X-ray Crystallography(1).pdfhsshsgshwhsghshshshs

X-ray Crystallography
Dr. Md. Abdul Kader
Professor
Department of Pharmacy, RU

Many drugs absorb electromagnetic radiations that help
to determine the quantity and nature of drugs in a
dosage form, in a reaction vessel or in a biological
system.
Radiant energy is the energy transmitted as
electromagnetic radiation. The sun is the most
important source of radiant energy.
Introductions

The wave length of a beam of EMR is the linear distance
measured along the line of propagation, between two
points which are in phase of an adjacent waves. The
wave length is indicated by λ.The unit of wave length is
expressed as Å or angstrom. 1Å = 10-8 cm
Electromagnetic radiation:
It may be described as wave like properties. The following
terms are used to describe EMR-
Wavelength:

The number of cycles occurring per second is called frequency. It is
indicated by nu (ν).
Mathematically,
Nu = C/λ C = velocity of EMR = 2.998 X 108 m/s
Unit=(cycle/sec) or Hz
1 Hz = 1 cycle/second
From equation,
Frequency α 1/wavelength
So, greater the wave length smaller the frequency. Wave length
range of visible light is 3800Å – 7600Å. Thus the corresponding
frequency range of visible light is 7.88 X 108 MHz – 3.94 X 108 MHz.
Frequency

It is the reciprocal of the wave length and is expressed
in per centimeter or cm-1. In other words, it is defined
as the total number of waves which can pass through a
space of 1cm. It is frequently used in IR technique.
Wave number

The total energy in a molecule is the sum of the energies
associated with the transitional, rotational, vibrational and
electronic motion of the molecule, or electrons and nuclei in
the molecule.
That is,
E = Et + Er + Ev + Em
Where,
E = Total energy
Et = Transitional energy
Er = Rotational energy
Ev = Vibrational energy
Em = Electronic energy
Absorption of Radiant Energy

If a large amount / number of energy is absorbed by certain
substances, the bonds of the substance may be ruptured
and new compounds are formed.
Example-
Ergosterol Calciferol
When a molecule absorbs radiant energy an electron or
electrons will be raised to a higher energy level; if the
energy requirement for the transition is equal to the energy
of the incoming photon.
UV

An excited electron returns to the ground state in about
10-4 to 10-8 seconds. Energy is now released to
compensate for the energy absorbed by the system. If
the molecule returns to the ground state by way of a
second excited state energy is released in the form of
heat and light.

It is the experimental science of determining the
arrangement of atoms in the crystalline solids.
Crystallography :

X-ray crystallography is a tool used for
identifying 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, rays measuring the angles
and intensities of these diffracted beams.
X-ray Crystallography

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 can be obtained.

In a single crystal X-ray diffraction
measurement, a crystal is mounted on a
Goniometer. The Goniometer is used to position
the crystal at selected orientations. The crystal
is illuminated with a finely focused
monochromatic beam of X-rays, producing a
diffraction pattern of regularly spaced spots
known as reflections.

In its first decades of use, this method
determined the size of atoms, the length and
differences among various materials. The
method also revealed the structure and
function of many biological molecules
including vitamins, drugs, proteins and
nucleic acids such as DNA. It is still the chief
method for characterizing the atomic
structure of new materials.

An ideal crystal is a regular polyhedral solid
bounded by plane faces which represents an
extended array of atoms arranged in a definite order
in all directions. Such a crystal contains a unit cell
or a unit of structure, repetition of which in three
dimensional pattern produces the crystal.
Crystal:

The particles in crystal are arranged in regular patterns that
extend in all directions. The overall arrangement of
particles in a crystal is called the crystal lattice, Space
lattice or Simply lattice.
Crystal lattice:
The simple basic unit or the building block of the crystal
lattice is called the Unit cell.
Unit cell:

(a) relative lengths of the edges along the three axes (a, b, c)
(a) the three angles between the edges (α,β,γ)
Unit cell are categorized by following parameters-

Seven types of Bravis unit cell

There are several properties of X-ray which make it useful for
radiographic inspection. X-ray is the same form of energy as
visible light. Like light it is reflected when it passes through glass;
such as lens or any other medium. Although the properties of X-
ray and visible light are theoretically similar, the differences in
applications make X-ray more convenient to consider it as being
different. It's absorbable effects are quite different from those of
light.
Properties of X-ray

It is invisible to human.
It propagates in straight line in free space.
It is reflected, diffracted and polarized as is light in
special cases.
It propagates at a velocity of 3X 108 m/s as does light.
It consists of transverse electromagnetic vibration.
Some of the important properties of X-ray may be
as follows-

