Order and disorder are everywhere
©1996 - Institut Laue-Langevin
Defects in crystals.
Order in polymers and liquids
Crystalline solids, (metals, minerals, ...) are
dominated by geometrical order. In a perfect crystal,
the atoms are perfectly arranged in the three
dimensions of space. In reality, perfection is not of this
world, even the most beautiful diamonds have defects;
artificial crystals of silicon (electronic chips), of piezoelectric quartz (watches) and of CCDs (video cameras)
all have defects in spite of considerable efforts to
avoid them. These defects, with such important
technological implications, represent a fraction of the
static disorder in an otherwise perfect order.
Liquid are at the other extreme. The particles
(atoms or molecules) which make them up are
disordered and in constant movement. We can
however observe a local, partial order, which is both
fluctuating and short lived; this is dynamic order in a
sea of disorder.
Polymers (plastics) are made up of chains of a
large number of small identical molecules
(monomers). These are long molecules, more or less
folded up on each other and tangled up, whose relative
order can vary from the perfect crystal to amorphous
randomness, through partial crystalline order. The
properties of the same polymer can be radically
different depending on whether order is dominant or
not; and so this is another important field of study.
Why neutrons?
Figure 1. Photo of the D7 instrument at the ILL. With its 64
mobile detectors, it measures the diffuse scattering due to
defects in the sample. Its 6000 polarizing supermirrors can
also be used to distinguish diffuse scattering due to magnetic
atoms or those having spin.
Neutrons are the ideal tool for measuring different
aspects of these phenomena which cannot be
investigated by more classical techniques such as
electron microscopy or X-ray diffraction. The D7
instrument (Fig. 1) at the ILL is particularly well
adapted to this task since it takes advantage of both the
world's most powerful neutron source, the ILL's high
flux reactor and the technique of spin1 analysis
described below.
Crystals: apparent perfection
Defects in crystals can be of various kinds: point or
atomic defects (vacancies, interstitial atoms, impurity
atoms), linear defects (dislocations), two-dimensional
(surfaces, grain boundaries, stacking faults), or threedimensional (phase segregation, internal voids, gas
bubbles).
The study of point defects is very difficult or
impossible using an electron microscope, since the
technique requires especially cut and treated samples.
On the other hand, X-ray techniques, are well
adapted. However, the methods are generally
destructive since this radiation does not penetrate well
into the sample, especially when it contains heavy
atoms (particularly metals).
However, neutrons, penetrate deep into the
samples and using the technique of diffuse scattering,
can be used non-destructively. One can, for example
follow the evolution of defects in a turbine blade at
various stages of its use.
Defects in a metal alloy
Figure 2 shows the results of a neutron
measurement on a crystal of a copper aluminium alloy
(CuAl). If the crystal is perfect we would only observe
the red spots, but in fact we record a contoured
1
The neutron turns around itself (spin) and behaves like a
small magnet. Because of this spin, the neutron interacts
specifically with atoms whose nucleus also have spin
(hydrogen, sodium, ...) whereas other radiation (X-rays,
electrons, ...) cannot see any difference.
surface. The width and the orientation of the mounds
indicate in which direction and by how much a certain
proportion of atoms have moved from their ideal
position in the crystal. They also show if the
neighbouring atoms of a given atom have, on average,
moved closer or further away, compared to their
"ordered" position (short-range order).
The study of different metal alloys made up from
the same elements but different compositions, helps to
understand the behaviour of each type of atom. This
can be used in the future to create materials having
different properties.
neutrons, spin analysis1.
Figure 3 shows the diffusion behaviour of
individual atoms in liquid sodium.
Polymers: order within disorder
Most polymers contain many hydrogen atoms, and
their number can be precisely known. These atoms
have a nucleus with spin and this means that we can
use spin analysis to study the disorder. We can also
precisely measure the destruction of the short-range
order, by introducing a small quantity of a foreign
monomer (impurity) into the sample.
Figure 3. Distribution of displacement velocities of atoms
and the corresponding energies in liquid sodium (diffusion).
The probability contours show a peak which indicates that
low energies and slow movements occur most frequently.
Figure 2. : A perfect crystal only scatters neutrons in certain
defined directions (the red spots). Defects in the sample give
rise to a weak diffuse scattering (blue contours in the inset)
in regions between those of the perfect crystal.
Liquids: temporary order
Let us take a look at liquid sodium (Na), the
coolant of the Creys-Malville breeder reactor. The
atoms of liquid sodium are, as with any liquid, in a
permanent state of movement (thermal motion). To
study it we use a technique uniquely available with
Atoms also have collective behaviour (short-range
order). They are constantly in motion like young
children in a playground, and similarly form small
dispersed groups (clusters) which move around
together, disperse and regroup continuously and
randomly. In the liquid, the atoms are disordered, but
in the clusters they organise themselves just as in
crystals, although this order is only local.
Only polarized neutrons2 can distinguish this
phenomenon (Fig. 4) from the previous one (Fig. 3).
2
Neutrons with their spins all aligned in the same direction.
They are obtained by reflection by special mirrors called
supermirrors.
Figure 4. : Short-range order in liquid sodium.
In red: solid sodium; the atoms are in fixed positions from
which they cannot move.
In blue: Liquid sodium. The contours show that the atoms
remember the order in the solid state, but that other
distances between atoms are now possible (horizontal
broadening of the peak) and they can move relative to each
other (vertical broadening of the peak).
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