Researchers discover geometric movement pattern of grain boundaries

Mathieu Baltussen and Marjolein Dijkstra from Utrecht University, together with researchers from Radboud University, discovered how grain boundaries in crystalline materials move according to a geometric pattern. This discovery may in the future help in developing stronger materials. 

Crystalline materials, such as aluminium, consist of many small crystals. The boundaries between these crystals, known as grain boundaries, determine how strong a material is: the more grain boundaries, the stronger the material. Grain boundaries move through the material, but how this movement works had until now remained unclear. Roel Dullens, a physical chemist at Radboud University, and his team have now discovered a geometric mechanism that can predict this movement.

Colloids

The team studied grain boundaries in colloidal crystals. Colloids are substances whose particles are roughly between one nanometre and a few micrometres in size: milk, blood, and opal are examples. "Colloids are therefore considerably larger than molecules and atoms, and as a result much easier to observe under a microscope," says Dullens. "They are also interesting because they behave in the same way as molecules and atoms in terms of phase transitions — from liquid to crystal, for instance — something Einstein already described in 1905."

From liquid to crystal

Particles in a colloidal liquid move constantly back and forth due to Brownian motion, which is caused by collisions with the smaller molecules of the surrounding liquid. This motion effectively causes them to scan their environment, seek out the most favourable position, and arrange themselves on a lattice: a crystal structure. Because colloids are so large, they move relatively slowly, allowing researchers to observe, track, and manipulate individual particles.

Colloids are considerably larger than molecules and atoms, and as a result much easier to observe under a microscope

Cooking – Looking - Tweezing

Roel Dullens: "In our lab, chemists and physicists work together. This gives us the ability to create particles with very specific properties ourselves, and to build specialist microscopes to go with them." The research team also makes use of an optical tweezer — a focused beam of light with which you can, in effect, pick up a particle. "When you move the laser, the particle moves with it, so we can direct particles and observe what happens inside the crystal."

Circle

Studying grain boundaries in a material is normally difficult, as they are connected in a network and influence one another's movements. The researchers therefore used a circular optical tweezer to create a single, circular grain boundary. "That is important, because it has one curvature, perfectly defined," explains Dullens. "The only thing that matters then is the difference in orientation between the crystals on the inside and the outside."

Once the desired difference in orientation is achieved by rotating with the optical tweezer, the grain boundary is released and subsequently shrinks. "It shrinks because it seeks to use as little energy as possible. Interfaces always cost energy, and nature resists that."

Hexagonal pattern

The researchers observed what the particles do as the grain boundary shrinks. They monitored the boundary move slowly through the crystal, with particles transitioning from one orientation to the other. By photographing this process and overlaying the images, it became clear which particles remained stationary and which moved: stationary particles appeared as a dot, moving particles as a streak.

The result was surprising: some particles remained entirely still as the grain boundary passed, whilst others moved around it in a kind of dance. The stationary particles arranged themselves in a hexagonal pattern.

Geometric framework

A significant part of the geometric model describing this movement was developed at Utrecht University. During his master's research, Mathieu Baltussen collaborated with Marjolein Dijkstra on the theoretical elaboration of grain boundary dynamics. When his experimental work came to a standstill during the COVID-19 pandemic, Baltussen set to work on the mathematical calculations behind the experiments. He discovered that a geometric movement lay behind the shifting grain boundaries and, using his calculations, was able to determine which particles remain stationary and how the rest of the system moves.

"We then built a model from this: a geometric framework," says Dullens. "With it, we can predict where the stationary particles will be and where the rest will move to. All we need are the two crystal lattices and the difference in orientation between them. I can then tell you precisely where all those particles will go."

Dislocations

What is particularly remarkable is that the framework predicts not only the movement of particles, but also that of dislocations: defects in the crystal lattice. "A dislocation is not a particle, but a defect in the lattice that can move without individual particles needing to travel far," explains Dullens. "Think of it like people passing something along a queue: the object travels the entire length of the queue without anyone actually needing to leave their spot."

Applications

Dullens: "Grain boundaries have a major influence on the strength of a material. Now that we understand how these grain boundaries move, this may in the future help us to design stronger materials. In addition, this framework opens up possibilities for further research into crystals, not only in colloidal materials, but we believe our framework has broader applicability."

This text is based on a news item written by Lottie Pohlmann of Radboud University.