Remarks on Texture Coefficients of Polycrystals with Improper Crystallite Symmetry
Source abstract
Abstract
The orientation distribution function (ODF) in classical texture analysis is defined on the rotation group SO(3). For polycrystalline aggregates with crystallite symmetry defined by a crystallographic point group (G_{mathrm{cr}}) which is not a subgroup of SO(3), the improper group (G_{mathrm{cr}}) is routinely replaced by its proper peer (i.e., a subgroup of SO(3)) in the same Laue class. In this note we examine how the texture coefficients obtained from such a practice are related to their counterparts that pertain to the corresponding ODF defined on the orthogonal group O(3) as it should.
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Research context
OpenAlex topics: X-ray Diffraction in Crystallography · Elasticity and Material Modeling · Medical Image Segmentation Techniques
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References (27)
Show source-provided references
1. Rousseau, J.-J.: Basic Crystallography. Wiley, Chichester (1988)
2. Bunge, H.-J.: Texture Analysis in Materials Science: Mathematical Methods. Butterworths, London (1982)
3. Roe, R.-J.: Description of crystallite orientation in polycrystalline materials, III: general solution to pole figures. J. Appl. Phys. 36, 2024–2031 (1965)10.1063/1.1714396 ↗
4. Kocks, U.F., Tomé, C.N., Wenk, H.-R. (eds.): Texture and Anisotropy: Preferred Orientations in Polycrystals and Their Effects on Material Properties. Cambridge University Press, Cambridge (1998)
5. Randle, V., Engler, O.: Introduction to Texture Analysis: Macrotexture, Microtexture and Orientation Mapping. Gordon and Breach, Amsterdam (2000)10.1201/9781482287479 ↗
6. Adams, B.L., Kalidindi, S.R., Fullwood, D.T.: Microstructure-Sensitive Design for Performance Optimization. Butterworth-Heinemann, Waltham (2013)
7. Newnham, R.E.: Properties of Materials: Anisotropy, Symmetry, Structure. Oxford University Press, Oxford (2005)
8. Du, W., Man, C.-S.: Material tensors and pseudotensors of weakly-textured polycrystals with orientation distribution function defined on the orthogonal group. J. Elast. 127, 197–233 (2017)10.1007/s10659-016-9610-5 ↗
9. Du, W.: Material tensors and pseudotensors of weakly-textured polycrystals with orientation measure defined on the orthogonal group. Doctoral dissertation, University of Kentucky, Lexington (2015)10.1007/s10659-016-9610-5 ↗
10. Esling, C., Bunge, H.J., Muller, J.: Description of the texture by distribution functions on the space of orthogonal transformations. Implications on the inversion centre. J. Phys. Lett. 41, 543–545 (1980)10.1051/jphyslet:019800041022054300 ↗
11. Bunge, H.J., Esling, C., Muller, J.: The role of the inversion centre in texture analysis. J. Appl. Crystallogr. 13, 544–554 (1980)10.1107/S0021889880012757 ↗
12. Bunge, H.J., Esling, C., Muller, J.: The influence of crystal and sample symmetries on the orientation distribution function of the crystallites in polycrystalline materials. Acta Crystallogr., Sect. A 37, 889–899 (1981)10.1107/S0567739481001915 ↗
13. Biedenharn, L.C., Louck, J.D.: Angular Momentum in Quantum Physics: Theory and Application. Addison-Wesley, Reading (1981)
14. Varshalovich, D.A., Moskalev, A.N., Khersonskii, V.K.: Quantum Theory of Angular Momentum. World Scientific Publishing, Singapore (1988)10.1142/0270 ↗
15. Man, C.-S.: On the constitutive equations of some weakly-textured materials. Arch. Ration. Mech. Anal. 14, 77–103 (1998)10.1007/s002050050101 ↗
16. Lee, J.M.: Introduction to Smooth Manifolds. Springer, New York (2006)
17. Lee, J.M.: Manifolds and Differential Geometry. American Mathematical Society, Providence (2009)10.1090/gsm/107 ↗
18. Boothby, W.M.: An Introduction to Differentiable Manifolds and Riemannian Geometry. Academic, New York (1975)
19. Bauer, H.: Measure and Integration Theory. Walter de Gruyter, Berlin (2001)10.1515/9783110866209 ↗
20. Folland, G.B.: Real Analysis: Modern Techniques and Their Applications. Wiley, New York (1999)
21. Tjur, T.: Probability Based on Radon Measures. Wiley, Chichester (1980)
22. Dieudonné, J.: Foundations of Modern Analysis (Enlarged and Corrected Printing). Academic, New York (1969)
23. Conway, J.B.: A Course in Functional Analysis, 2nd edn. Springer, New York (2000)
24. Roe, R.-J.: Inversion of pole figures for materials having cubic crystal symmetry. J. Appl. Phys. 37, 2069–2072 (1966)10.1063/1.1708672 ↗
25. Knightly, A., Li, C.: Traces of Hecke Operators. American Mathematical Society, Providence (2006)10.1090/surv/133 ↗
26. Paroni, R.: Optimal bounds on texture coefficients. J. Elast. 60, 19–34 (2000)10.1023/A:1007612211180 ↗
27. Man, C.-S., Noble, L.: Designing textured polycrystals with specific isotropic material tensors: the ODF method. Rend. Semin. Mat. 58, 155–170 (2000)