What’s the point?
There are several other techniques that utilize
concepts studied in this class, that may be of
use in geologic or material science research:
Diffraction — using either electron or x-ray
sources—for determining crystallographic
information
This can be either macro- or micro-analytical
(vis a vis the volumes being studied)
Diffraction—Defined*
Diffraction is the spreading of waves around obstacles. It
takes place with sound; with electromagnetic radiation, such as
light, X-rays, and gamma rays; and with such fast moving
particles such as atoms, neutrons, and electrons, which show
wavelike properties.
It is the result of interference
(i.e., when waves are
superimposed, they may
reinforce or cancel each other
out) and is most pronounced
when the wavelength of the
radiation is comparable to the
linear dimensions of the
obstacle.
* Encyclopedia Britannica, 1974
Coherent Scattering
When x-rays interact with matter, the dominant effect is
scattering. Considering x-rays as waves we deal with coherent
scattering (rather than as particles, where we deal with
incoherent scattering).
With coherent scattering, photons scatter with no loss of
energy, and give rise to scattered radiation of the same
wavelength.
Classical physical theory says that when electromagnetic
radiation (waves) hit electrons, the electron begins to vibrate
and become the source of a wave whose phase is determined by
that of the incident wave. All the electrons in the material that
the wave meets then form a group of coherent sources whose
radiation can interfere constructively or destructively.
This discussion (above) is taken mainly from Andre Guinier’s X-ray Cryallographic
Technology, a 1952 translation of his 1945 classic. Some of the following material is taken
from Jim Connolly’s highly recommended UNM CXRD Class Notes.
Constructive Interference
The distance between atoms in solids are of the same order
size as the x-ray wavelength, and therefore interference
phenomena are observed:
Instead of feeble energy being distributed throughout space,
it is concentrated in certain directions. These concentrations are
diffraction patterns whose particular geometries are functions of
the positions of the atoms in the material (the crystallography of
the solid) and the wavelength of the x-rays.
There is another kind of scattering, incoherent (Compton) which is easiest
understood in terms of the particle nature of photons: the photon deviates
from path and electron takes from it part of its energy. The scattered photon
has lost energy (so has a higher wavelength), and there is no relationship
between the phases of the 2 waves. There is no interference and of little
significance here (though it is for XRF) and we will not consider it further.
Geometry of Diffraction”
“Point Source”
The electrons within an atom
will scatter x-rays, and because
the electrons are “everywhere”
within the atom, a secondary
point source of scattered
radiation appears to originate
from the center of the atom (i.e.,
the nucleus).
Geometry of Diffraction:
“Row source”
Consider a one-dimensional
row of equally spaced atoms.
Each atom in the path of the xray beam (wave) can be
considered to be the center of
radiating, spherical wave shells
of x-rays.
Most scattered x-rays destructively interfere, i.e. cancel out. In
certain directions, however, “in phase” scattered x-rays will add
together to form a new wave. Since wavelengths of l, 2 l and 3 l
will all add to produce a different wavefront, these are called first-,
second- and third-order wavefronts.
Diffraction Methods
There are several standard experimental techniques used in Xray diffraction studies:
1. Laue method: a single crystal is held stationary in a beam
of polychromatic x-ray radiation. The crystal diffracts the
discrete values of l for which planes exist of spacing d and
incidence angle q;
2. Rotating-crystal method: a single crystal is rotated about a
fixed axis in a beam of monchromatic x-rays. The variation
in q brings different atomic planes into position for
reflection;
3. Powder (Debye-Scherrer-Hull) method: a finely powdered
sample is placed in a holder in a monochromatic x-ray
beam, with the angle q gradually changing due
synchronous movement of holder and detector. Assuming
random orientation of the tiny crystallites, there will be
diffraction off of different atomic planes at specific angles.
Our Powder Diffractometer
Scintag PAD V (Room 308 Weeks)
Powder Patterns
Set up the machine to scan a range of q (here, 4-70°); typical time
is ~60 minutes; reconnaissance scans can be much quicker. Then
need to process data (model the background, subtract it) and
proceed to software identification -->
Powder Patterns
-> Identification of natural or synthetic crystalline
materials using software (here, MDI’s “Jade” program)
Other Powder XRD
Applications
• Crystallographic structural analysis and unit-cell calculations
• Quantitative determination of amounts of different phases (in
multi-phase mixture) by peak-ratio calculations
• Quantitative determination of phases by whole-pattern
(Rietveld) refinement
• Determination of crystallite size from peak broadening
• Determination of crystallite shape from peak symmetry
• Study of thermal expansion by using in-situ heating stage.
EBSD
Electron backscatter diffraction (EBSD) is a technique for determining
crystallographic information of submicron regions of flat polished samples.
It has made possible studies of microtextures, phase identification (of
polymorphs), grain boundary distribution, and deformation microstructures.
EBSD is also known by the names backscatter Kikuchi diffraction BKD, or
electron backscatter pattern EBSP. The phenomenon has been known since
1928 by Kikuchi, who noted ‘remarkable lines’ resulting from electron
diffraction thru a thin mica crystal. Two research groups (in UK) started
working on EBSD ~1973, and it has only been commercially available
since 1994.
In many cases it replaces more time-consuming/difficult TEM or XRD,or
possibly electron channeling studies, with the benefit of SEM’s point by
point high spatial resolution (<1 mm) together with its ability to scan large
areas (~cm). It is relatively inexpensive ($50-100K), in being an add-on
attachment to a previously existing SEM.
EBSD
Kikuchi recognized the importance of a divergent electron beam being
diffracted -- how the spreading of the incident beam (by inelastic scattering
in upper surface of sample)
Orientation mapping (OIM, orientation imaging microscopy)
Phase identification by step by step deduction of pattern point group
symmetry, though some problems; other technique is to determine approx
value of unit cell volume from measured lattice spacing and interplanar
angles, together with EDS, searching a database for possible matches, then
match angles
EBSD
The sample is tilted steeply (70°, so
beam is 20° to sample) which enhances
the number of BSEs able to undergo
diffraction and escape the surface. The
HV electrons are scattered by the
electrons of the atoms in the top unit cells
of the material, scattering from electrons
in crystallographic planes producing
intersecting bands imaged by film or a
phosphor screen immediately adjacent.
The pattern and bands provide
information about the crystal structure:
• Symmetry of crystal lattice
• Width and intensity of bands are a
measure of the plane spacing (and unit
volume)
• Angles between bands are related to the
angles between planes in the lattice.
Specimen Prep
Specimen prep important: surface must have
damaged layer (esp from coarse polishing)
removed, e.g. with colloidal silica (which is also
chemical etching action); carbon coat must be very
very thin (~10Å)
From
Microscopy
Today,
Jan/Feb 1993
Some References
Introduction to X-Ray Powder Diffraction, by Jim Connolly (notes for U NM
EPS400-002, epswww.unm.edu/xrd)
X-Ray Crystallographic Technology by Andre Guinier (English Translation, 1952)
Modern Powder Diffraction by D. L. Bish and J. E. Post (eds), Mineralogical
Society of America Reviews in Mineralogy, Vol 20, 1989
Electron Backscatter Diffraction in Materials Science, Edited by Adam J. Schwartz,
Mukul Kumar and Brent L. Adams, Kluwer/Plenum, 2000, ISBN 0-306-46487-X
(25 articles)
An Atlas of Electron Backscatter Diffraction Patterns by D. J. Dingley, K. BabaKishi, and V. Randle, 1994, Institute of Physics Publishing.