Intergranular forces of dynamic coalescence in very thin metallic films

Abstract

Because of the polarization by the electromagnetic field, the grains of very thin metallic films spread over an amorphous substratum are under bipolar interaction forces. One of them, F₀, is created by the field due to the electromagnetic oscillations at zero temperature. Another one, F_T, is due to the field maintaining the radiation of the thermodynamic equilibrium. A third one, F_E, is superimposed onto the first ones, F₀ and F_T, at the time of illumination of the films by the evaporating cell or by an auxiliary source. F₀, F_T, and F_E are expressed with the same function φ(ω) depending upon not only the permittivity ε_g of the grains and the permittivity ε_s of the substratum but also on the shape of the grains, their distances, and their dimensions. The last two modify ε_g, which is very different from ε_∞ in the bulk metal. φ(ω) shows a first maximum which is dependent upon geometrical data, located in the infrared or the visible. Its amplitude is limited only by the imaginary part of F₀. However, the main part of F₀ is concentrated in the far ultraviolet. Nevertheless, an intense illumination in the first‐maximum spectral interval can superimpose a nonnegligible force F_E onto F₀ and F_T. The relative magnitude of these forces can be discussed in the case of granular films of silver on carbon. The fact is that structural modification can be obtained by illumination of these films when they are maintained under ultravacuum until 21 h after their formation.