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Legaturi in cristale

Legaturi in cristale. Klein, 1993 : capitolul 4. Unit Cell Geometry. Arrangement of atoms determines unit cell geometry: Primitive = atoms only at corners Body-centered = atoms at corners and center Face-centered = atoms at corners and 2 (or more) faces

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Legaturi in cristale

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  1. Legaturi in cristale Klein, 1993: capitolul4

  2. Unit Cell Geometry • Arrangement of atoms determines unit cell geometry: • Primitive = atoms only at corners • Body-centered = atoms at corners and center • Face-centered = atoms at corners and 2 (or more) faces • Lengths and angles of axes determine six unit cell classes • Same as crystal classes

  3. Coordination Polyhedron and Unit Cells • They are not the same! • BUT, coordination polyhedron is contained within a unit cell • Relationship between the unit cell and crystallography • Crystal systems and reference, axial coordinate system Halite (NaCl) unit cell; Z = 4 Cl CN = 6; octahedral

  4. Unit Cells and Crystals • The unit cell is often used in mineral classification at the subclass or group level • Unit cell = building block of crystals • Lattice = infinite, repeating arrangement of unit cells to make the crystal • Relative proportions of elements in the unit cell are indicated by the chemical formula (Z number) Sphalerite, (Zn,Fe)S, Z=4

  5. Unit Cells and Crystals • Crystals belong to one of six crystal systems • Unit cells of distinct shape and symmetry characterize each crystal system • Total crystal symmetry depends on unit cell and lattice symmetry • Crystals can occur in any size and may (or may not!) express the internal order of constituent atoms with external crystal faces • Euhedral, subhedral, anhedral

  6. What is Crystal Chemistry? • study of the atomic structure, physical properties, and chemical composition of crystalline material • basically inorganic chemistry of solids • the structure and chemical properties of the atom and elements are at the core of crystal chemistry • there are only a handful of elements that make up most of the rock-forming minerals of the earth

  7. Chemical Layers of the Earth SiO2 – 45% MgO – 37% FeO – 8% Al2O3 – 4% CaO – 3% others – 3% Fe – 86% S – 10% Ni – 4%

  8. Composition of the Earth’s Crust

  9. Average composition of the Earth’s Crust(by weight, elements, and volume)

  10. The Atom The Bohr Model The Schrodinger Model Nucleus - contains most of the weight (mass) of the atom - composed of positively charge particles (protons) and neutrally charged particles (neutrons) Electron Shell - insignificant mass - occupies space around the nucleus defining atomic radius - controls chemical bonding behavior of atoms

  11. Structure of the Periodic Table # of Electrons in Outermost Shell Noble Gases Anions --------------------Transition Metals------------------ Primary Shell being filled

  12. Ions, Ionization Potential, and Valence States Cations – elements prone to give up one or more electrons from their outer shells; typically a metal element Anions – elements prone to accept one or more electrons to their outer shells; always a non-metal element Ionization Potential – measure of the energy necessary to strip an element of its outermost electron Electronegativity – measure strength with which a nucleus attracts electrons to its outer shell Valence State (or oxidation state) – the common ionic configuration(s) of a particular element determined by how many electrons are typically stripped or added to an ion

  13. 1st Ionization Potential Anions Cations Elements with a single outer s orbital electron Electronegativity

  14. Valence States of Ions common to Rock-forming Minerals Cations – generally relates to column in the periodic table; most transition metals have a +2 valence state for transition metals, relates to having two electrons in outer Anions – relates electrons needed to completely fill outer shell Anionic Groups – tightly bound ionic complexes with net negative charge +1 +2 +3 +4 +5 +6 +7 -2 -1 -----------------Transition Metals---------------

  15. Reprezentari structurale Exemple: Cristobalit (SiO2) Reprezentare de descrie tipul de impahetare a atomilor Reprezentare prin poliedre de coordinare Descrierea configuratiei golurilor Bragg jun. (1920) Sphere packing Bragg jun. (1920) Sphere packing Pauling (1928) Polyhedra Pauling (1928) Polyhedra Wells (1954) 3D nets Wells (1954) 3D nets

