scholarly journals The theory of the Raman effect in crystals, in particular rock-salt

1947 ◽  
Vol 188 (1013) ◽  
pp. 161-178 ◽  
Keyword(s):  
Rock Salt ◽  
Lattice Dynamics ◽  
Raman Effect ◽  
Order Effect ◽  
Second Order ◽  
Coupling Constants ◽  
Combination Frequency ◽  
First Order ◽  
Combination Frequencies ◽  
Arbitrary Assumption

The Raman effect in crystals is treated in this paper with the help of Placzek’s approximation. It consists of contributions of different orders with respect to the amplitudes of the vibrations; the first-order effect is a line spectrum depending only on the vibrations of infinite wavelength, the second-order effect is a continuous spectrum depending on combination frequencies of all pairs of branches of the lattice vibrations, each pair taken for the same wave vector. In highly symmetrical crystals like rock-salt the first-order effect is zero. The second order effect can be calculated for rock-salt with the help of the tables of the lattice frequencies published by Kellermann. It consists of thirty-six peaks, each belonging to a combination frequency. The superposition of these allows us to determine without any arbitrary assumption about the coupling constants, the frequency of the observable maxima in fair agreement with Krishnan’s measurements. By adapting three coupling constants one can also determine the relative intensities of the most prominent peaks and obtain a curve which in its main features agrees with the observed one. The results show that lattice dynamics can account quantitatively for the Raman effect in crystals and that Raman’s attacks against the theory are unfounded.

scholarly journals The Raman spectrum of rock-salt

1946 ◽  
Vol 187 (1009) ◽  
pp. 188-196 ◽  
Keyword(s):  
Raman Spectrum ◽  
Rock Salt ◽  
Lattice Dynamics ◽  
Vibration Spectrum ◽  
Raman Effect ◽  
Frequency Shifts ◽  
Crystal Lattices ◽  
Absorption Frequency ◽  
Infra Red ◽  
Quartz Spectrograph

Using a non-luminescent crystal of rock-salt, a quartz spectrograph with a fine slit, and the 2536.5 A resonance radiations of mercury arc as exciter, the Raman effect in rock-salt has been studied. The spectrum exhibits nine distinct Raman lines with frequency shifts 135, 184, 202, 235, 258, 278, 314, 323 and 350 cm. -1 . The frequency shifts 235 and 184 cm. -1 representing conspicuous lines in the Raman spectrum agree as nearly as could be expected with the position of the two subsidiary infra-red absorption maxima observed by Barnes & Czerny with thin films of rock-salt. The principal infra-red absorption frequency of 163 cm. -1 is inactive in the Raman effect, but its octave is represented. The nature of the Raman spectrum to be expected is deduced on the basis of a theory due to Tamm, as also on the basis of another due to Fermi, the vibration spectrum of the rock-salt lattice being taken to be that worked out by Kellermann on the basis of the Born lattice dynamics. The results are altogether of a different nature from those actually observed experimentally in the present investigation. The conclusion is thus reached that the Born lattice dynamics does not correctly picture the vibration spectrum of the rock-salt lattice. On the other hand the observed facts, both in respect of Raman effect and infra-red absorption, fit into the theoretical picture provided by the dynamics of crystal lattices recently worked out by Sir C. V. Raman.

scholarly journals Application of multiplet structure deconvolution to extract scalar coupling constants from 1D NMR spectra

2021 ◽  
Author(s):  
Damien Jeannerat ◽  
Carlos Cobas
Keyword(s):  
Nmr Spectra ◽  
Chemical Shifts ◽  
Second Order ◽  
Coupling Constants ◽  
Scalar Coupling ◽  
Order Effects ◽  
Robust Method ◽  
Multiplet Structure ◽  
First Order ◽  
Coupling Structure

Abstract. Multiplet structure deconvolution provides a robust method to determine the values of the coupling constants in first-order 1D NMR spectra. Functions simplifying the coupling structure for any spins and for doublet with unequal amplitudes were introduced. The chemical shifts of the coupling partners causing mild second-order effects can, in favourable cases, be calculated from the slopes measured in doublet structures. Illustrations demonstrate that deconvolution can straightforwardly analyse multiplet posing difficulties to humans and, in some cases, extract coupling constants from unresolved multiplets.

Tool-Life Testing by Response Surface Methodology—Part 2

1964 ◽  
Vol 86 (2) ◽  
pp. 111-116 ◽  
Author(s):  
S. M. Wu
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Tool Life ◽  
Statistical Significance ◽  
Cutting Speed ◽  
Order Effect ◽  
Second Order ◽  
First Order ◽  
Independent Variable ◽  
Basic Philosophy

This paper is a continuation of a previous paper in which the basic philosophy of response surface methodology has been explained and a first-order tool-life-predicting equation has been developed. This part of the paper illustrates the development of a second-order tool-life-predicting equation in 18 and 24 tests. It was found that the second-order effect did not show statistical significance within the cutting ranges of this project; however, the second-order effect of cutting speed has been found important by the study of residuals. If only one independent variable is investigated, a minimal number of tests can be used to find a second-order equation. Examples of designs in three, five, and six tests are illustrated.

Second Order Boundary Layer Solutions on a Curved Surface

1972 ◽  
Vol 94 (3) ◽  
pp. 649-654 ◽  
Author(s):  
W. F. Van Tassell ◽  
D. B. Taulbee
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Order Effect ◽  
Second Order ◽  
Two Dimensional ◽  
First Order ◽  
Boundary Layer Equations ◽  
Similar Solutions ◽  
Nonsimilar Solutions ◽  
Different Altitudes

Solutions of the second order longitudinal curvature boundary layer equations near the stagnation point of a two-dimensional circular cylinder are presented. Four cases corresponding to 1 first order locally similar solutions, 2 first order nonsimilar solutions, 3 second order locally similar solutions, and 4 second order nonsimilar solutions are considered. For each of the four cases, results for four different altitudes are given. The only second order effect considered is longitudinal curvature. Based on the numerical results, it is concluded that similarity and curvature assumptions can alter the skin friction calculations significantly. The heat transfer calculations are much less sensitive to the various assumptions, at least for the cases studied in this paper.

