Phase Of Betaine Calcium Chloride Dihydrate Research Articles

The Commensurate Phases of BCCD Revisited: Domain Walls, Condensates, and Quantum Effects

A new analysis of previously published experimental findings on ferroelectric (fe) BCCD (betaine calcium chloride dihydrate) is presented. The commensurately (c) modulated phases, which exist in the temperature interval 46 K ≤ T ≤ 115 K at ambient pressure (sixfold, fivefold, fourfold modulated structures), display a highly anharmonic soliton regime. The domain walls separating the fe microdomains are not static but discrete, spatially localized, stable topological objects, breaking ergodicity, formed by twodimensional Bose-Einstein condensates of nonlinear, time-periodic vibrational excitations in molecular monolayers at low frequencies (≈20 cm−1), derived from the lowest optical (librational) mode of the crystal. These 2d-condensates are stacked coherently along the modulation c-axis, following the soliton wave and forming a 3-dimensional system with extreme anisotropy along c. This remarkable system is the first example, which displays strong quantum pressure effects due to quantum fluctuations, e.g. giving rise to the observed steps and other anomalies in thermal dilatation of BCCD. This interaction between adjacent layers of condensates follows near 46 K quantitatively the predictions of the Gross-Pitaevskii equation. A simple expression for the free energy of the system of domain walls is derived from this equation, which describes quantitatively all thermodynamic properties of the domain wall system with their density as a complex scalar order paramenter in an inverted phase diagram in the c phases of BCCD. Arguments are given for the breaking of gauge symmetry by the domain walls, the existence of a proper temperature scale of this system, especially with a pseudo-zeropoint of temperature, and the existence of a quantum phase transition between 46 K and 160 K, depending on external pressure.

Anisotropic Effects of Bromine Substitution in Betaine Calcium Chloride Dihydrate

The effects of partial substitution of chlorine by bromine in incommensurate betaine calcium chloride di-hydrate (BCCD) have been investigated by FTIR reflectivity and elastic neutron scattering. Bromine distorts the H-bonds linking the Ca complexes and induces local symmetry breaking. The temperature dependence of b and c lattice parameters of the 4% and 8% brominated compounds reveals that this distortion has effects that are markedly anisotropic. This anisotropy may help to clarify why bromine progressively destabilizes the low temperature phases of BCCD.

Structural modulation of the commensurate phases of betaine calcium chloride dihydrate (BCCD) within a model with nearest neighbour anharmonic couplings

The structural modulation of the four-fold phase of BCCD has been studied by neutron and X-ray difraction, and the discrepancies between the results given by both techniques are quite remarkable. Although neutron measurements show that the modulation is clearly anharmonic and the effect of third order satellites is essential to describe the structural modulation, the intensity of these satellites is very low in the case of X-rays. In the present work the theoretical structural modulation is analyzed within the framework of a symmetry based semi-microscopic model in the mean-field approximation. The model takes into account the three degrees of freedom associated with the lowest energy phonon branches as well as the anharmonic interactions between nearest neighbours to reproduce the essential experimental features of the phase diagram. Although the model is not able to predict the structural modulation at the atomic level, the well defined symmetry of the variables allows a comparison of the theoretical and experimental modulations.

Betaine calcium chloride dihydrate (BCCD): Present status and recent experimental results>

A review of the presently available experimental information on the modulated phases of BCCD, which display a devil's-staircase behavior, is given. Some basic experimental results using methods of dielectric, high-frequency and optical spectroscopy are compiled and discussed. Data from X-ray and elastic and inelastic neutron scattering studies are also considered. This paper also includes some previously unpublished results, mainly about the role of lattice imperfections (doping, radiation-induced defects) on the sequence and stability of modulated phases and about solitons. Some problems hitherto unsolved or still under discussion are mentioned at the end of this article.

1H ENDOR investigations on gamma-irradiated betaine calcium chloride dihydrate in the incommensurate phase

The electron nuclear double resonance (ENDOR) technique is applied to study the influence of the incommensurate modulation on the proton hyperfine structure (hfs) tensors of the N(CH3)3 radical in betaine calcium chloride dihydrate (BCCD). The temperature dependence of the edge singularities due to the increasing of the incommensurate (IC) modulation amplitude could be observed in the1H ENDOR of the CH3 groups for the first time. The rotation pattern of the edge singularities observed in the1H spectra in the IC phase of BCCD can be explained by a libration around the C1-N axis with a tilt angle of about ±7°.

2H and 14N NMR Studies of the Dynamics in the Incommensurate Phases of Betaine Calciumchloride Dihydrate

Abstract 2H and 14N NMR spin-lattice relaxation rates were measured in the structurally incommensurately (IC) modulated phases of deuterated and undeuterated betaine calciumchloride dihydrate, respectively. The results are related to the elementary excitations of these phases. The presence of low-frequency phase fluctuations of the modulation wave leads to higher spin-lattice relaxation rates compared with the high-temperature normal phase and the commensurate (C) phases. The corresponding "phason" contributions are found to be nearly constant in the whole IC phases. In the IC phases near the transitions to the C phases the relaxation rates decrease due to the formation of the soliton lattice. This interpretation is in agreement with the results of previous dielectric measurements

Symmetry of the normal and low-temperature phase of betaine calciumchloride dihydrate as revealed by 35Cl NMR

Quadrupolar perturbed 35Cl NMR spectra are measured in the high-temperature normal (N) phase and in the low-temperature (LT) phase of betaine calciumchloride dihydrate (BCCD) single crystals. The electric field gradient (EFG) tensors at the chlorine sites are precisely determined for both phases. In the N phase, the symmetry of the tensors is in agreement with the space group Pnma known from X-ray studies. The symmetry of the tensors in the LT phase allows to exclude the P11a symmetry proposed previously and confirms the space group Pn2 1a derived theoretically on the assumption that one order parameter drives the phase transitions in BCCD.

Static and Dynamic Behaviour of the Crystal Water Molecules in the Normal Phase of Deuterated Betaine Calciumchloride Dihydrate

AbstractThe static and dynamic behaviour of the deuterated crystal water molecules in the normal (N) phase of betaine calciumchloride dihydrate (BCCD) single crystals is investigated by means of quadrupolar perturbed 2H NMR. The temperature dependence both of the 2H NMR spectra and of the 2H spin‐lattice relaxation time 7i can be interpreted consistently by a thermally activated exchange process of the deuterons within the D2O molecule. At 170 K, under the condition of slow exchange, the electric field gradient (EFG) tensors of both deuterium sites are determined. From their principal axes and the quadrupole coupling constants information is derived about the structure of the C1D2O unit in BCCD in comparison with previous X‐ray studies.