The origin of incommensurate structures in insulators

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Abstract
The authors set out in detail their recent theory of the origin of incommensurate structures. It relates to a whole class of cases where none of the previously known causes apply, particularly in insulators. The mechanism involves two different modes of transformation psi and phi from the high-temperature disordered (or undistorted) phase. If psi and phi have different symmetry they cannot be present in a uniform commensurate phase. However they can interact in a modulated phase to lower the free energy if their symmetries satisfy a certain connecting relationship. They discuss the mechanism from both the microscopic and the phenomenological points of view, and show how psi , phi in practice are two complete 'component structures' which are modulated 90 degrees out of phase with one another. The 'exaggerated gradient ploy' helps in discovering the second component and the detailed forces involved when one component is more or less known. They treat various temperature effects including the transition to a commensurate phase at lower temperature.