Melting and superheating of low-dimensional materials

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1 Current Opinion in Solid State and Materials Science 5 (2001) Melting and superheating of low-dimensional materials * K. Lu, Z.H. Jin State Key Laboratory for Rapidly Solidified Non-equilibrium Alloys, Institute of Metal Research, Chinese Academy of Sciences, Shenyang , China Abstract The state-of-art of melting and superheating for low-dimensional materials is reviewed. Irregular size dependence of melting kinetics was found for ultrafine particles. Substantial melting point elevation (superheating) was observed in both nanoparticles and thin films with an epitaxial confinement. These findings might significantly advance our understanding of the nature of melting of solids providing the relevant theoretical and computer simulation investigations are stimulated Elsevier Science Ltd. All rights reserved. Keywords: Superheating; Melting; Low-dimensional materials; Nanoparticles; Thin films 1. Introduction adjacent solid still needs further efforts, which will help to understand the melting of low-dimensional materials such Melting of solids is a common phenomenon in nature as nanotubes [12] as well as other materials to be discussed and is normally initiated at solid surface or interfaces [1]. in this short review. As low-dimensional materials (such as nanoparticles, In this paper, we restrict our attention to the most recent nanowires, thin films, and nanophase materials) possess progress on melting and superheating of low-dimensional large areas of surfaces or interfaces, their melting kinetics materials, and especially with emphasis on nano-granular deviate much from that for conventional bulk solids. For structures such as embedded nanoparticles and confined example, the melting points (T m) of free-standing thin films that mainly constitute metallic elements. Several nanometer-sized metal particles are remarkably depressed key issues on melting and superheating will be discussed relative to the equilibrium Tm for bulk materials [2,3]. in terms of experimental measurements, theoretical analy- Meanwhile, it is also observed that when the nanoparticles ses, as well as computer simulations. are properly coated by (or embedded in) a high-tm metal, the melting point can be elevated above the equilibrium T m for bulk solids [4 10]. The dramatic Tm variations for 2. Size-dependence of melting point for nanoparticles various low-dimensional materials have stimulated increasing interest in recent years. Investigations on melting and It has been well known that free-standing nanometersuperheating of low-dimensional materials, on the one sized particles may melt below the equilibrium bulk T m hand, provide a unique opportunity for advancing our due to the extremely high surface/ volume ratio. The understanding of the nature of melting, and on the other depression of melting point (DT m) is found to be propor- hand, are crucial for the technological applications of this tional to 1/D (D the particle size) even when D is as small new materials family with novel properties. as a few nanometers. Such a particle size dependence of Because of the significant role of the free surface on melting point can be well interpreted by the classical melting, there have been extensive studies on the surface thermodynamic arguments. melting (see a recent review article [*11]). A typical However, when the particle size is reduced to be of tens example is the melting of a two-dimensional (2D) sample or hundreds or thousands of atoms, very different melting which may represent the outermost layer of any real behavior appears. The melting point of the particles (or substance. To clarify how the liquid layer consumes the clusters) depends sensitively on their size, as observed in Na particles by Schmidt et al. [**13,14]. Highly irregular *Corresponding author. Tel.: ; fax: patterns were detected for the variation of melting point and latent heat of fusion with the particle size. Changing address: kelu@imr.ac.cn (K. Lu). the size of the Na clusters by a few atoms can change their / 01/ $ see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S (00)

2 40 K. Lu, Z.H. Jin / Current Opinion in Solid State and Materials Science 5 (2001) melting temperature by tens of percent. Local maxima in 3. Effect of interfacial structure on superheating melting point and latent heat of fusion seem to exist at several specific cluster sizes with magic numbers of The melting kinetics of the embedded nanoparticles atoms. Though the effects of geometric shells and elec- depends significantly upon the conditions of the particle/ tronic shells were considered to be responsible for this matrix interfacial structure. When a low-energy coherent or irregular variation in melting point, this phenomenon has semi-coherent interface is formed between the nanoparticle not yet been fully understood theoretically and needs and the matrix, melting of the nanoparticle can be effecfurther in-depth investigations. tively suppressed at elevated temperatures and the melting When nanoparticles are embedded randomly (in crystal- point is higher than the equilibrium bulk T m, i.e. superheat- lographic orientations) in a high-tm matrix (i.e. a nanog- ing of the nanoparticle occurs. This phenomenon has been ranular structure), a depression of melting point is also observed in a number of