INTRODUCTION
This discussion focuses on the development of nano-structured materials through controlled primary crystallization reactions of amorphous alloys. The nanocrystalline state is at the forefront of study in a variety of disciplines involving condensed matter. In broad terms the main activities can be classified into material synthesis strategies, property measurement and evaluation, applications, and computer simulation and modeling. A key attribute of the nanocrystalline state that offers a broad attraction for many disciplines is derived from the nanometer length scale. At this length scale the chemical, biological, physical, mechanical, and structural properties and performance of materials are susceptible to significant changes during synthesis,[1] and the current computational capabilities allow for effective simulation and analysis of nanocrystalline assemblies.1-21
The principles that govern the kinetics of microstruc-tural evolution apply directly to other devitrification reactions that yield nanostructured intermetallic phases and quasi-crystalline phases that are also promising in terms of their structural and functional performance. Some of the key issues concerning synthesis and stability are illustrated from the observed behavior in specific amorphous alloys, but the discussion also applies to other similar alloy systems.
OVERVIEW
The nanocrystalline state, where the microstructural size scales are in the 1- to 100-nm range, can be synthesized by a variety of processing routes starting with the vapor, liquid, or solid state.[1] Although it may be expected that the final nanocrystalline state is independent of the processing route, in practice this is not the case. For example, for deposition from the vapor at the high rates that promote nanocrystalline grain sizes, residual impurities or entrapped gas can be present in the deposit. Similarly, from an initial solid, the nanocrystalline state is often achieved by the mechanical milling of powders. During subsequent consolidation of powders to a bulk form, it is common to incorporate impurities from the medium used for milling and to retain a residual po-rosity.[3] The attainment of nanocrystalline structures from the liquid or vapor requires the attainment of a high crystal nucleation rate, which in turn is promoted by a large undercooling before the onset of crystallization. Actually, there are two pathways that may be followed to achieve the high crystal nucleation density.[4] If a liquid is rapidly quenched at a rate that happens to coincide with the conditions for a high nucleation rate a nanocrystalline structure is possible by direct quenching.[5] However, under most conditions of rapid quenching it is difficult to control the processing and the reproducibility. Instead, a direct cooling to an amorphous state and a subsequent low-temperature crystallization treatment is usually preferred as a method of achieving reproducible nanostruc-ture synthesis including the fabrication of nanostructures in bulk sample volumes.1-6-8-1
The classes of metallic glasses that provide the most effective routes to nanocrystallization are closely related to two important aspects of solidification that involve kinetic competition: 1) avoidance of crystallization upon cooling of the liquid and 2) the control of crystallization upon heating of the glass. Although there are connections between these aspects, including the common underlying important role of melt undercooling as a measure of liquid metastability, in each case the controlling reactions occur under regimes of different kinetic con-straints.[9] In addition to the closed-system methods involving liquid or vapor quenching, it is recognized that open systems involving continuous deformation1-10-1 or irradiation1-11-1 can drive a material toward nanocrystalli-nity and in some cases to an amorphous structure. In this case, the stored energy due to defects, grain refinement, and solute supersaturation is a measure of the level of metastability that is crucial to consider in the analysis of amorphization and the development of nanostructured microstructures.
NANOCRYSTALLIZATION REACTIONS
The crystallization behavior of amorphous materials is of central importance in the synthesis of nanostructured materials. The reaction pathways that are operative during crystallization must be identified and controlled to develop successful strategies for the consolidation of amorphous powders or ribbons that can be processed into bulk nano-structured solids. Moreover, the control of the reaction path during crystallization provides for the option to develop nanoscale structures with different phase selection.
