuous heating regime (b ¼ 10 K min1 ) from 450 to 680 K. The calorimetric curves show a shift of the base line consequent with the heat capacity changes from the glass to the undercooled liquid state at the glass transition, and two or three exothermic transformations occurring successively on increasing the temperature. Samples Ag10, Ag15 and Ag20 have a similar calorimetric behavior showing a glass transition and two exothermic peaks. The Ag25 sample is quite different. It shows a different shape of the glass transition shift, and a small exothermic peak (intermediate peak) between the two main peaks. Fig. 3 shows the DCS curves of sample Ag10 for all heating rates. This figure is representative of the behavior observed when changing the heating rate. That is, since on increasing b the transformations are shifted to higher temperatures showing the thermally activated nature of the process. Some of the peaks cannot be seen on increasing the heating rate. Consequently, the kinetic analysis of
β=10 Kmin
-1
460 480 500 520 540 560 580 600 620 640 660 680
Fig. 2. DSC curves (dH=dT vs T ) obtained along the crystallization of the studied samples for heating rate of 10 K/min.
the crystallization process will be restricted to the first exothermic peak. The changes with composition of the glass transition temperature, Tg (defined as the temperature of the curve inflexion point in the glass transition), and the crystallization peak temperatures, Tp determined for the different values of b are reported in Table 2. 3.2. Experimental XRD patterns The powder XRD patterns of the as-quenched samples confirm their glassy character. XRD experiments were carried out at several temperatures for sample Ag15 show the presence of the crystalline phase c-Ag8 GeSe6 (the high temperature allotropic form) up to 578 K. On increasing temperatures, above 623 K, the GeSe2 phase crystallizes. The Bragg lines associated to GeSe2
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β=80Kmin
ENDO
-1
β=40Kmin-1
β=20Kmin
-1
EXO
β=10Kmin-1
-1 -1
0.1 JK g
Sample Ag10 460 480 500 520 540 560 580 600 620 640 660 680
Fig. 3. DSC curves (dH =dT vs T ) obtained along the crystallization of the sample Ag10 for different heating rates.
disappear at 773 K (still remaining the c-Ag8 GeSe6 lines). It could indicate the beginning of the fusion. The XRD experiments performed after the continuos DSC heating up to the first crystallization peak only show lines corresponding to b0 Ag8 GeSe6 in all the samples. One can suppose that the crystalline phase c-Ag8 GeSe6 appears as the first crystallization product but during the cooling, b0 -Ag8 GeSe6 is formed due to its allotropic transformation at 48 C. Since the beginning of the second crystallization peak, and in the sample Ag25 at the intermediate peak, the GeSe2 appears. Lines of Se crystalline phase associated with the GeSe2 crystallization seem to be present in the XRD patterns. Figs. 4 and 5 show the XRD patterns of samples Ag20 and Ag25 corresponding to as-prepared glasses (bottom curve) and at different stages of the crystallization process. These also include the continuous regime DSC curves showing the different reached stages.
Figs. 6 and 7 show the XRD patterns for the samples Ag20 and Ag25 heated under isothermal regime. Bragg peaks corresponding to b0 Ag8 GeSe6 , GeSe2 and Se are identified. For low annealing temperatures only the ternary compound b0 -Ag8 GeSe6 appears in the XRD patterns (Tiso ¼ 548 and 553 K for sample Ag20 and Tiso ¼ 553 and 558 K for sample Ag25). This phase is observed in the sample Ag25 by XRD exclusively. At these temperatures it could not be detected any peak by DSC because its crystallization rate is too low. The first isothermal DSC peak in sample Ag25, is clearly observed at Tiso ¼ 563 K, and its XRD patterns correspond to the b0 Ag8 GeSe6 phase. On increasing the annealing temperature up to 568 K, GeSe2 becomes also a crystallization product. Selenium crystalline phase appears in the XRD patterns of the samples heated at the highest temperatures. Probably the presence of the selenium crystalline phase in the XRD patterns was due to its solidification from the remaining undercooled liquid during cooling after the heating treatment. The overall XRD and DSC results indicate that the as-quenched samples are amorphous. As observed in all the experiments, the first crystallization product is the Ag8 GeSe6 phase and the second product is the GeSe2 phase. Although the samples compositions are in the GeSe2 phase primary crystallization field, this phase appears as secondary crystallization product.
3.3. Analysis of the first crystallization process: Ag8 GeSe6 phase The kinetic analysis of the first crystallization peak has been performed from both continuous heating and isothermal calorimetric measurements. As it was observed by XRD, the first crystallization product is the Ag8 GeSe6 . This phase precipitates from the supersaturated liquid alloy as a primary phase. In other words, the compositions of the sample and that of the first crystallization product are not the same. Therefore, diffusion plays an important role in the last steps of the process [19].
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Table 2 Calorimetric parameters of amorphous phase: Tg , DCp , Tpi , DHpi (i ¼ 1, 2, 3) are the glass temperature, the heat capacity change in the glass transition, the crystallization temperature and the enthalpy of the first, second and third crystallization peak b (K/min)
10
20
40
80
Glass transition
First pick
Tg (K)
DCp (J/gK)
Tp1 (K)
DHp1 (J/g)
Intermediate pick
Second pick
Tpi (K)
DHpi (J/g)
Tp2 (K)
DHp2 (J/g)
Ag10 Ag15 Ag20 Ag25
494 3 488 3 488 3 496 3
0.12 0.02 0.18 0.02 0.18 0.02 0.15 0.02
579.1 0.5 578.3 0.5 580.0 0.5 595.0 0.5
6.2 0.5 8.6 0.5 10.8 0.5 15.2 0.5
615.2 0.5
1.5 0.5
672.8 0.5 665.0 0.5 657.5 0.5 652.4 0.5
15.5 0.5 12.1 0.5 10 0.5
Ag10 Ag15 Ag20 Ag25
494 3 491 3 490 3 499 3
0.12 0.02 0.15 0.02 0.16 0.02 0.17 0.02
588.8 0.5 586.5 0.5 587.1 0.5 602.3 0.5
5.5 0.5 8.6 0.5 11.5 0.5 16.4 0.5
624.3 0.5
1.5 0.5
677.5 0.5 665.0 0.5
8.5 0.5 8.0 0.5
Ag10 Ag15 Ag20 Ag25
497 3 494 3 493 3 500 3
0.10 0.02 0.12 0.02 0.13 0.02 0.15 0.02
596.5 0.5 594.5 0.5 596.9 0.5 611.6 0.5
6.20 0.5 9.0 0.5 11.5 0.5 18.2 0.5
635.6 0.5
2.1 0.5
Ag10 Ag15 Ag20 Ag25
501.5 3 496 3 497 3 503 3
0.08 0.02 0.12 0.02 0.12 0.02 0.13 0.02
608.6 0.5 605.3 0.5 607.7 0.5 618.4 0.5
6.6 0.5 10.0 0.5 13.1 0.5 18.0 0.5
647.0 1
1.5 0.5
These parameters were determined for the scan at 20 K/m.
In the DCS continuous regime curve, the glass transition appears as an endothermic shift in the DSC base line, due to the change of heat capacity from the amorphous to the undercooled liquid state, prior to crystallization. The primary crystallization follows as an exothermic transformation. After that, the base line remains close to the extrapolated base line of the amorphous state. This indicates that there is a significant change of the heat capacity of the sample during the first exothermic transformation due to the sample transforming from undercooled liquid to crystal. To account for the specific heat changes occurring during the transformation, a procedure already published was followed [20]. It requires estimation of the fraction x transformed from the DSC trace which includes the heat capacity change contribution. It is grounded on the decomposition of the overall signal, dQ=dt, in two parts: dQ=dt ¼ ðdQ=dtÞcrystallization
alone
þ ðdQ=dtÞDCp :
ð1Þ
The first part is proportional to the reaction rate, dx=dt, and the second one to the net specific heat
change occurring during the transformation, DCp , through the amount of already transformed material, x. The result of such a procedure allows an accurate determination of the reaction rate in continuous heating DSC measurements. An example is presented in Fig. 8 when applied to the DSC curve obtained at a heating rate of b ¼ 10 K min1 for sample Ag25. Fig. 9 shows the kinetic data obtained for the first crystallization process. These are: x versus temperature at several b, under continuous heating for the alloys Ag10, Ag15, Ag20 and Ag25. Such results show that crystallization is thermally activated and follows the general trend characteristic of an Arrhenius behavior. The crystallization by heat treatment of initially amorphous alloys occurs under high undercooling regime and traditionally there have been two different approaches to study this process. One of then, mostly empirical, is related to the general study of reaction kinetics and deals with the evaluation of the apparent activation energy of the process. The other one is grounded on the nucleation and growth theories based in the Johnson– Mehl–Avrami–Kolmogorov (JMAK) formalism
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Sample Ag20
T=600 K T=633 K T=574 K
T=683 K
β=20 Kmin-1 500
550
600
650
700
Temperature (K)
Tend =683 K
Tend=633 K
Tend=600 K
Tend=574 K
as-quenched 12
14
16
18
20
22
24
26
28
30
32
34
36
Fig. 4. XRD patterns of sample Ag20, as-quenched glass (bottom curve) and at different stages of the crystallization process under continuous heating. DSC curve showing the different reached stages is included. . Ag8 GeSe6 , GeSe2 , Se.
[21–23]. Both approaches are complementary and results of the analysis performed are presented in the following. 3.3.1. Determination of the kinetic parameters: apparent activation energy In the initial attempt, for a thermally activated crystallization process, it was assumed that the rate of primary crystallization dx=dt, may be given by the kinetic fundamental equation: dx=dt ¼ KðT Þf ðxÞ;
ð2Þ
where f ðxÞ reflects the mechanisms driving the crystallization and only depend on the transformed fraction and KðT Þ is the rate constant following the Arrhenius law, that is KðT Þ ¼ K0 expðEa =kT Þ
ð3Þ
Fig. 5. XRD patterns of sample Ag25, as-quenched glass (bottom curve), and at different stages of the crystallization process under continuous heating. DSC curve showing the different reached stages is included. . Ag8 GeSe6 , GeSe2 , Se.
with K0 the pre-exponential factor and Ea the apparent activation energy of the process. The apparent activation energy Ea , was obtained by the Kissinger method [24] (from continuous heating data) and by the maximum reaction rate method [25] (from the isothermal data). These methods provide the value of Ea without any need to evaluate dx=dt or x. Table 3 reports the Ea values obtained with both methods. As presented there, the apparent activation energy is quite similar in all the analyzed compositions (close to 200 kJ mol1 ). Such similarity in the Ea values is expected on considering that: (i) at high undercooling the temperature dependence of crystallization is dominated by that of the viscosity of the metastable liquid alloy, and (ii) the apparent activation energy of the viscosity has a small composition dependence.
