Thermodynamics of Ionic Crystal Formation

1
Ch 7 Lecture 2 Solid State Bonding and
Applications

• Thermodynamics of Ionic Crystal Formation
• The Born-Haber Cycle series of elementary steps
  leading to an overall reaction
• Used to determine electron affinity when all
  other reactions experimentally known
• Today, we can measure EAs easily, so Cycle is
  used to find Lattice Enthalpies
• Sample Cycle
• Li(s) ? Li(g) DHsub 161 kJ/mol
• ½ F2(g) ? F(g) DHdis 79 kJ/mol
• Li(g) ? Li(g) e- DHion 531 kJ/mol
• F(g) e- ? F-(g) DHioin -328 kJ/mol
• Li(g) F-(g) ? LiF(s) DHxtal -1239 kJ/mol
• Li(s) ½ F2(g) ? LiF(s) DHform -769
  kJ/mol
• The Madelung Constant
• Calculating Lattice Enthalpy appears
  straightforward calculate attractions

e 1.602 x 10-23 C 4peo 1.11 x 10-10 C2N-1m-2
2.307 x 10-28 J m
2

• Problem Long-range interactions change the
  Lattice Enthalpy
• NaCl Na has 6 Cl- nearest neighbors at ro ½ a
  (accounted for in equation)
• Na also has 12 Na neighbors at r 0.707 a (not
  accounted for)
• Na also has many other Na and Cl- neighbors at
  longer distances
• M Madelung Constant takes into account all
  attractions
• Born-Mayer Equation incorporates Madelung
  Constant as well as accounting for repulsions
  (much more complicated than attractions)
• r constant 30 pm works well
• Increase in charge causes corresponding increase
  in Lattice Enthalpy
• 2/2 charges would give 4 x Lattice Enthalpy

3

• Solubility, Size, and HSAB
• 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
• Factors effecting solubility
• Size
• Small ions have strong attractions larger ions
  have small attractions
• Large ions may have more water molecules
  surrounding them
• Large/Large and Small/Small salts are less
  soluble than Large/Small
• LiF CsI lt LiI CsF 1. Lattice Energy 2.
  HSAB

4

• Molecular Obitals and Band Structure
• Band Formation
• Overlap of 2 AOs gives 2 MOs
• Overlap of n AOs gives n MOs
• Solids have very large values of n, sometimes
  multiples of N
• Band many closely spaced MOs of nearly
  continuous energy
• Valence Band highest occupied band (HOMO)
• Conduction Band next highest empty band (LUMO)
• Insulator large energy gap between Valence and
  Conduction bands
• Electrons cant move through material
• Electron motion is what allows conduction of
  electricity and heat
• Conductor partly filled Valence and Conduction
  bands (Most Metals)
• Little energy required for electron movement

holes
Insulator Conductor w/ no
Voltage Conductor with applied Voltage
5

• Density of State concentration of E levels in a
  Band N(E)
• Temperature Effect on Conductors (Metals)
• Vibrations increase as temperature increases
• Vibrations interfere with electron movement, slow
  conductance (increase resistance)
• Semiconductors full Valence Band, Empty
  Conductance Band, close together
• Energy gap lt 2 eV
• Si, Ge are common pure substances that are
  semiconductors
• At low temperature they are insulators (not as
  good as true insulators)
• At higher temperature they are conducturs (not as
  good as true conductors)
• Opposite temperature effects as metals (true
  conductors)

6

• Doped Semiconductors
• We can closely control on/off properties of
  semiconductors this has led to the entire field
  of solid state electronics (computers)
• Intrinsic Semiconductor pure form is
  semiconductor (Si, Ge)
• Doped Semiconductor small amount of impurity
  effects semiconduction
• n-type semiconductor dopant has more e- than
  host (P in Si)
• p-type semiconductor dopant has less e- that
  host (Al in Si)
• Careful doping results in tailored materials
• Fermi Level EF Energy at which e- equally
  likely to be in either band
• Intrinsic EF about in middle of gap
• n-type EF raised above new band
• p-type EF lowered below new band

n-type semiconductor p-type semiconductor
7

• Devices Using Semiconductors
• p-n Junction
• Diode device where current flows only in one
  direction
• 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
• Apply negative pot. to n-type and positive pot.
  to p-type
• Forward Bias
• Extra electrons allow e- in n-type to flow to
  p-type holes
• Holes move to junction from p-type side
• Current flows readily
• Reverse Bias holes and electrons move away from
  juction no current flows

????
????
8

• Photovoltaic Cells
• A p-n Junction with the energy gap hn of a
  light source
• Light causes e- to jump to p-type even under
  reverse bias conditions
• Light detector Calculator battery
• LED Light Emitting Diode
• A p-n Junction with forward bias
• Electrons move from n to p and release energy in
  the form of light
• Lower temp increases efficiency by decreasing
  vibrations
• 4) Laser Light Amplification by Stimulated
  Emission of Radiation
• LED with large band gap in p-type to prevent e-
  from escaping middle band

