X-Ray Line Profile Analysis for Single Crystals

2014 ◽  
pp. 242-270
Keyword(s):  
Single Crystals ◽  
Intensity Distribution ◽  
Profile Analysis ◽  
Reciprocal Lattice ◽  
Lattice Points ◽  
Polycrystalline Materials ◽  
Line Profile Analysis ◽  
Line Profiles ◽  
X Ray ◽  
Lattice Misorientation

The features of the dislocation structure in plastically deformed single crystals can be determined from diffraction line broadening. Both the measuring and the evaluation procedures of X-ray line profiles are somewhat different from the methods used for polycrystalline materials. In this chapter, these procedures are overviewed, and their effectiveness is illustrated by representative examples. It is shown that the intensity distribution in the vicinity of the reciprocal lattice points can be mapped by rocking the single crystal about appropriate axes. From the detected intensity distribution, the density, the slip systems, and the arrangement of dislocations, as well as the lattice misorientation can be determined. The average misorientation obtained from rocking curve measurement can be related to the density of geometrically necessary dislocations. It is also shown that the inhomogeneous distribution of dislocations in plastically deformed single crystals usually results in asymmetric line profiles. The evaluation of these peaks enables the determination of the long-range internal stresses besides the dislocation densities in the dislocation cell walls and interiors.

Fundamentals of Kinematical X-Ray Scattering Theory

2014 ◽  
pp. 1-14
Keyword(s):  
Scattering Theory ◽  
Profile Analysis ◽  
Reciprocal Lattice ◽  
Line Profile Analysis ◽  
X Ray ◽  
X Ray Scattering ◽  
Basic Concepts ◽  
Lattice Planes ◽  
The Relationship ◽  
Ray Scattering

The broadening of X-ray line profiles is usually described by the kinematical scattering theory. In this chapter, the basic concepts and equations of the kinematical X-ray scattering are presented in order to better understand the theory of line profile analysis. The correlation between the crystal structure and the diffracted intensity distribution is shown. The scattering angles of the diffracted peak maxima are given by the Ewald construction in the reciprocal space. The correspondence between the reciprocal lattice vectors and the lattice planes is also presented, and the relationship between the scattering angle and the lattice plane spacing is given by Bragg’s law.

Microstructural parameters and layer disorder accompanying dehydration transformation in Na-montmorillonite

2000 ◽  
Vol 215 (4) ◽  
Author(s):  
S.K. Srivastava ◽  
P. Bala ◽  
B.K. Samantaray ◽  
Hartmut Haeuseler
Keyword(s):  
Crystallite Size ◽  
Structural Changes ◽  
Profile Analysis ◽  
Thermal Transformation ◽  
Initial Slope ◽  
Line Profile Analysis ◽  
Line Profiles ◽  
X Ray ◽  
Microstructural Parameters ◽  
Layer Disorder

Structural changes accompanying thermal transformation in Na-montmorillonite samples up to a temperature of 500°C have been investigated by X-ray line profile analysis. The method of Fourier initial slope and variance analysis of X-ray line profiles have been used to calculate the different microstructural parameters like crystallite size, r.m.s. strain (<e

Practical Applications of X-Ray Line Profile Analysis

2017 ◽  
pp. 1094-1132
Author(s):  
Jenő Gubicza
Keyword(s):  
Crystallite Size ◽  
Twin Boundary ◽  
Line Profile ◽  
Profile Analysis ◽  
Vacancy Concentration ◽  
Direct Method ◽  
Line Profile Analysis ◽  
Line Profiles ◽  
X Ray ◽  
Practical Applications

In the previous chapters, the theory and the main methods of diffraction peak profile analysis were presented. Additionally, the specialties in the measurement and the evaluation of line profiles in the cases of thin films and single crystals were discussed. In this chapter, some practical considerations are given in order to facilitate the evaluation of peak profiles and the interpretation of the results obtained by this method. For instance, the procedures for instrumental correction are overviewed. Additionally, how the prevailing dislocation slip systems and twin boundary types in hexagonal polycrystals can be determined from line profiles is shown. Besides the dislocation density, the vacancy concentration can also be obtained by the combination of electrical resistivity, calorimetric, and line profile measurements. The crystallite size and the twin boundary frequency determined by X-ray peak profile analysis are compared with the values obtained by the direct method of transmission electron microscopy. Furthermore, the limits of line profile analysis in the determination of crystallite size and defect densities are given. Finally, short overviews on the results obtained by peak profile analysis for metals, ceramics, and polymers are presented.

Practical Applications of X-Ray Line Profile Analysis

2014 ◽  
pp. 271-318
Keyword(s):  
Crystallite Size ◽  
Twin Boundary ◽  
Line Profile ◽  
Profile Analysis ◽  
Vacancy Concentration ◽  
Direct Method ◽  
Line Profile Analysis ◽  
Line Profiles ◽  
X Ray ◽  
Practical Applications

In the previous chapters, the theory and the main methods of diffraction peak profile analysis were presented. Additionally, the specialties in the measurement and the evaluation of line profiles in the cases of thin films and single crystals were discussed. In this chapter, some practical considerations are given in order to facilitate the evaluation of peak profiles and the interpretation of the results obtained by this method. For instance, the procedures for instrumental correction are overviewed. Additionally, how the prevailing dislocation slip systems and twin boundary types in hexagonal polycrystals can be determined from line profiles is shown. Besides the dislocation density, the vacancy concentration can also be obtained by the combination of electrical resistivity, calorimetric, and line profile measurements. The crystallite size and the twin boundary frequency determined by X-ray peak profile analysis are compared with the values obtained by the direct method of transmission electron microscopy. Furthermore, the limits of line profile analysis in the determination of crystallite size and defect densities are given. Finally, short overviews on the results obtained by peak profile analysis for metals, ceramics, and polymers are presented.

