PHYS 254, Problem Set 2. Reciprocal lattice,
Diraction on Bravais lattices.
The homework is due Friday, Jan 30th, 2014
1. What determines the width of diraction maxima? (10p) Kittel
problem 2.4.
2. Diraction on graphene. (20p) In 2007, two years after the
Mm+k3QM '- £otvb\ m1]. . 0.x
: / '
f {7* 2 I77 n
J F [gin-[1": (e, #2,) :61 7 s :~ 1:2: MA?!
'I ' Z -.
o A- : *J-"i- = FPS: t-|=-L-_,7nzga+rve W donol'mr"
KW -* Mam Jane, and :92 W _.
Q _
(2m 2; 20 + Zen ces(1_.'m%) Jr 551421526)
0h 0L
p.
./ A
W, ' °
PHYS 254, Problem Set 1 Solutions
Problem 1.
p
a. Square root is a multi-valued function (
1 = 1). If we keep both the
roots, no problems arise:
p
p
p
p
1 = 1 =
1 1 = ( 1) ( 1) = i i
R +1
b. By denition of the Fourier transform, f (k) = 1 f (x)e ikx dx.
0
Problem 1
1 exp[ iM(a k)] 1 exp[iM(a k)]
1 exp[ i(a k)] 1 exp[i(a k)]
|F|2
sin 2 1 M(a k)
2
.
sin 2 1 (a k)
2
1 cos M(a k)
1 cos(a k)
(b) The first zero in sin
sin M( h
1
M occurs for = 2 /M. That this is the correct consideration follows from
2
1
1
) sin
P /"50t,ml'l in Email. IGOKTaMM, ldqg_pnonj
Mnons .
,1, 0n 0|le reach MOM 54+;
Sjcwljc. 0L+om Po§$0w5 «a dnaMic, [00950113, ssumryons- m w .0. Sh
. u I Z. Ech-suons 41mm, _l£ awn!
We Mule +0 Plan : Sharpmssl 04' dlw #SJ) Wm} Pmm (5 0+ salidag' {
Mould; E
PHYS 254, Problem Set 1. Crystal structure
The homework is due Tuesday, Jan 21st, 2014
1. Math (10p).
a. What is wrong with the the following derivation?
1 = 1 1 = 1 1 = i i = 1
Please provide enough detail to understand your answer.
b. Suppose the Fourie
,.
PHYS 635 Solid State Physics
Assignment VI (Oct 6, 2000)
Solutions
1. For a 2-dimensional crystal of area A, the area in reciprocal space occupied by each phonon state is
1
(2n? /A. For N phonon states, the total area in reciprocal space is thus N(47r
PHYS 254, Problem Set 3. Cohesion and
Phonons
The homework is due Tue, Feb 11th , 2014
1. Linear ionic crystal (15p). Review Kittel, Chapter 3. Please pay attention
to the repulsive energy that is treated in more details in the book compared to
the lectur