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MSE_Structure of solids.pdf

The document outlines the structures and properties of solids, including classification based on degree of order and various bonding types. It covers basics of solid-state chemistry, characterization methods, and synthesis techniques alongside visualizations of crystal structures such as close-packed arrangements. Key examples include the properties of covalent, ionic, and metallic solids, as well as specific structure types and rules like Pauling's rules.

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Structures and Properties of Solids
Dates Dates • Friday 20.10.06: 12.00-14.00, F002 • Friday 27.10.06: 12.00-14.00, F002 • Friday 03.11.06: 12.00-14.00, F002 • Friday 10.11.06: 12.00-14.00, F002
Outline Outline 1. Introduction 2. Structure of solids 2.1 Basics of structures (geometrical concepts) 2.2 Simple close packed structures: metals 2.3 Basic structure types 3. Characterization of solids 3.1 Diffraction 3.2 Imaging 4. Synthesis 4.1 HT-synthesis 4.2 CVT
1. Introduction
1.Introduction Why is the solid state interesting? Most elements are solid at room temperature Solid Biomaterials (enamel, bones, shells…) Nanomaterials (quantum dots, nanotubes…)
1. Introduction Special aspects of solid state chemistry Close relationship to solid state physics and materials science Importance of structural chemistry • Knowledge of several structure types • Understanding of structures Physical methods for the characterization of solids • X-ray 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 • HT-synthesis, hydrothermal synthesis, soft chemistry (chemistry) • Strategies for crystal growth (physics) Physics Chemistry
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 Structure and Symmetry • Packing of atoms: close packed structure (high space filling) • Characteristic symmetry: cubic, hexagonal, centrosymmetric/non-centrosymmetric…
2. Basic Structures
2.1 Basics of Structures Visualization of structures How can we display structures in the form of images? Example: Cristobalite (SiO2) Approach 2 Approach 3 Approach 1 Atoms = spheres SiO4-tetrahedra no atoms, 3D nets Coordination polyhedra Pauling (1928) Packing of spheres Bragg jun. (1920) Description of topology Wells (1954) One structure but very different types of structure images
2.1 Basics of Structures Approximation: atoms can be treated like spheres Approach 1: Concepts for the radius of the spheres depending on the nature of the chemical bond compounds elements or compounds („alloys“) element or compounds cation unknown radius = d – r(F, O…) problem: reference! = d/2 of single bond in molecule = d/2 in metal
2.1 Basics of Structures Trends of the atomic / ionic radii • Increase on going down a group (additional electrons in different shells) • Decrease across a period (additional electrons in the same shell) • Ionic radii increase with increasing CN (the higher its CN, the bigger the ions seems to be, due to increasing d!!!) • Ionic radius of a given atom decreases with increasing charge (r(Fe2+) > r(Fe3+)) • Cations are usually the smaller ions in a cation/anion combination (exception: r(Cs+) > r(F-)) • Particularities: Ga < Al (d-block) (atomic number)
2.1 Basics of Structures Structure, lattice and motif Example: Graphite • Lattice: Determined by lattice vectors and angles • Motif: Characteristic structural feature, e. g. molecule • Structure = Lattice + Motif • Unit cell: Parallel sided region from which the entire crystal can be constructed by purely translational displacements (Conventions!!!)
2.1 Basics of Structures Determine the unit cells
2.1 Basics of Structures Unit cells and crystal system • Millions of structures but 7 types of primitive cells (crystal systems) • Crystal system = particular restriction concerning the unit cell • Crystal system = unit cell with characteristic symmetry elements (SSC) Crystal system Restrictions axes Restrictions angles Triclinic - - Monoclinic - α = γ = 90° Orthorhombic - α = β = γ = 90° Tetragonal a = b α = β = γ = 90° Trigonal a = b α = β = 90°, γ = 120° Hexagonal a = b α = β = 90°, γ = 120° Cubic a = b = c α = β = γ = 90°
2.1 Basics of Structures Fractional coordinates (position of the atoms) • possible values for x, y, z: [0; 1], atoms are multiplied by translations • atoms are generated by symmetry elements (see SSC) • Example: Sphalerite (ZnS) 1/2 1/2 1/2 • Equivalent points are represented by one triplet only • equivalent by translation • equivalent by other symmetry elements (see SSC)
2.1 Basics of Structures Number of atoms/cell (Z: number of formula units) Molecular compounds: molecules determine the stoichiometry Ionic or metallic compounds: content of unit cell ↔ stoichiometry How to count atoms? 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 Fraction of the atoms in unit cell Example 1: Sphalerite Example 2: Wurzite Occupancy factor: number of atoms on one particular site
2.2 Simple close packed structures (metals) Close packing in 2D Metal atoms → Spheres Arrangements in 2D primitive (square) packing (large holes, low space filling) close (hexagonal) packing (small holes, high space filling)
2.2 Simple close packed structures (metals) Close packing in 3D 3D close packing: different stacking sequences of close packed layers Example 1: HCP Example 2: CCP stacking sequence: AB stacking sequence: ABC Polytypes: mixing of HCP and CCP, e. g. La, ABAC
2.2 Simple close packed structures (metals) Unit cells of HCP and CCP HCP (Be, Mg, Zn, Cd, Ti, Zr, Ru ...) CCP (Cu, Ag, Au, Al, Ni, Pd, Pt ...) Common properties: CN = 12, space filling = 74% B A B A C
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, cube space filling = 52% CN = 6, octahedron (α-Po) Example 2: primitive packing Example 3: structures of manganese
2.2 Basics of Structures Visualization of structures - polyhedra Example: Cristobalite (SiO2) Bragg jun. (1920) Sphere packing Pauling (1928) Polyhedra Wells (1954) 3D nets
2.2 Simple close packed structures (metals) Holes in close packed structures Different point of view → description of the environment of holes Tetrahedral hole TH Octahedral hole OH 2D close packing position of B-layer-atom Filled holes: Concept of polyhedra
2.2 Simple close packed structures (metals) Properties of OH and TH in CCP Number OH/TH (with respect to n-atoms/unit cell) n: 12/4 +1 2n: 8 Distances OH/TH Location OH: center, all edges TH: center of each octant OH-OH: no short distances TH-TH: no short distances !OH-TH!
