Born Haber Cycles Relate Lattice Enthalpy and Heat of Formation  H f Must be (-) for a stable solid ionic solid Elements in Standard States: M(s), X 2 (g) Energy

Born Haber Cycles  H f must be (-) for a stable solid ionic solid, MX M(s), X 2 (g) Energy M + (g), X - (g) M + (g) M(g) X - (g) X (g)  H sub  H I.E.  H BD  H lattice  H EA Elements in Standard States

Born Haber Cycles ionic solid, MX M(s), X 2 (g) Energy M + (g), X - (g) M + (g) M(g) X - (g) X (g)  H sub  H I.E.  H BD  H lattice  H EA HfHf  H f =  H sub +  H I.E +  H BD +  H EA +  H lattice

Born Haber Cycles ionic solid, MX M(s), X 2 (g) Energy M + (g), X - (g) M + (g) M(g) X - (g) X (g)  H sub  H I.E.  H BD  H lattice  H EA  H f =  H sub +  H I.E +  H BD +  H EA +  H lattice HfHf For NaCl: -381 = – in [kJ/mol]

 H f =  H sub + DH I.E +  H BD +  H EA +  H lattice For NaCl: -381 = – For NaO: +600 = ½ (493) Positive  H f : NaO does not (can not) exist! For Al 2 O 3 : = 2( ) + 3/2 (493) + 3 (639) - 15,600

For NaCl: -381 = – Compare these  H lattice values: why is NaCl so small? Al 2 O 3 so large? For Al 2 O 3 : = 2( ) + 3/2 (493) + 3 (639) - 15,600

Lattice Enthalpy  lattice ~ Lattice Energy, U Born equation for Lattice energy, U N Z+ Z- A e 2 4  e o d ( 1 - n ) U = Where: N is Avogadro’s # x ion pairs/mol Z+ Z- is the charge product A is the Madelung constant e 2 and e o are charge on e- and permittivity constants d is the distance (cm) between r+ and r- n is a number, Born constant

A is the Madelung constant: It expresses the geometry of charge arrangement in a particular lattice d - d+d+ d+d+ d+d+ √3d + √5d + √2d - √6d - Madelung Constant, A =  [ /√2 + 8/√3 - 6/2 + 24/√5 ….] A converges to: (NaCl) (CaF 2 ) 1/4 NaCl unit cell

Lattice Enthalpy  lattice ~ Lattice Energy, U Born Lattice energy, U N Z+ Z- A e 2 4  e o d ( 1 - n ) U = Where: N is Avogadro’s # x ion pairs/mol Z+ Z- is the charge product A is the Madelung constant e 2 and e o are charge on e- and permittivity constants d is the distance (cm) between r+ and r- n is a number, Born constant

n is a number, Born constant n is a number related to the electronic configurations of the ions involved. The n values and the electronic configurations (e.c.) of the corresponding inert gases are given below: n = e.c.He Ne Ar Kr Xe The following values of n have been suggested for some common solids: n = e.c.LiF LiCl LiBr NaCl NaBr

For NaCl: 6.022x10 23 /mol * (1+1-) * * ( E -19 ) 2 U = ( 1 - 1/9.1) 4  * 8.854x C 2 /m * 282x m = J/mol = kJ/mol N Z+ Z- A e 2 4  e o d ( 1 - n ) U =

For NaCl: 6.022x10 23 /mol * (1+1-) * * ( E -19 ) 2 U = ( 1 - 1/9.1) 4  * 8.854x C 2 /m * 282x m  U = kJ/mol N Z+ Z- A e 2 4  e o d ( 1 – 1/n ) U = For Al 2 O 3 as corundum: 6.022x10 23 /mol * (3+2-) * * ( E -19 ) 2 U = ( 1 - 1/7) 4  * 8.854x C 2 /m * 191x m  U = - 15,600 kJ/mol

The same reaction occurs in the commercial drain cleaner Drano. This consists of sodium hydroxide, blue dye, and aluminum turnings. When placed in water, the lye removes the oxide coating from the aluminum pieces causing them to fizz as they displace hydrogen from water. This makes it sound like the Drano is really working effectively, even though it's the lye that actually cleans out the drain clog. 2Al(s) + 3/2 O 2 (g)  Al 2 O 3 (s)

