STABILITY OF MULTIPLY-TWINNED PARTICLES

A theory is developed which allows one to discuss the stability of multiply-twinned particles and to calculate critical sizes for stable and quasi-stable states. An icosahedral particle is essentially stable for r≦riw*, quasi-stable for riw*<r≦ rit0 and unstable for r>rit0 where r is an edge length of the particle, while a decahedral particle is not essentially stable but quasi-stable for r≦rdt0 and unstable for r>rdt0. The critical sizes riw*, rit0 and rdt0 are formulated as functions of the specific surface energy γhkl, the twin boundary energy γt, the elastic strain energy W and the adhesive energy γa to the substrate. Calculated critical diameters 2riw*, 2rit0 and 2rdt0 for the particles grown in free space for several elements range between 15.5Å and 106.8Å, between 109.8Å and 486.1Å and between 725Å and 3961Å, respectively. These values are in good agreement with experimental results. © 1969, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.