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Structural aspects of amorphization in metallic materials
S c r i p t a METALLURGICA e t MATERIALIA
STRUCTURAL
Vol.
28, p p . 1 0 1 1 - 1 0 1 6 , 1993 Printed in the U.S.A.
ASPECTS OF AMORPHIZATION
Pergamon Press Ltd. All rights reserved
IN METALLIC MATERIALS
A.Serebryakov Solid State Physics Institute, Chernogolovka, Moscow District, 142432, Russia (Received
D e c e m b e r 28,
1992)
1. Introduction Crystal to glass as well as liquid to glass transformations in metallic materials are of growing interest because of a large field of possible applications of metallic glasses. However, physical mechanisms which underlie amorphization reactions are not fully understood yet [1] mainly due to the lack of direct information on the structure of amorphous reaction products. So structure modeling is usually used to clarify the problem, the modeling as a rule being based on the concept of liquid-like structure of amorphous alloys. In the present work Fujita's cluster model of an amorphous state (see, e.g., [2]) is further developed to get insight into amorphization reactions. An amorphous metallic alloy is conceived as consisting of small (of some coordination shells in size) crystal-like clusters (with the chemical and topological medium-range order corresponding to a stable or metastable compound in the relevant concentration field of the phase diagram) and liquid-like intercluster layers. Thermodynamic analysis of the cluster model is made assuming that (i) clusters are spheres (of radius r~), (ii) the specific volume energy of clusters does not depend on r~, (iii) the specific interfacial energy is independent of the interface curvature and the composition of the intercluster liquid-like solution, and (iv) the specific free energy of the intercluster layer depends both on its thickness and its composition, the thickness dependence being described by a continuous function. These are rather rough assumptions though (like in the nucleation theories based on similar assumptions) they seem reasonable to reveal the trends in the cluster amorphous structure formation and behaviour. It will be seen that a wide range of observations can be explained using these assumptions and one and the same structural model of an amorphous state irrespective of the type of transformations leading to this state. 2. Free energy and some properties of the cluster s y s t e m
2.1. Single amorphous phase In order to simplify the analysis we will suppose that the system is a binary AyB1-~ alloy with the number of atoms equal to Avogadro's number, the structure and composition of crystal-like clusters correspond to a linear compound A~,B~, an intercluster layer is filled with a liquid-like binary AxBI_~ solution. The total specific free energy, g, of the cluster system can be expressed as the sum of three contributions, uc, ut and ut=, which are due to the clusters (u=), the intercluster layers (ut), and the interfaces between the clusters and intercluster layers (utc), uc and ut~ being defined by uc = (v~/V~)gc and u~ = STl~, where v~ = (4/3)~rr~m is the total volume of the clusters, m - the number of dusters in the system, s = 4~r~m the total surface of the cluster/intercluster layer interfaces, 71~ - the specific interfacial free energy, g~ - the specific volume free energy of the AoBo compound formation, V~ - the compound molar volume. We would expect that the specific free energy of the intercluster layer, gt, will depend both on its thickness, d, and its composition, x. It will be assumed that, to a first approximation, gt can be expressed as the sum of two terms, one, gt,, being the specific free energy of the bulk liquid-like solid solution of the same composition and the other, g~u, a thickness-dependent term which is due to interaction between clusters and intercluster layers, particularly, due to constraints on the atomic configuration of the layer arising from the neighbouring
I011 0956-716X/93 $6.00 + .00 Copyright (c) 1993 Pergamon Press Ltd.
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crystM-like clusters. The last term decreases as the layer thickness increases. The exact dependence of gtd on d is not crucial for the present qualitative consideration, so representing gtd by the continuous function of d gtd = s ( V t J v t ) T t ~ b l e x p ( - b 2 d ) , we finally obtain
(1)
g = (vJVo)gc + (~,~lV~,)g~, + , 7 .
