Thermal conductivity of solid cyclohexane in orientationally ordered and disordered phases

Thermal conductivity Λ _P of solid cyclohexane is measured at a pressure P = 0.1 MPa in the temperature range from 80 K to the melting point, which covers the ranges of low-temperature orientationally ordered phase II and high-temperature orientationally disordered phase I. Thermal conductivity Λ _V is measured at a constant volume in orientationally disordered phase I. The thermal conductivity measured at atmospheric pressure decreases with increasing temperature as Λ _P ∝ T ^−1.15 in phase II, whereas Λ _P ∝ T ^−0.3 in phase I. As temperature increases, isochoric thermal conductivity Λ _V in phase I increases gradually. The experimental data are described in terms of a modified Debye model of thermal conductivity with allowance for heat transfer by both phonons and “diffuse” modes.     

The rotational kinetic energy in the orientationally disordered phase of solid methane. A quasi-classical approach

It is shown that, as a consequence of the orientational correlations, the quantum rotational kinetic energy of interacting molecules in the orientationally disordered phase of solid methane exceeds the free rotor value. The expectation value of kinetic energy is obtained from the initial terms of a quasiclassical high temperature expansion of the free energy. The calculation is based on an analytic function approximating the configuration representation of the statistical density operator of the free spherical top. It is demonstrated that in the classical limit the function tends asymptotically to the true density operator, the error being exponentially dependent on temperature. As an application, the quantum correction to the second moment of an infrared absorption band is estimated.     

NMR investigations of dynamical processes in orientationally ordered and disordered NaCN,RbCN and CsCN

The nuclear spin lattice relaxation timeT ₁ of the²³Na,⁸⁵Rb,⁸⁷Rb,¹³³Cs,¹⁴N nuclei is measured in NaCN, RbCN and CsCN as a function of temperature below and above the ferroelastic phase transition temperatureT _c. BelowT _c the behaviour ofT ₁ of the alkali nuclei renders possible to determine the flip frequency of the CN molecules and its temperature dependence. AboveT _c from the¹⁴NT ₁ the correlation time τ_c of the rotational motions of the CN molecules and its temperature dependence is determined. An empirical rule is verified demonstrating that atT _c the correlation times take nearly the same values for all cyanides. For the high and low temperature phases one obtains atT _c about τ_c=5·10^?13s and τ_c=5·10^?11s, respectively. The results are discussed with respect to the mechanism of the phase transition.     

Structural relationships between the orientationally disordered (plastic) and ordered phases of tetrahedral molecules

A systematic study of the crystal structures of both the plastic and ordered phases of a number of pseudo-spherical tetrahedral molecules has revealed some generalized relationships which apply to all the molecular crystals studied, including those which exhibit significant hydrogen bonding. The following rule is proposed: equal-sphere closest-packing principles control the crystal structures of both orientationally-disordered and ordered phases of tetrahedral, pseudo-spherical molecules.     

Theory of phonon linewidth in orientationally disordered crystals

The dynamics of coupled translational (T) and rotational (R) modes is studied with special reference to the experimental situation in the alkali cyanides. The dynamic equations are extended and, in addition to the bilinear T-R coupling, anharmonic interactions of the form T-T-R are considered. These interactions lead to additional friction coefficients for translational and rotational motion. Transport coefficients are evaluated with mode-mode coupling theory. The validity of orientational relaxation models coupled to lattice vibration is confirmed as a particular case of the present theory at low frequencies. An extension to the high frequency regime is proposed.Dedicated to Prof. Dr. H.E. Müser ob the occasion of his 60th birthday     

The thermoelastic behaviour of the orientationally disordered ionic crystals in two dimensions

The anomalous temperature dependence of the elastic constantsc ₁₁ andc ₆₆ and the elastic instability temperatureT _c are obtained in the two-dimensional microscopic model of the alkali cyanides crystals. It has been found, by means of the Michel and Naudts' theory of the translation rotation coupling, that the orientational disorder in the high-temperature phase leads to the critical softening of the shear elastic constantc ₆₆.     

The transition from the ordered to the merohedral disordered phase in oxygenated solid C60

C₆₀ powder, pellets and single crystals were oxygenated at 0.11 kbar and then studied with MAS ¹³C NMR, DSC and XRD. In agreement with reports by other authors, powder samples exhibited minor NMR resonances, indicative of blocking of fullerene rotation by interstitial oxygen, the distribution of which had yet to attain the equilibrium state. Also, as reported by others, DSC showed two endothermic peaks near 260 K, and both, we found, corresponded to a discontinuous change in the lattice parameter. The peak on the low-temperature side moved up in temperature with elapsed time. Pellets, in which presumably oxygen diffused easily, displayed only one peak but shifted in the same manner. Single crystals, in contrast, had only the higher-temperature “immobile” peak. We suggest that the shifting endotherm originates from the transition of oxygen-intercalated C₆₀ to a merohedral disordered phase, in which the rotation of fullerene molecules is partially impeded by oxygen. A phenomenological model is proposed for this transition.     

