CHEM 3200 Notes PDF

-old Crystalline solids solids exhibit long range order · :...

-old Crystalline solids solids exhibit long range order · : have localized order Amorphous : can · Bonding in Solids Metallic Bonding found lowionization 7 1 2 · + group Elemental elements bonding in - - Nuclei floating of electrons in a sea · Free e model - Accounts for physical and chemical properties of metals · Luster , ote conductive malleable , ductive , Fonic Bonding · interactions between Solids held together by coulombic - cations and anions · Hard sphere model Typically elements found in compounds of electropositive electro- negative (directional) · Covalent Bondingbonds shared electrons forming weaker intramolecular - , forces like V/d Waal's forces · Distribution ofa around nuclei or around nucli in bonds Crystalline Solids Typically ionis metallic bunding · or Form regular structures w) long range order Lattice regular repeating pattern in crystal structure : a Can be reproduced by translational motion of unit · cell in all directionsno rotation mirroring or  - Unit cell smallest possible : unit used to reconstruct lattice only using translation The Hard Sphere Model (monoatomic - tonic or metallic solids can be modeled as hard sphere Particularly true for non-directional bonding Limitations for packingane purely geometric - Results in highest possible density of spheres - Each has 12 nearest sphere neighbours · Hexagonal Packing Cubic Close only usedimple o a ways (polytypes) 2 to CCP Hop pack spheres w/min energy. ABAB structure hexagonal packing cose - ABCABC structure cubic close Coordination 12 packing * · Closest packing (FCC or HCP) result in a coordination number of 12 Hard Sphere Packing Example · Well behaved : Group 18 Ha Fa - ,. - Elemental metals late TM CCP : , Cu. An (softer malleable), , TM and alkali earth HCP Co , brittle early , MgCharder , · Less well behaved : Maingroupmetalsrangeofpolymorphs + noaas - Mid TM , alkali metals favour BCC Packing Efficiency and Holes Using a little geometry and some diagrams , we can show that 74 % of the unit all of a CCP structure is filled / hard spheres 26 % is empty (sort of - tetrahedral Empty holes octahedral and - : Octahedral Holes Found between 2 of parallel triangles spheres - Nspheres = Noctahedral holes Tetrahedral Holes · Found dimples between in 4 spheres 2 down types arbitrary : + up · IN holes for N spheres Size Matters · Size of the hole is a function of the radius of the spheres that make it On 0 414r goldy locks fit most Estable - : :. - Ta = 0 225. r similar size ? Fonic Solids and Holes by paniontin on Smaller of cation or anion fit into holes Larger ion forms lattice Non Close Packed Solids BCC : lattice point in middle of cube · Simple cubic Polymorphism Type of crystal structure adopted by metal varies with  conditions under which it was formed To pressure - , formed at Typically less dense structures higher To - , are and lower pressures Alloyseate mixture or compound of a metal with other metals or nonmetals Prepared by mixing molten components and appropriate tempering Substitutional Alloyslattice - Additives displace points formed Typically by rapid cooling of molten mixture - distribution Entirely random avoid intermetallic - bonds -Successful formulations similarities typically require significantS in : crystal structure radii, , electronegativity Eg sterling silver Ag(CCP : 144pm grp 11) Cu(CCP+ 128 1) · : , , , pm. Interstitial Alloys holes · - Additives occupy small atom additives that fit lattice holes - Requires in Usually stoichiometrically random Small quantities can dramatically change the physical properties Eg steel - : : Fe + 0. 