2.3 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 NaCl AgCl, BaS, CaO, CeSe, GdN, NaF, Na3BiO4, V7C8 CCP n and 0n NiAs TiS, CoS, CoSb, AuSn HCP n and 0n CaF2 CdF2, CeO2, Li2O, Rb2O, SrCl2, ThO2, ZrO2, AuIn2 CCP 0 and 2n CdCl2 MgCl2, MnCl2, FeCl2, Cs2O, CoCl2 CCP 0.5n and 0 CdI2 MgBr2, PbI2, SnS2, Mg(OH)2, Cd(OH)2, Ag2F HCP 0.5n and 0 Sphalerite (ZnS) AgI, BeTe, CdS, CuI, GaAs, GaP, HgS, InAs, ZnTe CCP 0 and 0.5n Wurzite (ZnS) AlN, BeO, ZnO, CdS (HT) HCP 0 and 0.5n Li3Bi Li3Au CCP n and 2n ReB2 !wrong! (SSC) HCP 0 and 2n
2.3 Basic structure types Pauling rule no. 1 A polyhedron of anions is formed about each cation, A polyhedron of anions is formed about each cation, the cation the cation- -anion distance is determined by the sum of ionic radii anion distance is determined by the sum of ionic radii and the coordination number by the radius ratio: r(cation)/r(ani and the coordination number by the radius ratio: r(cation)/r(anion) on) Scenario for radius ratios: r(cation)/r(anion) = optimum value r(cation)/r(anion) > optimum value r(cation)/r(anion) < optimum value worst case (not stable) low space filling (switching to higher CN) optimum
2.3 Basic structure types Pauling rule no. 1 coordination anion polyhedron radius ratios cation 3 triangle 0.15-0.22 B in borates 4 tetrahedron 0.22-0.41 Si, Al in oxides 6 octahedron 0.41-0.73 Al, Fe, Mg, Ca in oxides 8 cube 0.73-1.00 Cs in CsCl 12 close packing 1.00 metals (anti)cuboctahedron
2.3 Basic structure types NaCl-type Crystal data Formula sum NaCl Crystal system cubic Unit cell dimensions a = 5.6250(5) Å Z 4 Variations of basic structure types: Exchange/Decoration Cl → C2 2- Superstructure Na → Li, Fe Features: Features: • All octahedral holes of CCP filled, type = antitype • Na is coordinated by 6 Cl, Cl is coordinated by 6 Na • One NaCl6-octaherdon is coordinated by 12 NaCl6-octahedra • Connection of octahedra by common edges
2.3 Basic structure types Sphalerite-type Crystal data Formula sum ZnS Crystal system cubic Unit cell dimensions a = 5.3450 Å Z 4 Features: Features: • Diamond-type structure, or: 50% of TH in CCP filled • Connected layers, sequence (S-layers): ABC, polytypes • Zn, S coordinated by 4 S, Zn (tetrahedra, common corners), type = antitype • Hexagonal variant (wurzite) and polytypes • VEC = 4 for ZnS-type (AgI, CdS, BeS, GaAs, SiC) • Many superstructures: Cu3SbS4 (famatinite, VEC = 32/8) • Vacancy phases: Ga2Te3 (1SV), CuIn3Se5 (1 SV), AgGa5Te8 (2 SV) • Applications: semiconductors, solar cells, transistors, LED, laser…
2.3 Basic structure types CaF2-type Crystal data Formula sum CaF2 Crystal system cubic Unit cell dimensions a = 5.4375(1) Å Z 4 Fracture is closed by monoclinic ZrO2 (increase of volume) Features: Features: • All TH of CCP filled • F is coordinated by 4 Ca (tetrahedron) • Ca is coordinated by 8 F (cube) • Oxides MO2 as high-temperature anionic conductors • High performance ceramics
2.3 Basic structure types NiAs-type Crystal data Formula sum NiAs Crystal system hexagonal Unit cell dimensions a = 3.619(1) Å, c = 5.025(1) Å Z 2 Features: Features: • All OH of HCP filled, metal-metal-bonding (common faces of octahedra!) • Ni is coordinated by 6 As (octahedron) • As is coordinated by 6 Ni (trigonal prism) • Type ≠ antitype
2.3 Basic structure types Oxides: Rutile (TiO2) Crystal data Formula sum TiO2 Crystal system tetragonal Unit cell dimensions a = 4.5937 Å, c = 2.9587 Å Z 2 Features: Features: • No HCP arrangement of O (CN(O,O) = 11, tetragonal close packing) • Mixed corner and edge sharing of TiO6-octahedra • Columns of trans edge sharing TiO6-octahedra, connected by common corners • Many structural variants (CaCl2, Markasite) • Application: pigment…
2.3 Basic structure types Oxides: undistorted perovskite (SrTiO3) Crystal data Formula sum SrTiO3 Crystal system cubic Unit cell dimensions a = 3.9034(5) Å Z 1 Features: Features: • Filled ReO3 phase, CN (Ca) = 12 (cuboctaehdron), CN (Ti) = 6 (octahedron) • Ca and O forming CCP, Ti forms primitive arrangement • Many distorted variants (BaTiO3, even the mineral CaTiO3 is distorted!) • Many defect variants (HT-superconductors, YBa2Cu3O7-x) • Hexagonal variants and polytypes YBa2Cu3O7-δ
2.3 Basic structure types Oxides: Spinel (MgAl2O4) Crystal data Formula sum MgAl2O4 Crystal system cubic Unit cell dimensions a = 8.0625(7) Å Z 8 Features: Features: • Distorted CCP of O • Mg in tetrahedral holes (12.5%), no connection of tetrahedra • Al in octahedral holes (50%), common edges/corners • Inverse spinel structures MgTHAl2OHO4 → InTH(Mg, In)OHO4 • Application: ferrites (magnetic materials), biomagnetism Magnetospirillum (Fe3O4) 500 nm