X-ray has energy roughly between 1KeV and 50 MeV.
X-ray can stimulate fluorescence and phosphorescence
in some materials.
Capable of ionizing gases and changing the electrical
properties of some liquids and solids.
Able to damage and kill living cells and produce genetic
mutations.
Properties of X-rays-

X-ray crystallography is a tool used for identifying the atomic
and molecular structure of a crystal. Atoms and molecules
are arranged internally in an order within a crystal. This inner
structure of crystal (a three-dimensional repeated pattern
called a ‘space lattice’) is responsible for the diffraction of X-
rays.
Principle of X-ray Crystallography
A crystal lattice is considered to be made up of regular layers
or planes of atoms equal distance apart. Since the wave
length of X-rays is comparable to the inter-atomic distance, it
is suggested that crystal can act as grating to X-rays.

Upon impingement, the X-rays are scattered by the
electrons within the atoms making up the space
lattice. As the atoms are regularly arranged in a
repeated pattern, the wave fronts emerging from each
scattering center form a particular pattern.

If the diffracted waves are in the same phase, they reinforce
each other and a series of bright spots are produced on a
photographic plate placed in their path. On the other hand
if the diffracted waves are out of phase, dark spots are
produced on the photographic plate

X-ray diffraction and Bragg`s Law
Diffraction occurs as radiation/waves interact with a regular
structure whose repeated distance is about the same as
wavelength.
X-rays have wavelengths in the order of few angstroms, the same
as typical, interatomic distances in crystalline solids. That means
X-rays can be diffracted from minerals which by definition, are
crystalline and have regularly repeating atomic structure.

When geometric requirements are met, X-rays scattered from
crystalline solid and constructively interfere producing a diffracted
beam. In 1913 W. L. Bragg and W.H. Bragg worked out a
mathematical relation to determine interatomic distances from x-
ray diffraction patterns. This relation is called Bragg`s equation.
They showed that:

(a) the X-ray diffracted from atoms in crystal planes obey the laws
of reflection.
(b) the two rays reflected by successive planes will be in phase if
the extra distance travelled by the second ray is an integral
number of wavelengths.

Derivation of Bragg`s Law
Figure: Reflection of X-rays from two different planes of a
crystal

Derivation of Bragg`s Law
Figure shows a beam of X-rays falling on the crystal surface. Two
successive atomic planes of the crystal are shown separated by a
distance d. Let the X-rays of the wavelength λ strike the first plane
at an angle θ. Some of the rays will be reflected at the same angle.
Some of the rays will penetrate and get reflected from the second
plane. These rays will reinforce those reflected from the first plane
if the extra distance travelled by them (CB + BD) is equal to
integral number, n, of wavelengths. That is,

nλ = CB + BD --------------------- (i)
Derivation of Bragg`s equation
CB = BD = AB sin θ --------------------- (ii)
Geometry shows that
From (i) and (ii) it follows that
nλ = 2AB sin θ
nλ = 2d sin θ
or
This is known as
the Bragg equation

Application of Bragg`s Law
(a) Solving Bragg`s equation gives the d-spacing between crystal
lattice planes of atoms that produce constructive interference. A
given unknown crystal is expected to have many rational planes
of atoms in its structure, therefore the collection of reflections of
all the planes can be used to uniquely identify an unknown crystal.
(b) In the case of X-ray fluorescence spectroscopy crystals of
known d-spacing are used as analyzing crystals in the
spectrometer.

Measurement of the angle of diffraction diffraction
(1) The Rotating Crystal Method:
A beam of X-rays of known wavelength fall on a face of
the crystal mounted on a graduated turn table. The
diffracted rays pass into the ionization chamber of the
recorder. Here they ionize the air and a current flows
between the chamber wall and an electrode inserted in it
which is connected to an electrometer.

Rotating Crystal Method:
Figure: Rotating crystal method to determine the angle
of diffraction θ

The electrometer reading is proportional to the intensity
of X-rays. As the recorder along with the crystal is
rotated, the angles of maximum intensity are noted on
the scale. Thus values of θ for n = 1, 2, 3, etc. are used
to calculate the distance d between the lattice planes
parallel to the face of the crystal.
Rotating Crystal Method:

(2) The Powder Method:
The rotating crystal method could only be used if a
single undistorted crystal is available. To overcome this
limitation, the powder method was devised. Here, the
crystalline material contained in a capillary tube is
placed in the camera containing a film strip. The

Figure: Powder method

The sample is rotated by means of a motor. The X-rays pass
through the gap between the ends of the film. The powdered
sample contains small crystals arranged in all directions. Some of
these will reflect X-rays from each lattice plane at the same time.
The reflected X-rays will make an angle 2θ with the original
direction. Hence on the photo are obtained lines of constant θ.
From the geometry of the camera, θ can be calculated for
different crystal planes.