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159
Sample Ag25
Sample Ag20
Tiso=578 K
Tiso= 568 K
Tiso=573 K
Tiso=568 K
Tiso= 553 K
Tiso=558 K
Tiso= 548 K Tiso=553 K
12
14
16
18
20
22
24
26
28
30
32
34
36
Fig. 6. XRD patterns of sample Ag20, after isochronal anneal (2 h) at several temperatures. . Ag8 GeSe6 , GeSe2 , Se.
Eqs. (2) and (3) may be rewritten in the form dx=dt ¼ fK0 f ðxÞg expðEa =kT Þ:
ð4Þ
To go further in the analysis, the simultaneous evaluation of Ea and K0 f ðxÞ was performed from the Arrhenius plot of Eq. (4) at fixed values of x, either from continuos heating or from isothermal data (multiple scan method [26]). Figs. 10 and 11 show the multiple scan method results from continuous heating data at x ¼ 0:2 and x ¼ 0:8 for samples Ag20 and Ag25, respectively. The kinetic parameters K0 and Ea are indicated in these figures. Again, the apparent activation energy obtained in the multiple scan method increases with the Ag content and decreases with x remaining close to 200 kJ mol1 . The spread in apparent activation energy values obtained by each method suggests that either the nucleation frequency or the growth rate or both of
12
14
16
18
20
22
24
26
28
30
32
34
36
Fig. 7. XRD patterns of sample Ag25, after isochronal anneal Se. (2 h) at several temperatures. . Ag8 GeSe6 , GeSe2 ,
them depend on the degree of advancement of the process. 3.3.2. Modeling of the initial steps of the primary crystallization The analysis of the crystallization using nucleation and growth theories is based in the JMAK formalism [21–23]. The JMAK formalism assumes spatially random nucleation. This theory is compatible with homogeneous, time, temperature or pressure dependent nucleation rates and also interface, diffusion and time, temperature and pressure dependent growth rates. However, nonrandom nucleation, non-isotropic growth protocols and finite size effects are not properly described by the JMAK theory [27]. For the initial crystallization stages (x 6 0:1) we can assume homogeneous nucleation followed by three-dimensional interface-controlled growth,
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Ag25
0.6
β ∆Cp
0.4
(dQ/dt)∆Cp
0.2
(dQ/dt) reaction alone
0.0 1.0
-0.05
Fraction transformated x
0.8
-0.10
-0.15
Ag20
0.6 0.4 0.2 0.0 1.0 0.8
Ag15
0.6 0.4 0.2 0.0 1.0 0.8
Ag10
0.6
-0.20
β=10 K/min β=20 K/min β=40 K/min β=80 K/min
0.4 560
570
580
590
600
610
0.2 0.0
Fig. 8. Decomposition of the overall DSC curve (thick line) in two parts. Qreaction alone proportional to dx=dt, and QDCp proportional to the crystallized fraction x.
even for primary crystallization [19]; then, the transformed fraction, in the JMAK formalism, is given by [27] • Under isothermal annealing at temperature T and time t:
550 560 570 580 590 600 610 620 630 640 650
Temperature (K) Fig. 9. Kinetic data x ¼ xðT ; bÞ obtained for the first crystallization process under continuous heating, respectively, for the alloy Ag10, Ag15, Ag20 and Ag25.
Table 3 Apparent activation energy obtained from the methods of Kissinger and maximum reaction rate First pick
3 4
xðT ; tÞ ¼ 1 expððp=3ÞIðT ÞuðT Þ t Þ ½TTT diagrams:
ð5Þ
• Under continuous heating at a constant rate b and temperature T : Z T xðT ; bÞ ¼ 1 exp b1 IðT 0 ÞvðT 0 ; T Þ dT 0 0
½THRT diagrams;
ð6Þ
where vðT 0 ; T Þ is the volume at temperature T of a nucleus formed at temperature T 0 , given by 3 Z T 1 0 00 00 vðT ; T Þ ¼ ð4p=3Þ b uðT ÞdT : ð7Þ T0
Ag10 Ag15 Ag20 Ag25
Kissinger method Ea (kJ/mol)
Max. reaction rate method Ea (kJ/mol)
197 10 216 10 202 10 224 10
194 10 233 10 195 10 218 10
In Eqs. (5) and (6) the nucleation frequency IðT Þ and the crystal growth uðT Þ are given by the classical theory of crystallization. The nucleation process can be classified into two main categories: homogeneous and heterogeneous. Homogeneous nucleation occurs in the bulk of the matrix; heterogeneous nucleation oc-
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161
liquid and the crystal. We assume that r is isotropic. In Eq. (8), DG is given by [30,31] DG ¼ DHm ½ð1 Tr Þð1 cÞ cTr lnðTr Þ:
ð9Þ
Here Tr ¼ T =Tm , c ¼ DCp =DSm , T is the temperature, DCp is the heat capacity difference between the liquid and the crystal, Tm , DSm and DHm are the melting temperature, melting entropy and melting enthalpy. In Eq. (8), r can be written as r ¼ aDHm [30]. a is difficult to evaluate and, normally is only estimated. Some interfacial energies of pure metals have been calculated [32,33]. The classical equation for the nucleation frequency I and the crystal growth u are given by [27,32]
Fig. 10. Multiple scan method for the sample Ag20.
IðT Þ ¼ ½4ðr=RT Þ
1=2
Nv b=g expðDG =RT Þ;
ð10Þ
uðT Þ ¼ ða0 kb=gÞ½1 expðDG=RT Þ;
ð11Þ
b ¼ kT =ð3pL2 a30 Þ;
ð12Þ
where Nv is the mean density of atoms, a0 the mean atomic diameter, k is the product of the fraction of surface sites where atoms are preferentially added and the length of the interface in units of a0 , and L is the mean interfacial thickness in units of a0 , and a Vogel–Fulcher expression for the viscosity g: Fig. 11. Multiple scan method for the sample Ag25.
g ¼ g0 expðA=ðT T0 ÞÞ:
curs in the presence of a solid interface of a foreign seed [28]. Since the original glasses are homogeneous, we assume that nuclei are formed via heterophase thermal composition fluctuations (or embryos) in the matrix. The free energy of the embryos is the sum of two terms: the free energy released due to the formation of a crystalline volume and the free energy absorbed due to the new surface created. The main assumption is the ÔcapillarityÕ approximation: the thickness of the interface region is small compared with the size of nuclei [29]. The formation Gibbs free energy DG of a spherical nucleus of critical size is given by DG ¼ 16pr3 =ð3DG2 Þ;
ð8Þ
where r is the molar interface energy between the spherical nucleus and the liquid and DG, the Gibbs free-energy difference between the supercooled
ð13Þ
The main complications and/or uncertainties relating to the nucleation are [34] (a) For alloys that normally crystallize to two or more phases of different compositions, bulk inter-diffusion of the constituent atoms will be required to facilitate the nucleation whereas the basic theory assumes transformation to a single phase iso-compositional with the liquid matrix. (b) It is generally recognized that a transient period is required before steady state nucleation is established. (c) Heterogeneous nucleation may also occur. We used the preceding assumptions to calculate the time–temperature transformation (TTT) and temperature–heating rate transformation (THRT)
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Table 4 Estimated and assessed values used to model the first crystallization steps of the samples Ag10, Ag15, Ag20 and Ag25 Sample Ag10
Ag20
Ag25
Estimated parameters: DHm ¼ 6:9 KJ/mol, r ¼ 0:32DHm , c ¼ 1:8 1.857 1010 1.862 1010 a0 (m) Tm (K) 840 851 L2 =k 10.0 10.0 T0 (K) 469 463 100 100 gðTm Þ (Poisse)
1.852 1010 857 10.0 463 100
1.852 1010 827 10.0 471 100
Fitted parameters Nv =L2 (1/m3 ) A (K)
7.15 1017 1100
1.78 1018 1200
5.09 1014 750
Ag15
4.87 1016 1000
for crystalline fraction x ¼ 106 , 103 and 0.1 using equations (5) and (6) following previous work [30,31,35,36]. It is well known that the crystallization is controlled by the level of undercooling DT ¼ Tm T , when T is close to Tm (solidification). If DT is very high (smaller T ), the degree of undercooling is not the limiting factor and the crystallization process becomes controlled by the atomic mobility or the viscosity. The competition between DT and the viscosity generates a point with the shortest time of the curve TTT (for a determined transformed fraction). This point is called ÔnoseÕ of the TTT curves and its coordinates are (tN , TN ). Summarizing, when T > TN , the limiting mechanism of the crystallization is the degree of undercooling through nucleation and crystal growth (since u / DT when DT ! 0). If T < TN , the crystallization is controlled by the viscosity. The crystallization of amorphous phases corresponds to the temperature range T < TN . In other words, the viscosity controls the crystallization at high undercooling. Therefore, as a first approximation, we assume that the thermodynamic parameters (DHm , r, cÞ used in Eqs. (8)–(12) are the same in all the samples and the different compositions only modify the values of viscosity (experimentally observed through the change of the glass transition temperature, Tg ) and Nv =L2 . This assumption agrees with the consideration that viscosity is controlling the transformation for the range of temperatures fitted in the curves TTT and THRT.
