Trouble with Lifshitz, Slyozov and Wagner

A physics theory used to create cutting-edge "designer materials" doesn't work as scientists expect. A new experiment on the ISS could reveal why.

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July 7, 2003:  A quiet revolution is happening in the science of designing materials.

In times past, finding a material with just the right strength, elasticity, or other desirable traits involved a process of trial and error. People would "discover" a new material like steel or rubber, not "invent" it. Only after the fact would scientists figure out why that certain mixture of chemicals behaved a certain way.

But the burgeoning field of materials science is turning all of that on its head. Scientists can now start with a list of desired traits and design a custom material to suit--specifying the atomic structure, grain structure, and even heat treatments needed--without needing to resort to the old cycle of make, test, refine.

Right: Computers can simulate the physics of solid materials before they're made. This, for instance, is a model of a metal-ceramic interface calculated by the Computational Materials Science Group at Arizona State University. [more]

The secret behind this radical new ability is a combination of two modern trends: the availability of powerful, affordable computers; and advances over the last 50 years in the fundamental physics of solids. By plugging the equations of physics into a fast enough computer, you can see how a certain material will behave before it's ever made.

But experiments flown on the space shuttle in 1997 showed that one of the classic physics theories used to design materials doesn't work as scientists expected.

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The theory in question, known as the Lifshitz-Slyozov-Wagner theory, is important to designers of metal alloys--that is, mixtures of two or more metals. Stainless steel is an alloy (it's a mixture of iron, nickel, and chromium) as is most gold jewelry (gold and nickel). Why make alloys? Because a mixture of metals can be, e.g., tougher or lighter-weight than any one metal by itself.

Alloys are formed by heating the ingredients until they liquefy, mixing them together, and letting the batch cool. As the mixture cools and solidifies, tiny crystalline grains form. With the passage of time, these grains do something odd: larger grains tend to grow while smaller ones vanish--a process called "coarsening." Surprisingly, this coarsening continues to happen long after the alloy has fully solidified, often weakening the alloy. This could be a catastrophic problem if, say, the material was used to make the fast-spinning blade of a jet turbine.

The Lifshitz-Slyozov-Wagner (LSW) theory predicts the rate of coarsening in alloys. What's wrong with the theory? Strictly speaking, nothing. It's the way engineers have been using it that's wrong. The equations of LSW describe how fast materials will coarsen if you let them sit for an infinite amount of time. Forever. Most engineers can't wait that long, so they've assumed that the theory also works for shorter times--like hours and days.

Above: Solid tin particles coarsen within a liquid mixture of tin and lead over a 24-hour period. Snapshots of three different samples were combined to create this time series. [more]

Testing this assumption was one of the goals of the Coarsening in Solid-Liquid Mixtures (CSLM) experiment, which flew onboard the space shuttle in 1997.

"The first shuttle experiments worked just as we'd hoped," recalls principal investigator Peter Voorhees, professor of materials science at Northwestern University near Chicago, Illinois. "But when we looked at the sizes of the grains, they were larger on average than the theory would predict."

Something was amiss.

Scientists had never been able to fully test the predictions of LSW in a liquid mixture because gravity always interfered with the most ideal experiments. To mirror the assumptions of the theory, an experiment would need to have solid, microscopic grains scattered evenly within a liquid. If you try this on the ground, the solid particles will quickly settle out of the liquid and accumulate at the top or bottom of the container, ruining the experiment.

Above: Gravity causes the tin particles to quickly sediment to the top of the chamber during ground experiments (right). For the same experiment run in orbit, the particles remain evenly dispersed (left). Image courtesy NASA Glenn Research Center.

"In space, the solid particles stay evenly dispersed for hours or even days, so we can compare the results directly with the theory," Voorhees says.

The shuttle experiments, however, ran for only 10 hours. And perhaps that's the problem. Computer simulations suggest that when coarsening is allowed to continue somewhat longer, the theory redeems itself.

With longer trials in mind, Voorhees and his colleagues designed CSLM-2, a 2nd-generation coarsening experiment for the International Space Station. The device will heat a mixture of lead and tin until it melts. Because pure tin has a higher melting temperature than the lead-tin mixture, tiny embedded crystals of tin will remain solid at the experiment's temperature: about 185°C, or 365°F. (Tin melts at 232°C, or 449°F.) Scientists use lead and tin because the basic physical properties of this mixture are well understood, making the analysis of the results more fruitful.

Right: Many applications employing alloys will benefit from  improved theories for coarsening.

As the furnaces keep the samples melted, the tiny tin crystals will coarsen for times ranging from 1.5 to 48 hours. After the larger crystals have grown and the smaller ones shrunk, the samples will be cooled and solidified to preserve them, then returned to Earth where Voorhees and his team of scientists will slice them open and examine them to see if the theory held true for the longer experiment runs.

Although there's still much to learn about coarsening, some of the results from the first CSLM experiment are already being used by industry. For example, Voorhees helped an Evanston, Illinois, company called QuesTek to integrate the findings of the first experiment into the computer software they use to make material design recommendations. QuesTek's clients--which include major manufacturing companies--then use those materials to build a wide range of products.

This means the physics revealed by CSLM may already be finding its way to a jet engine, or an aluminum car chassis, or a suspension bridge near you. CSLM-2 will teach us even more....

Coarsening in Solid-Liquid Mixtures 2 -- home page, from NASA Glenn Research Center

Peter Voohees -- the Frank C. Engelhart Professor of Materials Science and Engineering at Northwestern University

Materials by Design -- (Cornell University) the basics of metals and metal alloys

"LSW theory applies to solid-solid coarsening [which is a slow process]," notes Marshall Space Flight Center materials scientist Donald Gillies. "Voorhees and others are experimenting with solid-liquid mixtures to speed things up. You can do the experiments so much more quickly and convincingly within liquids, but you need microgravity to avoid sedimentation."