CHEMISTRY OF SOLID STATE
SYLLABUS
UNIT III: CHEMISTRY OF SOLID STATE II: DIFFRACTION METHODS
Band theory of solids- non-stoichiometry- point defects – linear defects- effects
due to dislocations-electrical properties of solids-conductor, insulator,
semiconductor-intrinsic-impurity semiconductors-optical properties-lasers and
phosphors-elementary study of liquid crystals.
Difference between point group and space group – screw axis – glide plane -
symmetry elements –relationship between molecular symmetry and
crystallographic symmetry – The Concept of reciprocal lattice – X-ray diffraction
by single crystal – rotating crystal – powder diffraction. Neutron diffraction:
Elementary treatment – comparison with X-ray diffraction. Electron diffraction-
Basic principle. Crystal Growth methods: From melt and solution (hydrothermal,
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UNIT III: CHEMISTRY OF SOLID STATE II: DIFFRACTION METHODS
1. BAND THEORY OF SOLIDS
According to band theory the energy spectrum of materials contains
conduction band and valence band. On the basis of distance between conduction
band and valence band, the materials are classified in to three categories.
1. Conductors:
If there is no energy gap between conduction band and valence band,
such materials are called conductors.
Examples: metals
2. Insulators:
Those materials in which the energy gap between conduction band and
valence band is very high , are called insulators.
3. Semiconductors:
If the gap between conduction band and valence band is very low , the
materials are called semiconductors.
Example: germanium and silicon
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2. NON-STOICHIOMETRY
Definition:
Compounds with non- integer values of atomic composition are called
non- stoichiometric compounds.
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Example : Ni 0.999O
Origin of non- stoichiometry
Impurities are the main reason
For example NaCl heated in Na vapour results Na 1.5 Cl
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Stoichiometric Defects
The compounds in which the number of positive and negative ions are exactly in
the ratios indicated by their chemical formulae are called stoichiometric
compounds. The defects do not disturb the stoichiometry (the ratio of numbers of
positive and negative ions) are called stoichiometric defects. These are of
following types,
(a) Interstitial defect: This type of defect is caused due to the presence of ions in
the normally vacant interstitial sites in the crystals.
(b) Schottky defect: This type of defect when equal number of cations and anions
are missing from their lattice sites so that the electrical neutrality is maintained.
This type of defect occurs in highly ionic compounds which have high co-
ordination number and cations and anions of similar sizes. e.g., NaCl, KCl, CsCl
and KBr etc.
(c) Frenkel defect: This type of defect arises when an ion is missing from its
lattice site and occupies an interstitial position. The crystal as a whole remains
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electrically neutral because the number of anions and cations remain same. Since
cations are usually smaller than anions, they occupy interstitial sites. This type of
defect occurs in the compounds which have low co-ordination number and cations
and anions of different sizes. e.g., ZnS, AgCl and AgI etc. Frenkel defect are not
found in pure alkali metal halides because the cations due to larger size cannot get
into the interstitial sites. In AgBr both Schottky and Frenkel defects occur
simultaneously.
CRYSTAL IMPERFECTIONS( CRYSTAL DEFECTS)
Any deviation in a crystal from a perfect periodic lattice structure is called
crystal defects. The three types of defects are
1. Point defects 2. Line defects( dislocations) 3. Surface defects(plane defects)
3. POINT DEFECTS
1. POINT DEFECTS
The deviation in a crystal,
from a perfect periodic lattice structure is localised in the vicinity of only few
atoms, it is called point defects. The different point defects are
1.1Vacancies
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1.2Interstial defects
1.3Frenkel defects (Vacancies and interstitial
1.4Schotky defects
1.5Substitutional defects
Stoiciometric defects:
1.3 FRENKEL DEFECTS (VACANCIY AND INTERSTITIAL DEFECTS):
When a missing atom, occupies the interstitial position, the defect caused is
known as Frenkel defects. This is most common in ionic crystals in which the
positive ions are smaller in size.
interstial
Fe 2+ O 2-Fe 2+ O 2-Fe 2+ O 2-
Fe 2+ vacancy
Fe 2+ O2-O 2-Fe 2+ O 2-
Fe 2+ O 2-Fe 2+ O 2-Fe 2+ O 2-
Number of Frenkel defects in a crystal can be calculated by the formula
N = √ N N i√e−EKT
Where N total number of atoms and Ni number of interstitial positions
Derivation:
Let the energy required to displace an atom, from its proper position to an
interstitial position be E1. If there are N atoms and Ni interstitial positions , then
the number of ways in which ‘n’ Frenkel defects can be formed is given by
W = N !
n ! (N−n )!× ¿ !
n ! (¿−n )!