2.3 Basic structure types Oxides: Silicates- overview 1 From simple building units to complex structures Structural features: Structural features: • fundamental building unit (b.u.): SiO4 tetrahedron • isolated tetrahedra and/or tetrahedra connected via common corners • MO6 octahedra , MO4 tetrahedra (M = Fe, Al, Co, Ni…) Composition of characteristic b.u.: Determine the composition and relative number of different b.u. SiO4 SiO3O0.5 SiO2O2×0.5 c.c: 2 common corners (c.c): 0 c.c: 1 Cyclosilicates Cyclosilicates Nesosilicates Nesosilicates Sorosilicates Sorosilicates SiO4 4- Olivine: (Mg,Fe)2SiO4 Si2O7 6- Thortveitite: (Sc,Y)2Si2O7 SiO3 2- Beryl: Be3Si6O18
2.3 Basic structure types Oxides: Silicates- overview 2 c.c: 2 c.c: 2, 3 SiOO3×0.5 c.c: 3 Inosilicates Inosilicates SiO2O2×0.5 SiO2O2×0.5 SiOO3×0.5 Phyllosilicates Phyllosilicates Si2O5 2- Biotite: K(Mg,Fe)3AlSi3O10(OH)2 single chain: SiO3 2- Pyroxene: (Mg,Fe)SiO3 double chain: Si4O11 6- Tremolite: Ca2(Mg,Fe)5Si8O22(OH)2
2.3 Basic structure types Oxides: Silicates- overview 3 Tectosilicates Tectosilicates c.c: 4, SiO2, Faujasite: Ca28.5Al57Si135O384 Pores •mH2O [Si1-xAlxO2] Ax/n Pores T (= Si, Al)O4-Tetrahedra sharing all corners, isomorphous exchange of Si4+, charge compensation x: Al content, charge of microporous framework, n: charge of A Zeolites • Alumosilicates with open channels or cages (d < 2 nm, “boiling stones”) • Numerous applications: adsorbent, catalysis…
2.3 Basic structure types Intermetallics- overview Solid solutions: random arrangement of species on the same position Examples: RbxCs1-x BCC, AgxAu1-x CCP The species must be related • Chemically related species • Small difference in electronegativity • Similar number of valence electrons • Similar atomic radius • (High temperature) Au Ag Ordered structures: from complex building units to complex structures Exception: simple structures
3. Characterization of Solids
• 1901 W. C. Roentgen (Physics) for the discovery of X-rays. • 1914 M. von Laue (Physics) for X-ray diffraction from crystals. • 1915 W. H. and W. L. Bragg (Physics) for structure derived from X-ray diffraction. • 1917 C. G. Barkla (Physics) for characteristic radiation of elements. • 1924 K. M. G. Siegbahn (Physics) for X-ray spectroscopy. • 1927 A. H. Compton (Physics) for scattering of X-rays by electrons. • 1936 P. Debye (Chemistry) for diffraction of X-rays and electrons in gases. • 1962 M. Perutz and J. Kendrew (Chemistry) for the structure of hemoglobin. • 1962 J. Watson, M. Wilkins, and F. Crick (Medicine) for the structure of DNA. • 1979 A. Cormack and G. Newbold Hounsfield (Medicine) for computed axial tomography. • 1981 K. M. Siegbahn (Physics) for high resolution electron spectroscopy. • 1985 H. Hauptman and J. Karle (Chemistry) for direct methods to determine structures. • 1988 J. Deisenhofer, R. Huber, and H. Michel (Chemistry) for the structures of proteins that are crucial to photosynthesis. 4. Introduction Noble prizes associated with X-ray diffraction
4.1 Diffraction Generation of X-rays Atomic scale scenario • Inner shell electrons are striked out • Outer shell electrons fill hole • Production of X-rays due to energy difference between inner and outer shell electron X-ray tube
4.1 Diffraction Geometrical approach, Bragg’s law (BL) A D d θ hkl plane B C • S1 S2 kD • • • kI Constructive Interference π/4 Destructive Interference AC + CD = nλ = 2dsinθB 2sinθB/λ = n/d = nId*I
4.1 Diffraction Results of diffraction studies- Overview Lattice parameters Position of the reflections (Bragg’s law), e. g. (1/d)2 = (1/a)2 [h2 + k2+ l2] Symmetry of the structure Intensity of the reflections and geometry of DP = symmetry of DP Identification of samples (fingerprint) Structure, fractional coordinates…: Intensity of the reflections, quantitative analysis (solution and refinement) Crystal size and perfection Profile of the reflections Special techniques • Electron diffraction: highly significant data, SAED (DP of different areas of one crystal) • Neutron diffraction: localization of H, analyses of magnetic structures • Synchrotron: small crystals, large structures (protein structures)
4.2 Imaging Optical microscopy and SEM- Possibilities • Analysis of the homogeneity of the sample (color…) • Selection of single crystals for structure determination • Determination of the crystal class by analyzing the morphology • Analysis of peculiar features of the morphology (steps, kinks…) • SEM: Determination of the stoichiometry (EDX, cf. X-ray tube) HRTEM SEM optical microscope naked eye 1Å 10Å 100Å 10µm 0.1µm 1µm 100µm 1mm
