X-rays are electromagnetic radiation of wavelengths shorter than visible light. They have typical wavelengths ranging from 0.01 to 10 nanometers. X-rays are produced when high-speed electrons collide with a metal target in an X-ray tube. There are two main production methods - bremsstrahlung and characteristic line emission. Bremsstrahlung produces a continuous X-ray spectrum, while characteristic lines produce peaks at specific wavelengths. X-ray diffraction is used to determine crystal structures by analyzing the diffraction pattern produced when X-rays interact with a crystalline material. Bragg's law describes the angles at which diffraction occurs based on the wavelength and crystal plane spacing.

2. DEFINATION
• An electromagnetic wave of high energy and very
short wavelength, which is able to pass through many
materials opaque to light.
• Most X-rays have a wavelength ranging from 0.01 - 10
nm.
• Corresponding to frequencies in the range 30
petahertz to 30 exahertz (3×1016 Hz to 3×1019 Hz) and
energies in the range 100 eV to 100 keV.
• X-ray wavelengths are shorter than those of UV rays
and typically longer than those of gamma rays. 2

3. • Based on energy ranges :
• HARD X-RAY – are those with high photon
energies (above 5–10 keV, below 0.2–0.1 nm
wavelength) are called hard X-rays.
• Due to their penetrating ability, hard X-rays are
widely used to image the inside of objects. e.g: in
medical radiography and airport security.
• Since the wavelengths of hard X-rays are similar
to the size of atoms they are also useful for
determining crystal structures by X-ray
crystallography.
3

4. • SOFT X-RAY
 Are those with low photon energies.
 soft X-rays are easily absorbed in air.
 The attenuation length is 600 eV (~2 nm).
 USE - Soft X-ray Microscopy is used to study
the elemental composition and structure of very
thin slices of biological and materials samples,
where An X-ray microscope uses
electromagnetic radiation in the soft X-ray band
to produce images of very small objects.
4

5. RANGE OF X-RAY IN EMR
5

6. BASIC PRINCIPALS
 In an atom, the electrons are arranged in
layers or shells, like :
 K-shell
 L-shell
 M-shell
 N-shell
6

7.  When the atom is bombarded with an electron,
one of the electron ejects from the inner shell.
 The electrons migrate from the outer shell to the
inner shell to fill the gap with higher energy.
 A quantum of radiation (X-rays)is emitted
corresponding to this transition , time scale is
approximately 10 -4 sec.
 Emitted radiation is called X-rays.
7

8. PRODUCTION OF X-RAYS
X-rays may be produced when a beam of electrons of
sufficient energy interact with matter.
When electrons impinge on a target (metal) a number
of possible processes can occur:-
i. Back-scattering from the target - For high atomic
number elements.
ii. Collisions with weakly bound valence electrons -
Most electrons which are not back scattered undergo
this process, Many of these electrons are ejected
from the target with energies of < 50eV and are
termed secondary electrons.
8

9. X-RAYS can be produced as parcels of energy called photons,
just like light.
PRODUCTION OF
X-RAYS
BREMSSTRAHLUNG
(CONTINUOUS
SPECTRA)
K-SHELL EMISSION
(LINE SPECTRA)
9

10. BREMSSTRAHLUNG (CONTINUOUS
SPECTRA)
In BREMSSTRAHLUNG the radiation is emitted when
the velocity of the electron shot at the tungsten
changes.
This electron slows down after swinging around the
nucleus of a tungsten atom and loses energy by
radiating X-rays.
After emitting the spectrum of X-ray radiation the
original electron is slowed down or stopped.
Lot of photons of different wavelengths are produced,
but none of the photons has more energy than the
initial electron. 10

11. 11

12.  The incoming electron is accelerated and strikes
the tungsten at a high speed and has a lot of
energy.
 The electron might be slowed a little or a lot – this
is called as "breaking radiation"
 So the amount of "breaking" determines which
wavelength of photons are emitted.
12

