NMR relaxation study of disorder in condensed matter: solid solutions of betaine phosphate and phosphite

Proton NMR relaxation measurements have been carried out in anti-ferroelectric Betaine phosphate (BP), ferroelectric Betaine phosphite (BPI) and the mixed system BPI(1-x)BPx, at 11.4MHz and 23.3MHz from 300K to 80K for x=0.0, 0.25, 0.45, 0.85, and 1.0. The temperature dependence of spin lattice relaxation time T, exhibits two minima as expected from the BPP model in BP and BPI. The Larmor frequency dependence of T, in the mixed system is rather unusual and exhibits different slopes for the low temperature wings at the two frequencies, which is a clear experimental evidence of the presence of different methyl groups with different activation energies (E-a) indicating disorder.

Temperature- and pressure-dependent study of Cl-35 NQR frequency and spin lattice relaxation time in 2,3-dichloroanisole

The temperature and pressure dependence of Cl-35 NQR frequency and spin lattice relaxation time (T-1) were investigated in 2,3-dichloroanisole. Two NQR signals were observed throughout the temperature and pressure range studied. T-1 were measured in the temperature range from 77 to 300 K and from atmospheric pressure to 5 kbar. Relaxation was found to be due to the torsional motion of the molecule and also reorientation f motion of the CH3 group. T-1 versus temperature data were analyzed on the basis of Woessner and Gutowsky model, and the activation energy for the reorientation of the CH3 group was estimated. The temperature dependence of the average torsional lifetimes of the molecules and the transition probabilities were also obtained. NQR frequency shows a nonlinear behavior with pressure, indicating both dynamic and static effects of pressure. The pressure coefficients were observed to be positive for both the lines. A thermodynamic analysis of the data was carried out to determine the constant volume temperature coefficients of the NQR frequency. The variation of spin lattice time with pressure was very small, showing that the relaxation is mainly due to the torsional motions of the molecules. Copyright (C) 2010 John Wiley & Sons, Ltd.

A molecular theory of collective orientational relaxation in pure and binary dipolar liquids

A molecular theory of collective orientational relaxation of dipolar molecules in a dense liquid is presented. Our work is based on a generalized, nonlinear, Smoluchowski equation (GSE) that includes the effects of intermolecular interactions through a mean‐field force term. The effects of translational motion of the liquid molecules on the orientational relaxation is also included self‐consistently in the GSE. Analytic expressions for the wave‐vector‐dependent orientational correlation functions are obtained for one component, pure liquid and also for binary mixtures. We find that for a dipolar liquid of spherical molecules, the correlation function ϕ(k,t) for l=1, where l is the rank of the spherical harmonics, is biexponential. At zero wave‐vector, one time constant becomes identical with the dielectric relaxation time of the polar liquid. The second time constant is the longitudinal relaxation time, but the contribution of this second component is small. We find that polar forces do not affect the higher order correlation functions (l>1) of spherical dipolar molecules in a linearized theory. The expression of ϕ(k,t) for a binary liquid is a sum of four exponential terms. We also find that the wave‐vector‐dependent relaxation times depend strongly on the microscopic structure of the dense liquid. At intermediate wave vectors, the translational diffusion greatly accelerates the rate of orientational relaxation. The present study indicates that one must pay proper attention to the microscopic structure of the liquid while treating the translational effects. An analysis of the nonlinear terms of the GSE is also presented. An interesting coupling between the number density fluctuation and the orientational fluctuation is uncovered.

Polarization relaxation, dielectric dispersion, and solvation dynamics in dense dipolar liquid

