Healing of defects in a two-dimensional granular crystal

Abstract

Using a macroscopic analog for a two dimensional hexagonal crystal, we perform an experimental investigation of the self-healing properties of circular grain defects with an emphasis on defect orientation. A circular grain defect is introduced into a nearly perfect hexagonal array of millimeter-sized spherical brass particles enclosed in a square tray. The array is oscillated uniaxially, causing the particles to vibrate randomly with respect to each other, which in turn induces the curved grain boundary around the misoriented defect region to migrate toward its center of curvature. Images of the healing crystal are acquired and analyzed to determine particle locations and quantify the size of the defect at prescribed time intervals. This procedure was repeated ninety-four times in order to collect data on a range of misorientations. In some cases, the misorientation angle varied significantly during healing so both initial misorientation and time averaged misorientation angle were considered as possible driving variables for healing rate. Healing times were fit to an exponential curve dependent on misorientation angle but there was a high degree of scatter from this correlation. Despite this variation in path shape, there was some correlation between healing time and misorientation, though there was significant scatter. In an effort to identify the source of this scatter by differentiating between defects with different healing times but nearly the same misorientation angle, the time dependence of healing rate was investigated. This more detailed examination of the time evolution of defect size revealed substantial variation in time dependence type. Both linear and nonlinear time dependence of defect area size was observed among the healing samples. The nonlinear time dependence of defect size was not common among defects with low healing times. However, degree of linearity did not effectively distinguish between defects with similar misorientation and widely different healing times nor did it correlate meaningfully with misorientation. Though the self-healing behavior of grain defects has not yet been fully characterized, there is evidence that geometric parameters influence overall healing time.