Zener pins and needles

Abstract

The behaviour of two-dimensional grain structures anchored by circular or elongated pins (needles) is examined in two ways: experimentally, using soap films trapped between two glass plates, and computationally, using a Potts model. In the simulations, the Zener pins are exactly equivalent in size, position and orientation to the pins in the experiment. Rapid grain growth starts without an incubation period and with an underlying time exponent of 1/2. The effective radius of curvature of a growing grain is four times its actual radius. Rapid growth continues until the grain size reaches about half the spacing between pins. Thereafter, growth decelerates and finally stagnates. Repeated simulations and experiments, in which the pattern of pins is identical always show similar kinetic behaviour and similar final grain sizes but no two grain structures are the same. The stagnant grain sizes obey the Friedel ∫;^−1/2 dependence on the area fraction of pins. Also in agreement with the Friedel model, the pinned grains have equiaxed shapes even when the needles are aligned and have aspect ratios as large as 7.