topic 12 - ionic bonding

what are the 5 most common structure types for 1:1 monoatomic AX structures

• NaCl - rock salt

• zinc blend (ZnS)

• NiAs

• wurtzite (ZnS)

• CsCl (not body centred cubic)

what percentage of space do spheres in close packed arrangements take up?

74%

tetrahedral holes in close-packed structures

• tetrahedral holes occur where a sphere from one layer is over the centre of a triangle in the layer above and below

octahedral holes in close-packed structures

• octahedral holes occur between layers where the centres of triangles from adjacent layers overlap

• coordination number = 6

number of holes in HCP unit cell

• octahedral - 2

• tetrahedral - 4

• (2 spheres per unit cell)

number of holes in CCP unit cell

• octahedral - 8

• tetrahedral - 4

• (4 spheres per unit cell)

radius ratio = ?

radius ration = (r⁺/(r^-)

• whatever is bigger / whatever is smaller

equation for calculating radius ration for an octahedral hole

• sqrt(2) x a = 4r^-

• a = edge length of unit cell

• r^- = radius of anion

• r⁺ = radius of cation

• assumes spheres are touching

• a = 2r^- + 2r⁺

equation for calculating radius ration for a tetrahedral hole

• sqrt(2) x L = 2r^-

• sqrt(3) x L = 2r^- + 2r⁺

• L = edge of the cube (with anion spheres at 4 of the 8 corners)

• anion spheres touch along the face diagonal of the cube

coordination number + shape of radius ratio: < 0.225

3, trigonal planar

coordination number + shape of radius ratio: 0.225-0.413

4, tetrahedral

coordination number + shape of radius ratio: 0.414 - 0.731

6, octahedral

coordination number + shape of radius ratio: 0.732 - 0.999

8, cubic

coordination number + shape of radius ratio: 1

12, close-packed structure

NaCl structure + holes filled? + eg.s

• CCP anions

• oct holes filled

• eg.s - most group 1 halides, most oxides/sulphides/selenides of group 2, compounds of group 15 elements w trivalent metals

zinc blende structure + holes filled? + eg.s

• CCP anions

• ½ tet holes filled

• eg.s - CuX, CdS, HgS etc.

• only half tet sites filled to minimise cation-cation repulsions

NiAs structure + holes filled? + eg.s

• HCP anions

• oct holes filled

• the unit cell is distorted from ideal HCP lattice by compression along hexagonal packing axis

• Nickle “octahedra” are compressed w Ni-Ni distances not much longer than Ni-As distance due to some covalent

• generally found for combinations of polarisable cations + anions such as NiS, FeS, CoS, VS, NiTe and MnBi

• structure only found with transition metal ions that can form M-M bonds by direct overlap of d-orbitals

wurtzite structure + holes filled? + eg.s

• HCP anions

• ½ tet holes filled

• a polymorph of ZnS

• half of the tet sites are filled and in a way to minimise cation-anion repulsions

• eg.s- ZnO, BeO, MnS, AgI, AlN, SiC and NH₄F

CsCl structure + holes filled? + eg.s

• primitive cubic array

• 8-coord. cation

• a primitive cubic anion lattice with a cation in the centre of the cube

• halides of the larger univalent cations eg. CsX and TiX

• miscellaneous other phases such as CaS, TiSb and CsCN

delta G⁰ = ?

delta G⁰ = delta H⁰ - T delta S⁰

lattice enthalpy (U)

• the amount of energy required to break up a solid and form gaseous ions

• +ve U = stable lattice - energetically unfavourable to break up

measuring lattice enthalpy

• a direct measurement is v difficult but an indirect measurement can be done using Hess’ law and a born-Harber thermodynamical cycle based on the enthalpy of formation of the solid

Hess’ law

• the energy change of a process depends only upon the energies of the initial and final states and not the route taken

U = ?

U = deltaH^o_atom + deltaH^o_IE + ½ deltaH^o_BDE + delta H^o_EA - deltaH^o_f

E_total = ?

E_total = E_attractive + E_repulsive

E_attractive = ?

E_attractive = - (z⁺z^-e²)/d_o

what is e?

the charge of an electron = 1.602×10^-19 C

what is d?

• the repulsion constant

what is d_o?

• the interatomic distance

• IN METRES

• r(anion) + r(cation)

what is A?

the madelung constant = 1.7476

what is curly E/backwards 3 ₀?

the permittivity of vacuum = 8.854 × 10^-12 J^-1 C² m^-1

what is n in the Born-lande equation?

the born exponent

use the average of n when the n is different for each element

what are the non-ionic factors to consider in solids?

• metal-metal bonding

• effects of covalency

• crystal field effects eg. stabilisation of square planar geometry for d8 transition metals