The glories of ESEEM: Measuring electron-nuclear dipolar couplings in orientationally disordered solids

In orientationally disordered solids, the anisotropy of spin interactions can cause a spectral line-broadening that severely complicates the acquisition and analysis of ESEEM (electron spin echo envelope modulation) spectra. The reduction or removal of powderbroadening is accomplished in ESEEM spectroscopy through the cancellation of antagonistic, static interactions. Three, distinct examples of this approach to spectral line-narrowing in nuclear spin one-half systems are described, together with their implications regarding the determination of electron-nuclear dipolar couplings. Applications involving¹⁵N and¹H nuclei in protein and model systems are discussed.     

Phonon damping by translation-rotation coupling in orientationally disordered molecular crystals

A simple model for the translation-rotation coupling in orientationally disordered molecular crystals (ODIC) is used to investigate the effect of the coupling to the damping of acoustic phonons in an fcc-ODIC composed of tetrahedral molecules. The influence of the coupling is calculated as a function of molecular and lattice parameters in the framework of linear response theory. The results are applied to the plastic phase I of solid CD₄, revealing a strong damping of short-wavelength phonons. This is consistent with experimental and molecular dynamics observations.     

Lattice vibrations in ordered and disordered thiourea

Raman scattering and infrared reflection spectra of single crystals of thiourea were recorded at several temperatures between 2 K and 240 K in the spectral region (03500) cm^–1. The intention was to search for changes in frequency, linewidth, and intensity of optical phonon modes near the various phase transitions which are known to exist in this material. All observed phonon modes have been tabulated according to a group-theoretical enumeration, and they are attributed to internal motions of the molecular groups and external lattice vibrations. A survey of the temperature dependence of all observed lines is given.Some modes are in fact influenced by the phase transitions in a characteristic manner. The observed temperature dependences can be interpreted by a simple pseudospinphonon coupling model (following contribution II).     

Lattice vibrations in ordered and disordered thiourea

The critical dynamics of the Syozi model for dilute ferromagnetism is considered by the use of master equations. The dynamics is soluble as it is assumed that the time scale of motion on the sublattice on which the impurities move is so much faster than on the other sublattice that fast relaxing variables may be adiabatically eliminated, leaving a new soluble master equation. It is found that the linear and non-linear relaxation of magnetization exponents ^(l) and ^(nl) increase on dilution to ^(l)/(1–) and ^(nl)/(1–) respectively ( is the specific heat exponent for the pure system, which itself changes on dilution to –/(1–)). Thus if the exponents for the pure system obey the scaling law of Rácz and Fisher ^(nl)= ^(l)– ( is the magnetization exponent which changes on dilution to /(1–)) then so do the exponents for the diluted system. Similarly the exponent for spin diffusion changes on dilution to /(1–).     

Characteristics of ESEEM and HYSCORE spectra of S>1/2 centers in orientationally disordered systems

One- and two-dimensional electron-spin echo envelope modulation (ESEEM) spectra of Kramers’ multiplets in orientationally disordered systems are simulated using a simple mathematical model. A fairly general high-field spin Hamiltonian is considered with a general g-tensor and arbitrary relative orientations between all tensors involving the electron-spin S, the nuclear spin I, and their interaction. The zero field splitting (ZFS) and the nuclear quadrupole interactions are, however, approximated by their respective secular part in a way that retains all orientation dependencies and it is assumed that the nuclear quadrupole interaction is smaller than the hyperfine interaction. These approximations yield an effective sublevel nuclear Hamiltonian for each EPR transition and are sufficient to account for the most important characteristics of the ESEEM spectra of high electronic multiplets in orientationally disordered systems. Moreover, they allow to obtain some analytical expressions that for I=1/2 illuminate important aspects of 2D hyperfine sublevel correlation (HYSCORE) experiments in S=3/2, 5/2 systems. The pulses are considered as ideal and selective with respect to the different EPR transitions. The contributions of the latter to the echo intensity are weighed according to their different nutation angles and equilibrium Boltzmann populations. For simple axial cases with I=1/2, analytical expressions, analogous to the S=1/2 case, were derived for: (i) the modulation depth, (ii) the lineshapes of the HYSCORE cross-correlation ridges, and (iii) ENDOR powder pattern. Experimental results obtained from Mn(D₂O)₆²⁺ and VO(D₂O)₅²⁺ in frozen solutions are presented, compared, and analyzed in light of the theoretical part.     

On the dynamics of the orientationally disordered ionic crytals in two dimensions

The translational and rotational generalized susceptibilities have been calculated in a two-dimensional model crystal with orientational disorder. The Michel and Naudts' method has been employed to account for the rotation-translation coupling. The elastic and displacive character of the phase transition in the system has been shown to be independent of the mass and of the size of the disordered molecular ions. The plausibility of the third order continuous fraction expansion of the dynamic susceptibilities has been evidenced. The influence of the rotation-translation coupling on the dispersion relations are shown to be of the character observed experimentally.