Incommensurate structures

Abstract

A review is given of recent neutron scattering studies of displacive incommensurate structures, and the instabilities that occur within periodic crystalline structures that lead to their formation. The concept of a soft phonon, in some cases associated with an electronic screening anomaly, is useful but not always capable of a completely satisfactory description. An unusual one-dimensional liquid-like phase has been studied in the non-stoichiometric mercury compound Hg 3-8 AsF 6.

Supersonic propagation of lattice energy by phasons in fresnoite

“…In contrast to the acoustic phonons, there is no significant difference in the dispersion of the T-phason and L-phason (the phasons are shifted to the zone center for comparison to the acoustic phonons). The shapes of the phason dispersion curves are similar to the acoustic modes, as expected 16,23 , but the phasons are much steeper at low energies. At 2 meV the T-phason is ~4.3 times steeper than the TA phonon and the L-phason is ~2.8 times steeper than the LA phonon, confirming that at low energies the phasons propagate at highly supersonic velocities.…”

“…This indicates that the phasons are gapped ahead of the static incommensurate modulation. While ideally phasons are expected to be gapless since the phase energy is translational invariant for true incommensurate modulations, small gaps are possible if the phase is pinned by crystal defects 16,23 or by any mechanism that breaks translational invariance, including a high-order commensurate modulation 28 . For example, if the soliton thickness is similar to the lattice spacing it may tend to lock-in to a site in the unit cell, resulting in the phase not being strictly incommensurate and the phasons being pinned 28 .…”

“…Previous measurements of phasons in other systems have been challenging not just because of damping that broadens the mode 17,23–25 , but also because the phasons appear in reciprocal space just below and often covered by the driving soft phonon mode that becomes the amplitudon 23 .…”