The change in Helmholtz free energy by the creation of ‘n’ Frenkel defects is
∆A = nE – TS
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= nE – T [ kln W]
= nE – T k ln [ N !
n ! (N−n )!× ¿ !
n ! (¿−n )! ]
= nE – T k [ ln N! + ln Ni! - 2 ln n! – ln( N-n)! – ln( Ni – n) !]
Using Sterling ‘s approximation ln N! = N ln N - N we get
∆A = nE – T k{[ N ln N – N] +[Ni ln Ni – Ni] - 2 [ nln n – n] –[ (N – n) ln( N-
n)] –
(N – n) ] – [( Ni – n) ln( Ni – n) - ( Ni – n) ] }
= nE – T k{[ N ln N – N +Ni ln Ni - Ni - 2 nln n +2 n – (N – n) ln( N-n)+
(N – n) – ( Ni – n) ln( Ni – n) + ( Ni – n) }
= nE – T k{[ N ln N – N +Ni ln Ni - Ni - 2 nln n +2 n – (N – n) ln( N-n)+
(N – n) – ( Ni – n) ln( Ni – n) + ( Ni – n) }
= nE – T k{ N ln N +Ni ln Ni - 2 nln n – (N – n) ln( N-n)– ( Ni – n) ln( Ni – n)
}
Differentiating with respect to ‘n’ at constant temperature,
¿ ) T = E - T k { -2 [n (1n) + ln n] - [ ( N-n) ( −1
N−n¿+ ln (N-n) (0-1)]
- [ ( Ni – n) × ( −1
(¿ – n)¿ + ln ( Ni – n) ( 0-1)}
= E - T k { -2 -2 ln n] - [ -1 - ln (N-n) ] -[- 1- ln ( Ni – n) }
= E - T k { -2 -2 ln n] + 1 + ln (N-n) + 1+ ln ( Ni – n) }
= E - T k { -2 ln n + ln (N-n) + ln ( Ni – n) }
= E - T k { ln (1n2 ) + ln [ (N-n) × ( Ni – n) ] }
= E - T k { ln(N−n)×(¿ – n)
n2 }
When equilibrium is attained, the Helmholtz free energy is constant and its first
derivative is equal to zero. i. e ¿ ) T = 0
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∴0 = E - T k { ln(N−n)×(¿ – n)
n2 }
E = T k { ln(N−n)×(¿ – n)
n2 }
ET k = { ln
(N−n)×(¿ – n)n2 }
When N >>n, N- n ≈ N similarly, When Ni >>n, Ni- n ≈ Ni
Therefore the above equation becomes, ET k = { ln
(N )×(¿)n2 }
Taking exponential on both sides,
eE
T k = N ∋ ¿n2 ¿
n2 = NNie−ET k
∴ n = (NNie−ET k ) ½
This is the expression for the number of ways of forming the defects
SCHOTKY DEFECTS
When a positive as well as negative ions of a crystal are missing, the defect
is known as Schotky defects.
In Schotky defect the displaced atom migrates in successive steps
eventually settles at the surface. Since the number of missing positive ions and
negative ions is same, the crystal remains as neutral
Na + Cl-
Na + Cl- Na + Cl- Na + Cl–
Na + Cl- Na + Na + Cl-
Na + Cl- Cl- Na + Cl-
Na + Cl- Na + Cl- Na + Cl-
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Number of Schotky l defects in a crystal can be calculated by the formula
n = N×e−E2 KT
Where N total number of atoms .
Derivation:
Suppose a crystal contains N atoms and ‘n’Schotky defects are produced
by removing ‘n’ cations and ‘n’ anions from the crystal. Let the energy required
to displace an atom, from its proper position to an interstitial position be E1. The
number of ways in which ‘n’ schotky defects can be formed is given by
W = N !
n ! (N−n )!× N !
n ! (N−n )!
