Dislocation model of strain anisotropy

Powder Diffraction

Volumn 23, Issue 2, 2008, Pages 125-132

  Ungár, Tamás ^a  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

Author keywords

Contrast factors; Dislocations; Strain anisotropy

Indexed keywords

BURGERS VECTOR POPULATIONS; CONTRAST FACTOR; DISLOCATION CONTRASTS; DISLOCATION MODELING; EFFECT OF STRAIN; LINE PROFILE ANALYSIS; SLIP ACTIVITY; STRAIN ANISOTROPIES;

DISLOCATIONS (CRYSTALS);

ANISOTROPY;

EID: 44649102153     PISSN: 08857156     EISSN: 19457413     Source Type: Journal    
DOI: 10.1154/1.2918549     Document Type: Article

References (65)

1. Aqua, E. N. and Wagner, C. N. J. (1966). " X-ray diffraction study of deformation of Nb-Re alloys.," Trans. Metall. Soc. AIME 236, 1085-1089.
2. Balogh, L., Ribárik, G., and Ungár, T. (2006). " Stacking faults and twin boundaries in fcc crystals determined by x-ray diffraction profile analysis.," J. Appl. Phys. 100, 023512.
3. Becker, K. (1927). " Der röntgenographische Nachweis von Kornwachstum und Vergütung in Wolframdraeten mittels des Debye-Scherrer-Verfahrens.," Z. Phys. 42, 226-245.
4. Borb́ly, A., Dragomir-Cernatescu, J., Ribárik, G., and Ungár, T. (2003). " Computer program ANIZC for the calculation of diffraction contrast factors of dislocations in elastically anisotropic cubic, hexagonal and trigonal crystals.," J. Appl. Crystallogr. 36, 160-162.
5. Brindley, G. W. (1940). " Lattice distortion in cold-worked metals.," Proc. Phys. Soc. 52, 117-126.
6. Caglioti, G., Paoletti, A., and Ricci, F. P. (1958). " Choice of collimators for a crystal spectrometer for neutron diffraction.," Nucl. Instrum. 3, 223-228.
7. Cordier, P., Ungár, T., Zsoldos, L., and Tichy, G. (2004). " Dislocations creep in MgSiO3 perovskite at conditions of the earth's uppermost lower mantle.," Nature (London) 428, 837-840.
8. Dehlinger, U. and Kochendoerfer, A. (1939). " Roentgenographische Messung der Teilchengroesse und der verborgen elastischen Spannungen in kaltverformten Blechen.," Z. Metallkd. 31, 231-234.
9. Dehlinger, U. and Schäcke, H. (1943). " Messung der reflektierten Röntgenintensität in Abhängigkeit vom Grad der plastischen Verformung bei Metallen.," Naturwiss. 31, 548-548.
10. Dragomir, I. C. and Ungár, T. (2002). " The contrast factors of dislocations in the hexagonal crystal system.," J. Appl. Crystallogr. 35, 556-564.
11. Eastabrook, J. N. and Wilson, A. J. C. (1952). " The diffraction of x-rays by distorted-crystal aggregates. III. Remarks on the interpretation of the Fourier coefficients.," Proc. Phys. Soc. London, Sect. B 65, 67-75.
12. Fischer, J. E., Bendele, G., Dinnebier, R., Stephens, P. W., Lin, C. L., Bykovetz, N., and Zhu, Q. (1995). " Structural analysis of fullerene and fulleride solids from synchrotron x-ray diffraction.," J. Phys. Chem. Solids 56, 1445-1457.
13. Gaál, I. (1984). " Effect of dislocation distribution on the X-ray scattering from deformed metals.," in Proceedings of the 5th Riso International Symposium on Metallurgy and Material Science, edited by, N. Hessel Andersen, M. Eldrup, N. Hansen, D. Juul Jensen, T. Leffers, H. Lilholt, O. B. Pedersen, and, B. N. Singh, (Riso National Lab., Roskilde, Denmark), pp. 249-254.
14. Gillies, D. C. and Lewis, D. (1968). " Lattice strain in tungsten carbide.," Powder Metall. 11, 400-410.
15. Hall, W. H. (1949). " X-ray line broadening in metals.," Proc. Phys. Soc., London, Sect. A 62, 741-743.
16. Jaswon, M. A. and Wheeler, J. A. (1948). " Atomic displacements in the austenite-martensite transformation.," Acta Crystallogr. 1, 216-224.
17. Jones, F. W. and Sykes, C. (1937). " The superlattice in Β brass.," Proc. R. Soc. London, Ser. A 161, 440-446.
18. Klimanek, P. and Kužel, Jr., R. (1988). " X-ray diffraction line broadening due to dislocations in non-cubic materials. I. General considerations and the case of elastic isotropy applied to hexagonal crystals.," J. Appl. Crystallogr. 21, 59-66.
19. Kocks, U. F. and Scattergood, R. O. (1969). " Elastic interactions between dislocations in a finite body.," Acta Metall. 17, 1161-1170.
20. Kostorz, G. (1996). Physical Metallurgy, edited by, R. W. Cahn, and, P. Haasen, (North-Holland, Amsterdam), pp. 1115-1199.
