Physics 315
Physics of Materials
Midterm exam February 2004
Allowed aids: Calculator, 2 page "cheat sheet".
Answer all questions

1: The NaCl structure is face centered cubic with a basis vector ${\bf d}=\frac{a}{2}\hat{\bf x}$. (a) If the two types of ions in the structure were of the same size, what would be the packing fraction $f$?
(b) What is the packing fraction if the radius of one type of ions is twice that of the other type?
2: Copper is face centered cubic with the side of the unit cube $a=3.61$ Å.
(a) Find a set of primitive reciprocal lattice vectors for copper.
(b)What is the distance between the (111) lattice planes?
c: What is the density of atoms (number of atoms/unit area) in the (111) planes of copper?
3: In an isotropic material it is conventional to describe the elastic constants in terms of the Lamé constants $\lambda=C_{12}$ and $\mu=C_{44}$. The elastic constant $C_{11}$ is then given by $\lambda +2\mu$. In a certain material $\lambda=1.\times 10^{10}Nm^{-2}$, $\mu=0.4 \times 10^{10} Nm^{-2}$.
a: A sample made of this material is subject to the pressure of 1000 bar ($= 10^8$ Nm$^{-2}$). What is the fractional change in volume?
(b) A wire of the material has a cross section of 1 mm$^2$. It is pulled by a force of 100 N without breaking. Calculate the fractional change in length and volume.