Angular autocorrelation functions in molecular crystals: Application to nuclear magnetic resonance relaxation and Raman spectra

The theory of hindered molecular motion (HMM) in crystals, extended by taking the molecular site symmetry into account, is used in the calculation of the angular autocorrelation functions (ACFs). The basic model of motion involves a molecular rearrangement by means of random angular jumps of an intramolecular vector according to a crystallographic point symmetry group G between the potential wells in which the probability density of the vector orientation is continuously distributed over the angles. New physical quantities, the dynamical weights of the irreducible representations of the group G, are introduced to relate the molecular site symmetry in the ACFs. The polycrystalline ACFs are convenient for describing the HMM in liquids. The ACFs of the second-rank unitary spherical tensors are presented in an explicit form for all the point groups of pure rotation. The surface-plot graphs of the ACF amplitude, drawn as functions of a dynamical weight and an angle of crystal orientation, make the features of the HMM description more comprehensible. The new ACFs are applied to processing the exponential magnetic relaxation of the dipole and quadrupole nuclei and the line shape of Raman scattering in molecular crystals. Quantitative data about the NH+ 4-ion motion and its site symmetry are obtained from the anisotropic magnetic spin-lattice relaxation of protons and deuterons in ammonium chloride. The theoretical anisotropy of the Raman line intensities corresponding to the internal vibration modes is in accord with experiment and with the common methods of group-theoretical analysis in the vibration spectroscopy of molecular crystals

Proton spin-lattice relaxation in monocrystalline ammonium chloride

New symmetry-adapted autocorrelation functions are used in the theoretical description of the nuclear magnetic dipole-dipole relaxation in molecular crystals. They are obtained in the model frame that a molecule rotates by means of the finite angular jumps between the hindered states of the same symmetry in different potential wells. The experimental data of the temperature dependence of the proton relaxation times T1 and T1p in the mono- and polycrystalline NH4Cl are revised. As a result, it is proposed to classify the NH4 ion motion by two kinds of the hindered states corresponding to the two-dimensional (E) and three-dimensional (F) irreducible representations of a point group of the cubic system. The dynamical weight of the state F is defined to be equal to 0.25 and that of the state E to be equal to 0.73 from the experiments in the ordered phase of NH4Cl. Based on abstract geometric groups, the respective weights are 0.4 and 0.6. This discrepancy in the weights of the states is explained by the effect of the tetragonal distortion of the tetrahedral site symmetry of the NH4 + ion. The result of the prevalence of a C3 reorientation in comparison to a C2 reorientation of the ion is also justified. Because of the absence of the experimental temperature minima of T1 or T1p, assumptions are only made about the dynamical parameters of the NH4 + ion motion in the disordered phase of NH4Cl. © 1995 Academic Press, Inc

Spontaneous break of symmetry in molecular crystals

The structural dissymmetry of crystals with coordinated groups of atoms performing some motion in the crystal is described in terms of the theory of hindered molecular motion based on the dynamic principles of invariance for the extended angular jump model. The spontaneous break of the symmetry in the ordered ammonium chloride phase is discussed with the invocation of the proton-relaxation data. © 2007 MAIK "Nauka/Interperiodica"

Angular auto-correlation functions in molecular crystals and liquids: Application to incoherent neutron scattering law

The effect of the local hindered molecular motion in the incoherent neutron scattering spectra in crystals and liquids is studied theoretically on the basis of the angular auto-correlation functions symmetrized on the dynamical point groups. The extended angular jump model simulates the motion. The microscopic properties of the matter, the time scale and the point symmetry of the molecule motion as well as the site symmetry of the molecule, are taken into account with the help of the dynamical variables of the model. The incoherent neutron scattering function is anisotropic in a monocrystalline sample. The scattering function consists of elastic plus quasi-elastic components. The shape of the quasi-elastic scattering spectrum is expressed by the sum of the weighted Lorentzian curves symmetrized with respect to the non-identical irreducible representations of the molecule motion point symmetry group. The elastic part of the intensity is increased by the contribution arising from the molecule motion of the identity representation symmetry. The scattering expression related to the molecule motion symmetry of a perfect cubic group is similar to the well-known expression derived for the scattering from the spherical top molecules exhibiting rotation diffusion