4.2 Imaging TEM- Basics of physics 200 nm Light microscope Disadvantage: low resolution Abbe (Theory of light microscops resolution) The smaller the wavelength, the higher the resolution De Broglie (Electrons as waves) Fast electrons possess small wavelength Consequence: Microscopy with high-energy radiation Consequence: Microscopy with “fast electrons” Advantage of electrons: negative charge Acceleration and focusing in magnetic or electric fields
4.2 Imaging TEM- Basics of Hardware Interactions Focusing 1 mm Beam formation 1mm
4.2 Imaging HRTEM- Basics Imaging of real structures on the atomic scale (HRTEM) 1 nm Black dots: positions of atoms White dots: positions of cavities of the structure
4. Synthesis
4. Introduction Goals of synthesis / preparation • Synthesis of new compounds • Synthesis of highly pure, but known compounds • Synthesis of highly pure single crystals (Iceberg-principle) • Structural modification of known compounds bulk-structures and nanostructures 2 nm
4.1 HT-synthesis Introduction Standard procedure: “Shake and bake”, “heat and beat”, “trial and error” “The starting materials are finely grinded, pressed to a pellet and heated to a temperature „near“ the melting temperature.” Parameters influencing the reaction: • Purity of educts (sublimation) • Handling of educts (glove box, Schlenck technique) • Temperature: T(reaction) > 2/3 T(melting point), rule of Tamann. Effects on real structure (more defects at elevated T) and diffusion (increase with T) • Solid state reactions are exothermic, “thermodynamically controlled“: Consequence: No metastable products (see e.g. Zeolites) • Porosity, grain size distribution and contact planes: High reactivity of nanoparticles / colloids (low CN)
4.1 HT-synthesis Practical work Experimental consequences: (1) large contact areas (2) small path lengths (3) small pore volume Reactive sintering: pellets of fine powders Problems / Pitfalls: • “Chemical problems” of containers materials: use of reactive materials remedy: double / coated containers • “Physical problems” of containers: compatible expansion/compression coefficients, sufficiently stable to withstand pressure • Separation of educts, remedy: special furnaces, reduced free volume, tricks • No intrinsic purification processes Ex.: 2 Li2CO3 + SiO2 → Li4SiO4 + 2CO2 (800 °C, 24 h) • Li-compounds are highly reactive against containers (use of Au) • Production of a gas, consequence: cracking of containers
4.1 HT-synthesis Tricks • Application of a “gaseous solvent” chemical or vapour phase transport Ex.: Cr2O3(s) + 3/2 O2(g) → 2 CrO3(g) MgO(s) + 2 CrO3(g) → MgCr2O4(s) + 3/2 O2(g) • Separation of educts in a temperature gradient (to avoid explosions) Ex.: 2 Ga(l) + 3 S(g) → Ga2S3(g) • Use of precursors for reactive educts Ex.: Thermal decomposition of MN3 (M = Na, K, Rb, Cs) Thermal release of reactive gases: (O2: MnO2, CO2: BaCO3, H2: LnH2) Coprecipitation and thermal decomposition (e.g. oxalates to oxides) • Use of fluxes Ex.: Li2CO3 + 5 Fe2O3 → 2 LiFe5O8 + CO2(g) (incompl. :grind-fire-regrind, etc.) Or: Flux of Li2SO4/Na2SO4 (dissolves Li2CO3, remove flux with water) • Metathesis reaction Ex.: 2GaCl3 + 3Na2Te → Ga2Te3 + 6NaCl, very exothermic!
4.2 CVT Introduction A solid is dissolved in the gas phase at one place (T=T1) by reaction with a transporting agent (e.g. I2). At another place (T=T2) the solid is condensed again. Use of a temperature gradient. T1 T2 ZnS(s) + I2(g) = ZnI2(s) + S(g) • Used for purification and synthesis of single crystals (fundamental research) • Reactions with large absolute value of ∆H° gives no measurable transport • The sign of ∆H° determines the direction of transport: exothermic reactions: transport from cold to hot endothermic reactions: transport from hot to cold.
4.2 CVT Examples • Mond-process: Ni(s) + 4 CO(g) = Ni(CO)4(g) ∆H° = -300 kJ/mol, transport from 80° to 200°C • Van Arkel / De Boer: Zr(s) + 2 I2(g) = ZrI4(g); (280 to 1450 °C) • Si(s) + SiX4(g) = 2 SiX2(g); (1100° to 900°) • Mixtures of Cu and Cu2O: 3 Cu(s) + 3 HCl(g) = Cu3Cl3(g) + (3/2) H2(g); (High T to Low T) 3/2 Cu2O(s) + 3 HCl(g) = Cu3Cl3(g) + 3/2 H2O(g); (Low T to High T) • Transport of Cu2O(s): 3/2 Cu2O(s) + 3 HCl(g) = Cu3Cl3(g) + 3/2 H2O(g); (Low T to High T) Cu2O(s) + 2 HCl(g) = 2 CuCl(g) + H2O(g); (High T to Low T)

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MSE_Structure of solids.pdf

  • 1.
  • 2.
    Dates Dates • Friday 20.10.06:12.00-14.00, F002 • Friday 27.10.06: 12.00-14.00, F002 • Friday 03.11.06: 12.00-14.00, F002 • Friday 10.11.06: 12.00-14.00, F002
  • 3.
