1

Materials Scienceand

Engineering I

Chapter OutlineReview of Atomic Structure

Electrons, Protons, Neutrons, Quantum number

of atoms, Electron states, The Periodic Table

Atomic Bonding in Solids

Bonding Energies and Forces

Periodic Table

Primary Interatomic Bonds

Ionic, Covalent, Metallic

Secondary Bonding (Van der Waals)

Three types of Dipole Bonds

Molecules and Molecular Solids

Understanding of interatomic bonding is the first step

Towards understanding/explaining materials properties

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2

Structure of Atoms

3

ATOM

Basic Unit of an Element

Diameter : 10 –10 m.

Neutrally Charged

Nucleus

Diameter : 10 –14 m

Accounts for almost all mass

Positive Charge

Electron Cloud

Mass : 9.109 x 10 –28 g

Charge : -1.602 x 10 –9 C

Accounts for all volume

Proton

Mass : 1.673 x 10 –24 g

Charge : 1.602 x 10 –19 C

Neutron

Mass : 1.675 x 10 –24 g

Neutral Charge

Review of Atomic Structure

4

Atoms = nucleus (protons and neutrons) + electrons

Charges:

Electrons and protons have negative and positive charges of the same magnitude, 1.6 ×10-19 Coulombs. Neutrons are electrically neutral.

Masses:

Protons and Neutrons have the same mass, 1.67 × 10-27 kg. Mass of an electron is much smaller, 9.11 × 10-28 kg and can be neglected in calculation of atomic mass.

The atomic mass (A) = mass of protons + mass of neutrons

# protons gives chemical identification of the element

# protons = atomic number (Z)

# neutrons defines isotope number

3

Atomic Number and Atomic Mass

AtomicNumber =NumberofProtonsinthenucleusUniquetoanelement

Example:‐ Hydrogen=1,Uranium=92

Relativeatomicmass =Massingramsof6.02x1023

(AvagadroNumber)Atoms. Example:‐ Carbonhas6Protonsand6Neutrons.AtomicMass=12.

OneAtomicMassunitis1/12th ofmassofcarbonatom.Onegrammole=Gramatomicmassofanelement.

Example:‐

One gram

Mole of

Carbon

12 Grams

Of Carbon

6.023 x 1023

Carbon

Atoms

2-3

6

A 100 gram alloy of nickel and copper consists of 75 wt% Cu and 25 wt% Ni. What are percentage of Cu and Ni Atoms in this alloy?Given:- 75g Cu Atomic Weight 63.54

25g Ni Atomic Weight 58.69

Number of gram moles of Cu =

Number of gram moles of Ni =

Atomic Percentage of Cu =

Atomic Percentage of Ni =

mol.g/mol.

g18031

5463

75

mol.g/mol.

g42600

6958

25

%5.73100)4260.01803.1(

1803.1

%5.25100)4260.01803.1(

4260.0

Example Problem

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7

8

MaxPlanck,discoveredthatatomsandmoleculesemitenergyonlyincertaindiscretequantities,calledquanta.

JamesClerkMaxwellproposedthatthenatureofvisiblelightisintheformofelectromagneticradiation.

E=hυ =hc/λ Energyisalwaysreleasedinintegermultiplesofhυ

8

Planck’s Quantum Theory

5

Electron Structure of Atoms

Electron rotates at definite energy levels.

Energy is absorbed to move to higher energy level.

Energy is emitted during transition to lower level.

Energy change due to transition = ΔE =

h=Planks Constant

= 6.63 x 10-34 J.s

c= Speed of light

λ = Wavelength of light

hc

Emit

Energy

(Photon)

Absorb

Energy

(Photon)

Energy levels

9

Energy in Hydrogen Atom

Hydrogen atom has one proton and one electron

Energy of hydrogen atoms for different energy levels is given by (n=1,2…..) principal quantum numbers

Example:- If an electron undergoes transition from n=3 state to n=2 state, the energy of photon emitted is

Energy required to completely remove an electron from hydrogen atom is known as ionization energy

evEn

2

6.13

evE 89.16.136.13

2322

2-7 10

6

Energy-Level diagram for the line spectrum of hydrogen

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12

7

Quantum Numbers of Electrons of Atoms

Principal Quantum Number (n)

Represents main energy levels.

Range 1 to 7.

Larger the ‘n’ higher the energy.

Subsidiary Quantum Number (l)

Represents sub energy levels (orbital).

Range 0…n-1.

