The plane form is the equilibrium one for surfaces of condensed matter. Deviations can be caused usually by crystal structure. Herein we will describe an effect of surface instability due to self- diffusion processes of atoms and molecules in the near surface electric field.
Self-diffusion processes (as it was shown by Mullins) cause relaxation of any deviation (protuberance) from the plane form due to the increased concentration of surface atoms and its consequent smoothing. This process we studied for the case when there is an electric field near the surface. The near surface electric field can be due to either the location of material in an external (homogeneous or inhomogeneous) electrical field or self-charges on the surface. There is an increasing of electric field intensity near protuberances both in external and self-formed electrical fields: the higher is the curvature of surface the stronger is the intensity of the near surface electrical field. Consequently two competing processes occur during surface molecules mass transfer: both the self- diffusion smoothing of surface molecule concentration and drawing of molecules in the strong electric field regions. Depending on the initial shape of the protuberance either relaxation or instability occurs. There is a critical wavelength λ0=RskBT/2Uz, which shows that shorter wavelength deviations decrease their amplitudes and longer wavelength deviations grow in amplitude by time. Here Rs is characteristic of the material, T is temperature, and Uz is the interaction energy of surface molecules with the electric field. Since there are random variations of any surface from the plane form, being placed in an electric field these surfaces will be unstable depending on the intensity of electric field and properties of material.
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