    Outline Outline 1. Introduction 2. Structureof solids 2.1 Basics of structures (geometrical concepts) 2.2 Simple close packed structures: metals 2.3 Basic structure types 3. Characterization of solids 3.1 Diffraction 3.2 Imaging 4. Synthesis 4.1 HT-synthesis 4.2 CVT
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  • 5.
    1.Introduction Why is thesolid state interesting? Most elements are solid at room temperature Solid Biomaterials (enamel, bones, shells…) Nanomaterials (quantum dots, nanotubes…)
  • 6.
    1. Introduction Special aspectsof solid state chemistry Close relationship to solid state physics and materials science Importance of structural chemistry • Knowledge of several structure types • Understanding of structures Physical methods for the characterization of solids • X-ray 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 • HT-synthesis, hydrothermal synthesis, soft chemistry (chemistry) • Strategies for crystal growth (physics) Physics Chemistry
  • 7.
    1. Introduction Classifications forsolids (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 Structure and Symmetry • Packing of atoms: close packed structure (high space filling) • Characteristic symmetry: cubic, hexagonal, centrosymmetric/non-centrosymmetric…
  • 8.
  • 9.
    2.1 Basics ofStructures Visualization of structures How can we display structures in the form of images? Example: Cristobalite (SiO2) Approach 2 Approach 3 Approach 1 Atoms = spheres SiO4-tetrahedra no atoms, 3D nets Coordination polyhedra Pauling (1928) Packing of spheres Bragg jun. (1920) Description of topology Wells (1954) One structure but very different types of structure images
  • 10.
    2.1 Basics ofStructures Approximation: atoms can be treated like spheres Approach 1: Concepts for the radius of the spheres depending on the nature of the chemical bond compounds elements or compounds („alloys“) element or compounds cation unknown radius = d – r(F, O…) problem: reference! = d/2 of single bond in molecule = d/2 in metal
  • 11.
    2.1 Basics ofStructures Trends of the atomic / ionic radii • Increase on going down a group (additional electrons in different shells) • Decrease across a period (additional electrons in the same shell) • Ionic radii increase with increasing CN (the higher its CN, the bigger the ions seems to be, due to increasing d!!!) • Ionic radius of a given atom decreases with increasing charge (r(Fe2+) > r(Fe3+)) • Cations are usually the smaller ions in a cation/anion combination (exception: r(Cs+) > r(F-)) • Particularities: Ga < Al (d-block) (atomic number)
  • 12.
    2.1 Basics ofStructures Structure, lattice and motif Example: Graphite • Lattice: Determined by lattice vectors and angles • Motif: Characteristic structural feature, e. g. molecule • Structure = Lattice + Motif • Unit cell: Parallel sided region from which the entire crystal can be constructed by purely translational displacements (Conventions!!!)
  • 13.
    2.1 Basics ofStructures Determine the unit cells
  • 14.
    2.1 Basics ofStructures Unit cells and crystal system • Millions of structures but 7 types of primitive cells (crystal systems) • Crystal system = particular restriction concerning the unit cell • Crystal system = unit cell with characteristic symmetry elements (SSC) Crystal system Restrictions axes Restrictions angles Triclinic - - Monoclinic - α = γ = 90° Orthorhombic - α = β = γ = 90° Tetragonal a = b α = β = γ = 90° Trigonal a = b α = β = 90°, γ = 120° Hexagonal a = b α = β = 90°, γ = 120° Cubic a = b = c α = β = γ = 90°
  • 15.
    2.1 Basics ofStructures Fractional coordinates (position of the atoms) • possible values for x, y, z: [0; 1], atoms are multiplied by translations • atoms are generated by symmetry elements (see SSC) • Example: Sphalerite (ZnS) 1/2 1/2 1/2 • Equivalent points are represented by one triplet only • equivalent by translation • equivalent by other symmetry elements (see SSC)
  • 16.
    2.1 Basics ofStructures Number of atoms/cell (Z: number of formula units) Molecular compounds: molecules determine the stoichiometry Ionic or metallic compounds: content of unit cell ↔ stoichiometry How to count atoms? 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 Fraction of the atoms in unit cell Example 1: Sphalerite Example 2: Wurzite Occupancy factor: number of atoms on one particular site
  • 17.
    2.2 Simple closepacked structures (metals) Close packing in 2D Metal atoms → Spheres Arrangements in 2D primitive (square) packing (large holes, low space filling) close (hexagonal) packing (small holes, high space filling)
  • 18.
    2.2 Simple closepacked structures (metals) Close packing in 3D 3D close packing: different stacking sequences of close packed layers Example 1: HCP Example 2: CCP stacking sequence: AB stacking sequence: ABC Polytypes: mixing of HCP and CCP, e. g. La, ABAC
  • 19.
    2.2 Simple closepacked structures (metals) Unit cells of HCP and CCP HCP (Be, Mg, Zn, Cd, Ti, Zr, Ru ...) CCP (Cu, Ag, Au, Al, Ni, Pd, Pt ...) Common properties: CN = 12, space filling = 74% B A B A C
  • 20.
    2.2 Simple closepacked structures (metals) Other types of metal structures Example 1: BCC (Fe, Cr, Mo, W, Ta, Ba ...) space filling = 68% CN = 8, cube space filling = 52% CN = 6, octahedron (α-Po) Example 2: primitive packing Example 3: structures of manganese
  • 21.
    2.2 Basics ofStructures Visualization of structures - polyhedra Example: Cristobalite (SiO2) Bragg jun. (1920) Sphere packing Pauling (1928) Polyhedra Wells (1954) 3D nets
  • 22.
    2.2 Simple closepacked structures (metals) Holes in close packed structures Different point of view → description of the environment of holes Tetrahedral hole TH Octahedral hole OH 2D close packing position of B-layer-atom Filled holes: Concept of polyhedra
  • 23.