13. K-SHELL EMISSION
 The process of producing X-Rays can be explained in
terms of Bohr’s Theory of atomic structure.
 An atom consists of nucleus and numerous electrons.
 These electrons are arranged in layers or shells with
valence electrons in the outer shells.
 The different shells are called K shell , L shell , M shell
and so on.
13

14. 14

15.  The electron in the inner most orbit is attracted by the
nucleus with greatest force and to detach it from the
atom maximum energy is required.
 For the electron lying in the outer orbit smaller
amount of energy is required to detach it from the
orbits.
15

16.  Whenever a fast moving electron impinges on an
atom, it may knock out an electron from one of the
inner shells of that atom.
 Following the loss of the inner- shell electron a ‘hole'
is created.
 This ‘hole’ causes a domino effect
wherein Immediately an electron
from one of the higher orbit
jumps to occupy vacant space
with the simultaneous emission
of an X-ray photon.
16

17.  The energy of the emitted X-ray photon = difference in energy
between the two levels involved.
 For ex. If a K-SHELL loses one electron and it is replaced by
the electron from the L-SHELL, the resulting X-ray is termed
as the K X-ray and its energy is given as :-
EK = EL – EK and frequency is given as :-
ʋ = (EL – EK) / h
 These K lines have been further divided into Kα and Kß
depending on whether the electrons falling into the K-SHELL
comes from the L-SHELL OR M – SHELL.
17

18.  Starting from the K shell the binding energy decreases (
binding energy K>L>M>N). Each shell is defined by a
set of quantum numbers (n ,l and m)
 K radiation - occurs when a vacancy is formed in the K
shell of an atom, X-rays are produced from transitions of
electrons dropping into the K shell (n=1) from higher
quantum states (n=2, 3, …).
 L radiation - occurs when a vacancy is formed in the L
shell of an atom. X-rays are produced from transitions
of electrons from n=3,4,…. to the L shell (n=2).
 M radiation - occurs when a vacancy is formed in the M
shell (n=3) and electronic transitions arises from n=4, 5,
… down to n=3.
18

19. 19

20.  For low atomic number elements only K radiation is generated,
(like NEODYNIUM  Z=60).
 L and M radiation is only generated from higher atomic number
elements. Generally the higher the atomic number the higher the
energy of the X-ray.
(L-Lines Start from LANTHANUM  Z=57)
 For a given element EK > EL > EM .
 Henry Mosley stated that more the atomic number more intense
radiations are produced.
 He derived a relationship between the atomic number of the
element and wavelength of the emitted X-Ray lines as follows:-
c /  = a ( Z – σ ) 2
20

21. X-RAY TECHNIQUES
• THERE ARE FOUR METHODS
AVAILABLE:
i. X-RAY ABSORPTION METHOD
ii. X-RAY EMISSION METHOD
iii. X-RAY FLUOROSCENCE METHOD
iv. X -RAY DIFFRACTION METHODS
21

22. X-RAY ABSORPTION METHOD
• A beam of X-ray is passed to the sample.
• X-ray photons are absorbed by the substance.
• Measuring the concentration of absorbing substance.
• Applications:- Elemental analysis such as barium and
iodine in the body
22

23. 23

24. X-RAY FLUOROSCENCE METHOD
Beam of X-ray fall on sample
Sample Emits secondary X-ray
Fluorescent X-ray
Intensity of X-ray provides how much is present
Applications:- Elemental analysis.
24

25. 25

26. X-RAY DIFFRACTION
• When X-rays interact with a solid material, the
scattered beams can add together in a few directions
and yield diffraction.
26

27. • X-RAY diffraction methods are generally used
for investigating the internal structures, However
the following methods are used:
i. Laue photographic method
ii. Bragg x-ray spectrometer method
iii. Rotating crystal method
iv. X-ray powder technique
27

28. GENERAL PRINCIPAL FOR X-RAY
DIFFRACTION
• A beam of X-rays directed at a crystal interacts with the
electrons of the atoms in the crystal.
• The electrons oscillate under the influence of the incoming
X-Rays and become secondary sources of EM radiation.
• The secondary radiation is in all directions.
• The waves emitted by the electrons have the same
frequency as the incoming X-rays
28

