structures of simple solidsocw.nctu.edu.tw/course/ichemistry/ichemistry_lecture...basis of madelung...
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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-