The dislocation densities and arrangement parameters and the crystallite size and size-distributions are determined in tensile or cyclically deformed polycrystalline copper specimens by X-ray diffraction peak profile analysis. The Fourier coefficients of profiles measured by a special high resolution X-ray diffractometer with negligible instrumental broadening have been fitted by the Fourier transforms of ab-initio size and strain profiles. It is found that in the fatigued samples the dislocations are mainly of edge type with strong dipole character. In the fatigued specimens the dislocation densities are found to be larger than in the tensile deformed samples when the saturation and flow stress levels are the same.

1.
Gil Sevillano
,
J.
, and
Aernoudt
,
E.
,
1987
, “
Low Energy Dislocation Structures in Highly Deformed Materials
,”
Mater. Sci. Eng.
,
86
, pp.
35
51
.
2.
Bay
,
B.
,
Hansen
,
N.
,
Hughes
,
D. A.
, and
Kuhlmann-Wilsdorf
,
D.
,
1992
, “
Evolution of fcc Deformation Structures in Polyslip
,”
Acta Metall. Mater.
,
40
, pp.
205
219
.
3.
Hughes
,
D. A.
, and
Nix
,
W. D.
,
1989
, “
Strain Hardening and Substructural Evolution in Ni-Co Solid Solutions at Large Strains
,”
Mater. Sci. Eng.
,
A122
, pp.
153
172
.
4.
Mughrabi
,
H.
,
1983
, “
Dislocation Wall and Cell Structures and Long Range Internal Stresses in Deformed Metal Crystals
,”
Acta Metall.
,
31
, pp.
1367
1379
.
5.
Unga´r
,
T.
,
Mughrabi
,
H.
,
Ro¨nnpagel
,
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
, pp.
333
342
.
6.
Gaa´l, I., 1984, “Effect of Dislocation Distribution on the X-Ray Scattering from Deformed Metals,” Proc. 5th Riso Int. Symp. on Metallurgy and Material Science, N. Hessel Andersen, M. Eldrup, N. Hansen, D. Juul Jensen, T. Leffers, H. Lilholt, O. B. Pedersen and B. N. Singh, eds., Riso National Lab., Roskilde, Denmark, pp. 249–254.
7.
Groma
,
I.
,
Unga´r
,
T.
, and
Wilkens
,
M.
,
1988
, “
Asymmetric X-Ray Line Broadening of Plastically Deformed Crystals. Part I: Theory
,”
J. Appl. Crystallogr.
,
21
, pp.
47
53
.
8.
Krivoglaz
,
M. A.
,
Martynenko
,
O. V.
, and
Ryaboshapka
,
K. P.
,
1983
, “
Influence of correlation in position of dislocations on X-ray diffraction by deformed crystals
,”
Phys. Met. Metallogr.
,
55
, pp.
1
12
.
9.
M. A. Krivoglaz, 1996, Theory of X-ray and Thermal Neutron Scattering by Real Crystals, Plenum Press, N.Y. 1969; and X-ray and Neutron Diffraction in Nonideal Crystals, Springer-Verlag, Berlin Heidelberg, New York.
10.
Wilkens
,
M.
, and
Bargouth
,
M. O.
,
1968
, “
Die Bestimmung der Versetzungsdichte verformter kupfer Einkristalle aus Verbreiterten Roentgenbeugungsprofilen
,”
Acta Metall.
,
16
, pp.
465
468
.
11.
Wilkens
,
M.
,
1970
, “
The Determination of Density and Distribution of Dislocations in Deformed Single Crystals from Broadened X-Ray Diffraction Profiles
,”
Phys. Status Solidi A
,
2
, pp.
359
370
.
12.
M. Wilkens, 1970, “Theoretical Aspects of Kinematical X-ray Diffraction Profiles from Crystals Containing Dislocation Distributions,” Fundamental Aspects of Dislocation Theory, J. A. Simmons, R. de Wit, R. Bullough, eds., Vol. II. Nat. Bur. Stand. (US) Spec. Publ. No. 317, Washington, DC, USA, pp. 1195–1221.
