2. Find the ionic radii of Ti4+ and O2- from your textbook, and
apply the Paulings 1st
and 2nd rules in predicting the coordination number for the
cation and the anion, respectively. Sol.
The ionic radii of Ti4+ and O2- are 0.60 and 1.40 ,
respectively. Therefore,
43.040.160.0
2
4
O
Ti
a
c
rr
rr
There should exist a polyhedron with 6 anions (O2-) surrounding
1 cation (Ti4+) according to the 1st Paulings rule. For maintaining
the charge neutrality in the polyhedron (i.e., the 2nd Paulings
rule), we obtain
3
)4()1)(12(
))(1()1)()(6( 42
CNCN
TiCN
O
Therefore, the coordination numbers for the cations (Ti4+) and
anions (O2-) are 6 and 3, respectively. Note that the coordination
number for the anions (O2-) can also be solved alternatively by
recognizing that the stoichiometric form of TiO2 is 1:2 in molar
ratio. Since 6 O2- ions are required to form a polyhedron for
surrounding 1 Ti4+ ion, the number of Ti4+ ions for 1 O2- ion must
therefore be one half of 6 in order to maintain the
stoichiometry.
3. Starting with the cubic close packing of oxygen ions:
1. How many tetrahedral and how many octahedral sites are there
per unit cell? 2. What is the ratio of octahedral sites to oxygen
ions? What is the ratio of
tetrahedral sites to oxygen ions? 3. What oxide would you get if
one-half of the octahedral sites are filled?
Two-thirds? All? 4. Locate all the tetrahedral sites and fill
them up with cations. What structure
do you obtain? If the anions are oxygen, what must be the charge
on the cation for charge neutrality to be maintained?
Sol. (a) 8 tetrahedral and 4 octahedral (b) Octahedral sites to
oxygen ions = 1:1; tetrahedral sites to oxygen ions = 2:1
(c) 1/2 filled = MO2; 2/3 filled = M2O3; and all filled = MO (d)
M2O (anti-fluorite); charge = 1+
4. We have mentioned in class about ceramic materials with
crystalline structures of rocksalt, fluorite, anti-fluorite,
zincblende, wurtzite, etc. Try to use any search engines available
on the web, and find more details of ONE ceramic material that
interests you. Give me what kind of structure it is, specific
properties and applications about this particular ceramics.
Suggestions There are plenty of examples that can be found from the
web for almost all existing ceramics. My favorite website (or
recommendation) is Wikipedia (), which is an on-line encyclopedia
written by experts from all over the world in particular area of
interests.
(Any queries about the solution or if you have any difficulties
in understanding my lecture, feel free to come in and talk with
me
during the office hours.)
