Structures of Simple Solids

The Structures of Simple Inorganic Solidshttp://www.chem.ox.ac.uk/course/inorganicsolids/default.htmlInteractive Tutorial about Diffractionhttp://www.uni-wuerzburg.de/mineralogie/crystal/teaching/Crystal Lattice Structureshttp://cst-www.nrl.navy.mil/lattice/index.html

X-ray Diffractometer

ORTEP and Ball-and-Stick Model

Choices of Unit Cell

Formation of Two Close-Packed Polytypes

C.N. = 12

hcp and fcc structures

Location of Octahedral Holes

rh = 0.414 rC.N. = 6

Location of Tetrahedral Holes

rh = 0.225 rC.N. = 4

Simple Cubic

C.N. = 6

Body Centered Cubic (bcc)

C.N. = 8

-Tin Structure (Diamond Structure)

C.N. = 4

Substitutional and Interstitial Alloys

Rock-Salt Structure

M+ C.N. = 6 octahedral hole of fccX- C.N. = 6 fcc

Cesium Chloride Structure

M+ C.N. = 8 cubic hole

X- C.N. = 8 simple cubic

Sphalerite (Zinc Blend Structure)

M+ C.N. = 4½ tetrahedral hole

X- C.N. = 4 fcc

Fluorite Structure

M+ C.N. = 8 fccX- C.N. = 4

all tetrahedral hole

Ca

F

F

Ca

Wurtzite Structure

M+ C.N. = 4½ tetrahedral hole

X- C.N. = 4 hcp

Nickel Arsenide Structure

M+ C.N. = 6octahedral hole

X- C.N. = 6 hcp

Rutile Structure

M+ C.N. = 6½ octahedral hole

X- C.N. = 3 hcp

Pervoskite Structure

cubicA C.N. = 12XB C.N. = 6XX C.N. = 6

Spinel Structure

A 1/8 tetrahedral holeB octahedral holeO fcc

Ionic RadiiIonic Radii

Variation of Ionic Radii with C.N.

Radius Ratio Rule

Radius Ratio C.N.0.7 80.4 - 0.7 60.2 - 0.4 40.1 - 0.2 3

Increase with C.N.Decrease with increasing charge number

Variation in Electron Density alongLi-F axis in LiF

Structure Map for MX Compounds

Structure Map for MX2 Compounds

CdI2 & MoS2

Born-HaberCycle forKCl

BDE

I.E.

Hsubo

Hfo

E.A.

HLo

Contribution to Potential Energyof Ions in Crystal

Born-Mayer Equation

V =

attraction repulsion

Good for E.N. difference for theneutral atoms is more than 2

NAe2ZAZB

4e0dd*d

1 - A

A: Madelung Constantd* = 0.345 A

O

Basis of Madelung ConstantCalculation

Madelung Constants

Structural Type ACesium Chloride 1.763Fluorite 2.519Rock Salt 1.748Rutile 2.408Sphalerite 1.638Wurtzite 1.641

Kapustinskii Equation

Kapustinskii discoveredA / nd ~ constant

n: number of ion per formula unitd = rA + rB

For any ionic ionic solid:HL

0 Hypothetical Rock Salt Structure =HL

0 True Structure

HL0 =

HL0 can be estimated for any ionic solid

nZAZB

dd*d

1 - K

O

OK = 1.21 MJ A mol-1

d* = 0.345 Ad = rA + rB (table value)

Change in Lattice Parameter for Cationof Different Sizes

+

+ +

+

-

-

-

-

MCO3 MO + CO2M: Group 2 metals

Grxn = Hrxn - TSrxnSrxn similar for Mg, Ca, Sr, Ba

Smaller r+ larger HL

Large CationStabilize

Large Anion

Small CationStabilize

Small Anion

More Stability

Lower Decom. Temp.

Less Stability

Higher Decom. Temp.

Stability of Oxidation States

Solubility

Cations with high oxidation states are stabilized bysmall anions.

Compounds that contain ions with widely different radiiare generally soluble in water. The least water solublesalts are ions with similar radii.

CorrelationbetweenEnthalpy ofSolution of Xand DifferencesbetweenHydrationEnthalpies

HL Proportional to 1/(r+ + r-)Hhyd Proportional to 1/r+ + 1/r-