9

• Superconductivity
• The Phenomenon
• The conductivity of some metals changes abruptly
• around 10 K (Critical Temperature TC)
• 2) Superconductor no resistance to e- flow
• Kammerling and Onnes 1911 discover
• for Hg cooled by liquid He
• Major use today is superconducting magnets for
  NMR
• Low Temperature Alloys
• Type I Superconductors are often Nb-Ti alloys
• Abrupt change between superconducting and normal
  conduction
• Meissner Effect no magnetic flux can enter
  superconductor below TC
• Floating Magnets demonstration
• Strong magnetic fields destroy superconduction
  above HC
• Nb3Ge has highest TC 23.3 K for this type of
  superconductor
• Type II Superconductors work below TC1 and are
  complex between TC1 and TC2
• Some magnetic flux can enter them in complex
  region (Floating Magnets)

10

• Theory Cooper Pairs
• 1950s Bardeen, Cooper, and Schrieffer propose
  BCS Theory
• Electrons travel through superconductors in pairs
  (Cooper Pairs)
• Opposite spin electrons are slightly attracted at
  low temperatures
• As one e- moves past nucleus in metal, the next
  nucleus attracts it
• This increases the charge density, so the second
  e- of the pair is attracted to
• Cooper pairs move through metal like a wave
• Lattice helps push/pull e- through no resistance
  because energetically favorable
• When T gt TC the thermal motion of the nuclei
  disrupt the wave
• High Temperature Superconductors
• (La2-xSrX)CuO4 found to have TC 30 K in 1986
• YBa2Cu3O7 found to have TC 92 K in 1987
• Type II superconductors
• Cool with N2(l) cheap, bp 77K instead of
  He(l) expensive, bp 3K
• Ceramic brittle cant easily make into wire,
  etc
• Structure copper oxide planes and chains
• Theory BCS Theory applies, but not completely
  understood

11

• Bonding in Ionic Crystals
• Simplest Idea hard spheres with only
  electrostatic interactions
• Deviations form Simple Idea
• Ionic size is difficult to measure
• Pauling Li 60 pm (from calculations)
• Shannon Li 90 pm (from crystal structures)
• Sharing of electrons back from anion effects the
  size of the cation
• Covalent Interactions very important as well ZnS
  is strongly covalent
• Complex theory involving MOs Crystal Field
  Theory (Chapter 10)
• Imperfections in Solids
• Crystal Growth
• Slowly grown crystals are more perfect
• Quickly grown crystals are usually made up of
  many small crystals which have run into each
  other grain boundaries
• Even perfect crystals have impurities and
  vacancies
• Vacancies and Self-Interstitials
• Vacancy missing atom, ion, or molecule in the
  crystal simplest imperfection
• More formed at higher T, but only 1/10,000 even
  near the melting point
• Effect is small localized in one unit cell
  and/or layer of the crystal

12

• Self-Interstitials atoms/ions/molecules in the
  wrong place
• Effect is felt for several layers of the crystal
• Usually much rarer than vacancies
• Substitutions one element/ion in place of the
  expected element/ion
• Common occurrence leading to a Solid Solution
• Ni/Cu similar in size and electronegativity both
  have (fcc) structure
• Mixtures stable in any proportion alloy
• Random arrangement of atoms since they are so
  similar
• Small atoms in holes between larger ones
• Occupying a hole usually has small effect on the
  rest of the structure
• May have large effect on properties of the
  material (C in Fe makes steel)
• If impurity is large than hole lattice strain or
  new solid phase
• Dislocations
• Atoms in one layer dont match up with the next
• Distances and angles effected for several layers
  in each direction
• Screw Dislocation one layer shifted a fraction
  of unit cell
• Rapid growth location (more attraction into
  solution) helical result

13

• The Silicates
• Abundance
• O, Si 80 of Earths Crust
• Many compounds and minerals formed, some
  industrially important
• Silica SiO2
• Three crystalline forms Quartz (low T form),
  Tidymite, and Cristobalite
• Molten SiO2 often forms glasses instead of
  crystalline forms
• Glass disordered solid structure
• Actually a solution that continues to flow but
  very slowly
• SiO4 tetrahedra in all crystal forms with SiOSi
  angle 143.6o
• Quartz
• Most common form
• Helical chains of SiO4 tetrahedra make it chiral
• Each full turn of the helix has 3 Si and 3 O
  atoms
• Six helices combine to give a hexagonal structure

14

• Other Silicates also have SiO4 units in chains,
  sheets, rings, arrays, etc
• Al3 can substitute for Si4 Aluminosilicates
• Other cations needed to balance charge
• Al3, Mg2, Fe2, Ti3 common cations occupy
  holes
• Kaolinite Al2(OH)2Si4O10
• Talc 3 Mg substitute for 2 Al Mg3 (OH)2Si4O10

15

• Mica
• Layers of K ions between silicate and aluminate
  layers
• Al in about 25 of the Si positions
• Can be cleaved into incredibly smooth, flat
  sheets
• Used in nail polish
• Asbestos fibrous mineral
• Chrysotile Mg3(OH)4Si2O5
• Mg and Silicate layers differ in size leading to
  curling fibrous structure
• Zeolites mixed aluminosilicates with
• (Si,Al)nO2n frameworks and cations added to
  balance the charge
• Used as water softeners before polymer resins
  developed (Cation exchange)
• Cavities large enough for molecules to enter may
  make stable complex
• Water removal from organic solvent Molecular
  Sieves
• Cat litter and oil absorbant
• Catalysts and catalyst support for petroleum
  cracking