metallic systems, such as Pb/Al observed, analogous to that for free-standing nanoparticles. [5 7,9], In/Al [5,16,17], Ag/ Ni [18], etc. In all of these In this case, the Tm depression is found to depend upon not cases, a common feature is that a specific shape of the only the particle size but also the contact angle between nanoparticle is formed and every particle/ matrix interface the solid matrix and the liquid nucleus, which is de- is semi-coherent with a cubic cubic orientation relationtermined by the nature of the particle/ matrix interface. In ship. The elevated melting point is believed to result from other words, beside the size-effect, the particle/ matrix an effective suppression of the heterogeneous nucleation of interface structure is also a vital parameter controlling the melting at the epitaxial particle/ matrix interfaces. When Tm depression. Recent experimental measurements of the epitaxy is broken at the interface, no superheating will several kinds of metal nanoparticles embedded in Al be obtained [1], as experimentally demonstrated in the indicated that both the melting point and the latent heat of Pb/Al [9] and In/Al samples (see Fig. 1). Two kinds of fusion for the nanoparticles decreases linearly with an nanogranular In/Al samples were prepared via different increase of 1/D [15]. The contact angle between the liquid approaches: rapidly quenching from the In/Al melt to form nucleus and the solid matrix is determined by the nature of In nanoparticles embedded in Al with a specific shape and the two elements (particle and matrix), and it increases semicoherent In/Al interfaces; ball-milling of the mixture with a reduction of the heat of mixing between two solids. of In and Al powders to form nanogranular In in Al with Fig. 1. Variation of melting point with the particle size for In nanoparticles embedded in an Al matrix in two kinds of In/Al nanogranular samples prepared by means of melt-spinning and ball-milling. The remarkable different melting point variations in these two cases might be attributed to the In/Al interfacial structures. For the melt-spun sample a semi-coherent In/Al interface was formed as evidenced by the HRTEM image of the In particle and the electron diffraction pattern, and for the ball-milled sample, the In/Al interfaces are random (see inserted HRTEM image).

3 K. Lu, Z.H. Jin / Current Opinion in Solid State and Materials Science 5 (2001) random interfaces. The melting points of the In nanoparticles (with comparable particle sizes) in these two samples are completely different. Superheating is observed in the melt-quenched sample but melting point depression in the ball-milled one. In the first case, the degree of superheating is also strongly dependent upon the particle size. The smaller the particle, the higher the superheating, as clearly seen in Fig. 1. Molecular dynamics (MD) simulation of the melting process in confined nanoparticles has been performed to illustrate the effect of interface structure on superheating [*19]. Comparison of the melting behavior for Pb clusters (of 201 and 249 atoms, respectively) coated by Al with and without epitaxial interfaces, simulated by using the Sutton Chen type many-body potential, indicated quite different melting pictures. The coated cluster with a semicoherent Pb/Al interface is superheated up to 750 K (the equilibrium Tm for the Sutton Chen bulk Pb is about K), while for the coated Pb cluster without semicoherent interfaces, premelting dominates and the melting point is merely 500 K. This observation coincides with the Fig. 2. Cross-sectional snapshot views (after energy minimizations) of the experimental evidence. MD simulation of an Ag3055 cluster coated by Ni at different temperatures (1322 K (a), 1335 K (b), 1333 K (c), and 1328 K (d)) around the melting point to illustrate the nucleated melting [20]. 4. Nucleated melting in superheated crystals Obviously, nucleation of melt is the most important It should be pointed out that superheating of confined process for superheating of solids. In order to identify the crystals might be due to two different kinetic mechanisms. melt nucleation in superheated nanoparticles, a MD simu- One is the kinetic nucleation of melting and the other is lation on an Ag cluster (3055 atoms) coated by Ni was kinetic melt front growth. Both mechanisms, with their performed. Experimental measurements indicated that the thermodynamic basis, differ from that for the kinetic Ag nanoparticles embedded in Ni with a cubic cubic superheating due to sluggish melting kinetics under fast epitaxial Ag/ Ni interfaces can be substantially superheated heating rates. The fast heating technique is an effective (up to 40 K for an average particle size of about 30 nm) approach to obtain kinetic superheating for surfaces as well owing to the relatively smaller lattice mismatch ( 16% as bulk solids. compared with 23% for Pb/Al) [18]. MD results demon- While the effect of confinement on melt nucleation has strated that the coated Ag3055 cluster can be superheated, been demonstratively studied by means of MD simulaand the melting process of the superheated Ag cluster is tions, the (interface) confinement effect on the growth initiated at the defective interfacial region and then prop- process of the melt is still unclear, though that seems to be agates inwards, as shown in Fig. 2 [20]. This observation equally important for