29. • The emission will undergo constructive or destructive
interference.
29

30. DIFFRACTION PATTERN
 Consider Crystalline substances have an ordered three-
dimensional arrangement with a particular spacing of
atoms.
 When X- rays strike these atoms within the crystal, the
atoms absorb and re-emit the energy from the X- rays in
the form of spherical wave fronts emanating from each
atom.
 The waves traveling outward from each atom interact
with other waves in the processes known as constructive
and destructive interference.
30

31.  The resulting pattern of constructive and destructive
interference is known as a diffraction pattern.
 The patterns are controlled by the spacing of atoms
within the matrix and are unique to that substance.
31

32. LAUE PHOTOGRAPHIC METHOD
• X-rays are reduced to a narrow fine pencil by passing them
through pin holed collimator.
• The beam is now allowed to pass though a NaCl crystal,
The emergent rays are made to fall on a photographic
plates .
• The diffraction pattern so obtained consist of a central
spot at o and a series of spots arranged in a definite
patterns about o.
• The pattern shows that most of X rays goes directly
through the crystal and produce a black spot at the center
of the film.
32

33.  But there are many weak diffracted beams which
emerge in different directions and produce a series of
dark spots on the same film.
 According to BRAGG the spots are produced due to the
reflections of some of incident X-rays from the various
sets of parallel crystal planes .
33

34.  This method is divided into two types.
a. Transmission method
b. Back Reflection method.
 Transmission method :- A beam of X-ray is passed
through the crystal, after passing through the crystal,
X-rays are diffracted and recorded on a photographic
plate.
34

35. • Back reflection method:- This method provides
similar information as the transmission method
35

36. BRAGG’S X-RAY
SPECTROMETER
• Using the Laue's photograph, Bragg analysed the
structures of crystals of NaCl , Kcl .
• Bragg devised a spectrometer to measure the intensity of
X-ray beam.
• The spectra obtained in this way can be employed for
crystallographic analyses.
• This is based on the Bragg’s equation: n λ = 2dsin ϴ .
36

37. 37

38. ROTATING CRYSTAL METHOD
• X-rays are generated in the X-ray tube and the beam is
made monochromatic by filter.
• Form the filter, the beam is then allowed to pass through
collimating system which permits a fine pencil of parallel X-
rays.
• From the collimator, X-ray beam is made to fall on a crystal
mounted on a shaft which can be rotated at a uniform
angular rate by a small motor.
• Now the shaft is moved to put the crystal in to slow rotation
about a fixed axis. 38

39.  Each plane will produce a spot on the photographic
plate.
 One can take photograph of the diffraction pattern in
two ways namely:
a. Complete rotation method
b. Oscillation method
39

40. POWDER CRYSTAL METHOD
 A beam of X-ray falls on to the powdered specimen through
slits.
 The sharp lines to be obtained on the photographic film
which is surrounding the powder crystal in the form of
circular arc.
 Powder diffraction patterns are typically plotted as the
intensity of the diffracted X-rays vs the angle 2 θ.
 Peaks will appear in the diffraction pattern at 2 θ values
when constructive interference is at its maximum, when
Bragg’s Law is satisfied. n λ = 2 d sin θ 40

41. 41

42. 42

43. BRAGG’S LAW
 Gives relationship between wavelength of X-ray (),
interplanar distance (d) in the crystal & angle of
reflection().
n = 2dSin
 According to Bragg, scattering of X-rays by crystals can be
considered as reflection from successive planes of atoms in
the crystal.
 This reflection of X-rays take place only at certain angles
which are determined by the wavelength of X-rays & the
distance between the planes in the crystal. 43

44.  Consider a set of parallel lattice
planes of a crystal separated by a
distance ‘d’.
 The X-ray hitting the lower plane
must travel the extra distance AB
and BC.
 To remain in phase with the first
X-ray, this distance must be a
multiple of the wavelength thus:
 n = AB+BC = 2AB
 (since the 2 triangles are identical)
44

