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Advanced Inorganic Chemistry

Advanced Inorganic Chemistry
Advanced Inorganic Chemistry (Part 1) Basic Solid State Chemistry WS 05/06 (H.J. Deiseroth)Topics of the complete lecture Topics 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 • Structureproperty relationsResources ResourcesResources Resources Textbooks: Shriver, Atkins, Inorganic Chemistry (3rd ed, 1999) W.H. Freeman and Company (Chapter 2, 18 ...) recommendation german very good, but not basic level Internet resources • http://ruby.chemie.unifreiburg.de/Vorlesung/ (german) • http://www.chemistry.ohiostate.edu/woodward/ch754... (pdfdownloads) • IUCRteaching resources (International Union for Crystallography, advanced level)Resources Resources JournalsOutline – 15.10.04 Outline – 15.10.04 1. Introduction 2. Structure of solids 2.1 Basics of structures 2.2 Simple close packed structures: metals 2.3 Basic structure types (structure of simple salts) 2.4 More complex structures Oxides... 2.5 Complex structures 2.6 Structure of nanomaterials1. Introduction1.Introduction Why is the solid state interesting Most elements are solid at room temperature1. Introduction Special 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 • Xray structure analysis, electron microscopy… • thermal analysis, spectroscopy, conductivity measurements ... • Investigation and tuning of physical properties • magnetism, conductivity, sorption, luminescence • defects in solids: point defects, dislocations, grain boundaries • Synthesis • HTsynthesis, hydrothermal synthesis, soft chemistry • strategies for crystal growth (physics)1. Introduction Classifications for solids (examples) • Degree of order • long range order: crystals (3D periodicity) • long range order with extended defects (dislocations…) • crystals with disorder of a partial structure (ionic conductors) • amorphous solids, glasses (short range order) • Chemical bonding – typical properties • covalent solids (e.g. diamond, boron nitride): extreme hardness ... • ionic solids (e.g. NaCl): ionic conductivity ... • metals (e.g. Cu): high conductivity at low temperatures • conductivity: metals, semiconductors, insulators, superconductors… • magnetism: ferromagnetism, paramagnetism… • Structure and Symmetry • packing of atoms: close packed structure (high space filling) • characteristic symmetry elements: cubic, hexagonal…2. Basic Structures2.1 Basics of Structures Visualization of structures Example: Cristobalite (SiO ) 2 Description of packing Description of environment Description of topology Bragg jun. (1920) Sphere packing Pauling (1928) Polyhedra Wells (1954) 3D nets2.1 Basics of Structures Approximation: atoms can be treated like spheres Concepts for the radius of the spheres elements or element or compounds compounds compounds only („alloys“) = = = d/2 of single bond d – r(F, O…) d/2 in metal in molecule problem: reference2.1 Basics of Structures Trends of the atomic radius • atomic radii increase on going down a group. • atomic radii decrease across a period • particularities: Ga Al (dblock) (atomic number)2.1 Basics of Structures Trends of the ionic radii • ionic radii increase on going down a group cf. atomic radii • radii of equal charge ions decrease across a period • ionic radii increase with increasing coordination number (the higher its CN the bigger the ions seems to be ) • the ionic radius of a given atom decreases 2+ 3+ with increasing charge (r(Fe ) r(Fe )) • cations are usually the smaller ions in a cation/anion combination + (exception: r(Cs ) r(F ))2.1 Basics of Structures Determination of the ionic radius Structure analyses, most important method: Ionic radius = d – r(F, O…) Xray diffraction L. Pauling: 2 • Radius of one ion is fixed to a reasonable value (r(O ) = 140 pm) • That value is used to compile a set of self consistent values for other ions.2.1 Basics of Structures Structure and lattice – what is the difference Example: structure and lattice in 2D • 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 atoms…) • Structure = Lattice + Motif • contains chemical information (e. g. environment, bond length…) • describes the arrangement of atoms2.1 Basics of Structures