When cleavage is a bad thing

Glass: it's so much more than just the clear stuff in your windowpanes that keeps the cold out. In fact, we've just learned of a glass that is actually stronger than steel, and just about as tough.

(And yes, I'll explain the difference between strength and toughness.)

When cleavage is a bad thing

Glass is a contrarian to nature's general preference for order. If I mix together two types of atoms (which I'll represent as red and black) as liquids and allow them to slowly cool, they will almost always form a nicely ordered crystal, as shown in the diagram at left. The atoms line up in a nice square lattice, with all the atoms the same distance from each other. Red and black atoms alternate, so that every atom has four neighbors of the same color and four neighbors of the opposite color.

The early days of solid-state physics focused on growing 'perfect' crystals, as the high degree of order made understanding the fundamental properties of those materials much easier. Pure materials, however, are a little limiting. A crystalline element - or alloy - has specific properties that are the same for every piece of that element or alloy. As we became better and better at understanding the atomic-level properties of materials, we realized that we can change the properties of materials by changing the atomic and nano-scale organization of those materials.

When cleavage is a bad thing

For example, what if I let my red and black atoms form their nice square lattice, but I disrupt them just enough so that red atoms sit in places where black atoms ought to be, and vice-versa? This can have a significant effect on the crystal properties. Understanding how the atomic arrangement affects materials properties lets us make materials that have the properties we need.

Despite the difference in chemical order, both of the materials I've shown you thus far are crystals. Inherent in being a crystal is the presence of long-range order, as illustrated by the square lattice of my pictures. When you grow rock candy from a sugar-water solution, the pieces have square edges that reflect the crystalline nature of their underlying atomic-level order. When you cut a crystal - like diamond - you get nice smooth faces because the crystal cleaves along particular crystal planes. You might imagine that if I went to the crystal above and pushed on the rightmost four columns of atoms, I could separate those four columns from the others, leaving two very smooth faces where I made the split. Mica cleaves in planes, which is how the early settlers made it into windows. Graphite, too, cleaves into places, which is why it makes such a good lubricant (and writing media).

Cleavage is a good thing for materials you want to break; however, this is not a desireable property if you are trying to build airplanes or buildings. You need a material that is strong which means that it resists changing shape when it is pushed or pulled. You want to be able to put a heavy load on your material without the material denting or bending. You're also looking for toughness, which is a resistance to shattering. If a material is going to give, you'd like it to bend or dent, not shatter.

Window glass (which is made mostly from silicon dioxide) is very strong; however, it is not at all tough. When this type of glass breaks, it does so catastrophically. A glass window doesn't bend: it shatters into a million tiny pieces. Metals don't shatter, but they also deform when the stress placed on them becomes too large. When we talk about toughness, we're really concerned with how much energy can be put into the material before it breaks. Toughness tests are great fun to do in the lab, because they often involve a large mass on a pendulum. You raise the mass to different heights and release it so that the mass strikes your sample at the bottom-most part of its swing. The higher you lift your mass, the more energy you impart to your sample.

When cleavage is a bad thing

Glass is not a crystal: it is amorphous, meaning that it has no long-range order. A few clusters of atoms here or there might be trying to arrange themselves in some pattern, but the material as a whole is just a mess. Atoms everywhere. Red next to red (or black, depends on which red atom you're looking at) and none of the atoms are regularly located.

You might think that the lack of order places amorphous materials at a disadvantage, but sometimes amorphous materials have superior properties to their better-organized crystalline counterparts. For example, there isn't an obvious place where the amorphous sample to the left looks weaker. There aren't any cleavage planes. It takes more energy to break the material, although when it does break, it does so in spectacular fashion.

There are many different kinds of glass: lead glass and borosilicate glass (Pyrex), just to name two; however, not all glass is transparent. The term 'glass' covers a much broader range of materials that includes metals. 'Glass' indicates the lack of long-range order, not the transparency of the material.

There is technically a difference betweren glassy and amorphous. A glass has a glass transition - a transition from glass to liquid - that occurs on time scales that depend on the rate of heating. The glass transition is a very different type of transition than a phase transition, such as the transition from solid to liquid. Ice melts at a very specific temperature and essentially instantaneously at that temperature. The glass transition is more like easing into a new phase. Technically, there is a discontinuity in a true phase transition, which the glass transition is more continuous.

The first metallic glasses were produced in 1960 by Klement Jr., Willens and Duwez at Caltech, which is where much of the most exciting work on metallic glasses happens. Metals are difficult to make into glasses because they naturally prefer to order. You have to trick them into becoming amorphous by cooling them very quickly - literally stopping them where they stand before they have time to move into their ordered positions. The earliest metallic glasses needed cooling rates on the order of a million Kelvin a second, although many of the newer metallic glasses don't need quite as high cooling rates.

