PROF. M. BARSOUM WINTER 1991

E 848

First Exam

(90 Mins)

1) Carefully read the following statements which may or may not be true. First note whether statement is true or false. If the statement is correct elaborate on why you think it is correct. If you think statement is incorrect change it so as make it correct and explain why you made the changes. Use because in your answer.

EACH Worth 10 points:

a) Vacancies form in solids because their enthalpy of formation is negative.

b) If the enthalpy of forming a defect is negative the equilibrium number of defects would be infinite.

c) The structure of CaSi0₃ is most likely made up of ___ [discrete ion/chain/ sheet/3-D network/ etc.]

d) The stiffness of Si3N4 is greater/lower than SiO2 because

e) The density of MgO is less than SiC because

f) Frenkel defects are non-stoichiometric defects because they result in a change in the site ratio in the crystal.

g) Thermal expansion is related to the ________ of the energy well. Covalent ceramics usually have (higher/lower) thermal expansion coefficients than ionic ceramics because _______

h) Frenkel defects are less likely to occur in the fluorite and antifluorite structures than in the NaCl structure.

i) Al₂O₃ has a higher melting point than Mg0 because ___.

Write down the defect reactions and corresponding mass action expressions for:

a

j) Oxygen from atmosphere going interstitial

k) Schottky defect in M₂0₃.

l) Metal loss from ZnO

2) Consider Li₄SiO₄

20 a) What is the most likely structure Li₄SiO₄. State reasons for choosing structure and draw it

20 b) Calculate the theoretical density of Li₄SiO₄. Note you can solve this problem in terms of a lattice parameter, a. If you have time go back and figure it out in terms of the radii given below.

20 c) Write down a possible stoichiometric and a possible non-stoichiometric reaction for this oxide. In each case state starting and final composition. i.e. before and after reaction.

Information you may find useful

The radius of Li¹⁺ is 73 pm while that of the (SiO₄)^4- is 240 pm. radius of Si4+ 40 pm. The molecular wt of Si is 28, that of oxygen os 16 and that of lithium is 6.9 gms.

40 3) Compare the concentration of positive ion vacancies in a NaCl crystal due to the presence of a mole fraction of 10^-4 of CaCl₂ impurity with the concentration present in equilibrium in a pure NaCl crystal at 400°C. The formation energy (?h) of a Schottky defect is 2.12 ev, and the mole fraction of Schottky defects at the melting point of 800°C is 2.8x10^-4.

30 4) Starting with the energy distance curve, show that the theoretical strength of a solid is ˜ E/8.

50 For energy of a hypothetical bond is given as: E = - 1/r + 1/r² (J)

a) Estimate the theoretical strength of this bond as was done in class. i.e. similar to problem 4 above

b) Calculate an exact value for the theoretical strength of the bond.

c) How do the two numbers compare.