The Matrix Method for Data Evaluation and its Advantages in Comparison to the Sin2ψ and Similar Methods

2011 ◽  
Vol 681 ◽  
pp. 7-12 ◽  
Author(s):  
Balder Ortner
Keyword(s):  
Matrix Method ◽  
Stress Measurement ◽  
Data Evaluation ◽  
Traditional Methods ◽  
X Ray ◽  
Data Treatment ◽  
The Matrix

This article gives an overview of different methods for data treatment in x-ray stress measurement, and how these methods should be replaced with the matrix method, which in general is more versatile, more accurate and, in most cases, also easier to handle. It also shows how much the accuracy could be improved by replacing the traditional methods with the matrix method.

Properties and general use of the X-ray elastic factors

2007 ◽  
Vol 22 (2) ◽  
pp. 103-107 ◽  
Author(s):  
Balder Ortner
Keyword(s):  
Plastic Deformation ◽  
Stress Measurement ◽  
Measured Data ◽  
Least Square ◽  
Data Evaluation ◽  
X Ray ◽  
Rank Tensor ◽  
The Matrix ◽  
Hooke's Law ◽  
Linear Regressions

The equation ε(φ, ψ, hkl)=Fij(φ, ψ, hkl)σij can be directly deduced from Hooke’s law. It is shown that the matrix Fij(φ, ψ, hkl) which is usually called X-ray elastic factors, behaves as a second rank tensor. Since this behaviour is the only criterion for the question of whether or not it is a tensor, the F-matrix must be regarded as a second rank tensor. This allows us to make some statements about the structure of the F-matrix on the basis of Neumann’s principle, to find relationships among F-matrices in different measurement directions, and to apply the methods and strategies for the measurement of a second rank tensor. All this is shown in a few examples. It is further shown that a consistent use of the F-matrix can replace all methods for data evaluation which makes use of linear regressions and, in addition, avoids all difficulties and disadvantages of these methods. One of these disadvantages is that the sin2 ψ-method, as well as its derivatives, is generally not correct least square fits of the measured data. This is also shown in an example. The more complicated cases with stress or constitution gradients in the range of the probed volume or stress measurement after plastic deformation are not discussed.

scholarly journals Matrix Method for X-Ray Stress Measurement in Single Crystals, and the Rational Planning of the Measurements

2014 ◽  
Vol 996 ◽  
pp. 58-63
Author(s):  
Balder Ortner
Keyword(s):  
Single Crystals ◽  
Matrix Method ◽  
Stress Measurement ◽  
X Ray Diffraction ◽  
X Ray ◽  
Stress Calculation ◽  
Rational Planning ◽  
The Matrix ◽  
Experimental Effort

With the so-called matrix method stress calculation from x-ray diffraction measurements is much easier than it used to be with older methods. The matrix method is also well suited to optimize the choice of reflections (hkl) to be measured in order to obtain the best results with least experimental effort. Pseudocodes for the stress calculation are given.

Simulation of the powder diffraction pattern of randomly restacked Ca2Nb3O10nanosheets

2009 ◽  
Vol 42 (6) ◽  
pp. 1062-1067 ◽  
Author(s):  
Mitsuko Onoda ◽  
Yasuo Ebina ◽  
Takayoshi Sasaki
Keyword(s):  
Diffraction Pattern ◽  
Powder Diffraction ◽  
Matrix Method ◽  
Powder Pattern ◽  
X Ray ◽  
The Matrix ◽  
Pattern Simulation

From X-ray powder diffraction pattern features, layered KCa2Nb3O10·nH2O synthesized through flocculation of delaminated Ca2Nb3O10nanosheets with K ions appeared to be composed of randomly stacked nanosheets. Powder pattern simulation was conducted based on the matrix method using a random stacking model. When seven sheets were used as the coherent thickness, agreement in pattern fitting between the experimental and calculated intensities was satisfactory, and information about textures and atomic positions was obtained.

Two-Dimensional X-Ray Diffraction for Structure and Stress Analysis

2005 ◽  
Vol 490-491 ◽  
pp. 1-6 ◽  
Author(s):  
Bob B. He ◽  
Ke Wei Xu ◽  
Fei Wang ◽  
Ping Huang
Keyword(s):  
Stress Analysis ◽  
Stress Measurement ◽  
Unit Vector ◽  
Sample Space ◽  
Matrix Transformation ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Texture Measurement ◽  
X Ray ◽  
The Matrix

This paper introduces the recent progress in two-dimensional X-ray diffraction as well as its applications in microstructure and residual stress analysis. Based on the matrix transformation between diffraction space, detector space and sample space, the unit vector of the diffraction vector can be expressed in the sample space corresponding to all the geometric parameters and Bragg conditions. The same transformation matrix can be used for texture and stress analysis. The fundamental equations for both stress measurement and texture measurement are developed with the matrix transformation defined for the two-dimensional diffraction. Stress measurement using twodimensional detector is based on a direct relationship between the stress tensor and the diffraction cone distortion. The two-dimensional detector collects texture data and background values simultaneously for multiple poles and multiple directions.

