X-ray studies of irradiation induced dislocation loops in metals Page: 2 of 19
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used to characterize loops during thermal annealing to roora temperature
after low temperature electron and neutron irradiations, integral diffuse
scattering measurements have been applied to ambient temperature and above
irradiation and annealing studies. These latter studies have included ion
irradiations as well as those of electrons and neutrons.
The results of the diffuse scattering studies will be compared with
electron microscopy, electrical resistivity and lattice parameter measure-
ments where possible in order to establish a direct correspondence and
identify areas where additional work is needed.
THEORY
The theory of diffuse scattering from lattice defects has been
discussed thoroughly in a number of review papers(69,16) in -the past few
years with the result that rather detailed accounts of the underlying
assumptions and approximations are available.
Assuming small concentrations of defects distributed randomly through-
out a crystal lattice, the scattering eross section per defect is given by
da(q) = [r f eN]2 jA (q)u2 (1)
-dR
where q is the vector distance of the scattering vector K from the nearest
reciprocal lattice vector h and r is the classical electron radius. fh is
the atomic scattering factor, e i is the thermal Debye-Waller factor and
A(c) is the scattering amrplitude of the defect. The scattering amplitude
is given in terms of lattice sums by.
+ +d 4 - -
-- iK-r + + + iK-r iK-s + +
An(q) = F e j + ik-s(q) + F e i(e i -1-iK-s.) (2)
+ 1
where r, is the position of the atoms of the defect (dislocs.tion loop)
an t p th
and r. + s. is the position of the i atom displaced a distance s. front
the mean lattice position r . We can recognize the first term as the
direct or Laue scattering from the defect, the second term as the Huang
scattering which diverges as q + o.and the third term as higher order
corrections to*the Huang scattering that tends to a constant as q + o.
In general, the relative size of q compared to the inverse of the loop
radius determines the relative importance of these terms(5) and indeed for
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Larson, B.C. X-ray studies of irradiation induced dislocation loops in metals, article, January 1, 1975; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc863859/m1/2/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.