Advanced Inorganic Chemistry (Part 1) Basic Solid State ...

1 Advanced InorganicChemistry ( part 1) Basic Solid StateChemistryWS 05/06( )Topics of the complete lectureTopics of the complete lecture Introduction special aspects of the Solid State Structure of solids Basic crystallography Characterization of solids:diffraction techniques, electron microscopy,spectroscopy, thermal analysis Bonding in solids Real structure of crystals, defects Electrical, magnetic and optical properties Synthesis of solids Structure-property relationsResourcesResourcesInternet resources ( german) ~ (pdf-downloads) IUCR-teaching resources (International Union for Crystallography, Advanced level)ResourcesResourcesTextbooks:Shrive r, Atkins, Inorganic Chemistry (3rd ed, 1999) Freeman and Company (Chapter 2, 18 ..)recommendationgermanvery good, but not Basic of basics of Simple close packed structures: Basic structure types (structure of simple salts) More complex Complex Structure ofnanomaterialsOutlineOutline is the Solid State interesting?

2 Most elements are Solid at room temperature1. IntroductionSpecial aspects of Solid State Chemistry Close relationship to Solid State physics Importance of structural Chemistry knowledge of several structure types understanding of structures Physical methods for the characterization of solids X-ray structure analysis, electron thermal analysis, spectroscopy, conductivity measurements .. Investigation and tuning of physical properties magnetism, conductivity, sorption, luminescence defects in solids: point defects, dislocations, grain boundaries Synthesis HT-synthesis, hydrothermal synthesis, soft Chemistry strategies for crystal growth (physics) Degree of order long range order: crystals (3D periodicity) long range order with extended defects ( ) crystals with disorder of a partial structure (ionic conductors) amorphous solids, glasses (short range order) Chemical bonding typical properties covalent solids ( diamond, boron nitride): extreme ionic solids ( ): ionic conductivity.

3 Metals ( Cu): high conductivity at low temperatures conductivity: metals, semiconductors, insulators, superconductors .. magnetism: ferromagnetism, Structure and Symmetry packing of atoms: close packed structure (high space filling) characteristic symmetry elements: cubic, IntroductionClassifications for solids (examples) basics of StructuresVisualization of structuresBraggjun. (1920)Sphere packingPauling (1928)PolyhedraWells (1954)3D netsExample:Cristobalite(SiO2)Descriptio n of packingDescription of environmentDescription of basics of StructuresApproximation: atoms can be treated like sphereselement orcompoundselements orcompounds( alloys )compoundsonlyConcepts for the radius of the spheres=d/2 in metal=d/2 of single bondin molecule=d r(F, )problem: reference! basics of StructuresTrends of the atomic radius atomic radii increase on goingdown a group.

4 Atomic radii decrease across a period particularities:Ga< Al (d-block)(atomicnumber) basics of StructuresTrends of the ionic radii ionic radii increase on going down a group radii of equal charge ions decreaseacross a period ionic radii increase with increasingcoordination number (the higher its CNthebigger the ions seems to be !!) the ionic radius of a given atom decreaseswith increasing charge (r(Fe2+) > r(Fe3+)) cationsare usually the smaller ions in acation/anion combination(exception:r(Cs+) >r(F-))cf . atomicradiiIonic radius = d r(F, ) basics of StructuresDetermination of the ionic radiusStructure analyses,most important method:X-ray diffractionL. Pauling: Radius of one ion is fixed to a reasonable value (r(O2-) = 140 pm) That value is used to compile a set of self consistent values for other basics of StructuresStructure and lattice what is the difference?

5 Lattice pattern of points no chemical information, mathematical description no atoms, but points and lattice vectors (a, b, c, , , ), unit cell Motif (characteristic structural feature, atom, group of ) Structure = Lattice + Motif contains chemical information (e. g. environment, bond ) describes the arrangement of atomsExample:structureandlatticein basics of StructuresUnit cellUnit Cell (interconnection of lattice and structure) an parallel sided region of the lattice from which the entirecrystal can be constructed by purely translational displacements contents of unit cell represents chemical composition(multiples of chemical formula) primitive cell: simplest cell, contain one lattice basics of StructuresUnit cell which one is correct?Conventions:1. Cell edges should,whenever possible,coincide withsymmetry axes orreflection planes2.

6 The smallestpossible cell (thereduced cell) whichfulfills 1 should basics of StructuresUnit cells and crystal system a = b = cCubic a = bHexagonal a = bTrigonal a = bTetragonal -Orthorhombic -Monoclinic--TriclinicRestrictions anglesRestrictions axesCrystal system millions of structures but 7 crystal systems crystal system = particular restriction concerning the unit cell crystal system = unit cell with characteristic symmetry elements (later) basics of StructuresIndices of directions in space1. Select0002. Markpositionof second point3. Drawvector [110] , square brackets for directionsProcedure in three stepsConvention: right-handed coordinate system middle finger: a forefinger: b thumb: basics of StructuresIndices of directions in space examples[111][110] basics of StructuresIndices of planes in space1.

