X-RAY-DIFFRACTION STUDY OF GENERALIZED FIBONACCI LATTICES

Generalized Fibonacci lattices which are generated by the inflation transformation A --> A(m)B 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 gamma(m)=[m2(m2 + 4)1/2]/2. When the ratio of alternating layer thicknesses (d(A)/d(B) is equal to gamma(m), the intervals of peaks are indexed by only q1gamma(m)s with adequate q1 and integer s. When the value of d(A)/d(B) is not equal to gamma(m), the intervals of peaks are indexed by q2gamma(m)u and q3gamma(m)upsilon with integers mu and upsilon(q2 not-equal q3). The correlation of lattice arrangements becomes weaker with increasing m, but the correlation is independent of sample size N of the lattice.