where % = 3'to[1 + b l e x p ( - b 2 d ) ] , b~ = %~/2~t~ - 1, vt is the total volume of the liquid-like solid solution in the system, Vl= - the g-atomic volume of this solution, %~ - the specific surface energy of the "sharp boundary" between clusters (d = 0), b2 - the "interaction parameter" defining the rate of gld changing with d. To illustrate some properties of the cluster system described we will use a model binary system with parameters typical of systems exhibiting the glass transformation. A free energy diagram for this system at some temperature T is shown in Fig. 1, l represents the liquid-like solution and the circled point --the linear compound A B (g¢ = g~o). %~ is taken to be equal to 800 ergs/cm 2, w~ = 2 2 . 1 0 T M cm 3, wb = 11 • 10 T M cm 3, w~b = w, + wb, where w,, wb, and w,b are correspondingly the volumes of the atoms A and B and of the molecule of A B compound, d = 2 ( r / - r~), ( 4 / 3 ) r r } m = v, + v~ = v. Fig. 2 shows variations of the total free energy, g, of the cluster system with the number i of A B molecules in the cluster for different sets of values of the specific surface energy of the cluster/intercluster layer interfaces, 3%, the number of clusters, m, and the interaction parameter, b2. f5
-30
//f
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-5
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~-15
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-25 -35
m2
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-55 0.0
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~
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I 0.6
L
I 0.8
i
-40 f.O
0
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I 50
i 100
150
i
FIG. 1. Free energy diagram for the model binary system (see text). FIG. 2. Variations of the cluster system free energy g with the number i of A B molecules in the cluster (y = 0.4, gc = gco; solid lines: m l / m ~ = 3, m 1 = 4.8 • 1021, 7zc = 50 ergs/cm 2, b2 = 0.5 .~-1; dashed lines: m = ms, curve 1 ~/~c= 50 ergs/cm 2, b2 = 0.1/~-1, curve 2 - 3% = 100 ergs/cm 2, b2 = 0.5/~-1). Variations of the system free energy go = g(io) where io corresponds to the m i n i m u m of g, and those of the volume fraction of the intercluster layers fo = f ( i o ) with the distance between neighbouring cluster centers, L, for two sets of the parameters are shown in Fig. 3. L dependence of the system free energy g m = g ( i m ) corresponding to the system state in which one of the elements (or both at y -- 0.5) is completely bonded in clusters (r = rc(i,~) being equal to rf at y = 0.5) is also shown in Fig. 3. It can be seen from Fig. 2 and Fig. 3 that changes in the cluster structure may be of both reversible and irreversible nature. Reversible changes can result from shifts in the position, io, of the system free energy minimum (Fig. 2) due to variations of temperature, pressure, etc, provided the number of clusters m remains unchanged. A decrease in this number brings about irreversible changes of the structure (Fig. 3). If there is a repulsive interaction between neighbouring intercluster layers (which are at short distances from each other in a cluster system and can interact with each other as elastic inhomogeneities, for example) then in a real system with some cluster distribution in size after amorphi~ation this interaction would irreversibly lead to the formation of a metastable structure with a uniform cluster size (in other words, would lead to the
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formation of an "equilibrium" spatial net of intercluster layers in which small shifts of its elements from their equilibrium positions would cause a force driving them back). A decrease of the free energy difference between the undercooled liquid and the cluster state of the system as the temperature is raised will lead to an increase of the critical size of cluster nuclei, i., and decrease of the cluster size io corresponding to the system free energy minimum (it is schematically illustrated by Fig. 4). At some temperature T. a state can be reached where this minimum (as well as the maximum at i = i,) vanishes. Just above T. clusters (which become thermodinamically unstable at T >_ I'.) will disappear, the cluster system being transformed as a result into the undercooled liquid. We believe that T. may be identified with the glass transition temperature, Ta, as measured upon heating in actual experiments. -20
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~:~
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~:~ I
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,
I
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L (rim)
0..99 o.o
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40.0
i
FIG. 3. L dependence of go = g(io), gm = g(i,~), and fo = f(io) (y = 0.4, Vie = 50 ergs/cm 2, b2 = 0.5/~-*; solid lines: gc = 0.8gco; dashed lines: gc = gco). FIG. 4. Schematic relative free energy curves for a cluster system at different temperatures. It should be noted that restricting the intercluster layer thickness to some predetermined value as is usual in treatments of cluster models is not necessary and, moreover, incorrect in principle. Once the temperature and pressure of the system are specified, this thickness is no longer an independent variable: its value can be find by minimization of the system free energy. 2.2. Coexistence of amorphous phases
Fig. 1 shows (curves al and a2) variations of go = g(io) with the alloy composition for a binary system where two linear compounds, A B and AB2, may be formed (AB2 compound is represented by the circled cross in Fig. 1). It is clear that two "amorphous phases" (a~ and a2) can occur in such a system, one of them (al) is described above, and the other (as) is that with the cluster structure and composition corresponding to AB2 compound. A single amorphous phase within the two-phase field of the metastable phase diagram is thermodynamically unstable against the decomposition into two amorphous phases with compositions corresponding to the common tangent construction. There is much experimental evidence of the phase separation in metallic glasses (see, for example, [3]). It should be stressed that a description of the system with coexisting amorphous phases requires some additional structure parameters, such as a characteristic size of "precipitates" of one amorphous phase in the other, parameters for the interface between the amorphous phases and so on. 2.3. Coexistence of amorphous and crystalline phases
In a mixed amorphous-crystalline system the atom transfer between amorphous and crystalline phases is possible. Fig. 5 shows the free energy variation of a mixed system initially containing a single al amorphous phase of the composition yo = 0.5 with amorphous phase composition, the composition change being due to the B atom transfer from B elemental crystalline to the amorphous phase (B indiffusion) at y <_ Yo and due
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to A indiffusion at g ~ ~/o. It can be seen that ~/decreasing in the al phase at y < ~/o can lead to az --+ as transformation. It is also evident that outdiffusion will take place instead of the indiffusion at some initial system states, leading (as is the case with indiffusion when it takes place) to a metastable equilibrium between crystalline and amorphous phases. Recent results by Aaen Andersen et al [4], who observed the indiffusion of cobalt in the amorphous Co-Zr phase, seem to support the above consideration. This is a relatively new area of research and further experiments are needed to better clarify the problem.
