Abstract
Recent work on laboratory parallel-beam diffraction is summarized. Special attention is paid to instrumental aberrations and their corrections. Two types of primary beam optics are considered: X-ray lenses and X-ray multilayer mirrors. A high photon flux, high brilliance and minimal divergence of the incident beam make a recently pioneered setup, based on a combination of a microfocus rotating anode X-ray source with a single-reflection mirror, particularly suitable for grazing-incidence diffraction, and thus for the investigation of very thin films (yielding low diffracted intensities) and of stress and the anisotropy of the microstructure of materials (such as the crystallographic texture, requiring the acquisition of large measured data sets, corresponding to the variation of the orientation of the diffraction vector with respect to the specimen frame of reference). A comparative discussion of primary optics which can be used to realize parallel-beam geometry demonstrates the range of possible applications of parallel-beam diffractometers. Such advances in laboratory parallel-beam diffraction instrumentation enable highly accurate diffraction investigations of thin films and, in particular, diffraction measurement at constant, tuneable penetration depth. These novel possibilities thereby provide a pathway for fundamental investigations of thin films and nanocrystalline materials. In particular, breakthroughs have been realized in the fields of elastic grain interaction in ultrathin films and the understanding of whisker formation on Sn coatings.
References
[1] S.Suresh, L.B.Freund: Thin Film Materials: Stress, Defect Formation and Surface Evolution, Cambridge University Press, Cambridge (2009).Search in Google Scholar
[2] C.C.Koch, I.A.Ovid'ko, S.Seal, S.Veprek: Structural nanocrystalline materials, Cambridge University Press, Cambridge, (2007).10.1017/CBO9780511618840Search in Google Scholar
[3] E.Arzt: Acta Mater.46 (1998) 5611.10.1016/S1359-6454(98)00231-6Search in Google Scholar
[4] M.A.Meyers, A.Mishra, D.J.Benson: Jom58 (2006) 41.10.1007/s11837-006-0214-6Search in Google Scholar
[5] M.A.Meyers, A.Mishra, D.J.Benson: Prog. Mater Sci.51 (2006) 427.10.1016/j.pmatsci.2005.08.003Search in Google Scholar
[6] L.Lu, M.L.Sui, K.Lu: Science287 (2000) 1463.10.1126/science.287.5457.1463; Search in Google Scholar PubMed
[7] J.J.Croat, J.F.Herbst, R.W.Lee, F.E.Pinkerton: J. Appl. Phys.55 (1984) 2078.10.1063/1.333571Search in Google Scholar
[8] B. Palosz, J. Rius, U. Welzel (Eds.): 11th European Powder Diffraction Conference, Zeitschrift für Kristallographie (Supplement) 30, (2009).Search in Google Scholar
[9] E.J.Mittemeijer, U.Welzel, R.Kuzel (Eds.): State of the Art of Powder Diffraction, Zeitschrift für Kristallographie222 [3–4], 1007.10.1524/zkri.2007.222.3-4.IIISearch in Google Scholar
[10] H. Fuess, P. Scardi, U. Welzel (Eds.): 12th European Powder Diffraction Conference (EPDIC 12); Powder Diffraction – Moving on to pastures new, Zeitschrift für Kristallographie 225 [12], 2010.10.1524/zkri.2010.0006Search in Google Scholar