    2.2 Simple closepacked structures (metals) Properties of OH and TH in CCP Number OH/TH (with respect to n-atoms/unit cell) n: 12/4 +1 2n: 8 Distances OH/TH Location OH: center, all edges TH: center of each octant OH-OH: no short distances TH-TH: no short distances !OH-TH!
  • 24.
    2.3 Basic structuretypes Overview „Basic“: anions form CCP or HCP, cations in OH and/or TH Structure type Examples Packing Holes filled OH and TH NaCl AgCl, BaS, CaO, CeSe, GdN, NaF, Na3BiO4, V7C8 CCP n and 0n NiAs TiS, CoS, CoSb, AuSn HCP n and 0n CaF2 CdF2, CeO2, Li2O, Rb2O, SrCl2, ThO2, ZrO2, AuIn2 CCP 0 and 2n CdCl2 MgCl2, MnCl2, FeCl2, Cs2O, CoCl2 CCP 0.5n and 0 CdI2 MgBr2, PbI2, SnS2, Mg(OH)2, Cd(OH)2, Ag2F HCP 0.5n and 0 Sphalerite (ZnS) AgI, BeTe, CdS, CuI, GaAs, GaP, HgS, InAs, ZnTe CCP 0 and 0.5n Wurzite (ZnS) AlN, BeO, ZnO, CdS (HT) HCP 0 and 0.5n Li3Bi Li3Au CCP n and 2n ReB2 !wrong! (SSC) HCP 0 and 2n
  • 25.
    2.3 Basic structuretypes Pauling rule no. 1 A polyhedron of anions is formed about each cation, A polyhedron of anions is formed about each cation, the cation the cation- -anion distance is determined by the sum of ionic radii anion distance is determined by the sum of ionic radii and the coordination number by the radius ratio: r(cation)/r(ani and the coordination number by the radius ratio: r(cation)/r(anion) on) Scenario for radius ratios: r(cation)/r(anion) = optimum value r(cation)/r(anion) > optimum value r(cation)/r(anion) < optimum value worst case (not stable) low space filling (switching to higher CN) optimum
  • 26.
    2.3 Basic structuretypes Pauling rule no. 1 coordination anion polyhedron radius ratios cation 3 triangle 0.15-0.22 B in borates 4 tetrahedron 0.22-0.41 Si, Al in oxides 6 octahedron 0.41-0.73 Al, Fe, Mg, Ca in oxides 8 cube 0.73-1.00 Cs in CsCl 12 close packing 1.00 metals (anti)cuboctahedron
  • 27.
    2.3 Basic structuretypes NaCl-type Crystal data Formula sum NaCl Crystal system cubic Unit cell dimensions a = 5.6250(5) Å Z 4 Variations of basic structure types: Exchange/Decoration Cl → C2 2- Superstructure Na → Li, Fe Features: Features: • All octahedral holes of CCP filled, type = antitype • Na is coordinated by 6 Cl, Cl is coordinated by 6 Na • One NaCl6-octaherdon is coordinated by 12 NaCl6-octahedra • Connection of octahedra by common edges
  • 28.
    2.3 Basic structuretypes Sphalerite-type Crystal data Formula sum ZnS Crystal system cubic Unit cell dimensions a = 5.3450 Å Z 4 Features: Features: • Diamond-type structure, or: 50% of TH in CCP filled • Connected layers, sequence (S-layers): ABC, polytypes • Zn, S coordinated by 4 S, Zn (tetrahedra, common corners), type = antitype • Hexagonal variant (wurzite) and polytypes • VEC = 4 for ZnS-type (AgI, CdS, BeS, GaAs, SiC) • Many superstructures: Cu3SbS4 (famatinite, VEC = 32/8) • Vacancy phases: Ga2Te3 (1SV), CuIn3Se5 (1 SV), AgGa5Te8 (2 SV) • Applications: semiconductors, solar cells, transistors, LED, laser…
  • 29.
    2.3 Basic structuretypes CaF2-type Crystal data Formula sum CaF2 Crystal system cubic Unit cell dimensions a = 5.4375(1) Å Z 4 Fracture is closed by monoclinic ZrO2 (increase of volume) Features: Features: • All TH of CCP filled • F is coordinated by 4 Ca (tetrahedron) • Ca is coordinated by 8 F (cube) • Oxides MO2 as high-temperature anionic conductors • High performance ceramics
  • 30.
    2.3 Basic structuretypes NiAs-type Crystal data Formula sum NiAs Crystal system hexagonal Unit cell dimensions a = 3.619(1) Å, c = 5.025(1) Å Z 2 Features: Features: • All OH of HCP filled, metal-metal-bonding (common faces of octahedra!) • Ni is coordinated by 6 As (octahedron) • As is coordinated by 6 Ni (trigonal prism) • Type ≠ antitype
  • 31.
    2.3 Basic structuretypes Oxides: Rutile (TiO2) Crystal data Formula sum TiO2 Crystal system tetragonal Unit cell dimensions a = 4.5937 Å, c = 2.9587 Å Z 2 Features: Features: • No HCP arrangement of O (CN(O,O) = 11, tetragonal close packing) • Mixed corner and edge sharing of TiO6-octahedra • Columns of trans edge sharing TiO6-octahedra, connected by common corners • Many structural variants (CaCl2, Markasite) • Application: pigment…
  • 32.
    2.3 Basic structuretypes Oxides: undistorted perovskite (SrTiO3) Crystal data Formula sum SrTiO3 Crystal system cubic Unit cell dimensions a = 3.9034(5) Å Z 1 Features: Features: • Filled ReO3 phase, CN (Ca) = 12 (cuboctaehdron), CN (Ti) = 6 (octahedron) • Ca and O forming CCP, Ti forms primitive arrangement • Many distorted variants (BaTiO3, even the mineral CaTiO3 is distorted!) • Many defect variants (HT-superconductors, YBa2Cu3O7-x) • Hexagonal variants and polytypes YBa2Cu3O7-δ
  • 33.
