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 ≦ r i w * , quasi-stable for r i w * r i t 0 where r is an edge length of the particle, while a decahedral particle is not essentially stable but quasi-stable for r ≦ r d t 0 and unstable for r > r d t 0 . The critical sizes r i w * , r i t 0 and r d t 0 are formulated as functions of the specific surface energy γ h k l , the twin boundary energy γ t , the elastic strain energy W and the adhesive energy γ a to the substrate. Calculated critical diameters 2 r i w * ,2 r i t 0 and 2 r d t 0 for the particles grown in free space for several elements range between 15.5A and 106.8A, between 109.8A and 486.1A and between 725A and 3961A, respectively. These values are in good agreement with experimental results.