A New Program to Calculate the Texture Vector for the VectorMethod

Vadon, A.; Heizmann, J.J.

doi:10.1155/tsm.14-18.37

Cited by 7 publications

(3 citation statements)

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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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“…The information which is presented in different pole figures is combined by means of pole figure inversion algorithms (e.g. Bunge and Esling, 1985;Matthies, 1991;Pawlik et al 1991;Schaeben and Siemes, 1991;Vadon and Heizmann, 1991) to an orientation distribution function (ODF). From the measured pyrite reflections the (200)-, (220)-and (111)-pole figures were used to calculate a MENTEX-ODF according to the inversion method involving finite series expansion and entropy optimisation (Schaeben, 1988;Schaeben et al, 1990;Schaeben, 1991).…”

Section: Measurement and Analysis Of Preferred Orientationmentioning

confidence: 99%

Preferred orientation of experimentally deformed pyrite measured by means of rieutron diffraction

et al. 1993

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Neutron diffraction texture goniometry indicates that naturally deformed polycrystalline pyrite ores from Mt. Lyell (Tasmania) and Degtiarka (Ural Mountains) have weak lattice preferred orientations. During experimental deformation involving dislocation flow at elevated temperatures and pressures, these initial fabrics have been modified to produce new lattice preferred orientations.Polycrystalline pyrite form Mt. Lyelt (B-l) has an initial -fibre texture perpendicular to a grain-size layering. After 24% shortening perpendicular to the -fibre axis at 700 ~ a new, but weak <100> texture has developed parallel to the shortening axis. The Degtiarka pyrite (PN-6) initially has two weak fibre components. The somewhat stronger component is a < 100>-fibre texture, similar to that in the experimentally deformed B-1 pyrite. The other one is a -fibre texture similar to the intital B-1 preferred orientation. After 30% shortening oblique to both initial fibre axes at 600 ~ weak < 110>-and < 111 >-fibre textures have developed. The experimentally produced fabrics have developed during deformation involving dislocation flow, dynamic recrystallisation and some microcracking. Intergranular sliding may also have been involved. Differences between lattice preferred orientations developed in the 600 ~ and 700 ~ experiments are interpreted to indicate a change in the dominant flow mechanism with changing temperature.tn comparison with other cubic minerals that have been deformed experimentally by dislocation flow mechanisms, the pyrite shows an unusually weak preferred orientation which can be detected only by means of neutron diffraction texture goniometry.

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“…Due to this practical importance there are a lot of papers by engineers and physicists on the inversion of the Funk transform, see e.g. [1,4,6,10,13,22,23,28,29,31,32,34,35,37,38,43]. There are also a few mathematical papers on this topic covering quite different inversion methods, i.e., splines [3,12,40], Fourier expansion [11], Gabor frames [7] and wavelets [2].…”

Section: Introductionmentioning

confidence: 99%

Numerical inversion of the Funk transform on the rotation group

Hielscher¹

2013

Inverse Problems

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The reconstruction of a function on the rotation group from mean values along all geodesics is an overdetermined problem, i.e., it is sufficient to know the mean values for a three dimensional subset of all geodesics on the rotation group. In this paper we give a Fourier slice theorem for the restricted problem. Based on the Fourier slice theorem and fast Fourier transforms on the rotation group and the sphere we introduce a fast algorithm for the forward transform. Analyzing the inverse problem we come up with an exact inversion formula for bandlimited functions on the rotation group. Unfortunately, this inversion formula turns out to be extremely ill conditioned. Therefore, we introduce an iterative approach which makes use of regularization and the fast algorithm for the forward transform. Numerical experiments indicate the applicability of our algorithms.

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A New Program to Calculate the Texture Vector for the VectorMethod

Cited by 7 publications

References 0 publications

Monte Carlo simulation of neutron scattering by a textured polycrystal

Monte Carlo simulation of neutron scattering by a textured polycrystal

Preferred orientation of experimentally deformed pyrite measured by means of rieutron diffraction

Numerical inversion of the Funk transform on the rotation group

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