Metallic glasses have a lot of properties you don't expect from metals. One of the more suprising is that metallic glasses are springy. These glasses store energy when hit, then return it to the object that hit them. The video below shows this by dropping a metal ball on two disks: a metallic glass disk on the left and a regular metal on the right. (Don't let the 'liquid metal' appelation fool you: it's a metallic glass, not a liquid. LiquidMetal is the name of a company)

Most metallic glasses are corrosion resistant, meaning that they don't rust. Because there are no grain boundaries, metallic glasses can be polished to a very high sheen, which makes them attractive for things like cell phone or computer cases. The springy property has been taken advantage of in commercial products already. The digital light processor (DLP) projectors that have tiny mirrors that are actuated to point in different directions use a metallic glass (Al3Ti) as the hinges for these rotating mirrors.

Even though metallic glasses are strong, they share the property with silica glasses that they lack toughness (which means they are brittle). Although there are no cleavage planes, there are small areas of the material that are inherently weaker than others. Those areas start to break first when the material is stressed. Once a crack starts, it behaves much like a run in a pair of nylons - it propagates through the entire material and you have a critical failure. What you need for metallic glasses is the equivalent of clear nail polish - some mechanism for stopping the crack before it gets big enough. The problem is that usually, the properties that make a glass strong also make it brittle. Materials developers have historically regarded strength and toughness as competing properties. You can't optimize both at the same time.

In the January 9, 2011 issues of Nature Materials, a group from Caltech and Lawrence Berkeley National Laboratory (Demetriou, et al) report on a metallic glass that is strong, but also toughness - a combination significantly better than any previously realized materials. The alloy is a mouthful: Pd79Ag3.5P6Si9.5Ge2, which means that, out of every hundred atoms in the compound, 79 are palladium (Pd), three-and-a-half are silver (Ag), six are phosphorus (P), nine and a half are silicon (Si) and two are germanium (Ge). For you chemists (since you aren't technically supposed to have fractions in compounds) out of every two hundred atoms, 168 are Pd, seven are silver, 12 are P, 19 are Si and 4 are Ge.

When cleavage is a bad thing

Like many glasses, the material reported upon by the Caltech/LBNL group is strong, with a bulk modulus of 172 gigapascals (GPa) - which corresponds to a pressure of about 25 million pounds per square inch (psi). I've compared the bulk modulus of the new material with some other materials below. The bulk modulus of silicon-based glass is around 35-55 GPa, steel is around 160 GPa and diamond is 440 GPa. This metallic glass is literally stronger than steel - but it is also just as tough.

Some of the first investigations of toughness in metallic glasses were done by DaVinci, who studied the mechanical properties of brittle iron wires. DaVinci measured how much force it took to break a wire as a function of the wire length. You might naively think that the more wire you have, the more force the wire should withstand before fracturing.

The opposite happened: the longer the wire, the easier it was to fracture it. Remember that our amorphous materials have local defects. The longer the wire, the more defects present and the higher the probability that a defect of critical size - one that will grow rapidly when the material is stressed - is present. Fracture toughness is reported in weird units: megapascal-root meters (MPa m1/2). The more brittle metallic glasses have toughness values of a little more than 1 MPa-m1/2, while a typical steel might be 50-60 MPa m1/2. High-strength metal alloys (which are crystalline or quasi-crystalline), may have toughnesses up to a couple hundred MPa m1/2. The fracture toughness of the new metallic glass is reported to be around 200 MPa m1/2 - comparable to the highest strength steels and higher than any other metallic glasses known at this point.

In metallic glasses, the dominant type of defect are very small groups of atoms (on the order of hundreds to thousands) that move together in a shear band. As the strain level increases, the shear bands turn into nanoscopic cracks. Those cracks eventually lead to macroscopic materials failure.

You would think this would indicate that you want to eliminate shear bands in a material; however, the new material has high toughness because it has a very large number of shear bands. Normally, the problem is that shear bands offer a path for the cracks to propagate. In this material, there are so many shear bands that they form an interpenetrating systems of cracks, preferentially around the tip of a starting crack. This network prevents the crack from propagating, which increases the material's toughness of the material. Essentially, the many shear bands are pulling in many different directions, so there is no single preferred way for a crack to propagate. The new metallic glass has higher strength and toughness than previously discovered glasses.

The downside? The largest samples reported upon are 6mm-diameter rods. Cooling metals quickly is a challenge: a large piece of metal takes so long to cool that the inside will crystallize before you can cool it. Most things made from metallic glasses must have at least one dimension be pretty small. One of the common ways of making metallic glasses is the poetically named method called 'splat-cooling'. You drop molten metal on a very cold surface. A rotating wheel constantly exposes a new cold surface, and the cooled material is collected as it falls off the wheel. The samples from the Nature Materials paper were made the old-fashioned way: Heat the alloys in thin (0.5mm wall thickness) closed quartz tubes and drop them in cold water.

Another issue is that the material is mostly palladium, which - in bulk - is selling at somewhere around $16,000 a kilogram. Pure material is even more costly. You're not going to be making many bridges out of this; however, it might be good for the aerospace industry, or for biological implants, where the high cost could be justified by higher strength and toughness reducing the number of surgeries a person would require to replace or repair the device.

This post originally appeared on Cocktail Party Physics. Image via Nesster's Flickr.