The change in Helmholtz free energy by the creation of ‘n’ Frenkel defects is
∆A = nE – TS
= nE – T [ kln W]
= nE – T k ln [ N !
n ! (N−n )! ] 2
= nE – 2T k [ ln N! - ln n! – ln( N-n)! ]
Using Sterling ‘s approximation ln N! = N ln N - N we get
∆A = nE– 2T k{[ N ln N – N] - [ nln n – n] –[ (N – n) ln( N-n)] – (N – n) ]
= nE – 2T k{[ N ln N – N - nln n + n – (N – n) ln( N-n)+ (N – n)
= nE – 2T k{[ N ln N – N - nln n + n – (N – n) ln( N-n)+ (N – n) }
= nE – 2T k{ N ln N - nln n – (N – n) ln( N-n) }
Differentiating with respect to ‘n’ at constant temperature,
¿ ) T = E - 2T k { - [n (1n) + ln n] - [ ( N-n) ( −1
N−n¿+ ln (N-n) (0-1)]
= E - 2T k { -1 - ln n] - [ -1 - ln (N-n) ]
= E - 2 T k { -1 - ln n] + 1 + ln (N-n)
= E - 2T k { - ln n + ln (N-n) }
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= E - 2T k { ln(N−n)n }
When equilibrium is attained, the Helmholtz free energy is constant and its first
derivative is equal to zero. i. e ¿ ) T = 0
∴0 = E - 2T k ln(N−n)n
E = 2T k ln(N−n)n
ET k = 2 ln(N−n)
n
When N >>n, N- n ≈ N
Therefore the above equation becomes, E2T k = ln(N )
n
Taking exponential on both sides,
eE
2 T k = Nn
∴ n = N ×e−E2 T k
This is the expression for the number of ways of forming the defects
4. linear defects
5. effects due to dislocations
6. electrical properties of solids
7. CONDUCTOR, INSULATOR, SEMICONDUCTOR
1. Conductors:
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If there is no energy gap between conduction band and valence band,
such materials are called conductors.
Examples: metals
2. Insulators:
Those materials in which the energy gap between conduction band and
valence band is very high , are called insulators.
3. Semiconductors:
If the gap between conduction band and valence band is very low , the
materials are called semiconductors.
Example: germanium and silicon
8.INTRINSIC SEMICONDUCTORS:
A semi conductor which is pure and contains no impurity is known as intrinsic
semiconductor.
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9. IMPURITY SEMICONDUCTORS
Extrinsic Semiconductors:
A semiconducting material in which, the charge carriers originate from
impurity atoms added to the material, is called extrinsic semiconductor or
impurity semiconductor.
Theses are divided in to two types.
1 n- type semi conductor:
Pentavalent elements such as P, As, Sb , have five electrons in their
outermost orbits. When any one such impurity is added to the intrinsic semi
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conductor, four electrons are engaged in covalent bonding with four
neighbouring semi conductor atoms and the fifth electron is free.
Free electron
2 p- type semi conductor:
Trivalent elements such as Al, Ga or In have three electrons in their outer
most orbits. When such impurity is added to the intrinsic semi conductor, all the
three electrons are engaged in covalent bonding with three neighbouring semi
conductor atoms and creating a hole ( vacant electron site) on the semiconductor
atom.
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OPTICAL PROPERTIES
The optical properties of semiconductors have been studied extensively for
their relevance to applications such as lasers, light-emitting diodes, and solar cells
LASERS AND PHOSPHORS
The term "laser" originated as an acronym for "Light Amplification by
Stimulated Emission of Radiation"
A laser is a device that emits light through a process of optical amplification
based on the stimulated emission of electromagnetic radiation.
Types
Solid-state lasers
Solid-state lasers use a crystalline or glass rod which is "doped" with ions that
provide the required energy states.
For example, the first working laser was a ruby laser, made
from ruby (chromium-doped corundum).
The population inversion is actually maintained in the dopant.
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Neodymium is a common dopant in various solid-state laser crystals,
including yttrium orthovanadate (Nd:YVO4), yttrium lithium fluoride (Nd:YLF)
and yttrium aluminium garnet (Nd:YAG).
Ytterbium, holmium, thulium, and erbium are other common "dopants" in solid-
state lasers.
Gas lasers
helium–neon laser (HeNe)
carbon dioxide (CO2) lasers
Chemical lasers
hydrogen fluoride laser
deuterium fluoride laser
RUBY LASER
A ruby laser consists of a ruby rod that must be pumped with very high energy,
usually from a flashtube, to achieve a population inversion.