25-1 5% C. consistent stoich. Intermetallic Compounds difference in portion · -Complete filling of holes begins to form new lattice Eg : Al alloys -> Specific metal-additive bonding Nonstoich throughout resulting grains of diff - in comp... Fonic Lattices · Limitations of hard sphere model : Fonic radii is arbitrary - - Radii depends on coordination and environment Does not allow for When solid covalent component of bonding is a ionic ? · Lattices of the model ionic adequately describes - are thermodynamic their Ionic Solids properties model ol olf-exp. · Soluble in polar solvents occupied holes prevent latticepts. lower than metals from touching Brittle hard density · , , Lower coordination number purely ionic or cove is somewhat Hard to tell between covalent and ionic solids artificial Fonticstomost in To or On holes common ionicsa Cesium Chloride 1 1 : anion cation : Simple rubic lattice with filled cubic hole · Similar size cations and anious Halite (Rock Salt or NaCl 1 1 ratio interchangeable · : · FCC anions of cations in On holes Fluorite 2: 1 anionication holes Cafe , occupied ta  Antifluorite cation ? · 2 : 1 : anion oxides , sulphides Sphalerite · 1 / FCC w/ 50 % To holes : filled All of one type of Te hole used - Wurtzite · HCP lattice - Only one To hole orientation filled - InS : S"make up lattice Rutile · 1 :2 lattice holes : central lattice pt. + 2 corners holes & BCC w/ filled trigonal planar · Perovskite · ABX3 A , Bications for · Important superconductors & X occupiesOn holes ish. Simple cubic B or BCC where lattice are A and B Many potential distortions non-strich solids +. Layer Structures MX2 species of polarizable arious and polarizing cations often formed layered structures - CdEz CdClz TM , , Oxides , metal OH · Halide forms HCP or FCC lattice w/ cation in On holes other stuff in every layer-vacancies in On 2 holes Sandwitches held together by V/d Waals bonds can stuff & in there Cintercolation - CdCIz : Cl FCC lattice = - Cd(OH)2 : Cd+ in On holes Semiconductor Structure Diamond type network for SiGe · common - Dopants added as sub alloyscharge defects , not lattice Sphalerite lattice · Predicting Structures Complicated · : difficulty defining radii - in ionic - Variations in atomic radii - Conditions for formation Radius ratio simple but rule of thumb : suspect Structure methods maps empirical : Radius Ratio ratio Fonic Lattic U Geometry : F _ coord No.. 0 2-0 4.. 4 Tetrahedral Zinc blende Wurtzite fluorite , , 0 4-0 7.. 6 Octahedral Halite 0 7-1.. 0 g Cubic CSCI > 1. 0 12 Caboctohedral Metallic lattice Structure Maps Correlation of X and n to see of structures - n relates for grouping - Xcat Xan relates to ionic character- Thermodynamics · of lattice Formation Lattice formed under TD control has lowest G formation conditions Depending on - formation of metastable state Quenching : - is common - Interconversion of structures slow is very  Lattice · Enthalpy For lattice formation at low To OH dominates , Definition Formation of from solid gas phase ions · : positive lattice *Hn MX(S) Micgc + Xig)Hy highly = - > atomicatassociation Born-Haber Cycle M(s) +" X2(g) N2 D (x2 , 9) Mcgh+Xgc Calculation of WHL · F -H politionfitCyclic approachto Yieldaseriesof ris whthe MXnYs Mig Xigs Only unknown < + - H2 total H @ is · = Why Calculate Lattice Energies & · Assess ionic nature compare to exp. Predict lattice energies of hypothetical or poorly understood compounds calculated lattice E to Use cycle Ion Lattice Interactions + yield other TD data Madelung Constants - · Lattice is made up of effectively infinitions in each direction Can coulombic interactions and collapsed · sum up into : U = -Kie AnyMadelung constant Born Forces Fonic lattices aren't just hard spheres Forces · Born · Need to include repulsive forces (e--e- nuc-nuc , BornMagentine · p usually 35pm : , reflects lattice compressibility - U is generally around 50s-100s k5/mo  Kapustinkskii Equation Approximates lattice enthalpy without the lattice rather thana type usingthe number of ions (v -U = r+ + V- Lattice Defects At Tabove OK defects are energetically · any , favourable due to the entropy advantage Important as reaction sites Schottky Defect lattice Vacancy in (both - Changed balanced Nat and Cl must be missing Will lower density Frenkel Defect · Dislocation of atom or ion from its proper place to an otherwise vacant hole - Charge differences theory -hand The problem : if we consider simple valence, localized bonding solids have a problem There aren't valence to enough e- around - go to form the bonds to nearest 12 neighbours Multicentre bonding ? too localized to explain : conductivity - Band Theory Massively delocalized approach to bonding Appropriatefo metallic bonding systems to number of atoms MO theory large Most appropriate for crystalline lattices Bottom Up Approach Consider Lithium atoms to metal Species Bonding Resulting Mo How many are filled ? Li 2s' None filled valence orbital Liz 2x2s' 2 1 of the 2 MOS 3x2s' 3 32 of the 3 MOS Lis Lin nx2s' n 2 of the n MOS · Result is continuous band of MO levels energy a Energy difference between vacant us filled MOS is non existant Electrons freely - can more - Undercuts quantization Berglium is inert actually · an gas Same band made of 25 MOs process suggests - up will be filled for Be Solved by overlap w/vacant &p orbitals - The Fermi Level (EF) EnergyHere ofthe highest · E o a At higher To e-thermally populate MOs above EF ·. leaving below EF vacancies Fermi Dirac Distribution · Distribution of electronic population in a band for a metal Pi = i+ ecei-ekT - Where k = Boltzman constant Explains why conductors To dependent - are Band Gaps · Some electronic & configurations have no easily accessible empty bands EF at top of band Gap occurs between "HOMO" and "LUMO" Electronic size of properties of the material depend · on the band gab Semiconductors A poor insulator · - has band gap -Conductivity dependent is on giving -- enough E to jump the gap Resistance decreases as To increases because the # of e-with sufficient thermal E to the increases jump gap - Vs conductors where resistance increases w/ To cuz thermal motion of disrupt nuclei e-mobility  Density of States Measurement of the degeneracy at particular energy level · a -# of orbitals at E level decreases the a particular near top and bottom of each band -Important for the of electrons material if the Fermi level mobility in a at of low occurs a point or zero d of states Intrinsic Semiconductors Si , Ge have Natively band of appropriate size · a an gap Band gap depends on separation of filled and vacant levels energy differences - the top Increasingly diffuse AOs lead to and bottom of the bands and therefore the bant in 9- Diffuse AUs lead to smaller MO due to weaker bonds smaller band => splitting - gaps More metallic behaviour at bottom of P.. T Extrinsic Semiconductors Possible to tailor the band by doping in species that · p-type either contribute gap n-type excesse or e-vacancies to the band [ structure can toy with width (or semicond.) element with Doping insulating - a pure other atoms is used to tune the band structure & p-type (defficient relative to host) holes close to filled - one - (one more e-than hostt close to -n-type empty band Group III-V (13-15) SCs GaAs AlAs AlSb GaP GaSb ,InSbetc : , ,. , , symmetry Mirror Planes o Or us Od · -Generally Or includes atoms and on cuts through bonds Improper Rotation S · Cn + On molecule with Every planar In has Sr - an - S : On , Sa = i Point Groups Short form method for elements present identifying all the symmetry in a molecule Character Tables Lists of behaviour under the symmetry elements in a point group are fabulated These called are irreducible representations A portion of molecule can be described by - a some leniar comb. of these irr. reps. Mulliken Labels ABST degeneracy · : Aus B symmetric antisymmetric w/ respect to Cn : or 1,2 wrt Ce sym antisym : or · , or axis or gin Sym antisym Wit : or. i ' " sym or , , antisym. wot On Vibrational Vibrations Spectroscopy win molecule that : atomic displacements leave centre of orientation mass and unchanged Measured by FR and Raman -  Normal Modes · Vibration of molecule can be broken down into a sum of normal modes Do not interfere with other modes transforms as irr. rep. Must be consistent w/ of molecule symmetry - HowManyNomaMosadisplacement rectors for the whole molecule Translation all displacements point the same - : (3) -- way 2 if linear Rotation orientation changes about some axis (3) : Therefore there are 3N-6 possible normal modes , FR and Raman Activity IR motion must change dipole moment · : Transforms - as It order basis function Raman motion alter must polarizability · : - Transforms as 2nd order basis function Does not give info intensity · on