-40
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.....
.....
I ~ m l .
B< -60 0.1
I
0.2
I
0.3
I ..... .
•
>A I
0.4
0.5
t 0.6
t 0.7
0.8
Y FIG. 5. Free energy variations of the mixed amorphous-crystalline system with the amorphous phase composition. FIG. 6. Illustration of the model for an amorphous zone growth in a diffusion couple. Finally it should be noted that all calculated data used in Sections 2.2 and 2.3 were obtained assuming that the system parameters m, b2, 7~ and 7~c have the same values (4.8.10 sl, 0.5 A - l , 800 ergs/cm 2 and 50 ergs/cm s, correspondingly) in both amorphous phases (al and as) and the number of clusters, m, remains unchanged as the system changes, but it can be shown that the situations described are typical and may be realized in a wide range of sets of the system parameters. E4. Remark on structure-sensitive properties Taking into account that in a general case local values of different physical properties, e.g. of elastic and magnetostriction constants, differ in clusters and intercluster layers the evolution of structure-sensitive properties of an amorphous phase under various treatments can be explained, in particular the magnetic anisotropy of as-quenched as well as stress-annealed ribbons of amorphous near-zero magnetostrictive alloys [5,6] which has found no satisfactory explanation in terms of structural models of an amorphous state other than the cluster one. 3. T h e cluster structure f o r m a t i o n In discussion that follows we shall return for brevity to a binary A B system with a single compound, though a great variety of interesting situations will be left beyond the scope of discussion in this case. 9.1. Melt quenching The liquid to glass transition in metallic alloys can be regarded as a usual first-order phase transition (primary crystallization) which proceeds, however, under unusual conditions (the system is far from its equilibrium state and under severe kinetic constraints) where nuclei of a new phase "collide" with each other at the beginning of their growth. Copious nucleation can be facilitated by a small surface energy of the undercooled liquid/nucleus interface. Depending on the quenching conditions the formation of the cluster structure may be not fully completed in as-quenched alloy and can proceed at ambient or elevated temperatures, leading to a reduction of the volume fraction and changes in the compositon of intercluster layers and corresponding changes in alloy properties.
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3.2. Solid state amorphization 3.2.1. Diffusion couples Solid state amorphization in diffusional couples has been found for many metal-metal combinations which meet requirements for a negative free energy of mixing and the asymmetry in the atomic mobility of the two participating species. The amorphous phase usually forms and grows as a planar zone at the interfaces between the elements by diffusion of the fast species alone. At some temperature dependent critical thickness a crystalline reaction product forms. A detailed analysis of experimental observations can be found in [1]. The most complicated and questionable is here a problem of a critical thickness at which a crystalline reaction product appears. We will now try to treat this problem using the above described cluster model of an amorphous structure. Let us assume that the formation of an amorphous phase takes place in some reaction front (RF) ahead of a growing amorphous zone (AZ, see the scheme in Fig. 6) and B atoms are the dominant moving species. As the thickness of the amorphous zone, ~, increases the incoming into the front flux of B atoms decreases as well as the concentration of B atoms in the cluster-free (liquid-like) zone of the front (see Fig. 6); therefore, the rate of the cluster nucletion on the left side of the cluster-free zone where the B concentration is higher than in its remaining part will decrease too. Starting from some critical thickness ~ = ~3 only the previously formed clusters grow in the reaction front, a liquid-like zone disappears and a crystalline reaction product appears. It should be emphasized that in terms of the cluster model an amorphous zone of a diffusion couple is nonhomogeneous, which has to be taken into account in treating the atomic transport within the zone and finding the time law of its growth.