[11] E.J.Mittemeijer, P.Scardi (Eds.): Diffraction Analysis of the Microstructure of Materials, Springer-Verlag, Heidelberg, New York (2004).10.1007/978-3-662-06723-9Search in Google Scholar
[12] E.J.Mittemeijer, U.Welzel: Z. Kristall.223 (2008) 552.10.1524/zkri.2008.1213Search in Google Scholar
[13] R.Delhez, A.C.Vermeulen: A practical vision on Line Profile Analysis today and in the years to come, in: B.Palosz, J.Rius, U.Welzel (Eds.), Zeitschrift für Kristallographie (Supplement), 30, (2009) 77.Search in Google Scholar
[14] U.Welzel, E.J.Mittemeijer: Powder Diffr.20 (2005) 376.10.1154/1.2138066Search in Google Scholar
[15] P.Scardi, S.Setti, M.Leoni: Multicapillary optics for materials science studies, in: R.Delhez, E.J.Mittemeijer (Eds.), European Powder Diffraction, Pts. 1 and 2, Vol. 321–3, Trans Tech Publications Ltd, Zurich-Uetikon, 2000, 162.10.4028/www.scientific.net/MSF.321-324.162Search in Google Scholar
[16] P.Debye, P.Scherrer: Physikalische Zeitschrift17 (1916) 277.Search in Google Scholar
[17] P.Debye, P.Scherrer: Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse (1916) 1.Search in Google Scholar
[18] A.W.Hull: Phys. Rev.10 (1917) 661.10.1103/PhysRev.10.661Search in Google Scholar
[19] A.W.Hull: J. Am. Chem. Soc.41 (1919) 1168.10.1021/ja02229a003Search in Google Scholar
[20] H.Seemann: Ann. Phys.59 (1919) 455.10.1002/andp.19193641305Search in Google Scholar
[21] H.Bohlin: Ann. Phys.61 (1920) 421.10.1002/andp.19203660502Search in Google Scholar
[22] J.C.M.Brentano: Arch. Sci. Phys. et Nat.44 (1917) 66.Search in Google Scholar
[23] J.C.M.Brentano: Arch. Sci. Phys. et Nat.1 (1919) 550.Search in Google Scholar
[24] J.Brentano: Nature112 (1923) 652.10.1038/112652b0Search in Google Scholar
[25] J.Brentano: Proceedings of the Physical Society of London 37 (1925) 184.10.1088/1478-7814/37/1/326Search in Google Scholar
[26] H.P.Klug, L.E.Alexander: X-ray diffraction procedures for polycrystalline and amorphous materials, Wiley (1974).Search in Google Scholar
[27] D.L.Bish, J.E.Post (Eds.): Modern Powder Diffraction, Mineralogical Society of America, Washington (1989).10.1515/9781501509018Search in Google Scholar
[28] R.Jenkins, R.L.Snyder: Introduction to X-ray powder diffractometry, Wiley (1996).10.1002/9781118520994Search in Google Scholar
[29] W.H.Bragg: Nature90 (1913) 572.10.1038/090572c0Search in Google Scholar
[30] W.H.Bragg: Nature91 (1913) 477.10.1038/091477b0Search in Google Scholar
[31] W.H.Bragg, W.L.Bragg: Proc. R. soc. Lond. Ser. A-Contain. Pap. Math. Phys. Character88 (1913) 428.Search in Google Scholar
[32] W.H.Bragg: Proceedings of the Physical Society of London 33 (1921) 222.10.1088/1478-7814/33/1/321Search in Google Scholar
[33] U.Welzel, J.Ligot, P.Lamparter, A.C.Vermeulen, E.J.Mittemeijer: J. Appl. Crystallogr.38 (2005) 1.10.1107/S0021889804029516Search in Google Scholar
[34] V.H.P.Wenk: Rep. Prog. Phys.67 (2004) 1367.10.1088/0034-4885/67/8/R02Search in Google Scholar
[35] A.C.Vermeulen: Z. Kristall.222 (2007) 204.10.1524/zkri.2007.222.3-4.204Search in Google Scholar
[36] D.E.Cox, J.B.Hastings, W.Thomlinson, C.T.Prewitt: Nucl. Instrum. Methods Phys. Res.208 (1983) 573.10.1016/0167-5087(83)91185-7Search in Google Scholar
