QUANTUM STRUCTURE OF THE SURFACE LAYER OF ATOMICALLY SMOOTH CRYSTALS

In this paper, we propose a model for determining the thickness of the surface layer of metals and the quantum structure of this layer. An atomically smooth metal is represented as a diagram: nanolayer → mesolayer → bulk phase, which differ from each other in the nature of size effects. There is no size effect in the bulk phase. The thickness of the surface layer of metals R(I) has a size from 1 nm to 10 nm, except for cesium, i.e. they represent a nanostructure. It is shown that the energy levels En of the nanolayer are determined by one fundamental parameter - the lattice constant of the metal a. As soon as the parameter a stops changing, the spectrum of quantum states passes into a continuous spectrum. The nanolayer R(I) is a step function in En, which can be easily reduced to the Lebesgue integral, which plays an important role in quantum theory. Quantum threads (quantum planes) in the nanolayer R(I) can be interpreted as solitons, crowdions, discrete breathers turning into nanocracks. Quantum threads in the R(I) nanolayer and the nanolayer itself can be represented as a nanoparticle with a diameter of R(I) and pre-melting occurs in it in a stepwise manner. It is shown that all metal monolayers differ significantly from each other.