On the use of crenel functions for occupationally modulated structures

Abstract

The use of a crenel function, i.e. a difference between two Heaviside functions of amplitude 1, for strong occupation modulation waves and its influence on the refinement of accompanying displacive modulation waves is discussed. The basic set of harmonic functions that is usually employed for the modelling of the displacive modulation wave is no longer orthogonal on the interval where the crenel function takes the value 1. This causes severe correlations between different displacive modulation amplitudes during refinement. The best solution to prevent these correlations is to select functions for inclusion in the refinement according to the criterion that their generalized cosine to the subspace of already selected functions has to be smaller than a certain threshold value. A quality-of-selection parameter is used to estimate the completeness of the selected functions. Finally, the selected functions are orthogonalized. One artificial illustration and one real example are given to demonstrate the use and application of the proposed methods.