solid state bounceback.pdf
tvelocity2022
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Dec 27, 2023
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About This Presentation
Notes
Slide Content
SOLID STATE
#BOUNCEBACK
#BOUNCEBACK
❏7+ years Teaching experience
❏10th, 12th CBSE State Topper
❏KVPY fellow
Sakshi Vora
IIT Roorkee
❏10th, 12th CBSE State Topper
❏KVPY fellow
Sakshi Vora
IIT Roorkee
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SAKSHI SAKSHI
Types of solids
1.Crystalline
2.Amorphous
Types of Solids
2.Amorphous
Types of Solids
1.Particles are arranged in a regular pattern.
2.They have flat surfaces and sharp edges.
3.They have a fixed value of Melting Point.
Crystalline Solids
2.They have flat surfaces and sharp edges.
3.They have a fixed value of Melting Point.
Crystalline Solids
4. They are called true solids.
5. Sodium Chloride, Copper Sulfate, ICE, Fe, Na, Graphite, Diamond, etc
6. They are anisotropic ie, different properties along different directions.
Crystalline Solids
5. Sodium Chloride, Copper Sulfate, ICE, Fe, Na, Graphite, Diamond, etc
6. They are anisotropic ie, different properties along different directions.
Crystalline Solids
1.Particles are arranged in a random fashion.
2.No flat surfaces or sharp edges
3.They have diffused (not fixed) melting point.
Amorphous Solids
2.No flat surfaces or sharp edges
3.They have diffused (not fixed) melting point.
Amorphous Solids
4. They are called Pseudo Solids or Super cooled Liquids
5. Glass, Plastics, Rubbers.
6. They are isotropic ie, they have same physical properties in all directions
over a macroscopic length ie, over a larger length
Amorphous Solids
5. Glass, Plastics, Rubbers.
6. They are isotropic ie, they have same physical properties in all directions
over a macroscopic length ie, over a larger length
Amorphous Solids
Types of crystalline solids
1.Molecular Solids
2.Ionic Solids
3.Covalent or Network Solids
4.Metallic Solids
Classification of crystalline solids
2.Ionic Solids
3.Covalent or Network Solids
4.Metallic Solids
Classification of crystalline solids
Molecular Solids
Ionic Solids
Ionic Solids
Ionic Solids
Metallic Solids
Metallic Solids
Metallic Solids
Covalent or Network Solids
Covalent or Network Solids
Covalent or Network Solids
[Main Jan. 09, 2020 (I)]
A.
B.
C.
D.
Zinc sulphide
Mercury
Silicon carbide
Carbon tetrachloride
A.
B.
C.
D.
Zinc sulphide
Mercury
Silicon carbide
Carbon tetrachloride
Unit Cell
Unit Cell
The smallest part of a crystal which upon its continuous repetition in 3D,
again forms the crystal.
Physical properties of the crystal are directly proportional to that of the unit
cell.
Mass of crystal ∝Mass of unit cell
Volume of crystal ∝Volume of unit cell
Density of crystal = Volume of unit cell
Unit Cell
The smallest part of a crystal which upon its continuous repetition in 3D,
again forms the crystal.
Physical properties of the crystal are directly proportional to that of the unit
cell.
Mass of crystal ∝Mass of unit cell
Volume of crystal ∝Volume of unit cell
Density of crystal = Volume of unit cell
Unit Cell
Classification of Unit Cell : On the basis of shape
In known solids, only 7 unique shapes of unit cells are observed so far.
Cubic
Tetragonal
Orthorhombic
Monoclinic
Triclinic
Rhombohedral
Hexagonal
Except HEXAGONAL, all shapes have 6 faces. Hence, for HEXAGONAL (8
faces), some properties are different as compared to other unit cells.
Classification of Unit Cell : On the basis of shape
Cubic
Tetragonal
Orthorhombic
Monoclinic
Triclinic
Rhombohedral
Hexagonal
Except HEXAGONAL, all shapes have 6 faces. Hence, for HEXAGONAL (8
faces), some properties are different as compared to other unit cells.