Dependence of Stress Constant on Microstructure of Quenched and Tempered Steels in X-Ray Stress Measurement

1991 ◽  
Vol 35 (A) ◽  
pp. 519-525
Author(s):  
Masanori Kurita ◽  
Akira Saito
Keyword(s):  
Residual Stress ◽  
Stress Measurement ◽  
Practical Importance ◽  
Carbon Steels ◽  
X Ray Diffraction ◽  
Tempered Martensite ◽  
Tempering Temperature ◽  
X Ray ◽  
The Matrix ◽  
High Residual Stress

AbstractThe residual stress measurement of quenched and tempered steels is of practical importance because the quenching can sometimes induce the high residual stress which affects the strength of materials. The stress constants of carbon steels quenched and tempered at various temperatures were measured in order to determine the residual stress of steels by x-ray diffraction. The stress constant increased slowly with increasing tempering temperatures below 500°C; it increased rapidly with tempering temperatures above about 500°C, This rapid increase in the stress constant is closely related to the change in microstructure of the steels in tempering; above the tempering temperature of around 500°C, the tempered martensite recrystallized and transformed to ferritic iron and fine cementite particles dispersed in the matrix; these coalesced and grew to be speroidized cementites and finally laminar cementite plates.

Lateral resolution of the electron microbeam analysis

1978 ◽  
Vol 36 (1) ◽  
pp. 542-543
Author(s):  
H.J. Dudek
Keyword(s):  
Quantitative Analysis ◽  
Depth Resolution ◽  
Lateral Resolution ◽  
Cylindrical Particle ◽  
Correction Procedure ◽  
X Ray ◽  
Element Concentrations ◽  
Microbeam Analysis ◽  
The Matrix

The chemical inhomogenities in modern materials such as fibers, phases and inclusions, often have diameters in the region of one micrometer. Using electron microbeam analysis for the determination of the element concentrations one has to know the smallest possible diameter of such regions for a given accuracy of the quantitative analysis.In th is paper the correction procedure for the quantitative electron microbeam analysis is extended to a spacial problem to determine the smallest possible measurements of a cylindrical particle P of high D (depth resolution) and diameter L (lateral resolution) embeded in a matrix M and which has to be analysed quantitative with the accuracy q. The mathematical accounts lead to the following form of the characteristic x-ray intens ity of the element i of a particle P embeded in the matrix M in relation to the intensity of a standard S

Analysis and lattice imaging of a transitional event on garnets

1978 ◽  
Vol 36 (1) ◽  
pp. 270-271
Author(s):  
J.Y. Laval
Keyword(s):  
Yttrium Iron Garnet ◽  
Reciprocal Lattice ◽  
Transitional Zone ◽  
Lattice Imaging ◽  
Yttrium Iron ◽  
X Ray ◽  
Ionic Process ◽  
The Matrix ◽  
High Resolution Technique ◽  
Iron Garnet

The exsolution of magnetite from a substituted Yttrium Iron Garnet, containing an iron excess may lead to a transitional event. This event is characterized hy the formation of a transitional zone at the center of which the magnetite nucleates (Fig.1). Since there is a contrast between the matrix and these zones and since selected area diffraction does not show any difference between those zones and the matrix in the reciprocal lattice, it is of interest to analyze the structure of the transitional zones.By using simultaneously different techniques in electron microscopy, (oscillating crystal method microdiffraction and X-ray microanalysis)one may resolve the ionic process corresponding to the transitional event and image this event subsequently by high resolution technique.

Phase identification in SiC whisker reinforced Al2O3-R2O3-based composites

1992 ◽  
Vol 50 (1) ◽  
pp. 152-153
Author(s):  
C.M. Sung ◽  
K.J. Ostreicher ◽  
M.L. Huckabee ◽  
S.T. Buljan
Keyword(s):  
Analytical Electron Microscopy ◽  
Phase Identification ◽  
Reinforced Composites ◽  
Ion Milling ◽  
X Ray ◽  
Binary Oxides ◽  
Analytical Electron ◽  
The Matrix ◽  
Second Phases ◽  
Convergent Beam

A series of binary oxides and SiC whisker reinforced composites both having a matrix composed of an α-(Al, R)2O3 solid solution (R: rare earth) have been studied by analytical electron microscopy (AEM). The mechanical properties of the composites as well as crystal structure, composition, and defects of both second phases and the matrix were investigated. The formation of various second phases, e.g. garnet, β-Alumina, or perovskite structures in the binary Al2O3-R2O3 and the ternary Al2O3-R2O3-SiC(w) systems are discussed.Sections of the materials having thicknesses of 100 μm - 300 μm were first diamond core drilled. The discs were then polished and dimpled. The final step was ion milling with Ar+ until breakthrough occurred. Samples prepared in this manner were then analyzed using the Philips EM400T AEM. The low-Z energy dispersive X-ray spectroscopy (EDXS) data were obtained and correlated with convergent beam electron diffraction (CBED) patterns to identify phase compositions and structures. The following EDXS parameters were maintained in the analyzed areas: accelerating voltage of 120 keV, sample tilt of 12° and 20% dead time.

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