Some parameters (a0 , Tm , DHm , r, cÞ in Eqs. (8)– (12) were determined or estimated from either thermodynamic data (a0 , Tm , DHm , c) or experimental data (r) [35,36]. DHm was estimated using DCp , DHp1 , Tp1 and Tm . a0 was determined using density measurements [7]. Tm was estimated extrapolating the liquidus curves of the stable ternary diagram GeSeAg. c was estimated using DCp , DHm and Tm . The viscosity of liquid state at Tm ; and the parameters L2 =k and T0 are estimated following a previous work [27], that is gðTm Þ ffi 10 Pa s;
L2 =k ffi 10;
and
T0 ffi 0:95Tg :
The choice of T0 is proper because the viscosity is of the order of 1013 Poisse at T ¼ Tg . Assuming that only the phase Ag8 GeSe6 crystallizes in the initial steps of the first peak detected by DSC, the remaining parameters (Nv =L2 , A) were fitted using Eqs. (5) and (6) to reproduce the experimental DSC data (x ¼ 0:1). Both continuous heating and isothermal experimental data have been used. The estimated as well as the fitted parameters are given in Table 4. The calculated THRT and TTT curves for different values of the crystallized fraction (x ¼ 106 , 103 and 0.1) as well as the experimental data obtained for x ¼ 0:1 are reported in Figs. 12 and 13. 3.4. Discussion The results of Table 4 show that the viscosity (parameter A) and the pre-exponential factor of
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163
Ag10
Ag15
Ag20
Ag25
Fig. 12. TTT curves for the crystallization of Ag8 GeSe6 in the samples Ag10, Ag15, Ag20 and Ag25. Curves represent calculated values for x ¼ 106 (- - -), 103 ( ) and 0.1 (––) using Eq. (5), black squares correspond to experimental values for x ¼ 0:1.
the nucleation frequency Nv =L2 increase with the Ag content. The calculated TTT and THRT curves of Figs. 12 and 13 are in agreement with the experimental data. For each composition, the seven or eight experimental data (obtained by isothermal or continuous DSC regimen) are fitted by only two parameters (A and Nv =L2 ). The glass and crystallization temperatures Tg and Tc reported by Mitkova et al. [9] and Kawasaki et al. [10] are compared with our results in Fig. 14. The crystallization temperature presents a
Fig. 13. THRT curves for the crystallization of Ag8 GeSe6 in the samples Ag10, Ag15, Ag20 and Ag25. Curves represent calculated values for x ¼ 106 (- - -), 103 ( ) and 0.1 (––) using Eq. (6), black squares correspond to experimental values for x ¼ 0:1.
good agreement. We observe that Tc increases with the Ag content. On the other hand, the values obtained for the glass temperature do not exhibit a good agreement. Possibly this is due to the fact that the calorimetric curves are dependent on the sample preparation (sample mass, size powder) as is mentioned in Section 2. We can detach the following ideas. First, the values of Tg reported in Ref. [10] present a great dispersion. Second, Mitkova et al. [9] detected two glass transitions
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Fig. 14. Glass and crystallization temperatures Tg and Tc vs. Ag content plot for the studied glasses. The results are compared with the references: Mitkova et al. [9] () and (j), Kawasaki et al. [10] (O), this work ( ).
(black and white squares in Fig. 14). We only detected one glass transition in the samples Ag10, Ag15 and Ag20. A meticulous analysis of the calorimetric scans of the sample Ag25 could indicate a second glass transition at the technique detection limit. Third, Tg obtained by Kawasaki et al. [10] for the sample of composition GeSe3 is 23 K higher than that reported by Mitkova et al. [9]. The glass temperatures in our work agree with the values reported by Mitkova et al. [9] for the first glass transition.
Another possible and useful way to analyze the glass transition temperature values is by correlating them with the liquidus temperature, Tm , of the particular alloy. In the present study Tm was not measured; however, it was estimated from Ref. [11] and the binary Ge–Se phases diagram extrapolating the liquidus curves. This analysis indicates that no major changes will happen in the melting temperatures by increasing the Ag content of the alloys. The estimated Tm of the alloys are showed in Table 5. Consequently, Tg =Tm and Tm Tg were calculated (see Table 5). These approaches for Tg =Tm are in agreement with the fact that these alloys compositions are good glass-formers. The composition dependence of the GFA can be analyzed. The GFA is a non-quantifiable concept, however an idea can be introduced: the GFA of a sample can be defined as the capacity to obtain amorphous phase when the sample is rapidly quenched. If the cooling rate b is sufficiently high, the crystallization is inhibited. In this case, the sample in liquid state at the temperature Tm is rapidly quenched down to the glass temperature Tg where the undercooled liquid structure is frozen and the liquid is transformed in an amorphous phase. In order to compare to the GFA of different samples, we analyze the influence of Tm , Tg and b on the GFA. Then the GFA enhances when (a) the critical cooling rate in order to obtain the glass bM decreases, or (b) Tm Tg decreases (if b is maintained constant). Therefore, one can determine which compositions (in decreasing order) have greater GFA, i.e.: shorter Tm Tg in Table 5. Consequently, the best glass-former is the sample Ag25, following in decreasing order by Ag10, Ag15 and Ag20. Now, these results will be com-
Table 5 The glass and the melting temperatures Tg and Tm , Tg =Tm , Tm Tg and the greatest cooling rate bM in order to obtain the crystalline phase Sample Tg (K) 3 K Tm (K) 5 K Tg =Tm Tm Tg (K) bM (K/min) 15%
Ag10
Ag15
Ag20
Ag25
494 840 0.59 346 750
487 851 0.57 364 1500
487 857 0.57 370 2600
496 827 0.60 331 750
M.A. Ure~na et al. / Journal of Non-Crystalline Solids 320 (2003) 151–167
bM ¼ ðTm TN Þ=tN :
ð14Þ
The composition dependence of bM is shown in Table 5. Then, shorter bM involves greater GFA. In consequence, Ag25 and Ag10 are the best glass forming alloys, following Ag15 and Ag20. These results are in agreement with those calculated above. The critical cooling rate in order to obtain the glass bM in Table 5 is in the order of magnitude of the experimental cooling rate reported by Dejus et al. [3]. They estimated an effective cooling rate in the order of 500 K/s for the sample of composition Ag25. There is a significant shift on the onset of the Ag25 first crystallization peak towards high temperatures. On the contrary, for this alloy, the intermediate and the second crystallization peaks occur at a lower temperature than those of the other alloys. The amorphous GeSeAg samples show a quite unusual behavior in comparison with other ionic conducting glasses. As it was mentioned in Section 1, a sharp transition from semiconductor to superionic conductor in (Ge25 Se75 )100y Agy is detected [10]. The conductivity r (obtained from the Ref. [10]) is showed as a function of y in Fig. 15. It increases from 1013 to 105 X1 cm1 at about y ¼ 10. This is a phenomenon of percolation that was explained by Kawasaki et al. [10] considering a work of Armand et al. [14] for the GeSeAg and GeSAg systems. They suggested that GeXAg glasses (X ¼ S, Se), containing a small amount of Ag2 X, has an inhomogeneous structure composed of Ag2 X clusters and GeX2 network, which becomes homogeneous at high concentration of Ag2 X. The existence of these clusters could be questioned due to the first crystallization product
σ Vo
10
-4
10
-5
10
-6
10
-7
10
-8
10
-9
10
-10
10
-11
10
-12
10
-13
10
-14
σ (1/Ωcm)
pared with TTT curves of Fig. 12 calculating the critical cooling rate to obtain the glass. The critical cooling rate bM in order to obtain the crystalline phase Ag8 GeSe6 can be estimated using the ÔnoseÕ of the curves TTT for the curve of the transformed fraction x ¼ 106 (this transformed fraction, x ¼ 106 , is the experimental detection limit for a crystalline phase). The ÔnoseÕ coordinates are (tN , TN ). Therefore, bM can be estimated using
165
Fig. 15. Molar volume and the ionic conductivity vs. Ag content.
that is Ag8 GeSe6 . Furthermore, the diffusion of Ge and Se towards the Ag2 Se clusters for the formation of the Ag8 GeSe6 crystals should be very small. Although the idea of the phase separation is also reported by Mitkova et al. [9] to explain a bimodal glass transition temperature, the SRO of the glass (Table 1) does not show significant structural changes with the composition. At this stage, it is very interesting to compare the composition dependence of the ionic conductivity with other structural parameters. The molar volume V0 , obtained from density measurements [7] is also depicted in Fig. 15. For y < y the range of the conductivity values is (5 1013 –1 1012 ) X1 cm1 and V0 ffi 18:75–18 cm3 for y ¼ 0 and 5. For y > y ffi 10, r and V0 are practically constant (r ffi 5 104 X1 cm1 , V0 ffi 16 cm3 ). When the molar volume V0 is about 16 cm3 the GeSeAg glass is an ionic conductor. On the other hand, the molar volume for the ionic conducting crystalline phase Ag2 Se is V0 ffi 11:8 cm3 . Then, the value of the molar volume could be connected with the semiconductor–superionic transition. One could conclude that a necessary condition for the ionic conduction property in the AgGeSe system is V0 6 16:5 cm3 . A qualitative explication can be formulated assuming a homogeneous glass structure. As V0 increases, the atomic distance increases too, in particular the Agþ ion sites distance dþþ , and so does the activation energy for the hoping of the Agþ ion Eaþþ . If V0 is greater than a threshold
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value V0 , dþþ and Eaþþ is overmuch great and then the ionic conduction does not occur.
4. Conclusions Preliminary calorimetric experiments have shown an interesting dependence on the particle size of the sample. In order to obtain consistent calorimetric results, the bulk samples have been milled to have uniform grain size ranging between 25 and 50 lm. The first crystallization product is Ag8 GeSe6 as was observed by XRD in continuous heating calorimetric regime. In isothermal treatments, the crystallization of this phase is clearly detected both calorimetrically and by XRD in samples Ag10, Ag15, Ag20 and Ag25 (only at 568, 573 and 578 K). In sample Ag25, the ternary phase is observed at 553 and 558 K annealing temperatures by XRD exclusively. However, at these temperatures it could not be detected any peak by DSC because its crystallization rate is too low. The first step of the crystallization of the Ag8 GeSe6 phase in all the (Ge25 Se75 )100y Agy samples is modelled considering that the changes on the composition only modify the viscosity of the undercooled liquid. We propose that overlapping of the two processes is occurring in isothermal experiments at high temperatures: the crystallization of Ag8 GeSe6 and GeSe2 phases. We assume that the first steps correspond to the primary crystallization of Ag8 GeSe6 and then the GeSe2 crystallization starts. As mentioned above the results associated with the glass structure are controversial: • Armand et al. [14] suggested that glasses (GeX2 )ð100zÞ (Ag2 X)z (X ¼ Se, S), containing small amount of Ag2 X (z < 30), have an inhomogeneous structure composed of Ag2 X clusters and GeX2 network. The main size of these Ag2 X clusters is about 5.5 nm (z ¼ 10). The structure becomes homogeneous at high concentration of Ag2 X (z > 30). Must be noted that the samples (GeSe2 )ð100zÞ (Ag2 Se)z with z < 25 are in the limit of the glass forming range proposed by Mitkova et al. [9].
