Ch 7 Lecture 2 Solid State Bonding and Applications
II.
Thermodynamics of Ionic Crystal Formation
A) The Born-Haber Cycle = series of elementary steps leading to an overall reaction
1) Used to determine electron affinity when all other reactions experimentally known
2) Today, we can measure EA’s easily, so Cycle is used to find Lattice Enthalpies
3) Sample Cycle
Li(s) ----> Li(g)
DHsub = 161 kJ/mol
½ F2(g) ----> F(g)
DHdis = 79 kJ/mol
Li(g) ----> Li+(g) + eDHion = 531 kJ/mol
F(g) + e- ----> F-(g)
DHion = -328 kJ/mol
Li+(g) + F-(g) ----> LiF(s)
DHxtal = -1239 kJ/mol
Li(s) + ½ F2(g) ----> LiF(s)
DHform = -769 kJ/mol
B) The Madelung Constant
1) Calculating Lattice Enthalpy appears straightforward: calculate attractions
Zi Z j  e 
U


ro  4o 
2
e = 1.602 x 10-23 C
4o = 1.11 x 10-10 C2N-1m-2
[ ] = 2.307 x 10-28 J m
2)
Problem: Long-range interactions change the Lattice Enthalpy
a) NaCl Na+ has 6 Cl- nearest neighbors at ro = ½ a (accounted for in equation)
b) Na+ also has 12 Na+ neighbors at r = 0.707 a (not accounted for)
c) Na+ also has many other Na+ and Cl- neighbors at longer distances
3)
M = Madelung Constant takes into account all attractions
4)
Born-Mayer Equation incorporates Madelung Constant as well as accounting for
repulsions (much more complicated than attractions)
NMZ  Z 
U
ro
a)
b)
 e 2  r 

1  
 4o  ro 
r = constant = 30 pm works well
Increase in charge causes corresponding increase in Lattice Enthalpy
2+/2+ charges would give 4 x Lattice Enthalpy
C)
Solubility, Size, and HSAB
1) We can use a Born-Haber Cycle to calculate dissolution energies
AgCl(s) ----> Ag+(g) + Cl-(g)
DHLattEnth = 917 kJ/mol
Ag+(g) + H2O ----> Ag+(aq)
DHsolvation = -475 kJ/mol
Cl-(g) + H2O ----> Cl-(aq)
DHsolvation = -369 kJ/mol
AgCl(s) + H2O ----> Ag+(aq) + Cl-(aq)
DHdissolution = 73 kJ/mol
2)
Factors effecting solubility
a) Size
i. Small ions have strong attractions; larger ions have small attractions
ii. Large ions may have more water molecules surrounding them
iii. Large/Large and Small/Small salts are less soluble than Large/Small
iv. LiF = CsI < LiI = CsF 1. Lattice Energy 2. HSAB
Cation
Hydr. E.
Anion
Hydr. E
Latt. Enth Net Enth.
Li+
-519
F-
-506
-1025
0
Li+
-519
I-
-293
-745
-67
Cs+
-276
F-
-506
-724
-58
Cs+
-276
I-
-293
-590
+21
Reaction: LiI(s) + CsF(s) ----> CsI(s) + LiF(s) DH = -146 kJ/mol
III. Molecular Obitals and Band Structure
A) Band Formation
1) Overlap of 2 AO’s gives 2 MO’s
2) Overlap of n AO’s gives n MO’s
3) Solids have very large values of n, sometimes multiples of N
4) Band = many closely spaced MO’s of nearly continuous energy
a) Valence Band = highest occupied band (HOMO)
b) Conduction Band = next highest empty band (LUMO)
holes
Insulator
Conductor w/ no Voltage
Conductor with applied Voltage
5) Insulator = large energy gap between Valence and Conduction bands
a) Electrons can’t move through material
b) Electron motion is what allows conduction of electricity and heat
6) Conductor = partly filled Valence and Conduction bands (Most Metals)
a) Little energy required for electron movement
b) Hole = electron vacancy that can also “move” in partially occupied bands
7)
Density of States = concentration of E levels in a Band = N(E)
8)
Temperature Effect on Conductors (Metals)
a) Vibrations increase as temperature increases
b) Vibrations interfere with electron movement, slow conductance (increase
resistance)
9)
Semiconductors= full Valence Band, Empty Conductance Band, close together
a) Energy gap < 2 eV
b) Si, Ge are common pure substances that are semiconductors
c) At low temperature they are insulators (not as good as true insulators)
d) At higher temperature they are conductors (not as good as true conductors)
e) Opposite temperature effects as metals (true conductors)
10) Doped Semiconductors
a) We can closely control on/off properties of semiconductors: this has led to
the entire field of solid state electronics (computers)
Band Gap (eV)
b) Intrinsic Semiconductor = pure form is semiconductor (Si, Ge)
c) Doped Semiconductor = small amount of impurity effects semiconduction
i. n-type semiconductor = dopant has more e- than host (P in Si)
ii. p-type semiconductor = dopant has less e- that host (Al in Si)
iii. Careful doping results in tailored materials
d) Fermi Level = EF = Energy at which e- equally likely to be in either band
i. Intrinsic: EF about in middle of gap
ii. n-type: EF raised above new band
iii. p-type: EF lowered below new band
n-type semiconductor
p-type semiconductor
B.
