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

François Fillaux; Alain Cousson

doi:10.1063/1.4745181

paper

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

arXiv:1209.4261 · doi:10.1063/1.4745181

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 $\approx 2.50$ 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 $T_{c} \approx 85.5$ K, that 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 $_{L 1/2} -$ H $_{R 1/2}$ or D $_{L 1/2} -$ D $_{R 1/2}$ whose separation lengths are $l_{H} \approx 0.16$ Å\ or $l_{D} \approx 0.25$ Å. The vibrational eigenstates for the center of mass of H $_{L 1/2} -$ H $_{R 1/2}$ revealed by inelastic neutron scattering are amenable to a square-well and we suppose the same potential holds for D $_{L 1/2} -$ D $_{R 1/2}$ . In order to explain dielectric and calorimetric measurements of mixed crystals K $_{3}$ D $_{(1 - ρ)}$ H $_{ρ}$ (SO $_{4})_{2}$ ( $0 \leq ρ \leq 1$ ), we replace the classical notion of order-disorder by the quantum notion of discernible (eg D $_{L 1/2} -$ D $_{R 1/2}$ ) or indiscernible (eg H $_{L 1/2} -$ H $_{R 1/2}$ ) 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 $ρ$ .

10 pages

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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

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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

Neutron scattering studies of K3​H(SO4​)2​ and K3​D(SO4​)2​: The particle-in-a-box model for the quantum phase transition

Abstract

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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