Resonant excitations of ions channeled in quasicrystal structures

Abstract

The resonant excitation of channeling ions is proposed as a method to measure the periodicity and structure of quasicrystals. In principle, such an experiment could provide information about quasicrystal lattice structures because the channeling ion probes only special parts of the crystal. guasicrystals have fivefold rotational symmetry axes, but they lack true periodicity. ' Much of the controversy associated with quasicrystals lies in the possible ambiguity of experimental data which characterize these materials. It is our view that the channeling of ions through these structures, and the resonant excitation of the channeled ions, has the potential to give a one-dimensional probe of quasicrystals. Such a probe could help distinguish between di6'erent models of quasicrystal structure.A channeling ion moving along a (nominal) crystal axis direction is almost exclusively sensitive to the quasicrystal structure in the immediate neighborhood of the channel. Even in situations where the overall structure of a quasicrystal might be ambiguous, one may be able to see quasiperiodicity along the channeling direction. With this motivation, we propose the following simple model of excitation in a one-dimensional quasiperiodic structure.We assume that along the channeling direction, the quasicrystal is a lattice of the Fibonacci type. ' Atoms along the channel can excite the channeled ion. The quasicrystal aspects of the model are reflected in the spacing between the atoms, which is either d or xd. An arbitrarily long piece of the quasicrystal channel can be generated through the following prescription: Let A represent the spacing d, and B represent the spacing xd.Then the Fibonacci sequence is generated by beginning with A and using the replacement rules A -+AB and B~A at each step. The spacing of the first 21 sites of the channel is specified by the sequence ABAABABAABAABABAABABA .We take the ratio of the spacing, x, to be a variable, and do not require that it be the Golden Mean, ( 1+~5)/2, as is often done. For long channels, the fraction of d spacings approaches the inverse of the Golden Mean.The channeled ion is assumed to move at a constant velocity. Each time it passes near one of the lattice atoms, it receives an electrostatic pulse. This pulse couples the ion's electronic ground state to an excited state, so that the ion may be excited as it passes each lattice atom. In actual channeling experiments, the larger orbital dimension of the excited state yields a greatly enhanced probability that one additional electron will be stripped from the excited ion. Thus the excitation is readily observed in the charge state of the ion leaving the quasicrystal.The electric-field pulses which excite the ion can add coherently to increase greatly the excitation probability.For a simple crystal, this implies special channeling velocities which cause the amplitudes of the excited state to add in phase. ' For a quasicrystal structure, the situation is clearly more complicated, since there is only pseudoperiodicity.To consider the i...