Estimate the coordination number for the cations in each of these ceramic oxides and also the coordination numbers of the oxygen anions: Al2O3, B2O3, CaO, MgO, TiO2, LaAlO3, Mg2SiO4, and NiCo2O4.

CN cation, anion ] respectively are thus [6,4] , [2,3] ,[6,6] , [6,6] , [6,3] , [12,6,2] , [6], [6].

Explanation:

The coordination number CN is the number of ligand atoms bonded (coordinate bonds) directly to the central of the metal ion. It is not the same as the oxidation state of the metal ion or complex.

Coordination number – the number of anions surrounding the cation.

In solving for CN we need to understand Pauling's rules.

According to Linus Pauling, 1932

“Pauling’s rules” for crystal structures, makes assumptions for ionic bonding. It states that ionic structure is understood using electrostatic rules of attraction and repulsion.

Cations and anions surround each other to neutralize charge – and these one can rationalize crystal structure with coordination number.

Ratio of cationic/anionic radius

• The structure of D-Al2O3 results in coordination number of 6 and 4 for cation and anion respectively.

• The average oxygen coordination number in v-B2O3 is equal to the average cation coordination number × cation/anion ratio (2/3).

• Co-ordination number of Ca2+ ion is =6;

In CaO crystal, Ca2+ is a cation and O2- is an anion. Cationic (Ca2+) has radius 100 pm and anionic (O2-) has radius  145 pm.

Ratio of cationic/anionic radius is:

r⁺/r⁻ = 100 / 145

r⁺/r⁻ = 0.69

CaO will form FCC lattice.

Coordination number in FCC lattice is 6. Therefore CN of Ca2+ = 6.

For MgO:

r Mg2+/ r O2- = 86pm / 126 pm =0.683

The cordination number for the cation is 6. MgO with ions Mg+2 and O-2 will have a AX type stochiometry exhibiting the

crystal structure of sodium chloride.

For TiO2:

The CN of the titanium (IV) cation is 6, which is twice the CN of the oxide anion, which is 3.

This fits with the formula unit of TiO2, since there are twice as many O2− ions as Ti4+ ions.

Consequently the crystal structure of all ionic compounds reflects the formula unit.

For LaAlO3 a Cubic perovskites (ABX3)

In perovskite structures, B cations are coordinated by six X anions, while A

cations present CN = 12 (also coordinated by X anions). The X anions have CN = 2, being

coordinated by two A cations, since the distance A-O is about 40% larger than the B-O

bond distance. The correct ionic radii (rA, rB, rX), taken from one of Shannon’s work.

rA = 1.36 pm

rB = 0.535 pm

rX = 1.35 pm

Forsterite Mg2SiO4

We have mixed sites of Si4+ in tetrahedral site, Mg2+ in octahedral site, O atoms anions .

They all forms octahedral chains/strips. The CN is estimated to (6) octahedral, with an average ratio 0.414

Nickel Cobaltite Ni(Co2O4)3

bidentate ligand includes the Oxalate, three oxalate ligands form six-coordinate bonds around the Ni2+ ion.

Co-ordinate number of Nickel in [Ni(C2O4)3] 4− is 3×2=6.

From the right triangle we can find its leg using Pythagorean theorem,

50² =14² + leg²

leg² = 2304

leg = √2304 = 48,

This leg is one of the sides of the rectangle, so we can find a perimeter of this rectangle.

P=2*(W+L) = 2*(14+48) = 124

Answer : the perimeter is 124.