X-ray diffraction (complete notes)

1. X-RAY
DIFFRACTION

2. X-RAYS
1.X-rays are short wave length electromagnetic
radiations produced by the deceleration of high
energy electrons or by electronic transitions of
electrons in the inner orbital of atoms
2.X-ray region 0.1to100 A˚
3.Analytical purpose 0.7 to 2 A˚

3. • x-rays are electromagnetic radiation of exactly the same nature
as light but of very much shorter wavelength.
• The unit of measurement in the x-ray region is the angstrom
(A), equal to 10~8 cm, and x-rays used in diffraction have
wave- lengths lying approximately in the range 0.5-2.5A,
whereas the wavelength of visible light is of the order of
6000A.
• X-rays therefore occupy the region between gamma and
ultraviolet rays in the complete electromagnetic spectrum.

5. X-ray diffraction
• X-ray diffraction (XRD) is a powerful nondestructive
technique for characterizing crystalline materials.
• It provides information on structures, phases, preferred crystal
orientations (texture), and other structural parameters, such as
average grain size, crystallinity, strain, and crystal defects.
• X-ray diffraction peaks are produced by constructive
interference of a monochromatic beam of X-rays scattered at
specific angles from each set of lattice planes in a sample.
• The peak intensities are determined by the distribution of
atoms within the lattice. Consequently, the X-ray diffraction
pattern is the fingerprint of periodic atomic arrangements in a
given material.

6. • This review summarizes the scientific trends associated with
the rapid development of the technique of X-ray diffraction
over the past five years pertaining to the fields of
pharmaceuticals, forensic science, geological applications,
microelectronics, and glass manufacturing, as well as in
corrosion analysis.
• X-ray diffraction (XRD) relies on the dual wave/particle
nature of X-rays to obtain information about the structure of
crystalline materials. A primary use of the technique is the
identification and characterization of compounds based on
their diffraction pattern.

7. • The dominant effect that occurs when an incident beam of
monochromatic X-rays interacts with a target material is scattering
of those X-rays from atoms within the target material. In materials
with regular structure (i.e. crystalline), the scattered X-rays undergo
constructive and destructive interference. This is the process of
diffraction. The diffraction of X-rays by crystals is described by
Bragg’s Law,
nλ= 2d sinϴ
• The directions of possible diffractions depend on the size and shape
of the unit cell of the material. The intensities of the diffracted
waves depend on the kind and arrangement of atoms in the crystal
structure. However, most materials are not single crystals, but are
composed of many tiny crystallites in all possible orientations called
a polycrystalline aggregate or powder. When a powder with
randomly oriented crystallites is placed in an X-ray beam, the beam
will see all possible interatomic planes. If the experimental angle is
systematically changed, all possible diffraction peaks from the
powder will be detected.

8. • X-ray diffraction is important for:
• Solid-state physics
• Biophysics
• Medical physics
• Chemistry and Biochemistry

9. BRAGG’s EQUATION
The path difference between ray 1 and ray 2 = 2d Sinϴ
For constructive interference: nλ = 2d Sinϴ

10. • Constructive interference of the reflected
beams emerging from two different planes will
take place if the path lengths of two rays is
equal to whole number of wavelengths”. for
constructive interference,
nλ=2dsinϴ
this is called as BRAGG’S LAW

12. INSTRUMENTATION
• Production of x-rays
• Collimator
• Monochromator
a. Filter
b. Crystal monochromator
• Detectors
a. Photographic methods
b. Counter methods

13. Instrumentation of XRD

14. X-RAY PRODUCTION
• x-rays are produced whenever high-speed electrons collide
with a metal target. Any x-ray tube must therefore contain :-
(a) a source of electrons,
(b) a high accelerating voltage, and
(c) a metal target.
• Furthermore, since most of the kinetic energy of the
electrons is converted into heat in the target, the latter must
be water-cooled to prevent its melting.

15. • All x-ray tubes contain two electrodes, an anode (the
metal target) maintained, with few exceptions, at
ground potential, and a cathode, maintained at a high
negative potential, normally of the order of 30,000 to
50,000 volts for diffraction work.
• X-ray tubes may be divided into two basic types,
according to the way in which electrons are provided:
filament tubes, in which the source of electrons is a
hot filament, and gas tubes, in which electrons are
produced by the ionization of a small quantity of gas
in the tube.

