Stability of Multiply-Twinned Particles

Abstract

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