Physics 927 E.Y.Tsymbal
Section 4: Elastic Properties
Elastic constants Elastic properties of solids are determined by interatomic forces acting on atoms when they are displaced from the equilibrium positions. At small deformations these forces are propor
Physics 927
E.Y.Tsymbal
Section 6: Thermal properties
Heat Capacity
There are two contributions to thermal properties of solids: one comes from phonons (or lattice
vibrations) and another from electrons. This section is devoted to the thermal properties o
Physics 927
E.Y.Tsymbal
Section 2: X-ray Diffraction and Reciprocal Lattice
Bragg law. Most methods for determining the atomic structure of crystals are based of the idea of
scattering of radiation. X-rays is one of the types of the radiation which can be
Physics 927
E.Y.Tsymbal
Section 11: Methods for calculating band structure
The computational solid state physics is a very fast growing area of research. Modern methods for
calculating the electronic band structure of solids allow predicting many importan
Physics 927
E.Y.Tsymbal
Section 9: Energy bands
The free electron model gives us a good insight into many properties of metals, such as the heat
capacity, thermal conductivity and electrical conductivity. However, this model fails to help us
other importa
Physics 927
E.Y.Tsymbal
Section 14: Dielectric properties of insulators
The central quantity in the physics of dielectrics is the polarization of the material P. The
polarization P is defined as the dipole moment p per unit volume. The dipole moment of a
Physics 927
E.Y.Tsymbal
Section 10
Metals: Electron Dynamics and Fermi Surfaces
Electron dynamics
The next important subject we address is electron dynamics in metals. Our consideration will be
based on a semiclassical model. The term semiclassical comes
Physics 927
E.Y.Tsymbal
Section 12: Semiconductors
Crystal structure and bonding
Semiconductors include a large number of substances of widely different chemical and physical
properties. These materials are grouped into several classes of similar behavior
Physics 927
E.Y.Tsymbal
Section 15: Magnetic properties of materials
Definition of fundamental quantities
When a material medium is placed in a magnetic field, the medium is magnetized. This
magnetization is described by the magnetization vector M, the di
Physics 927 E.Y.Tsymbal
Section 13: Optical properties of solids
Optical methods are very useful for the quantitative determination of the electronic band structure of solids. Experiments on optical reflectivity, transmission and refraction provide the wa
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98224593
Physics 927
8.2-Density of Levels
(a) In the free electron case the density of levels at Fermi energy can be written in the form (Eq.
(2.64) g(F ) = mkF /~2 2 . Show that the general form (8.63) reduces to this when F = ~2 k 2 /2m and
PHYS/ELEC 422/822 Homework #1 (due Thurs., Jan. 21)
1. One important property of all lattices is the so-called packing fraction. It refers to
the fraction of the volume of the unit cell that is occupied by the atoms, assuming the
atoms are hard spheres an
PHYS/ELEC 422/822 Homework #2 (due Thurs., Jan. 28, in class)
1. 1. Draw the following planes in an orthorhombic unit cell: (001), (011), (112), (201),
(101).
2. (a) How many <110> directions are contained in the (111) plane in the BCC
structure? List the
PHYS/ELEC 422/822 Homework #5 (due Thurs., Feb. 18)
1. Van Hove Singularities.
a) Using the dispersion relation for the monoatomic linear lattice of N atoms
with nearest neighbor interactions, show that the density of vibrational
2N
PHYS/ELEC 422/822 Homework #4 (due Tues., Feb. 16)
1. Prove the following results of the average energy for an oscillator and the
specific heat Cv in the Einstein model:
;
2. Show that for long wavelengths the equation of m
H { [J * ~§Tr (Mr? Ms) ~,‘1r{m,+m5) ~}1r(m‘1~m;:]
~ 6 ‘r e, + e,
i
2134f I M1,m2,WI5 and/(won or oddéMm‘mm
inmw?
(Hawk
0 WznA. «‘MM‘V
\
EL « ‘5 71'”
rz‘ L“ x
misoM. 30:
(cf,
C3 M
12C M r,
S
w: M
it
o2 41t§°( .475
“I T
s-u o 8‘.
37L .6-
ﬂ? ‘““
f2
PHYS/ELEC 422/822 Homework #6 (due Thurs., Mar. 3)
1. A onedimensional continuous solid has Youngs modulus of Y and density of .
a) Derive the specific heat of this 1D continuous solid per mole using the Debye theory.
Discuss its temperature dependence
PHYS422/822 Homework #1 (due Thurs., Jan. 21)
K m Pym)1. One important property of all lattices is the so—called “packing fraction”. It refers to
the fraction of the volume of the unit cell that is occupied by the atoms, assuming the
atoms are hard sphere
Physics 927
E.Y.Tsymbal
Section 8: Electronic Transport
Drude model
The simplest treatment of the electrical conductivity was given by Drude. There are four major
assumptions within the Drude model.
1. Electrons are treated as classical particles within a
Physics 927 E.Y.Tsymbal
Section 5: Lattice Vibrations
So far we have been discussing equilibrium properties of crystal lattices. When the lattice is at equilibrium each atom is positioned exactly at its lattice site. Now suppose that an atom displaced fro
Physics 927 E.Y.Tsymbal
Section 1: Crystal Structure
A solid is said to be a crystal if atoms are arranged in such a way that their positions are exactly periodic. This concept is illustrated in Fig.1 using a two-dimensional (2D) structure. y
T
C Fig.1
A
Physics 927 E.Y.Tsymbal
Section 2: X-ray Diffraction and Reciprocal Lattice
Bragg law. Most methods for determining the atomic structure of crystals are based of the idea of scattering of radiation. X-rays is one of the types of the radiation which can be
Physics 927 E.Y.Tsymbal
Section 3: Crystal Binding
Interatomic forces Solids are stable structures, and therefore there exist interactions holding atoms in a crystal together. For example a crystal of sodium chloride is more stable than a collection of fr
Physics 927 E.Y.Tsymbal
Section 4: Elastic Properties
Elastic constants Elastic properties of solids are determined by interatomic forces acting on atoms when they are displaced from the equilibrium positions. At small deformations these forces are propor
Physics 927 E.Y.Tsymbal
Section 5: Lattice Vibrations
So far we have been discussing equilibrium properties of crystal lattices. When the lattice is at equilibrium each atom is positioned exactly at its lattice site. Now suppose that an atom displaced fro
Physics 927 E.Y.Tsymbal
Section 6: Thermal properties
Heat Capacity There are two contributions to thermal properties of solids: one comes from phonons (or lattice vibrations) and another from electrons. This section is devoted to the thermal properties o
Physics 927 E.Y.Tsymbal
Section 7: Free electron model
A free electron model is the simplest way to represent the electronic structure of metals. Although the free electron model is a great oversimplification of the reality, surprisingly in many cases it
Physics 927 E.Y.Tsymbal
Section 8: Electronic Transport
Drude model The simplest treatment of the electrical conductivity was given by Drude. There are four major assumptions within the Drude model. 1. Electrons are treated as classical particles within a
Physics 927 E.Y.Tsymbal
Section 9: Energy bands
The free electron model gives us a good insight into many properties of metals, such as the heat capacity, thermal conductivity and electrical conductivity. However, this model fails to help us other importa
Physics 927 E.Y.Tsymbal
Section 10 Metals: Electron Dynamics and Fermi Surfaces
Electron dynamics The next important subject we address is electron dynamics in metals. Our consideration will be based on a semiclassical model. The term "semiclassical" come