This preview shows page 1. Sign up to view the full content.
Physics 481: Condensed Matter Physics  Test prep Homework 7
due date: Friday, March 5, 2011
Problem 1: Tetragonal lattice
(15 points)
A hypothetical monoatomic substance crystallizes in a centered tetragonal structure. The con
ventional unit cell can described by primitive vectors (
a,
0
,
0)
,
(0
,a,
0)
,
(0
,
0
,c
) with
c
= 3
a/
2 and
a basis consisting of two atoms at positions (0
,
0
,
0) and (
a/
2
,a/
2
,c/
2). The lattice constant is
a
= 4
.
2
˚
A.
a) Calculate the maximum space ﬁlling for this lattice.
b) Find the primitive vectors of the reciprocal lattice.
c) A powder specimen of the substance is analyzed by Xray diﬀraction using the DebyeScherrer
method. The wavelength of the Xrays is 1.5
˚
A. Calculate the angles of the ﬁrst four diﬀraction
rings.
Problem 2: Phonon dispersion in a chain with longrange interactions
(AshcroftMermin
22.1 , 15 points)
Consider a onedimensional chain of identical atoms of mass
M
. The springs are not only between
nearest neighbors but between all pairs of atoms. Thus, the elastic energy reads
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 ThomasVojta
 Physics, Work

Click to edit the document details