I tried it, the answers is not .98%. One way to determine a structural defect mo
ID: 989166 • Letter: I
Question
I tried it, the answers is not .98%. One way to determine a structural defect model (such as that shown in the figure below for a solid solution of A12O3 in MgO) is to make careful density measurements. A substitutional solid solution of Al2O3 in MgO is not as simple as the case of NiO in MgO. The requirement of charge neutrality in the overall compound permits only two Al3+ ions to fill every three Mg2+ vacant sites, leaving one Mg2+ vacancy. What would be the percent change in density for a 5 mol % solution of Al2O3 in MgO (compared with pure. defect-freeMgO) Express your answer to three significant figures.
Explanation / Answer
MgO has NaCl type structure with 4 Mg2+ and 4 O2- ions per unit cell.
Hence for pure MgO, Zeff = 4
Now we added 5 mol% of Al2O3 in MgO.
Affter the defect, only 2 Al3+ can be accomodated in place of 3 Mg2+ ions. Hence 1/3 rd of Mg2+ will remain vacant. Hence for the impure MgO the value of Zeff will be
Zeff = 4x(1 - 0.05x1/3) = 3.9333
The density of a crystal lattice is directly proportional to Zeff.
Hence density of pure MgO, dp = KxZeff = 4K (where K is a constant)
Density of the defect MgO, di = KxZeff = 3.9333K
Hence percentge change in density = [(dp - di) / dp] x 100
= [(4K - 3.9333K) / 4K]x100 = 1.67 % (answer)