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Introduction to Solid State Physics
Introduction to Solid State Physics
Solid State Physics
Prof. Igor Shvets
Slide 1 Lecture 1Syllabus
Lattice structure: lattice with a basis.
Lattice structures of common chemical elements.
Concept of Bravais lattice, definition and examples.
Primitive vectors of Bravais lattice.
Primitive/Conventional unit cell.
Wigner-Seitz primitive cell.
Examples of common crystal structures.
Body-centered cubic lattice.
Face-centered cubic lattice.
First Brillouin zone.
Lattice planes and Miller indices.
Slide 2 Lecture 1Syllabus
Determination of crystal structures by X-ray diffraction.
Bragg formulation of X-ray diffraction by a crystal.
Von Laue formulation of X-ray diffraction by a crystal.
Equivalence of Bragg and Von Laue formulations.
Symmetry, elements of point groups
Geometrical structure factor.
Atomic form factor.
Stress and Strain.
Slide 3 Lecture 1Recommended Reading
Solid State Physics Ashcroft & Mermin, Holt-Saunders
• A great text for anyone with an interest in the subject.
Solid State Physics Hook & Hall, Wiley
• Useful text. Read as a compliment to Ashcroft or Elliott.
Introduction To Solid State Physics Kittel, Wiley
• Covers a huge amount in basic detail.
The Physics and Chemistry of Solids Elliott, Wiley
• Lateral reading. Quite Chemistry based. Good for problem solving.
Structure of materials De Graef, McHenry,
• Covers a huge amount in basic detail, good for problem solving.
Slide 4 Lecture 1Crystals
Solids can be categorised into either crystalline or non-
This course deals with the structures found in crystalline
solids i.e. crystals.
A Crystal is a solid in which the
constituent atoms, molecules,
or ions are packed in a
regularly ordered, repeating
pattern extending in all three
Slide 5 Lecture 1Crystals
Despite an underlying crystalline
structure the crystal itself may
not appear regular in shape.
A closer look at the
substance reveals a
Slide 6 Lecture 1Examples
Principle component of
More on that later
Slide 7 Lecture 1Examples
Silicon Dioxide or Silica with a
definite crystalline structure.
Each Silicon atom is surrounded
by four Oxygen atoms.
Silicon Dioxide is an example of
Tetrahedral oxygen termination.
Oxidation State Electron
O -2 He.2s .2p
Si 4 Ne
Slide 8 Lecture 1Examples
Amorphous SiO (Silica gel)
As with the crystalline SiO
- Most silicon atoms have 4
- Most oxygen atoms have 2
Silica gel is an example of a non-
The local symmetry is the same
as the crystalline SiO
However, translational symmetry
Slide 9 Lecture 1Oxygen Termination
The two forms of oxygen termination are Tetrahedral and
These refer to the structure of the oxide in relation to the original
structure of the crystal.
Tetrahedral Oxygen termination
is when four oxygen atoms
create a tetrahedron around the
original atom e.g. Silicon
Octahedral Oxygen termination
is when six oxygen atoms create
a octahedron around the original
atom e.g. Aluminium
Slide 10 Lecture 1Examples
Aluminium Oxide (Al O )
Each Aluminium atom is
surrounded by six Oxygen
Aluminium Oxide is an
example of Octahedral oxygen
O -2 He.2s .2p
Al 3 Ne
Slide 11 Lecture 1Examples
Magnesium Oxide (MgO)
Structure is the same as
that of Sodium Chloride.
i.e. F.C.C. lattice with a two
Again more on that later
Oxidation State Electron Configuration
O -2 He.2s .2p
Mg 2 Ne
Slide 12 Lecture 1Examples
Magnetite ( Fe O )
32 oxygen anions form an F.C.C. lattice
This is an example
of Spinel structure.
8 tetrahedral interstices are occupied
by Fe ions
(Basic repeat unit)
16 octahedral interstices are occupied by
a = 0.8397nm
Fe and Fe ions in equal proportions
Slide 13 Lecture 1Spinel Group
Refers to a class of minerals with the general formulation
2+ 3+ 2-
A B O
The oxide anions arrange in a cubic lattice with the A and B
cations occupying the Tetrahedral and Octahedral sites.
Possibilities for A and B include Magnesium, Zinc, Iron,
Manganese, Aluminium, Chromium, Titanium and Silicon.
In the case of Magnetite (Fe O ) the Iron is both A and B. That is,
A and B are the same metal under different charges.
3+ 3+ 2-
Fe (Fe Fe )O
Slide 14 Lecture 1High Performance Materials
The majority of the worlds electricity supply is generated in
power stations using steam turbines.
Through the use of coal,
nuclear power, etc.
steam is generated and
is passed through the
giant steam turbines.
The turbines rotate and
Assuming the system can be considered
a Carnot Engine and using current
average values of temperatures in the
T 2 system (T =35°C and T =540°C) the
efficiency is calculated to be 62%.
Slide 15 Lecture 1High Performance Materials
As supplies of fossil fuels are
diminishing, there is large interest
in making the steam turbine a
more efficient process for
A way to increase this efficiency
is to operate the system with a
larger temperature gap, ie by
making T larger.
Slide 16 Lecture 1High Performance Materials
This is not as simple as it sounds. To
increase the efficiency by just 5% would
require an average operating temperature
increase from 540°C to 660°C.
The turbine blades themselves must be able
to withstand these high temperatures
without melting or buckling.
This is where knowledge of the crystal structure of
the materials used in their production is
invaluable. Without a detailed analysis of the
structure engineers and scientists would not be
able to combat the problem of creating a more
Slide 17 Lecture 1Lattice
When dealing with crystal structures it is best to firstly
consider the mathematical idea of a lattice, without the
notion of atoms or molecules at this stage.
A Lattice is a regular, periodic
array of points throughout an area
(2D) or a space (3D).
This picture shows one of many
possible lattice types.
Example of a 2D Lattice
IMPORTANT NOTE: The lattice is the underlying pattern of
the crystal. The crystal is being described by the lattice
that can contain more than one atom/ion assigned to
each point of the lattice. This is called a Basis.
Slide 18 Lecture 1Basis
You have a lattice
with more than one
atom/ion assigned to
each lattice point.
Atoms can be the
same or different.
will have larger/more
All crystal structure
consists of identical
Consider a point of the lattice
copies of the same
Then apply to the rest of the lattice
physical unit, called Now introduce a arbitrary basis of two atoms
the basis, assigned
to all the points of
Lattice + Basis = Crystal
Slide 19 Lecture 1Basis
While the basis is
assigned to each point
of the lattice there is
nothing to say that it is
anywhere near this
Consider the same
lattice and basis as
Increase the separation
between the basis and
the lattice point.
We discover that the
same lattice is revealed
when the new position
of the basis is applied
to each lattice point.
Slide 20 Lecture 1