What is the parallel with metals? Metals have Bonding “Bands”

How Band Theory Evolves from Molecular Orbital Theory Recall the most basic view of MOT atomic orbital, Like 1s atomic orbital, Like 1s bonding orbital antibonding orbital Energy

Make a little more complex: 2 a.o.’s 2 bonding MO’s 2 antibonding MO’s Energy 2 a.o.’s

Make a lot more complex: 20 a.o.’s 20 bonding MO’s 20 antibonding MO’s Energy 20 a.o.’s

Make a mole of a metal M: x M a.o.’s: Energy x a.o.’s make a Band of many, many closely spaced Atomic orbitals x MO.’s: a Band of Bonding MO’s x MO.’s: a Band of AntiBonding MO’s

The Type of Element Determines Band Gap, Band Gap = the energy separation between Bonding and Anti-bonding Bands Energy AntiBonding Band Of a Metal Bonding Band Of a Metal Band Gap ~ 0 eV

The Type of Element Determines Band Gap Energy AntiBonding Band Of a Metal Bonding Band Of a Metal Band Gap ~ 0 eV AntiBonding Band Of a Network Solid Bonding Band Of a Network Solid Band Gap is Large

~0 Band Gap Allows Electronic Movement  makes Metal a Conductor Energy AntiBonding Band of a Metal is Empty Bonding Band of a Metal is e- filled Band Gap ~ 0 eV Conduction Band Valence Band e-

Large Band Gap Prevents Electronic Movement  makes Metal an Insulator Energy Conduction Band at High Energy Valence Band At Low Energy Band Gap is Too Large for Electrons to “jump”

~Small Band Gap Allows Electronic Movement if Energy added  makes a Semiconductor Energy Band Gap overcome Conduction Band Valence Band e- by E = Light: Solar Cells by E = Heat: Thermisters (heat regulators)

Caption: This is a digital model showing how molybdenite can be integrated into a transistor. One of molybdenite's advantages is that it is less voluminous than silicon, which is a three-dimensional material. "In a 0.65-nanometer-thick sheet of MoS 2, the electrons can move around as easily as in a 2-nanometer-thick sheet of silicon," explains Kis. "But it's not currently possible to fabricate a sheet of silicon as thin as a monolayer sheet of MoS2." Another advantage of molybdenite is that it can be used to make transistors that consume 100,000 times less energy in standby state than traditional silicon transistors. A semi-conductor with a "gap" must be used to turn a transistor on and off, and molybdenite's 1.8 electron-volt gap is ideal for this purpose. Tuesday, February 22, 2011 New transistors: An alternative to silicon and better than graphene Smaller and more energy-efficient electronic chips could be made using molybdenite. In an article appearing online January 30 in the journal Nature Nanotechnology, EPFL's Laboratory of Nanoscale Electronics and Structures (LANES) publishes a study showing that this material has distinct advantages over traditional silicon or graphene for use in electronics applications.

Defects: Impurities Create New Possibilities

~Impurities Decrease Band Gap  makes a Better Semiconductor Energy Conduction Band Valence Band Ge Ga doped Ge –is a p-type semiconductor e- Ga orbitals (empty) e-

~Impurities Decrease Band Gap  makes a Better Semiconductor Energy Conduction Band Valence Band Ge As doped–Ge is an n-type semiconductor e-

Combining a P-type and N-type Semiconductors Makes a Diode N-type e- P-type e- Current  this way only

A Diode made of the right materials causes  E loss to be converted to Light: Light Emitting Diode (LED) N-type e- P-type e-

Semiconductors: where do they come from?

