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 filling = 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)

74.062

24344

.

344)(

24)(

24

3

3

3

33

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 manganesefar 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

CdCl2 MgCl2, 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, 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! (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 scadeMP

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

LegaturiLinus 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 ForcesVan 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 ForcesVan der Waals bond:

Covalent bond

Van

der W

aals

bond

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

67x

89

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