The rod is often placed between two mirrors, forming an optical cavity, which
oscillate the light produced by the ruby's fluorescence, causing stimulated
emission.
The ruby laser is a three level solid state laser.
The active laser medium (laser gain/amplification medium) is a synthetic ruby rod
that is energized through optical pumping, typically by a xenon flashtube.
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SEMI CONDUCTOR LASERS:
They consist of complex multi-layer structures
GaAs LASER:
The gallium Arsenide laser is designed in such a way that a piece of N-type Gallium Arsenide material is taken and a layer of natural gallium aluminum arsenide material is
pasted, The third layer of p-type gallium arsenide material is pasted over that.
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Uses:
All these lasers can produce high powers in the infrared spectrum at 1064 nm.
They are used for cutting, welding and marking of metals and other materials, and
also in spectroscopy and for pumping dye lasers
PHOSPHOR
A phosphor, is a substance that exhibits the phenomenon of luminescence;
it emits light when exposed to some type of radiant energy.
The term is used both for fluorescent or phosphorescent substances which glow on
exposure to ultraviolet or visible light,
The energy from the lasers' light activates the phosphors, which emit photons,
producing an image.
Phosphors are usually made from a suitable host material with an added activator.
The best known type is a copper-activated zinc sulfide and the silver-activated zinc
sulfide (zinc sulfide silver).
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ELEMENTARY STUDY OF LIQUID CRYSTALS.
Solids yield a viscous cloudy liquids at a temperature known as transition
point. If the temperature is increased beyond the transition point, the cloudiness
disappear at the temperature called melting point
Between transition point and melting point the cloudy liquid shows double
refaction. This state is called mesomorphic state. And the compounds in this state
are called liquid crystals.
SMECTIC TYPE CRYSTALS WITH EXAMPLES
1.The word "smectic" originates from the Latin word having soap-like properties
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2.There are two phases in smectic type. They are named as smectic A and smectic
C
3. The smectic A phase has molecules organized into layers.
4. In the smectic C phase , the molecules are tilted inside the layers.
5. The layers can slide over one another .
Example:
Smectic phase Transition
temperature
Melting
temperature
Ethyl – p- azoxy benzoate 114K 121 K
Ethyl – p- azoxy cinnamate 140K 249 K
NEMATIC TYPE CRYSTALS WITH EXAMPLES
. 1.The word nematic comes from the Greek which means "thread".
2. In a nematic phase, organic molecules have no positional order,
3. The molecules are free to flow
4. Nematics are uniaxial:
5. Nematics have fluidity similar to that of ordinary liquids
6. They can be easily aligned by an external magnetic or electric field.
Example:
Nematic phase Transition
temperature
Melting
temperature
p- azoxy anizole 390K 410 K
p- azoxy phenetole 410K 440K
CHOLESTERIC TYPE CRYSTALS WITH EXAMPLES
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They exhibit the unique property that they reflect circularly polarized light
when it is incident along the helical axis
Example: cholestryl benzoate
DIFFERENCE BETWEEN POINT GROUP AND SPACE GROUP
Point groups and space groups:
There can be 32 different combination of elements of symmetry of a
crystal. These are called point groups. Some of the systems have been grouped
together, so that we have only 7 different categories.
The 32 point groups, further produce 230 space groups.
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SCREW AXIS
In crystallography, a screw axis symmetry is a combination of rotation about
an axis and a translation parallel to that axis which leaves a crystal unchanged.
Diagram:
Figure 1 represents the normal 2-fold rotation and fig.2 represents a 2-fold
screw axis in which rotation through 180 o , followed by t/2 transition, parallel to
the axis. This is expressed as 2t screw axis.
Similarly, a 3-fold axis generate two screw axis namely 31 and 32 . The
former represents rotation through 120 followed by translation t/3 and the latter
corresponds to rotation through 240 o followed by translation through 2t/3.
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Similarly 4-fold axis generates three screw axis and 6- fold axis generates five
screw axis.
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GLIDE PLANE
A glide plane is defined as an operation which involves a translation t/2
parallel to the reflecting plane followed by reflection across the plane. Here t is
the distance between the successive atoms.
or
In geometry and crystallography, a glide plane (or transflection) is a
symmetry operation describing how a reflection in a plane, followed by a
translation parallel with that plane, may leave the crystal unchanged. Glide
planes are noted by a, b or c, depending on which axis the glide is along.