3.2.2. Ball milling Milling in a high energy ball mill can lead to amorphization of elemental powder mixtures as well as intermetallic compound powders [1,7]. A general feature of all types of amorphization reactions via ball milling is that amorphization is always preceded by extreme grain refinement.
FIG. 7. Illustration of the grain refinement (GR) and "wetting" transition (WT) under ball milling. The simplest type of the amorphization reaction in an elemental powder mixture can be expected to be the same as in diffusion couples. It was experimentally observed, however, that amorphization in some systems is preceded by the formation of the crystalline supersaturated solid solution or compound. As the grain refinement in a single phase powder proceeds the free energy difference between the system with ordinary ("sharp") grain boundaries and the system with liquid-like (wetting) layers between grains (with "thick" grain boundaries) increases, so the transition from the state with "sharp" boundaries to the state with "thick" boundaries (resembling the first-order wetting transition [8]) can occur at some grain size [9]. If the grain size after the formation of the wetting layers falls within the range corresponding to the cluster model [2] the transition can be regarded as the crystal to glass transition. If the grain size after the "wetting" transition is beyond the cluster range the cluster amorphous state can be reached by further grain refinement under ball milling. It is worth noting that very few systems are known with a positive heat of mixing which can undergo amorphization due to ball milling. The amorphization in some of these systems is a composition-induced process as was unambiguously demonstrated by Ogino et al [10]. The system composition can be changed,
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for example, by indiffusion from the ambient atmosphere. The amorphization in this case can involve the formation of a liquid-like layer between grains with grain refinement, indiffusion from the atmosphere of D atoms, for example, with strong affinity to one of the system species (A atoms, for example), the nucleation of an amorphous zone (with clusters of the compound formed by A and D atoms) between grains and its growth as indiffusion from the atmosphere continues, which may be accompanied by B indiffusion in the zone. 3.2.3. Other amorphizing treatments Amorphization of some metallic alloys under heat treatment in the atmosphere of hydrogen gas is another example of a composition-induced amorphization [1]. The systems amorphized are initially polycrystalline solid solutions with one of the elements having strong affinity to hydrogen. It can be expected that hydrogen indiffusion would lead to a copious nucleation of hydride clusters at the grain boundaries if the cluster growth is kinetically suppressed. A heterogeneously nucleated amorphous zone will grow at the expense of grains and incoming hydrogen atoms. Spontaneous vitrification after quenching of a high temperature [11] or high pressure [12] single phase state into a two-phase field of the equilibrium phase diagram can be understood as the phase separation under severe kinetic constraints, with nuclei of the primarily precipitated phase as clusters and the remainder as intercluster liquid-like layers. The process does not involve atomic diffusion at long distances. It may occur by heterogeneous nucleation of an amorphous phase at grain boundaries. This consideration could be valid for a pressure-induced amorphization [13].
References 1. W.L.Johnson, Progr. Mat. Sci. 30, 81 (1986). 2. T.Hamada and F.E.Fujita, Jap. J. Appl. Phys. 21,981 (1982). 3. A.R.Yavari, Acta metall. 36, 1863 (1988). 4. L.-U. Aaen Andersen, J.Bottiger, J.Janting, N.Karpe, K.K.Larsen, A.L Greer and R.E.Somekh, Mater. Sci. Eng. A133, 415 (1991). 5. B.L.Shtangeev, A.V.Serebryakov and V.A.Kislov, Metallofizika 13, 83 (1991) (in russian). 6. V.Kislov, Yu.Levin, A.Serebryakov, M.Tejedor and B.Hernando, Acta Phys. Pol. A77, 701 (1990). 7. A.W.Weeber and H.Bakker, Physica B 153, 93 (1988). 8. P.G. de Gennes, Rev. Mod. Phys. 57,827 (1985). 9. A.Serebryakov, Mater. Sci. Forum 88-90, 133 (1992). 10. Y.Ogino, S.Murayama and T.Yamasaki, J. Less-Common Met. 168, 221 (1991). 11. A.Blatter, M. yon Allmen and N.Baltzer, J. Appl. Phys. 62,276 (1987). 12. E.G.Ponyatovsky and O.I.Barkalov, Mater. Sci. Eng. A133, 726 (1991). 13. Y.Fujii, M.Kowaka and A.Onodera, J. Phys. C 18, 789 (1985).