(1) It should have a characteristic geometrical shapes.
(2) The atoms, molecules or ions should be arranged in
a regular repeating three dimensional pattern.
(3) It should be made up of regular layer or planes of
atom separated by equal distance from one to another.
The essential requirements of a material for
scattering X-ray?

(4) It should have the ability for penetrating of light
or radiation.
(5) The crystal must follow the Bragg’s equation.
Essential requirements for scattering X-rays

Crystal lattice consists of unit cells arranged in
parallel planes. Thus each crystal plane lies parallel
to the crystal face as also to the unit cell face. These
planes cut the three axes along the three
crystallographic axes (OX, OY, OZ).
Miller indices:

A given crystal plane could be described in terms of
intercepts along the axes (law of Rational
intercepts). The reciprocals of these intercepts are
small whole numbers. These numbers are called
Miller indices according to the name of British
scientist W. H Miller. Thus Miller indices of a plane
may be defined as “the reciprocals of the intercepts
which the plane makes with the axes.
Miller indices:

Solution:
The unit cell intercepts are a, b, c
The intercepts of given plane are 2a, 3b, 2c
The lengths of the intercepts in terms of unit cell
intercepts are 2, 3, 2
Math: Determine the Miller indices for a plane when
intercepts along the axes are 2a, 3b and 2c.

The reciprocals are 1/2, 1/3, 1/2
Clear fractions by multiplying with 6, gives the whole
number 3, 2, 3
Thus the Miller indices of given plane are (3,2,3)
Math:

A perfect crystal is one in which all the atoms or ions
are lined up in a precise geometric pattern. But
crystals are never actually perfect. The real crystals
that are found in nature or prepared in the laboratory
always contain imperfections in the formation of the
crystal lattice. These crystal defects can profoundly
affect the physical and chemical properties of a
solid. The various types of crystal defects are-
Crystal defects:

When a crystal site be rendered vacant by
removal of a structural unit in the lattice, the
defect is referred to as the vacancy defect. In an
ion crystal, a cation and an anion may leave the
lattice to cause two vacancies. Such a defect
which involves a cation and an anion vacancy in
the crystal lattice is called a Schottky defect.
This defect is found in the crystals of NaCl and
CsCl.
1. Vacancy defect:

Fig: Schottky defect (left) & interstitial defect (right)

When an ion leaves its regular sites to occupy a position in
the space between the lattice sites, this causes a defect
which is known as interstitial defect or Frenkel defect.
Ordinarily, the cation moves as it is smaller than the anion
and can easily fit into the vacant spaces in the lattice. Thus
in AgCl crystal, Ag+ ion occupies an interstitial position
leaving a vacancy or hole at the original site.
2. Interstitial defect:

This defect arises due to the incorporation of foreign atoms
or ions in regular lattice sites or interstitial sites. When
foreign particles are substituted for normal lattice particles,
it is called substitution impurity.
2. Impurity defect:
When foreign particles are trapped in vacant interstitial
spaces, it is called interstitial impurity. Both types of
impurities can have drastic effect on the properties of solid

Two hazards are involved in working with X-rays.
Such hazards can be lethal but fortunately the
manufacturers of modern day equipment have built in many
protective features and thus risks from high voltages are
virtually non existent with proper use of the equipment.
1. High voltage associated with X-ray generators (20 to 60
kv):
Describe the hazards involve in working with X-rays.
or How X-rays can safely be used?

From sufficient exposure, somatic injuries include leukemia
and other malignant diseases, ocular lens opacities,
impaired fertility and shortening of life.
2. X-rays themselves:
The routine use of equipment allows many opportunities for
oversight on the part of operator which results in radiation
exposure. This can be scattered radiation throughout the
room as well as from the direct X-ray beam itself. It is of two
types.
a. Somatic injury:

From sufficient exposure, genetic injury include- various
types of diseases for individuals. The injury of the offspring
of the irradiated individuals may not become apparent for
many generations. Constant awareness and concerns of the
operator for the safety of himself and other is essential.
b. Genetic injury:

(i) Convenient radiation monitoring device in the form of "r-
meters" are available commercially and should be used to
monitor the laboratory routinely.
(ii) It is also advisable for operating personnel to wear a film
badge with a small plastic device clipt with clothing and
which contains a strip of unexposed film. This film usually a
standard dental pack that is replaced and developed
regularly, providing evidence of accumulated exposure.
Protection:

(i) The technique may be applied to materials in any physical state i.e.,
solid, liquid or gas.
(ii) This provides analysis of chemical elements rather than
compounds.
(iii) It is applicable to all elements except those of low atomic number.
They are largely insensitive to the combination state of an elements.
Advantages and disadvantages of X-ray absorption
method:
Advantages:
Disadvantages:

