legaturi in cristale klein, 1993: capitolul 4. arrangement of atoms determines unit cell geometry:...
TRANSCRIPT
Legaturi in cristale
Klein, 1993: capitolul 4
• 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
Unit Cell Geometry
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 = 4Cl 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
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
Fe – 86%Fe – 86%S – 10%S – 10%Ni – 4%Ni – 4%
Chemical Layers of the EarthChemical Layers of the Earth
SiO2 – 45%SiO2 – 45%MgO – 37%MgO – 37%FeO – 8%FeO – 8%Al2O3 – 4%Al2O3 – 4%CaO – 3% CaO – 3% others – 3%others – 3%
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 ModelNucleus
- 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 StatesCations – 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
Electronegativity
Elements with a single outer s orbital electron
Anions
Cations
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
Bragg jun. (1920)Sphere packing
Pauling (1928)Polyhedra
Wells (1954)3D nets
Exemple: Cristobalit (SiO2)
Bragg jun. (1920)Sphere packing Pauling (1928)
Polyhedra
Wells (1954)3D nets
Reprezentare de descrie tipul de impahetare a atomilor
Descrierea configuratiei golurilor
Reprezentare prin poliedre de coordinare
2.1 Basics of Structures Structure and lattice – what is the difference?
• 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
Example: structure and lattice in 2D
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
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) Unit cells of HCP and CCP
space fillin
g =
74%, C
N =
12
2.2 Simple close packed structures (metals) Calculation of space filling – example CCP
Volume of the unit cell
Volume occupied by atoms (spheres)
74.06
2
2
434
4.
3
44)(
2
4)(
24
3
3
3
3
3
r
rspacef
rsphereZV
racellV
ar
Space filling =
(Fe, Cr, Mo, W, Ta, Ba ...)
2.2 Simple close packed structures (metals) Other types of metal structures
Example 1: BCC
Example 3: structures of manganese
far beyond simple close packed structures!
space filling = 68%
CN = 8
Example 2: primitive packing
space filling = 52%
CN = 6(-Po)
2.2 Simple close packed structures (metals) Holes in close packed structures
Tetrahedral holeTH
Octahedral holeOH
2.1 Basics of Structures Approximation: atoms can be treated like spheres
element or compounds
elements or compounds
(„alloys“)
compounds only
Concepts for the radius of the spheres
= d/2 in metal
= d/2 of single bond
in molecule
= d – r(F, O…)
problem: reference!
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)
(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
Ionic radius = d – r(F, O…)
2.1 Basics of Structures Determination of the ionic radius
Structure analyses,most important method:
X-ray diffraction
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.
ImpachetariImpachetarea 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 structuraleCoordinari. Poliedrii de coordinare
Impachetarehexagonala compacta ABAB...
Impachetarecubica compacta ABCABC...
B
B BCC
C
strat A A A A A A
A A A A A
A A A A A
Astrat B
strat C
Impachetari
coordinare octaedrica(6 anioni, NC=6)
coordinare tetraedrica(4 anioni, NC=4)
Arhetipuri structuraleCoordinari. Poliedrii de coordinare
2.3 Basic structure types Overview
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
CaF2CdF2, CeO2, Li2O, Rb2O,
SrCl2, ThO2, ZrO2, AuIn2
CCP 0 and 2n
CdCl2MgCl2, MnCl2, FeCl2, Cs2O, CoCl2
CCP 0.5n and 0
CdI2MgBr2, PbI2, SnS2, Mg(OH)2, Cd(OH)2, Ag2F
HCP 0.5n and 0
Sphalerite (ZnS) AgI, BeTe, CdS, CuI, GaAs,
GaP, HgS, InAs, ZnTeCCP 0 and 0.5n
Wurzite (ZnS) AlN, BeO, ZnO, CdS (HT) HCP 0 and 0.5n
Li3Bi Li3Au CCP n and 2n
ReB2 !wrong! (LATER) HCP 0 and 2n
„Basic“: anions form CCP or HCP, cations in OH and/or TH
tetraedru de coordinare TO4
T = Si, Al
O
T
O
M octaedru de coordinare MO6
M = Al, Mg, Fe2+, Fe3+ , Ca, Na, K
Coordinari. Poliedrii de coordinareArhetipuri structurale
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: 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 ioni incarcati (+) si (-)care formeaza NaCl
2 atomi neutrii
Legaturi Legatura ionica: Punct de topire (MP) vs. distanta inter-Legatura ionica: Punct de topire (MP) vs. distanta inter-
ionica (ID)ionica (ID)
(Fig. 3.18)
Daca DI creste → MP scade
MP
DI
MP
ID
MP
ID
Legaturi
Legatura ionica: Duritate (H) vs. distanta inter-ionica (DI) Legatura ionica: Duritate (H) vs. distanta inter-ionica (DI) Fig. 3.19Fig. 3.19
HH
DI DI
Distante inter-ionice mici → legatura puternica
LegaturiLegatura covalenta
→obtinerea configuratiei de gaz nobil prin punere in comun de é
Ex.: Carbon, CLegatura covalenta a diamantului
Legaturi
Linus Pauling 1901-1994– Premiul Nobel pt. chimie 1954– Premiul Nobel pentru pace
1962 (testele atomice)
1939: Metoda de estimare a caracterului ionic (%) Electronegativitatea
“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.”
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 ElectronegativitateaElectronegativitatea (scade in grupa & creste in perioada)
Acceptori
Donori
nemetale
EN>
metale- EN<
NOTA: gazele nobile au electronegativitate zero→stabile
Bonding ForcesMetallic 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 > Metals: Electrons v. mobile
Red circles = nuclei
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 graphiteOrganic compounds
Johannes Diederik van der Waals1837-1923
1910 Nobel prize in Physics
Bonding Forces
Van der Waals bond:Covalent bond
Van d
er
Waals
bon
d
GRAPHITEC
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 structurewhen 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
Hydrogen bond - electrostatic or polar bond
Eg. water
Bonding Forces
Crystals with more than one bond type:
– Bond types are end membersExample: Bonds can be partly ionic & partly covalent
– More than 1 bond type can exist in one crystalEg: 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 radiuspmpm
pm
NOTE: 100 pm = 10 nm = 1 Angstrom
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- are in 6-coordination 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 Ra:Rx=1 the ions will show the closest packing, so coordination number (CN)=12
1 2
3
45
67
x89
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)
11
2
1
1
2
45o
Pythagoras
2
1 + x
~ 8 anions around a cation
Atomic and ionic radii
Octahedral (CN=6)Octahedral (CN=6)
1
1
2
45o
Pythagoras
~ 6 anions around a cation
Limiting value ~ 0.414
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
Linear CN=2This is very rareExamples are copper in cuprite, Cu2OUranyl group, UO2
2+
Nitrite group, No2 2-
3 anions around a cation
Stable between 0.155 & 0.255
In nature: CO3, NO3 & BO3
Atomic and ionic radii
Fig 3.36
Ra:Rx = 1
Ra:Rx <0.155Radius ratio
Next Lecture
• Crystal Chemistry IIBondingAtomic and Ionic Radii
• Read p. 56-69