Legaturi in cristale Klein, 1993: capitolul 4 GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Legaturi in cristale Klein, 1993: capitolul 4 3 Bonding forces

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

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

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

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

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

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

Composition of the Earth’s Crust

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

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

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

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

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

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---------------

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

Structure and lattice – what is the difference? 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

2.1 Basics of Structures Unit cell Conventions: 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

2.2 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

2.2 Simple close packed structures (metals) Unit cells of HCP and CCP (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)

Volume occupied by atoms (spheres) 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

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!

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

elements or compounds („alloys“) 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

2.1 Basics of Structures Trends of the radii atomic radii increase on going down a group. atomic radii decrease across a period particularities: Ga < Al (d-block) 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 number)

most important method: 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.

Impachetari Impachetarea cea mai compacta a unor atomi identici (monezi, bile de biliard…) se face sub forma hexagonala in care fiecare atom este inconjurat de 6 atomi vecini Impachetare hexagonala compacta

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

Impachetari

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

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 CaF2 CdF2, CeO2, Li2O, Rb2O, SrCl2, ThO2, ZrO2, AuIn2 0 and 2n CdCl2 MgCl2, MnCl2, FeCl2, Cs2O, CoCl2 0.5n and 0 CdI2 MgBr2, PbI2, SnS2, Mg(OH)2, Cd(OH)2, Ag2F Sphalerite (ZnS) AgI, BeTe, CdS, CuI, GaAs, GaP, HgS, InAs, ZnTe 0 and 0.5n Wurzite (ZnS) AlN, BeO, ZnO, CdS (HT) Li3Bi Li3Au n and 2n ReB2 !wrong! (LATER)

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

Legaturi (bonding forces) GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens 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. Principalele tipuri de legaturi: Ionica Covalenta Metalica Van der Waals Hidrogen 3 Bonding forces

Tipuri de legaturi in minerale GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Tipuri de legaturi in minerale 1/ Legatura ionica Cedare sau acceptare de é pentru a obtine configuratie stabila (gaz nobil) → completarea stratul de valenta Ex: Na: Z=11: 1s2 2s2 2p6 3s1 Devine ion pozitiv prin cedarea unui é Ex2: Cl: Z=17: 1s2 2s2 2p6 3s2 3p5 Devine ion negativ prin acceptarea unui é 2 atomi neutrii 2 ioni incarcati (+) si (-)care formeaza NaCl 3 Bonding forces

Legaturi Legatura ionica in Na+Cl- GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Legaturi Legatura ionica in Na+Cl- 3 Bonding forces

GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Legaturi Legatura ionica: Punct de topire (MP) vs. distanta inter-ionica (ID) Daca DI creste → MP scade MP MP DI ID (Fig. 3.18) MP ID 3 Bonding forces

GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Legaturi Legatura ionica: Duritate (H) vs. distanta inter-ionica (DI) Fig. 3.19 H H DI DI Distante inter-ionice mici → legatura puternica 3 Bonding forces

Legaturi Legatura covalenta GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Legaturi Legatura covalenta →obtinerea configuratiei de gaz nobil prin punere in comun de é Ex.: Carbon, C Legatura covalenta a diamantului 3 Bonding forces

Legaturi Linus Pauling 1901-1994 Premiul Nobel pt. chimie 1954 GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens 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 3 Bonding forces

GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Legaturi Electronegativitatea reprezintă 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 3 Bonding forces

Legaturi Electronegativitatea (scade in grupa & creste in perioada) GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Legaturi Electronegativitatea (scade in grupa & creste in perioada) metale- EN< nemetale EN> Acceptori Donori NOTA: gazele nobile au electronegativitate zero→stabile 3 Bonding forces

Bonding Forces Metallic bond Properties: GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens 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 3 Bonding forces

Johannes Diederik van der Waals GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens 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 3 Bonding forces

Bonding Forces Van der Waals bond: GRAPHITE C Covalent bond GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Bonding Forces Van der Waals bond: Covalent bond GRAPHITE C Van der Waals bond 3 Bonding forces

GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens 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) 3 Bonding forces

Bonding Forces Hydrogen bond - electrostatic or polar bond Eg. water GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Bonding Forces Eg. water Hydrogen bond - electrostatic or polar bond 3 Bonding forces

Bonding Forces Crystals with more than one bond type: GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens 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. 3 Bonding forces

GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens 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 3 Bonding forces

Atomic and ionic radii 2r Atomic radius GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Atomic and ionic radii 2r pm Atomic radius pm pm NOTE: 100 pm = 10 nm = 1 Angstrom 3 Bonding forces

Atomic radii Distances in picometers, pm GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Atomic radii Distances in picometers, pm 3 Bonding forces

Atomic and ionic radii Assume: GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens 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 3 Bonding forces

GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Atomic and ionic radii Coordination polyhedron of halite (NaCl) ions in cubic arrangement Both Na+ and Cl- are in 6-coordination or CN=6 (6 near -neighbours) Octahedron around Cl- ion 3 Bonding forces

Atomic and ionic radii Radius ratio GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Atomic and ionic radii Radius ratio The strongest forces exist between the nearest neighbors: The first coordination shell The geometrical arrangement of this shell or coordination number is a function of relative ionic size. Remember: Ions and atoms are not rigid spheres so they do not have established constant radii. 3 Bonding forces

GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Atomic and ionic radii When the 2 ions are about the same size, so Ra:Rx=1 the ions will show the closest packing, so coordination number (CN)=12 1 2 7 6 3 x 9 8 5 4 And 3 more in the layer below make 12 where Ra=radius of cation & Rx=radius of anion 3 Bonding forces

Atomic and ionic radii Cubic coordination (CN=8) GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Atomic and ionic radii Cubic coordination (CN=8) ~ 8 anions around a cation 1 1 2 1 + x 1 2 Pythagoras 2 1 45o 1 3 Bonding forces

Atomic and ionic radii Octahedral (CN=6) ~ 6 anions around a cation GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Atomic and ionic radii Octahedral (CN=6) ~ 6 anions around a cation Limiting value ~ 0.414 Pythagoras 2 1 45o 1 3 Bonding forces

Atomic and ionic radii Tetrahedral coordination GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Atomic and ionic radii Tetrahedral coordination CN=4 or 4 anions about a cation Limiting value Ra:Rx=0.225 3 Bonding forces

Atomic and ionic radii Triangular CN=3 3 anions around a cation GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Atomic and ionic radii Triangular CN=3 3 anions around a cation Linear CN=2 This is very rare Examples are copper in cuprite, Cu2O Uranyl group, UO2 2+ Nitrite group, No2 2- Stable between 0.155 & 0.255 In nature: CO3, NO3 & BO3 3 Bonding forces

Atomic and ionic radii Radius ratio Ra:Rx <0.155 Ra:Rx = 1 Fig 3.36 GEOL 3056 Crystal chemistry and the geochemistry of mineral systems JHSchellekens Atomic and ionic radii Radius ratio Ra:Rx <0.155 Ra:Rx = 1 Fig 3.36 3 Bonding forces

Next Lecture Crystal Chemistry II Bonding Atomic and Ionic Radii Read p. 56-69