Chapter 12, Crystal Structure Video Solutions, The Oxford Solid State Basics

Problem 1

Crystal Structure of NaCl
Consider the NaCl crystal structure shown in Fig. 12.21. If the lattice constant is $a=0.563$ $\mathrm{nm}$, what is the distance from a sodium atom to the nearest chlorine? What is the distance from a sodium atom to the nearest other sodium atom?

Dading Chen

Numerade Educator

01:01

Problem 3

Crystal Structure
The diagram of Fig. 12.22 shows a plan view of a structure of cubic ZnS (zincblende) looking down the $z$ axis. The numbers attached to some atoms represent the heights of the atoms above the $z=0$ plane expressed as a fraction of the cube edge $a$. Unlabeled atoms are at $z=0$ and $z=a$.
(a) What is the Bravais lattice type?
(b) Describe the basis.
(c) Given that $a=0.541 \mathrm{~nm}$, calculate the nearestneighbor $\mathrm{Zn}-\mathrm{Zn}, \mathrm{Zn}-\mathrm{S}$, and S-S distances.
$$
\mathrm{Zn}=\square \quad \mathrm{S}=\square
$$
Fig. $12.22$ Plan view of conventional unit cell of zincblende.

Narayan Hari

Numerade Educator

01:35

Problem 4

Packing Fractions
Consider a lattice with a sphere at each lattice point. Choose the radius of the spheres to be such that neighboring spheres just touch (see for example, Fig. 12.18). The packing fraction is the fraction of the volume of all of space which is enclosed by the union of all the spheres (i.e., the ratio of the volume of the spheres to the total volume). (a) Calculate the packing fraction for a simple cubic lattice.
(b) Calculate the packing fraction for a boc lattice.
(c) Calculate the packing fraction for an foc lattice.

Suzanne W.

Numerade Educator

02:51

Problem 5

Fluorine Beta Phase
Fluorine can crystalize into a so-called betaphase at temperatures between 45 and 55 Kelvin. Fig. $12.23$ shows the cubic conventional unit cell for beta phase fluorine in three-dimensional form along with a plan view.

Fig. 12.23. A conventional unit cell for fluorine beta phase. All atoms in the picture are fluorine. Lines are drawn for clarity Top: Threedimensional view. Bottom: Plan view. Unlabeled atoms are at height 0 and 1 in units of the lattice constant.
$\frac{1}{4}$ and $\frac{3}{4}$
D. How many atoms are in this conventional unit cell?

D. What is the lattice and the basis for this crystal?

Freddie Montague

Numerade Educator