Represented by letters s,p,d and f.

n=1n=2

s orbital (l=0)

p Orbital

(l=1)

n=1

n=2

n=3

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Quantum Numbers of Electrons of Atoms (Cont..)

Magnetic Quantum Number ml.

Represents spatial orientation of single atomic orbital.Permissible values are –l to +l.Example:- if l=1,

ml = -1,0,+1.

I.e. 2l+1 allowed values.No effect on energy.

Electron spin quantum number ms.

Specifies two directions of electron spin.

Directions are clockwise or anticlockwise.

Values are +1/2 or –1/2.

Two electrons on same orbital have opposite spins.

No effect on energy.

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8

15

S, p and d Orbitals

16

Solutionofthewaveequationisintermsofawavefunction,ψ (orbitals).

Thesquareofthewavefunctionrepresentselectrondensity.

Boundarysurfacerepresentation.

Totalprobability

0.05 nm

0.1 nm

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Electron Density

9

Electron Structure of Multielectron Atom

Maximumnumberofelectronsineach atomicshellisgivenby2n2.Atomicsize(radius)increaseswithadditionofshells.ElectronConfiguration liststhearrangementofelectronsinorbitals.

Example:‐

1s22s22p63s2

ForIron,(Z=26),Electronicconfigurationis1s2 2s2 2p6 3s2 3p6 3d6 4s2

Principal Quantum Numbers

Orbital letters Number of Electrons

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18

Electronic Configurations

ex:ZFe =26

valence

electrons

1s

2s2p

K-shell n = 1

L-shell n = 2

3s3p M-shell n = 3

3d

4s

4p4d

Energy

N-shell n = 4

1s2 2s2 2p6 3s2 3p6 4s2 3d 6

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19

Elementsareclassifiedaccordingtotheirgroundstateelectronconfiguration.

Orbital Box Diagram

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11

21

Periodic Table

Source: Davis, M. and Davis, R., Fundamentals of Chemical Reaction Engineering, McGraw-Hill, 2003.

22

Periodic Variations in Atomic Size Atomicsize:halfthedistancebetweenthenucleioftwoadjacentatoms(metallicradius)ORidentical(covalentradius).

Affectedbyprincipalquantumnumberandsizeofthenucleus.

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Atomic Structure

Valence electrons determine all of the following properties

1) Chemical

2) Electrical

3) Thermal

4) Optical

Electron Structure and Chemical Activity

ExceptHelium,mostnoblegasses (Ne,Ar,Kr,Xe,Rn)arechemicallyverystable

Allhaves2 p6 configurationforoutermostshell.

Heliumhas1s2 configuration

Electropositive elementsgiveelectronsduringchemicalreactionstoformcations.

Cationsareindicatedbypositiveoxidationnumbers Example:‐

Fe:1s2 2s2 sp6 3s2 3p6 3d6 4s2

Fe2+ :1s2 2s2 sp6 3s2 3p6 3d6

Fe3+ :1s2 2s2 sp6 3s2 3p6 3d5

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13

25

Trends in Ionization Energy

Energyrequiredtoremoveanelectronfromitsatom. Firstionizationenergy playsthekeyroleinthechemicalreactivity.

Astheatomicsizedecreasesittakesmoreenergytoremoveanelectron.

asthefirstoutercoreelectronisremoved,ittakesmoreenergytoremoveasecondoutercoreelectron

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Electronegative elementsacceptelectronsduringchemicalreaction.Someelementsbehaveasbothelectronegativeandelectropositive.Electronegativity isthedegreetowhichtheatomattractselectronstoitself

Measuredonascaleof0to4.1 Example:‐ Electronegativity ofFluorineis4.1

Electronegativity ofSodiumis1.

0 1 2 3 4K

Na N O Fl

W

Te

SeH

Electro-

positive

Electro-

negative

Electron Structure and Chemical Activity (Cont..)

14

27 27

• Ranges from = 0.7 to 4.0, dimensionless!

• Large values: tendency to acquire electrons.

Electronegativity

Larger electronegativity

TM: Uniformly low EN

2828

Adapted from Fig. 2.6, Callister 7e.

Electropositive elements:

Readily give up electrons

to become + ions.

Electronegative elements:

Readily acquire electrons

to become - ions.

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

ClS

Li Be

H

Na Mg

BaCs

RaFr

CaK Sc

SrRb Y

The Periodic Table

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29

Trends in Electron Affinity

Electronaffinity:Tendencytoacceptoneormoreelectronsandreleaseenergy.

