Influence of initial structure of stainless steels on self-organizing process of second structures under boundary friction is investigated. At the minimal wear rate in near-surface friction layers the syncretic ratio between quantity of γ- and α-phases, and also dislocation density in them is established. This ratio corresponds to fractions which are quotient of Fibonacci numbers taken through one: 1/1, 1/2, 2/3, 3/5, 5/8, 8/13, ....

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