Absolute measurement of the critical scattering cross section in cobalt Page: 4 of 9
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a resultant uniform level of scattering was obtained
which could then be associated entirely with the
incoherent scattering.
Since the Debye-Waller factor in the neutron
cross section is nearly unity in the forward direction,
the small-angle incoherent scattering is effectively
temperature independent. Hence the difference between
identical angular scans taken at room temperature and
at temperatures near T could be attributed entirely
to magnetic critical scattering. Even very close to
Tc, however, the critical scattering was observed to be
inelastic to an appreciable degree. Because of this
inelasticity, the total intensity measured at a fixed
scattering angle represents a spread of scattering
vectors q. Extensive triple-axis measurements of the
energy distribution of the critical scattering at and
above T did provide the necessary information to
enn"le cthe effects of the inelasticity to be removed
from our double-axis data in a manner which has been
described in Ref. 4. When corrected for inelasticity,
the angular dependence of our double-axis data is quite
adequately described by the Ornstein-Zernike expression
given in Eq.(1). This can be seen in Fig. 1 in which
the reciprocal of the corrected double-axis intensity
is plotted versus q2 for several temperatures up to
100*C above T . The intercepts of the straight lines
in Fig. 1 witf the q2-axis determine the value of Ki
for each temperature.
After correcting for inelasticity, the critical
scattering intensity measured in double-axis scans
above Tc is directly proportional to the differential
cross section,6
(d = 2 S(S+l) Ye2 If(q)-2 1 1 (3)
d d/crit 3 mc2 r2 K2+q2
where S is the effective spin of the scatterer, y is
the neutron magnetic moment in nuclear magnetons, and
f(q) is the magnetic form factor. The same constant of
proportionality relates the level of incoherent scatter-
ing deduced from the room temperature cans to the
cross section
do = oincoh(4
4S/incoh ~~4n
Hence, ratios of the critical to incoherent intensities
can be equated to those obtained by dividing Eqs.(3)
and (4), evaluated at the corresponding wave vector q.
Since the value of K in Eq.(3) is known from plots
like those shown in Fig. 1 and If(q)j2 = 1 over the
small-angle range of our data, these ratios yield
absolute values for the interaction range rl. Using
for the value of the effective spin appropriate for
face-centered cubic cobalt,? S=0.88, we obtain from
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Glinka, C. J.; Minkiewicz, V. J. & Passell, L. Absolute measurement of the critical scattering cross section in cobalt, article, January 1, 1975; Upton, New York. (https://digital.library.unt.edu/ark:/67531/metadc866365/m1/4/: accessed July 15, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.