[37] W.Parrish, M.Hart, T.C.Huang: J. Appl. Crystallogr.19 (1986) 92.10.1107/S0021889886089859Search in Google Scholar
[38] W.Parrish, M.Hart: Z. Kristall.179 (1987) 161.10.1524/zkri.1987.179.1-4.161Search in Google Scholar
[39] J.B.Hastings, W.Thomlinson, D.E.Cox: J. Appl. Crystallogr.17 (1984) 85.10.1107/S0021889884011043Search in Google Scholar
[40] P.Thompson, A.M.Glazer, A.Albinati, J.S.Worgan: J. Appl. Crystallogr.14 (1981) 315.10.1107/S002188988100945XSearch in Google Scholar
[41] W.Parrish: Aust. J. Phys.41 (1988) 101.10.1071/PH880101Search in Google Scholar
[42] M.Schuster, H.Göbel, in: J.V.Gilfrich, I.C.Noyan, R.Jenkins, T.C.Huang, R.L.Snyder, D.K.Smith, M.A.Zaitz, P.Predecki (Eds.), Advances in X-Ray Analysis, Plenum Press, 1995.Search in Google Scholar
[43] V.A.Kogan, J.Bethke: X-ray optics for materials research, in: R.Delhez, E.J.Mittemeijer (Eds.), Epdic 5, Pts. 1 and 2, Vol. 278–2, Transtec Publications Ltd, Zurich-Uetikon, 1998, 227.10.4028/www.scientific.net/MSF.278-281.227Search in Google Scholar
[44] C.A.Reiss: Comparison of optical elements for X-ray diffraction analysis in para-focusing and parallel beam geometries, in: R.Delhez, E.J.Mittemeijer (Eds.), Epdic 7: European Powder Diffraction, Pts. 1 and 2, Vol. 378–3, Trans Tech Publications Ltd, Zurich-Uetikon, 2001, 218.10.4028/www.scientific.net/MSF.378-381.218Search in Google Scholar
[45] P.B.Hirsch, J.N.Kellar: Proceedings of the Physical Society of London Section B 64 (1951) 369.10.1088/0370-1301/64/5/301Search in Google Scholar
[46] P.Gay, P.B.Hirsch, J.S.Thorp, J.N.Kellar: Proceedings of the Physical Society of London Section B 64 (1951) 374.10.1088/0370-1301/64/5/302Search in Google Scholar
[47] M.A.Kumakhov, F.F.Komarov: Phys. Rep.-Rev. Sec. Phys. Lett.191 (1990) 289.Search in Google Scholar
[48] M.A.Kumakhov: X-Ray Spectrom.29 (2000) 343.10.1002/1097-4539(200009/10)29:5<343::AID-XRS414>3.0.CO;2-SSearch in Google Scholar
[49] M.Leoni, U.Welzel, P.Scardi: J. Res. Natl. Inst. Stand. Technol.109 (2004) 27.Search in Google Scholar
[50] X.Jindong, H.Yejun, D.Xunliang, P.Qiuili, Y.Yiming: J. Anal. At. Spectrom.14 (1999) 391.10.1039/a806836dSearch in Google Scholar
[51] T.Sun, X.Ding: J. Appl. Phys.97 (2005) 124904.10.1063/1.1935134Search in Google Scholar
[52] U.Welzel, M.Leoni: J. Appl. Crystallogr.35 (2002) 196.10.1107/S0021889802000481Search in Google Scholar
[53] W.J.Bartels: J. Vac. Sci. Technol. B1 (1983) 338.10.1116/1.582553Search in Google Scholar
[54] T.Johansson: Naturwissenschaften20 (1932) 758.10.1007/BF01493394Search in Google Scholar
[55] T.W.Barbee: Opt. Eng.25 (1986) 898.Search in Google Scholar
[56] U.W.Arndt: J. Appl. Crystallogr.23 (1990) 161. PMid:18883922;10.1107/S0021889890000334Search in Google Scholar
[57] P.Kirkpatrick, A.V.Baez: J. Opt. Soc. Am.38 (1948) 766.10.1364/JOSA.38.000766Search in Google Scholar PubMed
[58] J.W.M.DuMond, J.P.Youtz: Phys. Rev.48 (1935) 703.10.1103/PhysRev.48.703Search in Google Scholar
[59] J.DuMond, J.P.Youtz: J. Appl. Phys.11 (1940) 357.10.1063/1.1712784Search in Google Scholar
[60] M.Schuster, H.Göbel: J. Phys. D: Appl. Phys.28 (1995) A270.10.1088/0022-3727/28/4A/053Search in Google Scholar