21. Krivoglaz, M. A. (1969). X-ray and Neutron Diffraction in Nonideal Crystals (Plenum, New York).
22. Krivoglaz, M. A. (1996). Theory of X-ray and Thermal Neutron Scattering by Real Crystals (Springer-Verlag, Berlin).
23. Kuhn, H.-A., Biermann, H., Ungár, T., and Mughrabi, H. (1991). " An x-ray study of creep-deformation induced changes of the lattice mismatch in the γ′ hardened monocrystalline Ni -base superalloy SRR 99.," Acta Metall. Mater. 39, 2783-2794.
24. Kužel, Jr., R. and Klimanek, P. (1988). " X-ray diffraction line broadening due to dislocations in non-cubic materials. II. The case of elastic anisotropy applied to hexagonal crystals.," J. Appl. Crystallogr. 21, 363-368.
25. Kužel, Jr., R. and Klimanek, P. (1989). " X-ray diffraction line broadening due to dislocations in non-cubic crystalline materials. III. Experimental results for plastically deformed zirconium.," J. Appl. Crystallogr. 22, 299-307.
26. Kužel, R., Matěj, Z., Cherkaska, V., Pešička, J., Čižek, J., Procházka, I., and Islamgaliev, R. K. (2004). " Structural investigations of submicrocrystalline metals obtained by high-pressure torsion deformation.," J. Alloys Compd. 378, 242-247.
27. Lahrman, D., Field, R., Darolia, R., and Fraser, H. (1988). " Investigation of techniques for measuring lattice mismatch in a rhenium containing nickel base superalloy.," Acta Metall. 36, 1309-1317.
28. Leineweber, A. and Mittemeijer, E. J. (2006). " Anisotropic microstrain broadening due to compositional inhomogeneities and its parametrisation.," Z. Kristallogr. 2006, 117-122.
29. Martinetto, P., Anne, M., Dooryh́e, E., Drakopoulos, M., Dubus, M., Salomon, J., Simionovici, A., and Walter, Ph. (2001). " Synchrotron x-ray micro-beam studies of ancient egyptian make-up.," Nucl. Instrum. Methods Phys. Res. B 181, 744-748.
30. Mughrabi, H., Ungár, T., Kienle, W., and Wilkens, M. (1986). " Long-range internal stresses and asymmetric x-ray line-broadening in tensile-deformed [001]-oriented copper single crystals.," Philos. Mag. A 53, 793-813.
31. Nabarro, F. R. N. (1952). " The mathematical theory of dislocations.," Adv. Phys. 1, 269-395.
32. Noyan, I. C. and Cohen, J. B. (1987). Residual Stress: Measurement by Diffraction and Interpretation (Springer-Verlag, New York).
33. Nye, J. F. (1957). Physical Properties of Crystals: Their Representation by Tensors and Matrices (Clarendon Press, Oxford).
34. Ribárik, G., Ungár, T., and Gubicza, J. (2001). " MWP-fit: A program for multiple whole-profile fitting of diffraction peak profiles by ab initio theoretical functions.," J. Appl. Crystallogr. 34, 669-676.
35. Ribárik, G., Gubicza, J., and Ungár, T. (2004). " Correlation between strength and microstructure of ball-milled Al-Mg alloys determined by x-ray diffraction.," Mater. Sci. Eng., A 387-389, 343-347.
36. Scardi, P. and Leoni, M. (2002). " Whole powder pattern modelling.," Acta Crystallogr., Sect. A: Found. Crystallogr. 58, 190-200.
37. Scardi, P., Dong, Y., and Leoni, M. (2001). " Line profile analysis in the Rietveld method and whole-powder-pattern fitting.," Mater. Sci. Forum 378-381, 132-141.
38. Scardi, P., Leoni, M., and Delhez, R. (2004). " Line broadening analysis using integral breadth methods: A critical review.," J. Appl. Crystallogr. 37, 381-390.
39. Schonfeld, B., Reinhard, L., Kostorz, G., and Bohrer, W. (1997). " Diffuse scattering of Ni-Al.," Acta Mater. 45, 5187-5194.
40. Shen, T. D., Schwarz, R. B., and Thompson, J. D. (2005). " Soft magnetism in mechanically alloyed nanocrystalline materials.," Phys. Rev. B 72, 14431-14438.
41. Stokes, A. R. (1948). " A numerical Fourier-analysis method for the correction of widths and shapes of lines on x-ray powder photographs.," Proc. Phys. Soc. 61, 382-391.
42. Stokes, A. R. and Wilson, A. J. C. (1942). " A method of calculating the integral breadths of Debye-Scherrer lines.," Proc. Cambridge Philos. Soc. 38, 313-322.
43. Stokes, A. R. and Wilson, A. J. C. (1944). " The diffraction of x-rays by distorted crystal aggregates-I.," Proc. Phys. Soc. 56, 174-181.
