Solid State Physics - I
Dr. Ram Chand
February 10, 2019
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Contents
1 Crystal Structure
1.1 Introduction . . . . . . . .
1.1.1 Solid State Physics
1.1.2 Classification . . .
1.1.3 Crystallography . .
1.1.4 Crystal Structure .
1.1.5 Terminology . . . .
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2 The Second Chapter
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CONTENTS
Chapter 1
Crystal Structure
1.1
1.1.1
Introduction
Solid State Physics
Solid-state physics is the study of rigid matter, or solids, through methods
such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics.
1.1.2
Classification
The solids may be broadly classified as crystalline and non-crystalline (amorphous) depending upon the arrangement of atoms or molecules.
CRYSTALLINE SOLIDS
The crystalline state of solids is characterized by regular or periodic arrangement of atoms or molecules.
Crystalline solids may be sub-divided into single crystals and polycrystalline solids.
Single Crystal
In single crystals, the periodicity of atoms extends throughout the material
as the case of diamond, quartz, mica, etc.
Polycrystalline
A polycrystalline material is made up of smaller crystallites. Each small
crystallite is known as grain and there grain boundaries between two
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CHAPTER 1. CRYSTAL STRUCTURE
grains.
Single cystals may be classified as elemental crystal (e.g., Al. Fe, Cu,
etc.) and ionic crystal (AgCl, CuSO4 , etc.).
AMORPHOUS SOLIDS
The non-crystalline or amorphous solids are characterized by the completely random arrangement of atoms or molecules. These solids exhibit
short range order. Glass is an example of amorphous materials. Most of the
plastics and rubbers are also amorphous.
1.1.3
Crystallography
The science which deals with the study of geometrical forms and physical
properties of crystalline solids is called crystallography.
1.1.4
Crystal Structure
A crystal is a 3-dimensional body. Regular and periodic arrangement of 3dimensional pattern of atoms or molecules in space, is called crystal structure,
where each and every atom or molecule have the same environment.
1.1.5
Terminology
Point Lattice
An arrangement of infinite number of imaginary points in three-dimensional
space with each point having identical surroundings is known as point lattice.
Space Lattice
A space lattice is defined as an array of imaginary points which are so arranged in space that each point has identical surroundings.
Lattice Plane
Within crystal any plane passing through at least one lattice point is called
a lattice plane.
1.1. INTRODUCTION
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Basis
An atom or group of atoms which is placed on each lattice points in regular
fashion is known as basis. The basis acts as building unit or structural unit
for a complete crystal structure. It can be expressed as:
Space lattice + basis = Crystal Structure
A lattice is mathematical concept and crystal is physical concept.
Unit Cell
A unit cell may be defined as the smallest unit of the lattice which, on
continuous repetition, generates the complete lattice. Both primitive and
non-primitive translation vectors may be used to construct a unit cell.
Primitive unit cell is the smallest volume cell. All the lattice points
belonging to a primitive cell lie at its corners. Therefore, the effective number
of lattice points in a primitive unit cell is one. A non-primitive cell may
have the lattice points at the corners as well as at other locations both inside
and on the surface of the cell and, therefore, the effective number of lattice
points in a non-primitive cell is greater than one.
The distance (a) between two atoms or ions of same type is called the
length of unit cell.
Lattice Parameter
The primitive vectors ~a, ~b, ~c and the inter-facial angles α, β, γ are together
called as ”lattice parameter” of the crystal.
Lattice Vector and Direction
To specify certain point or direction in unit cell, we use lattice vector ~a, ~b, ~c
as:
T~ = n1~a + n2~b + n3~c
where n1 , n2 , n3 are three integers.
Symmetry Operation
A symmetry operation is that which transforms the crystal to itself, i.e.,
crystal remains invariant under symmetry operation. These operations are
translation, rotation, reflection and inversion.
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CHAPTER 1. CRYSTAL STRUCTURE
Chapter 2
The Second Chapter
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CHAPTER 2. THE SECOND CHAPTER