    2.3 Basic structuretypes Oxides: Spinel (MgAl2O4) Crystal data Formula sum MgAl2O4 Crystal system cubic Unit cell dimensions a = 8.0625(7) Å Z 8 Features: Features: • Distorted CCP of O • Mg in tetrahedral holes (12.5%), no connection of tetrahedra • Al in octahedral holes (50%), common edges/corners • Inverse spinel structures MgTHAl2OHO4 → InTH(Mg, In)OHO4 • Application: ferrites (magnetic materials), biomagnetism Magnetospirillum (Fe3O4) 500 nm
  • 34.
    2.3 Basic structuretypes Oxides: Silicates- overview 1 From simple building units to complex structures Structural features: Structural features: • fundamental building unit (b.u.): SiO4 tetrahedron • isolated tetrahedra and/or tetrahedra connected via common corners • MO6 octahedra , MO4 tetrahedra (M = Fe, Al, Co, Ni…) Composition of characteristic b.u.: Determine the composition and relative number of different b.u. SiO4 SiO3O0.5 SiO2O2×0.5 c.c: 2 common corners (c.c): 0 c.c: 1 Cyclosilicates Cyclosilicates Nesosilicates Nesosilicates Sorosilicates Sorosilicates SiO4 4- Olivine: (Mg,Fe)2SiO4 Si2O7 6- Thortveitite: (Sc,Y)2Si2O7 SiO3 2- Beryl: Be3Si6O18
  • 35.
    2.3 Basic structuretypes Oxides: Silicates- overview 2 c.c: 2 c.c: 2, 3 SiOO3×0.5 c.c: 3 Inosilicates Inosilicates SiO2O2×0.5 SiO2O2×0.5 SiOO3×0.5 Phyllosilicates Phyllosilicates Si2O5 2- Biotite: K(Mg,Fe)3AlSi3O10(OH)2 single chain: SiO3 2- Pyroxene: (Mg,Fe)SiO3 double chain: Si4O11 6- Tremolite: Ca2(Mg,Fe)5Si8O22(OH)2
  • 36.
    2.3 Basic structuretypes Oxides: Silicates- overview 3 Tectosilicates Tectosilicates c.c: 4, SiO2, Faujasite: Ca28.5Al57Si135O384 Pores •mH2O [Si1-xAlxO2] Ax/n Pores T (= Si, Al)O4-Tetrahedra sharing all corners, isomorphous exchange of Si4+, charge compensation x: Al content, charge of microporous framework, n: charge of A Zeolites • Alumosilicates with open channels or cages (d < 2 nm, “boiling stones”) • Numerous applications: adsorbent, catalysis…
  • 37.
    2.3 Basic structuretypes Intermetallics- overview Solid solutions: random arrangement of species on the same position Examples: RbxCs1-x BCC, AgxAu1-x CCP The species must be related • Chemically related species • Small difference in electronegativity • Similar number of valence electrons • Similar atomic radius • (High temperature) Au Ag Ordered structures: from complex building units to complex structures Exception: simple structures
  • 38.
  • 39.
    • 1901 W.C. Roentgen (Physics) for the discovery of X-rays. • 1914 M. von Laue (Physics) for X-ray diffraction from crystals. • 1915 W. H. and W. L. Bragg (Physics) for structure derived from X-ray diffraction. • 1917 C. G. Barkla (Physics) for characteristic radiation of elements. • 1924 K. M. G. Siegbahn (Physics) for X-ray spectroscopy. • 1927 A. H. Compton (Physics) for scattering of X-rays by electrons. • 1936 P. Debye (Chemistry) for diffraction of X-rays and electrons in gases. • 1962 M. Perutz and J. Kendrew (Chemistry) for the structure of hemoglobin. • 1962 J. Watson, M. Wilkins, and F. Crick (Medicine) for the structure of DNA. • 1979 A. Cormack and G. Newbold Hounsfield (Medicine) for computed axial tomography. • 1981 K. M. Siegbahn (Physics) for high resolution electron spectroscopy. • 1985 H. Hauptman and J. Karle (Chemistry) for direct methods to determine structures. • 1988 J. Deisenhofer, R. Huber, and H. Michel (Chemistry) for the structures of proteins that are crucial to photosynthesis. 4. Introduction Noble prizes associated with X-ray diffraction
  • 40.
    4.1 Diffraction Generation ofX-rays Atomic scale scenario • Inner shell electrons are striked out • Outer shell electrons fill hole • Production of X-rays due to energy difference between inner and outer shell electron X-ray tube
  • 41.
    4.1 Diffraction Geometrical approach,Bragg’s law (BL) A D d θ hkl plane B C • S1 S2 kD • • • kI Constructive Interference π/4 Destructive Interference AC + CD = nλ = 2dsinθB 2sinθB/λ = n/d = nId*I
  • 42.
    4.1 Diffraction Results ofdiffraction studies- Overview Lattice parameters Position of the reflections (Bragg’s law), e. g. (1/d)2 = (1/a)2 [h2 + k2+ l2] Symmetry of the structure Intensity of the reflections and geometry of DP = symmetry of DP Identification of samples (fingerprint) Structure, fractional coordinates…: Intensity of the reflections, quantitative analysis (solution and refinement) Crystal size and perfection Profile of the reflections Special techniques • Electron diffraction: highly significant data, SAED (DP of different areas of one crystal) • Neutron diffraction: localization of H, analyses of magnetic structures • Synchrotron: small crystals, large structures (protein structures)
  • 43.