13.
Sze´kely
,
F.
,
Groma
,
I.
, and
Lendvai
,
J.
,
2001
, “
Statistic Properties of Dislocation Structures Investigated by X-ray Diffraction
,”
Mater. Sci. Eng., A
,
309
, pp.
352
355
.
14.
Groma
,
I.
,
1998
, “
X-ray Line Broadening Due to an Inhomogeneous Dislocation Distribution
,”
Phys. Rev. B
,
57
, pp.
7535
7542
.
15.
Sze´kely
,
F.
,
Groma
,
I.
, and
Lendvai
,
J.
,
2000
, “
Characterization of Self-Similar Dislocation Patterns by X-ray Diffraction
,”
Phys. Rev. B
,
62
, pp.
3093
3098
.
16.
Wilkens, M., 1988, “X-ray diffraction line broadening and crystal plasticity,” Proc. 8th Int. Conf. Strength Met. Alloys (ICSMA 8), Tampere, Finland, P. O. Kettunen, T. K. Lepisto¨, M. E. Lehtonen, eds., Pergamon Press, pp. 47–152.
17.
Williamson
,
G. K.
, and
Hall
,
W. H.
,
1953
, “
X-Ray Line Broadening from Filed Aluminum and Wolfram
,”
Acta Metall.
,
1
, pp.
22
31
.
18.
Warren
,
B. E.
, and
Averbach
,
B. L.
,
1950
, “
The Effect of Cold Work Distortions on X-ray Pattern
,”
J. Appl. Phys.
,
21
, pp.
595
610
.
19.
Loue¨r
,
D.
,
Auffredic
,
J. P.
,
Langford
,
J. I.
,
Ciosmak
,
D.
, and
Niepce
,
J. C.
,
1983
, “
A Precise Determination of the Shape, Size and Distribution of Size of Crystallites in Zinc Oxide by X-ray Line Broadening Analysis
,”
J. Appl. Crystallogr.
,
16
, pp.
183
191
.
20.
Caglioti
,
G.
,
Paoletti
,
A.
, and
Ricci
,
F. P.
,
1958
, “
Choice of Collimators for a Crystal Spectrometer for Neutron Diffraction
,”
Nucl. Instrum.
,
3
, pp.
223
228
.
21.
Schwartz, L. H., and Cohen, J. B., 1977, Diffraction from Materials, Springer-Verlag, Berlin.
22.
Klimanek
,
P.
, and
Kuzel
, 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
, pp.
59
66
.
23.
van Berkum
,
J. G. M.
,
Vermuelen
,
A. C.
,
Delhez
,
R.
,
de Keijser
,
T. H.
, and
Mittemeijer
,
E. J.
,
1994
, “
Applicabilities of the Warren-Averbach Analysis and an Alternative Analysis for Separation of Size and Strain Broadening
,”
J. Appl. Crystallogr.
,
27
, pp.
345
357
.
24.
Unga´r
,
T.
, and
Borbe´ly
,
A.
,
1996
, “
The effect of dislocation contrast on X-ray line broadening: a new approach to line profile analysis
,”
Appl. Phys. Lett.
,
69
, pp.
3173
3175
.
25.
Scardi
,
P.
, and
Leoni
,
M.
,
1999
, “
Fourier modelling of the anisotropic line broadening of X-ray diffraction profiles due to line and plane lattice defects
,”
J. Appl. Crystallogr.
,
32
, pp.
671
682
.
26.
Chatterjee
,
P.
, and
Sen Gupta
,
S. P.
,
1999
, “
Microstructural investigation of plastically deformed Pb1−xSnx alloys: an X-ray profile-fitting approach
,”
J. Appl. Crystallogr.
,
32
, pp.
1060
1068
.
27.
Cheary
,
R. W.
,
Dooryhee
,
E.
,
Lynch
,
P.
,
Armstrong
,
N.
, and
Dligatch
,
S.
,
2000
, “
X-ray diffraction line broadening from thermally deposited gold films
,”
J. Appl. Crystallogr.
,
33
, pp.
