An analytic and generalized formulation of the sin2 ψ-method
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Balder Ortner
Abstract
X-ray stress measurements can be done without the accurate knowledge of the unstressed lattice parameters, if the specimen’s surface can be assumed as stress-free and provided that the measured strains depend linearly on sin2 ψ. This is usually done in the so-called sin2 ψ method. An analytical formalism is proposed with which the same task can be performed even if the linear sin2 ψ dependence is not given. Therefore, one is completely free in choosing and combining measurement parameters φ;ψ, and (hkl). It can be used for single-crystalline, textured, texture-free, isotropic or anisotropic materials. Further advantages are an easy way for correct error calculus and a means to optimize the whole procedure for minimum errors in φ.
References
[1] B. Ortner: Adv. X-Ray Analysis 29 (1986) 113.10.1154/S0376030800010181Search in Google Scholar
[2] H. Dölle: J. Appl. Cryst. 12 (1979) 489.10.1107/S0021889879013169Search in Google Scholar
[3] M. Barral, J.L. Lebrun, J.M. Sprauel, G. Maeder: Met. Trans. A 18 (1987) 1229.10.1007/BF02647192Search in Google Scholar
[4] P. Van Houtte, L. De Buyser: Acta Metall. Mater. 41 (1993) 323.10.1016/0956-7151(93)90063-XSearch in Google Scholar
[5] V. Hauk: Structure and residual stress analysis by nondestructive methods, Elsevier, Amsterdam 1997.Search in Google Scholar
[6] U. Welzel, J. Ligot, P. Lamparter, A.C. Vermeulen, E.J. Mittemeijer: J. Appl. Cryst. 38 (2005) 1.10.1107/S0021889804029516Search in Google Scholar
[7] R.A. Winholz, J.B. Cohen: Aust. J. Phys. 41 (1988) 189.10.1071/PH880189Search in Google Scholar
[8] G. Gisen, R. Glocker, E. Oswald: Z. Techn. Physik 17 (1936) 145.Search in Google Scholar
[9] G.A. Hawkes: Brit. J. Appl. Phys. 8 (1957) 229.10.1088/0508-3443/8/6/302Search in Google Scholar
[10] E. Macherauch, P. Müller: Z. Angew. Physik 13 (1961) 305.Search in Google Scholar
[11] B.D. Cullity: Elements of X-Ray Diffraction, Addison Wesley (1978).Search in Google Scholar
[12] I.C. Noyan, J.B. Cohen: Residual Stress, Springer New York, Berlin, Heidelberg, London, Paris, Tokyo (1987).10.1007/978-1-4613-9570-6Search in Google Scholar
[13] V. Hauk, R.W.M. Ondelhoven, G.H.J. Vaessen: Met. Trans. A 13 (1982) 1239.10.1007/BF02645507Search in Google Scholar
[14] J.F. Nye: Physical Properties of Crystals, Oxford Univ. Press (1957).Search in Google Scholar
[15] B. Ortner: Adv. X-Ray Analysis 29 (1986) 387.10.1154/S0376030800010491Search in Google Scholar
[16] J. Keckéš: J. Appl. Cryst. 38 (2005) 311.10.1107/S0021889805001044Search in Google Scholar
[17] A. Ben-Israel, T.N.E. Greville: Generalized Inverses: Theory and applications, Krieger, Huntington (1980).10.1007/978-3-642-46414-0_8Search in Google Scholar
[18] H. Behnken, in: [5].Search in Google Scholar
[19] S. Haussühl: Kristallphysik, Physik Verlag, Weinheim 1983.Search in Google Scholar
[20] B. Ortner: to be published.Search in Google Scholar
[21] H. Dölle, V. Hauk: Z. Metallkd. 69 (1978) 410.10.1515/ijmr-1978-690609Search in Google Scholar
© 2005 Carl Hanser Verlag, München
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- Kösterpreis
- Award/Preisverleihung
- Editorial
- Editorial
- Articles Basic
- Effect of interface strength on electromigration-induced inlaid copper interconnect degradation: Experiment and simulation
- Application of factor analysis in electron spectrometry (AES, XPS) for materials science
- Focussing and defocussing effects at radio frequency glow discharge optical emission spectroscopy analyses of thin films with partly nonconductive components
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- Microstructure and phase formation of Heusler thin film compounds
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