CondMat07PS4 - mixes substitutionally with copper, its main...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
1 CONDENSED MATTER PHYSICS 171.405 / 171.621 Instructor: N.P. Armitage Grader: Paula Mellado Fall 2007 Problem Set 4 Due to Graders mail box by Nov. 14th ============================= Q 1: Kittel 9.4 ============================= Q 2: As a simple model of a metal consider a one-dimensional chain of 2N atoms at distances a 0 from each other. Let φ ( x - na 0 ) be the correct wavefunction for an electron with energy E i at the atom located at na 0 (eigenvalue for a single-isolated atom). Under what conditions can the one-electron wavefunction ψ ( x ) for an electron delocalized over the whole chain of atoms be approximated by a linear combination of atomic orbitals ψ ( x ) = N X n = - N c n φ i ( x - na 0 ) (1) Choose the coefficients c n such that for N → ∞ the wavefunction ψ ( x ) is a Bloch wave. ============================= Q 3: Kittel 9.11 ============================= Q 4: Copper is a monovalent fcc nearly free electron metal. Zinc is a fcc divalent metal. In small quantities, zinc
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: mixes substitutionally with copper, its main eect being to increase the electron concentration. (a) Assume that the zinc-copper alloy will undergo a phase transition to bcc as soon as the Fermi sphere rst touches some point of the edge of the Brillouin zone. Show that this transition occurs on the order of 36% zinc concentration. Remember that in a fcc conventional unit cell there are four ions. You should assume that the free electron approximation is valid. (b) As the concentration of zinc further increases, another phase transition occurs when the Fermi surface intersects the Brillouin zone of the bcc lattice. What is this second concentration of zinc? (c) Why do these transitions occur? ============================= For students of 621 only: Q 5: Kittel 9.8...
View Full Document

This note was uploaded on 12/06/2009 for the course PHYSICS 171.405 taught by Professor N.peterarmitage during the Fall '07 term at Johns Hopkins.

Ask a homework question - tutors are online