    4.2 Imaging Optical microscopyand SEM- Possibilities • Analysis of the homogeneity of the sample (color…) • Selection of single crystals for structure determination • Determination of the crystal class by analyzing the morphology • Analysis of peculiar features of the morphology (steps, kinks…) • SEM: Determination of the stoichiometry (EDX, cf. X-ray tube) HRTEM SEM optical microscope naked eye 1Å 10Å 100Å 10µm 0.1µm 1µm 100µm 1mm
  • 44.
    4.2 Imaging TEM- Basicsof physics 200 nm Light microscope Disadvantage: low resolution Abbe (Theory of light microscops resolution) The smaller the wavelength, the higher the resolution De Broglie (Electrons as waves) Fast electrons possess small wavelength Consequence: Microscopy with high-energy radiation Consequence: Microscopy with “fast electrons” Advantage of electrons: negative charge Acceleration and focusing in magnetic or electric fields
  • 45.
    4.2 Imaging TEM- Basicsof Hardware Interactions Focusing 1 mm Beam formation 1mm
  • 46.
    4.2 Imaging HRTEM- Basics Imagingof real structures on the atomic scale (HRTEM) 1 nm Black dots: positions of atoms White dots: positions of cavities of the structure
  • 47.
  • 48.
    4. Introduction Goals ofsynthesis / preparation • Synthesis of new compounds • Synthesis of highly pure, but known compounds • Synthesis of highly pure single crystals (Iceberg-principle) • Structural modification of known compounds bulk-structures and nanostructures 2 nm
  • 49.
    4.1 HT-synthesis Introduction Standard procedure: “Shakeand bake”, “heat and beat”, “trial and error” “The starting materials are finely grinded, pressed to a pellet and heated to a temperature „near“ the melting temperature.” Parameters influencing the reaction: • Purity of educts (sublimation) • Handling of educts (glove box, Schlenck technique) • Temperature: T(reaction) > 2/3 T(melting point), rule of Tamann. Effects on real structure (more defects at elevated T) and diffusion (increase with T) • Solid state reactions are exothermic, “thermodynamically controlled“: Consequence: No metastable products (see e.g. Zeolites) • Porosity, grain size distribution and contact planes: High reactivity of nanoparticles / colloids (low CN)
  • 50.
    4.1 HT-synthesis Practical work Experimentalconsequences: (1) large contact areas (2) small path lengths (3) small pore volume Reactive sintering: pellets of fine powders Problems / Pitfalls: • “Chemical problems” of containers materials: use of reactive materials remedy: double / coated containers • “Physical problems” of containers: compatible expansion/compression coefficients, sufficiently stable to withstand pressure • Separation of educts, remedy: special furnaces, reduced free volume, tricks • No intrinsic purification processes Ex.: 2 Li2CO3 + SiO2 → Li4SiO4 + 2CO2 (800 °C, 24 h) • Li-compounds are highly reactive against containers (use of Au) • Production of a gas, consequence: cracking of containers
  • 51.
    4.1 HT-synthesis Tricks • Applicationof a “gaseous solvent” chemical or vapour phase transport Ex.: Cr2O3(s) + 3/2 O2(g) → 2 CrO3(g) MgO(s) + 2 CrO3(g) → MgCr2O4(s) + 3/2 O2(g) • Separation of educts in a temperature gradient (to avoid explosions) Ex.: 2 Ga(l) + 3 S(g) → Ga2S3(g) • Use of precursors for reactive educts Ex.: Thermal decomposition of MN3 (M = Na, K, Rb, Cs) Thermal release of reactive gases: (O2: MnO2, CO2: BaCO3, H2: LnH2) Coprecipitation and thermal decomposition (e.g. oxalates to oxides) • Use of fluxes Ex.: Li2CO3 + 5 Fe2O3 → 2 LiFe5O8 + CO2(g) (incompl. :grind-fire-regrind, etc.) Or: Flux of Li2SO4/Na2SO4 (dissolves Li2CO3, remove flux with water) • Metathesis reaction Ex.: 2GaCl3 + 3Na2Te → Ga2Te3 + 6NaCl, very exothermic!
  • 52.
    4.2 CVT Introduction A solidis dissolved in the gas phase at one place (T=T1) by reaction with a transporting agent (e.g. I2). At another place (T=T2) the solid is condensed again. Use of a temperature gradient. T1 T2 ZnS(s) + I2(g) = ZnI2(s) + S(g) • Used for purification and synthesis of single crystals (fundamental research) • Reactions with large absolute value of ∆H° gives no measurable transport • The sign of ∆H° determines the direction of transport: exothermic reactions: transport from cold to hot endothermic reactions: transport from hot to cold.
  • 53.
    4.2 CVT Examples • Mond-process:Ni(s) + 4 CO(g) = Ni(CO)4(g) ∆H° = -300 kJ/mol, transport from 80° to 200°C • Van Arkel / De Boer: Zr(s) + 2 I2(g) = ZrI4(g); (280 to 1450 °C) • Si(s) + SiX4(g) = 2 SiX2(g); (1100° to 900°) • Mixtures of Cu and Cu2O: 3 Cu(s) + 3 HCl(g) = Cu3Cl3(g) + (3/2) H2(g); (High T to Low T) 3/2 Cu2O(s) + 3 HCl(g) = Cu3Cl3(g) + 3/2 H2O(g); (Low T to High T) • Transport of Cu2O(s): 3/2 Cu2O(s) + 3 HCl(g) = Cu3Cl3(g) + 3/2 H2O(g); (Low T to High T) Cu2O(s) + 2 HCl(g) = 2 CuCl(g) + H2O(g); (High T to Low T)