The different reaction paths and product selection options are identified in Fig. 1, which illustrates schematically the free energy relationships between an initial amorphous phase that is considered as an undercooled liquid solution and several crystalline product phases that include stable a and p phases and a metastable g phase.[13'14] Within the alloy composition ranges that are usually favored for glass formation there are several types of crystallization reactions that can be used to develop nanocrystalline structures during controlled heating or isothermal reaction. One of the simplest reactions is the direct transformation from the glass to a single-phase crystal without composition change as illustrated in Fig. 1A and b by pathways (1) and (2) for either stable or meta-stable initial product phases. The composition invariant or polymorphic reaction can yield metastable structures such as supersaturated solid solution phases or metastable intermediate phases that can undergo further transformation that is indicated by pathways (1′) and (2′) in Fig. 1A and b. With primary crystallization, a single phase is the initial product, but the reaction proceeds with a partitioning of solute to yield a solute lean primary crystal and a residual amorphous phase matrix that is enriched in solute.[6,15-18] The kinetics of primary crystallization is evidently related to the rate of solute diffusion in the amorphous matrix that is necessary to dissipate the solute that is rejected during primary crystal growth.[19] It is also apparent that primary crystallization does not result in a stable equilibrium product structure that is indicated by the compositions ae and pe in Fig. 1A and B. To complete the primary crystallization, a subsequent multiphase crystallization develops either from the nucleation site provided by the primary crystal or directly from the amorphous phase. For example, with eutectic crystallization that is indicated by pathway (3) in Fig. 1A, the product phases (i.e., a and p) often develop by a coupled growth and appear with a lamellar or rod type of regular morphology in a spherulitic pattern.[8,19] In this case the synthesis of a nanoscale microstructure requires a high density of a and p colonies with an ultrafine lamellar spacing. A schematic illustration of the characteristic microstructural morphologies associated with each of the nanocrystallization reactions is provided in Fig. 2. Often, under high-undercooling conditions metastable phase reactions can develop as a precursor to the formation of stable crystallization products. For example, as indicated in Fig. 1B, the un-dercooled liquid or amorphous phase can undergo a phase separation reaction leading to the formation of two liquids with different compositions that are indicated by Ga and Gb in Fig. 1b. At low temperature or high undercooling, limited atomic mobility will result in a fine scale of phase separation that can extend into the nanoscale regime.[20] Moreover, in some cases the interfaces between the different liquid regions can serve as heterogeneous nucle-ation sites for subsequent crystallization reactions and establish high nucleation product number densities. In addition, there is evidence that in some systems minor impurity levels can promote the development of phase separation reactions.[14] Another example of a precursor reaction is the formation of an intermediate phase as a metastable product as illustrated in Fig. 1A for the g phase.
Fig. 1 Schematic free energy vs. composition diagrams illustrating some of the possible nanocrystallization reactions of an amorphous phase. (A) reaction pathways for an alloy with a negative heat of mixing and a metastable g phase. (B) reaction pathways for an alloy with a positive heat of mixing.
Fig. 2 Schematic illustration of the characteristic microstruc-tural morphologies that develop during nanocrystallization by (a) polymorphic, (b) eutectic, and (c) primary phase reactions. In (c) the dotted curve around primary phase nanocrystals denotes the extent of the solute diffusion field.
KINETICS OF NANOCRYSTALLIZATION
One of the key requirements that must be satisfied for the development of a nanoscale microstructure by a crystallization reaction is the attainment of a very high nuc-leation product number density. The main features of the steady-state nucleation rate kinetics can be described by
where Jjs is the steady state nucleation rate on a volume (i=v) or surface basis (i=a).[12] Respective values for the prefactor, Oi, activation barrier, AG*, and the contact angle function, f(0), are used in Eq. 1, and kT is the thermal energy. The expressions for Oi involve a product of a nucleation site density on a catalytic surface or volume basis, the number of atoms on a nucleus surface and a jump frequency. For most cases, 0v=1030/z cm sec-1 and 0a=01022/z cm-2 sec-1, with z the liquid shear viscosity (in poise) given by Ref. [6- as
in terms of the liquidus temperature, TL, and the glass transition, Tg, and f, the fraction of active catalytic sites. The activation barrier for nucleation is given by
where s is the liquid-solid interfacial energy,[21] AGv is the driving free energy for nucleation of a unit volume of product phase, and b =16p/3 for spherical nuclei. With a planar catalytic surface site and spherical nuclei f(0) = [2- 3 cos +cos30]/4. Following the establishment of a supersaturation or undercooling, there is an initial time period during which the nucleation cluster population evolves toward the steady-state distribution.1-22-1 During this transient period the time-dependent nucleation rate, Ji(t), is given by
where t is the time lag or delay time that is estimated by (n*2/p2b). The critical nucleus size, n*, in atoms is obtained from n* = 4pr*3/(3Va) where Va is the volume per atom and r* = – 2s/AGv is the critical nucleus radius. The atomic jump frequency, b, can be estimated by D/l2, where D is the diffusion coefficient in the undercooled phase and l is the jump distance.[23,24]
To achieve a nanocrystalline microstructure (i.e., with a size scale < 100 nm) in a fully crystallized volume, the nucleation number density should be at least of the order of 1021 m- 3. Of course, nanocrystallization can be achieved only if there are also restrictions on the kinetics of nanocrystal growth following nucleation.
