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Neutron scattering studies of K(3)H(SO(4))(2) and K(3)D(SO(4))(2): The particle-in-a-box model for the quantum phase transition
Authors:François Fillaux  Alain Cousson
Affiliation:UMR 7075, CNRS, Universite? Pierre et Marie Curie, Box 49, 4 place Jussieu, 75252 Paris Cedex 05, France.
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 A?. 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 A? or l(D) ≈ 0.25 A?. 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.
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