Unit cell Unit Cell (interconnection of lattice and structure) • an parallel sided region of the lattice from which the entire crystal 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 point2.1 Basics of Structures Unit cell – which one is correct Conventions: 1. Cell edges should, whenever possible, coincide with symmetry axes or reflection planes 2. The smallest possible cell (the reduced cell) which fulfills 1 should be chosen2.1 Basics of Structures Unit cells and crystal 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) Crystal system Restrictions axes Restrictions angles Triclinic  ° Monoclinic  ° Orthorhombic  ° Tetragonal a = b  ° ° Trigonal a = b  ° ° Hexagonal a = b  ° Cubic a = b = c2.1 Basics of Structures Indices of directions in space “110”, square brackets for directions Procedure in three steps c b a 1. Select 000 2. Mark position of second point 3. Draw vector Convention: righthanded coordinate system • middle finger: a • forefinger: b • thumb: c2.1 Basics of Structures Indices of directions in space – examples c 111 b a c 110 b a2.1 Basics of Structures Indices of planes in space “(110)” round brackets for planes Procedure in three steps c b a 1. Select 000 2. Mark intercept (1/h 1/k 1/l) 3. Draw plane of the axes (if possible) Convention: righthanded coordinate system2.1 Basics of Structures Indices of planes in space – examples c (112) b a c (110) b a2.1 Basics of Structures Fractional 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 1.0, values 1.0: substract 1.0 (or multiples) • Example: Sphalerite (Zincblende) factional coordinates • Equivalent points are represented by one triplet only • equivalent by translation • equivalent by other symmetry elements, later2.1 Basics of Structures Number of atoms per unit cell (Z) • Rectangular cells: • atom completely inside unit cell: count = 1.0 • atom on a face of the unit cell: count = 0.5 • atom on an edge of the unit cell: count = 0.25 • atom on a corner of the unit cell: count = 0.125 Example 1: Sphalerite Example 2: Wurzite number of atoms 2 number of atoms 1 • Wyckoffnotation: number of particular atom per unit cell2.1 Basics of Structures Wyckoffnotation example Crystal data Formula sum Mg SiO (Olivine) 2 4 Crystal system orthorhombic Space group P b n m (no. 62) Unit cell dimensions a = 4.75(2) Å, b = 10.25(4) Å, c = 6.00(2) Å Z 4 Atomic coordinates Atom Ox. Wyck. x y z Mg1 +2 4a 0.00000 0.00000 0.00000 Mg2 +2 4c 0.00995(600) 0.27734(600) 0.75000 Si1 +4 4c 0.07373(500) 0.4043(50) 0.25000 O1 2 4c 0.23242(1000) 0.0918(100) 0.75000 O2 2 4c 0.2793(100) 0.05078(1000) 0.25000 O3 2 8d 0.22266(1000) 0.33594(1000) 0.46289(1000)2.1 Basics of Structures Wyckoffnotation and occupancyfactors Crystal data Formula sum Cu In Se 0.8 2.4 4 Crystal system tetragonal Space group I 4 2 m (no. 121) Unit cell dimensions a = 5.7539(3) Å c = 11.519(1) Å Z 2 Atomic coordinates Atom Ox. Wyck. Occ. x y z Cu1 +1 2a 0.8 0 0 0 In1 +3 4d 1.0 0 1/2 1/4 In2 +3 2b 0.4 0 0 1/2 Se1 2 8i 1.0 1/4 1/4 1/8 • Occ. factor 1.0: mixing of atoms and vacancies on the same position • Calculation of the composition: Cu: 20.8; In: 41 + 20.4; Se: 81Summary to 2.1 Summary to 2.1 • Atoms can be treated (and visualized) like spheres • Different types of radii • Structure and lattice • Unit Cell • 7 crystal sytems • Indexation of directions and planes • Fractional coordinates • Z: number of atoms per unit cell • Wyckoffnotation and occupancy factors2.2 Simple close packed structures (metals) Close packing in 2D primitive packing (low space filling) close packing (high space filling)2.2 Simple close packed structures (metals) Close packing in 3D Example 1: HCP Example 2: CCP close packed layer close packed layer 1 22.2 Simple close packed structures (metals) Unit cells of HCP and CCP HCP (Be, Mg, Zn, Cd, Ti, Zr, Ru ...) close packed layer: (001) anticuboctahedron space filling = 74 CN = 12 cuboctahedron CCP (Cu, Ag, Au, Al, Ni, Pd, Pt ...) close packed layer: (111)2.2 Simple close packed structures (metals) Calculation of space filling – example CCP Volume occupied by atoms (spheres) Space filling = Volume of the unit cell 4r 2a 3 4r  3 V (cell)a  2  4 3 ZV (sphere)4 r 3  4  3 4 r  2 3 spacef .0.74  3 6 4r     