  16. 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 atoms

  17. 2.1 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 point • 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 chosen

  18. 2.2 Simple close packed structures (metals) Close packing in 2D primitive packing(low space filling) close packing(high space filling)

  19. 2.2 Simple close packed structures (metals) Close packing in 3D Example 1: HCP Example 2: CCP

  20. 2.2 Simple close packed structures (metals) Unit cells of HCP and CCP HCP (Be, Mg, Zn, Cd, Ti, Zr, Ru ...) close packed layer: (001) space filling = 74%, CN = 12 CCP (Cu, Ag, Au, Al, Ni, Pd, Pt ...) close packed layer: (111)

  21. 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

  22. 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% CN = 6 (-Po) Example 3: structures of manganese far beyond simple close packed structures!

  23. 2.2 Simple close packed structures (metals) Holes in close packed structures Octahedral hole OH Tetrahedral hole TH

  24. 2.1 Basics of Structures Approximation: atoms can be treated like spheres Concepts for the radius of the spheres elements or compounds(„alloys“) element or compounds compounds only = d/2 of single bond in molecule = d – r(F, O…) problem: reference! = d/2 in metal

  25. 2.1 Basics of Structures Trends of the radii (atomic number) • ionic radii increase on going • down a group • radii of equal charge ions decrease across a period • ionic radii increase with increasing coordination number • the ionic radius of a given atom • decreases with increasing charge • cations are usually smaller • than anions • atomic radii increase on going • down a group. • atomic radii decrease across • a period • particularities: Ga < Al (d-block)

  26. 2.1 Basics of Structures Determination of the ionic radius Structure analyses, most important method: X-ray diffraction Ionic radius = d – r(F, O…) • L. 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 ions.

  27. Impachetari Impachetareaceamaicompacta a unoratomiidentici (monezi, bile de biliard…) se face sub forma hexagonala in care fiecare atom esteinconjurat de 6 atomivecini Impachetare hexagonala compacta

  28. strat A A A A A A B C C A A A A A A B B strat B C A A A A A strat C Impachetare cubica compacta ABCABC... Impachetare hexagonala compacta ABAB... Arhetipuri structurale Coordinari. Poliedrii de coordinare

  29. Impachetari

  30. Arhetipuri structurale coordinare tetraedrica (4 anioni, NC=4) coordinare octaedrica (6 anioni, NC=6) Coordinari. Poliedrii de coordinare

  31. 2.3 Basic structure types Overview „Basic“: anions form CCP or HCP, cations in OH and/or TH

  32. Arhetipuri structurale Coordinari. Poliedrii de coordinare tetraedru de coordinare TO4 T = Si, Al octaedru de coordinare MO6 M = Al, Mg, Fe2+, Fe3+ , Ca, Na, K

  33. Legaturi (bonding forces) • Legaturile dintre atomi sunt de natura electrica; • Tipul de legatura este responsabil de proprietatile fizice si chimice ale mineralelor: duritate, clivaj, temperatura de topire, conductivitate electrica, termica, proprietati magnetice, compresibilitate, etc… • Legaturile puternice produc: • 1/ duritate ridicata; • 2/ temperatura de topire ridicata; • 3/ coeficient de expansiune termica mai scazut. • Principaleletipuri de legaturi: • Ionica • Covalenta • Metalica • Van der Waals • Hidrogen

  34. Tipuri de legaturi in minerale • 1/ Legaturaionica • Cedaresauacceptare de é pentru a obtineconfiguratiestabila (gaznobil) → completareastratul de valenta • Ex: Na: Z=11: 1s2 2s2 2p6 3s1 • Devine ion pozitivprincedareaunuié • Ex2: Cl: Z=17: 1s2 2s2 2p6 3s2 3p5 • Devine ion negativprinacceptareaunuié 2 atomi neutrii 2 ioni incarcati (+) si (-)care formeaza NaCl

