ISSN 0031-918X, The Physics of Metals and Metallography, 2013, Vol. 114, No. 12, pp. 1069–1073. © Pleiades Publishing, Ltd., 2013.
1069
1
1. INTRODUCTION
Hossein Nedjad et al. [1] reported preferred storage
of screw dislocations in the equal-channel angular
pressed 18Ni maraging steel recently. This report was in
agreement with the storage of screw dislocations in hot-
deformed germanium and silicon crystals reported by
Siethoff and Schroeter [2] but in contrary to the pre-
ferred storage of edge dislocations observed in severely-
deformed commercially-pure copper and some alumi-
num alloys [3–7]. The preferred storage of screw dislo-
cations in the 18Ni maraging steel was interpreted in
terms of the difficulties for cross slipping of screw dislo-
cations augmented by reduced stacking faults energies
and short range ordering due to the higher amounts of
alloying additions such as cobalt. However, the possible
role of the body-centered cubic (BCC) crystal symme-
try remained controversial. It is noteworthy that those
alloys that exhibit preferred edge dislocations invariably
possess the face-centered cubic (FCC) crystal symme-
try. Taking into account the effect of crystal symmetry
on the preferred storage of dislocations, this paper was
aimed at studying the relative fraction of stored edge
and screw dislocations in the commercially pure copper
and iron chips, which were severely-deformed by a
high-energy planetary ball milling.
Precision analysis of the integral breadths of X-ray
diffraction peak profiles in accordance with the Will-
iamson–Hall equations makes possible the determi-
nation of the specific features of the dislocation struc-
ture in severely-deformed metals. In the classical Wil-
1
The article is published in the original.
liamson–Hall equation (Eq. 1), the integral breadths
of the diffraction lines are plotted versus the diffrac-
tion vector K. In the case of isotropic strain distribu-
tion, those integral breadths fit well into a linear
regression so that the intersection with vertical axis
and the slope determine apparent size parameter and
lattice distortions, respectively [8].
(1)
where β is the integral breadth of an individual diffrac-
tion line, d is the apparent size parameter, and ε is the
lattice distortions. However, solids are often elastically
anisotropic and, therefore, lattice distortions are usu-
ally distributed anisotropically. Similarly, dislocations
stored in the deformed metals cause anisotropic lattice
distortions which, consequently, leads to non-mono-
tonic increasing of the integral breadths of the diffrac-
tion lines corresponding to the elastically soft direc-
tions which, subsequently, makes the linear regression
difficult and the classical equation inefficient. Alter-
natively, the strain anisotropy is compensated in the
modified Williamson–Hall equation by taking into
account the average dislocation contrast factor ( ) as
given in Eq. 2 [9].
(2)
where ρ is the dislocation density, T is a constant
depending on the density and effective outer cut-off
radius of dislocations, b is the modulus of the Burgers
vector of dislocations, and O is an unknown overall
β 1 / d 2 ε K, + =
c
β 1 / d
π T
2
b
2
( )
2
--------------- ρ
1 / 2
Kc
1 / 2
( )
2
O Kc
1 / 2
( )
4
, + + =
A Comparison Between the Dislocation Structure
of Ball-Milled Iron and Copper as Derived
from the X-Ray Diffraction Peak Profile Analyses
1
F. Hosseini Nasab, S. Hossein Nedjad, and S. Karimi
Faculty of Materials Engineering, Sahand University of Technology, P. O. Box 51335-1996, Tabriz, Iran
e-mail: hossein@sut.ac.ir
Received August 13, 2013
Abstract—X-ray diffraction line profile analyses were used for determination of the dislocation structure of
ball-milled copper and iron samples. Plots of integral breadths of the diffraction line profiles in accordance
with the classical Williamson–Hall equation clarified stronger strain anisotropy in iron than copper. By the
analyses of the integral breadths in accordance with the modified Williamson–Hall equation, the relative
fractions of edge and screw dislocations were determined. Prevailing dislocation structure of copper had edge
character while those of iron showed mainly screw character.
Keywords: X-ray diffraction, dislocation structure, ball-mill, Williamson–Hall, strain anisotropy
DOI: 10.1134/S0031918X13220031
STRUCTURE, PHASE TRANSFORMATIONS,
AND DIFFUSION