Determine the coefficient of thermal expansion

Question

1. The potential energy between two atoms can be represented as follows:

                                            V = -A/r + B/r¹⁰

Where A and B are constants and r the interatomic separation distance. Plot the potential energy verses distance relationships for these atoms when A= 8 x 10^-30 J.m and B= 5 x 10^-119 J.m¹⁰. Determine the coefficient of thermal expansion (in m/m.K) for the material over the following temperature ranges:
a) 0^oK to 0^oC,
b) 0^oC to 820^oC.
assume that thermal energy of the system is 3kT/2 where k is Boltzman's constant k = 1.381 x10^-23 J/K.

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.

                      Covalent Radius                Atomic Mass
           Ga        1.26 Ångstroms               69.7 g/mole
           As        1.19 Ångstroms                74.9 g/mole

Avogadro's number (NAv) is 6.02 x 10²³ atoms per mole.

3. Using the phase diagram below for the copper-silver system, determine:

i) the phases present

ii) the composition (wt % Cu) of those phases and

iii) the amount (wt %) of each phase for

a) a copper-silver alloy (70 wt % copper) at 900^oC

b) a copper-silver alloy (70 wt % copper) at 600^oC

c) a copper-silver alloy (5 wt % copper) at 800^oC