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ScienceWeek
MATERIALS SCIENCE: ON METALLIC GLASSES
The following points are made by Alain Reza Yavari (Nature 2006 439:405):
1) Metallic glasses are peculiar metallic materials, usually alloys, that lack the long-range order of normal, crystalline metals. The attractive interactions, and differences in size, of atoms of different types in metallic glasses do, however, lead to a short-range order characterized by clusters of "solute" atoms of one type surrounded by atoms of a more numerous species, the solvent. This much has been known for a long time. But just how these atomic clusters connect to fill space nearly as densely as crystalline solids with the same atomic composition has remained a mystery.
2) Some 45 years after the discovery of the first metallic glasses[1], Sheng et al[2] provide an essential missing piece of the puzzle, determining the three-dimensional structure of several metallic glasses that contain two different types of atoms. In these "binary" glasses, they find nanoscale medium-range order, often consisting of closely packed icosahedral (20-faced) assemblies of some 13 neighboring atomic clusters each centered on a solute atom.
3) The lack of long-range order in metallic glasses is signalled by the absence of sharp Bragg peaks -- features characteristic of a periodically structured material -- in the angular distribution of diffracted beams (X-rays, electrons, and neutrons) used to probe them. These missing peaks led early researchers to consider atomic packing in metallic glasses to be similar to John Bernal's "dense random packing" of hard spheres in liquids[3]. In this picture, the larger solvent atoms are densely, randomly packed[4], and the solute atoms are jammed into cavities left available to them by the geometry of this packing. Such models were later abandoned -- in part because metallic glasses such as copper zirconium [Cu(60)Zr(40)] were discovered whose solvent atoms were smaller than their solute atoms -- in favor of packings of atom clusters in fixed ratios[5] with short-range order similar to that of crystalline compounds of the same atomic composition. These "stereochemical" models could reproduce the experimental diffraction patterns and the corresponding distributions (known as radial distribution functions) of nearest and next-to-nearest neighbor atomic shells. But metallic glasses also exhibit order over 1 1.5 nanometers (for comparison, a typical metallic atom has a diameter of around 0.3 nm), and, until recently, no tangible description of how clusters of atoms interconnect to generate this medium-range order was available.
4) This situation changed with the proposal a couple of years ago of dense packings of overlapping atomic clusters as the fundamental scheme for metallic glasses. In this model, an arbitrary "face-centered-cubic" (fcc) lattice of clusters is chosen to achieve high density. (The fcc lattice is the densest possible cubic packing, and consists of elements placed at each vertex, and in the middle of each face, of a cubic structure.) But to maintain long-range disorder -- to keep the material glassy -- a strain factor has to be introduced to limit the coherence of such a lattice to the 1 1.5-nm scale. This model has been successful in predicting the compositions of most glass-forming alloys, and alloys with lower melting points than any of their constituents, known as eutectics.
References (abridged):
1. Klement, W. , Willens, R. H. & Duwez, P. Nature 187, 869 871 (1960)
2. Sheng, H. W. , Luo, W. K. , Alamgir, F. M. , Bai, J. M. & Ma, E. Nature 439, 419 425 (2006)
3. Bernal, J. D. Nature 185, 68 70 (1960)
4. Polk, D. E. Acta Metall. 20, 485 489 (1972)
5. Gaskell, P. H. Nature 276, 484 485 (1978)
Nature http://www.nature.com/nature
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Related Material:
DIFFUSION IN GLASSES AND SUPERCOOLED LIQUIDS
Notes by ScienceWeek:
In general, "ergodicity" is a property of dynamic systems containing a random variable (stochastic systems): a system is said to be ergodic if it tends in probability to a limiting form which is independent of the initial conditions. The term "mode coupling theory" (MCT) refers to a theory that describes the transition of super-cooled liquids to a non-ergodic state. The transition of the super-cooled liquid to the glass state represents a critical slowing down of the particle motions, leading to structural arrest. A characteristic property of the arrested state is that it has the static structure of a liquid. Apart from the parameters describing the microscopic motion, the static structure factor is the only input to the theory, which aims to give a complete description of the dynamical properties of the system.