Classification of Unit Cell : On the basis of shape
Classification of Unit Cell : On the basis of shape
CTOMaTRiH
Cubic a=b=c 0
Tetragonal a=b≠c 1
Orthorhombic a≠b≠c 2
Monoclinic a≠b≠c 2
Triclinic a≠b≠c 2
Rhombohedral a=b=c 0
Hexagonal a=b≠c 1
�= �= ??????= 90 Primitive, Body, face
�= �= ??????= 90 Primitive, body
�= �= ??????= 90 Primitive, body, face, end
�= ??????= 90 �≠ 90 Primitive, end
�≠ �≠ ??????≠ 90 primitive
�= �= ??????≠ 90 primitive
�= �= 90 ??????= 120 primitive
Classification of Unit Cell : On the basis of shape
CTOMaTRiH
Cubic a=b=c 0
Tetragonal a=b≠c 1
Orthorhombic a≠b≠c 2
Monoclinic a≠b≠c 2
Triclinic a≠b≠c 2
Rhombohedral a=b=c 0
Hexagonal a=b≠c 1
�= �= ??????= 90 Primitive, Body, face
�= �= ??????= 90 Primitive, body
�= �= ??????= 90 Primitive, body, face, end
�= ??????= 90 �≠ 90 Primitive, end
�≠ �≠ ??????≠ 90 primitive
�= �= ??????≠ 90 primitive
�= �= 90 ??????= 120 primitive
Classification of Unit Cell : On the basis of shape
C Cubic a=b=c 0 �= �= ??????= 90 Primitive, Body, face 3
T Tetragonal a=b≠c 1 �= �= ??????= 90 Primitive, body 2
O Orthorhombic a≠b≠c 2 �= �= ??????= 90 Primitive, body,
face, end
4
Ma Monoclinic a≠b≠c 2 �= ??????= 90 �≠ 90 Primitive, end 2
T Triclinic a≠b≠c 2 �≠ �≠ ??????≠ 90 primitive 1
Ri Rhombohedral a=b=c 0 �= �= ??????≠ 90 primitive 1
H Hexagonal a=b≠c 1 �= �= 90 ??????= 120 primitive 1
T Tetragonal a=b≠c 1 �= �= ??????= 90 Primitive, body 2
O Orthorhombic a≠b≠c 2 �= �= ??????= 90 Primitive, body,
face, end
4
Ma Monoclinic a≠b≠c 2 �= ??????= 90 �≠ 90 Primitive, end 2
T Triclinic a≠b≠c 2 �≠ �≠ ??????≠ 90 primitive 1
Ri Rhombohedral a=b=c 0 �= �= ??????≠ 90 primitive 1
H Hexagonal a=b≠c 1 �= �= 90 ??????= 120 primitive 1
[Main Jan. 10, 2019 (I)]
A.
B.
C.
D.
Triclinic
Hexagonal
Monoclinic
Tetragonal
A.
B.
C.
D.
Triclinic
Hexagonal
Monoclinic
Tetragonal
1.Simple/Primitive
2.Face centered
3.End centered
4.Body centered
Unit Cell : On the basis of position of particles
2.Face centered
3.End centered
4.Body centered
Unit Cell : On the basis of position of particles
Unit Cell : On the basis of position of particles
This classification is for all shapes except hexagonal unit cell.
Simple/Primitive Particles are at corners only
Face centered At all corners + at body centres
End centered At all corners + any 2 opposite faces
Body centered At all corners + all face centres
Unit Cell : On the basis of position of particles
This classification is for all shapes except hexagonal unit cell.
Simple/Primitive Particles are at corners only
Face centered At all corners + at body centres
End centered At all corners + any 2 opposite faces
Body centered At all corners + all face centres
Unit Cell : On the basis of position of particles
Simple/Primitive unit cell
Simple/Primitive unit cell
Simple/Primitive unit cell
FCC Unit cell
BCC unit cell
BCC unit cell
BCC unit cell
Crystal Space Lattice
Regular geometric pattern of similar type of particles in 3D space.
In known solids, only 14 unique lattices are observed : Bravais lattices
Bravais Lattice
Regular geometric pattern of similar type of particles in 3D space.
In known solids, only 14 unique lattices are observed : Bravais lattices
Bravais Lattice
Lattice points
Lattice Points
These are the locations where similar type of particles can be present.
In a unit cell, there are four types of lattice points
1.Corners
2.Face centres
3.Centre of body
4.Edge Centre
1.Everything here is excluding hexagonal unit cell.
2.At the lattice points, since the centre of the particle is situated, hence
the particle may be shared in multiple unit cells.
Lattice Points
These are the locations where similar type of particles can be present.
In a unit cell, there are four types of lattice points
1.Corners
2.Face centres
3.Centre of body
4.Edge Centre
1.Everything here is excluding hexagonal unit cell.
2.At the lattice points, since the centre of the particle is situated, hence
the particle may be shared in multiple unit cells.
Lattice Points
1.Each corner atom is shared by 8 unit cells.
2.Each body centre atom is shared by just 1 unit cell.
3.Each face centre atom is shared by 2 unit cells.
4.Each edge centre atom is equally shared by 4 unit cells.
Lattice Points
2.Each body centre atom is shared by just 1 unit cell.
3.Each face centre atom is shared by 2 unit cells.
4.Each edge centre atom is equally shared by 4 unit cells.
Lattice Points
Effective number of atoms
If particles are at corners only
8*(⅛) = 1
If particles are at all corners and all face centres
8*(⅛) + 6*(½) = 4
If particles are at all corners and at body centre
8*(⅛) + 1 = 2
If particles are at all corners and at two opposite edges.
8*(⅛) + 2*(½) = 2
Effective atoms per unit cell (Z)
8*(⅛) = 1
If particles are at all corners and all face centres
8*(⅛) + 6*(½) = 4
If particles are at all corners and at body centre
8*(⅛) + 1 = 2
If particles are at all corners and at two opposite edges.
8*(⅛) + 2*(½) = 2
Effective atoms per unit cell (Z)
[Main April 12, 2019 (II)]
A.