• Mitkova et al. [9] proposed that ternary (Gej Se100j )100y Agy bulk glasses in the Se-rich region (j < 33.33 and y < 30) are shown to be intrinsically phase separated into an Ag2 Se-rich glass and a residual Get Se100t . • Using neutron diffraction [3] and differential Xray scattering [8], some authors indicate that the structure of (Ge25 Se75 )75 Ag25 is homogeneous. Our results indicate that the existence of an inhomogeneous glass structure composed of Ag2 Se clusters and GeSe2 network could be questioned in the composition range studied (Ag at.% ¼ 10, 15, 20 and 25). Acknowledgements Financial support from the Universidad de Buenos Aires in project UBACYT TI02 and from the Comissi o Interdepartamental de Recerca y Tecnologıa (CIRIT) in project ACI-2000-19 is acknowledged. One of the authors (M.A.U.) gratefully acknowledges the grant released by the Instituto de Cooperaci on Iberoamericana of Spain. Thanks are also due to Lic. J.L. Tour on for his help in the data processing. References [1] Xingwei Fang, W.J. Bresser, P. Boolchand, Phys. Rev. Lett. 78 (23) (1997) 4423. [2] J. Hautala, S. Yamaski, P.C. Taylor, J. Non-Cryst. Solids 114 (1989) 85. [3] R.J. Dejus, S. Susman, K.J. Volin, D.G. Montague, D.L. Price, J. Non-Cryst. Solids 143 (1992) 162. [4] A. Pradel, M. Ribes, J. Solid State Chem. 96 (1992) 247. [5] Z.U. Borisova, Glassy Semiconductors, Plenum, New York, 1981. [6] Z.U. Borisova, T.S. Rykova, E.Yu. Turkina, A.R. Tabolin, Izv. Akad. Nauk. SSSR Neorg. Mater. 20 (1984) 1796. [7] A. Piarristeguy, M. Mirandou, M. Fontana, B. Arcondo, J. Non-Cryst. Solids 273 (2000) 30. [8] J.D. Westwood, P. Gergopoulos, D.H. Whitmore, J. NonCryst. Solids 107 (1988) 88. [9] M. Mitkova, Yu Wang, P. Boolchand, Phys. Rev. Lett. 83 (19) (1999) 3848. [10] M. Kawasaki, J. Kawamura, Y. Nakamura, M. Aniya, Solid State Ion. 123 (1999) 259.
M.A. Ure~na et al. / Journal of Non-Crystalline Solids 320 (2003) 151–167 [11] A. Prince, in: G. Petzow, G. Effenberg (Eds.), Ternary Alloys, VCH, New York, 1988, p. 195. [12] A. Pradel, M. Ribes, Mater. Chem. Phys. (1989) 45. [13] N. Ramesh Rao, P.S.R. Krishna, S. Basu, B.A. Dasannacharya, K.S. Sangunni, E.S.R. Gopal, J. Non-Cryst. Solids 240 (1998) 221. [14] P. Armand, A. Ibanez, H. Dexpert, D. Bittencourt, D. Raoux, E. Philippot, J. Phys. IV Colloq. C2 2 (1992) C2– 189. [15] S. Susman, K.J. Volin, D.G. Montague, D.L. Price, J. Non-Cryst. Solids 125 (1990) 168. [16] P. Vashishta, R.K. Kalia, I. Ebbsj€ o, Phys. Rev. B 39 (1989) 1651. [17] G. Lucovsky, F. Galeener, R.C. Keeser, R. Geils, H. Six, Phys. Rev. B 10 (1974) 5134. [18] T. Hatakeyama, F.X. Quinn, Thermal Analysis Fundamentals and Applications to Polymer Science, John Wiley, Chichester, 1994. [19] M. Fontana, B. Arcondo, M.T. Mora, N. Clavaguera, Philos. Mag. B 80 (2000) 1833. [20] N. Clavaguera, M.T. Clavaguera-Mora, M. Fontana, J. Mater. Res 13 (1998) 744. [21] M. Avrami, J. Chem. Phys. 7 (1939) 1103; M. Avrami, J. Chem. Phys. 8 (1940) 212; M. Avrami, J. Chem. Phys. 9 (1941) 177. [22] A.N. Kolmogorov, Bull. Acad. Sci. USSR Phys. Ser. 1 (1937) 355.
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[23] W.A. Johnson, P.A. Mehl, Trans. Am. Inst. Min. Metall. Engrs. 135 (1939) 416. [24] H.E. Kissinger, Anal. Chem. 2 (1957) 1702. [25] H.S. Chen, J. Non-Cryst. Solids 27 (1978) 257. [26] B. Carrol, Thermochim. Acta 3 (1972) 449. [27] M.T. Clavaguera-Mora, N. Clavaguera, D. Crespo, T. Pradell, Prog. Mater. Sci. 47 (6) (2002) 559. [28] J.A. Dirksen, T.A. Ring, Chem. Eng. Sci. 46 (10) (1991) 2389. [29] W. Kurz, D.J. Fisher, Fundamentals of Solidification, TransTech, Aedermannsdorf, 1986. [30] M.T. Clavaguera-Mora, J. Alloys Compd. 220 (1995) 197. [31] J.A. Diego, M.T. Clavaguera-Mora, N. Clavaguera, Mater. Sci. Eng. A 179&180 (1994) 526. [32] D. Turnbull, J. Appl. Phys. 21 (1950) 1022. [33] J.H. Perepezco, in: R. Mehrabian, B.H. Kear, M. Cohen (Eds.), Rapid Solidificaion Processing Principles and Technologies, Claitoras, Baton Rouge, LA, 1980, p. 56. [34] H.A. Davies, in: M. Vazquez, A. Hernando (Eds.), Nanostructured and Non-Crystalline Materials, Proceeding of the Fourth International Workshop on NonCrystalline Solids, World Scientific, Madrid, 1995, p. 3. [35] N. Clavaguera, J. Non-Cryst. Solids 162 (1993) 40. [36] M. Fontana, B. Arcondo, M.T. Clavaguera-Mora, N. Clavaguera, J.M. Greneche, J. Appl. Phys. 88 (6) (2000) 3276.
Crystallization processes of Ag–Ge–Se superionic glasses M.A. Ure~ na a, M. Fontana
a,*
, B. Arcondo a, M.T. Clavaguera-Mora
b
a
b
Laboratorio de S olidos Amorfos, Facultad de Ingenierıa, Universidad de Buenos Aires, Paseo Col on 850, (1063) Buenos Aires, Argentina Grup de Fısica dels Materials I, Facultat de Ci encies, Universitat Aut onoma de Barcelona, (08193) Bellaterra, Spain Received 19 February 2002; received in revised form 4 October 2002
Abstract The interest in superionic systems has increased in recent years because of the potential application of these materials as solid electrolytes. In this field, amorphous materials present important advantages when compared to the crystalline solids: larger conductivity, isotropy and absence of grain boundaries. In this work, amorphous alloys of compositions (Ge25 Se75 )100y Agy with y ¼ 10, 15, 20 and 25 at.% have been studied. Amorphous samples in bulk were obtained from the liquid by water quenching (melt-quenching technique). The crystallization kinetics of the amorphous alloys have been studied under continuous heating and isothermal conditions by means of differential scanning calorimetry. A glass transition and two exothermic transformations were observed in all the samples. The quenched samples and the crystallization products have been characterized by X-ray diffraction. The primary crystallization of the ternary phase Ag8 GeSe6 and the secondary phase GeSe2 was observed. The glass and crystallization temperatures, the activation energy and the crystallization enthalpy are reported. The first step of the crystallization of the Ag8 GeSe6 phase in all the (Ge25 Se75 )100y Agy samples is modelled taking into account the Johnson–Mehl–Avrami–Kolmogorov theory and considering that the changes in the composition only modify the viscosity of the undercooled liquid. The transformation diagrams (TTT and THRT) are calculated and the glass forming ability is analyzed. The experimental results are discussed and correlated with the structures proposed for the glass. The present results and conclusions are also compared with those reported by other authors. 2003 Elsevier Science B.V. All rights reserved.
1. Introduction Ge–Se glasses have been widely studied due to their extended amorphization composition range [1]. The fact that bulk glasses are easily obtained makes Ge–Se an ideal system to investigate a great variety of properties and their correlation with
*
Corresponding author. E-mail address: mfontan@fi.uba.ar (M. Fontana).
structure and composition. It has been reported [2] that the electric transport in these glasses can be strongly affected by the addition of metals. GeSeAg glasses evolve from semiconductors to superionic conductors as Ag concentration is increased (r ¼ 1 104 X1 cm1 for Ag25 Se56:25 Ge18:5 glass at room temperature) [3,4]. The interest in superionic glasses has increased in recent years because of the potential application of these materials as solid electrolytes. In this field, the amorphous materials present important advantages when
0022-3093/03/$ - see front matter 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-3093(03)00022-X
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compared to the crystalline solids: larger conductivity, isotropy and absence of grain border [5]. Borisova et al. [6] studied the glass forming ability (GFA) of this ternary system by water quenching. They found that in samples with a composition Ge25 Se75 the vitreous character could be retained introducing a maximum Ag content of 30 at.%. The structure of these glasses has been studied by several authors employing different sources of radiation [3,7,8]. Several associations have been reported and also a strong medium range order that the increasing of Ag concentration weakens. Moreover, a dual chemical role of Ag has been reported [9], network glass former and network modifier behaviors. In the second class of glasses, a bimodal glass transition temperature (Tg ) is reported and attributed to a phase separation of Ag centered structures (resembling a-Ag2 Se) from the host matrix. Recently, electrical properties of (Ge25 Se75 )100y Agy glasses were investigated by impedance spectroscopy. As the concentration of silver is increased the total electrical conductivity steeply increases from 1013 to 105 X1 cm1 at about y ¼ 10 [10]. They supposed a percolation transition is happening at y . The aim of this work is to analyze the thermal stability, the crystallization kinetics and the crystallization products of bulk glasses of atomic compositions (Ge25 Se75 )100y Agy with y ¼ 10, 15, 20 and 25 using differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The dependence of the crystallization kinetics on the concentration of Ag is discussed with reference to the equilibrium phase diagram and the amorphous structure.
system. The crystalline compound GeSe2 has a congruent melt point at 742 C and the compound Ag2 Se, at 897 C. On Ag2 Se–GeSe2 pseudobinary system the ternary compound Ag8 GeSe6 forms and melts congruently at 902 C. The Ag8 GeSe6 exists in at least three modifications: c-Ag8 GeSe6 a fcc structure from 902 to 48 C, b0 -Ag8 GeSe6 with orthorhombic structure from 48 to )4 C and, a0 Ag8 GeSe6 is stable below )4 C. The Ag8 GeSe6 separates two eutectics on the pseudobinary Ag2 Se–GeSe2 . The eutectic e1 : GeSe2 –Ag8 GeSe6 is located at 29 at.% Ag and 560 C. The eutectic e2 Ag2 Se–Ag8 GeSe6 occurs at 59 at.% Ag and 810 C (see Fig. 1). The pseudobinary section Ag8 GeSe6 –Se subdivides the partial ternary system Ag2 Se–GeSe2 –Se. A monotectic reaction, L1 () Ag8 GeSe6 + L2 , occurs at 700 C with L1 containing 50 at.% Se and L2 96 at.% Se. This reaction falls in temperature within the ternary and closures the region of the liquid immiscibility at a critical tie line L1 / L2 () Ag8 GeSe6 at 520 C. The eutectic separation e1 is shown by a monovariant curve descending from the eutectic towards the Se corner. In the projection of the liquidus, the monovariant
1.1. Background about the Ag–Ge–Se system 1.1.1. The Ag–Ge–Se equilibrium system The equilibrium phase diagram of the Ag–Ge– Se system was compilated and evaluated by Prince [11]. The Ag2 Se–GeSe2 pseudobinary system allows the invariant equilibria in the ternary system to be considered as resulting from the two partial ternary systems Ag2 Se–GeSe2 –Se and Ag2 Se– GeSe2 –Ge–Ag. All samples compositions studied in this work are included in the first partial ternary
Fig. 1. Liquidus surface of the AgGeSe ternary system in the Se rich corner. Ag10, Ag15, Ag20 and Ag25 are the compositions of the studied samples.