45.  The distance AB can be
expressed in terms of the
interplanar spacing (d) and
incident angle () because d is
the hypotenuse of right triangle
zAB shown at right.
 As sin() = opposite/hypotenuse
sin() = AB/d
Thus AB = d sin()
Therefore:
45

46. 46

47. INSTRUMENTATION
 Production of x-rays ( X-ray tube )
 Collimator
 Monochromators
 Detectors
47

48. PRODUCTION OF X-RAYS
48

49.  X-ray tube consists of a glass tube from which air has
been removed.
 The tube contains two electrodes, a negatively
charged electrode called the cathode and a positively
charged target called the anode.
 A beryllium foil is commonly used as a window for
retrieving incident X-rays.
 Tungsten, rhodium, molybdenum and chromium are
examples of anodes.
 The two electrodes are attached to a source of direct
(DC) current.
 When the current is turned on, electrons are ejected
from the cathode.
 They travel through the glass tube and strike a target.
49

50. 50

51.  The energy released when the electrons hit the target is
emitted in the form of X rays,The wavelength of the X
rays produced is determined by the metal used for the
target and the energy of the electrons released from the
cathode.
 X rays with higher frequencies and, therefore, higher
penetrating power are known as hard X rays , Those with
lower frequencies and lower penetrating power are known
as soft X rays.
 For production of high intensity X-rays a target element
should have a high atomic number, Pure transition metals
such as Cu, Cr etc are typical target materials.
51

52. WORKING
52
 X- ray tube is Composed of evacuated tube possessing cathode
(tungsten filament) at one end & anode(metal target) at another end.
 Passage of current through tube causes tungsten filament to glow &
emits electron.
 Among the two electrodes large voltage difference is applied, causing
electrons to move at high velocity from filament and strike to anode.
 Due to high velocity impact of electrons on to the target, inner shell
electrons of metal gets dislodge, which causes the outer shell electrons
to jump to a lower energy shell to replace the dislodge electrons.
 These electronic transitions results in the generation of X-rays.
 The produced X-rays are allowed to move through a window of X-ray
tube.

53. COLLIMATOR
53

54.  Collimators are used to get a narrow beam of X-
rays from an X- ray tube because X- rays
produced by the target material are randomly
directed.
 The generated X- rays are allowed to pass
through a collimator which consists of 2 sets
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.
54

55. MONOCHROMATOR
 Filter
 Crystal monochromator
a. Flat crystal monochromator
b. Curved crystal monochromator
55

56. FILTER MONOCHROMATOR
56

57.  When the wavelength of two spectral lines are
nearly the same and there is an element with an
absorption edge at the wavelength between the
lines , that element may be used as a filter to
reduce the intensity of the line of shorter
wavelength.
 The primary X- ray beam to remove the k-beta
lines from the spectrum while transmitting the k-
alpha lines with small loss of intensity.
 Eg: zirconium filter, which is used for molybdenum
radiation.
57

58.  When x rays are emitted from molybdenum are
allowed to pass through a zirconium filter.
 The zr strongly absorbs the radiation of
molybdenum as shorter wavelength but weakly
absorbs the k-alpha lines of molybdenum.
 Thus zr allows the k-alpha lines to pass however
the continuous radiation will also be reduced in
intensity.
 Zr acts as Beta filter.
58

59. CRYSTAL MONCHROMATOR
 Crystals are used as grating monochromators .
 The crystals are used in monochromators are made up of
materials like NaCl, LiF, Quartz,etc.
59

60. DETECTORS
 Photographic Methods
 Counter Methods ( Ionization detectors)
i Geiger-muller tube counter
ii Proportional counter
iii Scintillation detector
iv Solid-state-semi-conductor detector
v Semi-conductor detector
60

61. PHOTOGRAPHIC METHODS
 A plane or cylindrical film is used to record the
position & intensity of the X-ray beam.
 A Film after exposing to X-ray is developed.
 The blackening of developed film is expressed in
terms of density units D given by
 I0 & I refer to incident & transmitted intensities of X-rays
 D is related to total X-ray energy that causes the
blackening of photographic film
 Value of D is measured by densitometer
61