B.
C.
D.
8 : 1 : 6
1 : 2 : 4
4 : 2 : 1
4 : 2 : 3
A.
B.
C.
D.
8 : 1 : 6
1 : 2 : 4
4 : 2 : 1
4 : 2 : 3
Coordination number
The total number of surrounding atoms touching a particular atom.
If Coordination number is x for 1 atom of the system, that means
coordination number will be x for all the atoms of that system. (if nothing
mentioned)
Coordination Number (2D)
If Coordination number is x for 1 atom of the system, that means
coordination number will be x for all the atoms of that system. (if nothing
mentioned)
Coordination Number (2D)
The total number of surrounding atoms touching a particular atom.
If Coordination number is x for 1 atom of the system, that means
coordination number will be x for all the atoms of that system.
Coordination Number (2D)
If Coordination number is x for 1 atom of the system, that means
coordination number will be x for all the atoms of that system.
Coordination Number (2D)
Coordination Number (3D)
Coordination Number (3D)
Cubic system
Analysis of Cubic System
Considering a cube of edge length a
1.Corners = 8
2.Faces = 6
3.Edges = 12
4.Volume = a
3
5.Face Diagonals = 12
6.Length of face diagonal = √2 a
7.Body diagonals = 4
8.Length of Body diagonal = √3a
Analysis of Cubic System
1.Corners = 8
2.Faces = 6
3.Edges = 12
4.Volume = a
3
5.Face Diagonals = 12
6.Length of face diagonal = √2 a
7.Body diagonals = 4
8.Length of Body diagonal = √3a
Analysis of Cubic System
1.Similar types of particles are present at all the corners of the cube in
such a manner so that each corner atom touches all its adjacent
corner atoms.
Simple Cubic Lattice
such a manner so that each corner atom touches all its adjacent
corner atoms.
Simple Cubic Lattice
Relation between r and edge length
1.a = 2r
2.Z = 1
3.CNo. = 6
Simple Cubic unit cell
2.Z = 1
3.CNo. = 6
Simple Cubic unit cell
Similar type particles are present at all corners and at body centre in
such a manner so that the body centre atom touches all the corner atoms
but corner atoms will not touch each other.
Body centred Cubic unit cell or BCC
such a manner so that the body centre atom touches all the corner atoms
but corner atoms will not touch each other.
Body centred Cubic unit cell or BCC
Body centred Cubic unit cell or BCC
1.√3a= 4r
2.Z = 2
3.CNo. = 8
There are two types of atoms in BCC unit cell
Corners and body centre
and both these atoms have
CNo. =8
BCC
2.Z = 2
3.CNo. = 8
There are two types of atoms in BCC unit cell
Corners and body centre
and both these atoms have
CNo. =8
BCC
Similar type particles are present at all corners and at centre of all faces in
such a manner so that each face centre atom touches all the corner atoms
but corner atoms will not touch each other.
Face centred Cubic Unit cell
such a manner so that each face centre atom touches all the corner atoms
but corner atoms will not touch each other.
Face centred Cubic Unit cell
Face centred Cubic Unit cell
1.√2a= 4r
2.Z = 4
CNo. = 12 ( 4+ 4 +4 )
There are two types of atoms in FCC unit cell
Corners and face centres
1.Atom at thecornerdoes not touch other corner atoms but touches all
the atoms at the face centres. So CNo. = 12
2.Atom at the face centretouches 4 other corner atoms, 4 face centres of
left cube and 4 face centres of right cube.
FCC
2.Z = 4
CNo. = 12 ( 4+ 4 +4 )
There are two types of atoms in FCC unit cell
Corners and face centres
1.Atom at thecornerdoes not touch other corner atoms but touches all
the atoms at the face centres. So CNo. = 12
2.Atom at the face centretouches 4 other corner atoms, 4 face centres of
left cube and 4 face centres of right cube.
FCC
CNo 12 wrt atom at face centre
Packing Fraction
It is the measure of the space occupied by the atoms in a unit cell.
PF = Part occupied by the atoms
Total part of the cell
Packing Fraction
PF = Part occupied by the atoms
Total part of the cell
Packing Fraction
For 1D
PF = length occupied by the atoms
Total length of the cell
For 2D
PF =area occupied by the atoms
Total area of the cell
For 3D
PF = volume occupied by the atoms
Total volume of the cell
Packing Fraction
PF = length occupied by the atoms
Total length of the cell
For 2D
PF =area occupied by the atoms
Total area of the cell
For 3D
PF = volume occupied by the atoms
Total volume of the cell
Packing Fraction
PF = Volume occupied by the atoms
Total volume of the cell
Packing Fraction for Simple cubic unit cell
Total volume of the cell
Packing Fraction for Simple cubic unit cell
PF = Volume occupied by the atoms
Total volume of the cell
Packing Fraction for face centred unit cell
Total volume of the cell
Packing Fraction for face centred unit cell
PF = Volume occupied by the atoms
Total volume of the cell
Packing Fraction for body centred unit cell
Total volume of the cell
Packing Fraction for body centred unit cell
1-packing fraction
Void Fraction
Void Fraction
Density of unit cell
Density of crystal = Density of unit cell
Density of unit cell = mass of unit cell
Volume of unit cell
= mass of 1 atom * total number of atoms
Volume of unit cell
= A*Z
No * volume of unit cell
Density of Crystalline Substance
Density of unit cell = mass of unit cell
Volume of unit cell
= mass of 1 atom * total number of atoms
Volume of unit cell
= A*Z
No * volume of unit cell
Density of Crystalline Substance
Density of crystal = Density of unit cell
Density of unit cell = mass of unit cell
Volume of unit cell
= mass of 1 atom * total number of atoms
Volume of unit cell
= A*Z
N
o* a
3
Density of Cubic unit cell
Density of unit cell = mass of unit cell
Volume of unit cell
= mass of 1 atom * total number of atoms
Volume of unit cell
= A*Z
N
o* a
3
Density of Cubic unit cell
[Main Sep. 03, 2020 (I)]
A.