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curve intersects the liquid immiscibility gap at a composition 29 at.% Ag, 15 at.% Ge and 56 at.% Se (L3 ), showing the presence of the ternary monotectic reaction, L3 ! L4 + Ag8 GeSe6 + GeSe2 at 400 C (see Fig. 1). The solidification in the Ag8 GeSe6 –GeSe2 –Se system ends with a eutectic reaction in the Se rich corner at 217 C. All samples compositions studied in this work are at the homogeneous liquid region and at the GeSe2 primary crystallization field (see Fig. 1). 1.1.2. The Ag–Ge–Se glass Network former compounds are covalent alloys such as oxides (or chalcogenides) of silicon, boron, phosphorus, germanium, etc. They generally have a relevant glass-forming tendency. The crystalline structure consists of chains of tetrahedrons or triangles. However, a certain dispersion of valence angles and bond lengths appears in the vitreous phase and only short-range order (SRO) is conserved. Intermediate range order (IRO) appears to be maintained in certain cases and the glass then consists of clusters [12]. The GeSe system is an example of this kind of glasses. Network modifiers are compounds with a marked ionic feature and include in particular the oxides and chalcogenides of alkalis, alkaline earths and silver ions. They do not form glasses alone, but can easily react with a former and become incorporated in its network. The chemical reaction that results from the interaction can take the form of the breaking of chalcogenide bonds that connect two former cations and leads to the creation of ionic bonds. It is difficult to specify the precise environment of the modifier cation [12]. The structure of AgGeSe glasses is not yet fully determined, however, the basic framework of this structure is based on the Gey Se100y glassy network. There are many structural investigations on glassy Gey Se100y . All the reports indicate that the SRO in the GeSe2 glass is due to Ge(Se1=2 )4 tetrahedra [13,14]. However, the interconnection of the tetrahedra has given rise to many controversies; for example, assessing the proportion of edgeshared to corner-shared tetrahedra [15,16]. When the atomic composition moves towards the Se corner, the homopolar bond contribution to SRO
153
increases, i.e.: Se-rich Gey Se100y glasses contain Se-chains (homopolar bond Se–Se) which are cross-linked with the Ge(Se1=2 )4 tetrahedra [13,14]. This result supports the idea that the formation of these binary glasses is controlled by a chemically ordered process [17]. For y ¼ 20, 33 and 40 there is evidence for some of the tetrahedra being in an edge-shared configuration. The number of edgeshared tetrahedra in these glasses increases with increasing Ge content [13]. It was also established that a well-defined IRO exists in Gex Se100x glasses. The Ôpre-peakÕ or the first sharp diffraction peak (FSDP) in the structure 1 [13]. factor SðqÞ is around 1.0 A The GeSeAg glass is likely to share many structure and transport characteristic with the (network former)–(network modifier) family of glasses. In this glass, Ge is termed the network forming cation, Ag the mobile cation and Se the anion [8]. The previous work in the (Ge25 Se75 )75 Ag25 glass indicates that Ge remains tetrahedrally coordinated by Se, as it is in Gey Se100y glasses. The first . The network forming neighbour distance is 2.38 A character of Ge is apparently unchanged [3,7,8]. In the case of the Ag, the position of the first-neigh agrees with Ag–Se distances bour at 2.62–2.68 A found in Ag8 GeSe6 and Ag2 Se crystalline compounds [3,8]. Also the SRO in (Ge25 Se75 )100-y Agy glasses (y ¼ 0–25) was examined by XRD using Mo(Ka) radiation at room temperature [7]. The 1 , shows a systematic FSDP, located at q 1 A increase in intensity with decreasing Ag concentration revealing a substantial decrease of the IRO [3,7]. The coordination numbers and the bond lengths of the correlation GeSe, SeSe, SeAg, and AgAg as a function of composition were determined from the radial distribution function [7] and are reproduced in Table 1. Some studies propose that the (Ge25 Se75 )75 Ag25 glass is homogeneous [3,8]. However, in a recent study, ternary (Gez Se100z )100y Agy bulk glasses in the Se-rich region (z < 33:3) are reported to be intrinsically phase separated into an Ag2 Se-rich glass and a residual Get Se100t (t > z at y 6¼ 0) with Ag acting as a network modifier [10]. They observed bimodal glass transition temperatures. In contrast, Ge-rich glasses (z > 40) are homogeneous, wherein
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Table 1 The coordination numbers and the bond lengths of the correlation GeSe, SeSe, SeAg, and AgAg ) ) x Correlation Distance ( 0.05 A Width (A
Coordination numbers ( 0.1)
0
GeSe and SeSe (1st neighbours) SeSe (2nd neighbours)
2.36 3.87
0.37 0.84
2.5 11.5 0.4
10
GeSe and SeSe (1st neighbours) AgSe AgAg SeSe (2nd neighbours)
2.37 2.67 3.05 3.85
0.35 0.28 0.22 0.78
2.2 0.4 0.25 11.0 0.4
15
GeSe and SeSe (1st neighbours) AgSe AgAg SeSe (2nd neighbours)
2.37 2.67 3.05 3.89
0.35 0.31 0.31 0.80
2.05 0.65 0.35 11.0 0.4
20
GeSe and SeSe (1st neighbours) AgSe AgAg SeSe (2nd neighbours)
2.39 2.67 3.05 3.88
0.34 0.30 0.32 0.76
1.7 1.05 0.7 10.7 0.4
25
GeSe and SeSe (1st neighbours) AgSe AgAg SeSe (2nd neighbours)
2.39 2.67 3.06 3.90
0.38 0.37 0.37 0.73
1.55 1.3 0.85 10.0 0.4
They were determined from the radial distribution function study of the glasses (Ge25 Se75 )100x Agx [7].
Ag acts as a network former, replacing available Ge sites of the backbone to be 3-fold coordinated to Se. 2. Experimental procedure Samples with compositions (Ge0:25 Se0:75 )90 Ag10 (Ag10), (Ge0:25 Se0:75 )85 Ag15 (Ag15), (Ge0:25 Se0:75 )80 Ag20 (Ag20) and (Ge0:25 Se0:75 )75 Ag25 (Ag25) (see Fig. 1) were synthesized from liquid mixtures of elemental Ge, Se (99.99% purity) and Ag (99.9% purity). Stoichiometric proportions of the reactants were loaded into 10 mm diameter quartz tubes. The loaded tubes were evacuated to 3 105 mbar and sealed. The batches were heated in a furnace at 910 C for 8 h. Melts were rapidly quenched by immersing the ampoules into an ice–water bath. Amorphous bulk samples, stable in air and with a greyish and shiny appearance, were obtained. 2.1. DSC experiment The thermal analysis was carried out in a differential scanning calorimeter under dynamic
Ar atmosphere. Previous DSC experiments showed a dependence with the sample grain size. In order to reduce this effect, bulk samples were milled with agate mortar and the grain size was ranging between 25 and 50 lm using a set of sieves. Another factor involved during the heating is the temperature gradients developed between the furnace and the sample, and within the sample itself. The magnitude of the temperature gradients increases with increasing mass [18]. Therefore we performed the DSC experiments employing always the same (low) mass. All powder samples weighting 5.00 0.05 mg were sealed in aluminum pans. Continuous heating experiments were performed at scan rates b ¼ 10, 20, 40 and 80 K min1 . Isothermal experiments were carried out at several temperatures (Ag10: 548, 553, 558 and 563 K, Ag15: 548, 553, 558 and 563; Ag20: 548, 553, 558, 563 and 568 K and Ag25: 553, 558, 563, 568, 573 and 578 K) and the measurement temperatures were attained heating the amorphous samples from room temperature to the annealing temperature at a rate of 80 K min1 .
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2.2. XRD experiment
ENDO
Ag10
Ag15
Ag20
Ag25 EXO
The rapidly quenched samples and their crystallization products were analyzed by XRD using monochromatized Cu(Ka) radiation. The crystallization processes of the amorphous sample Ag15 were registered by XRD during the annealing at several temperatures (398–773 K). In order to identify the crystallized phases occurring under both DSC regimes, XRD experiments were carried out at room temperature. For continuous heating regime, the samples were annealed at a heating rate of 20 K/min up to different temperatures and then they were rapidly cooled to room temperature at a rate of 200 K/min in order to retain the structure obtained. For isothermal regimen, the samples were annealed for 2 h at several temperatures and cooled to room temperature at a rate of 200 K/min.
-1 -1
0.1 JK g
3. Results and discussion 3.1. DSC curves Fig. 2 shows the calorimetric evolution of the as-quenched specimens under a continuous heating regime (b ¼ 10 K min1 ) from 450 to 680 K. The calorimetric curves show a shift of the base line consequent with the heat capacity changes from the glass to the undercooled liquid state at the glass transition, and two or three exothermic transformations occurring successively on increasing the temperature. Samples Ag10, Ag15 and Ag20 have a similar calorimetric behavior showing a glass transition and two exothermic peaks. The Ag25 sample is quite different. It shows a different shape of the glass transition shift, and a small exothermic peak (intermediate peak) between the two main peaks. Fig. 3 shows the DCS curves of sample Ag10 for all heating rates. This figure is representative of the behavior observed when changing the heating rate. That is, since on increasing b the transformations are shifted to higher temperatures showing the thermally activated nature of the process. Some of the peaks cannot be seen on increasing the heating rate. Consequently, the kinetic analysis of
β=10 Kmin
-1
460 480 500 520 540 560 580 600 620 640 660 680
Fig. 2. DSC curves (dH=dT vs T ) obtained along the crystallization of the studied samples for heating rate of 10 K/min.
the crystallization process will be restricted to the first exothermic peak. The changes with composition of the glass transition temperature, Tg (defined as the temperature of the curve inflexion point in the glass transition), and the crystallization peak temperatures, Tp determined for the different values of b are reported in Table 2. 3.2. Experimental XRD patterns The powder XRD patterns of the as-quenched samples confirm their glassy character. XRD experiments were carried out at several temperatures for sample Ag15 show the presence of the crystalline phase c-Ag8 GeSe6 (the high temperature allotropic form) up to 578 K. On increasing temperatures, above 623 K, the GeSe2 phase crystallizes. The Bragg lines associated to GeSe2
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β=80Kmin
ENDO
-1
β=40Kmin-1
β=20Kmin
-1
EXO
β=10Kmin-1
-1 -1
0.1 JK g
Sample Ag10 460 480 500 520 540 560 580 600 620 640 660 680
Fig. 3. DSC curves (dH =dT vs T ) obtained along the crystallization of the sample Ag10 for different heating rates.
disappear at 773 K (still remaining the c-Ag8 GeSe6 lines). It could indicate the beginning of the fusion. The XRD experiments performed after the continuos DSC heating up to the first crystallization peak only show lines corresponding to b0 Ag8 GeSe6 in all the samples. One can suppose that the crystalline phase c-Ag8 GeSe6 appears as the first crystallization product but during the cooling, b0 -Ag8 GeSe6 is formed due to its allotropic transformation at 48 C. Since the beginning of the second crystallization peak, and in the sample Ag25 at the intermediate peak, the GeSe2 appears. Lines of Se crystalline phase associated with the GeSe2 crystallization seem to be present in the XRD patterns. Figs. 4 and 5 show the XRD patterns of samples Ag20 and Ag25 corresponding to as-prepared glasses (bottom curve) and at different stages of the crystallization process. These also include the continuous regime DSC curves showing the different reached stages.
