Neutron scattering studies of K3H(SO4)2 and K3D(SO4)2: The particle-in-a-box model for the quantum phase transition
Abstract
In the crystal of K3H(SO4)2, or K3D(SO4)2, dimers (SO4)...H...(SO4), or (SO4)...D...(SO4), are linked by strong centrosymmetric hydrogen or deuterium bonds whose O...O length is ≈ 2.50 . We address two open questions. (i) Are H or D sites split or not? (ii) Is there any structural counterpart to the phase transition observed for K3D(SO4)2 at Tc ≈ 85.5 K, that does not exist for K3H(SO4)2. Neutron diffraction by single-crystals at cryogenic or room temperature reveals no structural transition and no resolvable splitting of H or D sites. However, the width of the probability densities suggest unresolved splitting of the wavefunctions suggesting rigid entities HL1/2-HR1/2 or DL1/2-DR1/2 whose separation lengths are lH ≈ 0.16 \ or lD ≈ 0.25 . The vibrational eigenstates for the center of mass of HL1/2-HR1/2 revealed by inelastic neutron scattering are amenable to a square-well and we suppose the same potential holds for DL1/2-DR1/2. In order to explain dielectric and calorimetric measurements of mixed crystals K3D(1-)H(SO4)2 (0 1), we replace the classical notion of order-disorder by the quantum notion of discernible (eg DL1/2-DR1/2) or indiscernible (eg HL1/2-HR1/2) components depending on the separation length of the split wavefunction. The discernible-indiscernible isostructural transition at finite temperatures is induced by a thermal pure quantum state or at 0 K by .