62. COUNTER METHODS
1) Geiger-muller tube counter:- 800-2500V
OUTPUT PULSE- 1-10V
62

63. 63
It is composed of glass tube(19 mm dia), The tube is
comprised of a half metal cylinder of about 4 inches
length, made up of copper.
 Along the axis of cylinder a thin metal wire of tungsten
is tied.
The cylinder & wire are connected to an electrical
voltage source.
The tube is filled with gas, usually Argon at a low
pressure.
A voltage is set up between the cathode and anode .

64. WORKING
64
 When X-rays enters the Geiger tube, a collision occurs
between the gas molecule and X-rays. Thereby electrons
are ejected out of atoms of neutral molecules of argon gas.
 This causes production of positive molecular ions and free
electrons. These electrons being negatively charged,
moves towards anode and positively charged argon ions
moves toward cathode.
 A potential gradient is applied to accelerate electrons. This
causes electrons to pick much energy to eject more
electrons out of atom.
 This in turn picks up further energy and liberates even more
electrons. Such a progressive process is called avalanche.

65. 65
Merits:
1.significant signals are obtained for a given X-ray intensity
2.Economical
3.Requires less Maintenance
Demerits:
1.Used for measuring low rate X-rays.
2.Low efficiency below 1 Amstrong.
3.Unable to measure energy of ionizing radiation
 Positive ions hit the cathodic half cylinder with enough
energy to eject further more electrons. Therefore avalanche
of electrons incline on wire which is detected as a pulse of
electric current.
 The electric pulse so generated indicates passing of a
charged particle through the tube. This pulse can be read or
measured through a meter.

66. PROPORTIONAL COUNTER
 Its construction is same as that of Geiger tube
counter.
 Gas used - Xenon & Krypton
 The voltage applied is less than that of Geiger
plateau.
 Dead time – (~0.2 µs)
 Sensitivity & efficiency – is comparable with
Geiger tube counter. 66

67. 67
 Proportional counter is a combination of two ionization
regions namely -
a) Ion drift region: region that exist in outer volume
of the chamber.
b) Avalanche region: region that exist in the
immediate vicinity of the anode.
WORKING
 A specialized circuit is connected to tube so that X-rays of
particular energy can be measured.
 Therefore the output of proportional counter apparatus
depends upon incident X-ray intensity.
 Merits: count high rates without error good sensitivity and
efficiency.
 Demerits: expensive complex circuit.

68. SCINTILLATION DETECTOR
 Crystals used – sodium iodide, anthracene,
naphthalene, & p-terphenol in xylene.
 Dead time - very short and this allows for counting of
high rates.
68

69. 69
 Scintillator: a material that exhibits the property of
luminescence on excitement by ionizing radiation.
WORKING
 A scintillator detector is a combination of scintillator with an
electric light sensor such as PMT or photodiode.
 PMT absorbs the light emitted by the scintillator and further
re-emits in the form of electrons.
 The subsequent multiplication of those electrons result in an
electrical pulse which on analysis provides information about
incident radiation particles.
 There are different scintillation materials available such as
sodium iodide, anthracene and naphthalene etc.
 A scintillator counter possesses many advantages such as
resolution of gamma rays for linearity, density, speed,
transparency and also manufacturing cost.

70. SOLID STATE SEMI-CONDUTOR
DETECTOR
 X-ray beams are promoted to conduction bands and
the current which flows is directly proportional to the
incident x-ray energy.
 Main disadvantage – we have to use this detector at
low temperature to minimize the noise & prevent
deterioration in characteristics.
70

71. SEMI CONDUCTOR
DETECTORS
71

72. 72
 WORKING
 These detectors assists in promotion of X-rays through
generated electrons into conduction bands.
 Therefore the current so generated is a direct measurement
of X-rays intensity.
 These semiconductor detectors commonly makes use of
Indium antimonide or Lead telluride or Mercury cadmium
telluride.
 In these detectors the thin layer of p-type of semiconductor is
kept over the n-type surface to make a diffused p-n junction.
 The p-type surface is exposed to radiation which generates
hole and electron pairs.