Second Order Analysis on a Typical Steel Industrial Plant

2011 ◽  
Vol 243-249 ◽  
pp. 1405-1408
Author(s):  
Bo Li ◽  
Shao Bin Hu ◽  
Ya Xin Sun ◽  
Yan Wang
Keyword(s):  
Finite Element ◽  
Order Effect ◽  
Second Order ◽  
Nonlinear Finite Element ◽  
Effective Length ◽  
Industrial Plant ◽  
Order Analysis ◽  
First Order ◽  
Engineering Steel ◽  
Analysis Design

The deficiency of effective length approach and the necessity of second order analysis design on nonferrous engineering steel industrial plant are emphasized. Second order analysis approach by nonlinear finite-element with ANSYS is used to design an industrial plant. The example indicates that second-order effect should not be neglect and the result of first order analysis is not safe enough for industrial plant.

The second-order effect of free electrons on lattice conduction

1957 ◽  
Vol 53 (2) ◽  
pp. 508-513 ◽  
Author(s):  
I. C. Pyle
Keyword(s):  
Order Term ◽  
Order Effect ◽  
Order Theory ◽  
Second Order ◽  
Free Electrons ◽  
Phonon Interaction ◽  
First Order ◽  
Electron Phonon Interaction ◽  
First Order Theory ◽  
Second Order Perturbation Theory

ABSTRACTSecond-order perturbation theory, in conjunction with the usual treatment of electron-phonon interaction, allows us to calculate the correction to the first-order result for the scattering of phonons by electrons. It is shown that the second-order term is much smaller, and therefore negligible. This justifies the use of the first-order theory in the treatment of the interaction in metals and semi-conductors.

Microtube Gas Flows With Second-Order Slip Flow and Temperature Jump Boundary Conditions

2006 ◽  
Author(s):  
Nian Xiao ◽  
John Elsnab ◽  
Tim Ameel
Keyword(s):  
Nusselt Number ◽  
Boundary Conditions ◽  
Temperature Jump ◽  
Order Approximation ◽  
Slip Flow ◽  
Order Effect ◽  
Second Order ◽  
First Order ◽  
Slip Regime ◽  
Energy Equations

Second-order slip flow and temperature jump boundary conditions are applied to solve the momentum and energy equations in a microtube for an isoflux thermal boundary condition. The flow is assumed to be hydrodynamically fully developed, and the thermal field is either fully developed or developing from the tube entrance. In general, first-order boundary conditions are found to over predict the effects of slip and temperature jump, while the effect of the second-order terms is most significant at the upper limit of the slip regime. The second-order terms are found to provide a correction to the first-order approximation. For airflows, the maximum second-order correction to the Nusselt number is on the order of 50%. The second-order effect is also more significant in the entrance region of the tube. Nusselt numbers are found to increase relative to their no-slip values when temperature jump effects are small. In cases where slip and temperature jump effects are of the same order, or where temperature jump effects dominate, the Nusselt number decreases when compared to traditional no-slip conditions.

scholarly journals Representation of Rhetorical Presence in Virginia Woolf’s “Madame de Sévigné”

2020 ◽  
Vol 9 (1) ◽  
pp. 65-85
Author(s):  
Margarita Esther Sánchez Cuervo
Keyword(s):  
Virginia Woolf ◽  
Order Effect ◽  
Second Order ◽  
Order Effects ◽  
First Order ◽  
Letter Writer ◽  
Selection Of

AbstractThis paper seeks to represent rhetorical presence in “Madame de Sevigne”, an essay by Virginia Woolf that reviews Sevigne’s collection of letters. In general, Woolf’s essays that appraise an author and her/his work are organised into several sections that correspond to the traditional rhetorical levels of inventio, dispositio and elocutio. The synergy of arguments and figures that are found at each of these levels are first-order effects which can create rhetorical presence, defined as a strategy that relies on the selection of certain elements and how they are presented to the audience. Presence of this kind involves a second-order effect which transmits the persuasive and expressive value of the essay if several conditions pertaining to the values of the audience and Woolf’s expertise in writing are attained. “Madame de Sevigne” is persuasive in that it tries to increase readers’ admiration towards the letter writer and thus affects the readers in a positive way. This admiration is achieved by means of Woolf’s specific use of language, which amplifies Sevigne’s figure and grants expressive prominence to the text.

The misunderstood Sagnac effect

2021 ◽  
Vol 34 (4) ◽  
pp. 480-485
Author(s):  
John-Erik Persson
Keyword(s):  
Doppler Effect ◽  
Order Effect ◽  
Second Order ◽  
Red Shift ◽  
Sagnac Effect ◽  
First Order ◽  
Pioneer Anomaly ◽  
The Doppler Effect ◽  
Stellar Aberration

The Sagnac effect of first order (in one-way light) is shown to explain the aberration observed in the very long base interferometry tests. This fact is also consistent with Sagnac’s results and with the observed stellar aberration. The Sagnac effect of second order (in two-way light) is shown to be real, but not observable, in the experiments that were done by Michelson and Morley. However, it is also shown that the same second order effect is observable in the Pioneer anomaly. The Doppler effect of second order is also demonstrated to explain the cosmic red shift, due to a radial ether wind.

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