Devices Using Semiconductors
1) p-n Junction
a) Diode = device where current flows only in one direction
b) At equilibrium a few e- have moved from n-type to p-type (n is +, p is -)
EF is at same level in n-type and p-type at equilibrium
c) Apply negative pot. to n-type and positive pot. to p-type
a) Forward Bias
b) Extra electrons allow e- in n-type to flow to p-type holes
c) Holes move to junction from p-type side
d) Current flows readily
d) Reverse Bias: holes/electrons move away from junction = no current flows
2)
Photovoltaic Cells
a) A p-n Junction with the energy gap = hn of a light source
b) Light causes e- to jump to p-type even under reverse bias conditions
c) Light detector; Calculator battery
e3)
LED = Light Emitting Diode
a) A p-n Junction with forward bias
b) Electrons move from n to p and release energy in the form of light
c) Lower temp increases efficiency by decreasing vibrations
4)
Laser = Light Amplification by Stimulated Emission of Radiation
a) LED with large band gap in p-type to prevent e- from escaping middle band
b) If Length = l(n/2), reflection by edges stimulate more in-phase photons
http://en.wikipedia.org/wiki/Laser
5)
Quantum Dots
a) Semiconductors lose bulk properties and take on quantized energy levels as
they become smaller (like single molecule) = Quantum Confinement Effect
b) Nanoparticles < 10nm are called Quantum Dots, behave unlike bulk solids
c) Energy Level spacing is size dependent and can be tuned by adjusting size
d) Excited electron leaves a hole in the valence band as it moves to conduction
band. Electron + hole = Exciton
e) Exciton energy ~< lowest energy of the conduction band
f) Decay of electron back to valence band causes photoemission
g) Potential uses of quantum dots: solar energy, data storage, biosensors, etc…
Photoluminscence
Emission Spectrum
Of ZnSe Quantum Dots
IV. Superconductivity
A) The Phenomenon
1) The conductivity of some metals changes abruptly
around 10 K (Critical Temperature = TC)
2) Superconductor = no resistance to e- flow
a) Kammerling and Onnes 1911 discover
for Hg cooled by liquid He
b) Major use today is superconducting magnets for NMR
B)
Low Temperature Alloys
1) Type I Superconductors are often Nb-Ti alloys
a) Abrupt change between superconducting and normal conduction
c) Strong magnetic fields destroy superconduction above HC
d) Nb3Ge has highest TC = 23.3 K for this type of superconductor
2)
Type II Superconductors work below TC1 and are complex between TC1 and TC2
a) Some magnetic flux can enter them in complex region (Floating Magnets)
b) Meissner Effect = no magnetic flux can enter superconductor below TC
“Floating Magnets” demonstration
c) Possible to use for Levitated Trains
C)
Theory = Cooper Pairs
1) 1950’s Bardeen, Cooper, and Schrieffer propose BCS Theory
2) Electrons travel through superconductors in pairs (Cooper Pairs)
3) Opposite spin electrons are slightly attracted at low temperatures
4) As one e- moves past +nucleus in metal, the next +nucleus attracts it
5) This increases the charge density, so the second e- of the pair is attracted too
6) Cooper pairs move through metal like a wave
7) Lattice helps push/pull e- through; no resistance because energetically favorable
8) When T > TC the thermal motion of the +nuclei disrupt the “wave”
D) High Temperature Superconductors
1) (La2-xSrX)CuO4 found to have TC = 30 K in 1986
2) YBa2Cu3O7 found to have TC = 92 K in 1987
3) HgBa2Ca2Cu3Ox Tc = 133 K in 1994
a) Type II superconductors
b) Cool with N2(l) [cheap, bp = 77K]
c) instead of He(l) [expensive, bp = 4K]
d) Ceramic = brittle; can’t easily make into wire, etc…
4) Structure: copper oxide planes and chains
5) Theory: BCS Theory applies, but not completely understood
V.