Line Profile Analysis (LPA) Methods: Systematic Ranking of the Quality of their Basic Assumptions

2004 ◽  
Vol 443-444 ◽  
pp. 127-130
Author(s):  
Arnold C. Vermeulen ◽  
Rob Delhez
Keyword(s):  
Line Profile ◽  
Profile Analysis ◽  
Line Profile Analysis ◽  
Line Profiles ◽  
Qualitative Comparison ◽  
New Developments ◽  
X Ray ◽  
Basic Assumptions ◽  
Wide Range

All methods of analyzing the broadening of XRD line profiles have to take into account two basic effects: broadening by the instrument - including the X-ray spectrum - and the characteristics of broadening by size effects and by lattice defects - including their interaction. These effects are handled in practice by a wide range of auxiliary assumptions. In this paper these assumptions and their quality with respect to "appropriateness of purpose" are listed and compared. By systematic ranking of these assumptions in accordance with their quality, a 2-dimensional map can be constructed that visualizes the differences in the quality of the assumptions. This 2-dimensional map brings a new viewpoint to the various methods for line profile analysis, because it enables a qualitative comparison of the assumptions of existing methods and new developments.

Dislocation Densities, Slip-System Types and Burgers Vector Populationsinhexagonal and Cubiccrystalsfrom X-Ray Line Profile Analysis

2011 ◽  
Vol 702-703 ◽  
pp. 479-484
Author(s):  
Tamás Ungár
Keyword(s):  
Line Profile ◽  
Profile Analysis ◽  
Polycrystalline Materials ◽  
Line Profile Analysis ◽  
X Ray Diffraction ◽  
Burgers Vector ◽  
X Ray ◽  
Diffraction Line Profile ◽  
Vector Population ◽  
Dislocation Densities

X-ray diffraction line profile analysis can be carried out on the hkl planes corresponding to the same texture component or the same crystallographic orientation fiber. It is shown that in textured polycrystalline materials or in thin films or multilayers X-ray line profiles measured on planes corresponding either to the main or the minor texture components can provide the Burgers vector population and dislocations densities in the different texture components separately. The experimental technique is outlined for textured specimens and the multiple convolutional whole profile method, i.e. the CMWP line profile analysis procedure, is presented for its capacity to determine the substructure pertaining to different texture components in textured samples.

Determination of dispersion and polarization of thermal plane waves in crystals

1971 ◽  
Vol 134 (3-4) ◽  
Author(s):  
P. L. La Fleur
Keyword(s):  
Intensity Distribution ◽  
Phonon Scattering ◽  
Reciprocal Lattice ◽  
Plane Waves ◽  
Lattice Points ◽  
X Ray Diffraction ◽  
Diffraction Intensity ◽  
Reciprocal Lattice Point ◽  
X Ray

AbstractThe dispersion of the thermal plane waves (phonons) in crystals can be determined from the x-ray diffraction intensity distribution around a reciprocal lattice point. In the method presented here no higher-order phonon-scattering corrections are necessary. It is shown furthermore that polarizations and dispersion of the phonons can be determined from the intensity distributions around six properly chosen reciprocal lattice points.

Microstructure of post-deformed ECAP-Ti investigated by Multiple X-Ray Line Profile Analysis

2006 ◽  
Vol 2006 (suppl_23_2006) ◽  
pp. 129-134 ◽  
Author(s):  
E. Schafler ◽  
K. Nyilas ◽  
S. Bernstorff ◽  
L. Zeipper ◽  
M. Zehetbauer ◽  
...  
Keyword(s):  
Line Profile ◽  
Profile Analysis ◽  
Line Profile Analysis ◽  
X Ray

Crystal truncation rod X-ray scattering: exact dynamical calculation

2008 ◽  
Vol 41 (1) ◽  
pp. 18-26 ◽  
Author(s):  
Václav Holý ◽  
Paul F. Fewster
Keyword(s):  
Reciprocal Lattice ◽  
Dynamical Theory ◽  
Lattice Points ◽  
Space Distribution ◽  
Matrix Formalism ◽  
X Ray ◽  
Transmission Coefficients ◽  
X Ray Scattering ◽  
Crystal Truncation Rod ◽  
Scattering Geometry

A new method is presented for a calculation of the reciprocal-space distribution of X-ray diffracted intensity along a crystal truncation rod. In contrast to usual kinematical or dynamical approaches, the method is correct both in the reciprocal-lattice points and between them. In the method, the crystal is divided into a sequence of very thin slabs parallel to the surface; in contrast to the well known Darwin dynamical theory, the electron density in the slabs is constant along the surface normal. The diffracted intensity is calculated by a matrix formalism based on the Fresnel reflection and transmission coefficients. The method is applicable for any polarization of the primary beam and also in a non-coplanar scattering geometry.

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