1271
1283
.
28.
Le Bail
,
A.
, and
Jouanneaux
,
A.
,
1997
, “
A Qualitative Account for Anisotropic Broadening in Whole-Powder-Diffraction-Pattern Fitting by Second-Rank Tensors
,”
J. Appl. Crystallogr.
,
30
, pp.
265
271
.
29.
Dinnebier
,
R. E.
,
Von Dreele
,
R.
,
Stephens
,
P. W.
,
Jelonek
,
S.
, and
Sieler
,
J.
,
1999
, “
Structure of sodium para-hydroxybenzoate, NaO2C−C6H4OH by powder diffraction: application of a phenomenological model of anisotropic peak width
,”
J. Appl. Crystallogr.
,
32
, pp.
761
769
.
30.
Stephens
,
P. W.
,
1999
, “
Phenomenological Model of Anisotropic Peak Broadening in Powder Diffraction
,”
J. Appl. Crystallogr.
,
32
, pp.
281
288
.
31.
Wilkens
,
M.
,
1987
, “
X-ray Line Broadening and MeanSquare Strains of Straight Dislocations in Elastically Anisotropic Crystals of Cubic Symmetry
,”
Phys. Status Solidi A
,
104
, pp.
K1–K6
K1–K6
.
32.
Unga´r
,
T.
, and
Tichy
,
G.
,
1999
, “
The Effect of Dislocation Contrast on X-ray Line Profiles in Untextured Polycrystals
,”
Phys. Status Solidi A
,
171
, pp.
425
434
.
33.
Unga´r
,
T.
,
Dragomir
,
I.
,
Re´ve´sz
,
A.
, and
Borbe´ly
,
A.
,
1999
, “
The Contrast Factors of Dislocations in Cubic Crystals: the Dislocation Model of Strain Anisotropy in Practice
,”
J. Appl. Crystallogr.
,
32
, pp.
992
1002
.
34.
Unga´r
,
T.
,
Gubicza
,
J.
,
Riba´rik
,
G.
, and
Borbe´ly
,
A.
,
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
, pp.
298
310
.
35.
Guinier, A., 1963, X-ray Diffraction, Freeman, San Francisco, CA.
36.
Gubicza
,
J.
,
Sze´pvo¨lgyi
,
J.
,
Mohai
,
I.
,
Zsoldos
,
L.
, and
Unga´r
,
T.
,
2000
, “
Particle size distribution and the dislocation density determined by high resolution X-ray diffraction in nanocrystalline silicon nitride powders
,”
Mater. Sci. Eng., A
,
280
, pp.
263
269
.
37.
Hinds, W. C. 1982, Aerosol Technology: Properties, Behavior and Measurement of Airbone Particles, Wiley, New York.
38.
Krill
,
C. E.
, and
Birringer
,
R.
,
1998
, “
Estimating Grain-Size Distribution in Nanocrystalline Materials from X-ray Diffraction Profile Analysis
,”
Philos. Mag. A
,
77
, pp.
621
640
.
39.
Unga´r
,
T.
,
Ott
,
S.
,
Sanders
,
P. G.
,
Borbe´ly
,
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
, pp.
3693
3699
.
40.
Riba´rik
,
G.
,
Unga´r
,
T.
, and
Gubicza
,
J.
,
2001
, “
MWP-fit: a Program for Multiple Whole Profile Fitting Using Theoretical Functions
,”
J. Appl. Crystallogr.
,
34
, pp.
669
676
.
41.
Groma
,
I.
, and
Mohammed
,
G.
, 2001, “Analysis of asymmetric broadening of X-ray line profiles caused by randomly distributed polarized dislocation dipoles and dislocation walls,” Acta Mater., submitted for publication.
42.
Goettler
,
E.
,
1973
, “
Versetzungstruktur und Verfestigung von 100-Kupfereinkristallen I. Versetzungsanordnung und Zellstruktur zugverformter Kristalle
,”
Philos. Mag.
,
28
, pp.
1057
1076
.
You do not currently have access to this content.