  35. Legaturi • Legaturaionica: Punct de topire (MP) vs. distanta inter-ionica (ID) Daca DI creste → MP scade MP MP DI ID (Fig. 3.18) MP ID

  36. Legaturi • Legaturaionica: Duritate (H) vs. distanta inter-ionica (DI) Fig. 3.19 H H DI DI Distante inter-ionice mici → legatura puternica

  37. Legaturi • Legatura covalenta →obtinerea configuratiei de gaz nobil prin punere in comun de é • Ex.: Carbon, C • Legatura covalenta a diamantului

  38. Legaturi • Linus Pauling 1901-1994 • Premiul Nobel pt. chimie 1954 • Premiul Nobel pentru pace 1962 (testele atomice) “Linus Carl Pauling, who ever since 1946 has campaigned ceaselessly, not only against nuclear weapons tests, not only against the spread of these armaments, not only against their very use, but against all warfare as a means of solving international conflicts.” 1939: Metoda de estimare a caracterului ionic (%) Electronegativitatea

  39. Legaturi • Electronegativitateareprezintă capacitatea unui atom de a atrage é. • halogenii au cele mai mari valori ale electronegativității • metalele alcaline au cele mai mici valori si există elemente care au aceleași valori pentru electronegativitate. • Electronegativitate scazuta → cedeaza é • Electronegativitate ridicata → accepta é

  40. Legaturi • Electronegativitatea(scadein grupa& creste in perioada) metale- EN< nemetale EN> Acceptori Donori NOTA: gazele nobile au electronegativitate zero→stabile

  41. Bonding Forces • Metallic bond • Atomic nuclei plus non valence electron orbitals bound together by the aggregate charge of a cloud of valence electrons • electrons ‘free’ to move readily throughout structure - Metals aka ‘electron donors’ • Properties: • Conductivitate electrica ridicata • Plasticitate > Red circles = nuclei Metals: Electrons v. mobile

  42. Bonding Forces • Van der Waals bond: • Weak bond due to ‘dipole effect’ in molecular structure, small residual charges on surfaces. • Examples: • sulfur, S8 • chlorine, Cl2 • Between layers of graphite • Organic compounds Johannes Diederik van der Waals 1837-1923 1910 Nobel prize in Physics

  43. Bonding Forces • Van der Waals bond: Covalent bond GRAPHITE C Van der Waals bond

  44. Bonding Forces • Hydrogen bond - electrostatic bond (polar bond) between a positively charged hydrogen ion & a negatively charged ion eg O2- and N3- • Hydrogen - only one electron in structure • when it transfers the electron to a stronger attractor the remaining proton becomes unshielded and can make weak hydrogen bonds with other large negative ions or negative ends of polar molecules eg Ice (water) & hydroxides (OH- group)

  45. Bonding Forces Eg. water • Hydrogen bond - electrostatic or polar bond

  46. Bonding Forces • Crystals with more than one bond type: • Bond types are end members • Example: Bonds can be partly ionic & partly covalent • More than 1 bond type can exist in one crystal • Eg: graphite - strong covalent bond within sheets & weak van der Waals bonding between sheets.

  47. Atomic and ionic radii • Size of atoms or ions difficult to define but even more difficult to measure … • Definition: Radius of atom is the maximum radial charge density of the outermost shells • Effective radius depends on neighboring atoms or ions and on ‘charge’ of the ion

  48. Atomic and ionic radii 2r pm Atomic radius pm pm NOTE: 100 pm = 10 nm = 1 Angstrom

  49. Atomic radii Distances in picometers, pm

  50. Atomic and ionic radii • When oppositely charged ions unite to form a crystal structure each ion tends to ‘surround’ itself or to coordinate as many ions of the opposite sign as size permits • Assume: • Ions are approximately ‘spherical’ • Coordinated ions cluster about a central coordinating ion so that their centers lie on the apices of a polyhedron

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