9
STRUCTURAL
Vol.
28, p p . 1 0 1 1 - 1 0 1 6 , 1993 Printed in the U.S.A.
ASPECTS OF AMORPHIZATION
Pergamon Press Ltd. All rights reserved
IN METALLIC MATERIALS
A.Serebryakov Solid State Physics Institute, Chernogolovka, Moscow District, 142432, Russia (Received
D e c e m b e r 28,
1992)
1. Introduction Crystal to glass as well as liquid to glass transformations in metallic materials are of growing interest because of a large field of possible applications of metallic glasses. However, physical mechanisms which underlie amorphization reactions are not fully understood yet [1] mainly due to the lack of direct information on the structure of amorphous reaction products. So structure modeling is usually used to clarify the problem, the modeling as a rule being based on the concept of liquid-like structure of amorphous alloys. In the present work Fujita's cluster model of an amorphous state (see, e.g., [2]) is further developed to get insight into amorphization reactions. An amorphous metallic alloy is conceived as consisting of small (of some coordination shells in size) crystal-like clusters (with the chemical and topological medium-range order corresponding to a stable or metastable compound in the relevant concentration field of the phase diagram) and liquid-like intercluster layers. Thermodynamic analysis of the cluster model is made assuming that (i) clusters are spheres (of radius r~), (ii) the specific volume energy of clusters does not depend on r~, (iii) the specific interfacial energy is independent of the interface curvature and the composition of the intercluster liquid-like solution, and (iv) the specific free energy of the intercluster layer depends both on its thickness and its composition, the thickness dependence being described by a continuous function. These are rather rough assumptions though (like in the nucleation theories based on similar assumptions) they seem reasonable to reveal the trends in the cluster amorphous structure formation and behaviour. It will be seen that a wide range of observations can be explained using these assumptions and one and the same structural model of an amorphous state irrespective of the type of transformations leading to this state. 2. Free energy and some properties of the cluster s y s t e m
2.1. Single amorphous phase In order to simplify the analysis we will suppose that the system is a binary AyB1-~ alloy with the number of atoms equal to Avogadro's number, the structure and composition of crystal-like clusters correspond to a linear compound A~,B~, an intercluster layer is filled with a liquid-like binary AxBI_~ solution. The total specific free energy, g, of the cluster system can be expressed as the sum of three contributions, uc, ut and ut=, which are due to the clusters (u=), the intercluster layers (ut), and the interfaces between the clusters and intercluster layers (utc), uc and ut~ being defined by uc = (v~/V~)gc and u~ = STl~, where v~ = (4/3)~rr~m is the total volume of the clusters, m - the number of dusters in the system, s = 4~r~m the total surface of the cluster/intercluster layer interfaces, 71~ - the specific interfacial free energy, g~ - the specific volume free energy of the AoBo compound formation, V~ - the compound molar volume. We would expect that the specific free energy of the intercluster layer, gt, will depend both on its thickness, d, and its composition, x. It will be assumed that, to a first approximation, gt can be expressed as the sum of two terms, one, gt,, being the specific free energy of the bulk liquid-like solid solution of the same composition and the other, g~u, a thickness-dependent term which is due to interaction between clusters and intercluster layers, particularly, due to constraints on the atomic configuration of the layer arising from the neighbouring
I011 0956-716X/93 $6.00 + .00 Copyright (c) 1993 Pergamon Press Ltd.
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crystM-like clusters. The last term decreases as the layer thickness increases. The exact dependence of gtd on d is not crucial for the present qualitative consideration, so representing gtd by the continuous function of d gtd = s ( V t J v t ) T t ~ b l e x p ( - b 2 d ) , we finally obtain
(1)
g = (vJVo)gc + (~,~lV~,)g~, + , 7 .