[61] L.C.Jiang, Z.Al-Mosheky, N.Grupido: Powder Diffr.17 (2002) 81.10.1154/1.1482366Search in Google Scholar
[62] M.Wohlschlogel, T.U.Schulli, B.Lantz, U.Welzel: J. Appl. Crystallogr.41 (2008) 124.10.1107/S0021889807050005Search in Google Scholar
[63] M.Montel: Opt. Acta1 (1954) 117.10.1080/713818679Search in Google Scholar
[64] E.Eiper, K.J.Martinschitz, J.W.Gerlach, J.M.Lackner, I.Zizak, N.Darowski, J.Keckes: Z. Metallkd.96 (2005) 1069.Search in Google Scholar
[65] M.Galli, J.Botsis, J.Janczak-Rusch, G.Maier, U.Welzel: J. Eng. Mater. Technol.-Trans. ASME131 (2009) 021004.Search in Google Scholar
[66] A.C.Vermeulen: The sensitivity of focusing, parallel beam and mixed optics to alignment errors in XRD residual stress measurements, in: S. Denis, T. Hanabusa, B.P. He, E. Mittemeijer, J. Nan, I.C. Noyan, B. Scholtes, K. Tanaka, K.W. Xu (Ed (Eds.), Residual Stresses Vii, Proceedings, Vol. 490-491, Trans Tech Publications Ltd, Zurich-Uetikon, 2005, 131.10.4028/0-87849-969-5.131Search in Google Scholar
[67] Y.Kuru, M.Wohlschlogel, U.Welzel, E.J.Mittemeijer: Appl. Phys. Lett.90 (2007) 243113.10.1063/1.2748332Search in Google Scholar
[68] Y.Kuru, M.Wohlschlögel, U.Welzel, E.J.Mittemeijer: Thin Solid Films516 (2008) 7615.10.1016/j.tsf.2008.05.011Search in Google Scholar
[69] Y.Kuru, M.Wohlschlogel, U.Welzel, E.J.Mittemeijer: Appl. Phys. Lett.95 (2009) 163112.Search in Google Scholar
[70] J.Sheng, U.Welzel, E.J.Mittemeijer: Appl. Phys. Lett.97 (2010).10.1063/1.3500827Search in Google Scholar
[71] Y.H.Zhao, U.Welzel, J.van Lier, E.J.Mittemeijer: Thin Solid Films514 (2006) 110.10.1016/j.tsf.2006.02.076Search in Google Scholar
[72] J.Chakraborty, U.Welzel, E.J.Mittemeijer: J. Appl. Phys.103 (2008) 113512.10.1063/1.2938079Search in Google Scholar
[73] M.Wohlschlögel, W.Baumann, U.Welzel, E.J.Mittemeijer: J. Appl. Crystallogr.41 (2008) 1067.10.1107/S0021889808031026Search in Google Scholar
[74] M.Wohlschlögel, U.Welzel, E.J.Mittemeijer: J. Mater. Res.24 (2009) 1342.10.1557/jmr.2009.0153Search in Google Scholar
[75] R.Resel, E.Tamas, B.Sonderegger, P.Hofbauer, J.Keckes: J. Appl. Crystallogr.36 (2003) 80.10.1107/S0021889802019568Search in Google Scholar
[76] M.Wohlschlögel, U.Welzel, G.Maier, E.J.Mittemeijer: J. Appl. Crystallogr.39 (2006) 194.10.1107/S0021889806000513Search in Google Scholar
[77] M.Ortolani, C.L.A.Ricardo, P.Scardi: J. Appl. Crystallogr.42 (2009) 1102.10.1107/S0021889809035857Search in Google Scholar
[78] R.Delhez, T.H.de Keijser, E.J.Mittemeijer: Surface Engineering3 (1987) 331.Search in Google Scholar
[79] A.Kumar, U.Welzel, E.J.Mittemeijer: J. Appl. Crystallogr.39 (2006) 633.10.1107/S0021889806023417Search in Google Scholar
[80] H.Behnken, V.Hauk: Materials Science & Engineering, A: Structural Materials: Properties, Microstructure and Processing300 (2000) 41.10.1016/S0921-5093(00)01791-3Search in Google Scholar
[81] U.Welzel, E.J.Mittemeijer: Jom59 (2007) 66.10.1007/s11837-007-0121-5Search in Google Scholar
[82] J.Stickforth: Technische Mitteilungen Krupp, Forschungs-Berichte24 (1966) 89.Search in Google Scholar
