Metallic Glasses

Glasses have received a lot of attention because of their interesting structure and dynamics (indeed, Nobel Laureate Phil Anderson wrote that “The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition.”) Unlike crystals, they do not possess long-range order — only short or medium-range order, like liquids. Unlike liquids, however, glasses have mechanical properties akin to those of solids. A number of different approaches have been explored to study the physics of glasses, including harnessing the technology of colloidal physics as many in our and other research groups do. Metallic glasses are also model glassy systems, formed when a molten liquid precursor is supercooled at a rate fast enough that glass formation wins over crystal formation.

Here’s a quick description of two recent papers that look at two different aspects of metallic glasses…

1. How easy is it to form a glass? (Li et al., Science 2008)
Intuitively, one might expect that if the liquid precursor to a metallic glass has higher packing density, the atomic subunits making up the liquid have less “free” volume to explore and hence have a lower probability of forming an ordered cluster to nucleate crystal formation: the glass is “easier” to form. (Note that because the density at the glass transition is continuous, unlike the transition between a liquid and crystal, the density of the liquid precursor and the density of the newly-formed glass are the same thing).

Surprisingly, it seems there is very little clear experimental demonstration of this correlation between the density of a metallic glass and the ease with which it is formed. In this paper, Li et al. show a very nice route towards this. They use microfabrication to produce an array of silicon nitride cantilevers, sputter-coated with differing compositions of the binary alloy Cu_xZr_1-x, a popular system for studying metallic glasses. They measure the density difference between the as-deposited glass and the crystal that results from thermal annealing their samples by measuring the deflection of the cantilevers before and after annealing (the density of the resulting crystalline state can be estimated using equilibrium thermodynamics). On the other hand, they measure the ease of glass formation for glasses of differing composition by casting them in wedge-shaped molds; a cross-section of the resulting solid shows a clear boundary between the glassy and the crystalline state, and the thickness of the lower (denser) glassy state is a standard metric for how easily it formed. The beauty of these experiments is that they are quite straightforward, and look at this particular system over a range of relative compositions.

Sure enough, Li et al. see very nice correlation between the glass/crystal density difference and the ease of glass formation over the range of compositions they study. Interestingly, three particular compositions seem to form the glassy state very easily — and surprisingly, only one can be predicted using existing models!

2. What is the medium-range structure of a glass? (Ma et al., Nature Materials 2008)
A good deal of work has focused on understanding the microscopic nature of short-range – that is, on the lengthscale of just a few atoms – order (SRO) in metallic glasses (e.g. Miracle, 2004). A relatively recent model, which is accumulating more and more experimental support, is that alloyed metallic glass are composed of small clusters of majority atoms surrounding a minority atom “seed”. If one is willing to believe this model, the next question is: how do we use this understanding to better understand the nature of medium-range order (MRO) in metallic glasses? It has been suggested that these clusters may closely pack to form the metallic glass. In this paper, Ma et al. suggest another idea: these clusters form a fractal network of dimension 2.31.

The evidence Ma et al. compile to support this notion is compelling. For starters, fractal networks are ubiquitous in materials of interesting microstructure (e.g. see the references in Ma et al.’s paper). One close example is quasicrystals, which also lack translational symmetry, and have been shown to also be described as fractal networks. Second, Raman and neutron-scattering experiments performed in the 1990s suggested the existence of frequency-dependent vibrational excitations in metallic glasses, with a crossover between the phonons that are characteristic of ordered crystals and “fractons”, vibrational excitations of a fractal network. (This is the first time I come across the idea of a “fracton”, and I will have to spend some time rigorizing how I think about them.) In this paper, Ma et al. present their own and others’ neutron and X-ray diffraction data of a number of metallic glasses of different compositions (including the Cu_xZr_1-x mentioned in the previous paper).

In crystalline materials, the momentum-space position of the first Bragg peak in a powder diffraction pattern () is inversely proportional to the largest distance between two atomic planes of the sample — small ’s probe large lengthscales. Representing the atoms making up the crystal as hard spheres of volume , this distance scales as (that is, constant). The key idea in Ma et al.’s paper is that while metallic glasses do not have well-defined Bragg peaks because of their disordered structure, the medium-range order does give rise to a few diffuse scattering “haloes”. Thinking about the atoms of the metallic glass as hard spheres as well, on expects that constant, where mass density/(avogadro’s number * molecular weight) and is the fractal dimension of the network making up the metallic glass. Strikingly, they see this kind of scaling behavior, with . Further analysis of the atomic pair distribution function of their samples (essentially, a measure of how correlated atoms at different distances from each other are) supports this notion of a fractal network over medium-range length scales. It’ll be interesting to see how future work builds on this idea. I’m a bit confused as to what the “atomic volume” as calculated in Ma et al.’s paper physically represents in these alloyed metallic glasses, something the authors don’t go into too much detail on. Naively I would guess this is somehow related to the size of the clusters making up the fractal network — perhaps it would be interesting to use this kind of data to pull out this information and see if it agrees with other work on the structure of these SRO clusters.