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Chem 104A, UC, Berkeley

Solid State Structure

Reading:

MT Chapter 7DG Chapter 7

Chem 104A, UC, Berkeley

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Chem 104A, UC, Berkeley

MgB2, superconductor, Tc=39 K

Chem 104A, UC, Berkeley

CaB6

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Chem 104A, UC, BerkeleySand Silicon Computer Chips

Chem 104A, UC, Berkeley

Gemstone

Sapphire

GarnetTopaz

Synthetic ZrO2

The general formula X3Y2(SiO4)3Al2SiO4(F,H)2

O

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Chem 104A, UC, Berkeley

ZrO2 Diamond

Chem 104A, UC, Berkeley

Abalone Shell

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Chem 104A, UC, Berkeley

Source: National Mineral CollectionSmithsonian National Museum

CuPb(AsO4)(OH)

Chem 104A, UC, Berkeley

Source: National Mineral CollectionSmithsonian National Museum

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Chem 104A, UC, Berkeley

Chem 104A, UC, Berkeley

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Chem 104A, UC, Berkeley

Chem 104A, UC, Berkeley

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Chem 104A, UC, Berkeley

Fluorite with quartz

Chem 104A, UC, Berkeley

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Chem 104A, UC, Berkeley

diamond crystal in kimberlite

Chem 104A, UC, Berkeley

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Chem 104A, UC, Berkeley

Crystalline Solids

Chem 104A, UC, BerkeleyCARBON : Diamond

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Chem 104A, UC, Berkeley

Amorphous Solids

Chem 104A, UC, Berkeley

Molecular solids Covalent

Ionic Metallic

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Chem 104A, UC, Berkeley

Chem 104A, UC, Berkeley

Na+Cl-

IE(Na)= 5.14eV

EA(Cl) =3.61 eV ?? Why NaCl solid

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Chem 104A, UC, Berkeley

E

U0

r

nrc r

B

r

eZZEEU

0

2

4

Ionic Pair

0 Permittivity of vacuum

Chem 104A, UC, Berkeley

Ion Conf. n

He 5

Ne 7

Ar, Cu+ 9

Kr, Ag+ 10

Xe, Au+ 12

Born Exponent

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Chem 104A, UC, Berkeley

1

111 1

1

22

22

2

2 2

2

22

22

3

33

3

33

33

Chem 104A, UC, Berkeley

Lattice Stabilization Energy:Ions adopt a simple lattice structure that maximize favorable Electrostatic interactions.

......)5

24

4

6

3

8

2

126(

4 0

2

eZZ

E latticec

......5

24

4

6

3

8

2

126 NaClA

74756.1

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Chem 104A, UC, Berkeley

Structure Type Madelung ConstantCsCl 1.763NaCl 1.748

ZnS (Wurtzite) 1.641ZnS (Zinc Blende) 1.638

M& T: p227

Chem 104A, UC, BerkeleyFor one mole of a crystalline compound:

Lattice energy =nrc r

NB

r

eZNZAEEU

0

2

4N: Avogadvo’s constant, 6.02e23E

U0

r

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Chem 104A, UC, Berkeley

Energy is Minimum when 0dr

dU

n

reZAZB

r

nNB

r

eZNZA

n

n

0

12

120

2

4

04

)1

1(4 00

2

0 nr

eZANZU

Born-Lande Equation:

Chem 104A, UC, Berkeley

1

111 1

1

22

22

2

2 2

2

22

22

3

33

3

33

33

o

Ar 81.20 n=8 U0=-760kJ/mol

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Chem 104A, UC, Berkeley

Born-Haber Cycle:

M(g) M+ (g)

+X(g) X-(g)

M(s) + ½ X2 (g) MX (s)

IEH

EAH

AXHAMH

fH

0UHHHHH EAIEAXAMf

0U

Chem 104A, UC, Berkeley

For NaCl:

109kJ/mol

IE 493.7kJ/mol

1/2121kJ/mol

EA -356kJ/mol

U -764.4kJ/mol

fH =-396.7kJ/mol

Experimentally:

-410.9kJ/mol

AMH

AXH

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Chem 104A, UC, Berkeley

Ucalc. UBorn-Haber

AgF 920 953 33

AgCl 832 903 71

AgBr 815 895 80

AgI 777 882 105

U

Increasing covalent!

Chem 104A, UC, Berkeley

MgO 3938 kJ/mol

LiF 1024 NaF 911

CaO 3566 LiCl 861 KF 815

SrO 3369 LiBr 803 RbF 777

BaO 3202 LiI 744 CsF 748

Some Lattice Energies:

Melting point: MgO: 2800 CCaO: 2572 CBaO: 1923 C

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Chem 104A, UC, Berkeley

X-Ray Spectroscopy

/hchE

35KeV ~ 0.1-1.4ACu K 1.54 A

Mo:

X-Ray Diffraction

Chem 104A, UC, BerkeleyX-Ray Diffraction

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Chem 104A, UC, Berkeley

(200)

Powder diffraction

X-Ray

Chem 208 (X-ray Crystallography) - Raymond

Chem 104A, UC, Berkeley

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Chem 104A, UC, BerkeleyPowder diffraction

Chem 104A, UC, Berkeley

ZrO2 Diamond