H.R. Schober (Institute for Solid-State Research Julich, DE) discusses diffusion in glasses, the author making the following points:
1) Diffusion in glasses and their melts has been studied intensively for many years. These efforts are stimulated both by the technological importance of glassy and amorphous materials and by the desire to understand the physics of disordered systems in general and the liquid to glass transition in particular. Despite this effort there is still no agreement on the nature of diffusion on an atomic level or on its change at temperatures near the glass transition. This holds even for simple densely packed glasses such as binary metallic glasses.
2) In a hot liquid, diffusion is by flow, whereas, in the glass well below the transition temperature, it will be mediated by hopping processes. One key question is the transition between the two regimes. For fragile glasses, such as most polymers and amorphous metallic glasses, so-called "mode coupling theory" predicts an arrest of the homogeneous viscous flow in the undercooled melt at a temperature (Tc) well above the glass transition temperature. Hopping processes will suppress the predicted singularities and will become the dominant diffusion process near Tc.
3) The nature of the hopping process is another issue of controversy. Is it by a vacancy mechanism, similar to diffusion in the crystalline state, or is it via a collective process inherent to the disordered structure? Investigations are hampered by the fact that glasses are thermodynamically not in equilibrium, and one observes aging of the system. The diffusion coefficient of a glass that has been relaxed for a long time will be considerably lower than the diffusion coefficient of an “as quenched” glass.
4) The author reports a molecular dynamics simulation involving a calculation of the pressure dependence of the diffusion coefficient in a binary Lennard-Jones glass (i.e., a system described by a Lennard-Jones potential approximation). Four temperature regimes are observed. The apparent activation volume drops from high values in the hot liquid to a plateau value. It rises steeply near the critical temperature of mode coupling theory, but in the glassy state one finds again small values similar to those in the liquid. The peak of the activation volume at the critical temperature is in agreement with the prediction of mode coupling theory.
References (abridged):
1. H. Mehrer, Defect Diffus. Forum 129-130, 57 (1996).
2. W. Frank, Defect Diffus. Forum 143-147, 695 (1997).
3. Y. Loirat, J.L. Bocquet, and Y. Limoge, J. Non-Cryst. Solids 265, 252 (2000).
4. F. Faupel, K. Ratzke, H. Ehmler, P. Klugkist, V. Zollmer, C. Nagel, A. Rehmet, and A. Heesemann, Mater. Res. Soc. Symp. Proc. 664, L2.1.1 (2001).
5. F. Faupel, W. Frank, M.-P. Macht, H. Mehrer, V. Naundorf, K. Ratzke, S.K. Sharma, H.R. Schober, and H. Teichler, Rev. Mod. Phys. (to be published).
Phys. Rev. Lett.2002 88:145901
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Related Material:
ON THE BRAGG GLASS PHASE
The following points are made by T. Klein et al (Nature 2001 413:404):
1) Although crystals are usually quite stable, they are sensitive to a disordered environment: even an infinitesimal amount of impurities can lead to the destruction of crystalline order. The resulting state of matter has been a long-standing puzzle, and until recently it was believed to be an amorphous state in which the crystal would break into "crystallites". But a different theory predicts the existence of a novel phase of matter: the so-called "Bragg glass", which is a glass and yet nearly as ordered as a perfect crystal.
2) After the Bragg glass was first proposed in 1995, its existence was supported by further analytical and numerical calculations, but up to now experimental evidence for this phase has been indirect. The "lattice" of vortices containing magnetic flux in *type II superconductors provide a convenient system to investigate these ideas, and the authors demonstrate that neutron-diffraction data of the vortex lattice provides unambiguous evidence for a weak power-law decay of the crystalline order characteristic of a Bragg glass.
3) The theory also accurately predicts the electrical transport properties of superconductors, and naturally explains the observed phase transitions and the dramatic jumps in the critical current associated with the melting of the Bragg glass. Moreover, the model explains experiments as diverse as x-ray scattering in disordered liquid crystals and the conductivity of electronic crystals.
Nature http://www.nature.com/nature
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Notes by ScienceWeek:
type II superconductors: Examples of materials of this type are niobium and vanadium (the only type II superconductors among the chemical elements) and some alloys and compounds, including the high-temperature superconductivity compounds. The experiments in this report were performed on a large single-phase (K,Ba)BiO(sub3) crystal mass of 300 milligrams, superconducting transition temperature 23 kelvins.
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