The origin of the incommensurate phase III of biphenyl

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Abstract
Biphenyl is studied as a simple archetypal incommensurate material, with particular emphasis on the physical origin of its incommensurate nature, which persists to 0K. The authors present a simple picture of the enmeshing of the phenyl rings of biphenyl with those of neighbouring molecules within the crystal. Since the molecules are located on a triangular lattice (in the ab plane), twisting the molecules produces 'frustration' in the mutually intermeshed rotations of the phenyl rings. This leads directly to the singly incommensurate (phase III) of biphenyl, and several analogies are mentioned. The model is supported by calculations on the actual structure, using a model intermolecular potential. The symmetry of the incommensurate phase III is discussed more fully and accurately than previously, without the use of four-dimensional space groups. The librations and translations of the molecules, associated with the modulated structure, are given qualitatively by symmetry and the enmeshed rotations model, quantified by calculations, and used to explain the differences between the twisting phase transitions in biphenyl and p-terphenyl.

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