Order 1252715: Condensed Matter physics

Senior Condensed Matter Physics

Assignment B, 2018

This assignment is due Thursday 1 November 2018 (11:59pm). It should be submitted online

through the Canvas or Turnitin link provided on the Canvas site for this unit.

1. For the unit cell shown below, determine the Miller indices for the planes A and B (may be

helpful to shift the origin).

2. Below is the x-ray diffraction pattern for copper (which has the fcc crystal structure) showing

the first several peaks. The wavelength of the incident monochromatic x-radiation used is

0.1542 nm. (a) Determine the h, k, l, indicies for each of these peaks, (b) find the interplanar

spacing corresponding to each of the peaks and (c) work out the lattice constant obtained

from each peak.

3. For silicon at a temperature of 450 K, calculate the equilibrium electron and hole

concentrations (n and p) for donor and acceptor concentrations of ND=1.0x10 17 cm-3 and

NA=3.0x10 17 cm-3, respectively.

4. The susceptibility due to Pauli-spin paramagnetism is given by 𝜒 = 𝜇0 𝑀

𝐵𝑒𝑥 = 𝜇0𝜇𝐵

2𝑔(𝐸𝐹)

𝑔(EF) is the density of states per energy and per volume (so has the unit m -3 J-1). Given

sodium has an electron density of n=2.53x1028 m-3,

(a) find the value of χ of sodium.

(b) For an applied external field of Bex = 1 T, what is the internal magnetic field Bin = μ0 M?

(c) To produce an internal field equal to the outer field, how much higher would the density

of states have to be?

5. (a) Given a paramagnetic material with a susceptibility of 2x10-4. Calculate the Curie constant

C, at 300 K.

(b) An H-field of 20 A/m is applied to a ferromagnet with a saturation magnetization of

1.3x106 A/m. If the magnetic field inside the material is 0.5 Tesla (i) find what percentage

of the domains are aligned to the field? (ii) Determine the magnetic susceptibility and

(iii) find what H field should be applied to this material to align all the domains to the

field?

(5 marks)

6. Choose one topic from the list below. With permission, you may also choose a topic not from

the list. From the perspective of condensed matter physics (rather than applications), explain

the essential concepts and principles that underlie our understanding of the topic. You may

make use of headings and figures.

o Semiconductor Devices

o Superconductivity

o Magnetic Resonance

o Density Functional Theory

o Magnetism

o Nanostructures

o Optical Properties of Dielectrics

o Topological Insulators

o Interacting Electrons

o Quantum Hall effect

You are limited to a maximum of 2-pages (not counting references), 12 point font.

The assignment is designed to strengthen your ability to write concisely in a form appropriate for a

scientific report or publication. Focus on quality, rather than quality.

Do not simply reproduce material from the Lecture Notes, you must go beyond what is covered

in class.

Students taking the advanced stream should make use of journal publications, referencing published

work appropriately.

(10 marks)