Atomic Bonding

• PRIMARY• Covalent

– sharing electrons– strong– directional

• Ionic– trading of elecrons– electrostatic attraction or

ions– strong– non-directional

• Metallic– metal ions in sea or

electrons– moderately strong– non-directional

• SECONDARY– Van der Waals– H-bonding– electrostatic attraction of

electric dipole (local charge distribution

– weak

KEADAAN KRISTALCrystalline State

1. Sifat anisotrofik : - Cleavage

(anisotropic ) - Pleochroism

- Scratch

- Thermal conductivity

2. Sifat isotropik : gas,liquid,amorf

(isotropic)

Definition of Crystal

• A crystal is an anisotropic, homogeneous body, consisting of a three-dimensional periodic ordering of atoms, ions or molecules

Unit cells & description of crystal structures.

• A crystal can be regarded as consisting of regularly repeating structural elements.

• The “crystal lattice” is the pattern formed by the points.

• A unit cell is a subdivision of a crystal that, when stacked together without rotation or reflection, reproduces the crystal.

• The lattice is a three-dimensional, infinite array of points, the lattice points, each of which is surrounded in an identical way by neighbouring points, and which defines the basic repeating structure of the crystal.

Lattice and Unit cells

The line of dots is called the lattice and each lattice point (dot) must have identical surroundings.

• A unit cell is an imaginary parallelepiped from which the entire crystal can be built by simple displacement operations only.

• Unit cell fit perfectly without any empty space.

• Unit cell parameters– a, b and c are the unit cell edge

lengths , and are the angles (a

between b and c, etc....)

• Unit cells may be chosen in a variety of ways.

• A primitive unit cell has only one lattice point per unit cell.

(b) Generally preferred to (a) because its smaller

• The relationship between the lattice parameters in 3D gives rise to the seven crystal systems.

Bravais Lattice

Crystal System Centering

a

b

c

P: Primitive: (x,y,z)

I: Body-centered: (x,y,z); (x+½,y+½,z+½)

C: Base-centered: (x,y,z); (x+½,y+½,z)

F: Face-centered: (x,y,z); (x+½,y+½,z) (x+½,y,z+½); (x,y+½,z+½)

(x,y,z): Fractional coordinates - proportion of axis length, not absolute distanct

Centering must apply to all atoms in unit cell.

Bravais Lattices (14)

Crystal System

Parameters Primitive (Simple)

Body-Centered

Face-Centered

Base-Centered

Cubic abc

X X X

Tetragonal abc

X X

Orthorhombic abc

X X X X

Rhombohedral abc

X

Hexagonal abc

X

Monoclinic abc

X X

Triclinic abc

X

4

• Rare due to poor packing (only Po has this structure)• Close-packed directions are cube edges.

• Coordination # = 6 (# nearest neighbors)

SIMPLE CUBIC STRUCTURE (SC)

back

Body-Centered Cubic (BCC)

Face-Centered Cubic (FCC)

Atoms Per Unit Cell(General Rule)

• Corners - shared by eight unit cells (x 1/8)– (0,0,0)=(1,0,0)=(0,1,0)=(0,0,1)=

(1,1,0)=(1,0,1)=(0,1,1)=(1,1,1)• Edges - shared by four unit cells

(x 1/4)– (0,0,½)= (1,0,½)= (0,1,½)=

(1,1,½)• Faces - shared by two unit cells (x

1/2)– (½,½,0)= (½,½,1)

Packing Factor

• Fraction of space occupied by atoms• For FCC

• For BCC

cba

rFP i

3

34

..

a

ar

raraa2

44diagonalface 22

740

23

24

443

334

3

334

.r

a

r.F.P

raraaa3

44diagonalbody 322

680

83

34

223

334

3

334

.r

a

r.F.P

Calculating the unoccupied space in a close-packed array

The dimensions involved in the calculation of the packing fraction in a close-packed arrangement of identical spheres of radius r

Density

volume

massNaxVZxMr

cuvolume

moleatom

molemass

cuatom

Density

/

..

..