2  2.2 Simple close packed structures (metals) Other types of metal structures Example 1: BCC (Fe, Cr, Mo, W, Ta, Ba ...) space filling = 68 CN = 8 Example 2: primitive packing space filling = 52 ( Po) CN = 6 Example 3: structures of manganese alpha Mn beta Mn gamma Mn2.2 Basics of Structures Visualization of structures polyhedra Example: Cristobalite (SiO ) 2 Bragg jun. (1920) Sphere packing Pauling (1928) Polyhedra Wells (1954) 3D nets2.2 Simple close packed structures (metals) Holes in close packed structures Octahedral hole Tetrahedral hole OH TH Tetrahedron Octahedron2.2 Simple close packed structures (metals) Properties of OH and TH in HCP and CCP OH, TH in HCP OH, TH in CCP HCP CCP Number n/2n n/2n OH/TH OH: 4 corners, all edges OH: center, all edges Location TH: inside unit cell TH: center of each octant Distances very short very short no short distances OH/TH Connection of Connection of tetrahedra, HCP octahedra, HCPSummary to 2.2 Summary to 2.2 • Concept of close packing (layer sequences, unit cell, space filling) • Structure of metals • Holes in close packed structures2.3 Basic structure types Overview „Basic“: anions form CCP or HCP, cations in OH and/or TH Structure type Examples Packing Holes filled OH and TH AgCl, BaS, CaO, CeSe, NaCl CCP n and 0n GdN, NaF, Na BiO , V C 3 4 7 8 TiS, CoS, CoSb, AuSn NiAs HCP n and 0n CdF , CeO , Li O, Rb O, 2 2 2 2 CaF CCP 0 and 2n 2 SrCl , ThO , ZrO , AuIn 2 2 2 2 MgCl , MnCl , FeCl , Cs O, 2 2 2 2 CdCl CCP 0.5n and 0 2 CoCl 2 MgBr , PbI , SnS , 2 2 2 CdI HCP 0.5n and 0 2 Mg(OH) , Cd(OH) , Ag F 2 2 2 AgI, BeTe, CdS, CuI, GaAs, Sphalerite (ZnS) CCP 0 and 0.5n GaP, HgS, InAs, ZnTe AlN, BeO, ZnO, CdS (HT) Wurzite (ZnS) HCP 0 and 0.5n Li Au 3 Li Bi CCP n and 2n 3 ReB wrong (LATER) HCP 0 and 2n 22.3 Basic structure types Pauling rules: understanding polyhedral structures (1 (1)) A A p po olly yh he ed dr ro on n o off a an niio on ns s iis s fo for rm me ed d a ab bo ou utt e ea ac ch h c ca ati tio on n,, th the e c ca ati tio on na an niio on n d diis sta tan nc ce e iis s d de ete ter rm miin ne ed d b by y th the e s su um m o off iio on niic c r ra ad diiii a an nd d th the e c co oo or rd diin na ati tio on n n nu um mb be er r b by y th the e r ra ad diiu us s r ra ati tio o:: r r(c (ca ati tio on n)/ )/r r(a (an niio on n)) Scenario for radius ratios: worst case optimum low space filling2.3 Basic structure types Pauling rules: understanding polyhedral structures coordination anion polyhedron radius ratios cation 3 triangle 0.150.22 C 4 tetrahedron 0.220.41 Si, Al 6 octahedron 0.410.73 Al, Fe, Mg, Ca 8 cube 0.731.00 K, Na 12 close packing 1.00 (anti)cuboctahedron 2r(anion) Example: Octahedron Radius ratio octahedral coordination 2r(anion) + 2 2r(anion) 2r(cation) 2r(cation)  1 2r(anion) r(cation) 2 10.414 r(anion)2.3 Basic structure types Pauling rules: understanding polyhedral structures (2) Negative and positive local charges should be balanced. (2) Negative and positive local charges should be balanced. The sum of bond valencess should be equal to the The sum of bond valencess should be equal to the ij ij oxi oxidat datiion on s st tat ate e V V of of iion on ii: : V V = =s s ii ii ij ij Example 1TiO (Rutile) 2 4+ 2 CN(Ti ) = 6, CN(O ) = 3: s (TiO) =2/3 ij s (Ti) = 4,s (O) = 2 ij ij Example 2 GaAs (Sphalerite) Example 3 SrTiO (Perovskite) 3 3+ 3 2+ 4+ CN(Ga ) = 4, CN(As ) = 4: s = 3/4 CN(Sr ) = 12, CN(Ti ) = 6, ij 2 CN(O ) = 4(Sr) and 2(Ti) s (Ga) = 3,s (As) = 3 ij ij s (SrO) = 1/6 , s (TiO) = 2/3 ij ij2.3 Basic structure types Pauling rules: understanding polyhedral structures ( (3 3) ) The The p pre res senc ence e o of f sha shar red ed edge edges, s, an and d par part tiicul cula arl rly y sha share red d f fac aces es dec decre reas ases es t th he e s st tabi abilliit ty y of of a a s st truc ruct tur ure. e. Thi This s iis s pa par rt tiicul cular arlly y t tru rue e for cations with large valences and small CN. for cations with large valences and small CN. ( (4 4) ) IIn n a a cr cry yst stal al con cont tai aini nin ng g di dif ff fer erent ent c cat atiions ons t thos hose e w wiit th h llar arge ge v val alenc ence e and and sm smal alll C CN N do do not not t tend end t to o