where % = 3'to[1 + b l e x p ( - b 2 d ) ] , b~ = %~/2~t~ - 1, vt is the total volume of the liquid-like solid solution in the system, Vl= - the g-atomic volume of this solution, %~ - the specific surface energy of the "sharp boundary" between clusters (d = 0), b2 - the "interaction parameter" defining the rate of gld changing with d. To illustrate some properties of the cluster system described we will use a model binary system with parameters typical of systems exhibiting the glass transformation. A free energy diagram for this system at some temperature T is shown in Fig. 1, l represents the liquid-like solution and the circled point --the linear compound A B (g¢ = g~o). %~ is taken to be equal to 800 ergs/cm 2, w~ = 2 2 . 1 0 T M cm 3, wb = 11 • 10 T M cm 3, w~b = w, + wb, where w,, wb, and w,b are correspondingly the volumes of the atoms A and B and of the molecule of A B compound, d = 2 ( r / - r~), ( 4 / 3 ) r r } m = v, + v~ = v. Fig. 2 shows variations of the total free energy, g, of the cluster system with the number i of A B molecules in the cluster for different sets of values of the specific surface energy of the cluster/intercluster layer interfaces, 3%, the number of clusters, m, and the interaction parameter, b2. f5
-30
//f
5 0
-5
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-25 -35
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FIG. 1. Free energy diagram for the model binary system (see text). FIG. 2. Variations of the cluster system free energy g with the number i of A B molecules in the cluster (y = 0.4, gc = gco; solid lines: m l / m ~ = 3, m 1 = 4.8 • 1021, 7zc = 50 ergs/cm 2, b2 = 0.5 .~-1; dashed lines: m = ms, curve 1 ~/~c= 50 ergs/cm 2, b2 = 0.1/~-1, curve 2 - 3% = 100 ergs/cm 2, b2 = 0.5/~-1). Variations of the system free energy go = g(io) where io corresponds to the m i n i m u m of g, and those of the volume fraction of the intercluster layers fo = f ( i o ) with the distance between neighbouring cluster centers, L, for two sets of the parameters are shown in Fig. 3. L dependence of the system free energy g m = g ( i m ) corresponding to the system state in which one of the elements (or both at y -- 0.5) is completely bonded in clusters (r = rc(i,~) being equal to rf at y = 0.5) is also shown in Fig. 3. It can be seen from Fig. 2 and Fig. 3 that changes in the cluster structure may be of both reversible and irreversible nature. Reversible changes can result from shifts in the position, io, of the system free energy minimum (Fig. 2) due to variations of temperature, pressure, etc, provided the number of clusters m remains unchanged. A decrease in this number brings about irreversible changes of the structure (Fig. 3). If there is a repulsive interaction between neighbouring intercluster layers (which are at short distances from each other in a cluster system and can interact with each other as elastic inhomogeneities, for example) then in a real system with some cluster distribution in size after amorphi~ation this interaction would irreversibly lead to the formation of a metastable structure with a uniform cluster size (in other words, would lead to the
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formation of an "equilibrium" spatial net of intercluster layers in which small shifts of its elements from their equilibrium positions would cause a force driving them back). A decrease of the free energy difference between the undercooled liquid and the cluster state of the system as the temperature is raised will lead to an increase of the critical size of cluster nuclei, i., and decrease of the cluster size io corresponding to the system free energy minimum (it is schematically illustrated by Fig. 4). At some temperature T. a state can be reached where this minimum (as well as the maximum at i = i,) vanishes. Just above T. clusters (which become thermodinamically unstable at T >_ I'.) will disappear, the cluster system being transformed as a result into the undercooled liquid. We believe that T. may be identified with the glass transition temperature, Ta, as measured upon heating in actual experiments. -20
1.0
1,01
0 0.8
0.6
~-so
":.--4.
~:~
0
o.4
[
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~:~ I
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,
I
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i
FIG. 3. L dependence of go = g(io), gm = g(i,~), and fo = f(io) (y = 0.4, Vie = 50 ergs/cm 2, b2 = 0.5/~-*; solid lines: gc = 0.8gco; dashed lines: gc = gco). FIG. 4. Schematic relative free energy curves for a cluster system at different temperatures. It should be noted that restricting the intercluster layer thickness to some predetermined value as is usual in treatments of cluster models is not necessary and, moreover, incorrect in principle. Once the temperature and pressure of the system are specified, this thickness is no longer an independent variable: its value can be find by minimization of the system free energy. 2.2. Coexistence of amorphous phases
Fig. 1 shows (curves al and a2) variations of go = g(io) with the alloy composition for a binary system where two linear compounds, A B and AB2, may be formed (AB2 compound is represented by the circled cross in Fig. 1). It is clear that two "amorphous phases" (a~ and a2) can occur in such a system, one of them (al) is described above, and the other (as) is that with the cluster structure and composition corresponding to AB2 compound. A single amorphous phase within the two-phase field of the metastable phase diagram is thermodynamically unstable against the decomposition into two amorphous phases with compositions corresponding to the common tangent construction. There is much experimental evidence of the phase separation in metallic glasses (see, for example, [3]). It should be stressed that a description of the system with coexisting amorphous phases requires some additional structure parameters, such as a characteristic size of "precipitates" of one amorphous phase in the other, parameters for the interface between the amorphous phases and so on. 2.3. Coexistence of amorphous and crystalline phases
In a mixed amorphous-crystalline system the atom transfer between amorphous and crystalline phases is possible. Fig. 5 shows the free energy variation of a mixed system initially containing a single al amorphous phase of the composition yo = 0.5 with amorphous phase composition, the composition change being due to the B atom transfer from B elemental crystalline to the amorphous phase (B indiffusion) at y <_ Yo and due
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to A indiffusion at g ~ ~/o. It can be seen that ~/decreasing in the al phase at y < ~/o can lead to az --+ as transformation. It is also evident that outdiffusion will take place instead of the indiffusion at some initial system states, leading (as is the case with indiffusion when it takes place) to a metastable equilibrium between crystalline and amorphous phases. Recent results by Aaen Andersen et al [4], who observed the indiffusion of cobalt in the amorphous Co-Zr phase, seem to support the above consideration. This is a relatively new area of research and further experiments are needed to better clarify the problem.