understanding the melting of solids. suggests that heterogeneous nucleation at the interface This effect is believed to be more significant for the dominates the melting of the superheated nanoparticles melting of confined nanowires and thin films. Studies on even a low-energy semicoherent interface is constructed. If this aspect (experimental, theoretical, and simulation) are the lattice mismatch across the interface vanishes, as highly needed. demonstrated in MD simulations of a model thin-film crystal fully confined by Al matrix, the melting point is much elevated and the melting is initiated homogeneously 5. Superheating of thin films from the interior of the confined thin films [21]. The degree of superheating in this perfectly-confined crystal Analogous to that for nanoparticles, experimental obagrees well with the theoretical prediction based on the servations [23] and thermodynamic analysis [24] indicate kinetic stability limit determined by homogeneous nuclea- that the melting point of free-standing 2D thin films is tion events [*22]. The results clearly show that the depressed relative to the bulk T m. While there are plenty of confinement (the nature of the interfaces) is the key factor observations of superheating in confined nanoparticles, controlling the melt nucleation behavior, which, in turn, superheating of 2D thin films is rarely seen. Those determines the extent of superheating for the confined necessary conditions for superheating of particles (effective crystals. suppression of melt nucleation by the epitaxial interfaces)

4 42 K. Lu, Z.H. Jin / Current Opinion in Solid State and Materials Science 5 (2001) m sl m v are not practically feasible for 2D thin films. Even if a thin growth is DT 5 (2g T cos u )/DL (p/22u ) (where D film could be sandwiched by two high-tm films with is the film thickness, Lv is the latent heat per unit volume, epitaxial interfaces, heterogeneous nucleation of melt at u is the wetting angle which depends upon the Pb/Al solid various defects in the thin film (such as grain boundaries) interfacial energy and gsl is the solid/ liquid interfacial and at the defective interfaces would not be effectively energy). For the 20 nm thick Pb confined films, the suppressed. Therefore, 2D thin films are usually regarded calculated DTm is about 2 98C depending upon the value to be hardly capable of being superheated. of u, which agrees well with the experimental observations. However, a very recent experimental exploration Based on this model it is anticipated that with a reduction showed, for the first time, that confined thin films can be of the film thickness, or a decrease of the epitaxial substantially superheated [**25]. In the experiment, Pb interface energy, the extent of superheating would be thin films (of about 20 nm thick) were sandwiched by Al increased. This has been verified by our latest measurelayers (about 40 nm thick). In the multilayer thin film ment [26]. sample, Pb films are polycrystalline fragments with a grain The finding of superheating in 2D thin films provides an size (plan-view) of about nm. For a small fraction important clue that superheating might be achieved alterof Pb layers, a cubic cubic orientation relationship be- natively by suppression of melt growth without supprestween Pb and Al was detected from electron diffraction sion of nucleation. This is challenging our traditional patterns. An in situ X-ray diffraction analysis of the Pb/Al understanding of the superheating phenomenon. At the thin film sample heated to elevated temperatures clearly same time, superheating of thin films is extremely crucial indicated that the confined Pb thin films refuse to melt up for further development and application of novel thin film to 3348C, which is about 68C higher than the equilibrium materials. bulk Tm for Pb. Repeated measurements demonstrated that a metastable superheating of the confined thin film varies in a range of 3 108C. 6. Melting point limit Such a superheating phenomenon in confined thin films was reasonably attributed to suppression of growth of the It is of extreme interest to ask if there is any upper molten droplet by the epitaxial Al/ Pb/Al confinement, (temperature) limit for the existence of a superheated instead of suppression of melt nucleation (as in super- crystal. There are several models dealing with the question. heated nanoparticles) which may not be preventable due to Here we may put them into the following three categories. various kinds of defects in the polycrystalline films and at the Pb/Al interfaces. A simple model was developed based 1. By analogy to the argument of Kauzmann on the on thermodynamic analysis of the interfacial energy con- supercooled liquid-to-glass transition, an isentropic ditions for the growth of the Pb liquid droplet in the melting point (T s) can be defined at which the entropy confined 2D thin film, as schematically shown in Fig. 3. of a solid undergoing superheating is equal to that of The degree of superheating induced by suppression of melt the equilibrium liquid [27]. The superheated solid Fig. 3. A schematic illustration of interfacial conditions for the growth of a Pb liquid droplet confined by Al layers. The solid/ liquid interface for Pb at the equilibrium melting point is stable when an epitaxial Pb/Al interface is formed (a), while it is unstable when a high-energy Pb/Al interface exists (b) [**25].

