title: 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 K(3)H(SO(4))(2) or K(3)D(SO(4))(2), dimers SO(4)···H···SO(4) or SO(4)···D···SO(4) are linked by strong centrosymmetric hydrogen or deuterium bonds whose O···O length is ≈2.50 Å. 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 K(3)D(SO(4))(2) at T(c) ≈ 85.5 K, which does not exist for K(3)H(SO(4))(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 H(L1/2)-H(R1/2) or D(L1/2)-D(R1/2) whose separation lengths are l(H) ≈ 0.16 Å or l(D) ≈ 0.25 Å. The vibrational eigenstates for the center of mass of H(L1/2)-H(R1/2) revealed by inelastic neutron scattering are amenable to a square-well and we suppose the same potential holds for D(L1/2)-D(R1/2). In order to explain dielectric and calorimetric measurements of mixed crystals K(3)D((1-ρ))H(ρ)(SO(4))(2) (0 ≤ ρ ≤ 1), we replace the classical notion of order-disorder by the quantum notion of discernible (e.g., D(L1/2)-D(R1/2)) or indiscernible (e.g., H(L1/2)-H(R1/2)) 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 ρ.
authors.affiliation: UMR 7075, CNRS, Université Pierre et Marie Curie, Box 49, 4 place Jussieu, 75252 Paris Cedex 05, France. francois.fillaux@upmc.fr
authors.forename: François
authors.initials: F
authors.lastname: Fillaux
authors.forename: Alain
authors.initials: A
authors.lastname: Cousson
mesh_terms: D033363:Neutron Diffraction; D011789:Quantum Theory; D053838:Scattering, Small Angle; D013431:Sulfates / Q000737:chemistry*; D013696:Temperature
chemical_list: D013431:Sulfates