A unified treatment of polarization relaxation, dielectric dispersion and solvation dynamics in a dense, dipolar liquid is presented. It is shown that the information of solvent polarization relaxation that is obtained by macroscopic dielectric dispersion experiments is not sufficient to understand dynamics of solvation of a newly created ion or dipole. In solvation, a significant contribution comes from intermediate wave vector processes which depend critically on the short range (nearest‐neighbor) spatial and orientational order that are present in a dense, dipolar liquid. An analytic expression is obtained for the time dependent solvation energy that depends, in addition to the translational and rotational diffusion coefficients of the liquid, on the ratio of solute–solvent molecular sizes and on the microscopic structure of the polar liquid. Mean spherical approximation (MSA) theory is used to obtain numerical results for polarization relaxation, for wave vector and frequency dependent dielectric function and for time dependent solvation energy. We find that in the absence of translational contribution, the solvation of an ion is, in general, nonexponential. In this case, the short time decay is dominated by the longitudinal relaxation time but the long time decay is dominated by much slower large wave vector processes involving nearest‐neighbor molecules. The presence of a significant translational contribution drastically alters the decay behavior. Now, the long‐time behavior is given by the longitudinal relaxation time constant and the short time dynamics is controlled by the large wave vector processes. Thus, although the continuum model itself is conceptually wrong, a continuum model like result is recovered in the presence of a sizeable translational contribution. The continuum model result is also recovered in the limit of large solute to solvent size ratio. In the opposite limit of small solute size, the decay is markedly nonexponential (if the translational contribution is not very large) and a complete breakdown of the continuum model takes place. The significance of these results is discussed.

A note on the observed anisotropy in linear compressibility and thermal expansion of quasicrystals

The linear compressibility and the thermal expansion of Al-Fe and Al-Mn quasicrystals have been reported to be anisotropic. The authors suggest that the observed anisotropy in these properties could be due to the presence of decagonal quasicrystals rather than icosahedral quasicrystals.

A soluble random-matrix model for relaxation in quantum systems

We study the relaxation of a degenerate two-level system interacting with a heat bath, assuming a random-matrix model for the system-bath interaction. For times larger than the duration of a collision and smaller than the Poincaré recurrence time, the survival probability of still finding the system at timet in the same state in which it was prepared att=0 is exactly calculated.

Dynamics of polar solvation: Route to single exponential relaxation via translational diffusion

A microscopic theoretical calculation of time-dependent solvation energy shows that the solvation of an ion or a dipole is dominated by a single relaxation time if the translational contribution to relaxation is significant.

Curie-temprature of a spin one xy ferromagnet with uniaxial anisotropy

A spin one XY ferromagnet with uniaxial anisotropy has been investigated, using Green's function technique in random phase approximation (RPA). The Green functions associated with the anisotropy energy are treated without decoupling. A set of coupled equations have been obtained to find the critical temperature Tc and left angle bracket(SZ)2right-pointing angle bracket at Tc as function of the uniaxial anisotropy parameter D. Tc and left angle bracket(SZ)2right-pointing angle bracket at Tc are found to increase with D. The results are compared with the earlier results obtained in the Narath type of RPA.

Mechanical Anisotropy in Crystalline Saccharin: Nanoindentation Studies

The nanoindentation technique has been employed to relate the mechanical properties of saccharin single crystals with their internal structure. Indentations were performed on (100) and (011) faces to assess the mechanical anisotropy. The load-displacement (P-h) curves indicate significant differences in the nature of the plastic deformation on the two faces. The P-h curves obtained on the (011) plane are smooth, reflecting homogeneous plasticity. However, displacement bursts (pop-ins) are observed in the P-h curves obtained on the (100) plane suggesting a discrete deformation mechanism. Marginal differences exist in the hardness and modulus on the two faces that may, in part, be rationalized, although one notes that saccharin has a largely three-dimensional close-packed structure. The structural origins of the fundamentally different deformation mechanisms on (100) and (011) are discussed in terms of the dimensionality of the hydrogen bonding networks. Down the (100) planes, the saccharin dimers are stacked and are stabilized by nonspecific van der Wants interactions mostly between aromatic rings. However, down the (011) planes, the molecules are stabilized by more directional and cross-linked C-H ... O hydrogen bonds. This anisotropy in crystal packing and interactions is reflected in the mechanical behavior on these faces. The displacements associated with the pop-ins were found to he integral multiples oldie molecule separation distances. Nanoindentation offers an opportunity to compare experimentally, and in a quantitative way, the various intermolecular interactions that fire present in a molecular crystal.