The kinetic analysis of growth follows different forms that depend on the nature of the solute partitioning associated with phase growth. For example, during polymorphous transformation without solute redistribution, the growth rate, V, is controlled by interface attachment limited kinetics as represented by
where V0 is a prefactor of the order of 5 x 103 m/sec and Qd is the activation energy for interface jumps.[19,25] At low temperature where AGv ^ RT growth is diffusion controlled as expressed by
For the case of eutectic reaction where the solute redistribution is limited to the reaction interface
where DI is the interface diffusivity, d is the thickness of the reaction front, and l is the lamellar spacing.[25,26] With these kinetic modes, the reaction is relatively rapid and a metastable microstructure based on nanocrystals and an amorphous phase with the original composition is possible if the kinetics of subsequent decomposition reactions to a more stable phase constitution is sluggish.
When growth requires a redistribution of solute as in primary crystallization, the kinetics are limited by the rate of diffusion of the rejected solute into the amorphous matrix. For evolving nanocrystals that are isolated from each other the growth rate has the following form
where a is a dimensionless factor that is evaluated from the compositions at the particle/matrix interface and the average composition and D will be controlled by the slowest diffusing solute in a multicomponent alloy.[26] However, at high nucleation densities the isolation can be lost as the diffusion fields from neighboring nanocrystals begin to overlap (i.e., soft impingement).[25] Under this condition there is a kinetic inhibition to further growth. Concurrent with the growth of nanocrystals, the highly refined sizes indicate that capillarity effects such as Ostwald ripening due to curvature-driven transport (i.e., Gibbs-Thomson effect) can be important.[25,27]
AMORPHIZATION KINETICS AND TRANSITIONS
The kinetic transition between nanocrystalline products and an amorphous phase is a common structural change that occurs during solidification with increasing cooling rate as the liquid undercooling approaches Tg. Often, the initiation of the transition is represented by a critical cooling rate and interpreted as a sharp structural change.[28] However, there are also many reports of mixed crystal/glass phase structures indicating that the transition occurs over a range of cooling rates reflecting the kinetic competition and the probabilistic nature of nucle-ation.[29,30] It is useful to note that the glass transition is not a phase transformation in a thermodynamic sense, but it is a kinetic manifestation of the slowing of atomic transport in the liquid with cooling. In fact, the calorimet-ric glass transition signal is due to the large change in heat capacity that occurs when a liquid becomes configura-tionally frozen. The slowing of atomic transport is also reflected by an increase in liquid viscosity. The time for the liquid structure to relax during cooling is related to the viscosity, and for typical laboratory measurement conditions Tg corresponds to a viscosity in the range of 1012-10 P (10n-1012 Pa sec).[31]
Indeed, following amorphization by rapid melt quenching, many metallic glasses do not exhibit a clear glass transition signal, Tg, upon reheating. Instead, initial exothermic maxima are observed to develop that indicate a multiple-stage crystallization1-5,32,33-1 as shown in Fig. 3 for an amorphous Al88Y7Fe5 ribbon after melt spinning and after initial crystallization. The microstructural analysis has established that for many amorphous Al-base alloys that contain transition metal (TM) and rare earth (RE) solutes, the initial crystallization corresponds to primary phase formation (i.e., Al) yielding a sample that contains a high density of nanocrystals within an amorphous ma-trix.[5] This behavior is of importance in understanding the kinetic control of glass formation. The two basic strategies to synthesize amorphous alloys are illustrated schematically in Fig. 4. With nucleation control, the undercooling that is achieved during cooling bypasses the nucleation reaction and the nucleation size distribution,1-9-1 C(n) that may be retained by the cooling does not overlap with the critical nucleation size, n*, at the crystallization temperature, Tx. As a result, there is no precursor reaction to influence the evolution of crystalline clusters during subsequent thermal treatment. In this way, a clear separation in temperature between the Tg and Tx signals can be observed during reheating of a glass. These kinetic conditions are the basis for bulk glass formation during slow cooling. During isothermal annealing at Tx, the heat evolution rate exhibits a clear delay before the onset of the nucleation reaction and a peak maximum associated with the completion of nucleation and continued growth. On the other hand, under growth-controlled conditions the cooling rate is insufficient to bypass the nucleation onset completely so that some small fraction of crystallites may form initially, but the rapidly rising viscosity and falling growth rate with continued cooling near Tg prevents rapid cluster growth. In addition, the cluster size distribution that is retained overlaps in size with the critical nucleation size at Tx. In this case, as indicated in Fig. 4, upon reheating a sample with preexisting crystallites (i.e., quenched-in nuclei), rapid crystallization because of the development of quenched-in clusters as well as additional nucleation ensues at Tx, which will essentially coincide with Tg.