The Harder They Come

Over at Physical Review Focus, my latest story concerns a simple model that can deal with materials whose hardness varies with direction.

One important message, which gets diluted by the required pegging of the story to a current Physical Review article, is that there are some new ultrahard materials called transition-metal diborides. One of these, ReB₂, is said to be hard enough to scratch diamond. I'm a little confused about this, because the measurements of the Vickers microhardness, measured with a tiny diamond indenter, give numbers for the hardness that are a bit lower than diamond. (Other researchers complained about the claims, Science subscribers only.) But it's certainly competitive, and apparently easier to make than competitors like boron nitride, which need high temperatures and pressures.

It's important to be careful talking about "hardness," which is one of those dual-use words whose lay meaning is imprecise. Scientifically, hardness refers to permanent, "plastic" deformation, as contrasted with stiffness, which is characterized by the bulk modulus or compressibility and refers to reversible, elastic deformation. Water is incompressible but not at all hard, for example. In a crystalline solid, plastic deformation requires that planes of atoms slide by one another, breaking bonds as they do so. In normal materials, this process is sensitive to things like grains structure and defects, which is what smiths change when they "temper" steel. In principle, though, microhardness is an intrinsic, unchangeable property of a particular crystal.

The author of the paper, Antonín Šimůnek, (want to know how to pronounce Czech?) has developed a model for hardness that simply calculates the bond strengths for the various bonds in the material and combines them into an overall hardness. Apparently there's been a flurry of similar papers over the last few years, which is kind of surprising since hardness has been important for a long time. In fact, the ingredients of the models seem almost primitive in these days of massive computer simulations. Šimůnek told me that he recently realized that his overtly classical view of the forces between atoms is similar to work published in 1939 by Richard Feynman, then at MIT. In the current paper, he distinguishes between bonds aligned with and perpendicular to the force to calculate a direction-dependent hardness, which apparently has never been done before.

As an undergraduate at MIT, a hotbed of early metallurgy research, I heard an amusing story about calculations of hardness in metals. The story goes that the first calculations for a single crystal predicted a strength much greater than observed. At that point someone realized that, instead of a plane of atoms sliding all at once, the same overall motion could come from progressive motion of line, called a dislocation, moving one atomic row at a time in a zipper fashion, which of course takes much less energy. Sadly, the calculations then predicted much too low a strength. The researchers then realized that the motion of dislocations could be arrested if they were pinned by crystalline defects. The predicted strength was then in line with measurements.

Wisely, they stopped improving the models.