This document discusses different types of solids and their crystal structures. It describes crystalline solids as having long-range periodic atomic arrangements, while amorphous solids lack long-range order. Polycrystalline solids consist of many small crystallites. Common crystal structures include body-centered cubic, face-centered cubic, and hexagonal close-packed arrangements. Defects in crystal structures like point defects and dislocations are also summarized.

1. Solid State Chemistry (SSC)
By-
Saurav K. Rawat
(Rawat DA Greatt)
1

2. 2

3. CLASSIFICATION OF SOLIDS
SOLID MATERIALS
CRYSTALLINE POLYCRYSTALLINE
AMORPHOUS
(Non-crystalline)
Crystal Structure 3
Single Crystal

4.  Single crystals have a periodic atomic structure across its
4
SINGLE CRYSTALS
Single Crystals
Single Pyrite
Crystal
Amorphous
Solid
whole volume.
 At long range length scales, each atom is related to every
other equivalent atom in the structure by translational or
rotational symmetry

5.  Polycrystalline materials are made up of an aggregate of many small single
 Polycrystalline materials have a high degree of order over many atomic or
5
POLYCRYSTALLINE SOLIDS
crystals (also called crystallites or grains).
Polycrystalline
Pyrite form
(Grain)
molecular dimensions.
 Grains (domains) are separated by grain boundaries. The atomic order can vary
from one domain to the next.
 The grains are usually 100 nm - 100 microns in diameter.
 Polycrystals with grains less than 10 nm in diameter are nanocrystalline

6. AMORPHOUS SOLIDS
Amorphous (Non-crystalline) Solids are made up of randomly
orientated atoms , ions, or molecules that do not form defined
patterns or lattice structures.
Amorphous materials have order only within a few atomic or molecular
dimensions.
Amorphous materials do not have any long-range order, but they have
varying degrees of short-range order.
Examples to amorphous materials include amorphous silicon, plastics,
and glasses.
Amorphous silicon can be used in solar cells and thin film transistors.
6

7. Centre of symmetry
Planes of symmetry
 Axes of symmetry

8. Definitions
1. The unit cell
“The smallest repeat unit of a crystal structure, in 3D,
which shows the full symmetry of the structure”
The unit cell is a box with:
• 3 sides - a, b, c
• 3 angles - , , 

9. 3D – 14 BRAVAIS LATTICES AND SEVEN CRYSTAL TYPES
1) Cubic Crystal System (SC or P, BCC,FCC)
2) Hexagonal Crystal System (SC or P)
3) Triclinic Crystal System (SC or P)
4) Monoclinic Crystal System (SC or P, Base-C)
5) Orthorhombic Crystal System (SC or P, Base-C, BC, FC)
6) Tetragonal Crystal System (SC or P, BC)
7) Trigonal (Rhombohedral) Crystal System (SC or P)
9
TYPICAL CRYSTAL STRUCTURES

10. Crystal Structure 10

11. Three common Unit Cells in 3D
11

12. Type of
Cubic
Unit Cell
Unit cell
Content
(z)
Atomic
Radius
Packing
Fraction
P
I
FCC
1
2
4
a/2
a2 /4
a3/4
52.36%
67.98%
74.00%

13. Coordination Number in Cubic
Lattices
Simple Cubic Lattice or Primitive (P)
Face-centered Cubic Lattice (fcc)
Body-Centered Cubic Lattice (bcc or I)
Density of a substance,
d = mass in unit cell/ volume of unit cell
=n X atomic wt./ Avogadro no. X volume of unit cell
Where n= no. of particals in unit cell

14. Lattice planes (or crystal planes)
and Miller indices
Miller gave the method to specify planes, Used intigers
hkl and enclosed them in parenthesis like (h,k,l). To
determine Miller indices the intercepts by the given
plane on x,y and z axes (pa,qb,rc) are determined.
P-1 : q-1 : r-1 = h : k : l
The lattice plane then will be (h,k,l) and the spacing is
given by-d
= a/(h2 + k2 + l2 )

15. CRYSTALLOGRAPHY
15
Crystallography is a branch of science that deals with the geometric
description of crystals and their internal atomic arrangement.
It’s important the symmetry of a crystal because it has a profound influence
on its properties.
Structures should be classified into different types according to the
symmetries they possess.
Energy bands can be calculated when the structure has been determined.

16. Miller Indices: Equivalent Directions
z
y
Equivalent directions due to crystal symmetry:
x
1
2
3
1: [100]
2: [010]
3: [001]
Notation <100> used to denote all directions equivalent to [100]

17. The intercepts of a crystal plane with the axis defined by a set of
unit vectors are at 2a, -3b and 4c. Find the corresponding Miller
indices of this and all other crystal planes parallel to this plane.
The Miller indices are obtained in the following three steps:
1. Identify the intersections with the axis, namely 2, -3 and
4.
2. Calculate the inverse of each of those intercepts,
resulting in 1/2, -1/3 and 1/4.
3. Find the smallest integers proportional to the inverse of
the intercepts. Multiplying each fraction with the
product of each of the intercepts (24 = 2 x 3 x 4) does
result in integers, but not always the smallest integers.
4. These are obtained in this case by multiplying each
fraction by 12.
6 4 3
5. Resulting Miller indices is
6. Negative index indicated by a bar on top.