17. • X-rays are produced when any electrically charged particle of
sufficient kinetic energy is rapidly decelerated. Electrons are
usually used for this purpose.
• When a high voltage is applied between the electrodes,
streams of electrons (cathode rays) are accelerated from the
Cathode (Tungsten or any high melting point element) to the
anode and produce X-rays as they strike the anode.
• Filament tube consists of an evacuated glass envelope which
insulates the anode at one end from the cathode at the other,
the cathode being a tungsten filament and the anode a water
cooled block of copper containing the desired target metal
(mainly Mo, Cu, Co, Cr, Fe) as a small insert at one end.

19. • one lead of high-voltage transformer is connected to the
filament and the other to ground, the target being grounded by
its own cooling water connection.
• The filament is heated by a filament current of about 3 amp
and emits electrons which are rapidly drawn to the target by
the high voltage across the tube.
• A small metal cup maintained at the same high (negative)
voltage as the filament is present surrounding the filament. It
repels the electrons and tends to focus them into a narrow
region of the target, called the focal spot.
• X-rays are emitted from the focal spot in all directions and
escape from the tube through two or more windows in the tube
housing. Since these windows must be vacuum tight and yet
highly transparent to X-rays, they are usually made of
beryllium, aluminum, or mica,

20. COLLIMATOR:
•In order to get a narrow beam of x-rays, the x-rays generated by
the target material are allowed to pass through a collimator which
consists of two sets of closely packed metal plates separated by a
small gap.
•The collimator absorbs all the x-rays except the narrow beam
that passes between the gap.

21. MONOCHROMATORS
In order to do monochromatization,two methods
are available
1.Filter
2.Crystal monochromator
a)Flat crystal monochromator
b)Curved crystal monochromator
Materials used- Nacl, quartz etc,.

22. Filter
• X-ray beam may be partly monochromatized by insertion of a
suitable filter.
• A filter is a window of material that absorbs undesirable
radiation but allows the radiation of required wavelength to
pass.
• Purpose of added filtration is to remove low energy, (long
wavelength photons).
• Amplitude and position of continuous spectrum is affected.
• Amplitude of discrete spectrum is affected.
• Filters preferentially reduce the intensity of the Kβ line in the
X-ray spectrum compared to Kα as explained below.
• Note that absorption filters cannot be used to remove the
unwanted Kα2 component from Kα radiation.

23. Filters exploit the X-ray
absorption edge of the
particular element. At
wavelengths longer than
the absorption edge (i.e.
just above the edge), the
absorption of the X-rays is
considerably less than for
wavelengths shorter than
the absorption edge (i.e.
just below the edge) as
shown below for nickel
metal:

25. • The absorption edge of nickel metal at 1.488 Å lies between
the Kα (λ = 1.542 Å) and Kβ (λ = 1.392 Å) X-ray spectral
lines of copper. Hence nickel foil of an appropriate thickness
can be used to reduce the intensity of the Cu Kβ X-rays as
shown below:

26. • The choice of filter material depends upon the choice of anode
material in the X-ray tube as shown in the following table:
ANODE Cu Co Fe Cr Mo
FILTER Ni Fe Mn V Zr
The optimum thickness, x of the filter can be determined from the mass-absorption law:
Where;
(μ / ρ) is the mass absorption coefficient at the wavelength λ
ρ is the density of the material
I(λ) transmitted X-ray intensities and
Io(λ) are incident X-ray intensities,
I(λ) / Io(λ) = exp{− (μ / ρ)λ ρx}

27. The Directions of Diffracted X Rays
Several atomic planes and their &spacing's in a simple cubic
(sc) crystal (a); and Miller indices of atomic planes in an sc
crystal (b). As an example consider the (012) plane. This
intercepts the a-, b-, and c-axes at -, 1, and 112. respectively,
and thus, h = 1/- = 0, k = 1/1= 1, and I = 1/(1/2) = 2

28. where a˳ is the lattice constant of the crystal
When there is constructive interference from X rays scattered
by the atomic planes in a crystal, a diffraction peak is
observed. The condition for constructive interference from
planes with spacing d is given by Bragg's law: is the lattice
constant of the crystal:-
Where is the angle between the atomic planes and the
incident (and diffracted) X-ray beam.