338249158

1052393106020

71584

cm

g.

cmx.moleatom

x.

moleg

..c.u

atom

Density

For nickel:- Atomic weight = 58.71 g/mole- Lattice parameter = 3.5239 Å=3.5239 x 10-8 cm- Avogrado’s No. = 6.02 x 1023 = 0.602 x 1024 = atoms/mole

Miller Indices

Planes

Directions

(hkl)

{hkl}

[hkl]

<hkl>

specific

family

specific

family

A family of planes includes all planes which are equivalent by symmetry - depends on crystal system. - For cubic: (110),(011) and (101) are all {110} - For tetragonal: (011) and (101) are {101}

but (110) is not (ca)

- No commas- No fractions- Negative indicated by bar overnumber

Miller Index

• Defining particular plane of the atom with Miller Index

• 3 steps to determine the Miller Index

– Find the intercepts x = 2, y = 3, and z = 2 from figure

– Take the reciprocal of the axis length, 1/2, 1/3, and 1/2

– Find the lowest common multiplier and then multiply the reciprocal

– Then, the Miler Index is (3, 2, 3)…… 6*1/2, 6*1/3, 6*1/2.. Note ( )

• Example,

z

x

y

b=3

a=2

c=2

Miller Indices - Directions

ba

c

1

1/4

1/2

-1/3

1/2-1

x1

y1/4

z1/2 (x 4)

214

x1/2

y-1

z-1/3 (x 6)

263

Miller Indices - Planes4

1

21

ba

c

41

21

ba

c

x1/44

y0

z-1/2-2

204

interceptreciprocal

Miller Indices - Planes

31

21

ba

c

41

31

21

ba

c

41

x1/44

y-1/3-3

z-1/2-2

234

interceptreciprocal

Crystal ChemistryCrystals can be classified into 4 types:

1. Molecular CrystalsNeutral molecules held together by weak van der Waals

bonds

Rare as minerals

Mostly organic

Weak and readliy

decompose, melt, etc

Example: graphite

Crystal Chemistry2. Covalent Crystals

Atoms of similar high e-neg and toward right side of PT

Also uncommon as minerals (but less so than molecular)

Network of strong covalent

bonds with no weak links

Directional bonds low

symmetry and density

Example: diamond

Crystal Chemistry

The diamond structureAll carbon atoms in IV coordination

ball-and-stick modelball-and-stick model polyhedral modelpolyhedral model blue C onlyblue C only

hard-sphere modelhard-sphere model

FCC unit cellFCC unit cell

Crystal Chemistry3. Metallic Crystals

Atoms of similar e-neg and toward left side of PT

Metallic bonds are directionless bonds high

symmetry and density

Pure metals have same sized atoms

Closest packing 12 nearest mutually-touching neighbors

Cubic Closest Packing (CCP) abcabcabc stacking = FCC cell

Hexagonal Closest Packing (HCP) ababab = hexagonal cell

Also BCC in metals, but this is not CP (VII coordination)

More on coordination and closest packing a bit later

Crystal Chemistry4. Ionic Crystals

Most minerals

First approximation: • Closest-packed array of oxygen atoms • Cations fit into interstices between oxygens

– Different types of interstitial sites available– Occupy only certain types where can fit– Occupy only enough of them to attain electric

neutrality

3

• tend to be densely packed.

• have several reasons for dense packing:- Typically, only one element is present, so all atomic radii are the same.

- Metallic bonding is not directional.

• have the simplest crystal structures.

Metallic CrystalsMetallic Crystals

Common Metal Structures

• Simple Cubic (SC)• Face-Centered Cubic (FCC)• Body-Centered Cubic (BCC)• Hexagonal Close-Packed (HCP)

Metallic Crystal StructuresMetallic Crystal Structures

• The atoms in most simple metals are arranged in one of the configurations below

• Simple Cubic (sc) – Po-type :Po (sangat jarang)• Body-Centered Cubic (bcc) – W-type:Ba, Cs, Cr• Face-Centered Cubic (fcc)/ccp – Cu-type, Ag, • Hexagonal Close-Packed (hcp) – Mg-type:Zn, Co

• Nearest-neighbors atoms “touch” in all of these cases.

• Body centered cubic- atom centered in the cube– Atomic packing factor (APF) is 0.68 and represents the fraction of the unit cell occupied by the two atoms.– Ba, Ce, Li, K, molybdenum (less ductile metals)

• Face centered cubic- atom centered on each of the faces– Atomic packing factor (APF) is 0.74 and represents the fraction of the unit cell occupied by the two atoms.– Regular stackings of close-packed planes

• Fourth close pack layer lies precisely above the first one– Al, Cu, Au, Pb, Ni, Platinum, Ag (soft metals)

• Hexagonal close packed (HCP)– Two atoms are associated with each Bravais lattice point