The theory of hindered molecular motion and its application to spectroscopic studies

A stochastic theory of the classical local hindered motion of small molecules in molecular and ionic crystals is presented in detail. The so-called extended angular jump model, being intermediate between the rotational diffusion model and the model of fixed angular jumps, approximates the motion. In spite of the fact that dynamical quantities of the model do not relate to the hydrodynamic parameters of the continuous medium, the outcomes of the theory are suitable for molecular liquids. Two crystallographic point symmetries, the symmetry of the molecular motion and the site symmetry, including their distortions, are taken into account in the model. Applications of the theory to the description of NMR-relaxation rates and the homogeneous broadening of spectral lines excited by dielectric, infrared, Raman, Rayleigh and neutron spectroscopy techniques are given. The validity of the approach presented is confirmed by the experimental data performed in single crystalline and powder samples. © 2010 Taylor & Francis

Shape of Molecular Infrared Absorption and Raman Scattering Lines as Probe of Hindered Molecular Motion and Site Symmetry in Crystals

New symmetrized angular auto-correlation functions (ACFs) are applied to the theoretical description of the line-shape of internal modes in the polarized light scattering and infrared absorption spectra of molecular crystals. The model of hindered molecular motion (HMM) used to simulate the ACFs involves a molecular rearrangement by means of random angular jumps of an intramolecular vector between its hindered states in different potential wells whereas the probability density of the vector orientation is continuously distributed over the angles. The hindered states are classified according to the irreducible representations of a point symmetry group of the molecule motion. The ACFs of first and second ranks, which are important in molecular spectroscopy, are presented in an explicit form as a function of the crystal orientation in an axial laboratory coordinate frame. They depend on both the motion and site symmetry of the molecule through the correlation times and dynamic weights of the hindered states, respectively. The quantitative data important for practical applications are tabulated. The surface-plot graphs drawn for the initial amplitude of the ACFs show how an ACF anisotropy varies on changing the dynamic weights. The polycrystalline ACFs are in an agreement with the ACFs corresponding to rotation diffusion models. Therefore, the present theory of HMM can be considered as a general one and can be used in a description of the line extension caused by HMM in condensed matter. Some well known experiments on infrared, Raman and Rayleigh spectroscopy in molecular monocrystals and liquids show the reliability of the theory. © 1998 John Wiley & Sons, Ltd

Evaluating space and time oscillations of plasma radiant intensity by studying beam radial temperature

© Published under licence by IOP Publishing Ltd.Effects of space and time pulsations of non-stationary plasma on radiant intensity and the radial temperature of plasma are studied. The case, when plasma simultaneously non-stationary both in time and in space is examined. The influence of these perturbations on accuracy of definition of plasma optical features is shown

Influence of a dielectric medium on the phase state of carbon dioxide

The phase state of carbon dioxide gas dissolved in liquid n-heptane is determined by experimental investigations of the temperature dependences (180 < T < 250°K) of the spin-lattice relaxation time of protons, the coefficient of translational self-diffusion of n-heptane molecules and the nuclear magnetic resonance (NMR) linewidth of carbon13C. © 1987 Plenum Publishing Corporation

Method of combating fatigue destruction of steel structures of mine hoisting machines

The article presents the information of the identified defects of fatigue failure of steel structures of the brake mechanism of mine cable hoisting machines used to transport metallurgical coke from the mine to the surface. Using non-destructive testing methods a survey was carried out of the brake mechanisms of sixty mine cable hoisting machines. A method was developed to combat the fatigue failure of steel structures through the use of reinforcing elements to reduce their metal consumption and increase resistance to fatigue failure, while the use of expensive high-strength alloys is completely eliminated. To study the stress-strain state and fatigue failure of steel structures, a computer simulation method was used. Using the ANSYS computer program, the optimal forms of reinforcing elements were established and the loaded part of steel structures in continuous operation was simulated. Eleven computer models of a steel beam with various reinforcing elements were developed. The research results were used in practice in the repair of steel structures