Molecular hydrodynamic theory of non‐Markovian collective orientational relaxation in dense dipolar liquids

A microscopic study of the non‐Markovian (or memory) effects on the collective orientational relaxation in a dense dipolar liquid is carried out by using an extended hydrodynamic approach which provides a reliable description of the dynamical processes occuring at the molecular length scales. Detailed calculations of the wave‐vector dependent orientational correlation functions are presented. The memory effects are found to play an important role; the non‐Markovian results differ considerably from that of the Markovian theory. In particular, a slow long‐time decay of the longitudinal orientational correlation function is observed for dense liquids which becomes weaker in the presence of a sizeable translational contribution to the collective orientational relaxation. This slow decay can be attributed to the intermolecular correlations at the molecular length scales. The longitudinal component of the orientational correlation function becomes oscillatory in the underdamped limit of momenta relaxations and the frequency dependence of the friction reduce the frictional resistance on the collective excitations (commonly known as dipolarons) to make them long lived. The theory predicts that these dipolarons can, therefore, be important in chemical relaxation processes, in contradiction to the claims of some earlier theoretical studies.

Molecular theory of dielectric relaxation in a dense binary dipolar liquid

A molecular theory of dielectric relaxation in a dense binary dipolar liquid is presented. The theory takes into account the effects of intra- and interspecies intermolecular interactions. It is shown that the relaxation is, in general, nonexponential. In certain limits, we recover the biexponential form traditionally used to analyze the experimental data of dielectric relaxation in a binary mixture. However, the relaxation times are widely different from the prediction of the noninteracting rotational diffusion model of Debye for a binary system. Detailed numerical evaluation of the frequency-dependent dielectric function epsilon-(omega) is carried out by using the known analytic solution of the mean spherical approximation (MSA) model for the two-particle direct correlation function for a polar mixture. A microscopic expression for both wave vector (k) and frequency (omega) dependent dielectric function, epsilon-(k,omega), of a binary mixture is also presented. The theoretical predictions on epsilon-(omega) (= epsilon-(k = 0, omega)) have been compared with the available experimental results. In particular, the present theory offers a molecular explanation of the phenomenon of fusing of the two relaxation channels of the neat liquids, observed by Schallamach many years ago.

Relaxation dominated by inertia: Solvation dynamics of a small ion in a dipolar solvent

It is shown from an analytical theory that the solvation dynamics of a small ion can be controlled largely by the inertial response of the dipolar solvent when the liquid is in the underdamped limit. It is also shown that this inertial response arises primarily from the long wavelength (with wavevector k≃0) processes which have a collective excitation-like behaviour. The long time decay is dominated by the processes occurring at molecular lengthscales. The theoretical results are in good agreement with recent computer simulation results.

Sensitivity of the simulated precipitation to changes in convective relaxation time scale

The paper describes the sensitivity of the simulated precipitation to changes in convective relaxation time scale (TAU) of Zhang and McFarlane (ZM) cumulus parameterization, in NCAR-Community Atmosphere Model version 3 (CAM3). In the default configuration of the model, the prescribed value of TAU, a characteristic time scale with which convective available potential energy (CAPE) is removed at an exponential rate by convection, is assumed to be 1 h. However, some recent observational findings suggest that, it is larger by around one order of magnitude. In order to explore the sensitivity of the model simulation to TAU, two model frameworks have been used, namely, aqua-planet and actual-planet configurations. Numerical integrations have been carried out by using different values of TAU, and its effect on simulated precipitation has been analyzed. The aqua-planet simulations reveal that when TAU increases, rate of deep convective precipitation (DCP) decreases and this leads to an accumulation of convective instability in the atmosphere. Consequently, the moisture content in the lower-and mid-troposphere increases. On the other hand, the shallow convective precipitation (SCP) and large-scale precipitation (LSP) intensify, predominantly the SCP, and thus capping the accumulation of convective instability in the atmosphere. The total precipitation (TP) remains approximately constant, but the proportion of the three components changes significantly, which in turn alters the vertical distribution of total precipitation production. The vertical structure of moist heating changes from a vertically extended profile to a bottom heavy profile, with the increase of TAU. Altitude of the maximum vertical velocity shifts from upper troposphere to lower troposphere. Similar response was seen in the actual-planet simulations. With an increase in TAU from 1 h to 8 h, there was a significant improvement in the simulation of the seasonal mean precipitation. The fraction of deep convective precipitation was in much better agreement with satellite observations.