Diagram:
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The glide planes are further classified in to three types
1.Axial glides: These are planes having glide component parallel to the
crystallographic axis a,b and c and with length equal to a/2, b/2 and c/2. They are
denoted as a-glide, b-glide and c-glide.
2.Diagonal glides: These correspond to the planes whose glide component is the
vector sum of any two of the vectors a/2,b/2 and c/2. It is denoted by n.
3.Diamondglides:These are denoted by the symbol d and corresponds to the
planes, whose glide component is the vector sum of any of the two vectors a/4, c/4
and d/4.
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16.SYMMETRY ELEMENTS
There are three types of symmetry
1. Plane of symmetry:
If an imaginary plane, which divides the crystal into two parts, such that
one is the exact mirror image of the other, exists in a crystal , it is said to have
plane of symmetry.
a. Rectangular(vertical or horizontal) plane of symmetry
b. Diagonal plane of symmetry
2. Axis of symmetry:
If a crystal possesses an imaginary line, about which the crystal may be rotated
such that it presents similar appearance, then , it is said to have axis of symmetry.
If the similar appearance is repeated after an angle of 180 o , the axis is called
2- fold axis of symmetry. If it appears after 120 ,90, 60 o, it is called 3- fold axis
of symmetry, 4-fold and 6-fold axis of symmetry respectively. In general if a
rotation through an angle of 360n , brings the molecule to similar appearance, then
the crystal is said to have n – fold axis of symmetry
3. Centre of symmetry
Centre of symmetry of a crystal is such a point that any line drawn
through it intersects the surface of the crystal at equal distances in both
directions.
Elements of symmetry
The total number of planes, axes and centre of symmetries possessed by a
crystal is termed as elements of symmetry.
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Elements of symmetry in a cube:
Rectangular planes of symmetry = 3
Diagonal planes of symmetry = 6
2- fold axis of symmetry = 6
3- fold axis of symmetry = 4
4- fold axis of symmetry = 3
Centre of symmetry = 1
Total = 23
17.relationship between molecular symmetry and crystallographic symmetry
18.THE CONCEPT OF RECIPROCAL LATTICE
RECIPROCAL LATTICE:
, the reciprocal lattice represents the Fourier transform of another lattice (usually
a Bravais lattice).
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In normal usage, the initial lattice (whose transform is represented by
the reciprocal lattice) is usually a periodic spatial function in real-space and is
also known as the direct lattice. ?
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There are 14 space lattices belonging to all the seven crystal
systems( cubic ., orthorhombic …) These 14 lattices are called Bravais lattice
( primitive ,FC,BC- cubic, etc)
For each Bravaislattice , there is a corresponding reciprocal lattice of the
same symmetry which may be derived geometrically.
From the origin O lines are constructed normal to the families of the
plane (hkl). Points are marked off along each of these lines such that the distance
d of any first point from O is inversely proportional to the corresponding
interplanar spacing d
d(hkl) = 1 / d ( hkl)
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Thus the first point along OP the normal to the (100) family of plane in real
space is labelled 100 in the reciprocal space.
001 101
O
100
The particular reciprocal lattice points 100, 010, 001 define the reciprocal unit
cell.
A = K bc sin 𝛂/ V 001
100 002 003
200 104
300 204
304
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19.X-RAY DIFFRACTION BY SINGLE CRYSTAL
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20.ROTATING CRYSTAL METHOD
This method is used to determine the structure of crystals using diffraction
of X- rays The technique makes use of Bragg’s X-ray spectrometer, where
crystal is used as reflecting grating .
X- rays generated in the tube T are passed through a slit so as to obtain a
narrow beam. This narrow beam is allowed to strike the crystal C mounted on the
turn table. The reflected rays are sent to ionisation chamber where the intensities
are recorded.
The crystal is rotated gradually by means of the turn table , so as to increase
the incident angle at the exposed face of the crystal. The process is carried out for
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each plane of the crystal. The lowest angle at which , maximum reflection occurs
is , called first order reflection which corresponds to n= 1. The next higher angle ,
at which maximum reflection occurs again is called second order reflection.
Diagram:
The lattice constant d is found out using different planes of the crystal as
reflecting surface for the same known wavelength of X – rays.
