(Solved): need help w parts a and b please, thank you! 4. (a) The sizes of Ti+4,Ba+2, and O2 are 0.068,0.13 ...

4. (a) The sizes of $${\mathrm{Ti}}^{+4},{\mathrm{Ba}}^{+2}$$, and $${\mathrm{O}}^{?2}$$ are $$0.068,0.135$$, and $$0.14\mathrm{nm}$$, respectively. Based on Pauling's criteria choose the most suitable cage for each positive ion. What would be the appropriate crystal structure? Draw the unit cell of $${\mathrm{BaTiO}}_3$$ and show how many atoms of each element are in the unit cell. (b) $${\mathrm{BaTiO}}_3$$ becomes ferroelectric and the crystal structure changes from cubic to tetragonal when temperature is below $$130^{?}\mathrm{C}$$. Discuss how the crystal structural change can lead to the ferroelectric property of $${\mathrm{BaTiO}}_3$$.