29. CRYSTAL MONOCHROMATOR
• Crystal monochromators is made up of suitable crystalline
material positioned in the x-ray beam so that the angle of
reflecting planes satisfied the Bragg’s equation for the required
wavelength the beam is split up into component wavelengths
crystals used in monochromators are made up of materials like
Nacl, lithium fluoride , quartz etc.

30. Diffractometer
 Source
 Optics
 Detector
Source Incident Beam
Optics
Incident Beam Part Diffracted Beam Part
Sample Diffracted
Beam Optics
Detector

31. Diffraction
• A diffracted beam may be defined as a beam composed
of a large number of scattered rays mutually
reinforcing each other
Scattering
Interaction with a single particle
Diffraction
Interaction with a crystal

32. X-RAY DIFFRACTION METHOD

33. LAUE METHOD
• Laue method was the first diffraction method used. A
single crystal (fixed orientation) is required for this
method. The technique use white radiation, typically
unfiltered radiation from a X-ray tube. This falls on a
single crystal that is fixed. Thus, the diffraction angle,θ, is
fixed for every diffraction plane and for that particular θ
value a certain wavelength will get diffracted.
This method is used for checking crystal
orientation and quality but cannot be used for any
quantitative analysis, sine the wavelength of the X-ray
causing a particular spot is unknown.

34. 1. Transmission Laue method:- The film is
placed in the forward direction (behind the crystal)
so that forward scattered radiation is diffracted. The
film is flat and perpendicular to the incident beams
are partially transmitted through the sample before
striking the film
Transmission Zone axis
crystal
Incident beam
Film

35. 2. Back reflection Laue method:- The film is placed
between the incident beam and the crystal so that the back
reflected rays are used to form the image. The incident beam
passes through a hole in the film and falls on the crystal.
Reflection
Zone axis
crystal
Incident beam Film

36. ROTATING CRYSTAL METHOD
• In the rotating-crystal method a single crystal is mounted with one of its
axes, or some important crystallographic direction, normal to a
monochromatic x-ray beam.
• A cylindrical film is placed around it and the crystal is rotated about the
chosen direction, the axis of the film coinciding with the axis of rotation of
the crystal. As the crystal rotates, a particular set of lattice planes will, for
an instant, make the correct Bragg angle for reflection of the
monochromatic incident beam, and at that instant a reflected beam will be
formed.
• The reflected beams are again located on imaginary cones but now the cone
axes coincide with the rotation axis. The result is that the spots on the film,
when the film is laid out flat, lie on imaginary horizontal lines.
• The crystal is rotated about only one axis, the Bragg angle does not take on
all possible values between 0" and 90" for every set of planes. Not every
set, therefore, is able to produce a diffracted beam; sets perpendicular or
almost perpendicular to the rotation axis are examples

37. Rotating-crystal pattern of a quartz crystal
(hexagonal) rotated about its c axis. Filtered
copper radiation
The rotating crystal method can be used to find the unknown crystal
structure of the material But the drawback is that a good quality single
crystal is needed for this.

38. Powder Method
• In the powder method, the crystal to be examined is reduced to
a very fine powder and placed in a beam of monochromatic x-
rays.
• Each particle of the powder is a tiny crystal, or assemblage of
smaller crystals, oriented at random with respect to the
incident beam.
• Here, the angle is varied not by rotating the sample but by
having small crystallites with all possible orientations.
• Usually a powder sample is used, where the individual grains
can be considered as individual crystals.
• Thus, some grains will have 100 orientation, some will have
111 orientation and so on. Each of these will diffract at certain
Braggs angle so that we can consider the diffracted rays as
forming a cone, with the crystal the apex.

39. Different cones
for different
reflections
Also called Debyering
Usually the source
is fixed and the
detector and
sample are rotated

40. A
B
C

41. DETECTION OF X-RAYS
• The principal means used to detect x-ray beams are fluorescent
screens, photo- graphic film, and counters.
1. Fluorescent Screens :-Fluorescent screens are' made of a
thin layer of zinc sulfide, containing a trace of nickel,
mounted on a cardboard backing. Under the action of x-rays,
this com- pound fluoresces in the visible region, i.e., emits
visible light, in this case yellow light. Although most
diffracted beams are too weak to be detected by this method,
fluorescent screens are widely used in diffraction work to
locate the position of the primary beam when adjusting
apparatus.