Applying Bragg’s equation
2dsinθ = n λ
For first order spectrum n= 1, hence the above equation becomes
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2dsinθ = λ
1d = 2sin θ
λ
If the ratio 1d 1 : 1
d 2 : 1d 3 = 1 : √2 : √3 the crystal is simple cubic. If it is 1 :
1√ 2 : √3 then the crystal is body centred cubic whereas it is 1 : √2 : √ 3
2 the crystal
is face centred cubic
Problem1: The values of θ for the first order reflection from the three faces of
sodium chloride are 5.9 o, 8.4 o and 5.2 o .Find the crystal lattice.
Solution:
1sin 5.9: 1
sin 8.4 : 1sin 5.2 = 9.61 : 6.84: 11.04
= 1: 0.7 : 1.14
It has FCC structure.
Problem2: Find the crystal structure of potassium chloride .The values of θ for the
first order reflection from the three faces are 5.22 o, 7.30 o and 9.05 o .
Solution:
1d 1 : 1
d 2 : 1d 3 = sin 5.22 : sin 7.30 : sin 9.05
= 0.0910 : 0.1272 : 0.1570
= 1 : 1.4 : 1.73
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= 1 : √2 : √3
: It has simple cubic structure.
21.POWDER DIFFRACTION.
Powder method( Debye- Scherrer method)
The substance to be examined is finely powdered and is kept in the form of
cylinder inside a thin glass tube. This is placed at the centre of Debye Scherer
camera which consists of a cylindrical cassette,
X- rays are generated and allowed to fall on the powder specimen. The X-
ray beam enters through a small hole, passes through the sample and the unused
part of the beam leaves through the hole at the opposite end. The powder consists
of many small crystals which are oriented in all possible directions. So the
reflected radiation is not like a beam ; instead, it lies on the surface of a cone
whose apex is at the point of contact of the incident radiation with the specimen.
Diagram:
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For each combination of d and θ, one cone of reflection must result.
Therefore, many cones of reflection are emitted by the powder specimen. The
recorded lines from any cone are, a pair of arcs. The first arc on either side of the
exit point corresponds to the smallest angle of reflection.
The distance between any two corresponding arcs on the film ( S) is related
to the radius of the powder camera R
S = 4Rθ where θ is the Bragg angle in radians( 1 rad = 57.3 o ) . ---------1
Combining d(hkl) = a
√h2+k2+l 2 with Bragg equation, we get
nλ = 2 a
√h2+k2+l 2 sinθ
∴sin2 θ = λ 2
4 a2 ( h2 + k2 + l2 ) [ for first order reflection n = 1]
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Θ values can be obtained from the powder pattern using equation 1 The values of
sin2θ are compared with the below mentioned extinction rules.
1:2:3:4:5:6:8 SC [ 7 cannot be written in the form h2 + k2 + l2 ]
2:4:6:8 BCC [ odd integer for h + k+l are absent]
3:4:8:11:12 FCC [ h,k,l are either all odd or all even 111, 200,
220,311,222]
3:8:11:16 DC
Problem. From a powder camera of diameter 114.6 mm, using an X – ray beam of
wavelength 1.54 Ao , the following S values in mm are obtained for a material:
86,100,148,180,188,232,and 272.determine the structure and the lattice parameter
of the material.
Solution:
Given R = 114.6 / 2 = 57.3
S values are 86,100,148,180,188,232,and 272
The Bragg angles in degrees = S/4
21.5,25,37,45,47,58 and 68
Sin2 θ values are , 0.1346 : 0.1788 : 0.362 : 0.5003 : 0.5352 : 0.7195 : 0.8596
These values can be expressed in the ratio of integral numbers
3:4:8:11:12: 16: 19
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From the extinction rules, the structure is FCC.
The lattice parameter calculated from the highest Bragg angle is 3.62 A.
22.NEUTRON DIFFRACTION: ELEMENTARY TREATMENT
Neutron diffraction or elastic neutron scattering is the application of neutron
scattering to the determination of the atomic and/or magnetic structure of a
material.
A sample to be examined is placed in a beam of thermal or cold neutrons to obtain
a diffraction pattern that provides information of the structure of the material.
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Instrumental and sample requirements
The technique requires a source of neutrons.
Neutrons are usually produced in a nuclear reactor or spallation source.
At a research reactor, other components are needed, including a crystal
monochromator, as well as filters to select the desired neutron wavelength.
Some parts of the setup may also be movable.