B.
C.
D.
40 N
A
8 N
A
4 N
A
2 N
A
[Main Sep. 05, 2020 (I)]
B.
C.
D.
40 N
A
8 N
A
4 N
A
2 N
A
[Main Sep. 05, 2020 (I)]
[Main Jan. 11, 2019 (I)]
A.
B.
C.
D.
0.0432 kg mol
-1
0.0216 kg mol
-1
0.0305 kg mol
-1
0.4320 kg mol
-1
A.
B.
C.
D.
0.0432 kg mol
-1
0.0216 kg mol
-1
0.0305 kg mol
-1
0.4320 kg mol
-1
[Main Jan. 9, 2019 (II)]
A.
B.
C.
D.
A.
B.
C.
D.
Formulae of compounds
For a solid compound made of elements A,B and C, the empirical formula
may be written as
A
ZAB
ZBC
ZC
ZA, ZB and ZC are the number of atoms per unit cell.
Formula of Solid Compound
may be written as
A
ZAB
ZBC
ZC
ZA, ZB and ZC are the number of atoms per unit cell.
Formula of Solid Compound
Tell the formula of a compound which has A in BCC unit cell and B at all
edge centres
Practise Question
edge centres
Practise Question
Tell the formula of a compound which has A in FCC unit cell and B is at
body centre and C is at half edge centres.
Practise Question
body centre and C is at half edge centres.
Practise Question
[Main Jan. 10, 2019 (II)]
A.
B.
C.
D.
A.
B.
C.
D.
Voids
The empty space between the closely packed similar type particles.
The type of void is given by the shape created by joining the centres of all
the atoms surrounding the void.
Voids
The type of void is given by the shape created by joining the centres of all
the atoms surrounding the void.
Voids
1-packing fraction
Voids in 2D
Voids in 2D
Voids in 3D
There are three types of voids
1.Cubic void
Formed in simple cubic lattice at the body centre position.
When the centres of all atoms surrounding the voids are joined, it forms a
cube.
1.Tetrahedral Voids
Whenever a triangular void is covered by an atom, a tetrahedral void is
formed.
1.Octahedral Voids (8 faces/ square bipyramidal voids)
Whenever a triangular void is covered by an another triangular void in
opposite orientation.
Voids in 3D
There are three types of voids
1.Cubic void
Formed in simple cubic lattice at the body centre position.
When the centres of all atoms surrounding the voids are joined, it forms a
cube.
1.Tetrahedral Voids
Whenever a triangular void is covered by an atom, a tetrahedral void is
formed.
1.Octahedral Voids (8 faces/ square bipyramidal voids)
Whenever a triangular void is covered by an another triangular void in
opposite orientation.
Voids in 3D
Voids
1-packing fraction
Voids
1-packing fraction
Voids
8 faces of octahedral void
Voids
Voids
If a lattice has Z as effective number of particles,
Then, Effectively per unit cell
Number of Octahedral Voids -Z
Number of Tetrahedral Voids = 2Z
Voids
Then, Effectively per unit cell
Number of Octahedral Voids -Z
Number of Tetrahedral Voids = 2Z
Voids
In cubic lattices, only FCC has tetrahedral and Octahedral voids.
There are no tetrahedral and octahedral voids in Body centred cubic
unit cell.
Voids in cubic lattices
There are no tetrahedral and octahedral voids in Body centred cubic
unit cell.
Voids in cubic lattices
Tetrahedral voids:
There are 2 tetrahedral voids on each body diagonal at a distance of √3a/4
from each corner.
Location of voids in FCC unit cell
There are 2 tetrahedral voids on each body diagonal at a distance of √3a/4
from each corner.
Location of voids in FCC unit cell
Location of voids in FCC unit cell
Tetrahedral voids:
When three face centred atoms touch each other, they form a triangular
void, the corner atom touches these 3 atoms thus forming a tetrahedral
void.
Location of voids in FCC unit cell
Tetrahedral voids:
When three face centred atoms touch each other, they form a triangular
void, the corner atom touches these 3 atoms thus forming a tetrahedral
void.