-40
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.....
.....
I ~ m l .
B< -60 0.1
I
0.2
I
0.3
I ..... .
•
>A I
0.4
0.5
t 0.6
t 0.7
0.8
Y FIG. 5. Free energy variations of the mixed amorphous-crystalline system with the amorphous phase composition. FIG. 6. Illustration of the model for an amorphous zone growth in a diffusion couple. Finally it should be noted that all calculated data used in Sections 2.2 and 2.3 were obtained assuming that the system parameters m, b2, 7~ and 7~c have the same values (4.8.10 sl, 0.5 A - l , 800 ergs/cm 2 and 50 ergs/cm s, correspondingly) in both amorphous phases (al and as) and the number of clusters, m, remains unchanged as the system changes, but it can be shown that the situations described are typical and may be realized in a wide range of sets of the system parameters. E4. Remark on structure-sensitive properties Taking into account that in a general case local values of different physical properties, e.g. of elastic and magnetostriction constants, differ in clusters and intercluster layers the evolution of structure-sensitive properties of an amorphous phase under various treatments can be explained, in particular the magnetic anisotropy of as-quenched as well as stress-annealed ribbons of amorphous near-zero magnetostrictive alloys [5,6] which has found no satisfactory explanation in terms of structural models of an amorphous state other than the cluster one. 3. T h e cluster structure f o r m a t i o n In discussion that follows we shall return for brevity to a binary A B system with a single compound, though a great variety of interesting situations will be left beyond the scope of discussion in this case. 9.1. Melt quenching The liquid to glass transition in metallic alloys can be regarded as a usual first-order phase transition (primary crystallization) which proceeds, however, under unusual conditions (the system is far from its equilibrium state and under severe kinetic constraints) where nuclei of a new phase "collide" with each other at the beginning of their growth. Copious nucleation can be facilitated by a small surface energy of the undercooled liquid/nucleus interface. Depending on the quenching conditions the formation of the cluster structure may be not fully completed in as-quenched alloy and can proceed at ambient or elevated temperatures, leading to a reduction of the volume fraction and changes in the compositon of intercluster layers and corresponding changes in alloy properties.
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3.2. Solid state amorphization 3.2.1. Diffusion couples Solid state amorphization in diffusional couples has been found for many metal-metal combinations which meet requirements for a negative free energy of mixing and the asymmetry in the atomic mobility of the two participating species. The amorphous phase usually forms and grows as a planar zone at the interfaces between the elements by diffusion of the fast species alone. At some temperature dependent critical thickness a crystalline reaction product forms. A detailed analysis of experimental observations can be found in [1]. The most complicated and questionable is here a problem of a critical thickness at which a crystalline reaction product appears. We will now try to treat this problem using the above described cluster model of an amorphous structure. Let us assume that the formation of an amorphous phase takes place in some reaction front (RF) ahead of a growing amorphous zone (AZ, see the scheme in Fig. 6) and B atoms are the dominant moving species. As the thickness of the amorphous zone, ~, increases the incoming into the front flux of B atoms decreases as well as the concentration of B atoms in the cluster-free (liquid-like) zone of the front (see Fig. 6); therefore, the rate of the cluster nucletion on the left side of the cluster-free zone where the B concentration is higher than in its remaining part will decrease too. Starting from some critical thickness ~ = ~3 only the previously formed clusters grow in the reaction front, a liquid-like zone disappears and a crystalline reaction product appears. It should be emphasized that in terms of the cluster model an amorphous zone of a diffusion couple is nonhomogeneous, which has to be taken into account in treating the atomic transport within the zone and finding the time law of its growth.
