The melee of X-radiation from copper can be reduced
to the Ka peak and then directed by a series of
diffraction gratings, collimators, and slits.
The main features of an XRD analyser include an
X-ray source with collimators, slits, etc, a sample,
and an X-ray detector (Figure 9). The source and
detector are both rotated about the sample, an arbi-
trarily fixed point, and define the same angle (y)
relative to the sample. The angle between the source
and the detector is thus 2y relative to the sample.
Diffraction occurs when X-rays, light, or any other
type of radiation passes into, but is then bounced
back out of, a material with a regular series of layers.
Diffraction occurs within the body of the material
rather than from the surface (and so is quite different
from reflection). Regular layers are a characteristic
of all crystalline materials (minerals, metals, etc).
Each rock-forming mineral has a well-defined set
of these layers, which constitute the crystal lattice.
No two minerals have exactly the same crystal struc-
ture, so fingerprinting a mineral by its characteristic
set of lattice spacings helps to identify minerals. A
radiation beam from a pure source has a defined
wavelength, and the rays from such a pure source
will be ‘in phase’. Constructive interference occurs
only when all the outgoing (diffracted) X-rays are
also in phase. Destructive interference, the norm,
occurs when the diffracted X-rays are no longer in
phase. Constructive interference occurs when the
extra distance that X-rays travel within the body of
the material is an integer (whole number) multiple of
the characteristic wavelength of the incident X-ray
(Figure 10). The geometry of the XRD equipment,
the wavelength of the incident radiation, and the
lattice spacing are all important in defining whether
constructive interference occurs. The key equation
is known as the Bragg Law, which must be satisfied
for constructive interference (‘diffraction’) to occur:
2dsiny ¼ nl, where d is the lattice spacing, l is the
wavelength of the incident X-ray source, and n is an
integer (typically one in many cases). The value of y,
defined in Figure 9, is a function of the variable
geometry of the XRD equipment.
X-ray diffraction is most commonly used on
crushed (powered) rock samples to ensure homo-
geneity of the sample and randomness of the orien-
tations of all the crystal lattices represented by
different minerals. This is known as X-ray powder
diffraction.
XRD works by rotating the X-ray source and the
detector about the sample from small angles (e.g. 4
)
through to angles of up to 70
. The low angles can
detect large interlattice spacings (large values of d)
while the high angles detect smaller interlattice
spacings. For CuKa radiation these angles equate to
d-spacings from about 30 A
˚
down to about 1.5 A
˚
,
covering the dominant d-spacings of practically all
rock-forming minerals.
For a pure mineral sample, the diffraction peaks
from different lattice planes with discrete d-spacings
have different relative intensities. This is a function of
the details of the crystal structure of a particular
mineral, but the maximum-intensity trace (peak) for
many minerals has a low Miller Index value (a simple
notation for describing the orientation of a crystal).
For example, many clay minerals dominated by sheet-
like crystal structures have (001) as the maximum-
intensity peak. All other XRD traces have intensities
that are fixed fractions of the intensity of the max-
imum-intensity trace. The result for each pure min-
eral is a fingerprint of XRD peaks on a chart
of intensity on the y-axis and 2y on the x-axis
(Figure 11). This can be compared with collections
of standards to identify the mineral.
Figure 9 Basic elements of an X-ray diffraction device. An
X-ray source is directed at a sample at a controlled and variable
angle (y). The X-ray detector is at the equivalent angle on the
opposite side of the pivot point. The source and detector are at an
angle of 180
2y to one another. The source and detector are
thus simultaneously rotated about the pivot point. When diffrac-
tion occurs the X-ray detector records a signal above the back-
ground. The sample is usually a powder and preferably randomly
orientated.
Figure 10 Diffraction from a crystal. The incident X-rays are in
phase as they hit the mineral surface. The grey line shows the
path-length difference between the two X-rays. Constructive
interference occurs when the extra path length (2
d siny)isan
integral multiple (typically one) of the wavelength of the X-rays.
Constructive interference leads to an X-ray diffraction peak set
against a low level of background noise.
62 ANALYTICAL METHODS/Geochemical Analysis (Including X-ray)