Influence Of Thermal Motion Research Articles

Selective Reflection for a Fabry-Perot Interferometer in Presence of Electromagnetically Induced Transparency

The influence of thermal motion of atoms of alkali metals in a cell with the parallel windows on the formation of electromagnetically induced transparency in the Λ-system is considered. The solution of joint system of equations of density matrix and Maxwell was studied analytically and numerically. The spectra of single and multiple reflections for different optical lengths and parameters of interaction were obtained.

Potential surface waves in anisotropic plasma

The dependences of the frequency and damping rate of a potential surface wave on the wavenumber and the degree of anisotropy of a bi-Maxwellian electron distribution characterized by different temperatures along and across the plasma surface are established. It is demonstrated that the influence of electron thermal motion along the plasma surface on the surface wave properties is similar to the influence of thermal motion on the properties of a bulk Langmuir wave. On the contrary, thermal motion across the surface qualitatively affects the dispersion relation and substantially increases the damping rate.

On the influence of thermal motion on the crystal structures and polymorphism of even n-alkanes

# 2002 International Union of Crystallography Printed in Great Britain ± all rights reserved Discrepancies between the crystal structures of short nalkanes as obtained from experiment and as obtained from molecular mechanics tended to worsen at longer chain lengths. The same holds for the relative stabilities of the two experimentally observed polymorphs. In this paper it is argued that the discrepancies are caused by thermal effects, and that the triclinic polymorph is the most stable polymorph for all chain lengths at 0 K. A phase transition is predicted but has yet to be found experimentally. Current force ®elds cannot reproduce the experimental observations without explicit introduction of temperature by means of molecular dynamics. Received 27 November 2001 Accepted 4 March 2002

On the influence of thermal motion on the crystal structures and polymorphism of even n-alkanes.

Discrepancies between the crystal structures of short n-alkanes as obtained from experiment and as obtained from molecular mechanics tended to worsen at longer chain lengths. The same holds for the relative stabilities of the two experimentally observed polymorphs. In this paper it is argued that the discrepancies are caused by thermal effects, and that the triclinic polymorph is the most stable polymorph for all chain lengths at 0 K. A phase transition is predicted but has yet to be found experimentally. Current force fields cannot reproduce the experimental observations without explicit introduction of temperature by means of molecular dynamics.

Influence of thermal motion on 1H chemical shifts in proteins: the case of bovine pancreatic trypsin inhibitor.

The possible influence of thermal motion on 1H chemical shifts is discussed for a small stable protein, the bovine pancreatic Kunitz trypsin inhibitor (BPTI). The thermal effects on the aromatic side chains and on the backbone are treated separately. The thermal motion of the aromatic side chains is accounted for in terms of their rotation around the C(alpha)-C(beta) bond and the motion of each individual proton is interpreted as a ratio between the amount of ordered and quite disordered states. The influence of hydrogen bonds is introduced as an extra contribution to the chemical shifts of the bonded proton. Their contribution to the chemical shifts resulting from the polarization of the peptide bond is investigated, as is their influence on local flexibility. Finally, the relative importance of each contribution to the chemical shift information is compared.

Interaction of laser radiation with doppler-broadened media in coherent population trapping regime: law of light propagation

The influence of thermal motion of atoms on laser light propagation through a coherent optically dense medium is investigated theoretically. If the laser light intensity does not exceed a certain threshold value (intensity of coherent population trapping switching on multiplied by square of ratio of Doppler broadening to natural linewidth), the propagation law is strongly influenced by atomic motion: the laser intensity decreases neither exponentially, nor linearily, but as second-order polynomial of the optical depth. Above this threshold the propagation law is linear.

Diffraction by aperiodic structures at high temperatures

This paper studies, in the Einstein model, the influence of thermal motion on diffraction by aperiodic structures. In particular, it shows that in a quasicrystal thermal motion reduces the intensity of the Bragg peaks by a Debye-Waller factor in the same way as in a crystal. The result applies to a large class of aperiodic structures.