3.2.2. Ball milling Milling in a high energy ball mill can lead to amorphization of elemental powder mixtures as well as intermetallic compound powders [1,7]. A general feature of all types of amorphization reactions via ball milling is that amorphization is always preceded by extreme grain refinement.
FIG. 7. Illustration of the grain refinement (GR) and "wetting" transition (WT) under ball milling. The simplest type of the amorphization reaction in an elemental powder mixture can be expected to be the same as in diffusion couples. It was experimentally observed, however, that amorphization in some systems is preceded by the formation of the crystalline supersaturated solid solution or compound. As the grain refinement in a single phase powder proceeds the free energy difference between the system with ordinary ("sharp") grain boundaries and the system with liquid-like (wetting) layers between grains (with "thick" grain boundaries) increases, so the transition from the state with "sharp" boundaries to the state with "thick" boundaries (resembling the first-order wetting transition [8]) can occur at some grain size [9]. If the grain size after the formation of the wetting layers falls within the range corresponding to the cluster model [2] the transition can be regarded as the crystal to glass transition. If the grain size after the "wetting" transition is beyond the cluster range the cluster amorphous state can be reached by further grain refinement under ball milling. It is worth noting that very few systems are known with a positive heat of mixing which can undergo amorphization due to ball milling. The amorphization in some of these systems is a composition-induced process as was unambiguously demonstrated by Ogino et al [10]. The system composition can be changed,
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for example, by indiffusion from the ambient atmosphere. The amorphization in this case can involve the formation of a liquid-like layer between grains with grain refinement, indiffusion from the atmosphere of D atoms, for example, with strong affinity to one of the system species (A atoms, for example), the nucleation of an amorphous zone (with clusters of the compound formed by A and D atoms) between grains and its growth as indiffusion from the atmosphere continues, which may be accompanied by B indiffusion in the zone. 3.2.3. Other amorphizing treatments Amorphization of some metallic alloys under heat treatment in the atmosphere of hydrogen gas is another example of a composition-induced amorphization [1]. The systems amorphized are initially polycrystalline solid solutions with one of the elements having strong affinity to hydrogen. It can be expected that hydrogen indiffusion would lead to a copious nucleation of hydride clusters at the grain boundaries if the cluster growth is kinetically suppressed. A heterogeneously nucleated amorphous zone will grow at the expense of grains and incoming hydrogen atoms. Spontaneous vitrification after quenching of a high temperature [11] or high pressure [12] single phase state into a two-phase field of the equilibrium phase diagram can be understood as the phase separation under severe kinetic constraints, with nuclei of the primarily precipitated phase as clusters and the remainder as intercluster liquid-like layers. The process does not involve atomic diffusion at long distances. It may occur by heterogeneous nucleation of an amorphous phase at grain boundaries. This consideration could be valid for a pressure-induced amorphization [13].
References 1. W.L.Johnson, Progr. Mat. Sci. 30, 81 (1986). 2. T.Hamada and F.E.Fujita, Jap. J. Appl. Phys. 21,981 (1982). 3. A.R.Yavari, Acta metall. 36, 1863 (1988). 4. L.-U. Aaen Andersen, J.Bottiger, J.Janting, N.Karpe, K.K.Larsen, A.L Greer and R.E.Somekh, Mater. Sci. Eng. A133, 415 (1991). 5. B.L.Shtangeev, A.V.Serebryakov and V.A.Kislov, Metallofizika 13, 83 (1991) (in russian). 6. V.Kislov, Yu.Levin, A.Serebryakov, M.Tejedor and B.Hernando, Acta Phys. Pol. A77, 701 (1990). 7. A.W.Weeber and H.Bakker, Physica B 153, 93 (1988). 8. P.G. de Gennes, Rev. Mod. Phys. 57,827 (1985). 9. A.Serebryakov, Mater. Sci. Forum 88-90, 133 (1992). 10. Y.Ogino, S.Murayama and T.Yamasaki, J. Less-Common Met. 168, 221 (1991). 11. A.Blatter, M. yon Allmen and N.Baltzer, J. Appl. Phys. 62,276 (1987). 12. E.G.Ponyatovsky and O.I.Barkalov, Mater. Sci. Eng. A133, 726 (1991). 13. Y.Fujii, M.Kowaka and A.Onodera, J. Phys. C 18, 789 (1985).
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