At a spallation source, the time of flight technique is used to sort the energies of
the incident neutrons (higher energy neutrons are faster), so no monochromator is
needed, but rather a series of aperture elements synchronized to filter neutron
pulses with the desired wavelength.
The technique is most commonly performed as powder diffraction, which only
requires a polycrystalline powder. Single crystal work is also possible, but the
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crystals must be much larger than those that are used in single-crystal X-ray
crystallography. It is common to use crystals that are about 1 mm3.
23.COMPARISON WITH X-RAY DIFFRACTION.
Neutron diffraction technique is similar to X-ray diffraction but due to their
different scattering properties, neutrons and X-rays provide complementary
information:
X-Rays are suited for superficial analysis, strong x-rays from synchrotron
radiation are suited for shallow depths or thin specimens, while neutrons having
high penetration depth are suited for bulk samples.
24.Electron diffraction- Basic principle.
Electron diffraction refers to the technique used to study matter by
firing electrons at a sample and observing the resulting interference pattern.
This phenomenon is commonly known as wave–particle duality, which states that
a particle of matter (in this case the incident electron) can be described as a wave.
For this reason, an electron can be regarded as a wave much like sound or water
waves. This technique is similar to X-ray and neutron diffraction.
Electron diffraction is most frequently used in solid state physics and chemistry to
study the crystal structure of solids.
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Experiments are usually performed in a transmission electron microscope (TEM),
or a scanning electron microscope (SEM) as electron backscatter diffraction.
In these instruments, electrons are accelerated by an electrostatic potential in order
to gain the desired energy and determine their wavelength before they interact with
the sample to be studied.
The periodic structure of a crystalline solid acts as a diffraction grating, scattering
the electrons in a predictable manner. Working back from the observed diffraction
pattern, it may be possible to deduce the structure of the crystal producing the
diffraction pattern. However, the technique is limited by phase problem.
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25.CRYSTAL GROWTH METHODS: FROM MELT AND SOLUTION
(HYDROTHERMAL,
there are three general categories of crystal growth methods, viz.,
(1) growth from melt,
(2) growth from solution,
and (3) growth from vapour.
GROWTH FROM MELT
Melt growth is the most widely applied method, especially for the growth of not
too high melting point substances.
CZOCHRALSKI CRYSTAL PULLING TECHNIQUE
The process involved in this method is termed as ‘crystal pulling’, since it
involves relative motion between a seed and the melt so that crystal is literally
pulled out from the melt. The crystal pulling is applicable only to materials that
melt congruently. The melt is first raised to a temperature a few degrees above
melting point. Then the seed crystal, rotating slowly, is brought slowly into
contact with the melt surface, and then lowering is stopped. After getting the
desired length, the seeded crystal is slowly and carefully pulled out from the
melt The crystal can be observed as it grows and adjustment in both
temperature and the growth rate can be made as needed. With suitable
precautions, the material withdrawn from the melt solidifies as a large
cylindrical crystal. The practical aspects of the method have been discussed at
length by Draper36). Fig. 2.1 illustrates schematically the basic principle of the
technique.
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BRIDGEMANN - STOCKBARGER TECHNIQUE
The material to be crystallized is placed in a cylindrical, conical shaped
crucible, which can be lowered through a twozone vertical furnace where the
temperatures of upper and lower zones are respectively above and below the
melting point of the eventual material. The temperature profile of the growth
chamber is shown in Fig. 2.2(b). In some cases the Ch.2.Crystal growth
methods 22 crucible is raised through a furnace. The basic requirement for this
procedure is that the freezing isotherm should move systematically through the
molten charge, and this can be satisfied by moving the crucible or the furnace,
or by changing the furnace temperature. The tip of cone allows restricted
nucleation and therefore, under favorable conditions, the material is almost
entirely transformed into a large single crystal whose diameter is equal to the
internal diameter of the conical crucible. The method is useful in preparation of
crystals of metals and semiconductors, alkali and alkaline earth halides, and
complex ternary fluorides of alkali and transition metals. This method is,
however, not appropriate to materials, which expand on solidification, e.g.
aluminium tungstate.
VERNEUIL FLAME FUSION TECHNIQUE
This technique, developed by Verneuil in 190216,37), is mainly used to
grow crystals with high melting point, like ZrO2 (2700o C), SrO (2400o C) etc.