s share hare pol poly yhedron hedron el elem emen ent ts s w wiit th h ea each ch o ot ther her.. (5) The number of chemically different coordination environments (5) The number of chemically different coordination environments for a given ion in a crystal tends to be small. for a given ion in a crystal tends to be small.2.3 Basic structure types NaCltype Crystal data Formula sum NaCl Crystal system cubic Space group F m 3 m (no. 225) Unit cell dimensions a = 5.6250(5) Å Z 4 NaCl Atomic coordinates Atom Ox. Wyck. x y z Na +1 4a 0 0 0 Cl 1 4b 1/2 1/2 1/2 Structural features: Structural features: • all octahedral holes of CCP filled, type = antitype • Na is coordinated by 6 Cl, Cl is coordinated by 6 Na • One NaCl octaherdon is coordinated by 12 NaCl octahedra 6 6 • Connection of octahedra by common edges2.3 Basic structure types Bonding in ionic structures – Coulomb interaction Classic picture of ionic bonding: cations donate electrons to anions thus each species fullfills the octet rule. + i.e. Na + F→ Na + F Interaction between anions and cations: Coulomb interactions. Coulomb potential 2 of an ion pair z z e  V A N AB 4r 0 AB V : Coulomb potential (electrostatic potential) AB A: Madelung constant (depends on structure type) 19 z: charge number, e: elementary charge = 1.602 10 C 12 2 2 : dielectric constant (vacuum permittivity) = 8.85 10 C /(Nm ) o r : shortest distance between cation and anion AB 23 1 N: Avogadro constant = 6.023 10 mol2.3 Basic structure types Bonding in ionic structures – Coulomb interaction Calculating the Madelung constant (for NaCl) First term: attraction from the 6 nearest neighbors 12 8 6 A6 ... Second term: repulsion (opposite sign) 2 3 4 from 12 next nearest neighbors … First coordination Second Third coordination sphere A converges to a value of 1.748. coordination sphere sphere A CN Rock Salt 1.748 6 CsCl 1.763 8 Sphalerite 1.638 4 Fluorite 5.039 82.3 Basic structure types Bonding in ionic structures repulsion Repulsion arising from overlap of electron clouds Because the electron density of atoms decreases exponentially towards zero at large distances from the nucleus the Born repulsion shows the same r 0 behaviour r approximation: B  V Born n r B and n are constants for a given atom type; n can be derived from compressibility measurements (8)2.3 Basic structure types Lattice energy of a ionic structure 1) Set the first derivative of the sum to zero 2) Substitute Bparameter of repulsive part 2 z z e 1 0 0   ) Min.(V A N (1 )  V L Born AB L 4r n 0 0 1 • typical values, measured (calculated) kJ mol : • NaCl: –772 (757); CsCl: 652 (623) • measured means by Born Haber cycle (later) • fraction of Coulomb interaction at r : 90 0 • missing in our lattice energy calculations: • zero point energy • dipoledipole interaction • covalent contributions, example: AgCl: 912 (704)2.3 Basic structure types Sphaleritetype Crystal data Formula sum ZnS Crystal system cubic Layer in sphalerite Space group F 4 3 m (no. 216) Unit cell dimensions a = 5.3450 Å Z 4 Stacking sequence Atomic coordinates Atom Ox. Wyck. x y z Zn1 +2 4a 0 0 0 S2 2 4c 1/4 1/4 1/4 Structural and other features: Structural and other features: • diamondtype structure • 50 of tetrahedral holes in CCP filled • connected layers, sequence (Slayers): ABC, polytypes • Zn, S is coordinated by 4 S, (tetrahedra, common corners) • applications of sphaleritetype structures very important (semiconductors: solar cells, transistors, LED, laser…)2.3 Basic structure types Wurzitetype Crystal data Formula sum ZnS Crystal system hexagonal Space group P 6 m c (no. 186) 3 Unit cell dimensions a = 3.8360 Å, c = 6.2770 Å Z 2 Atomic coordinates Atom Ox. Wyck. x y z Zn1 +2 2b 1/3 2/3 0 Stacking sequence S1 2 2b 1/3 2/3 3/8 S St truc ruct tura urall f fe eat atur ures es: : • connected layers, sequence (Slayers): AB • Zn is coordinated by 4 S (tetrahedra, common corners) • polytypes2.3 Basic structure types CaF type 2 Crystal data Formula sum CaF 2 Crystal system cubic Space group F m 3 m (no. 225) Unit cell dimensions a = 5.4375(1) Å Z 4 Coordination Ca Atomic coordinates Atom Ox. Wyck. x y z Ca1 +2 4a 0 0 0 F1 1 8c 1/4 1/4 1/4 S St truc ruct tura urall f fe eat atur ures es: : • all