Disorder effects on curved-wave extended X-ray absorption fine structure

A general formulation is introduced to treat the influence of the displacements of some atomic centres on X-ray absorption in the single-scattering curved-wave formalism. This formulation is particularly suited to the study of small shifts, but it can also be used to consider finite displacements. As an application, they investigate the influence of thermal motion and structural disorder on the curved-wave extended X-ray absorption fine structure, thus generalising the Debye-Waller and asymmetry factors.

Interpretation of Experimental Charge Densities. The study of chemical bonding

The first question to be discussed here is what kind of diffraction theory is applicable to the sample under study. The range between kinematical and dynamical theory is so wide that the problem has to be considered very seriously. It is necessary to consider the relative influence of thermal diffuse scattering versus Bragg scattering, in order to obtain the average of the structure factors over the lattice modes. A limit of resolution results from the series termination error: the neglect of core polarisation and the necessity to define a deformation density; obtained by subtracting isolated vibrating atoms. Various sources of error are discussed, and especially the problems related to the scale factor. The experiments are concluded to be more reliable than most calculations at a distance larger than 0.3 Å from the nuclei. The analysis can be done either in real or reciprocal space. A qualitative description of the possible types of bonding has been undertaken few years ago and a systematisation is now becoming possible. The "chemical bonds" are described in different terms depending whether one looks at the total or deformation density. To go towards a quantitative description, two major problems have to be solved: the influence of thermal motion on the density or the molecular properties, and the definition of proper molecular regions in the solid. It should be kept in mind that intermolecular effects are now in the domain of observability and therefore a combination of theoretical and experimental work should become very fruitful for the study of crystalline forces. In reciprocal space, the problem is to find models that represent the structure factor. It is possible to think in terms of an orbital expansion: one has to deal with the very complicated two center form factors, and an attribution of a temperature factor to these factors is impossible. Better models are based in a functional partitioning of the density in terms of deformation functions around each nucleus. A careful study of correlation between different functions leads to a multipolar expansion. But, in order to deduce unbiased properties, the influence of internal modes of vibration has to be considered carefully. An interplay with other techniques is necessary if one wants to get precise information on the density near atomic positions.

Study of the NMR Results in Some Crystalline Hydrates

The NMR results have been studied in 12 crystalline hydrates whose neutron-diffraction structures are available. The purpose of this study is to examine the validity of the Pake technique which may appear questionable in view of recent studies, and to try to propose a general method for calculating hydrogen positions using the NMR data and the positions of the heavy atoms in the unit cell. Comparison of the NMR results with the neutron-diffraction structures shows that the Pake technique, when applied without considering the influence of thermal motion on the resonance spectrum, gives fairly accurate results. The method proposed for calculating hydrogen positions is described and the assumptions made are discussed in detail. It is found that in the general case, the positions calculated by this method are in close agreement with the corresponding positions obtained by neutron diffraction.

The influence of thermal motion on structure determination of linear molecules using the electron-diffraction method

The influence of thermal motion on structure determination of linear molecules using the electron-diffraction method

Thermal inelastic scattering of cold neutrons in polycrystalline solids

A general theory of the influence of thermal motion on the scattering of slow neutrons in polycrystals is discussed. Unlike Weinstock’s earlier treatment of the same problem, we express temperature displacements of the lattice points as a sum of emission and absorption operators. This alternative approach simplifies the calculation of the transition probability to a considerable extent and provides a simple proof of the Debye-Waller factor. The theory is also generalized to the case of multi-phonon processes. General expressions for both the incoherent and coherent cross-sections, corresponding to an ' l ' phonon process, are derived. The latter, hitherto not treated rigorously, is examined in detail. It is shown that it can be expressed as a sum of two terms, of which the main term, apart from a constant, is identical with the expression for the incoherent part and the other is a correction term. Both terms are put in 'Placzek’ form, and for cold neutrons explicit expressions are obtained for the cases: (i) M > 1 and T /0 > 1, and (ii) M ~ 10 and T/0 > 0.5. Numerical results for magnesium, aluminium, iron, lead and beryllium are discussed and compared with experiment. The agreement is found to be satisfactory.