An oxyhydrogen or oxy-acetylene flame is established and is used for heating
purpose. The feed powder of the material to be crystallized is shaken
mechanically or electrically from the hopper through a sieve, using a small
vibrator with a low amplitude capacity. The flame is made to impinge on a
pedestal where a small pile of partly fused alumina quickly builds up. As the
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pile rises, it reaches into the hotter part of the flame so that the tip becomes
completely molten. The molten region increases in size and starts to solidify at
the lower end. As more and more powder arrives, the solidifying region
broadens into a crystal growing in length. Such a crystal is called boule. The
method has been schematically illustrated in Fig. 2. 3. The largest use of this
method has been for the growth of gem - quality ruby and emeralds with high
melting point and for which no suitable crucible is found. Keck and Gulay18)
introduced floating zone variant to produce ultra pure silicon.
ZONE-MELTING TECHNIQUE
This technique, discovered by Pfann38) in 1852 was originally used for the
purification of semiconductor materials. But since the product is usually
crystalline, the technique is also used for growing single crystals. Zone refining
technique is the most important zone melting method, where numbers of molten
zones are passed along the charge in one direction either horizontally or
vertically. This technique is illustrated in Fig. 2.4(a). By moving either the boat
or the coil, the molten zone is moved along the boat, thus melting the material
in the front portion and solidifying at the back to form the crystalline material.
If the conditions are suitable, then the resultant material will be single
crystalline. Fig. 2.4(b) shows a modification of the float zone technique,
devised by Keck and Gulay18). In this method the material to be Ch.2.Crystal
growth methods 23 purified or grown is arranged in a vertical compacted rod.
The molten zone floats below the two solid parts of the rod held in place by
surface tension. Each zone carries a fraction of impurities to the end of the
charge, thereby purifying the remainder. This technique is used for growing
crystals as well, in addition to purifying several metals and compounds.
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GROWTH FROM SOLUTION
This is the simplest and one of the oldest methods42) of growing crystals in
which the material to be crystallized is dissolved in a solvent to the desired
degree of Ch.2.Crystal growth methods 24 supersaturation. The solution is then
slowly cooled or evaporated. If a suitable solvent is found, crystals can be
grown at temperatures much below the melting point of the eventual crystal.
The low temperatures involved here indeed relieve demand on expensive
furnaces and power supplies. Crystal growth from aqueous solutions has been
extensively and phenomenologically studied by measuring the concentration
and temperature gradient around crystals growing in two-dimensional cell at the
growth interface. The growth rate of the crystals is mostly found to be
proportional to the normal component of the gradients43).
GROWTH FROM WATER SOLUTION
This method is extensively used for obtaining single crystals of organic and
inorganic materials. Two basic methods (cooling and evaporation) are used to
grow large crystals from water solution. In both the cases, a saturated solution is
prepared and the seed crystal is inserted. In one of the methods, temperature is
lowered slowly so as to reduce the solubility and produce crystallization, while
in the other method, the temperature is held constant and the solvent is made to
evaporate isothermally to induce crystallization. Crystals like alkali halides44),
sodium borate45), barium strontium nitrate46), Rochelle salt47), potassium and
ammonium dihydrogen phosphate48-50), Ammonium Oxalate51,52),
Potassium Hydrogen tartrate53), potash alum54), oxalic acid have been grown
from water solution.
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HYDROTHERMAL METHOD
This method of crystal growth, schematically illustrated in Fig. 2.5, using
aqueous solution at high temperature and pressure, was first used by Spezia55)
to grow quartz hydrothermally, and quartz is still the prime material grown
commercially hydrothermally on a large scale. To obtain even a low solubility
of quartz in water, the temperature of water well above boiling point is
necessary. To prevent the water from the boiling away, necessary pressure is
applied. As this solubility is not sufficient for satisfactory growth, a mineralizer
is added to the system. The method is carried out using a sealed high pressure
vessel known as autoclave or bomb. Special, strong, corrosion-resistant and
chemically inert material is used for the construction of an autoclave to
withstand high pressure and temperature. It is kept at two different temperature
regions. In the upper cooler part, seed material is supported while in the lower
hotter part, feed material is used. The rate of growth depends on the temperature
difference between top and bottom of the autoclave, pressure and the amount of
mineralizer present. When hot solution from the bottom rises into the cooler
part of the autoclave on account of convection, excess material gets deposited
on the seed, which then grows in size.
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