5 K. Lu, Z.H. Jin / Current Opinion in Solid State and Materials Science 5 (2001) cannot exist at any temperature above T and it must opinions in regard to the prediction of the melting point s undergo the melting transition below that critical tem- limit [**32]. perature. It is predicted theoretically that T could be Other evidence for our opinion exists. Firstly, it is s located in the range T m [27,28]. In order to demonstrated by MD simulation that, the effective elastic reach this temperature, the system must be heated via modulus of the (310) symmetric tilt grain boundary under an ultrafast heating rate to suppress any nucleation or shear softens significantly and goes to zero at about 98% growth of liquid phase which may lead to complete of the bulk melting point, at which point the boundary will melting otherwise. Hence, in this sense such a catas- start to melt [34]. Secondly, a very recent detection of the trophic limit will be directly related to the dynamic so-called non-thermal melting by ultrafast X-ray diffracorigin of melting transitions, as in the case for super- tion from a Ge single crystal surface under heating by an cooled liquid-to-glass transitions. ultrashort-pulse laser indicated that there exists a large 2. Similar limits exist when one puts the volume and/ or difference in the melting speed between the crystal surface rigidity into consideration. It is found that the rigidity and the internal crystal which is undergoing transient limit is lower than both the isotropic and the isochoric superheating [**35]. The result indicated that homogelimit. The rigidity melting criterion was originally neous nucleation of melt should occur for superheated developed by Born and later was found to be closely single crystals. Though detailed information is still lacking related to possible superheating (instead of normal from the experimental side, MD simulations should be melting) of a crystal [29]. It can be regarded as used extensively to understand the important problems belonging to the same type of lattice instability models concerning the structure and properties of superheated as proposed by Lindemann at the beginning of this crystals and transient liquid phase growth from the solid century. lattice. The results also encourage us to make further 3. On the basis of the homogeneous nucleation theory for possible experimental verifications of the theoretical premelting, a kinetic limit for superheated crystals was diction based on MD simulations. proposed [*22]. According to both the classical nucleation theory [*22] and a density functional argument [30], a superheating of about 10% can be obtained with respect to the equilibrium Tm by neglecting the addi- tional 5 to 10% of the superheating due to the elastic strain effects originating from the density difference between the liquid and the solid. This is in good agreement with the MD simulation result of the super- heating in a surface-free bulk single crystal [31]. It is interesting to note that superheating by 20% of Tm is in numerical accordance with the prediction based on the rigidity model (22% of T m), that underlies some correlation between the lattice instability model and the kinetic theory. To clarify the argument we again benefit from the atomis- tic scale information provided by MD simulations. Our recent simulations [32,33] showed that loss of either crystallinity or, equivalently, lattice rigidity (from calcula- tion of the temperature dependence of shear modulus), not globally but locally, acts as the key factor to induce melting for a homogeneous crystal undergoing superheat- ing. Those thermally destabilized atoms, which satisfy Lindemann s criterion, will also satisfy Born s criterion, and they appear in a cooperative manner as the temperature is elevated. Melting occurs as those destabilized liquid-like clusters start to accumulate and percolate throughout the crystal. Thus, according to this picture, the instability model of either Lindemann type or Born type are basically correlated to each other and serves as the nucleation mechanism at the atomic scale. And based on such a scenario, a unified view of the melting origin can be achieved, which should be of value to narrow the different 7. Summary The work reviewed here has shown that low-dimension- al materials exhibit very different melting behavior from that of conventional bulk solids. With a reduction of size into the nanometer regime, irregular variation of the melting kinetics with size appears for ultrafine particles. For the embedded nanoparticles, the melting behavior is controlled not only by the particle size but also by the particle/ matrix interfaces. Melting point elevation has been observed in confined nanoparticles and in confined thin films as well, in which the epitaxial interface plays a key role. Although theoretical analysis and computer simulation investigations have deepened, to some extent, the understanding of these observations, further develop- ment along this direction is still highly needed. From a practical point of view, experimental studies of the melting process of thin films and nanowires that are finding more and more technological applications in modern industries, especially to explore effective approaches to elevate their thermal stability against melting, seem to be of great importance. Acknowledgements The authors would like to acknowledge the financial support by the National Science Foundation of China (Grants no , , and ) and Max-Planck Society of Germany.

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