TH of CCP filled • F is coordinated by 4 Ca (tetrahedron) • Ca is coordinated by 8 F (cube)2.3 Basic structure types CdCl type 2 Crystal data Formula sum CdCl 2 Crystal system trigonal Space group R 3 m (no. 166) Unit cell dimensions a = 6.2300 Å,= 36° Z 1 Atomic coordinates Stacking sequence Atom Ox. Wyck. x y z Cd1 +2 3a 0 0 0 One layer Cl1 1 36i 0.25(1) 0.25(1) 0.25(1) S St truc ruct tura urall f fe eat atur ures es: : • layered structure, sequence (Cllayers): ABC • Cd is coordinated octahedrally by 6 Cl (via six common edges) • polytypes2.3 Basic structure types CdI type 2 Crystal data Formula sum CdI 2 Crystal system trigonal Space group P 3 m 1 (no. 164) Unit cell dimensions a = 4.2500 Å, c = 6.8500 Å Z 1 Atomic coordinates Atom Ox. Wyck. x y z Stacking sequence Cd1 +2 1a 0 0 0 I1 1 2d 1/3 2/3 1/4 S St truc ruct tura urall f fe eat atur ures es: : • layered structure, sequence (Ilayers): AB • Cd is coordinated octahedrally by 6 I (via six common edges) • polytypesLi metal TiS 2 2.3 Basic structure types Intercalation of layered compounds • Reversible intercalation of atoms between the layers of a layered compound • Hostguest interactions, structureproperty relations Example 1: Graphite • Electron donors (alkali metals, e. g. KC ) 8 • Electron acceptors (NO , Br , AsF ...) 3 2 5 • Properties: Increase of interlayer spacing, color change, increase of conductivity, change of electronic structure Example 2: TiS (CdI type) 2 2 • Electron donors (alkali metals, copper, organic amines) • Application: LiTiS battery 2 + xLi (metal)→ xLi (solv) +xe + Li salt in DME/THF xLi (solv) + TiS + xe→ Li TiS (s) 2 x 22.3 Basic structure types Li Bitype 3 Crystal data Formula sum Li Bi 3 Crystal system cubic Space group F m 3 m (no. 225) Unit cell dimensions a = 6.7080 Å Z 4 Unit cell Atomic coordinates Atom Ox. Wyck. x y z Bi1 +0 4a 0 0 0 Li1 +0 4b 1/2 1/2 1/2 Li2 +0 8c 1/4 1/4 1/4 S St truc ruct tura urall f fe eat atur ures es: : • all holes of CCP filled by Li • not many examples of this structure type2.3 Basic structure types NiAstype Crystal data Formula sum NiAs Crystal system hexagonal Space group P 63/m m c (no. 194) Unit cell dimensions a = 3.619(1) Å, c = 5.025(1) Å Z 2 Octahedra Atomic coordinates Atom Ox. Wyck. x y z Trigonal prisms Ni1 +3 2a 0 0 0 As1 3 2c 1/3 2/3 1/4 Structural features: Structural features: Octahedron and trig. prism • all OH of HCP filled • Ni is coordinated by 6 As (octahedron) • metalmetalbonding (common faces of the octahedra) • As is coordinated by 6 Ni (trigonal prism) • type≠antitypeSummary to 2.3 Summary to 2.3 • Pauling rules • Lattice energy calculations of ionic structures • Structures of basis structure types: NaCl, ZnS, CaF , CdCl , CdI , Li Bi, NiAs 2 2 2 32.4 More complex structures Introduction “More complex”: • deviations from close packing of anions • no close packing of anions • cations in simple (highly symmetrical) polyhedra • other species besides tetrahedra and octahedra • complex interconnection of the polyhedra2.4 More complex structures Oxides: Rutile (TiO ) 2 Crystal data Formula sum TiO 2 Crystal system tetragonal Space group P 4 /m n m (no. 136) 2 Unit cell dimensions a = 4.5937 Å, c = 2.9587 Å Octahedra in Rutile Z 2 Atomic coordinates Atom Ox. Wyck. x y z Ti1 +4 2a 0 0 0 O1 2 4f 0.30469(9) 0.30469(9) 0 Structural features: Structural features: • no HCP arrangement of O (CN(O,O) = 11) • mixed corner and edge sharing of TiO octahedra 6 • columns of trans edge sharing TiO octahedra, 6 connected by common corners • many structural variants • application: pigment2.4 More complex structures Oxides: ReO 3 Crystal data Formula sum ReO 3 Crystal system cubic Space group P m 3 m (no. 221) Unit cell dimensions a = 3.7504(1) Å Z 1 Atomic coordinates Atom Ox. Wyck. x y z Unit cell Re1 +6 1a 0 0 0 O1 2 3d 1/2 0 0 S St truc ruct tura urall f fe eat atur ures es: : • no close packing (CN (O,O) = 8) • ReO octahedra connected by six common corners 6 • large cavity in the center of the unit cell • filled phase (A WO tungsten bronze) x 32.4 More complex structures Oxides: undistorted perovskite (SrTiO ) 3 Crystal data Formula sum SrTiO 3 Crystal system cubic Cuboctahedron Unit cell Space group P m 3 m (no. 