42. 2. Photographic Film:-Photographic film is affected by x-rays
in much the same way as by visible light. However, the
emulsion on ordinary film is too thin to absorb much of the
incident x-radiation, and only absorbed x-rays can be
effective in blackening the film. For this reason, x-ray films
are made with rather, thick layers of emulsion on both sides
in order to increase the total absorption. (Division of the total
emulsion thickness into two layers permits easier penetration
of the film-processing solutions.) The grain size is also made
large for the same purpose: this has the unfortunate
consequence that x-ray films are grainy, do not resolve fine
detail, and cannot stand much enlargement.

43. 3. Counters:- X-ray counters are devices that convert x-rays
into a pulsating electric current, and the number of current
pulses per unit of time is proportional to the intensity of the x-
rays entering the counter. Three types are currently in use:
proportional, scintillation, and semiconductor.
Fluorescent screens are used only for the
detection of x-ray beams, while photo- graphic film and the
various kinds of counters permit both detection and
measurement of intensity. Photographic film has the advantage
of being able to record a number of diffracted beams at one
time and their relative positions in space, and the film can be
used as a basis for intensity measurements if desired.
Intensities can be measured much more rapidly with counters,
and these instruments are more popular for quantitative work.
However, most counters record only one diffracted beam at a
time.

44. Sample Preparation
• The X-ray Diffractometer was originally designed for
examining powder samples. However, the Diffractometer is
often used for examining samples of crystalline aggregates
other than powder. Polycrystalline solid samples and even
liquids can be examined. Importantly, a sample should contain
a large number of tiny crystals (or grains) which randomly
orient in three-dimensional space because standard X-ray
diffraction data are obtained from powder samples of perfectly
random orientation. Relative intensities among diffraction
peaks of a non-powder sample can be different from the
standard because perfect randomness of grain orientation in
solid samples is rare. The best sample preparation methods are
those that allow analysis to obtain the desired information with
the least amount of treatment because chemical contamination
may occur during the sample treatments.

45. Sample preparation
• Single crystal X-ray diffraction
– The single crystal sample is a perfect crystal (all unit cells
aligned in a perfect extended pattern) with a cross section
of about 0.3 mm.
– The single crystal diffractometer and associated computer
package is used mainly to elucidate the molecular structure
of novel compounds.
• Powder (polycrystalline) X-ray diffraction
– It is important to have a sample with a smooth plane
surface. If possible, we normally grind the sample down to
particles of about 0.002 mm to 0.005 mm cross section.
The ideal sample is homogeneous and the crystallites are
randomly distributed. The sample is pressed into a sample
holder so that we have a smooth flat surface.

46. Data collection and analysis
• Collecting data: computer and software
• Analysis:
– ICDD database – Identification
– Structure refinement – GSAS
– Quantitative phase analysis – GSAS
– Novel structure – single crystal

47. Powder diffraction pattern from Al Radiation: Cu K,  = 1.54 Å
Note:
 This is a schematic pattern
 In real patterns peaks or not idealized  peaks  broadened
 Increasing splitting of peaks with g 
(1 & 2 peaks get resolved in the high angle peaks)
 Peaks are all not of same intensity
 No brackets are used around the indexed numbers
(the peaks correspond to planes in the real space)
Note that there are no
brackets around the indices!
These are Miller indices in
reciprocal space (these are not
planes they correspond to panes
in real space)

48. Powder diffraction pattern from Al
111
200
220
311
222
400
K1 & K2 peaks resolved in high angle peaks
(in 222 and 400 peaks this can be seen)
Radiation: Cu K,  = 1.54 Å
Note:
 Peaks or not idealized  peaks  broadened.
 Increasing splitting of peaks with g .
 Peaks are all not of same intensity.
 There is a ‘noisy’ background.
 Here the background is subtracted
(else we may have a varying background).
In low angle peaks K1 & K2 peaks merged

49. Applications of X-Ray Diffraction
• Find structure to determine function of proteins
• Convenient three letter acronym: XRD
• Polymer crystallinity
• Texture analysis
• Residual stress
• Distinguish between different crystal structures with
identical compositions
• Study crystal deformation and stress properties
• Study of rapid biological and chemical processes

50. Summary
• X-ray diffraction provides a powerful tool
to study the structure and composition of
the materials which is a key requirement
for understanding materials properties
• An X-ray diffraction system should not
be missing in a modern laboratory for
research on nano- and advanced
materials.