Figure $1$: XRD data

For an FCC crystal with lattice constant $a=0\mathrm{.}3nm,$ calculate the volume atomic density,

the planar atomic density of the $(011)$ plane, and the linear density in the $[111]$ direction.

Briefly describe what it means to be a polycrystalline solid

Briefly define isotropy$/$anisotropy and identify which materials in table $3\mathrm{.}4$ may be isotropic

vs anisotropic.

Briefly describe the process used to determine crystal orientation using X$-$Ray Diffractometry

$($XRD$)$

Calculate expected measured diffraction angle, $2,$ for a $(111)$ plane in an FCC crystal with

lattice constant $a=0\mathrm{.}4nm$ if a second order peak is observed using a $0\mathrm{.}1749$ nm laser

Calculate the lattice constant for the XRD data in figure $1$ below assuming it was illumi$-$

nated by a $0\mathrm{.}15$ nm monochromatic laser. You may assume all listed planes are first order

diffractions

Briefly describe the differences between interstitial and vacancy type defects

Calculate the vacancy concentration for the crystal described in problem $1$ at $100$ C if the

activation energy is $Q_v=1\mathrm{.}2eV.$

Why might vacancy concentration be temperature dependent?

Would an interstital or substitutional impurity participate in the bonding structure of the

crystal? Why?

Given an FCC crystal, what is the largest possible radius of an interstital impurity which

exists on an edge of a crystal with $a=0\mathrm{.}5nm($i$.$e$.$ on a direct line between two adjacent

corners$)?$

Calculate the weight percent, atomic percent, and density of a Tin $($ Sn