Abstract
The author studies the diffraction properties of a class of quasiperiodic superlattices described by the substitution rules A to ApB, B to A where p is a positive integer. These can be obtained by a projection method with a characteristic irrational sigma , e.g. for the Fibonacci lattice (p=1) A to AB, B to A, sigma =(1+ square root 5)/2. It is shown that the diffraction peak positions Kk.r can be labeled by two integers k, r and are given by the expression Kk.r=2 pi Lambda -1r sigma 'k where sigma ' are the so called precious means. It is shown that the Fibonacci lattice has the unique property that sigma = sigma '.
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