Determine the coefficient of thermal expansion

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Reference no: EM13292199

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= 5 x 10-30 J.m and B= 8 x 10-121 J.m10. Determine the coefficient of thermal expansion (in m/m.K) for the material over the following temperature ranges:

a) 0oK to 0oC,

b) 0oC to 820oC.

assume that thermal energy of the system is 3kT/2 where k is Boltzman's constant k = 1.381 x10-23 J/K.

2. Calculate the density of BaTiO3. It has the perovskite structure. In the perovskite structure, the Ba2+ and O2-combine to form a cubic close packed structure with the Ba2+ on the cube corners and the O2- in the face centre positions (because the Ba2+ and O2- have nearly the same radius). The small Ti4+ fits nicely in an octahedral site. Because of stoichometry and charge neutrality, only ¼ of the octahedral sites (those in the body centre position) are filled with Ti4+. See figure below.

2368_Calculate the density.png

Ionic Radius                     Atomic Mass
Ba2+ 1.36 Ångstroms        137.3 g/mole
Ti 4+ 0.61 Ångstroms         47.9 g/mole
O2- 1.40 Ångstroms           16.0 g/mole

Avogadro's number (NAv) 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 oC.
b) an aluminium-magnesium (20 wt % Mg) alloy at 550 oC.
c) an aluminium-magnesium (80 wt % Mg) alloy at 300 oC.

1855_Calculate the density1.png

Reference no: EM13292199

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