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X-ray diffraction and minerals
Is this mineral crystalline?
Bragg’s law
Why work on single crystals?
Why work on crystal powder?
The powder X-ray diffraction
pattern of an amorphous solid
- No sharp peak
- Broad hump
Bragg’s law: n = 2 d sin 
1) What do we know?
, i.e. the wavelenth of the X-ray radiation
2) What do we assume?
n=1
(Peaks for higher “n” are weaker.)
3) What do we want to know?
d, i.e. the interplanar spacings of the lattice
X-ray spectra used
to be recorded on
film strips rolled
up within a round
chamber.
The distance from the center of each line
to the center of the hole (where X-rays
entered the chamber) was proportional to
the angle 2-theta.
The intensities of the lines were originally
estimated by a human eye, on a scale of 1 to
100, before detectors became routine.
Ion order-disorder can be detected by
X-ray diffraction.
This is very different from the lack of
order found in an amorphous solid.
Powder X-ray diffraction is a routine
technique to measure the amount of
crystalline SiO2 (quartz) present in
mineral dust or soil.
A chemical analysis will not distinguish
the SiO2 of quartz from the silicate
“skeleton” of clays and many other
minerals.
Laue diffraction experiment
Large spots: aluminum. Small spots: silicon.
Laue photographs are used to study the
epitaxial relationships between thin films
and the material on which they are grown.
How to solve crystal structures?
The electron density ( ) at a point X, Y, Z in a
unit cell of volume V is;
(X,Y,Z) = 1/V Fhkl cos [ 2 (h  X + k  Y + l  Z) ]
Therefore if we know Fhkl and (for each h, k, l)
we can compute for all values of X, Y, and Z
and plot the values obtained to give a threedimensional electron density map. Then,
assuming atoms to be at the centres of the
electron density peaks, we would have the entire
structure.
The unit cell is described as being
the smallest regular repeat unit in
a crystalline lattice.
These cells are defined by three
unit lengths (a, b, c) along the
crystallographic axe,s and the
three interaxial angles (, , ).
E: this tube is the X-ray source. Inside it,
there is a 40,000 volt difference between a
tungsten filament and a copper target.
What
radiation does
the target
metal emit?
A spectrum
(i.e. many
wavelengths)
with two
sharp peaks.
A cathode filament is heated so that it
boils off electrons. A large voltage (20100kV) is maintained between the filament
and the target (a metal such as Mo, Cu, Co,
Fe or Cr).
The electrons are accelerated and hit the
target metal.
H: scintillation counter which measures the
intensity of the diffracted X-ray beams. It is
connected to a goniometer which measures the
2-theta angles at which diffracted beams are
detected.
G: the sample chamber holds the specimen.
Samples are ground to a fine powder before
mounting them in the chamber. X-rays enter
from the left, are diffracted by the powder,
and leave the chamber to the right.
A graphite monochromator is used to
let only one specific X-ray wavelength
escape the X-ray source.
piezoelectricity: production of electrical
polarization in a material by the application of
mechanical stress
- phonographs
- microphones
- quartz watches
When a chemical analysis will not tell
you what mineral this is....
This Anglo-Saxon brooch contains an
inlay of CaCO3, but is it calcite or
aragonite (2 common polymorphs)?
When detecting twinning matters !
Piezoelectric crystals may not display that
property if they are twinned.
Twinning can show up in
- external forms
- re-entrant angles (non-convex morphology)
Indices of diffracted X-ray peaks are
usually written without parentheses.
111, 222 and 333 correspond to the 1st,
2nd and 3rd order reflections of the (111)
planes.
222 is produced when the X-rays of
successive planes have a path difference
of 2*wavelength (two “lambdas”).
Bragg’s law predicts at which angles
the peaks will be diffracted, but not
their intensities.
Diffraction intensities are influenced
by the atomic number (Z) of the atoms
in the structure, by the shape and size
of the specimen, and by other factors
related to the machine.
We use the peak intensities to
determine where the atoms are in the
unit cell.
Structures with lighter elements can
be studied using neutron diffraction.
Neutrons are scattered by the nucleus,
and their scattering varies less from
element to element.
whereas
X-rays are scattered by the electron
cloud, and light elements barely reemit them.
Mineral structure can be
destroyed by radiation damage.