Determination of the Complete Orientation Distribution Function by the Zero‐Range Method

Lee, H. P.; Bunge, H. J.; Esling, Claude

doi:10.1155/tsm.6.289

Cited by 6 publications

(5 citation statements)

References 5 publications

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“…The latter method may be considered as a generalization of the zero-range method. Furthermore, this latter method can be made to converge towards a variety of different solutions for f(g) and hence for f(g) within the range of solutions of (9) Hence, an approximation to f(g) can be obtained by fitting an odd function to -f(g) in the zero range by the condition (Bunge & Esling, 1979;Esling, BechlerFerry & Bunge, 1981;Lee, Bunge & Esling, 1986) …”

Section: Odd-order Coefficientsmentioning

confidence: 99%

The iterative series-expansion method for quantitative texture analysis. I. General outline

Dahms¹,

Bunge²

1989

J Appl Crystallogr

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275

114

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The orientation distribution function (ODF) of the crystallites of polycrystalline materials can be calculated from experimentally measured pole density distribution functions (pole figures). This procedure, called pole-figure inversion, can be achieved by the series-expansion method (harmonic method). As a consequence of the (hkl)-(hkl) superposition, the solution is mathematically not unique. Rather it contains a range of possible solutions (kernel) which is only limited by the positivity condition of the distribution function. The complete distributio 9 functionf(g) can be split into two parts f(g) and f(g) expressed by even-and odd-order terms of the series expansions. For the calculation of the even part f(g), the positivity condition for all pole figures contributes essentially to an 'economic' calculation of this part, whereas, for the odd part, the positivity condition of the ODF is the essential basis. Both of these positivity conditions can be easily incorporated in the series-expansion method by using several iterative cycles. This method proves to be particularly versatile since it makes use of the orthogonality and positivity at the same time.

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Section: Odd-order Coefficientsmentioning

confidence: 99%

The iterative series-expansion method for quantitative texture analysis. I. General outline

Dahms¹,

Bunge²

1989

J Appl Crystallogr

Self Cite

275

114

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“…The orientation distribution functions for the ring sample were calculated by the iterative series expansion method using the (111), (200) and (220) pole figures . In the present software the so called ghost correction was implemented by using the zero range method, described in detail by Lee et al . The degree of series expansion was Lmax = 23.…”

Section: Resultsmentioning

confidence: 99%

Texture gradient studies of a Cu‐tube by the robot at STRESS‐SPEC

Al-Hamdany

Brokmeier

Randau

et al. 2014

Crystal Research and Technology

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The handling of larger samples for texture studies is limited when we using the Eulerian cradle. The robot Stäubli RX160 installed at STRESS‐SPEC offers much more freedom in sample manipulation on one hand to perform pole figure scanning and on the other hand to position the sample for a texture mapping. A key problem is that slit systems cannot be positioned close to large samples due to safety reasons which makes corrections more important. A very simple solution was tested to correct the scattered intensity for each pole figure point for constant volume and anisotropic absorption. A simple method to make these corrections is needed because engineering samples such as semi‐finished products have a large variety of shapes and weights and an ideal slit system is only seldomly available. The test sample was a Cu‐tube of 140 mm in diameter with an average wall thickness of 10 mm. To compare the corrections three kind of samples were measured, first a cube of 10 × 10 × 11 mm³ without any correction, second an 11 mm long tube segment and third a tube segment of 250 mm (12 kg weight) in length. Orientation Distribution Function (ODF) analysis of the average texture over the tube wall by the iterative series expansion method has shown that sufficient intensity corrections can be done to describe the texture gradient around the circumference of the Cu‐tube related to low ovality and eccentricity of the Cu‐tube.

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“…Pour ce faire, la m&hode de Bunge (1965Bunge ( , 1982 et de Roe (1965de Roe ( , 1966, qui utilise des d~veloppements en s6rie sur la base des harmoniques sph6riques est utilis6e jusqu'fi un ordre de d6veloppement L = 22. La mesure de la texture par des m6thodes statistiques telles que la diffration des rayons X ou des neutrons pr6sente cependant un inconv6nient majeur puisqu'elle ne permet de calculer que la partie paire F(9) de la fonction totale if(g), la partie impaire n'6tant pas directement d&erminable (Bunge, 1965(Bunge, , 1982Lee, Bunge & Esling 1986;Penelle, Baudin, Paillard & Mora, 1990).…”

Section: Diffraction Des Rayons Xunclassified

Caractérisation de la texture de recristallisation primaire et de la spécialité des joints de grains de tôles de Fe-3%Si par diffraction des electrons rétrodiffusés

Baudin¹,

Paillard²,

Pénelle³

1992

J Appl Cryst

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The EBSP (electron backscattering pattern) technique has been used to verify and to complete a study by Rouag [Th6se de Doctorat d'Etat (1988), Univ. de Paris Sud, Orsay, France] concerning the influence of crystallographic texture and grain boundaries during abnormal growth of Goss grains in Fe-3%Si sheets, grade Hi-B. 1000 individual orientations have been measured at three levels: at the surface, at a fifth of the thickness from the surface and at the middle of the sheet. This technique allows the calculation of a true orientation distribution function (ODF), which is not possible using X-ray (or neutron) diffraction. Indeed, for X-ray diffraction, only the even part of the ODF can be determined. For the even part of the ODF, the results obtained by EBSPs are in good agreement with those obtained by X-ray diffraction and show the importance of the contribution of the odd part (about 20% of the true ODF). Then the minimal value of the orientation number is determined to assess an ODF statistic. This short study shows that it is useful to determine a minimum of 1000 measurements at each level. From these 3000 measurements, the nature of the grain boundaries is determined showing a good agreement with results obtained in the literature. In particular, it appears that the percentage of coincidence site lattice (CSL) boundaries, which is about 10%, does not depend on the sampling position. Moreover, another short study of the influence of orientation number on the nature of grain boundaries shows that a good representation is obtained if about 750 measurements are taken into account.

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Determination of the Complete Orientation Distribution Function by the Zero‐Range Method

Cited by 6 publications

References 5 publications

The iterative series-expansion method for quantitative texture analysis. I. General outline

The iterative series-expansion method for quantitative texture analysis. I. General outline

Texture gradient studies of a Cu‐tube by the robot at STRESS‐SPEC

Caractérisation de la texture de recristallisation primaire et de la spécialité des joints de grains de tôles de Fe-3%Si par diffraction des electrons rétrodiffusés

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