X-ray diffraction methods are generally used for
investigating the internal structure. The application can be
summarized by following points-
Where it has been used to measure the size of the crystal
plane, the patterns obtained are characteristics of the
particular compound from which the crystal is formed. As
for example- NaCl, KCl etc.
Application of X-ray crystallography:
(i) Determination of the structure of crystal:

Powder method can be used to determine the degree of
crystallinity of the polymer.
State property of metals can be determined by X-ray
diffraction method.
ii. Polymer characterization:
iii. State property of metals:

Liquid Crystal:
Some organic solids having long rod-like molecules do not
melts to give the liquid substance directly. They instead
pass through an intermediate state called the liquid crystal
state, often referred to as the liquid crystal. Thus the
liquid crystal state is intermediate between the liquid
state and the solid state. One such substance that forms
liquid crystal is p-ozoxyanisole.
Solid state Liquid state
Liquid crystal

The liquid crystals have a structure between that of a
liquid and that of crystalline solid. In a liquid, the
molecules have a random arrangement and they are able
to move past each other. In a solid crystal, the molecules
have an ordered arrangement and are in fixed positions. In
a liquid crystal, however, the molecules are arranged
parallel to each other and can flow like a liquid.
Thus the liquid crystals have the fluidity of a liquid and
optical properties of solid crystals.

Liquid Crystal Types:
According to their molecular arrangement, the liquid
crystals are classified into three types -
Nematic liquid crystals:
They have molecules parallel to each other like soda
straws but they are free to slide or roll individually.

Smectic liquid crystals:
The molecules in this type of crystal are also parallel but
these are arranged in layers. The layers can slide past
each other.
Cholesteric liquid crystals:
As in nematic crystals, in this type of crystal the molecules
are parallel but arranged in layers. The molecules in
successive layers are slightly rotated with respect to the
layers above and below so as to form a spiral structure.

Applications of Liquid Crystals:
On account of their remarkable optical, electrical and
magnetic properties, liquid crystals find several practical
applications. Liquid crystals are using extensively in
pharmaceutical industries. These are listed are below -
1. Number displays: When a thin layer of nematic liquid
crystal is placed between two electrodes and an
electric field is applied, the polar molecules are
pulled out of alignment. This causes the crystal to be
opaque.

Transparency returns when electrical signal is
removed. This property is used in the number
displays of digital watches, electronic calculators
and other instruments.
Liquid crystal displays are common in
oscillaographic systems, television displays using
L.C. screens etc. Cholesteric liquid crystals have
also been used for novelty items such as toys and
decorative materials.

2. Monitoring body temperature: Like the solid crystals,
liquid crystals can diffract light. Only one of the
wavelengths of white light is reflected by the crystal
which appears coloured. As the temperature changes,
the distance between the layers of molecules also
changes. Therefore, the colour of the reflected light
changes correspondingly. These cholesteric liquid
crystal undergoes a series of colour changes with
temperature. These crystals are used in indicator tapes
to monitor body temperature or to spot areas of
overheating in mechanical systems.

3. Research at a number of industries, universities
and government laboratories began to focus on their
applications, which exploited the electro-magneto-
optic characteristics and photoelectric properties of
nematic and cholesteric type liquid crystals.
Cholesteric liquid crystal substances, when applied
to the surface of the skin, have been used to locate
veins, arteries, infections, tumors and the fetal
placenta which are warmer than the surrounding
tissues.

4. Nematic liquid crystal are useful research tools in
the application of magnetic resonance. Molecules that
are dissolved in nematic liquid crystal solvents give a
very highly resolved NMR spectrum exhibiting
intermolecular dipole-dipole fine structures. Analysis
of the spectra of molecules in liquid crystal solvents
yield information regarding the anisotropy of chemical
shifts, direct magnetic dipole-dipole interaction,
indirect spin-spin couplings, bond angles, bond
lengths, molecular order and relaxation process.

4. Liquid crystals have been used in
chromatographic separations as solvents to direct
the course of chemical reactions and to study
molecular arrangements and kinetics and as
anisotropic host fluid for visible, UV and IR
spectroscopy of organic molecules.
5. Liquid crystals are widely used in cosmetic
industry in manufacturing of liquid crystal makeup
removers, lipsticks and lip glosses containing
cholesteric liquid crystals.

8. Liquid crystal polymers also gained much interest
on industrial applications. Polyester liquid crystals
were developed for fire resistant, and are used as
coating for multifibre, optical cables due to good
surface roughness, low coefficient of friction.
Polyesters are used for moulding with improved
elastic modulus.

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