Figs. 6 and 7 show the XRD patterns for the samples Ag20 and Ag25 heated under isothermal regime. Bragg peaks corresponding to b0 Ag8 GeSe6 , GeSe2 and Se are identified. For low annealing temperatures only the ternary compound b0 -Ag8 GeSe6 appears in the XRD patterns (Tiso ¼ 548 and 553 K for sample Ag20 and Tiso ¼ 553 and 558 K for sample Ag25). This phase is observed in the sample Ag25 by XRD exclusively. At these temperatures it could not be detected any peak by DSC because its crystallization rate is too low. The first isothermal DSC peak in sample Ag25, is clearly observed at Tiso ¼ 563 K, and its XRD patterns correspond to the b0 Ag8 GeSe6 phase. On increasing the annealing temperature up to 568 K, GeSe2 becomes also a crystallization product. Selenium crystalline phase appears in the XRD patterns of the samples heated at the highest temperatures. Probably the presence of the selenium crystalline phase in the XRD patterns was due to its solidification from the remaining undercooled liquid during cooling after the heating treatment. The overall XRD and DSC results indicate that the as-quenched samples are amorphous. As observed in all the experiments, the first crystallization product is the Ag8 GeSe6 phase and the second product is the GeSe2 phase. Although the samples compositions are in the GeSe2 phase primary crystallization field, this phase appears as secondary crystallization product.
3.3. Analysis of the first crystallization process: Ag8 GeSe6 phase The kinetic analysis of the first crystallization peak has been performed from both continuous heating and isothermal calorimetric measurements. As it was observed by XRD, the first crystallization product is the Ag8 GeSe6 . This phase precipitates from the supersaturated liquid alloy as a primary phase. In other words, the compositions of the sample and that of the first crystallization product are not the same. Therefore, diffusion plays an important role in the last steps of the process [19].
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157
Table 2 Calorimetric parameters of amorphous phase: Tg , DCp , Tpi , DHpi (i ¼ 1, 2, 3) are the glass temperature, the heat capacity change in the glass transition, the crystallization temperature and the enthalpy of the first, second and third crystallization peak b (K/min)
10
20
40
80
Glass transition
First pick
Tg (K)
DCp (J/gK)
Tp1 (K)
DHp1 (J/g)
Intermediate pick
Second pick
Tpi (K)
DHpi (J/g)
Tp2 (K)
DHp2 (J/g)
Ag10 Ag15 Ag20 Ag25
494 3 488 3 488 3 496 3
0.12 0.02 0.18 0.02 0.18 0.02 0.15 0.02
579.1 0.5 578.3 0.5 580.0 0.5 595.0 0.5
6.2 0.5 8.6 0.5 10.8 0.5 15.2 0.5
615.2 0.5
1.5 0.5
672.8 0.5 665.0 0.5 657.5 0.5 652.4 0.5
15.5 0.5 12.1 0.5 10 0.5
Ag10 Ag15 Ag20 Ag25
494 3 491 3 490 3 499 3
0.12 0.02 0.15 0.02 0.16 0.02 0.17 0.02
588.8 0.5 586.5 0.5 587.1 0.5 602.3 0.5
5.5 0.5 8.6 0.5 11.5 0.5 16.4 0.5
624.3 0.5
1.5 0.5
677.5 0.5 665.0 0.5
8.5 0.5 8.0 0.5
Ag10 Ag15 Ag20 Ag25
497 3 494 3 493 3 500 3
0.10 0.02 0.12 0.02 0.13 0.02 0.15 0.02
596.5 0.5 594.5 0.5 596.9 0.5 611.6 0.5
6.20 0.5 9.0 0.5 11.5 0.5 18.2 0.5
635.6 0.5
2.1 0.5
Ag10 Ag15 Ag20 Ag25
501.5 3 496 3 497 3 503 3
0.08 0.02 0.12 0.02 0.12 0.02 0.13 0.02
608.6 0.5 605.3 0.5 607.7 0.5 618.4 0.5
6.6 0.5 10.0 0.5 13.1 0.5 18.0 0.5
647.0 1
1.5 0.5
These parameters were determined for the scan at 20 K/m.
In the DCS continuous regime curve, the glass transition appears as an endothermic shift in the DSC base line, due to the change of heat capacity from the amorphous to the undercooled liquid state, prior to crystallization. The primary crystallization follows as an exothermic transformation. After that, the base line remains close to the extrapolated base line of the amorphous state. This indicates that there is a significant change of the heat capacity of the sample during the first exothermic transformation due to the sample transforming from undercooled liquid to crystal. To account for the specific heat changes occurring during the transformation, a procedure already published was followed [20]. It requires estimation of the fraction x transformed from the DSC trace which includes the heat capacity change contribution. It is grounded on the decomposition of the overall signal, dQ=dt, in two parts: dQ=dt ¼ ðdQ=dtÞcrystallization
alone
þ ðdQ=dtÞDCp :
ð1Þ
The first part is proportional to the reaction rate, dx=dt, and the second one to the net specific heat
change occurring during the transformation, DCp , through the amount of already transformed material, x. The result of such a procedure allows an accurate determination of the reaction rate in continuous heating DSC measurements. An example is presented in Fig. 8 when applied to the DSC curve obtained at a heating rate of b ¼ 10 K min1 for sample Ag25. Fig. 9 shows the kinetic data obtained for the first crystallization process. These are: x versus temperature at several b, under continuous heating for the alloys Ag10, Ag15, Ag20 and Ag25. Such results show that crystallization is thermally activated and follows the general trend characteristic of an Arrhenius behavior. The crystallization by heat treatment of initially amorphous alloys occurs under high undercooling regime and traditionally there have been two different approaches to study this process. One of then, mostly empirical, is related to the general study of reaction kinetics and deals with the evaluation of the apparent activation energy of the process. The other one is grounded on the nucleation and growth theories based in the Johnson– Mehl–Avrami–Kolmogorov (JMAK) formalism
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Sample Ag20
T=600 K T=633 K T=574 K
T=683 K
β=20 Kmin-1 500
550
600
650
700
Temperature (K)
Tend =683 K
Tend=633 K
Tend=600 K
Tend=574 K
as-quenched 12
14
16
18
20
22
24
26
28
30
32
34
36
Fig. 4. XRD patterns of sample Ag20, as-quenched glass (bottom curve) and at different stages of the crystallization process under continuous heating. DSC curve showing the different reached stages is included. . Ag8 GeSe6 , GeSe2 , Se.
[21–23]. Both approaches are complementary and results of the analysis performed are presented in the following. 3.3.1. Determination of the kinetic parameters: apparent activation energy In the initial attempt, for a thermally activated crystallization process, it was assumed that the rate of primary crystallization dx=dt, may be given by the kinetic fundamental equation: dx=dt ¼ KðT Þf ðxÞ;
ð2Þ
where f ðxÞ reflects the mechanisms driving the crystallization and only depend on the transformed fraction and KðT Þ is the rate constant following the Arrhenius law, that is KðT Þ ¼ K0 expðEa =kT Þ
ð3Þ
Fig. 5. XRD patterns of sample Ag25, as-quenched glass (bottom curve), and at different stages of the crystallization process under continuous heating. DSC curve showing the different reached stages is included. . Ag8 GeSe6 , GeSe2 , Se.
with K0 the pre-exponential factor and Ea the apparent activation energy of the process. The apparent activation energy Ea , was obtained by the Kissinger method [24] (from continuous heating data) and by the maximum reaction rate method [25] (from the isothermal data). These methods provide the value of Ea without any need to evaluate dx=dt or x. Table 3 reports the Ea values obtained with both methods. As presented there, the apparent activation energy is quite similar in all the analyzed compositions (close to 200 kJ mol1 ). Such similarity in the Ea values is expected on considering that: (i) at high undercooling the temperature dependence of crystallization is dominated by that of the viscosity of the metastable liquid alloy, and (ii) the apparent activation energy of the viscosity has a small composition dependence.
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159
Sample Ag25
Sample Ag20
Tiso=578 K
Tiso= 568 K
Tiso=573 K
Tiso=568 K
Tiso= 553 K
Tiso=558 K
Tiso= 548 K Tiso=553 K
12
14
16
18
20
22
24
26
28
30
32
34
36
Fig. 6. XRD patterns of sample Ag20, after isochronal anneal (2 h) at several temperatures. . Ag8 GeSe6 , GeSe2 , Se.