Location of voids in FCC unit cell
If all tetrahedral voids are joined, if forms a cube with the edge length a/2
Location of voids in FCC unit cell
Location of voids in FCC unit cell
Octahedral Voids:
Present at all edge centres and at the
body centre.
For the void at body centre,there are
two opposite triangles formed,
which on joining form octahedral void.
Location of voids in FCC unit cell
Present at all edge centres and at the
body centre.
For the void at body centre,there are
two opposite triangles formed,
which on joining form octahedral void.
Location of voids in FCC unit cell
Location of voids in FCC unit cell
Octahedral Voids:
Present at all edge centres and at the
body centre.
For the void at edge centre,
two face centres and one corner will
form triangle, other two face centres
and corner will form another triangle,
once they overlap, they form
octahedral void.
Location of voids in FCC unit cell
Octahedral Voids:
Present at all edge centres and at the
body centre.
For the void at edge centre,
two face centres and one corner will
form triangle, other two face centres
and corner will form another triangle,
once they overlap, they form
octahedral void.
Location of voids in FCC unit cell
At centre = 1
At edge centres = 12*¼ = 3
Total 1+3 = 4
Number of octahedral voids in FCC lattice
At edge centres = 12*¼ = 3
Total 1+3 = 4
Number of octahedral voids in FCC lattice
[Main Sep. 06, 2020 (II)]
A.
B.
C.
D.
+2, +4
+1, +3
+3, +1
+4, +2
A.
B.
C.
D.
+2, +4
+1, +3
+3, +1
+4, +2
Close packing
Close Packing in crystals
Particles should be arranged in such a way that the packing fraction becomes
maximum.
1D Close Packing AAAA close packing/Linear close
packing
C No = 2
Close Packing in crystals
Particles should be arranged in such a way that the packing fraction becomes
maximum.
1D Close Packing AAAA close packing/Linear close
packing
C No = 2
Close Packing in crystals
2D Close Packing
Formed by repetition of 1D layers in same or different alignment.
Square Close Packing/ AAA close packing
CNo. = 4 Void: Square planar
Close Packing in crystals
Formed by repetition of 1D layers in same or different alignment.
Square Close Packing/ AAA close packing
CNo. = 4 Void: Square planar
Close Packing in crystals
2D Close Packing
Formed by repetition of 1D layers in same or different alignment.
Hexagonal Close Packing/ ABAB close packing/
CNo. = 6 Void: TRIANGULAR
Close Packing in crystals
Formed by repetition of 1D layers in same or different alignment.
Hexagonal Close Packing/ ABAB close packing/
CNo. = 6 Void: TRIANGULAR
Close Packing in crystals
3D Close Packing
Three type of Close packing is present in the known solids.
1.Square Close packing (SCP)
2.Cubic Close Packing (CCP)
3.Hexagonal Close Packing (HCP)
Close Packing in crystals
Three type of Close packing is present in the known solids.
1.Square Close packing (SCP)
2.Cubic Close Packing (CCP)
3.Hexagonal Close Packing (HCP)
Close Packing in crystals
Square Close Packing SCP in 3D/AAA Close
packing
CNo. 6 and Lattice:Primitive unit cell Void:Cubic void
Close Packing in crystals
packing
CNo. 6 and Lattice:Primitive unit cell Void:Cubic void
Close Packing in crystals
Close Packing in crystals
CCP and HCP unit cell
Both are formed by repetition of 2D hexagonal layers in 3D
Close Packing in crystals
CCP and HCP unit cell
Both are formed by repetition of 2D hexagonal layers in 3D
Close Packing in crystals
First Layer of atoms : Layer A
There are two types of triangular voids,
upper triangle cand lower triangle b
Close Packing in crystals
There are two types of triangular voids,
upper triangle cand lower triangle b
Close Packing in crystals
Close Packing in crystals
Second Layer of atoms : Layer B
●A second hexagonal layer this placed over Layer A in such a
manner that the c type (upper triangular) type of voids are covered
by the atoms of second layer.
●Since triangular void is covered by a 4th atom, this void turns out to
be a tetrahedral void.
●Because of this arrangement, the b (lower triangular) type voids of
layer A will be covered by the c (upper triangular) type voids of
layer B forming Octahedral Void.
Close Packing in crystals
Second Layer of atoms : Layer B
●A second hexagonal layer this placed over Layer A in such a
manner that the c type (upper triangular) type of voids are covered
by the atoms of second layer.
●Since triangular void is covered by a 4th atom, this void turns out to
be a tetrahedral void.
●Because of this arrangement, the b (lower triangular) type voids of
layer A will be covered by the c (upper triangular) type voids of
layer B forming Octahedral Void.
