Answer Set 2
Physics 140A
Myers 2.11 Ill use a symmetric set of primitive vectors, a1 = a [1, 1, 1], a2 = a [1, 1, 1],
2
2
and a3 = a [1, 1, 1]. (I will write minus signs in the normal place, not above the
2
2
3
number.) Then a2 a3 = a4 [0, 2, 2] and a1 a
Answer Set 1
Physics 140A
1. The rst six nearest-neighbor distances, and the number of atoms at each, are
Distance Number neighbors Sample coordinates
a
6
a(1,0,0)
2a
12
a(1,1,0)
3a
8
a(1,1,1)
6
a(2,0,0)
2a
5a
24
a(2,1,0)
6a
24
a(2,1,1)
a)
The sums become
Answer Set 3
Physics 140A
Myers 3.4 Since potassium and chlorine are very close in atomic weight, they have nearly identical
atomic form factors. Hence the structure factor at certain locations is small enough that the
diraction spot is not visible. In fa
Answer Set 4
Physics 140A
Myers 5.4 Were looking at a spring with spring constant K which is anchored at one end and
has a mass M at the other. For longitudinal displacement of the mass, along the direction of
the spring, a displacement x also corresponds
Answer Set 6, Physics 140A
1. a) Since springs are 1D creatures, we rst need to relate a 3D compression to what happens to the
d
d
d
springs. Note that dL = dV dV = 3V dV , where L = V 1/3 is the length of a side. Also, if there
dL
L
are N atoms in the cr
Answer Set 5
Physics 140A
Myers 5.3:
a) In 2D, each allowed k-value corresponds to an area (2/L)2 in k-space. (I am assuming the overall
crystal dimensions are LL; in fact the calculation is nearly identical if the sample is a rectangle
instead of a cube.
Answer Set 8
Physics 140A
Myers 6.7 Monovalent means one electron per atom. For bcc there are two atoms per cube 4.225 on a
A
side. This means kF = (3 2 n)1/3 = 9.2109 m1 , and EF = h2 kF /2m = 5.11019 J. A 1% relative
2
shift means the Fermi energy of o
Answer Set 7, Physics 140A
Myers 6.3: In three dimensions the Fermi energy is EF =
a)
dEF
dT
2
2
h
2
2 2/3 .
2m (3 n)
2
d
1 dL
h
h
h
= 2m (3 2 N )2/3 dT (V 2/3 ) = 3mV (3 2 n)2/3 dV = (3 2 n)2/3 L dT = 2EF . Note that the
dT
m
negative sign makes sense; a
Answer Set 9
Physics 140A
Myers 7.4 Reciprocal lattice is bcc, lattice constant 4/a. Edge of Brillouin zone in [111]
direction is at pi [111]. For x-axis plot as function of where . The
a
a
a
relevant k-vectors can be written as k = G + ( + y + ). Find en