[83] N.H.-J.Hauk, H.Weisshaupt: Z. Metallkd.76 (1985) 226.Search in Google Scholar
[84] V.Hauk (Ed.): Structural and Residual Stress Analysis by Nondestructive Methods, Elsevier, Amsterdam (1997).Search in Google Scholar
[85] U.Welzel, M.Leoni, E.J.Mittemeijer: Phil. Mag.83 (2003) 603.10.1080/0141861021000042299Search in Google Scholar
[86] U.Welzel, A.Kumar, E.J.Mittemeijer: Appl. Phys. Lett.95 (2009) 111907.Search in Google Scholar
[87] W.Voigt: Lehrbuch der Kristallphysik, Teubner, Leipzig (1910).Search in Google Scholar
[88] A.Reuss: Zeitschrift für angewandte Mathematik und Mechanik9 (1929) 49.10.1002/zamm.19290090104Search in Google Scholar
[89] R.Hill: Proceedings of the Physical Society of London, Section A 65 (1952) 349.10.1088/0370-1298/65/5/307Search in Google Scholar
[90] U.Welzel, E.J.Mittemeijer: J. Appl. Phys.93 (2003) 9001.10.1063/1.1569662Search in Google Scholar
[91] U.Welzel, S.Freour: Phil. Mag.87 (2007) 3921.10.1080/14786430701203176Search in Google Scholar
[92] R.W.Vook: J. Appl. Phys.36 (1965) 2169.10.1063/1.1714442Search in Google Scholar
[93] F.Witt, R.W.Vook: J. Appl. Phys.39 (1968) 2773.10.1063/1.1656671Search in Google Scholar
[94] Official Journal of the European Union Vol. 46, L37, p. 20, 2003.Search in Google Scholar
[95] G.T.Galyon, L.Palmer: IEEE Trans. Electron. Packag. Manuf.28 (2005) 17.10.1109/TEPM.2005.847443Search in Google Scholar
[96] G.T.Galyon: IEEE Trans. Electron. Packag. Manuf.28 (2005) 94.10.1109/TEPM.2005.847440Search in Google Scholar
[97] W.J.Boettinger, C.E.Johnson, L.A.Bendersky, K.-W.Moon, M.E.Williams, G.R.Stafford: Acta Mater.53 (2005) 5033.10.1016/j.actamat.2005.07.016Search in Google Scholar
[98] K.N.Tu, C.Chen, A.T.Wu: J. Mater. Sci. – Mater. Electron18 (2007) 269.10.1007/s10854-006-9029-zSearch in Google Scholar
[99] http://nepp.nasa.gov/whisker/index.html.Search in Google Scholar
[100] K.N.Tu: Phys. Rev. B: Condens. Matter49 (1994) 2030.10.1103/PhysRevB.49.2030Search in Google Scholar
[101] B.Z.Lee, D.N.Lee: Acta Mater.46 (1998) 3701.10.1016/S1359-6454(98)00045-7Search in Google Scholar
[102] G.T.Galyon, C.Xu, S.Lal, B.Notohardjono, L.Palmer: The integrated theory of whisker formation – A stress analysis, 55th Electronic Components & Technology Conference, Vols. 1 and 2, 2005 Proceedings, IEEE, New York, 2005, p. 421.Search in Google Scholar
[103] M.Sobiech, U.Welzel, R.Schuster, E.J.Mittemeijer, W.Hügel, A.Seekamp, V.Muller: The microstructure and state of stress of sn thin films after post-plating annealing: An explanation for the suppression of whisker formation?, 57th Electronic Components &Technology Conference, 2007 Proceedings, IEEE, New York, 2007, 192.10.1109/ECTC.2007.373797Search in Google Scholar
[104] M.Sobiech, U.Welzel, E.J.Mittemeijer, W.Hügel, A.Seekamp: Appl. Phys. Lett.93 (2008) 011906.10.1063/1.2953973Search in Google Scholar
[105] M.Sobiech, M.Wohlschlögel, U.Welzel, E.J.Mittemeijer, W.Hügel, A.Seekamp, W.Liu, G.E.Ice: Appl. Phys. Lett.94 (2009) 221901.10.1063/1.3147864Search in Google Scholar
[106] M.Sobiech, J.Teufel, U.Welzel, E.J.Mittemeijer, W.Hügel: submitted (2011).Search in Google Scholar
© 2011, Carl Hanser Verlag, München