Bonding in Ionic Crystals
A) Simplest Idea = hard spheres with only electrostatic interactions
B) Deviations from Simple Idea
1) Ionic size is difficult to measure
a) Pauling Li+ = 60 pm (from calculations)
b) Shannon Li+ = 90 pm (from crystal structures)
c) Sharing of electrons back from anion effects the size of the cation
2) Covalent Interactions very important as well: ZnS is strongly covalent
3) Complex theory involving MO’s = Crystal Field Theory (Chapter 10)
VI. Imperfections in Solids
A) Crystal Growth
1) Slowly grown crystals are more perfect
2) Quickly grown crystals are usually made up of many small crystals which have
run into each other = grain boundaries
3) Even “perfect crystals” have impurities and vacancies
B) Vacancies and Self-Interstitials
1) Vacancy = missing atom, ion, or molecule in the crystal = simplest imperfection
a) More formed at higher T, but only 1/10,000 even near the melting point
b) Effect is small; localized in one unit cell and/or layer of the crystal
2)
C)
Self-Interstitials = atoms/ions/molecules in the wrong place
a) Effect is felt for several layers of the crystal
b) Usually much rarer than vacancies
Substitutions = one element/ion in place of the expected element/ion
1) Common occurrence leading to a “Solid Solution”
2) Ni/Cu similar in size and electronegativity; both have (fcc) structure
a) Mixtures stable in any proportion = alloy
b) Random arrangement of atoms since they are so similar
3) Small atoms in holes between larger ones
a) Occupying a hole usually has small effect on the rest of the structure
b) May have large effect on properties of the material (C in Fe makes steel)
c) If impurity is larger than hole: lattice strain or new solid phase
D) Dislocations
1) Atoms in one layer don’t match up with the next
2) Distances and angles effected for several layers in each direction
3) Screw Dislocation = one layer shifted a fraction of unit cell
a) Rapid growth location (more attraction into solution) = helical result
b) Mechanically weak; Electronically inefficient
VII. The Silicates
A) Abundance
1) O, Si = 80% of Earth’s Crust
2) Many compounds and minerals formed, some industrially important
B)
Silica = SiO2
1) Three crystalline forms: Quartz (low T form), Tidymite, and Cristobalite
2) Molten SiO2 often forms glasses instead of crystalline forms
a) Glass = disordered solid structure
b) Actually a solution that continues to “flow” but very slowly
3) SiO4 tetrahedra in all crystal forms with Si—O—Si angle = 143.6o
4) Quartz
a) Most common form
b) Helical chains of SiO4 tetrahedra make it chiral
i. Each full turn of the helix has 3 Si and 3 O atoms
ii. Six helices combine to give a hexagonal structure
5)
Other Silicates also have SiO4 units in chains, sheets, rings, arrays, etc…
6)
Al3+ can substitute for Si4+ = Aluminosilicates
a) Other cations needed to balance charge
b) Al3+, Mg2+, Fe2+, Ti3+ common cations; occupy holes
7)
Kaolinite = Al2(OH)2Si4O10
1) Talc = 3 Mg substitute for 2 Al Mg3(OH)2Si4O10
2) OH- bridge between Al or Mg and Si
8)
9)
Mica
a) Layers of K+ ions between silicate and aluminate layers
b) Al in about 25% of the Si positions
c) Can be cleaved into incredibly smooth, flat sheets
Asbestos = fibrous mineral
a) Chrysotile = Mg3(OH)4Si2O5
b) Mg and Silicate layers differ in size leading to curling fibrous structure
10) Zeolites = mixed aluminosilicates with:
a) (Si,Al)nO2n frameworks and cations added to balance the charge
b) Used as water softeners before polymer resins developed (Cation exchange)
c) Cavities large enough for molecules to enter; may make stable complex
i. Water removal from organic solvent = Molecular Sieves
ii. Cat litter and oil absorbant
iii. Catalysts and catalyst support for petroleum cracking