The feasibility of the reproduction of the texture function by the vector method

Pośpiech, J.; Ruer, D.; Baro, R.

doi:10.1107/s0021889881009254

Cited by 7 publications

(5 citation statements)

References 7 publications

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“…The mathematical problem of extracting the ODF from pole figure measurements is called the pole figure inversion problem and was first addressed in the pioneering work of Bunge (1965) and Roe (1965). Since then, several methods have been proposed and perfected by several authors Jura et al, 1974Jura et al, , 1976Matthies & Pospiech, 1980;Pospiech et al, 1981;Houtte, 1983;Imhof, 1983;Pawlik, 1986;Schaeben, 1988;Matthies, 1988;Helming & Eschner, 1990;Houtte, 1991;Vadon & Heizmann, 1991;van den Boogaart et al, 2007;Bernier et al, 2006;Hielscher & Schaeben, 2008).…”

Section: Orientation Distribution Functionmentioning

confidence: 99%

Monte Carlo simulation of neutron scattering by a textured polycrystal

Laliena¹,

Vicente-Alvarez²,

Campo³

2020

J Appl Cryst

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A method of simulating the neutron scattering by a textured polycrystal is presented. It is based on an expansion of the scattering cross sections in terms of the spherical harmonics of the incident and scattering directions, which is derived from the generalized Fourier expansion of the polycrystal orientation distribution function. The method has been implemented in a Monte Carlo code as a component of the McStas software package, and it has been validated by computing some pole figures of a Zircaloy‐4 plate and a Zr–2.5Nb pressure tube, and by simulating an ideal transmission experiment. The code can be used to estimate the background generated by components of neutron instruments such as pressure cells, whose walls are made of alloys with significant crystallographic texture. As a first application, the effect of texture on the signal‐to‐noise ratio was studied in a simple model of a diffraction experiment, in which a sample is placed inside a pressure cell made of a zirconium alloy. With this setting, the results of two simulations were compared: one in which the pressure‐cell wall has a uniform distribution of grain orientations, and another in which the pressure cell has the texture of a Zr–2.5Nb pressure tube. The results showed that the effect of the texture of the pressure cell on the noise of a diffractogram is very important. Thus, the signal‐to‐noise ratio can be controlled by appropriate choice of the texture of the pressure‐cell walls.

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Section: Orientation Distribution Functionmentioning

confidence: 99%

Monte Carlo simulation of neutron scattering by a textured polycrystal

Laliena¹,

Vicente-Alvarez²,

Campo³

2020

J Appl Cryst

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“…Considering that the vector method requires much less data than the harmonic method, the results obtained were surprisingly good, especially when applied to analyze pole figures sufficiently different from uniformity and with large ranges of zero intensities (Ruer, 1976;Vadon, 1981;Pospiech et al, 1981;Ruer and Vadon, 1982). experiments in a series of pioneering papers by Matthies (1979;1980; 1981) it was understood that ambiguity enters the texture problem through the diffraction experiment itself.…”

Section: =1mentioning

confidence: 99%

Introducing a Conditional Ghost Correction Into the Vector Method

Schaeben

1984

Texture, Stress, and Microstructure

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The concept of conditional ghost correction is introduced into the vector method of quantitative texture analysis. The mathematical model actually chosen here reduces the texture problem to one of quadratic programming. Thus, a well defined optimization problem has to be solved, the singular system of linear equations governing the correspondence between pole and orientation distribution being reduced to a set of equality constraints of the restated texture problem. This new mathematical approach in terms of the vector method reveals the modeling character of the solution of the texture problem provided by the vector method completely.

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“…Bunge, 1965;Roe, 1965;Pospiech & Jura, 1974;Jura et al, 1976;Ruer, 1976;Matthies & Pospiech, 1980;Pospiech et al, 1981;Van Houtte, 1983;Imhof, 1983;Bunge & Esling, 1985;Pawlik, 1986;Schaeben, 1988;Matthies, 1988;Helming & Eschner, 1990;Vadon & Heizmann, 1991;Van Houtte, 1991;van den Boogaart et al, 2006;Bernier et al, 2006;Hielscher, 2008). Bunge, 1965;Roe, 1965;Pospiech & Jura, 1974;Jura et al, 1976;Ruer, 1976;Matthies & Pospiech, 1980;Pospiech et al, 1981;Van Houtte, 1983;Imhof, 1983;Bunge & Esling, 1985;Pawlik, 1986;Schaeben, 1988;Matthies, 1988;Helming & Eschner, 1990;Vadon & Heizmann, 1991;Van Houtte, 1991;van den Boogaart et al, 2006;Bernier et al, 2006;Hielscher, 2008).…”

Section: Introductionunclassified

“…Various methods for the resolution of the pole figure inversion problem have been proposed, the earliest dating back to 1965 (e.g. Bunge, 1965;Roe, 1965;Pospiech & Jura, 1974;Jura et al, 1976;Ruer, 1976;Matthies & Pospiech, 1980;Pospiech et al, 1981;Van Houtte, 1983;Imhof, 1983;Bunge & Esling, 1985;Pawlik, 1986;Schaeben, 1988;Matthies, 1988;Helming & Eschner, 1990;Vadon & Heizmann, 1991;Van Houtte, 1991;van den Boogaart et al, 2006;Bernier et al, 2006;Hielscher, 2008). However, most of these methods, and their implementation in a particular software code, do not allow for high-resolution diffraction pole figures measured with respect to arbitrarily scattered specimen directions, e.g.…”

Section: Introductionmentioning

confidence: 99%

A novel pole figure inversion method: specification of theMTEXalgorithm

2008

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A novel algorithm for ODF (orientation density function) estimation from diffraction pole figures is presented which is especially well suited for sharp textures and high‐resolution pole figures measured with respect to arbitrarily scattered specimen directions, e.g. by area detectors. The estimated ODF is computed as the solution of a minimization problem which is based on a model of the diffraction counts as a Poisson process. The algorithm applies discretization by radially symmetric functions and fast Fourier techniques to guarantee smooth approximation and high performance. An implementation of the algorithm is freely available as part of the texture analysis software MTEX.

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The feasibility of the reproduction of the texture function by the vector method

Abstract: The ability of the vector method to determine the complete orientation distribution function (ODF) with pole figures will be demonstrated for a particular case. A comparison of the results obtained by the vector method and the series expansion method will be presented.

Cited by 7 publications

References 7 publications

Monte Carlo simulation of neutron scattering by a textured polycrystal

Monte Carlo simulation of neutron scattering by a textured polycrystal

Introducing a Conditional Ghost Correction Into the Vector Method

A novel pole figure inversion method: specification of theMTEXalgorithm

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