Abstract
We report observations of space-group-forbidden Bragg reflections in Potassium (KH2PO4), at the potassium K edge. We find clear evidence for a transition from one class of space-group-forbidden reflections, where scattering is ruled out by the electric dipole approximation, to a second class, in the ferroelectric phase, where scattering can proceed due to resonant anisotropy within the dipole approximation. The change of symmetry is clearly evidenced by the sudden change of intensity and energy spectrum of the forbidden reflections.
Highlights
Diraction of x-rays, neutrons and electrons is a very sensitive technique for investigations of structural phase transitions because the reduction in symmetry that drives the transition is often heralded by the arrival of weak diraction peaks that become allowed due to the change in the space group extinction rules
When scalar scattering is forbidden, the crystal symmetry may allow resonant scattering to proceed via anisotropy in the resonant scattering within the electric dipole approximation, described by a second-rank tensor
Potassium Dihydrogen Phosphate (KH2PO4), known as KDP is a fascinating test-bed for these processes: the ferroelectric phase transition provides an example of a transition from forbidden- to super-forbidden scattering
Summary
Diraction of x-rays, neutrons and electrons is a very sensitive technique for investigations of structural phase transitions because the reduction in symmetry that drives the transition is often heralded by the arrival of weak diraction peaks that become allowed due to the change in the space group extinction rules Such a transition from forbidden to allowed scattering can be considered as a special case of a more general hierarchy of scattering processes that involve various ranks of the scattering tensor - in this case, scalar (rank-zero) scattering. 122 K in a complex mechanism that has long been debated This ferroelectric phase transition has triggered a lot of theoretical advances, based on the pseudospin model initially proposed by Slater [4] and later developed by many authors [5]. We will show that the subtle change of symmetry occurring at the phase transition can enable or disable some of the resonant terms involved in forbidden reections
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