[34- Whereas many of the early metallic glass alloys were synthesized under growth-controlled conditions (i.e., marginal glass formers)1-35-1 the primary crystallization particle densities in these alloys are of the order of 1018 m~ 3. For the class of amorphous Al- and Fe-base glasses, the primary crystallization number densities range from 1021 up to almost 1023 m~3. Both of the basic mechanisms for glass formation that are outlined in Fig. 3 can yield a high number density of nanocrystals upon devitrification. With nucleation control, nanostructure development can be achieved by controlled reheating, because the maximum in the growth rate typically occurs at a higher temperature than the maximum in the nuc-leation rate.[25- In addition to the two basic synthesis routes outlined in Fig. 4, there is another important distinction between alloys that form bulk glasses and the marginal glass-forming alloys based on the temperature dependence of the liquid viscosity.[31- The main features of the viscosity behavior are shown in Fig. 5 where ''strong'' liquids display an Arrhenius type of temperature dependence. A good example of a strong liquid is SiO2, but the bulk glass-forming alloys also display strong liquid characteristics.1-31-1 For the ''fragile'' liquid behavior shown in Fig. 5 the viscosity is low even in the un-dercooled regime, but increases sharply upon approaching the glass transition. It appears that the marginal glass-forming alloys exhibit a fragile type of viscosity behavior. It is evident that the transport behavior will impact both the ease of glass formation and the kinetics of nanocrystal development. The different synthesis routes that are shown in Fig. 4 originate from the relative time scales for the onset of nucleation and melt cooling. The transition from growth control to nucleation control can be achieved either by an increase in the cooling rate or by lengthening the time for onset of nucleation, tn. Because tn is related to atomic transport in the liquid, strong liquids with high viscosity are favored for bulk glass formation. It is also apparent that tn can be lengthened by removing active nucleation sites from the melt. In fact, this is the basis for the effectiveness of melt fluxing, which has been shown to promote bulk glass formation.[36,37] The actual mechanism for the development of the ultrahigh number densities of nanocrystals is under active study, and proposals based on homogeneous[38,39- and heteroge-neous[35,40] nucleation and precursor phase separation reactions1-41-1 are under examination.
Fig. 3 TEM bright-field images from an Al88Y7Fe5 melt-spun ribbon that was isothermally annealed at 245°C for (a) 10 min, (b) 30 min, (c) 100 min, and (d) continuous heating differential scanning calorimetry (DSC) trace at 40 K/Min showing a primary crystallization onset at 276°C.
Fig. 4 The principal forms of kinetic control for metallic glass formation.
Fig. 5 A schematic illustration of the liquid viscosity behavior vs. Tg/T for strong and fragile glasses.
The attainment of nanocrystal dispersions of essentially pure Al with ultrahigh number densities is a critical component of the attractive structural performance, but an equally important characteristic is the high thermal stability. One indication of this stability is the wide temperature range between the primary crystallization and final crystallization of between 75° and 100°C in Fig. 3. Within this range, there is a metastable two-phase coexistence involving the Al nanocrystals and the surrounding amorphous matrix with limited coarsening of the microstructure. The sluggish kinetics is related at least in part to the large differences in component atom sizes and diffusivities1-42-44-1 as well as the onset of impingement of the diffusion fields from neighboring nanocrystals.1-40-1 Indeed, even at a particle density of 1021 m-3 the average nanocrystal separation is only about 100 nm. It is also evident that for the Al nanocrystals to grow there is a rejection of solute (i.e., TM and RE) as is typical for primary crystallization reactions. The low solute diffusiv-ities, especially for the large RE atom, act to limit the growth,[45- and the transport is limited further by the reduced concentration gradient due to impingement as indicated by the asymmetric primary crystallization exotherm in Fig. 3. In fact, because the amorphous matrix composition will also be enriched in TM and RE components, it is possible to use the solute redistribution during primary crystallization to enhance the stability of the amorphous matrix (i.e., raise Tg ).[15,46- This kinetic restriction inhibits further nanocrystal growth and accounts for the asymmetric crystallization peak and the remarkable thermal stability.
