Dislocation Density Determination in Polycrystalline Copper by Neutron Diffraction Extinction Measurements.
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DISLOCATION DENSITY DETERMINATION IN POLYCRYSTALLINE NEUTRON DIFFRACTION EXTI NCTI ON MEASUREMENTS.
J. PALACIOS GOMEZ.
y MatemAticas Instituto Escuela Superior de Fisica Nacional. Apdo. Postal 75-544, 07300 Mexico D.F.
COPPER
BY
Polit~cnico
ABSTRACT: C200:, Cli1) AND C311 neutron diffraction peaks were measured on polycrystalline Cu samples with varying degrees of deformation by compression: O. 0.8%. 1.2%,, i. 5% and 2%. The first two reflections were measured with wavelength 2.358 A and the third one with wavelength i.55A. Integrated intensities vary more less monotonically and they tend to reach the kinematical value. This limit was estimated by extrapolation and used to evaluate extinction. To obtain dislocation densities a simple model was proposed which divides the crystal in regions of perfect periodicity and regions perturbed by dislocations, and evaluates the integrated intensity from perfect regions by the general theory of X-Ray diffraction of Zachariasen C19567. 7 Dislocation densities result between 1.2xiO cm 2 for the 2 sample without deformation, and approximately 5. OxiO? cmfor the 2%. deformed sample. These results are in the expected range.
I NTRODUCTI ON It is well known that measurements of diffraction on anealed polycrystals exhibit extinction. It is therefore expected that from extinction measurements dislocation densities could be determined. In fact. determintion of dislocatiorn density from X-ray diffraction measurements have been reported by Ivanov et al. [11. The present work intends to present a neutron diffraction treatment. The principles of the proposed method have already been published [21. but for the sake of completeness, the principal points of this theory are repeated here. It is assumed here that the diffracting volume consists of distorted domains around dislocation lines, whose contribution to the Bragg-reflection is well described by the kinematic theory, and domains of perfect periodicity. whose contribution should be calculated by means of the dynamical theory. It is also assumed that diffracted rays from individual domains are incoherent. For the sake of simplicity, the ideal domains are considered as spheres with mean diameter d. Their contribution to the integrated intensity is calculated from the general theory of X-Ray diffraction proposed by Zachariasen (3], with corresponding structure factor and constants for neutrons.
Mat. Res. Soc. Symp. Proc. Vol. 209. 01991 Materials Research Society
360
THE EXTINCTION FACTOR: the
According to the observed integrated I
where intensities
ik
and i per
assumptions mentioned intensity I as
= ikVk + i dCV
are unit
domain volume and kinematic diffraction
V
the theory
where
NCX)
is
the
total 14],
we
consider
Vk),
Cl)
the kinematic volume respectively,
i
wavelength
-
above,
and
dynamic Vk the
diffracted distorted
irradiated volume. for a powder sample
From
the
= N C:)Qe.
C_)
monochromatic
incoming
intensity
with
K and 5
ZX -
IFwC1r) F 1
2
C 3)
4V sine 0
Here
FN CT)
is
the
planes
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