1) The potential energy between two atoms can be represented as follows:
where A and B are constants and r the interatomic separation distance in metres. Plot the potential energy verses distance relationships for these atoms when A= 5 x 10-30 J.m and B= 8 x 10-121 J.m10. Determine the coefficient of thermal expansion (in m/moK) for the material over the following temperature ranges:
a) 0K to 0^{o}C,
b) 0^{o}C to 820^{o}C.
c) assume that thermal energy of the system is 3kT/2 where k is Boltzman's constant k = 1.381 x10-23 J/oK.
Submit a paper printout of the plot of the potential energy verses distance relationship including any markings necessary to understand how you determined the coefficient of thermal expansion.
2) Gallium arsenide (GaAs) has the zinc blende structure. The gallium atoms are in FCC packing and the arsenic atoms occupy half the tetrahedral sites. Calculate the density of Gallium arsenide (GaAs) using the following data.
Ga: Covalent Radius = 1.26 Ångstroms, Atomic Mass = 69.7 g/mole
As: Covalent Radius = 1.19 Ångstroms, Atomic Mass = 74.9 g/mole
Avogadro's number is 6.02 x 1023 atoms per mole.
3) Using the phase diagram below for the aluminium-magnesium system, determine
i) the phases present and
ii) the composition (wt% Mg) of each phase and
iii) the amount of each phase for:
a) an aluminium-magnesium (5 wt % Mg) alloy at 500^{o}C.
b) an aluminium-magnesium (20 wt % Mg) alloy at 550^{o}C.
c) an aluminium-magnesium (80 wt % Mg) alloy at 300^{o}C.