Eqs. (2) and (3) may be rewritten in the form dx=dt ¼ fK0 f ðxÞg expðEa =kT Þ:
ð4Þ
To go further in the analysis, the simultaneous evaluation of Ea and K0 f ðxÞ was performed from the Arrhenius plot of Eq. (4) at fixed values of x, either from continuos heating or from isothermal data (multiple scan method [26]). Figs. 10 and 11 show the multiple scan method results from continuous heating data at x ¼ 0:2 and x ¼ 0:8 for samples Ag20 and Ag25, respectively. The kinetic parameters K0 and Ea are indicated in these figures. Again, the apparent activation energy obtained in the multiple scan method increases with the Ag content and decreases with x remaining close to 200 kJ mol1 . The spread in apparent activation energy values obtained by each method suggests that either the nucleation frequency or the growth rate or both of
12
14
16
18
20
22
24
26
28
30
32
34
36
Fig. 7. XRD patterns of sample Ag25, after isochronal anneal Se. (2 h) at several temperatures. . Ag8 GeSe6 , GeSe2 ,
them depend on the degree of advancement of the process. 3.3.2. Modeling of the initial steps of the primary crystallization The analysis of the crystallization using nucleation and growth theories is based in the JMAK formalism [21–23]. The JMAK formalism assumes spatially random nucleation. This theory is compatible with homogeneous, time, temperature or pressure dependent nucleation rates and also interface, diffusion and time, temperature and pressure dependent growth rates. However, nonrandom nucleation, non-isotropic growth protocols and finite size effects are not properly described by the JMAK theory [27]. For the initial crystallization stages (x 6 0:1) we can assume homogeneous nucleation followed by three-dimensional interface-controlled growth,
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Ag25
0.6
β ∆Cp
0.4
(dQ/dt)∆Cp
0.2
(dQ/dt) reaction alone
0.0 1.0
-0.05
Fraction transformated x
0.8
-0.10
-0.15
Ag20
0.6 0.4 0.2 0.0 1.0 0.8
Ag15
0.6 0.4 0.2 0.0 1.0 0.8
Ag10
0.6
-0.20
β=10 K/min β=20 K/min β=40 K/min β=80 K/min
0.4 560
570
580
590
600
610
0.2 0.0
Fig. 8. Decomposition of the overall DSC curve (thick line) in two parts. Qreaction alone proportional to dx=dt, and QDCp proportional to the crystallized fraction x.
even for primary crystallization [19]; then, the transformed fraction, in the JMAK formalism, is given by [27] • Under isothermal annealing at temperature T and time t:
550 560 570 580 590 600 610 620 630 640 650
Temperature (K) Fig. 9. Kinetic data x ¼ xðT ; bÞ obtained for the first crystallization process under continuous heating, respectively, for the alloy Ag10, Ag15, Ag20 and Ag25.
Table 3 Apparent activation energy obtained from the methods of Kissinger and maximum reaction rate First pick
3 4
xðT ; tÞ ¼ 1 expððp=3ÞIðT ÞuðT Þ t Þ ½TTT diagrams:
ð5Þ
• Under continuous heating at a constant rate b and temperature T : Z T xðT ; bÞ ¼ 1 exp b1 IðT 0 ÞvðT 0 ; T Þ dT 0 0
½THRT diagrams;
ð6Þ
where vðT 0 ; T Þ is the volume at temperature T of a nucleus formed at temperature T 0 , given by 3 Z T 1 0 00 00 vðT ; T Þ ¼ ð4p=3Þ b uðT ÞdT : ð7Þ T0
Ag10 Ag15 Ag20 Ag25
Kissinger method Ea (kJ/mol)
Max. reaction rate method Ea (kJ/mol)
197 10 216 10 202 10 224 10
194 10 233 10 195 10 218 10
In Eqs. (5) and (6) the nucleation frequency IðT Þ and the crystal growth uðT Þ are given by the classical theory of crystallization. The nucleation process can be classified into two main categories: homogeneous and heterogeneous. Homogeneous nucleation occurs in the bulk of the matrix; heterogeneous nucleation oc-
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161
liquid and the crystal. We assume that r is isotropic. In Eq. (8), DG is given by [30,31] DG ¼ DHm ½ð1 Tr Þð1 cÞ cTr lnðTr Þ:
ð9Þ
Here Tr ¼ T =Tm , c ¼ DCp =DSm , T is the temperature, DCp is the heat capacity difference between the liquid and the crystal, Tm , DSm and DHm are the melting temperature, melting entropy and melting enthalpy. In Eq. (8), r can be written as r ¼ aDHm [30]. a is difficult to evaluate and, normally is only estimated. Some interfacial energies of pure metals have been calculated [32,33]. The classical equation for the nucleation frequency I and the crystal growth u are given by [27,32]
Fig. 10. Multiple scan method for the sample Ag20.
IðT Þ ¼ ½4ðr=RT Þ
1=2
Nv b=g expðDG =RT Þ;
ð10Þ
uðT Þ ¼ ða0 kb=gÞ½1 expðDG=RT Þ;
ð11Þ
b ¼ kT =ð3pL2 a30 Þ;
ð12Þ
where Nv is the mean density of atoms, a0 the mean atomic diameter, k is the product of the fraction of surface sites where atoms are preferentially added and the length of the interface in units of a0 , and L is the mean interfacial thickness in units of a0 , and a Vogel–Fulcher expression for the viscosity g: Fig. 11. Multiple scan method for the sample Ag25.
g ¼ g0 expðA=ðT T0 ÞÞ:
curs in the presence of a solid interface of a foreign seed [28]. Since the original glasses are homogeneous, we assume that nuclei are formed via heterophase thermal composition fluctuations (or embryos) in the matrix. The free energy of the embryos is the sum of two terms: the free energy released due to the formation of a crystalline volume and the free energy absorbed due to the new surface created. The main assumption is the ÔcapillarityÕ approximation: the thickness of the interface region is small compared with the size of nuclei [29]. The formation Gibbs free energy DG of a spherical nucleus of critical size is given by DG ¼ 16pr3 =ð3DG2 Þ;
ð8Þ
where r is the molar interface energy between the spherical nucleus and the liquid and DG, the Gibbs free-energy difference between the supercooled
ð13Þ
The main complications and/or uncertainties relating to the nucleation are [34] (a) For alloys that normally crystallize to two or more phases of different compositions, bulk inter-diffusion of the constituent atoms will be required to facilitate the nucleation whereas the basic theory assumes transformation to a single phase iso-compositional with the liquid matrix. (b) It is generally recognized that a transient period is required before steady state nucleation is established. (c) Heterogeneous nucleation may also occur. We used the preceding assumptions to calculate the time–temperature transformation (TTT) and temperature–heating rate transformation (THRT)
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Table 4 Estimated and assessed values used to model the first crystallization steps of the samples Ag10, Ag15, Ag20 and Ag25 Sample Ag10
Ag20
Ag25
Estimated parameters: DHm ¼ 6:9 KJ/mol, r ¼ 0:32DHm , c ¼ 1:8 1.857 1010 1.862 1010 a0 (m) Tm (K) 840 851 L2 =k 10.0 10.0 T0 (K) 469 463 100 100 gðTm Þ (Poisse)
1.852 1010 857 10.0 463 100
1.852 1010 827 10.0 471 100
Fitted parameters Nv =L2 (1/m3 ) A (K)
7.15 1017 1100
1.78 1018 1200
5.09 1014 750
Ag15
4.87 1016 1000
for crystalline fraction x ¼ 106 , 103 and 0.1 using equations (5) and (6) following previous work [30,31,35,36]. It is well known that the crystallization is controlled by the level of undercooling DT ¼ Tm T , when T is close to Tm (solidification). If DT is very high (smaller T ), the degree of undercooling is not the limiting factor and the crystallization process becomes controlled by the atomic mobility or the viscosity. The competition between DT and the viscosity generates a point with the shortest time of the curve TTT (for a determined transformed fraction). This point is called ÔnoseÕ of the TTT curves and its coordinates are (tN , TN ). Summarizing, when T > TN , the limiting mechanism of the crystallization is the degree of undercooling through nucleation and crystal growth (since u / DT when DT ! 0). If T < TN , the crystallization is controlled by the viscosity. The crystallization of amorphous phases corresponds to the temperature range T < TN . In other words, the viscosity controls the crystallization at high undercooling. Therefore, as a first approximation, we assume that the thermodynamic parameters (DHm , r, cÞ used in Eqs. (8)–(12) are the same in all the samples and the different compositions only modify the values of viscosity (experimentally observed through the change of the glass transition temperature, Tg ) and Nv =L2 . This assumption agrees with the consideration that viscosity is controlling the transformation for the range of temperatures fitted in the curves TTT and THRT.
Some parameters (a0 , Tm , DHm , r, cÞ in Eqs. (8)– (12) were determined or estimated from either thermodynamic data (a0 , Tm , DHm , c) or experimental data (r) [35,36]. DHm was estimated using DCp , DHp1 , Tp1 and Tm . a0 was determined using density measurements [7]. Tm was estimated extrapolating the liquidus curves of the stable ternary diagram GeSeAg. c was estimated using DCp , DHm and Tm . The viscosity of liquid state at Tm ; and the parameters L2 =k and T0 are estimated following a previous work [27], that is gðTm Þ ffi 10 Pa s;
L2 =k ffi 10;
and
T0 ffi 0:95Tg :
The choice of T0 is proper because the viscosity is of the order of 1013 Poisse at T ¼ Tg . Assuming that only the phase Ag8 GeSe6 crystallizes in the initial steps of the first peak detected by DSC, the remaining parameters (Nv =L2 , A) were fitted using Eqs. (5) and (6) to reproduce the experimental DSC data (x ¼ 0:1). Both continuous heating and isothermal experimental data have been used. The estimated as well as the fitted parameters are given in Table 4. The calculated THRT and TTT curves for different values of the crystallized fraction (x ¼ 106 , 103 and 0.1) as well as the experimental data obtained for x ¼ 0:1 are reported in Figs. 12 and 13. 3.4. Discussion The results of Table 4 show that the viscosity (parameter A) and the pre-exponential factor of
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163
Ag10
Ag15
Ag20
Ag25
Fig. 12. TTT curves for the crystallization of Ag8 GeSe6 in the samples Ag10, Ag15, Ag20 and Ag25. Curves represent calculated values for x ¼ 106 (- - -), 103 ( ) and 0.1 (––) using Eq. (5), black squares correspond to experimental values for x ¼ 0:1.
the nucleation frequency Nv =L2 increase with the Ag content. The calculated TTT and THRT curves of Figs. 12 and 13 are in agreement with the experimental data. For each composition, the seven or eight experimental data (obtained by isothermal or continuous DSC regimen) are fitted by only two parameters (A and Nv =L2 ). The glass and crystallization temperatures Tg and Tc reported by Mitkova et al. [9] and Kawasaki et al. [10] are compared with our results in Fig. 14. The crystallization temperature presents a
Fig. 13. THRT curves for the crystallization of Ag8 GeSe6 in the samples Ag10, Ag15, Ag20 and Ag25. Curves represent calculated values for x ¼ 106 (- - -), 103 ( ) and 0.1 (––) using Eq. (6), black squares correspond to experimental values for x ¼ 0:1.
good agreement. We observe that Tc increases with the Ag content. On the other hand, the values obtained for the glass temperature do not exhibit a good agreement. Possibly this is due to the fact that the calorimetric curves are dependent on the sample preparation (sample mass, size powder) as is mentioned in Section 2. We can detach the following ideas. First, the values of Tg reported in Ref. [10] present a great dispersion. Second, Mitkova et al. [9] detected two glass transitions
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Fig. 14. Glass and crystallization temperatures Tg and Tc vs. Ag content plot for the studied glasses. The results are compared with the references: Mitkova et al. [9] () and (j), Kawasaki et al. [10] (O), this work ( ).
