X-Ray Diffractogram, Principles and methods for identification of clay minerals based on Bragg's law.

1. X-Ray Diffractogram and Identification of
Minerals
ACSS-510
Dr. Pabitra Kumar Mani
Assoc. Professor
Deptt. Agril. Chemistry and Soil Science
Bidhan Chandra Krishi Viswavidyalaya,
E-mail: pabitramani@gmail.com, Website: www.bckv.edu.in
 : 91-33-25822132, 91-9477465968,

2. X-Rays Wavelengths used
for XRD

6. Schematic of an atom, depicting
electron shells and the energy
transitions for Kα, Kβ, and Lα
characteristic radiation.
Kα arises from the replacement of
K-shell electrons by electrons from
the L shell;
Kβ, by replacement of K-shell
electrons by M-shell electrons, and
 Lα, by replacement of L-shell
electrons by M-shell electrons.
(B) Generalized depiction of an X-ray
spectrum, showing peaks in intensity at
wavelengths (energy levels)
corresponding to characteristic
radiation. The highest-energy
(shortest wavelength) characteristic
radiation shown is Kβ. Peaks marked
Kα1and Kα2, which are seldom
resolved in XRD data, arise from
contribution of electrons from two
sublevels in the L shell.

8. • Crystalline substances (e.g. minerals) consist of parallel
rows of atoms separated by a ‘unique’ distance
• Diffraction occurs when radiation enters a crystalline
substance and is scattered
• Direction and intensity of diffraction depends on orientation
of crystal lattice with radiation

10. 10
X-ray diffraction
• The distance of atomic planes d can be determined based on the
Bragg’s equation.
BC+CD = nl, nl = 2d·sinq, d = nl/2 sinq
where n is an integer and l is the wavelength.
• Different clays minerals have various basal spacing (atomic planes).
For example, the basing spacing of kaolinite is 7.2 Å.
Mitchell, 1993
Bragg’s law: The two rays will constructively interfere if the extra distance ray
I travels is a whole number of wavelengths farther then what ray II travels.

11. X-ray diffraction is now a common technique for the
study of crystal structures and atomic spacing.
 X-ray diffraction is based on constructive interference
of monochromatic X-rays and a crystalline sample.
 These X-rays are generated by a cathode ray tube,
filtered to produce monochromatic radiation, collimated
to concentrate, and directed toward the sample. The
interaction of the incident rays with the sample produces
constructive interference (and a diffracted ray) when
conditions satisfy Bragg's Law (nλ=2d sin θ).

12. Bragg’s law can easily be derived by considering the
conditions necessary to make the phases of the beams
coincide when the incident angle = reflecting angle .
The second incident beam b continues to the next layer
where it is scattered by atom C
The second beam must travel the extra distance BC+CD
if the two beams a & b are to continue travelling
adjacent and parallel.
This extra distance must be an integral (n) multiple of
the wavelength for the phases of the two beams to be
the same.

13. • The space between diffracting planes of atoms determines peak
positions.
• The peak intensity is determined by what atoms are in the
diffracting plane.

15. Schematic representation of XRD by regularly spaced planes of atoms in a crystal. Theta (θ)
is the angle that the beam makes with the atomic planes; 2θ is the angle that the diffracted
beam deviates from the primary beam; d is the distance between equivalent atomic planes in
the crystal (d-spacing); and λ is wavelength of the radiation. Note that when DE + EF = nλ,
where n is an integer, the diffracted beams from each plane of atoms would be in phase,
leading to constructive interference which accounts for XRD. In effect, when that condition
is met, an XRD peak is observed. The Bragg equation can be used to calculate d-spacing from
the 2θ angle at which the diffraction peak occurs.

17. strong intensity = prominent crystal plane
nλ = 2dsinθ
(1)(1.54) = 2dsin(15.5 degrees)
1.54 = 2d(0.267)
d = 2.88 angstroms
background radiation

18. d-spacing Intensity
2.88 100
2.18 46
1.81 31
1.94 25
2.10 20
1.75 15
2.33 10
2.01 10
1.66 5
1.71 5

20. Instrumentation
• Production of X-Rays (X-ray Tube: the source of X Rays)
• The goniometer: the platform that holds and moves the sample,
optics, detector, and/or tube
• Collimator
• Monochromator
 Filter
 Crystal monochromator
• Detector (count the number of X Rays scattered by the sample)
 Photographic methods
 Counter methods

25. 25
Identification of Clay
Minerals

38. Fig. 4–6. Sequences of X-ray diffraction patterns for soil clays
(2.0–0.2 μm) scanned after specified cation-saturation (Mg and
K), glycerol (Gly) solvation, and heat treatments.
Peaks are labeled by d-spacings (Å).
(A)The clay from the Orangeburg series (Ap horizon, Georgia)
shows a 14-Å peak that is minimally affected by cation
saturation and shifts and broadens with heat treatment to a
peak at 12 Å. This behavior typifies hydroxy-interlayered
vermiculite as it occurs in the coastal plain of the southeastern
USA.
There is a small peak that persists at 14 Å at 500°C, which is
due to a small amount of chlorite.
Also present are kaolinite (7.18 and 3.57 Å), gibbsite (4.85 Å),
and quartz (4.26 and 3.34 Å).
Note that peaks for gibbsite and kaolinite disappear at 300 and
500°C, respectively, due to dehydroxylation.

40. (B) Clay from the Sharkey soil (Ap, Louisiana) shows peaks at 18 and
14 Å that have mainly shifted to 10 Å at 300°C. Note the increase in
intensity of the 10-, 5- (second-order), and 3.34-Å (third-order) peaks
with heat. This behavior suggests that both smectite and vermiculite
are present.
A small peak (not labeled) intermediate between 14 and 10 Å may be
attributable to some resistance to collapse of these expansible
phyllosilicates. The small 14-Å peak at 500°C indicates that some of
the 14-Å peak is attributable to chlorite.
Also present are mica (illite) (10, 5, and 3.34 Å), kaolinite (7.18 and
3.57 Å), and quartz (4.26 and 3.34 Å).
Note that at 25°C the 10-Å peak is completely attributable to mica, but
is enhanced by the collapse of expansible phyllosilicates with
increasing temperature.
Also, quartz, mica, smectite, and vermiculite all contribute to the 3.34-Å
peak at 500°C, whereas only mica and quartz contribute to it at 25°C.