73. 73
 These holes and electron pairs are separated by
internal field existing on p-n junction.
 As a result voltage is generated. This assembly of
semiconductor is arranged into a vacuum bottle
cooling unit.
 The cooling is done through liquid nitrogen or Joule
Thomson coolers of compressed nitrogen gas or
liquid helium.

74. X-RAY CRYSTALLOGRAPHY
• X-ray crystallography is a technique used for determining
the atomic and molecular structure of a crystal, in which
the crystalline atoms cause a beam of incident X-rays to
diffract into many specific directions.
• By measuring the angles and intensities of these
diffracted beams, a crystallographer can produce a
three-dimensional picture of the density of electrons
within the crystal. From this electron density, the mean
positions of the atoms in the crystal can be determined,
as well as their chemical bonds, their disorder, and
various other information.
74

75. • This method determines the size of atoms, the
lengths and types of chemical bonds, and the
atomic-scale differences among various
materials, especially minerals and alloys.
• The method also revealed the structure and
function of many biological molecules, including
vitamins, drugs, proteins and nucleic acids such
as DNA.
75

76. ELEMENTARY
CRYSTALLOGRAPHY
 In Solids, atoms, ions or molecules are held by strong
forces & are arranged in fixed and ordered positions.
 Solids can be divided into 2 classes :-
a) Crystalline Solids - atoms are arranged in a definite
pattern, have regular geometry. Eg:- NaCl ,Kcl.
b) Amorphous Solids – the atoms are not arranged in a
definite pattern, no regular geometry, Liquids at all
temperature. Eg:- glass,rubber,plastic,etc.
76

77. SL NO AMORPHOUS CRYSTALLINE
1) GEOMETRY No regular geometry Regular geometry
2) MELTING POINT No sharp M.P Sharp M.P
3) ISOTROPHY AND
ANISOTROPHY
Isotropic anisotropic
77

78.  CRYSTAL - a solid whose atoms or ions are
arranged in a periodic array.
 Important property of Crystal are :-
a. Interfacial angles.
b. Plane of symmetry – axis of symmetry
plane of symmetry and
center of symmetry.
78

79. LATTICE CONCEPTS
 Crystal /Space Lattice – Representation of
crystal structure as an array of points in space. If
in actual crystal we replace all the atoms or
groups of atoms or ions with structural unit, by
points we get a 3-D network of points, designated
as lattice.
 Unit cell – It is the smallest repeating unit in
space lattice which when repeated over & over
results in a crystal of given substance.
The fundamental elementary pattern of minimum
number of atoms, molecules which represent fully all
the characteristics of the crystal. 79

80. 80

81. EX : NaCl crystal
81

82. Unit Cell Dimensions:
 Unit cell can be represented by 3 vectors a, b, c with
angles ,  & .
 a, b and c are the unit cell edge lengths
 α, β and γ are the angles ( between a, b and c, etc.)
82

83. THE SEVEN CRYSTAL SYSTEMS :- based on
crystallographic axes, selective length of axes & angles of
inclination between axes, the crystals are classified as
follows:-
83

84. 84

85. EXAMPLES
1. Cubic – NaCl , CaF2 .
2. Tetragonal – NiSO4, SnO2 .
3. Orthorhombic – KNO3 , BaSO4 .
4. Monoclinic – Na2SO3 , FeSO4 .
5. Triclinic – CuSO4, K2Cr2O7 .
6. Rhombohedral – CaSO4.
7. Hexagonal – SiO2, AgI.
85

86. BRAVAIS LATTICES
 French scientist Auguste Bravais demonstrated in
1850 that the internal structures of crystals are of 14
basic arrangements i.e., there are 14 ways of
arranging the points in space.
 In case of cubic system they are three Bravais lattices
each of which has same collection of symmetry
element at the lattice point.
 They describe the geometric arrangement of the
lattice points, and thereby the translational symmetry
of the crystal.
86

