Neutron Scattering Studies Of K3h(So4)(2) And K3d(So4)(2): The Particle-In-A-Box Model For The Quantum Phase Transition

In the crystal of K3H(SO4)(2) or K3D(SO4)(2), dimers SO4 center dot center dot center dot H center dot center dot center dot SO4 or SO4 center dot center dot center dot D center dot center dot center dot SO4 are linked by strong centrosymmetric hydrogen or deuterium bonds whose O center dot center dot center dot O length is approximate to 2.50 angstrom. 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 T-c approximate to 85.5 K, which 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 H-L1/2 -H-R1/2 or D-L1/2 -D-R1/2 whose separation lengths are l(H) approximate to 0.16 angstrom or l(D) approximate to 0.25 angstrom. 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 K3D(1 - rho)H rho(SO4)(2) (0 <= rho <= 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 rho. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4745181]