18. z
y
Miller Indices of Planes
z=
x
y=
x=a
x y z
[1] Determine intercept of plane with each axis a ∞ ∞
[2] Invert the intercept values 1/a 1/∞ 1/∞
[3] Convert to the smallest integers 1 0 0
[4] Enclose the number in round brackets (1 0 0)

19. z
y
Miller Indices of Planes
x
x y z
[1] Determine intercept of plane with each axis 2a 2a 2a
[2] Invert the intercept values 1/2a 1/2a 1/2a
[3] Convert to the smallest integers 1 1 1
[4] Enclose the number in round brackets (1 1 1)

20. z
y
Planes with Negative Indices
x
x y z
[1] Determine intercept of plane with each axis a -a a
[2] Invert the intercept values 1/a -1/a 1/a
[3] Convert to the smallest integers 1 -1 1
[4] Enclose the number in round brackets 111

21. Closed Packing in crystals
Square packed structure Hexagonal packed
structure

22. A sites
B sites
A sites
HCP
FCC
Layer Stacking Sequence
= ABAB…
= ABCABC..

23. Structures of Ionic Substances
Having Closed Packed Lattices
In ionic compounds one type of the ions ( cations or
anions) form the closed packing structures whereas,
the second type of ions occupy the voids as mentioned
compoiunn dthe Ifoonlsl ofowrminingg tcalobseled -packed structure Ions in voids
NaCl Cl- ions form CCP structure Na+ ions occupy all
octahedral voids
ZnS S2- ions form CCP structure Zn2+ ions occupy alternate
tetrahedral voids
Fe3O4 or FeO,
Fe2O3
O2- ions form closed packed structure Fe2+ ions are in octahedral
voids. Fe3+ ions are in equal
no. of Oh and Td voids

24. Factors affecting Coordination Number
(i) Cation/anion radius ratio-
Range of r+/r- C.N. of the Cation
in the crystal
lattice
Arrangement of
Anions around
Cations in the
crystal Lattice or
Geometry
Examples
0.155-0.225 3 Planer Trigonal B2O3, BN
0.225-0.414 4 Tetrahedral ZnS,ZnO
0.414-0.732 6 Octahedral NaCl,AgX
(X=F,Cl,Br)
0.732-1.000 8 Cubic CsCl, CsBr
(ii) Arrangement of Anions around the Cation
(iii) Nature of void occupied by the Cation in closed packed
structure made by Anion

26. Sodium Chloride Structure (Rock Salt)
Sodium chloride also crystallizes in a
cubic lattice, but with a different unit
cell.
Sodium chloride structure consists of
equal numbers of sodium and
chlorine ions placed at alternate
points of a simple cubic lattice.
Each ion has six of the other kind of
ions as its nearest neighbours.
26

27. Structure of CsCl (Caesium Chloride)

28. Zinc Blende
Exhibited by many semiconductors
including ZnS, GaAs, ZnTe and CdTe.
GaN and SiC can also crystallize in this
structure.

29. Zinc Blende
Each Zn bonded to 4 Sulfur
- tetrahedral
Equivalent if Zn and S are reversed
Bonding often highly covalent
Wurtzite
Zinc sulfide crystallizes in two different
forms: Wurtzite and Zinc Blende.

30. Wurtzite (Hexagonal) Structure
•This is the hexagonal analog of the zinc-blende
lattice.
• Can be considered as two interpenetrating
close-packed lattices with half of the
tetrahedral sites occupied by another kind of
atoms.
• Four equidistant nearest neighbors, similar to a
zinc-blende structure.
•Certain compound semiconductors (ZnS, CdS,
SiC) can crystallize in both zinc-blende (cubic)
and wurtzite (hexagonal) structure.

32. CLASSIFICATION OF DEFECTS BASED ON DIMENSIONALITY
0D
(Point defects)
1D
(Line defects)
2D
(Surface / Interface)
3D
(Volume defects)
Vacancy
Impurity
Frenkel
defect
Schottky
defect
Dislocation Surface
Interphase
boundary
Grain
boundary
Twin
boundary
Twins
Precipitate
Faulted
region
Voids /
Cracks
Stacking
faults
Disclination
Dispiration
Thermal
vibration
Anti-phase
boundaries
Interstitial
defect

33. Point Defects Line Defects: Dislocations
Schottky Defects
Frenkel Defects
Metal Excess Defects:
The Color Centers
( F-center; Ger: farbenzentre)
Metal Deficiency Defects
Edge Dislocations
Screw Dislocations
Vacancy Defects
Interstitial Defects

34. Point Defects
Schottky
Defect
Frenkel
Defect
Vacancy
distortion Defect
of planes
Self-interstitial
distortion
of planes
Interstitial Atoms
Interstitial Defects

35. Metal Excess Defects: The Color Centers
Metal Deficiency Defects

36. Line Defects: Dislocations
Edge Dislocations Screw Dislocations
First elementary dislocation type:
edge dislocations

37. Rawat’s Creation-rwtdgreat@
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