Close Packing in crystals
Second Layer of atoms : Layer B
Close Packing in crystals
Close Packing in crystals
Third Layer of atoms (Layer B or Layer C)
If the third layer is Layer C : CCP
●A third 2D hexagonal layer is placed over the second layer in such a
manner that all the octahedral voids formed by layers A and B are
covered by the atoms of this third layer
Close Packing in crystals
If the third layer is Layer C : CCP
●A third 2D hexagonal layer is placed over the second layer in such a
manner that all the octahedral voids formed by layers A and B are
covered by the atoms of this third layer
Close Packing in crystals
Close Packing in crystals
CCP Unit cell
Close Packing in crystals
CCP Unit cell
Close Packing in crystals
CCP Unit cell or ABCABC Close packing
Close Packing in crystals
Close Packing in crystals
CCP Unit cell or ABCABC Close packing
Close Packing in crystals
Close Packing in crystals
Third Layer of atoms (Layer B or Layer C)
ABCABC close packing : CCP
1.Coordination number = 12
2.Voids: Octahedral and tetrahedral
3.Unit cell: Face centred Cubic Unit cell
Close Packing in crystals
ABCABC close packing : CCP
1.Coordination number = 12
2.Voids: Octahedral and tetrahedral
3.Unit cell: Face centred Cubic Unit cell
Close Packing in crystals
Looking at this figure from two angles
Side view: ABC ABC arrangement
Top view: FCC unit cell
Close Packing in crystals
Side view: ABC ABC arrangement
Top view: FCC unit cell
Close Packing in crystals
Third Layer of atoms (Layer B)
ABABAB close packing : HCP
1.A similar 2D layer is placed over layer B in same form as the layer A
Close Packing in crystals
ABABAB close packing : HCP
1.A similar 2D layer is placed over layer B in same form as the layer A
Close Packing in crystals
Close Packing in crystals
HCP Unit cell
1.A similar 2D layer is placed over layer B in same form as the layer A
2.The type of packing is ABABAB close packing
3.Both Octahedral and tetrahedral voids are present
4.C.No. will be 12
5.Type of lattice will be HEXAGONAL LATTICE
Close Packing in crystals
HCP Unit cell
1.A similar 2D layer is placed over layer B in same form as the layer A
2.The type of packing is ABABAB close packing
3.Both Octahedral and tetrahedral voids are present
4.C.No. will be 12
5.Type of lattice will be HEXAGONAL LATTICE
Close Packing in crystals
Hexagonal Lattice
1.No previous definitions are valid here.
2.Similar type of particles are present atall corners,at all hexagonal
faces and three particles within the body.
Hexagonal Lattice
1.No previous definitions are valid here.
2.Similar type of particles are present atall corners,at all hexagonal
faces and three particles within the body.
Hexagonal Lattice
Effective number of atoms per unit cell: 6
12*(⅙) + 2*(½) + 3 = 6
Octahedral Voids = 6
Tetrahedral voids = 12
Hexagonal Lattice
12*(⅙) + 2*(½) + 3 = 6
Octahedral Voids = 6
Tetrahedral voids = 12
Hexagonal Lattice
Relation between a and r
a = 2r
Height of unit cell
2a√(⅔)
Volume of hexagonal unit cell
Volume =height * area of hexagonal face
= 2a√(⅔)* 6*(area of eq triangle)
= 2a√(⅔)* 6*(√(¾)??????a
2
= 3√2??????a
3
Hexagonal Lattice
a = 2r
Height of unit cell
2a√(⅔)
Volume of hexagonal unit cell
Volume =height * area of hexagonal face
= 2a√(⅔)* 6*(area of eq triangle)
= 2a√(⅔)* 6*(√(¾)??????a
2
= 3√2??????a
3
Hexagonal Lattice
Packing fraction of hexagonal unit cell
Packing Fraction=Volume occupied/ volume available
= 6*volume of 1 atom/ 3√2a
3
= 0.74
= 74%
Hexagonal Lattice
Packing Fraction=Volume occupied/ volume available
= 6*volume of 1 atom/ 3√2a
3
= 0.74
= 74%
Hexagonal Lattice
Hexagonal Lattice
In a compound atoms of element Y form ccp lattice and those of element
X occupy 2/3rd of tetrahedral voids. The formula of the compound would
be :
A.
B.
C.
D.
X
2Y
3
X
2Y
X
3Y
4
X
4Y
3
In a compound atoms of element Y form ccp lattice and those of element
X occupy 2/3rd of tetrahedral voids. The formula of the compound would
be :
A.
B.
C.
D.
X
2Y
3
X
2Y
X
3Y
4
X
4Y
3
Radius Ratio
The type of void occupied by the smaller ion will be decided by Radius
Ratio.
RR = Radius of smaller ion
Radius of larger ion
RR can vary from 0 to 1
Radius Ratio
Ratio.
RR = Radius of smaller ion
Radius of larger ion
RR can vary from 0 to 1
Radius Ratio
RR Type of void Coordination Number
RR<0.155 Linear Void 2
0.155≤RR<0.225 Triangular Void 3
0.225≤RR<0.414 Tetrahedral 4
0.414≤RR<0.732 Square Planar (2D) 4
Octahedral (3D) 6
0.732≤RR<1 Cubic 8
Radius Ratio
RR<0.155 Linear Void 2
0.155≤RR<0.225 Triangular Void 3
0.225≤RR<0.414 Tetrahedral 4
0.414≤RR<0.732 Square Planar (2D) 4
Octahedral (3D) 6
0.732≤RR<1 Cubic 8
Radius Ratio
Radius Ratio
Radius Ratio
Radius Ratio
The situation is called IDEAL SITUATION.
