The Debye Equation

2020 ◽  
pp. 77-93
Keyword(s):  
Debye Equation

Debye equation versus Whole Powder Pattern Modelling: Real versus reciprocal space modelling of nanomaterials

2009 ◽  
Vol 2009 (30) ◽  
pp. 85-90 ◽  
Author(s):  
K. Beyerlein ◽  
A. Cervellino ◽  
M. Leoni ◽  
R. L. Snyder ◽  
P. Scardi
Keyword(s):  
Reciprocal Space ◽  
Powder Pattern ◽  
Equation Versus ◽  
Debye Equation

Determination of interface layer thickness of a pseudo two-phase system by extension of the Debye equation

2001 ◽  
Vol 34 (14) ◽  
pp. 2085-2088 ◽  
Author(s):  
Zhi Hong Li ◽  
Yan Jun Gong ◽  
Min Pu ◽  
Dong Wu ◽  
Yu Han Sun ◽  
...  
Keyword(s):  
Layer Thickness ◽  
Interface Layer ◽  
Phase System ◽  
Two Phase ◽  
Debye Equation

Moment representation of the Lyddane-Sachs-Teller relation for the Debye equation

1991 ◽  
Vol 44 (23) ◽  
pp. 13067-13070 ◽  
Author(s):  
J. D. Hwang ◽  
T. K. Song ◽  
T. W. Noh ◽  
S. I. Kwun
Keyword(s):  
Moment Representation ◽  
Debye Equation

scholarly journals Preferred Orientation, PDF and Debye Equation

2014 ◽  
Vol 70 (a1) ◽  
pp. C1077-C1077
Author(s):  
Reinhard Neder
Keyword(s):  
Fourier Transform ◽  
Diffraction Pattern ◽  
Complex Function ◽  
Good Alternative ◽  
Preferred Orientation ◽  
Spherical Average ◽  
Area Detector ◽  
Orientation Axis ◽  
The Fourier Transform ◽  
Debye Equation

The effect of preferred orientation is currently neglected in the Debye Equation and PDF calculations. This is to a large extend justified, especially for the PDF, as the scattering by large sample volumes is detected by an area detector. The integration of powder rings reduces the effects of preferred orientation. As more laboratory PDF measurements become available that use linear position sensitive detectors or single counter detectors, preferred orientation needs to be reconsidered. A Rietveld calculation treats preferred orientation by multiplying the Bragg intensity by a factor that depends on the angle between the reciprocal space vector and the preferred orientation axis. The powder intensity I(Q) is thus multiplied by a complex function that depends at each Q on the degree of preferred orientation, the lattice parameters, reflection multiplicity etc. The effect on the PDF is therefore the convolution by the Fourier transform of this complex function. The Debye equation is derived from a spherical average of the scattering intensity of a finite object. Thus completely random orientation of the powder grains is implicitly assumed. Both, the Debye algorithm and the PDF algorithm calculate the powder pattern, respectively the PDF from a histogram of interatomic distances, which correspond to a spherical average of all interatomic distance vectors. This histogram does not allow for a Rietveld preferred orientation correction. The effects of preferred orientation on the PDF will be presented on the basis of simulated diffraction pattern. An algorithm to describe the changes in the PDF and the inverse sine Fourier transform as a convenient tool to calculate the powder diffraction pattern will be introduced. This is a good alternative to the Debye equation and allows to take preferred orientation into account both for the PDF and the calculated powder.

Dielectric materials

2018 ◽  
Author(s):  
L. Solymar ◽  
D. Walsh ◽  
R. R. A. Syms
Keyword(s):  
Liquid Crystals ◽  
Frequency Response ◽  
Acoustic Waves ◽  
Dielectric Materials ◽  
Effective Field ◽  
Optical Fibres ◽  
Optical Phonons ◽  
Orientational Polarization ◽  
Dispersion Equations ◽  
Debye Equation

The macroscopic and microscopic approaches to determining polarization are explained. The types of polarization, frequency response, and anomalous dispersion are discussed. The Debye equation for orientational polarization is derived. The concept of effective field is introduced. The dispersion equations for acoustic waves and for optical phonons are derived. The properties of piezoelectricity, pyroelectricity, and ferroelectricity are discussed. The attenuation of optical fibres, the operation of a photocopier, and the ability of liquid crystals to rotate polarization are also discussed.

Domain structure investigation of non-stoichiometric strontium ferrites and cobaltites

2013 ◽  
Vol 28 (S2) ◽  
pp. S51-S64 ◽  
Author(s):  
U.V. Ancharova ◽  
S.V. Cherepanova
Keyword(s):  
Domain Structure ◽  
Domain Size ◽  
Orthorhombic Distortion ◽  
Synchrotron Powder Diffraction ◽  
Structure Simulation ◽  
Average Domain Size ◽  
Xrd Patterns ◽  
Average Domain ◽  
Debye Equation ◽  
Strontium Ferrites

Monte Carlo domain structure simulation and Debye equation calculation of XRD patterns were used to confirm the formation of domain structure and investigate its peculiarities. Correspondence of simulated XRD patterns with synchrotron powder diffraction experiments is achieved on the conditions that beside of 90o rotations of brownmillerite-like domains inside perovskite-like matrix each domain contains areas with perpendicularly oriented tetrahedral chains. Influence of such parameters as stoichiometry, average domain size, orthorhombic distortion degree on the XRD patterns is considered.

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