(black and white squares in Fig. 14). We only detected one glass transition in the samples Ag10, Ag15 and Ag20. A meticulous analysis of the calorimetric scans of the sample Ag25 could indicate a second glass transition at the technique detection limit. Third, Tg obtained by Kawasaki et al. [10] for the sample of composition GeSe3 is 23 K higher than that reported by Mitkova et al. [9]. The glass temperatures in our work agree with the values reported by Mitkova et al. [9] for the first glass transition.
Another possible and useful way to analyze the glass transition temperature values is by correlating them with the liquidus temperature, Tm , of the particular alloy. In the present study Tm was not measured; however, it was estimated from Ref. [11] and the binary Ge–Se phases diagram extrapolating the liquidus curves. This analysis indicates that no major changes will happen in the melting temperatures by increasing the Ag content of the alloys. The estimated Tm of the alloys are showed in Table 5. Consequently, Tg =Tm and Tm Tg were calculated (see Table 5). These approaches for Tg =Tm are in agreement with the fact that these alloys compositions are good glass-formers. The composition dependence of the GFA can be analyzed. The GFA is a non-quantifiable concept, however an idea can be introduced: the GFA of a sample can be defined as the capacity to obtain amorphous phase when the sample is rapidly quenched. If the cooling rate b is sufficiently high, the crystallization is inhibited. In this case, the sample in liquid state at the temperature Tm is rapidly quenched down to the glass temperature Tg where the undercooled liquid structure is frozen and the liquid is transformed in an amorphous phase. In order to compare to the GFA of different samples, we analyze the influence of Tm , Tg and b on the GFA. Then the GFA enhances when (a) the critical cooling rate in order to obtain the glass bM decreases, or (b) Tm Tg decreases (if b is maintained constant). Therefore, one can determine which compositions (in decreasing order) have greater GFA, i.e.: shorter Tm Tg in Table 5. Consequently, the best glass-former is the sample Ag25, following in decreasing order by Ag10, Ag15 and Ag20. Now, these results will be com-
Table 5 The glass and the melting temperatures Tg and Tm , Tg =Tm , Tm Tg and the greatest cooling rate bM in order to obtain the crystalline phase Sample Tg (K) 3 K Tm (K) 5 K Tg =Tm Tm Tg (K) bM (K/min) 15%
Ag10
Ag15
Ag20
Ag25
494 840 0.59 346 750
487 851 0.57 364 1500
487 857 0.57 370 2600
496 827 0.60 331 750
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bM ¼ ðTm TN Þ=tN :
ð14Þ
The composition dependence of bM is shown in Table 5. Then, shorter bM involves greater GFA. In consequence, Ag25 and Ag10 are the best glass forming alloys, following Ag15 and Ag20. These results are in agreement with those calculated above. The critical cooling rate in order to obtain the glass bM in Table 5 is in the order of magnitude of the experimental cooling rate reported by Dejus et al. [3]. They estimated an effective cooling rate in the order of 500 K/s for the sample of composition Ag25. There is a significant shift on the onset of the Ag25 first crystallization peak towards high temperatures. On the contrary, for this alloy, the intermediate and the second crystallization peaks occur at a lower temperature than those of the other alloys. The amorphous GeSeAg samples show a quite unusual behavior in comparison with other ionic conducting glasses. As it was mentioned in Section 1, a sharp transition from semiconductor to superionic conductor in (Ge25 Se75 )100y Agy is detected [10]. The conductivity r (obtained from the Ref. [10]) is showed as a function of y in Fig. 15. It increases from 1013 to 105 X1 cm1 at about y ¼ 10. This is a phenomenon of percolation that was explained by Kawasaki et al. [10] considering a work of Armand et al. [14] for the GeSeAg and GeSAg systems. They suggested that GeXAg glasses (X ¼ S, Se), containing a small amount of Ag2 X, has an inhomogeneous structure composed of Ag2 X clusters and GeX2 network, which becomes homogeneous at high concentration of Ag2 X. The existence of these clusters could be questioned due to the first crystallization product
σ Vo
10
-4
10
-5
10
-6
10
-7
10
-8
10
-9
10
-10
10
-11
10
-12
10
-13
10
-14
σ (1/Ωcm)
pared with TTT curves of Fig. 12 calculating the critical cooling rate to obtain the glass. The critical cooling rate bM in order to obtain the crystalline phase Ag8 GeSe6 can be estimated using the ÔnoseÕ of the curves TTT for the curve of the transformed fraction x ¼ 106 (this transformed fraction, x ¼ 106 , is the experimental detection limit for a crystalline phase). The ÔnoseÕ coordinates are (tN , TN ). Therefore, bM can be estimated using
165
Fig. 15. Molar volume and the ionic conductivity vs. Ag content.
that is Ag8 GeSe6 . Furthermore, the diffusion of Ge and Se towards the Ag2 Se clusters for the formation of the Ag8 GeSe6 crystals should be very small. Although the idea of the phase separation is also reported by Mitkova et al. [9] to explain a bimodal glass transition temperature, the SRO of the glass (Table 1) does not show significant structural changes with the composition. At this stage, it is very interesting to compare the composition dependence of the ionic conductivity with other structural parameters. The molar volume V0 , obtained from density measurements [7] is also depicted in Fig. 15. For y < y the range of the conductivity values is (5 1013 –1 1012 ) X1 cm1 and V0 ffi 18:75–18 cm3 for y ¼ 0 and 5. For y > y ffi 10, r and V0 are practically constant (r ffi 5 104 X1 cm1 , V0 ffi 16 cm3 ). When the molar volume V0 is about 16 cm3 the GeSeAg glass is an ionic conductor. On the other hand, the molar volume for the ionic conducting crystalline phase Ag2 Se is V0 ffi 11:8 cm3 . Then, the value of the molar volume could be connected with the semiconductor–superionic transition. One could conclude that a necessary condition for the ionic conduction property in the AgGeSe system is V0 6 16:5 cm3 . A qualitative explication can be formulated assuming a homogeneous glass structure. As V0 increases, the atomic distance increases too, in particular the Agþ ion sites distance dþþ , and so does the activation energy for the hoping of the Agþ ion Eaþþ . If V0 is greater than a threshold
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value V0 , dþþ and Eaþþ is overmuch great and then the ionic conduction does not occur.
4. Conclusions Preliminary calorimetric experiments have shown an interesting dependence on the particle size of the sample. In order to obtain consistent calorimetric results, the bulk samples have been milled to have uniform grain size ranging between 25 and 50 lm. The first crystallization product is Ag8 GeSe6 as was observed by XRD in continuous heating calorimetric regime. In isothermal treatments, the crystallization of this phase is clearly detected both calorimetrically and by XRD in samples Ag10, Ag15, Ag20 and Ag25 (only at 568, 573 and 578 K). In sample Ag25, the ternary phase is observed at 553 and 558 K annealing temperatures by XRD exclusively. However, at these temperatures it could not be detected any peak by DSC because its crystallization rate is too low. The first step of the crystallization of the Ag8 GeSe6 phase in all the (Ge25 Se75 )100y Agy samples is modelled considering that the changes on the composition only modify the viscosity of the undercooled liquid. We propose that overlapping of the two processes is occurring in isothermal experiments at high temperatures: the crystallization of Ag8 GeSe6 and GeSe2 phases. We assume that the first steps correspond to the primary crystallization of Ag8 GeSe6 and then the GeSe2 crystallization starts. As mentioned above the results associated with the glass structure are controversial: • Armand et al. [14] suggested that glasses (GeX2 )ð100zÞ (Ag2 X)z (X ¼ Se, S), containing small amount of Ag2 X (z < 30), have an inhomogeneous structure composed of Ag2 X clusters and GeX2 network. The main size of these Ag2 X clusters is about 5.5 nm (z ¼ 10). The structure becomes homogeneous at high concentration of Ag2 X (z > 30). Must be noted that the samples (GeSe2 )ð100zÞ (Ag2 Se)z with z < 25 are in the limit of the glass forming range proposed by Mitkova et al. [9].
• Mitkova et al. [9] proposed that ternary (Gej Se100j )100y Agy bulk glasses in the Se-rich region (j < 33.33 and y < 30) are shown to be intrinsically phase separated into an Ag2 Se-rich glass and a residual Get Se100t . • Using neutron diffraction [3] and differential Xray scattering [8], some authors indicate that the structure of (Ge25 Se75 )75 Ag25 is homogeneous. Our results indicate that the existence of an inhomogeneous glass structure composed of Ag2 Se clusters and GeSe2 network could be questioned in the composition range studied (Ag at.% ¼ 10, 15, 20 and 25). Acknowledgements Financial support from the Universidad de Buenos Aires in project UBACYT TI02 and from the Comissi o Interdepartamental de Recerca y Tecnologıa (CIRIT) in project ACI-2000-19 is acknowledged. One of the authors (M.A.U.) gratefully acknowledges the grant released by the Instituto de Cooperaci on Iberoamericana of Spain. Thanks are also due to Lic. J.L. Tour on for his help in the data processing. References [1] Xingwei Fang, W.J. Bresser, P. Boolchand, Phys. Rev. Lett. 78 (23) (1997) 4423. [2] J. Hautala, S. Yamaski, P.C. Taylor, J. Non-Cryst. Solids 114 (1989) 85. [3] R.J. Dejus, S. Susman, K.J. Volin, D.G. Montague, D.L. Price, J. Non-Cryst. Solids 143 (1992) 162. [4] A. Pradel, M. Ribes, J. Solid State Chem. 96 (1992) 247. [5] Z.U. Borisova, Glassy Semiconductors, Plenum, New York, 1981. [6] Z.U. Borisova, T.S. Rykova, E.Yu. Turkina, A.R. Tabolin, Izv. Akad. Nauk. SSSR Neorg. Mater. 20 (1984) 1796. [7] A. Piarristeguy, M. Mirandou, M. Fontana, B. Arcondo, J. Non-Cryst. Solids 273 (2000) 30. [8] J.D. Westwood, P. Gergopoulos, D.H. Whitmore, J. NonCryst. Solids 107 (1988) 88. [9] M. Mitkova, Yu Wang, P. Boolchand, Phys. Rev. Lett. 83 (19) (1999) 3848. [10] M. Kawasaki, J. Kawamura, Y. Nakamura, M. Aniya, Solid State Ion. 123 (1999) 259.
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