Here the cation will touch the anions and also anions will touch each others.
Case 1: If RR is 0.155: Perfect Triangular void
Here the cation will touch the anions and also anions will touch each others.
Case 1: If RR is 0.155: Perfect Triangular void
Case 2: If RR is 0.20: Imperfect Triangular void
Here the cation will touch the anions and but anions will not touch each
other.
●This case is valid for both the situations:
●the size of anion is kept the same but the size of cation increases.
●The size of cation is kept the same but the size of anion decreases then also
the anions won't touch each other.
Case 2: If RR is 0.20: Imperfect Triangular void
Here the cation will touch the anions and but anions will not touch each
other.
●This case is valid for both the situations:
●the size of anion is kept the same but the size of cation increases.
●The size of cation is kept the same but the size of anion decreases then also
the anions won't touch each other.
Case 2: If RR is 0.20: Imperfect Triangular void
Whatever the case may be, ideal or non ideal / perfect or imperfect
Remember,
The cation will always touch the anions
Most important
Remember,
The cation will always touch the anions
Most important
If no other data is given in the question, we need to consider the
limiting values for the voids:
Radius of tetrahedral void = 0.225*radius of lattice
Radius of octahedral void = 0.414*radius of lattice
Limiting cases
limiting values for the voids:
Radius of tetrahedral void = 0.225*radius of lattice
Radius of octahedral void = 0.414*radius of lattice
Limiting cases
[Adv.2013]
A.
B.
C.
D.
104 pm
183 pm
125 pm
57 pm
A.
B.
C.
D.
104 pm
183 pm
125 pm
57 pm
PYQ JEE Adv 2020
PYQ JEE Adv 2020
The cubic unit cell structure of a compound containing cation M and anion X
is shown below. When compared to the anion, the cation has smaller ionic
radius. Choose the correct statement (s)
A.
B.
C.
D.
The empirical formula of the compound is MX
The cation M and anion X have different
coordination geometries
The ratio of M-X bond length to the cubic unit cell
edge length is 0.866.
The ratio of the ionic radii of cation M to anion X is 0.414.
JEE Adv 2020
PYQ JEE Adv 2020
The cubic unit cell structure of a compound containing cation M and anion X
is shown below. When compared to the anion, the cation has smaller ionic
radius. Choose the correct statement (s)
A.
B.
C.
D.
The empirical formula of the compound is MX
The cation M and anion X have different
coordination geometries
The ratio of M-X bond length to the cubic unit cell
edge length is 0.866.
The ratio of the ionic radii of cation M to anion X is 0.414.
JEE Adv 2020
Defects
1.For a crystalline substance at 0K, entropy = 0
2.There are no defects in a crystalline substance at 0K
3.As the temperature increases, the defects arise in a crystal.
1.Point Defects:Imperfections at few random lattice points in
the crystal
Line Defects: Imperfections in a row of large number of lattice
points. Ie. when so many point defects are seen together, it is
seen as a line defect.
Plane defect:Imperfection in a plane of a large number of
lattice points. I.e, so many line defects are seen together
Defects or imperfection in Crystals
2.There are no defects in a crystalline substance at 0K
3.As the temperature increases, the defects arise in a crystal.
1.Point Defects:Imperfections at few random lattice points in
the crystal
Line Defects: Imperfections in a row of large number of lattice
points. Ie. when so many point defects are seen together, it is
seen as a line defect.
Plane defect:Imperfection in a plane of a large number of
lattice points. I.e, so many line defects are seen together
Defects or imperfection in Crystals
They are of 2 types
1.Stoichiometric Defect: The formula of compound does not change
2.Non Stoichiometric defect:The formula of the compound changes.
Point Defect
1.Stoichiometric Defect: The formula of compound does not change
2.Non Stoichiometric defect:The formula of the compound changes.
Point Defect
Schottky Defect: Stoichiometric defect
1.Pairs of cations and anions are missing from the crystal.
Density of crystal decreases.
2.Generally shown by compounds having high Coordination
Number.
3.Schottky defect = Theoretical density -observed density
4.For example, NaCl, KCl, CsCl and AgBr.
Schottky Defect: Stoichiometric defect
1.Pairs of cations and anions are missing from the crystal.
Density of crystal decreases.
2.Generally shown by compounds having high Coordination
Number.
3.Schottky defect = Theoretical density -observed density
4.For example, NaCl, KCl, CsCl and AgBr.
Schottky Defect: Stoichiometric defect
1.Some ions will leave their original positions and will be present at
different positions in the crystal.
2.The formula of the compound remains same.
3.The density of the compound remains same.
4.Shown by compounds having large difference in ionic radii.
5.for example, ZnS, AgCl, AgBr and AgI due to small size of Zn2+
and Ag+ ions
Frenkel Defect: Stoichiometric defect
different positions in the crystal.