• One atom centered within the unit cell and various fractional atoms at unit cells (four 1/6th atoms and four 1/12th atoms)– Close pack is efficient packing shperes as is the fcc structure.– Atomic packing factor (APF) is 0.74 and represents the fraction of the unit cell occupied by the two atoms.– Regular stackings of close-packed planes

• The third close-packed layer lies precisely above the first.– Be, Mg, Ti, Zn, Zr

• Hexagonal Close-packed structure (continued)– the distance between atoms in the bases are equal in the hexagonal structure. The bases are perpendicular to the sides. The angle between the sides is 120°.– Graphite has Close-packed hexagonal structure of Carbon– diamond has a form of face-centered closed -pack cubic structure, or complex cubic structure (diamond structure)– other materials with closed-packed hexagonal structure include Be, Cadmium, Co, Mg, Titanium, Zn, Zirconium

Hexagonal Close-Packed (HCP)

10

• Coordination # = 12

• ABAB... Stacking Sequence

• APF = 0.74

• 3D Projection

• 2D Projection

A sites

B sites

A sites

Bottom layer

Middle layer

Top layer

Adapted from Fig. 3.3, Callister 6e.

Hexagonal Close-Packed Structure (hcp) Note: this structure is NOT cubic

back

Cubic close-packed structure (c.c.p.) / Cubic close-packed structure (c.c.p.) / Face-centred cubic (f.c.p.)Face-centred cubic (f.c.p.)

• Also known as abcabc…type

• Each atom is surrounded by / in contact with 12 other atoms – its coordination number is also 12

12

Element Aluminum Argon Barium Beryllium Boron Bromine Cadmium Calcium Carbon Cesium Chlorine Chromium Cobalt Copper Flourine Gallium Germanium Gold Helium Hydrogen

Symbol Al Ar Ba Be B Br Cd Ca C Cs Cl Cr Co Cu F Ga Ge Au He H

Atomic radius (nm) 0.143 ------ 0.217 0.114 ------ ------ 0.149 0.197 0.071 0.265 ------ 0.125 0.125 0.128 ------ 0.122 0.122 0.144 ------ ------

Crystal Structure FCC ------ BCC HCP Rhomb ------ HCP FCC Hex BCC ------ BCC HCP FCC ------ Ortho. Dia. cubic FCC ------ ------

Adapted fromTable, "Charac-teristics ofSelectedElements",inside frontcover,Callister 6e.

Characteristics of Selected Elements at 20C

IONIC CRYSTAL STRUCTURES

• Ions form a crystal such that they are “closest packed”.

• This is a consequence of Coulomb’s law.• Ions arrange themselves such that

interionic distances are minimized.• If we assume ions are hard,

incompressible spheres (like billiard balls), we can use the concept of radius ratio as a key to explaining crystal structures.

Consider coordination of anions about a central cation

Coordination Polyhedra

HaliteHalite

ClCl

ClCl

ClCl

ClCl

NaNa

[6][6]NaClNaCl

Packing and GeometryPacking and Geometry

• close packing

• ABC.ABC... cubic close-packed CCP

gives face centered cubic or FCC(74.05% packed)

AB.AB... or AC.AC... (these are equivalent). This is called hexagonal close-packing HCP

Close Packed (CN=12)Highest packing density for same sized spheresFCC and HCP structures

Cube Center (CN=8)Same atoms: BCCDifferent atoms: CsCl

Octahedral Site (CN=6)In FCC:- Center (½,½,½)- Edges (0,0,½),(0,½,0),(½,0,0)- 4 per unit cell- All filled - NaCl structure

8-sided shape

Tetrahedral Site (CN=4)In FCC:- Divide cell into 8 boxes - center of small box- (¼,¼,¼),(¾,¼,¼),(¼,¾,¼),(¾,¾,¼)(¼,¼, ¾)(¾,¼, ¾),(¼,¾, ¾)(¾,¾, ¾)-8 per unit cell-All filled - CaF2 structure; half-filled - ZnS

4-sided shape

Radius Ratio Rules

Critical Radius for CN 8 = 0.732

Critical Radius for CN 6 = 0.414

Critical Radius for CN 4 = 0.225

CN 8

CN 6

CN 4

CN 3planar

Critical radius is size of atom which just fits in siteDefine minimum for bonding (i.e. atoms must touch to bond)

Close Packed PlaneA BA BA C

HCP: ABABABABABABABABFCC: ABCABCABCABCABCSame packing density (0.74)Same coordination (CN=12)