Materials by Design

Modeler at the Mesoscale

Modeling at the electronic/atomic scale based on quantum mechanics has been very successful in predicting the properties of new materials systems, but there are limitations.

Most of the calculations based on density functional theory are performed assuming a temperature of zero Kelvin and assuming a perfect crystal structure. And even really large computers can model only a few hundreds of atoms over a very brief time scale measured in picoseconds. We can increase the system size in atomic scale simulations to millions of atoms by using more approximate descriptions of interatomic interactions among atoms called empirical potentials. However, the sizes are still too small compared to most structures of interest in practical materials systems, such as the aluminum alloys used in automobiles and nickel alloys in turbine engines in which millions of nanoscale precipitate particles give them useful properties. Anything that changes over a large volume and a relatively long time, e.g., minutes or hours, cannot really be modeled atomically.

Modeling Microstructures

Long-Qing Chen, distinguished professor of materials science and engineering, works at a larger scale developing modeling techniques to predict features called microstructures. Microstructure refers to the mesoscale features that are intermediate in size between the nanoscale and bulk scale and can include grains of different shapes and sizes, different phases or crystal structures, different electrical or magnetic polarization, and various defects. These features are what determine the mechanical, electrical, magnetic, and optical properties of a material, according to Chen. Therefore, we achieve the desired properties by controlling microstructures. Chen is widely known among materials scientists for developing solutions to modeling at the mesoscale using a technique called phase-field modeling. "The phase-field approach is perhaps the most powerful approach for predicting microstructure evolution under different processing conditions with different compositions as a function of time," Chen says.

What is Phase-Field Modeling?

"We used to model the interface motion by assuming a sharp mathematical interface between two different materials," Chen remarks. "We thought the material on one side would behave in one way and that on the other side of the interface it would behave differently. Then at the interface you would somehow have to define some kind of boundary conditions."

Phase-field, however, assumes there is a gradual change from one material to another. The interface is smoothed out. This is not a new idea, says Chen, having been proposed by Dutch scientist Johannes van der Waals more than a century ago. But phasefield models really took off in the 1990s when two researchers, a mathematician and a physicist, tried to model the dendrite growth during solidification of a liquid. Since then it has been applied to many areas, including phase transformations in alloys, crystal growth in vapor deposition, grain growth,ferroelectric materials, topological optimization,and image processing. Chen has also applied phase-field equations to a variety of materials applications: alloy microstructures, ferroelectric domain microstructures, capacitor degradation, and battery or solid oxide fuel cell electrode microstructures. Some of the phase-field models proposed by Chen's group have been picked up by other computational groups. "It's nice to see other people utilizing what we proposed," he says. "Examples include phase-field models for grain growth, precipitate microstructures in alloys, and domain structures in ferroelectric materials."

Working with Experimentalists

The Chen group uses phase-field techniques to help experimental groups at Penn State and other universities, as well as industry partners who are developing new alloys for automotive and aerospace, to design and control microstructure. "One of the features of our group is our work with experimentalists," Chen says. "We work with more than a dozen experimental groups, many in the area of oxide ferroelectric and multiferroic thin films." Oxide ferroelectric thin films are used in applications as diverse as piezoelectric actuators, ferroelectric memory, etc. Multiferroics are materials with both ferroelectric and ferromagnetic properties. Ferroelectric materials have a permanent electric polarization that can be reversed by an external electric field. Ferromagnetic materials can be given magnetic properties by applying an external magnetic field. Chen's group helps experimentalists figure out how to produce particular domain structures in thin films by choosing different substrates, processing at different temperatures, or applying fields.

"Doing experiments, it is very difficult to get into the details of the physical mechanisms underlying the phenomenon that you observe. But using simulation, we can get at all the details of what's happening inside a material. A lot of times it can really help experimentalists understand what they've observed or measured," Chen says.

"Our collaborations with experimental groups have led to many joint publications. My students communicate with students in experimental groups, and sometimes we can even provide predictions and guidance to experiments," he continues. For example, classic lead-free materials such as BaTiO3 and KNbO3 undergo a series of ferroelectric transitions upon heating, sequentially adopting rhombohedral, orthorhombic, and tetragonal ferroelectric phases before reverting to the cubic parent phase in a single crystal single domain state. In multi-domain configurations however, his phasefield simulations predict the emergence of a new phase of monoclinic symmetry, thermodynamically stabilized in significant volume fractions (20-60%) over a wide temperature range of over 100 K. The figure shows an example of predicted domain structure consisting of several phases including the new monoclinic phases represented in different colors. Such a new phase was experimentally confirmed by Professor Gopalan's group at Penn State using a nonlinear optical Second Harmonic Generation (SHG) imaging technique.

In the future, if funding arrives, Chen could be working with battery experts at Penn State to try to solve one of the grand challenges in energy related research, which is to dramatically improve the solid electrolyte materials for batteries. He is currently involved in a GOALI (Grant Opportunities for Academic Liaison with Industry) program in collaboration with General Motors to study dendrite growth during battery charging and in a NETL project on modeling degradation of electrode microstructures in solid oxide fuel cells.

Long-Qing Chen is a fellow of the Materials Research Society and American Physical Society, and received a Guggenheim Fellowship in 2005-2006, in addition to many other awards. His publications have been cited over 12,000 times. He can be contacted at lqc3@psu.edu.