Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley 1 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley 2 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Metallic Hydrogen Metal Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Sodium According to Band Theory Conduction band: empty 3s antibonding No gap Valence band: full 3s bonding In extended solid, each atomic/molecular orbtial will develop into one band! 192 3 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Conduction Band Bonding in Metals The electron-sea model is a simple depiction of a metal as an array of positive ions surrounded by delocalized valence electrons. Valence bond Metals are good conductors of electricity because of the mobility of these delocalized valence electrons. A metal also conducts heat well because the mobile electrons can carry additional kinetic energy. 194 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Bonding in Metals Bonding in Metals Molecular orbital theory gives a more detailed picture of the bonding in metals. According to band theory, the electrons in a crystal become free to move when they are excited to the unoccupied orbitals of a band. In a metal, this requires little energy since the unoccupied orbitals lie just above the occupied orbitals of highest energy. 195 196 4 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Structure of Diamond Semiconductor 198 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Graphite Diamond Graphite has a layered structure, in which the carbon atoms in each layer bond to three other carbons with sp2 orbitals. Diamond has a three-dimensional network structure in which each carbon is singly-bonded to four others with sp3 hybridization. Why do diamonds conduct heat? Metals conduct heat because the the mobile electrons can carry additional kinetic energy. Diamonds are insulators and have no mobile electrons. Diamonds conduct heat through high frequency (= high energy) vibrations that transmit over long distances Diamonds conduct heat 4 times better than copper! Of the covalent network solids, only graphite conducts electricity. This is due to the delocalization of the resonant electrons in graphite's sp2 hybridization. 199 200 5 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Solids: Conductors, Insulators and Semiconductors Graphite Solids: Conductors, Insulators and Semiconductors Band Gap for Semiconductors Diamond 5.5 eV 1.1 eV 0.67 eV Band gap Diamond No gap Band gap = 5.5 eV 530 kJ/mol Si Ge Conductor Insulator 201 Semiconductor 202 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Fullerenes The fullerenes are a family of molecules with a closed cage of carbon atoms arranged in pentagons and hexagons. Each carbon is sp2 hybridized. The most symmetrical member is buckminsterfullerene, C60. Buckminsterfullerenes show potential for applications in superconductivity and catalytic activity. 203 6 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Conduction Band Fermi Level EF corresponds to the highest occupied energy at T=0 (HOMO energy) Fermi-Dirac distribution Valence bond P= 1 e ( E - EF ) / kT + 1 population P of the valence band orbitals. 7 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Fermi-Dirac distribution: f (E) = 1 exp[( E - E F ) / k BT ] + 1 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley 8 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Semiconductors Semiconductors Semiconducting elements form the basis of <a href="/keyword/solid-state-electronic-devices/" >solid state electronic devices</a> . When silicon is doped with boron, it becomes a p-type semiconductor, in which an electrical current is carried by positively charged holes Semiconducting elements form the basis of <a href="/keyword/solid-state-electronic-devices/" >solid state electronic devices</a> . When silicon is doped with phosphorus, it becomes an n-type semiconductor, in which electric current is carried by electrons. 213 214 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Semiconductors Semiconducting elements form the basis of <a href="/keyword/solid-state-electronic-devices/" >solid state electronic devices</a> . Joining a p-type semiconductor to an ntype semiconductor produces a p-n junction, which can function as a rectifier. A rectifier is a device that allows current to flow in one direction, but not the other. 215 216 9 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Doping in semiconductor: n-type Doping in semiconductor: p-type Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Light Emitting Diodes Forward bias at a - njunction forces minority p carriers across the junction. This causes electrons to fall into vacant holes radiatively, giving off light. radiatively, Dopants are important sites for localizing carriers, thus transitions are often CB acceptor, or donor VB 219 Common LED materials GaAs (Eg=1.43 eV) Near IR (E GaP:N (Eg = 2.25 eV) Yellow (E GaP:Zn,O (Eg = 2.25 eV) Red (E GaN, SiC, ZnO, AlN Blue, UV 10 Chem 104A, UC, Berkeley Common LED materials GaAs (Eg=1.43 eV) Near IR (E GaP:N (Eg = 2.25 eV) Yellow (E GaP:Zn,O (Eg = 2.25 eV) Red (E GaN, SiC, ZnO, AlN Blue, UV Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Atomic Structures Final Exam Dec 15th 8-11 am s, p, d orbitals, quantum numbers Nodal planes Radial Distribution Functions Contour diagram Hydrogen energy level Electron configuration, Aufbau Principle Ground State, Term symbol Periodic Trends: IE, EA, Radius, EN Lecture Notes/Slides/Homework Exams I, II 11 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Group Theory Bond Theory Valence Bond theory Lewis structure Orbital hybridization VSEPR Molecular orbital theory, Bond order sp mixing Ligand group orbitals Projection Operator Method Phtotoelectron spectroscopy Walsh Diagram LUMO-HOMO LUMO- Symmetry Point Group Character Table Representation Vibrational Spectroscopy Raman, IR Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Solid State Structures Band Theory Common crystal structures Madelung Constant Crystal symmetry Bravais Lattice Unit Cell Coordination No, Composition Close packed lattice Radius Ratio Rules Energy band formation Fermi level Fermi-Dirac distribution FermiBand gap Doping, p, n 12 Chem 104A, UC, Berkeley Chem 104A, UC, Berkeley Acid-Base Chemistry Bronsted Definition Lewis definition Oxyacid trend, PKa Conjugated acid-base acidSteric effect Hard, soft acid /base Reaction direction Some MO explanation Main Group Chemistry Boron bonding feature Boron clusters 13