Focus: Crystal Healing

Published January 28, 2008  |  Phys. Rev. Focus 21, 4 (2008)  |  DOI: 10.1103/PhysRevFocus.21.4

Current-Induced Stabilization of Surface Morphology in Stressed Solids

Vivek Tomar, M. Rauf Gungor, and Dimitrios Maroudas

Published January 24, 2008
+Enlarge image Figure 1
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Under Stress. A lake bed develops an array of cracks as the drying mud shrinks. New calculations suggest that an electric field can sometimes prevent the cracks that occur at the surface of a stressed crystal.

Pull hard enough on opposite ends of a crystal, and it cracks. In some cases, the flat crystal surface first develops a wavy shape before the cracks appear. But in the 25 January Physical Review Letters, researchers calculate that adding an electric field sometimes prevents waviness and cracks from forming by causing the valleys to fill up with extra atoms. In addition to suggesting a novel way to avoid cracks, the result illustrates the sometimes surprising effects of combining multiple forces.

Nature abounds with spontaneous patterns created by a constant force. In one familiar example, a steady breeze speeds up slightly as it passes over the crest of a small water wave, creating a partial vacuum that causes the wave to grow even higher. A somewhat similar instability occurs at the surface of any crystal that is laterally stretched. Extra atoms diffusing around on the surface respond to the stretch by spending more time on the tops of small hills, where they have fewer contacts with surface atoms and so aren’t tugged apart as strongly. So hills grow and valleys deepen. Eventually, the deepening valleys become sharp cracks that penetrate deep into the crystal. Although cracks can start in other ways, this wave-induced cracking is expected to happen eventually in any stressed material with mobile surface atoms.

Spontaneous hills and valleys also appear when an electric field drives atoms along a metal surface. Dimitris Maroudas and his team at the University of Massachusetts at Amherst have been studying this “electromigration” phenomenon, which can create voids that break the tiny wires in integrated circuits. Although either stress or electric field alone are known to create undulations, the researchers now calculate that, surprisingly, their combined action can stabilize the flat surface.

The stabilization occurs because the ease with which atoms move around on a crystal surface depends on the precise arrangement of atoms within the surface. On a wavy surface, this arrangement depends on the angle the surface takes through the crystal at any given spot–different “cuts” through a perfect crystal expose different surface structures. Maroudas and his colleagues analyzed cases where an electric field pushes atoms “downhill” faster than it pushes them “uphill”, thanks to the surface structure. So if a valley starts to appear because of stress, the electric field causes it to fill in immediately. The team calculated that a large-enough electric field has this flattening effect even when the hills and valleys are rather large.

“What has been done traditionally to improve fracture resistance is to try to modify the surface,” Maroudas says. He suggests that electricity could be a completely new way to prevent cracks in integrated circuit wiring and perhaps other metallic structures. But the approach might not work for cracks that start suddenly at localized crystal defects, which don’t go through a preliminary hill-and-valley stage.

“The whole idea that you can heal the material, not by changing material parameters, but just by turning on a voltage,” is a “cool result,” says David Srolovitz of Yeshiva University in New York City. Joachim Krug of the University of Köln in Germany says that it illustrates a general principle that “if you have several forces acting at the same time, they can combine in a beneficial way.” But he adds that “whether this can really be exploited is less clear.”

–Don Monroe


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