221) Unit cell dimensions a = 3.9034(5) Å Z 1 Atomic coordinates Atom Ox. Wyck. x y z Sr1 +2 1a 0 0 0 Ti1 +4 1b 1/2 1/2 1/2 O1 2 3c 0 1/2 1/2 Structural features: Structural features: • filled ReO phase, CN (Ca) = 12 (cuboctaehdron), CN (Ti) = 6 (octahedron) 3 • many distorted variants (even the mineral CaTiO ) 3 • many defect variants (HTsuperconductors, YBa Cu O ) 2 3 7x • hexagonal variants and polytyps2.4 More complex structures Oxides: Spinel (MgAl O ) 2 4 Crystal data Formula sum MgAl O 2 4 Crystal system cubic Space group F d 3 m (no. 227) Unit cell dimensions a = 8.0625(7) Å Z 8 Atomic coordinates Atom Ox. Wyck. x y z Diamond Document Mg1 +2 8a 0 0 0 Al1 +3 16d 5/8 5/8 5/8 O1 2 32e 0.38672 0.38672 0.38672 Diamond Document Structural features: Structural features: • distorted CCP of O • Mg in tetrahedral holes (25), no connection of tetrahedra • Al in octahedral holes (50), common edges • Inverse spinel structures Mg Al O→ In (Mg, In) O TH 2OH 4 TH OH 4 • Application: ferrites (magnetic materials)2.4 More complex structures Oxides: Spinel (Fe O ) 3 4 500 nm Magnetospirillum OcherSummary to 2.4 Summary to 2.4 • More complex structures • Rutile • ReO 3 • Perovskite and structural variations • Spinel and structural variations2.5 Complex structures Oxides: Silicates overview 1 From simple building units to complex structures Structural features: Structural features: • fundamental building unit: SiO tetrahedron 4 • isolated tetrahedra or connection via common corners • MO octahedra , MO tetrahedra (M = Fe, Al, Co, Ni…) 6 4 Nesosilicates Sorosilicates Cyclosilicates Nesosilicates Sorosilicates Cyclosilicates 4 6 2 SiO Si O SiO 4 2 7 3 Olivine: (Mg,Fe) SiO Thortveitite: (Sc,Y) Si O Beryl: Be Si O 2 4 2 2 7 3 6 182.5 Complex structures Oxides: Silicates overview 2 Inosilicates Inosilicates Phyllosilicates Phyllosilicates 2 2 6 single chain: SiO Si O double chain: Si O 3 2 5 4 11 Biotite: K(Mg,Fe) AlSi O (OH) Pyroxene: (Mg,Fe)SiO Tremolite: 3 3 10 2 3 Ca (Mg,Fe) Si O (OH) 2 5 8 22 22.5 Complex structures Oxides: Silicates overview 3 Tectosilicates SiO 2 Faujasite: Ca Al Si O 28 57 135 384  cage  cage TAtomrepresentation TAtomrepresentation2.5 Complex structures Concept for visualization of topology TAtom representation TAtom representation 3DNetsK : n ed og te en+ vertex 3DNetsK : n ed og te en+ vertex2.5 Complex structures Intermetallics overview Solid solutions: Example: Rb Cs BCCstructure, disordered x 1x • chemically related • small difference of electronegativity • similar number of valence electrons • similar atomic radius • (high temperature) Ordered structures: from complex building units to complex structures Rule: complex structures Exception: simple structures CuZn2.5 Complex structures Intermetallics HumeRotheryphases Trend 1: Intermetallics with a defined relation between structure and VEC (Valence Electron Concentration) Number (N) of valence electrons (empirical rules): 0: Fe, Co, Ni, Pt, Pd; 1: Cu, Ag, Au 2: Be, Mg, Zn, Cd; 3: Al; 4: Si, Ge, Sn; 5: Sb VEC = N(val. electr) / N(atoms) (both per formula unit) VEC 3/2 3/2 3/2 21/13 7/4 CuZn HCP HCP  Mn Brass Structure Cu Al Cu Si Cu Ga Cu Zn CuZn Example 3 5 3 5 8 3 CoAl Ag Al Ag In Cu Al Cu Sn 3 3 9 4 3 NiIn CoZn Au Sn Cu Si Ag Sn 3 5 31 8 32.5 Complex structures Intermetallics Lavesphases Trend 2: Intermetallics with a high space filling (71) Typical radius ratio: 1:1.225 MgCu MgZn MgNi Structure 2 2 2 TiCr BaMg FeB Example 2 2 2 AgBe FeBe TaCo 2 2 2 CeAl WFe ZrFe 2 2 22.5 Complex structures Zintlphases overview Experimental observation: element 1 + element 2→ compound (liquid ammonia) element 1: alkali, alkalineearth, rareearth metals element 2 (examples): GaTl, SiPb, AsBi… Properties of the compounds: • salt like structures, colored Characteristics of • soluble clusters in liquid ammonia Zintl phases • semiconductors • fixed composition, valence compounds • The structure of the anions follows the octet rule The Zintlrule • The number of bonds of each anion is 8N The Zintlrule („8Nrule“) (N = number of electrons of the anion) („8Nrule“) • The anions adopt structures related to the elements of group N2.5 Complex structures Zintlphases examples 4 • 8N = 0, N = 8: Mg Si: Si , isolated