2.The formula of the compound remains same.
3.The density of the compound remains same.
4.Shown by compounds having large difference in ionic radii.
5.for example, ZnS, AgCl, AgBr and AgI due to small size of Zn2+
and Ag+ ions
Frenkel Defect: Stoichiometric defect
Non Stoichiometric defect: Metal Excess defect by anion vacancy
1.Some anions will be missing from the crystal creating anion
vacancies.
2.These vacant sites will be occupied by electrons called F centres,
which are responsible for the colour of the system
3.Formula of the compound changes but electrical neutrality is
same.
4.Density decreases
5.Good conductors of heat and electricity.
Non Stoichiometric defect: Metal Excess defect by anion
vacancy
1.Some anions will be missing from the crystal creating anion
vacancies.
2.These vacant sites will be occupied by electrons called F centres,
which are responsible for the colour of the system
3.Formula of the compound changes but electrical neutrality is
same.
4.Density decreases
5.Good conductors of heat and electricity.
Non Stoichiometric defect: Metal Excess defect by anion
vacancy
1.Alkali halides like NaCl and KCl show this type of defect.
2.When crystals of NaCl are heated in an atmosphere of sodium
vapour, the sodium atoms are deposited on the surface of the
crystal.
3.The Cl–ions diffuse to the surface of the crystal and combine with
Na atoms to give NaCl. This happens by loss of electron by sodium
atoms to form Na+ ions
Non Stoichiometric defect: Metal Excess defect by anion
vacancy
2.When crystals of NaCl are heated in an atmosphere of sodium
vapour, the sodium atoms are deposited on the surface of the
crystal.
3.The Cl–ions diffuse to the surface of the crystal and combine with
Na atoms to give NaCl. This happens by loss of electron by sodium
atoms to form Na+ ions
Non Stoichiometric defect: Metal Excess defect by anion
vacancy
1.Some extra cations are present in the interstitial sites of the crystal.
2.Electrons are present in the other sites to maintain electrical neutrality.
3.Zinc oxide is white in colour at room temperature. On heating it loses
oxygen and turns yellow
Now there is excess of zinc in the crystal and its formula becomes Zn1+xO.
The excess Zn2+ ions move to interstitial sites and the electrons to
neighbouring interstitial sites.
Non Stoichiometric defect: Metal Excess defect by anion
vacancy
2.Electrons are present in the other sites to maintain electrical neutrality.
3.Zinc oxide is white in colour at room temperature. On heating it loses
oxygen and turns yellow
Now there is excess of zinc in the crystal and its formula becomes Zn1+xO.
The excess Zn2+ ions move to interstitial sites and the electrons to
neighbouring interstitial sites.
Non Stoichiometric defect: Metal Excess defect by anion
vacancy
1.There are many solids which are difficult to prepare in the
stoichiometric composition and contain less amount of the metal as
compared to the stoichiometric proportion.
2.A typical example of this type is FeO which is mostly found with a
composition of Fe0.95O.
3.It may actually range from Fe0.93O to Fe0.96O.
4.In crystals of FeO some Fe2+ cations are missing and the loss of
positive charge is made up by the presence of required number of
Fe3+ ions
Non Stoichiometric defect: Metal Deficiency defect by
cation vacancy
stoichiometric composition and contain less amount of the metal as
compared to the stoichiometric proportion.
2.A typical example of this type is FeO which is mostly found with a
composition of Fe0.95O.
3.It may actually range from Fe0.93O to Fe0.96O.
4.In crystals of FeO some Fe2+ cations are missing and the loss of
positive charge is made up by the presence of required number of
Fe3+ ions
Non Stoichiometric defect: Metal Deficiency defect by
cation vacancy
1.It is due to doping of a small amount of substance to a crystalline
substance.
2.If molten NaCl containing a little amount of SrCl2(cations now should
be of greeter charge) is crystallised, some of the sites of Na+ ions are
occupied by Sr2+
3.Each Sr2+ replaces two Na+ ions. It occupies the site of one ion and
the other site remains vacant. The cationic vacancies thus produced
are equal in number to that of Sr2+ ions.
4.Another similar example is the solid solution of CdCl2 and AgCl.
Impurity defect
substance.
2.If molten NaCl containing a little amount of SrCl2(cations now should
be of greeter charge) is crystallised, some of the sites of Na+ ions are
occupied by Sr2+
3.Each Sr2+ replaces two Na+ ions. It occupies the site of one ion and
the other site remains vacant. The cationic vacancies thus produced
are equal in number to that of Sr2+ ions.
4.Another similar example is the solid solution of CdCl2 and AgCl.
Impurity defect
[Main Jan. 08, 2020 (II)]
A.
B.
C.
D.
AgBr
CsCl
KBr
ZnS
A.
B.
C.
D.
AgBr
CsCl
KBr
ZnS
[2018
]
A.
B.
C.
D.
Schottky defect
Vacancy defect
Frenkel defect
Metal deficiency defect
]
A.
B.
C.
D.
Schottky defect
Vacancy defect
Frenkel defect
Metal deficiency defect
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