CMP Teaching Spring2013

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Condensed Matter Physics

Instructor: Dr. [Sabieh Anwar] Office hours: Monday and Wednesday (9:30 am to 10:30 am).

Textbooks: Elementary Solid State Physics by Muhammad Ali Omar (available in low priced edition). You should really possess the book.

Image:cmp1.jpg


Outline: Click here for the course outline.

Purpose of the course: The purpose of the course is to introduce students to the structure of the solid phase of matter and how the properties can be derived from a quantum understanding of electrons, phonons and their interactions, modulated by the periodic arrangement of atoms. Emphasis will be made on the band structure and methods to determine the same. There will be special focus, towards the end, on the burgeoning field of low-dimensional materials as well as the ubiquitous semiconductors. After the course, the students will be familiar with the basics of condensed matter physics, enabling them to take more advanced courses focusing on unique materials properties in the electronic, optical, magnetic, thermal, and acosutic regimes as well as specialized courses on mesoscopic physics and devices.


Describing the crystalline state (8 lectures)

  • Symmetry operations and elements, point groups, space groups, crystal systems, finding directions, planes and coordinates in crystals, important crystal structures (simple, fcc, bcc, CsCl, rocksalt, diamond, zincblende, wurtzite), close packing, coordination

Notes and background reading:

Miscellaneous handouts:

Software for visualization:

Homework: (due date=11 February 2013; 8:30 am)

Homework on the crystalline state
HW solution


Quiz: (date=13 February 2013; 8:30 am)

Quiz 1 and its solution

Classroom demonstration on the close packing of atoms Table tennis balls that are glued together can be stacked on top of one another showing the two most important kinds of packing - hexagonal and face centred cubic packing. One may use balls painted in different colors to bring home the ideas more vividly. Click on the images for close-ups.
A single layer of atoms.
A single layer of atoms.
A single row of atoms stacked on the bottom layer.
A single row of atoms stacked on the bottom layer.
A complete second layer stacked on top of the bottom layer. There is one and only one way in which the close packing is possible.
A complete second layer stacked on top of the bottom layer. There is one and only one way in which the close packing is possible.
A close up showing the interstices.
A close up showing the interstices.
The third layer is on top of the interstices in the bottom layer. Called ABC stacking (fcp).
The third layer is on top of the interstices in the bottom layer. Called ABC stacking (fcp).
The third layer is directly on top of the atoms in the bottom layer. Called AB stacking (hcp).
The third layer is directly on top of the atoms in the bottom layer. Called AB stacking (hcp).

Diffraction as a means of determining crystal structures (4 lectures)

  • Fourier transform formulation of the diffraction problem, reciprocal lattice is the Fourier transform of the direct lattice, sampling of atomic factors by the reciprocal lattice, allowed scattering angles: Laue formulation and Bragg formulation, Ewald's synthesis, atomic scattering, structure factor, systematic absences, common experimental arrangements

Notes and background reading:

  • X-ray diffraction. This is Ch 8 and 9 from Hammond's book: "The Basics of Crystallography and Diffraction". This is the closest description I could find to the approach we've covered in class.

Software for visualization:

  • Cambridge University has this very nice tutorial on the reciprocal space along with graphic visualizations.
  • See the online tutorial on diffraction of X-rays from crystal structures at the Department of Structural Biology, Madrid, Spain.
  • X-ray viewis a virtual X-ray crystallography laboratory that helps visualize the scattered intensities from various lattice types. Download, run and enjoy!

Homework: (due date=27 February 2013; 8:30 am) Homework on diffraction from the crystal
HW solution


Quiz: (date=6 March 2013; 8:30 am) Quiz 2 and its solution


Free electron theory of metals (4 lectures)

  • Classical Drude's model: modeling the electron as a gas of electrons obeying kinetic theory of gases, dc and ac conductivity, thermal conductivity, Lorenz number, Pauli paramagnetism, heat capacity, selected mechanical properties
  • Application of quantum statistical: Fermi-Dirac distribution, chemical potential and Fermi energy, dependence of chemical potential on temperature, heat capacity, Pauli paramagnetism, dc conductivity, density of states for 3D, 2D and 1D solids
  • Read Ch4 of Omar and attempt all back of chapter problems.

Midterm: (date=16 March 2013; 10:00 am)
Midterm
Solution


Waves in crystalline solids (4 lectures)

  • Elastic waves under the continuum limit: wave equation and the linear dispersion relationship (note that linear dispersion means no dispersion).
  • Einstein's model of heat capacity
  • Debye's model of heat capacity
  • Phonon
  • Waves in locally periodic media: transfer matrix approach
  • Crystal oscillations
  • Dispersion relations for monatomic and diatomic lattices
  • Brillouin Zones
  • Inelastic neutron scattering, Brillouin light scattering
  • Thermal conductivity, Normal and Umklapp processes
  • Read Ch3 of Omar.
  • Homework: (due date=8 April 2013; 8:30 am) Homework on heat capacities. HW solution
  • Quiz: (date=8 April 2013; 8:30 am) Quiz 3 and its solution
  • Homework: (due date=24 April 2013; 7 pm) Homework dealing with quantized crystal oscillations

HW solution


Final Exam: (date=20 May 2013; 8:30 am)
Final Exam
Solution


Notes and background reading:

  • Piecewise potentials. This is Ch 6 from Merzbacher's classic book on Quantum Mechanics from the 1961 edition. It has a treatment of wave propagation in periodic potentials, based on transfer matrices, that closely matches what we've covered in the class. Note that this is a big (7 MB) pdf file.
  • Here is a series of simulations imbedded in a nice tutorial on Brillouin zones, hosted at the University of Cambridge's website.
  • Some experimental results related to Thermal conductivity and phonons.
  • Ch 25 of Pedrotti's famous book on Optics deals with the macroscopic optical properties of solids. I find this a satisfying read.
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