X-ray diffraction study of generalized Fibonacci lattices

Generalized Fibonacci lattices which are generated by the inflation transformation A → AmB and B → A with integer m, have been grown by means of molecular beam epitaxy. Many sharp satellite peaks are observed in the diffraction patterns, and the peaks are specified by γ(m) = [m + (m2 + 4)1/2]/2. When the ratio of alternating layer thicknesses (dA/dB) is equal to γ(m), the intervals of peaks are indexed by only q1γ(m)s with adequate q1 and integer s. When the value of dA/dB is not equal to γ(m), the intervals of peaks are indexed by q2γ(m)u and q3γ(m)v with integers u and v(q2 ≠ q3). The correlation of lattice arrangements becomes weaker with increasing m, but the correlation is independent of sample size N of the lattice. (author)