7 Select0002. Mark intercept (1/h 1/k 1/l)of the axes (if possible)3. Draw plane (110) round brackets for planesProcedure in three stepsConvention: right-handed coordinate basics of StructuresIndices of planes in space examples(112)(110) basics of StructuresFractional coordinates Rules for marking the position of an atom in a unit cell: fractional coordinates are related to directions possible values for x, y, z: [0; 1] atoms are generated by symmetry elements negative values: add , values > (or multiples)factionalcoordinates Equivalent points are represented by one triplet only equivalent by translation equivalent by other symmetry elements, later Example: Sphalerite (Zincblende) basics of StructuresNumber of atoms per unit cell (Z) Rectangular cells: atom completely inside unit cell: count = atom on a face of the unit cell: count = atom on an edge of the unit cell: count = atom on a corner of the unit cell: count = of atoms 1 Example 1: SphaleriteExample 2:Wurzitenumber of atoms 2 Wyckoff-notation: number of particular atom per unit basics of StructuresWyckoff-notation- exampleCrystaldataFormulasumMg2 SiO4(Olivine)CrystalsystemorthorhombicSp acegroupPb n m (no.)

8 62)Unitcelldimensionsa= (2) ,b= (4) ,c= (2) + + (600) (600) + (500) (50) (1000) (100) (100) (1000) (1000) (1000) (1000) basics of StructuresWyckoff-notation and occupancy-factorsCrystal dataFormula systemtetragonalSpace groupI-4 2 m (no. 121)Unit cell dimensionsa= (3) c= (1) Z2 Atomic + + + Occ. factor < : mixing of atoms and vacancies on the same position Calculation of the composition: Cu: 2 ; In: 4 1 + 2 ; Se: 8 1 Summary to to Atoms can be treated (and visualized) like spheres Different types of radii Structure and lattice Unit Cell 7 crystalsytems Indexation of directions and planes Fractional coordinates Z: number of atoms per unit cell Wyckoff-notation and occupancy Simple close packed structures (metals)Close packing in 2 Dprimitive packing(low space filling)close packing(high space filling) Simple close packed structures (metals)Close packing in 3 DExample 1: HCPE xample 2: CCPclose packed layer1close packed layer2 HCP(Be,Mg, Zn,Cd, Ti,Zr , Ru.

9 Close packed layer: (001)CCP(Cu, Ag, Au, Al, Ni, Pd, Pt ..)close packed layer: (111) Simple close packed structures (metals)Unit cells of HCP and CCPspace filling = 74%CN = Simple close packed structures (metals)Calculation of space filling example CCPV olumeoftheunitcellVolumeoccupiedbyatoms( spheres) )(24)(2433333 rrspacefrsphereZVracellVarSpacefilling=( Fe, Cr, Mo,W, Ta, ) Simple close packed structures (metals)Other types of metal structuresExample 1: BCCE xample 3: structures ofmanganesegamma Mnbeta Mnalpha Mnspace filling = 68%CN = 8 Example 2: primitive packingspace filling = 52%CN = 6( -Po) basics of StructuresVisualization of structures- polyhedraBraggjun. (1920)Sphere packingPauling (1928)PolyhedraWells (1954)3D netsExample: Cristobalite(SiO2) Simple close packed structures (metals)Holes in close packed Simple close packed structures (metals)Properties of OH and TH in HCP and CCPOH, TH in HCPOH, TH in CCPHCPCCPN umberOH/THn/2nn/2nDistancesOH/TH!

10 Very short!!very short!LocationOH: 4 corners, all edgesTH: inside unit cellOH: center, all edgesTH: center of each octantConnection oftetrahedra, HCPC onnection ofoctahedra, HCPno short distancesSummary to to Structure of metals Concept of close packing (layer sequences, unit cell, space filling) Holes in close packed Basic structure and 0 CCPMgCl2, MnCl2, FeCl2, Cs2O, and 0 HCPMgBr2, PbI2, SnS2,Mg(OH)2, Cd(OH)2, Ag2 FCdI20 and , BeTe, CdS, CuI, GaAs,GaP, HgS, InAs, ZnTeSphalerite (ZnS)0 and , BeO, ZnO, CdS(HT)Wurzite(ZnS)n and 2nCCPLi3 AuLi3Bi0 and 2nHCP!wrong! (LATER)ReB20 and 2nCCPCdF2, CeO2,Li2O, Rb2O,SrCl2, ThO2, ZrO2, AuIn2 CaF2n and 0nHCPTiS, CoS, CoSb, AuSnNiAsn and 0nCCPAgCl, BaS, CaO, CeSe,GdN, NaF,Na3 BiO4, V7C8 NaClHolesfilledOH and THPackingExamplesStructuretype Basic : anions form CCP or HCP,cationsin OH and/or Basic structure typesPauling rules: understanding polyhedral structures(1) A polyhedron of anions is formed about each(1) A polyhedron of anions is formed about eachcationcation,,thethecationcation--an ion distance is determined by the sum of ionic radiianion distance is determined by the sum of ionic radiiand the coordination number by the radius ratio:and the coordination number by the radius ratio:r(cation)/r(anionr(cation)/r(anion ))Scenario for radius ratios.