Chemistry of materials | Assignment 2 ENGR20003 | Semester 2 – 2021 Bonding energy – Question 1 – (2marks) The potential energy between two atoms can be represented as follows: 10r B r A V + = 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. Important: Submit a plot of the potential energy verses distance relationship including any markings necessary to understand how you determined the coefficient of thermal expansion. Crystal structure – Question 2 – (2marks) 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 stoichiometry and charge neutrality, only of the octahedral sites (those in the body centre position) are filled with Ti4+ . See figure 1 below. Avogadro’s number (NAv) is 6.02 x 1023 atoms per mole. Chemistry of materials ENGR20003 | 6% weighing of the total score Assignment 2 Individual assignment Online submission 6% weighing Maximum 6 marks, 2 per question Due at Midnight 08/10/2021 — Engineering Materials ENGR20003 Contact: Senior tutor for questions Dr Madhu Address: Chemistry of materials| Assignment 2 ENGR20003 | Semester 2 – 2021 Ionic Radius Atomic Mass Ba2+ 1.36 ngstroms 137.3 g/mole Ti4+ 0.61 ngstroms 47.9 g/mole O2- 1.40 ngstroms 16.0 g/mole Figure 1: Representation of a BaTiO3 Perovskite structure, Oxygen atoms in red, Titanium atoms in blue and Barium atoms in green Important: Important: Submit a sketch of the unit cell and any diagram necessary to understand how you determined the atomic packing factor and the density. Phase diagram – Question 3 – (2marks) Using the phase diagram below (figure 2) 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 Chemistry of materials| Assignment 2 ENGR20003 | Semester 2 – 2021 Figure 2: Aluminium-magnesium phase diagram from Van Vlack, Elements of Materials Science and Engineering, 1975 . END OF ASSIGNMENT 3 6 marks in total