87.  Simple cubic(P) – One lattice point at each of the
eight corners of unit cell.
 Face centered cubic (F) - One lattice point at each
of the eight corners & one at the corner of each of the
six faces of unit cell
87

88.  Body centered cubic (I) - One lattice point at each
of the eight corners & one at the center of the body of
cell.
 End centered (C)- In which the corners of the cell
and the intersections of the face diagonals of two
opposite faces are occupied by same type of atom.
88

89. 89

90. 90

91. MILLER INDICES
 Miller Indices are the reciprocals of the fractional
intercepts (with fractions cleared) which the plane
makes with the crystallographic x,y,z axes of the
three nonparallel edges of the unit cell.
 Miller indices are used to specify the crystal
orientation of solids.
 Thus, miller indices are the three numbers (h, k, l)
which designate a plane in a crystal.
 Spacing between planes in a cubic crystal is given
as,
91

92.  where dhkl = interplanar spacing between
planes with Miller indices h,k,and l.
 a = lattice constant (edge of the cube)
 h, k, and l = Miller indices of cubic planes
being considered.
92

93.  The directions of the lattice vectors
a, b and c are first identified as the
lattice axes. The units of a, b and c
are the number of lattice points, for
example, the first lattice point lying
on the a axis has a value for a of 1.
 Having identified the plane of atoms
of interest, the points of intersection
of this plane with the lattice axes are
located. The reciprocals of these
values are taken to obtain the Miller
indices. The planes are then written
in the form (h k l) where h = 1/a, k =
1/b and l = 1/c.
93

94.  Consider the x, y, z axes with the dots representing atoms in a
single-crystal lattice.
 A plane with intercepts 4, 2, 3. 94

95.  To determine the Miller indices, the intercepts on the
three axes were found.
 The intercepts are: x = 4, y = 2, and z = 3.
 Then the reciprocals are taken, i.e., ¼, ½ ,1/3 and
finally these fractions are reduced to the smallest
integers, i.e., 3, 6, 4 by multiplying by 12.
 These are the Miller indices represented as (364).
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96. APPLICATIONS OF X-RAY
DIFFRACTION
• Identification of single phase materials-Minerals, chemical
compounds , ceramics.
• Identification of multiple phases in microcrystalline
mixtures(rocks).
• Determination of crystallite size and shape.
• Crystallographic structural analysis and unit cell calculation for
crystalline materials.
• Particle size determination, Spot counting methods,
Broadening of diffraction lines.
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APPLICATIONS OF XRD
1. Structure of crystals
2. Polymer characterization
3. State of anneal in metals
4. Particle size determination
a) Spot counting method
b) Broadening of diffraction lines
c) Low-angle scattering
5.Applications of diffraction methods to complexes
a)Determination of cis-trans isomerism
b)Determination of linkage isomerism
6.Miscellaneous applications

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1.STRUCTURE OF CRYSTALS
 a-x-ray pattern of salt Nacl b-x-ray pattern of salt Kcl c-
x-ray pattern of mixture of
 Nacl &Kcl d-x-ray pattern of a powder mixed crystal of
Nacl & Kcl
2.POLYMER CHARACTERISATION
Determine degree of crystanillity
Non-crystalline portion scatters x-ray beam to give a
continuous background(amorphous materials)
Crystalline portion causes diffraction lines that are not
continuous.(crystalline materials)

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3) State of anneal in metals: XRD is used to test the metals
without removing the part from its position and without
weakening it.
4.PARTICLE SIZE DETERMINATION
Spot counting method:
v=V.δθ.cosθ/2n
v=volume of individual crystallite
V=total volume irradiated
n=no. of spots in diffraction ring
δθ =divergence of x-ray beam

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MISCELLANEOUS APPLICATIONS
Soil classification based on crystallinity
Analysis of industrial dusts
Assessment of weathering & degradation of minerals
& polymers
Study of corrosion products
Examination of tooth enamel & dentine
Examination of bone state & tissue state
Structure of DNA&RNA

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