Transcript 1. Legaturi in cristale 2. Izomorfis, polimorfism
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 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 3
•
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 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 5
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
1 st Ionization Potential Elements with a single outer
s
orbital electron Anions Cations Electronegativity
+1 +2
Valence States of Ions common to Rock-forming Minerals
-----------------Transition Metals-------------- +3 +4 +5 +6 +7 -2 -1 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
Reprezentari structurale
Reprezentare de descrie tipul de impahetare a atomilor
Exemple: Cristobalit (SiO 2 )
Reprezentare prin poliedre de coordinare Descrierea configuratiei golurilor
Bragg jun. (1920)
Sphere packing
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 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 HCP (Be, Mg, Zn, Cd, Ti, Zr, Ru ...) close packed layer: (001) 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 Space filling = Volume occupied by atoms (spheres) Volume of the unit cell
4
r
2
a V
(
cell
)
a
3 4
r
2 3
ZV
(
sphere
)
spacef
.
4 4 3 4
r
4 2 4 3
r
3
r
3 3 2 0 .
74 6
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 (
-Po) space filling = 52% CN = 6 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
2.1 Basics of Structures Approximation: atoms can be treated like spheres Concepts for the radius of the spheres element or compounds compounds only elements or compounds („alloys“) = 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)
2.1 Basics of Structures Determination of the ionic radius Ionic radius = d – r(F, O…) Structure analyses, most important method: X-ray diffraction L. Pauling:
•
Radius of one ion is fixed to a reasonable value (r(O 2 ) = 140 pm)
•
That value is used to compile a set of self consistent values for other ions.
Impachetari
Impachetare hexagonala compacta 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
Arhetipuri structurale
Coordinari. Poliedrii de coordinare strat A strat B A A A A A A A A B C B A C A A C B A A A A A strat C Impachetare hexagonala compacta A B A B ...
Impachetare cubica compacta A B C A B C ...
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 NaCl NiAs CaF 2 CdCl 2 CdI 2 Sphalerite (ZnS) Wurzite (ZnS) Li 3 Bi ReB 2 AgCl, BaS, CaO, CeSe, GdN, NaF,
Na 3 BiO 4 , V 7 C 8
TiS, CoS, CoSb, AuSn CCP CdF 2 , CeO 2 ,
Li 2 O
, Rb 2 O, SrCl 2 , ThO 2 , ZrO 2 , AuIn 2 MgCl 2 , MnCl 2 , FeCl 2 , Cs 2 O, CoCl 2 MgBr 2 , PbI 2 , SnS 2 , Mg(OH) 2 , Cd(OH) 2 , Ag 2 F AgI, BeTe, CdS, CuI, GaAs, GaP, HgS, InAs, ZnTe AlN, BeO, ZnO, CdS (HT) HCP CCP CCP HCP CCP Li 3 Au !wrong! (LATER) HCP CCP HCP Holes filled OH and TH n and 0n n and 0n 0 and 2n 0.5n and 0 0.5n and 0 0 and 0.5n
0 and 0.5n
n and 2n 0 and 2n
Arhetipuri structurale
Coordinari. Poliedrii de coordinare O tetraedru de coordinare TO 4
T = Si, Al
T O M octaedru de coordinare MO 6
M = Al, Mg, Fe 2+ , Fe 3+ , Ca, Na, K
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
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: 1s 2 2s 2 2p 6 3s 1 Devine ion pozitiv prin cedarea unui é – Ex2: Cl: Z=17: 1s 2 2s 2 2p 6 3s 2 3p 5 Devine ion negativ prin acceptarea unui é 2 atomi neutrii 2 ioni incarcati (+) si (-)care formeaza NaCl
Legaturi
Legatura ionica: Punct de topire (MP) vs. distanta inter ionica (ID) Daca DI creste → MP scade MP MP MP DI ID (Fig. 3.18) ID
H
Legaturi
Legatura ionica: Duritate (H) vs. distanta inter-ionica (DI) Fig. 3.19
H DI DI Distante inter-ionice mici → legatura puternica
Legaturi
Legatura covalenta →obtinerea configuratiei de gaz nobil prin punere in comun de é Ex.: Carbon, C Legatura covalenta a diamantului
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
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
Legaturi
Electronegativitatea (scade in grupa & creste in perioada) metale EN< nemetale EN> Acceptori Donori NOTA: gazele nobile au electronegativitate
zero→stabile
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
Bonding Forces
Van der Waals bond:
– Weak bond due to ‘dipole effect’ in molecular structure, small residual charges on surfaces.
– Examples: sulfur, S 8 chlorine, Cl 2 Between layers of graphite Organic compounds Johannes Diederik van der Waals 1837-1923 1910 Nobel prize in Physics
Bonding Forces
Van der Waals bond: Covalent bond GRAPHITE C
Bonding Forces
Hydrogen bond a positively charged hydrogen ion & a negatively charged ion eg O 2 and N 3 electrostatic bond (polar bond) between 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)
Bonding Forces
Eg. water Hydrogen bond electrostatic or polar bond
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.
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
Atomic and ionic radii
2r
Atomic radius pm NOTE: 100 pm = 10 nm = 1 Angstrom pm pm
Atomic radii
Distances in picometers, pm
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
Atomic and ionic radii
Coordination polyhedron of halite (NaCl) ions in cubic arrangement Both Na + and Cl coordination are in 6 or CN=6 (6 near neighbours) Octahedron around Cl ion
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.
Atomic and ionic radii
When the 2 ions are about the same size, so R a :R x =1 the ions will show the closest packing, so coordination number (CN)=12 6 1 9 5 7 x 8 2 3 4 And 3 more in the layer below make 12 where Ra=radius of cation & Rx=radius of anion
Atomic and ionic radii
Cubic coordination (CN=8) ~ 8 anions around a cation 1 2 1 1 2 Pythagoras 1 2 1 45 o
Atomic and ionic radii
Octahedral (CN=6) ~ 6 anions around a cation Limiting value ~ 0.414
Pythagoras 1 2 1 45 o
Atomic and ionic radii
Tetrahedral coordination CN=4 or 4 anions about a cation Limiting value Ra:Rx=0.225
Atomic and ionic radii
Triangular CN=3 3 anions around a cation Linear CN=2 This is very rare Examples are copper in cuprite, Cu 2 O Uranyl group, UO 2 2+ Nitrite group, No 2 2 Stable between 0.155 & 0.255
In nature: CO 3 , NO 3 & BO 3
Radius ratio Ra:Rx <0.155
Atomic and ionic radii
Ra:Rx = 1 Fig 3.36