atoms (noble gases: HCP or CCP) 2 • 8N = 1, N = 7: Sr P : P , dimers (halogene) 2 2 2 • 8N = 2, N = 6: CaSi: Si , chains or rings (chalcogene) • 8N = 3, N = 5: CaSi : Si , sheets or 3D nets (pnicogene, black phosphorous) 2 • 8N = 4, N = 4: NaTl: Tl , 3D framework of tetrahedra (tetrel, diamond) Example: Ba Si 3 4 Ba3Si4Summary to 2.5 Summary to 2.5 • Complex structures • Silicates (six structure families, complex framework of tetrahedra) • Intermetallics (complex framework of complex polyhedra) • Simple Zintlphases2.6 Structure of nanomaterials What is nano Definition: at least one dimension 100 nm Nanotube2.6 Structure of nanomaterials Physical approaches to nanostructures Atom manipulation Building a Ni Dimer on Au(111)2.6 Structure of nanomaterials Why nano – what is the difference to micro Electronic structure (simple illustration, details later)2.6 Structure of nanomaterials Why nano – fundamental properties CdScolloids, different particle sizes • melting point: structure dominated by small CN (e.g. 9 instead of 12) • magnetism (increasing spin interactions with decreasing particle size) • optical properties (example: nanoAu, purple of cassius) • conductivity (deviations from the Ohm‘s law) Vision of nano: design of properties by designing the size of objects „wavefunction engineering“ and not the chemistry of the objects2.6 Structure of nanomaterials Structures containing large entities fullerenes Chemistry of fullerenes Chemistry of fullerenes • Synthesis: vaporization of carbon • ion implantation in C60 cage • partial filling of OH by alkali or rare earth metals (fullerides) • several chemical modifications2.6 Structure of nanomaterials Structures containing large holes MOF M MO OF F = = M Me et ta all o orga rgan niic c f frame ramew wo ork rk Synthesis: Diffusion of Zn(II)salts in organic acids simple chemistry (precipitation) – remarkable results C ZnO Tetraeder 4 O Secundary buiding unit Organic linker2.6 Structure of nanomaterials Structures containing large holes MOF M MO OF F = = M Me et ta all o orga rgan niic c f frame ramew wo ork rk Unique structural features Unique structural features • principle of scaling • highly crystalline materials 3 • lowest density of crystalline matter, up to 0.21 g/cm • ab initio design of materials2.6 Structure of nanomaterials Structures containing large holes – new materials ASU31 Scaling Solalitetype topology Sodalitetype topology Arizona State University2.6 Structure of nanomaterials Structures containing channels Zeolites C Co ompo mpos siit te e mat mate eri ria alls s,, e e.. g g.. d dy ye es s iin n ze zeo olliit te e c cr ry ys st ta alls s • dyes are highly persistent • interactions of dye molecules (use as antennas)2.6 Structure of nanomaterials 0D nanomaterials – synthesis by MBE • substrate wafers transferred to high vacuum growth chamber • elements kept in effusion cells at high temperatures • shutters over cells open to release vaporized elements, which deposit on sample • temperature of each KCell controls the rate of deposition of that element (Ga, In, Al, etc.) • precise control over temperatures and shutters allows very thin layers to be grown (1 ML/sec) • RHEED patterns indicate surface morphology (Reflection High Energy Electron Diffraction)2.6 Structure of nanomaterials 1D nanomaterials – Carbon nanotubes Single walled carbon nanotube (SWCNT) Graphene sheet • multiwalled carbon nanotubes (MWCNT) • different conformations: different conductivity • electron emission (field emission) • remarkable mechanical properties • hydrogen adsorption • easy electrolyte contact • polymer strengthening • transistor components • drug or chemical storage2.6 Structure of nanomaterials 1D nanomaterials – occurrence and synthesis Misfit of layers nanorolls (asbestos etc.) Templates nanorods, nanotubes highly anisotropic crystal structures (Se, Te, LiMo Se ) 3 3 Self assembley nanorods, nanotubes2.6 Structure of nanomaterials 2D nanomaterials synthesis • Sputtering • originally a method to clean surfaces + • Ar ions are accelerated in an electrical field and „hit“ the target • consequence: surface atoms are removed from the surface • application: SEM, getterpump (UHV devices)2.6 Structure of nanomaterials 2D nanomaterials synthesis • Epitaxy: • thin orientated layers of similar crystal structures • e.g. InAs: a=603,6 pm on GaAs: a=565,4 pm, both sphalerite structures • CVD (Chemical Vapour Deposition) • decomposition of molecules in the gas phase by electron beam or laser • deposition on suitable substrates • e.g. fabrication of LEDs with GaP and GaAs P , 1x x epitaxial layers are produced by thermal decomposition of compounds like AsH , AsCl , PH , PCl , ... 