Localization of electromagnetic field on the “Brouwer-island” and liquid metal embrittlement

Abstract

Liquid metal embrittlement (LME) manifests itself as a sudden destruction of a metal sample if it is covered by a thin liquid film of eutectic mixture of specially selected metals. The proposed theoretical model of this phenomenon is based on an assumption related to the possibility of electromagnetic field localization in folds of interface between the phases or components of eutectic mixture filling cracks in solid metal surface (the typical example is In–Ga eutectic on Al-surface). Based on simultaneous presence of three different components in each space point of eutectic mixture (homogeneous In + Ga melt, solid In, and solid Ga), the system of interface folds could be simulated by the Brouwer surface – well known in topology. This surface separates three different components presented at each of its point. Such fractal surfaces posses by a finite volume. The volume occupied by the surface is defined as a difference between the eutectic mixture volume and the sum of volumes of its components. We investigate localization of external electromagnetic radiation in this system of folds. Due to very large magnitude of effective dielectric permeability of the considered system, at relative small volume change and fractal dimension of interface close to the value 3, the wave length of incident radiation inside the system is considerably decreased and multiscale folds are filled with localized photons. A probability of this process and the life time of the localized photons are calculated. The localized photons play crucial role in destruction of primary cracks in the metal surface. They are capable “to switch of” the Coulomb attraction of charge fluctuations on opposite “banks” of the crack filled with the eutectic. As a result, the crack could break down.