44. Stokes, A. R., Pascoe, K. J., and Lipson, H. (1943). " X-ray evidence of the nature of cold work in metals.," Nature (London) 151, 137-137.
45. Treacy, M. M. J., Newsam, J. M., and Deem, M. W. (1991). " A general recursion method for calculating diffracted intensities from crystals containing planar faults.," Proc. R. Soc. London, Ser. A 433, 499-520.
46. Ungár, T. and Borb́ly, A. (1996). " The effect of dislocation contrast on x-ray line broadening: A new approach to line profile analysis.," Appl. Phys. Lett. 69, 3173-3175.
47. Ungár, T. and Tichy, G. (1999). " The effect of dislocation contrast on x-ray line profiles in untextured polycrystals.," Phys. Status Solidi A 171, 425-434.
48. Ungár, T., Mughrabi, H., Rönnpagel, D., and Wilkens, M. (1984). " X-ray line broadening study of the dislocation cell structure in deformed [001]-oriented copper single crystals.," Acta Metall. 32, 333-342.
49. Ungár, T., Ott, S., Sanders, P. G., Borb́ly, A., and Weertman, J. R. (1998). " Dislocations, grain size and planar faults in nanostructured copper determined by high resolution x-ray Diffraction and a new procedure of peak profile analysis.," Acta Mater. 46, 3693-3699.
50. Ungár, T., Dragomir, I., Ŕv́sz,., and Borb́ly, A. (1999a). " The contrast factors of dislocations in cubic crystals: the dislocation model of strain anisotropy in practice.," J. Appl. Crystallogr. 32, 992-1002.
51. Ungár, T., Leoni, M., and Scardi, P. (1999b). " The dislocation model of strain anisotropy in whole powder-pattern fitting: the case of an Li-Mn cubic spinel.," J. Appl. Crystallogr. 32, 290-295.
52. Ungár, T., Gubicza, J., Borb́ly, A., and Ribárik, G. (2001). " Crystallite size distribution and dislocation structure determined by diffraction profile analysis: principles and practical application to cubic and hexagonal crystals.," J. Appl. Crystallogr. 34, 298-310.
53. Ungár, T., Martinetto, P., Ribárik, G., Dooryh́e, E., Walter, Ph., and Anne, M. (2002). " Revealing the powdering methods of black makeup in ancient Egypt by fitting microstructure based Fourier coefficients to whole x-ray diffraction profiles of galena.," J. Appl. Phys. 91, 2455-2465.
54. Ungár, T., Nyilas, K., and Skrotzki, W. (2008). " Dislocation densities in soft and hard oriented grains of compressed NiAl polycrystals.," Int. J. Mater. Sci. 3, (in press).
55. Ustinov, A. I., Olikhovska, L. O., Budarina, N. M., and Bernard, F. (2004). Diffraction Analysis of the Microstructure of Materials, edited by, E. J. Mittemeijer, and, P. Scardi, (Springer-Verlag, Berlin), pp. 309-362.
56. Warren, B. E. (1959). " X-ray studies of deformed metals.," Prog. Met. Phys. 8, 147-202.
57. Warren, B. E. and Averbach, B. L. (1950). " The effect of cold work distortion on x-ray patterns.," J. Appl. Phys. 21, 595-598.
58. Wilkens, M. (1969). " Das Mittlere Spannungsquadrat 〈 2 〉 Begrenzt Regellos Verteilter Versetzungen in Einem Zylinderfoermigen Koerper.," Acta Metall. 17, 1155-1159.
59. Wilkens, M. (1970a). " The determination of density and distribution of dislocations in deformed single crystals from broadened x-ray diffraction profiles.," Phys. Status Solidi A 2, 359-370.
60. Wilkens, M. (1970b). Fundamental Aspects of Dislocation Theory (National Bureau of Standards Special Publication, No. 317), edited by, J. A. Simmons, R. de Wit, and, R. Bullough, (National Bureau of Standards, Washington), Vol. II., pp. 1195-1221.
61. Wilkens, M. (1987). " X-ray line broadening and mean-square-strains of straight dislocations in elastically anisotropic crystals of cubic symmetry.," Phys. Status Solidi A 104, K1-K6.
62. Williamson, G. K. and Hall, W. H. (1953). " X-ray line broadening from filed aluminium and wolfram.," Acta Metall. 1, 22-31.
63. Wilson, A. J. C. (1949). " The diffraction of x-rays by distorted-crystal aggregates. II. Diffraction by bent lamellae.," Acta Crystallogr. 2, 220-222.
64. Wilson, A. J. C. (1952). " The diffraction of x-rays by distorted-crystal aggregates. IV. Diffraction by a crystal with an axial screw dislocation.," Acta Crystallogr. 5, 318-322.
65. Wollan, E. O. and Shull, C. G. (1948). " The diffraction of neutrons by crystalline powders.," Phys. Rev. 73, 830-841.