Page 301 - Book Hosokawa Nanoparticle Technology Handbook

FUNDAMENTALS CH. 5 CHARACTERIZATION METHODS FOR NANOSTRUCTURE OF MATERIALS
examine the distribution of stress in a structural
material by this technique. There exists less influ-
ence of the pollution and oxidation of a sample
surface, thus, it is easy to obtain the information
of bulk inside a specimen. It is recommended to
examine the neutron absorption cross sections of
Ce Oxygen Oxygen the material before neutron studies, because some
X-RAY X-RAY NEUTRON elements such as B and Cd have quite large neu-
NEUTRON
tron absorption coefficients. The neutron beam
intensity I is expressed by the equation, I I exp
(a) (b) (c) 0
( N
t) when the incident beam with intensity I 0
Figure 5.2.6 passes a planer specimen with the thickness of t.
Comparison of scattering power of an oxygen atom when Here the N and
are an atomic number in a unit
the neutron and X-ray scattering powers of Ce atom: volume and the total scattering cross section,
(a) are assumed to be equal. (b) X-ray atomic scattering respectively. The
is calculated by adding the
–1
factor of oxygen atom (sin / 0.5Å ). (c) Neutron scattering cross section
to absorption cross
scattering power of oxygen atom. The area of the circle s
corresponds to the square of the scattering power [3]. section
. These cross sections
and
are
a
s
a
known, thus it is easy to calculate the absorption.
6. Neutron has magnetic moment, thus can analyze
3. Neutron can distinguish the isotopes from each
the configuration of spin in a crystal, namely,
other. For example, it is able to distinguish hydro-
the magnetic structure analysis is possible.
gen (neutron scattering length b 3.7423fm),
7. Using reciprocal vector k, the structure factor
deuterium (b 6.674fm) and tritium (b 5.10 fm)
can be described as,
58
from each other. It can distinguish Ni (b 14.4
60
fm) from Ni (b 2.8 fm). XRD cannot distin-
∫
F( ) ( ) exp( i k
d ) x x (5.2.20)
2
x
k
guish the isotopes from each other, because it
examines the electrons.
4. The X-ray atomic scattering factor steeply In XRD the (x) is the electron density at the
decreases with an increase of Bragg angle, position x, while it is nuclear density (strictly
while the neutron scattering length is independ- speaking, scattering amplitude distribution) in
ent of Bragg angle. Contrary to XRD, neutron neutron diffraction. Application of the maxi-
diffraction does not need to consider the polar- mum-entropy method (MEM) for the structure
ization factor. Therefore, in the neutron diffrac- factors and their errors obtained with a Rietveld
tion analysis, precise atomic displacement analysis program enables determination of pre-
parameters can be obtained. cise (x), compared with conventional Fourier
5. Penetration of neutron into a material is much method. The MEM technique is effective for
deeper than that of X-ray. Thus, the neutron dif- investigating the spatial distribution of atom
fraction experiments are usually performed in positions (positional disordering), ionic conduc-
transmission geometry. It is easy to design and tion (diffusion) path, and anisotropic thermal
fabricate the sample environmental attachments motions. It has been demonstrated that the
such as high-temperature furnace [3] and high- mobile oxygen ions in a fast-ion conductor bis-
pressure apparatus. It is easy to collect high-qual- muth oxide with the fluorite-type structure have
ity intensity data with higher precisions, because a large spatial distribution and anisotropic ther-
there are a large number of grains in the poly- mal motions. Anisotropic thermal motions and
crystalline or powdered sample, which contribute diffusion path of oxygen ions were studied for
to the diffraction intensity data, leading to less the lanthanum gallate perovskite (Fig. 5.2.7) [4].
influence of preferred orientation and large
In the present section, we have described mainly
grains. A part of the inside of a big specimen
neutron powder diffractometry. Neutron studies have a
(e.g., practical industrial material) can be exam- wide range of applications such as single-crystal dif-
ined by neutron diffraction, thus we are able to fractometry, small-angle scattering method, inelastic
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