3 3 3 3 • MBE Production of a Ga Al As 1x x on GaAs by the MBE process2.6 Structure of nanomaterials Chemical approaches to nanomaterials R. Tenne Inorganic fullerenes Inorganic nanotubes2.6 Structure of nanomaterials Hollow inorganic structures – how does it work compact MoO nanoparticle 2 H S 2 compact MoO nanoparticle covered 2 with a few layers of MoS 2 consequence: isolated particles diffusion controlled reaction density of MoS2 lower than MoO2 consequence: hollow particleSummary to 2.6 Summary to 2.6 • nanomaterials of different dimensionality • unique properties of small objects • 0D • 1D • 2D • chemical approaches to nanoparticlesExercises2.1 Basics of Structures Structure and lattice – what is the difference2.1 Basics of Structures Structure and lattice – full description Crystal data Formula sum C Structure Crystal system trigonal Space group R 3 m (no. 166) Lattice Unit cell dimensions a, b, c = 3.6350 Å,= 39.49 ° Atomic coordinates Atom Ox. Wyck. x y z C +0 2c 0.164 0.164 0.164 Structure2.1 Basics of Structures Determine the unit cell of the following pattern2.1 Basics of Structures Structures without translational symmetry2.1 Basics of Structures Indices of directions in space “110” Procedure in three steps c b a 1. Select 000 2. Mark position of second point 3. Draw vector Convention: righthanded coordinate system • middle finger: a • forefinger: b • thumb: c2.1 Basics of Structures Indices of directions in space – examples 1 c 111 b a c 110 b a2.1 Basics of Structures Indices of directions in space – examples 2 c b a2.1 Basics of Structures Indices of planes in space “(110)” Procedure in three steps c b a 1. Select 000 2. Mark intercept of the axes 3. Draw plane (if possible) Convention: righthanded coordinate system2.1 Basics of Structures Indices of planes in space – examples 1 c (112) b a c (110) b a2.1 Basics of Structures Indices of planes in space – examples 2 c b a2.1 Basics of Structures Determine the fractional coordinates and Z2.1 Basics of Structures Determine the fractional coordinates and Z2.1 Basics of Structures Determine the fractional coordinates and Z2.1 Basics of Structures Determine the fractional coordinates and Z2.1 Basics of Structures How many Zr,Si and O atoms are in one unit cell Crystal data Formula sum ZrSiO 4 Crystal system tetragonal Space group I 41/a m d (no. 141) Unit cell dimensions a = 6.625(6) Å c = 6.0313(70) Å Cell volume 267.00(46) Å3 Atomic coordinates Atom Ox. Wyck. x y z O1 2 16h 0 0.06592(10) 0.19922(70) Zr1 +4 4a 0 3/4 1/8 Si1 +4 4b 0 1/4 3/82.2 Simple close packed structures (metals) Calculation of space filling – example BCC Volume occupied by atoms (spheres) Space filling = Volume of the unit cell2.3 Basic structure types Calculate the radius ratio for a cubic coordination2.3 Basic structure types Pauling rules: understanding polyhedral structures Example 4 – Al O 2SiO 2H O (Kaolinite) 2 3 2 2 3+ 4+ CN(Al ) = 6, CN(Si ) = 4, sij (AlO) = 1/2 , sij (SiO) = 1 CN(O1) = 2(Al), CN(O2) = 2(Al) + 1(Si), CN(O3) = 2 sij (O1) = 1 (),sij (O2) = 2,sij (O3) = 2. Consequence: O1 is OH Example 5 – Determine possible coordination spheres of O in Na BiO 3 4 2 + 5+ • rock salt type structure CN(O) = 6, CN(cations) = 6, O , Na , Bi . • ONa with charge: 2 + 6/6 = 1 6 • ONa Bi with charge: 2 + 5/6 + 5/6 = 1/3 5 • ONa Bi with charge: 2 + 4/6 + 10/6 = +1/3 4 2 • ONa Bi with charge: 2 + 3/6 + 15/6 = +1 3 3 • Composition and frequency of octahedra: O(Na Bi)/6 + O(Na Bi )/6 = O Na Bi = O Na Bi 5 4 2 2 9/6 3/6 4 32.5 Complex structures Determine the formula of the characteristic units2.5 Complex structures Any suggestions for the anionic partial structure CaSi 2 KSnAs KSnSb 2 LiGaSn
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