# Electrical Properties of Materials: EEE 307

EEE 307: Level 3, Term 1. Section: A

(Semester: August, 2011.)

Important Notice:

Students should study all the mathematical derivations that they were advised to do during class (the derivations that were not completely shown in class and left for the students to do).

Students are strongly advised to study the class test questions of all three sections. Students should remember the value of important constants for math problems.

Students are advised to keep their answers concise, specially for those questions which have 3 or 4 parts (a, b,c, and d).

Overview of Term final Syllabus:

Introduction to quantum mechanics

Magnetic properties of materials

Band theory of solids

Modern theory metals

Carrier statistics

Crystal structure

Classical theory of electrical and thermal conduction

Carrier statistics

Dielectric properties of materials

Introduction to Superconductivity

Study Materials:

Crystal structures:

The 3D models of crystal structures and unit cells (BCC, FCC etc.): Download

To view the 3D structures (*.wrl files), a VRML file viewer is required. Cornota 3D is free software that can be used to view the files. The software can be downloaded from the following link:

http://jcrystal.com/steffenweber/gallery/StructureTypes/st1.html

http://www.ibiblio.org/e-notes/Cryst/Cryst.htm

Worked out problems related to crystal structure

Some links to worked out math problems are given below:

Note that the solution files are not prepared by me. I have not verified all the results the files contain. Students are advised to contact me if they find any irregularities within these files. They should also ignore the topics that were not covered in the class.

Crystal plane viewer MATLAB code:

The following MATLAB codes can be used to view different crystal planes. The code creates a 3D unit cell. The 3D figure can be rotated and zoomed for clarity. Different m files for BCC structure and FCC structure are provided. By varying the Miller indices inside the code, different crystal planes are superimposed over the 3D reduced sphere unit cell. The program will be helpful for students for calculation of planar concentrations.

Schrodinger's Equation: One dimensional potential barrier problem:

An example problem of how to solve Schrodinger's equation for one dimensional potential barrier problem is discussed. The analysis shows procedures of how to calculate the unknown coefficients that comes from the general solution of the differential equations.

Dielectric properties of materials: Electronic and orientational polarization (temperature effects):

An example problem of how to solve problem related to static dielectric constant, permanent electric dipole moment and polarizability from dielectric constant versus temperature graph is discussed.

Lattice Vibrations and Debye Heat Capacity:

The derivation of average energy of lattice vibration is uploaded.

Class test 1:

Syllabus:

Types of crystal, lattice and basis, atomic packing factor of FCC, BCC structure, Bravias lattice, crystal directions and planes, Miller indices, planar concentration of atoms, crystal defects, classical theory of electrical conduction, the Drude model, drift velocity, mobility, temperature dependency of pure metals.

(It is recommended that the students use the MATLAB crystal plane viewer codes to visualize the crystal planes in 3D, as only 2D figures are shown in the solution file).

Class test 2:

Syllabus:

Resistivity of alloys, Matthiessen's rule, Nordheim's rule, Stefan's law, the Hall effect, thermal conduction, Wiedemann-Franz-Lorenz law, photoelectric effect, work function, De Broglie relationship, time independent Schrodinger's equation and its application to 1D problems (free electron, infinite potential well etc.), Heisenberg's uncertainty principle, tunneling phenomenon, scanning tunneling microscope (STM), potential box and degeneracy, band theory of solids, energy bands of metals, Fermi energy, metal-metal contacts and contact potential.

Class test 3:

Syllabus:

Band theory, Bloch theorem, Kronig-Penney model, effective mass, density of states, Maxwell-Boltzmann distribution, Fermi-Dirac distribution, Fermi Energy, Average energy of electrons, quantum mechanical calculation of molar heat capacity and Debye equation, concepts of magnetic field, magnetic dipole moment, magnetization from a macroscopic view point, magnetic susceptibility, orbital magnetic dipole moment.

Class test 4:

Syllabus:

Magnetic properties: Lenz's law and induced dipole moments, Atomic interpretation of magnetic properties of materials, classification of magnetic materials, diamagnetism, origin of permanent magnetic dipoles in matter, paramagnetic spin system, Curie's law of paramagnetism, Ferromagnetism, properties of ferromagnetic materials (Curie temperature and hysteresis lopp), spontaneous magnetization and Curie-Weiss law, orbital angular momentum and space quantization, magnetic quantum number, electron spin and intrinsic angular momentum, ferromagnetism origin and the exchange interaction.

Dielectric properties: Relative permittivity, dipole moment and polarization, polarizability, polarization vector, local field (Lorentz field), Clausius-Mossotti equation, electronic polarization in covalent solids, ionic polarization, orientational polarization, frequency dependence: dielectric constant and dielectric loss, loss tangent, Debye equation of relative permittivity for dielectrics, piezoelectricity.

Incredible People: Paul A. Maurice Dirac (1902 – 1984)

“God used beautiful mathematics in creating the world.”

Dirac was one of the greatest theoretical physicists in the twentieth century. He is best known for his important and elegant contributions to the formulation of quantum mechanics; for his quantum theory of the emission and absorption of radiation, which inaugurated quantum electrodynamics; for his relativistic equation of the electron; for his “prediction” of the positron and of antimatter; and for his “large number hypothesis” in cosmology.