PHYS 353 Solid State Physics
Supplemental Problems
Part 1. Crystal Structure
1-1. Hooke & Hall 1.1
1-2. For each of the five planes listed below sketch a cubic unit cell and shade in the plane (like in Fig.
1.6 in Hook & Hall).
)111( )211( )011( )101( )001(
1-3. Consider the 2-D crystal shown below. A square unit cell is shown in the lower left along with the
lattice vectors a. The tick marks divide the unit cell axes into thirds. All atoms are of the same
species A and are denoted by the dots. An arbitrary plane is represented by the tilted solid line.
Draw the crystal on your paper and do the following.
(a) Put an asterisk at (1/3, 2/3).
(b) Draw an arrow from the origin in the direction of [1 2].
(c) Draw a line representing the plane (2 1).
(d) Write down the basis for the crystal.
(e) What are the Miller indices of the plane represented by the
tilted solid line?
1-4. Consider the 2-D square crystal shown below. The unit cell has a length of a. The lines represent
some consecutive planes of the crystal.
(a) Using geometry and trig, show that the spacing between
consecutive planes is
5/ad
.
(b) Verify this spacing using the equation
222
lkh
a
d
.
1-5. In an x-ray spectrometer, a specimen of copper has a strong reflection signal at a Bragg angle of
47.75 at a temperature of 293 K. At 1273 K, the same specimen has a Bragg angle of 46.60. Did
the atomic planes get closer together or farther apart when the temperature increased? By what
factor did the separation distance increase or decrease?
a
a
b
x
y
a
a
b
x
y