Can be designed to be ‘organic’ Can mix‘organic’ and coordination complexes Schematic of a junction between two organic semiconductors, an anthracene derivative containing free positive ions and a ruthenium, complex containing negative ions. When the two are joined, ions diffuse across the junction creating a difference in energy levels that facilitates rectification, electroluminiscence and photovoltaic response. For experimental purposes the materials were sandwiched between electrodes made of gold and indium tin oxide. The latter is transparent. Malliaras lab/Cornell University

Semi-conductor humor:

3. “toner” 1. Induces charge on surface 2. Blue dots are the “picture”/text The Xerox Process for Photocopying Based on semi-conductor properties of a photo-reactive material: Se

Big Idea 4. Ceramics go beyond Dirt

Ceramics: The Traditional View Make from pulverized rocks (“dirt”) Composition: MAl x Si y O z.H 2 O from silicate and aluminosilicate minerals Begin “Plastic” (workable, malleable) when mixed with water then HEAT causes vitrification (“glassification”) Structure: Amorphous with polycrystallites or vitreous (glass) Properties: very high melting points—refractories (furnace linings) brittle (not malleable) high mechanical strength and stability chemically inert Ceramics: can mean many things

Common examples and how they differ: Terra cotta - Stoneware- Porcelain - China – From “common” clay; red color from FeO iron oxides in “dirt” Fired at lowest temp; not glassy Most translucent, most vitreous, most white, most pure Clay (kaolin) from China: Al 2 O 3.2SiO 2.2H 2 O. “Bone China” originally made from calcined bone, CaO The ‘ring’ test… From “common” clay; Fired at higher temp From flint + feldspar clays; Fired at highest temp; more vitreous Firing process: evaporates remaining water away and initiates vitrification

Composition similar: silicates + flint + feldspar + “flux” (SiO 2 + SiAlO 3 ) (K 2 O, ZnO, BaCO 3 ) Structure : vitreous What goes on top of Ceramics is ceramic too — Glazes Color from Transition Metal minerals/salts added Fe(3+) – red-brown Cu(2+) – turquoise blue and green Co(2+) – “cobalt” blue Ni(2+) – green, brown Mn(2+) –purple, brown

Improved Properties: tougher, higher temperatures, fewer defects Advanced Ceramics or Materials: silicon carbides SiC and nitrides Si 3 N composites: SiC/Al 2 O 3 “whiskers” Examples from Dr. Lukacs golf heads Machine parts tiles All common stuff Ceramics: the Modern View

New Materials are Hot nanotube diamond graphite lonsdaleite fullerenes amorphous carbon C-60 fullereneC-70 fullerene Snazzy graphite relatives: fullerenes, carbon nanotubes

New Materials are Hot diamond graphite lonsdaleite Snazzy graphite relatives: fullerenes, carbon nanotubes For: drug delivery?? gene therapy? electronics? solar cells?

New Materials are Hot Knowledge for making Artificial bone? Biomineralization: how does it grow like that?

Snazzy graphite relatives: fullerenes, carbon nantubes drug delivery?? electronics? Biggest Idea 5. New Materials are Hot Better materials for Solar cells Superconducting Solids And Molecular Magnets Artificial bone? Biomineralization: how does it grow like that?

Get to know the perovskite unit cell Empirical formula: ABX 3 Prototype CaTiO 3 Introducing the Superconductor

Rare earth doped material YBa 2 Cu 3 O 7 : “1-2-3 type” superconductor: mixed valence Cu oxide Y 3+ (Ba 2+ ) 2 (Cu 2+ ) 2 (Cu 3+ )(O 2- ) 7

 Square planar (CuO4) and  Square Pyramidal (CuO5) Cu Sites CuOx planes carry e- Square planar Cu(2+) is d 9, with one e- in the high E d x2-y2 orbital

3 perovskite unit cells O vacancies

Housecroft: “A superconductor is a material whose electrical resistance drops to zero when cooled below its critical temperature, Tc”

The Meissner effect The Meissner effect in superconductors like this black ceramic yttrium based superconductor acts to exclude magnetic fields from the material. Since the electrical resistance is zero, supercurrents are generated in the material to exclude the magnetic fields from a magnet brought near it. The currents which cancel the external field produce magnetic poles which mirror the poles of the permanent magnet, repelling them to provide the lift to levitate the magnet. The levitation process is quite remarkable. Since the levitating currents in the superconductor meet no resistance, they can adjust almost instantly to maintain the levitation. The suspended magnet can be moved, put into oscillation, or even spun rapidly and the levitation currents will adjust to keep it in suspension.