Electronaffinityincreases(moreenergyisreleasedafteracceptinganelectron)aswemovetotherightacrossaperiodanddecreasesaswemovedowninagroup.

Groups6Aand7Ahaveingeneralthehighestelectronaffinities.

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Types of BondingPrimary bonding: e- are transferred or shared

Strong (100-1000 KJ/mol or 1-10 eV/atom)

Three primary bonding combinations : 1) metal-nonmetal, 2) nonmetal-nonmetal, and 3) metal-metal

Ionic: Strong Coulomb interaction among negative atoms (have an extra

electron each) and positive atoms (lost an electron). Example - Na+Cl-

Covalent: electrons are shared between the molecules, to saturate the

valency. Example -H2

Metallic: the atoms are ionized, loosing some electrons from the valence

band. Those electrons form a electron sea, which binds the charged nuclei

in placeSecondary Bonding: no e- transferred or shared Interaction of atomic/molecular dipoles

Weak (< 100 KJ/mol or < 1 eV/atom)

Fluctuating Induced Dipole (inert gases, H2, Cl2…)

Permanent dipole bonds (polar molecules - H2O, HCl...)

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31

Ionic Bonding (I)

Formation of ionic bond:

1.Mutual ionization occurs by electron transfer (remember

electronegativity table)

Ion = charged atom

Anion = negatively charged atom

Cation = positively charged atom

2. Ions are attracted by strong coulombic interaction

Oppositely charged atoms attract

An ionic bond is non-directional (ions may be attracted to one another in any direction

Electropositive

Element

Electronegative

AtomElectron

Transfer

Cation

+ve charge

Anion

-ve charge

IONIC BOND

Electrostatic

Attraction

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Ionic Bonding - Example

32

Ionic bond – metal + nonmetal

donatesacceptselectronselectrons

ex:MgO Mg 1s2 2s2 2p6 3s2 O 1s2 2s2 2p4

[Ne]3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

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33

Ionic Bonding - Example

3s1

3p6

Sodium

Atom

Na

Chlorine

Atom

Cl

Sodium Ion

Na+

Chlorine Ion

Cl -

I

O

N

I

C

B

O

N

D

34

Ionic Force for Ion Pair

Nucleus of one ion attracts electron of another ion.

The electron clouds of ion repulse each other when they are sufficiently close.

Force versus separation

Distance for a pair of

oppositely charged ions

Figure 2.11

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35

Ion Force for Ion Pair (Cont..)

Z1,Z2 =Numberofelectronsremovedoraddedduringionformation

e=ElectronChargea=Interionic seperation distance

ε=Permeabilityoffreespace (8.85x10‐12c2/Nm2)

(nandbareconstants)

a

eZZaZZF

eeattractive 2

0

2

212

0

21

44

aF

nrepulsive

nb

1

aaeZZF nnet

nb12

0

2

21

4

Attraction

Force

Repulsion

Force

3636

• Predominant bonding in Ceramics

Adapted from Fig. 2.7, Callister 7e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.

Give up electrons Acquire electrons

NaCl

MgO

CaF 2

CsCl

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37

Interionic Force - Example

Force of attraction between Na+ and Cl- ions

Z1 = +1 for Na+, Z2 = -1 for Cl-

e = 1.60 x 10-19 C , ε0 = 8.85 x 10-12 C2/Nm2

a0 = Sum of Radii of Na+ and Cl- ions

= 0.095 nm + 0.181 nm = 2.76 x 10-10 m

NC

aeZZFattraction

910-212-

219

2

0

2

21 1002.3m) 10x /Nm2)(2.76C 10x 8.85(4

)1060.1)(1)(1(

4

Na+ Cl-

a0

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Interionic Energies for Ion Pairs

Netpotentialenergyforapairofoppositelychargedions=

Enet isminimumwhenionsareatequilibriumseperation distancea0

aaeZZE nnet

b

0

2

21

4

Attraction

Energy

Repulsion

Energy

Energy

Released

Energy

Absorbed

20

39

40

21

41

Ion Arrangements in Ionic Solids

IonicbondsareNonDirectionalGeometricarrangementsarepresentinsolidstomaintainelectricneutrality.

Example:‐ inNaCl,sixCl‐ ionspackaroundcentralNa+Ions

Ionic packing

In NaCl

and CsCl

CsCl NaClFigure 2.13

2-20

42

Bonding Energies

Latticeenergiesandmeltingpointsofionicallybondedsolidsarehigh.Latticeenergydecreases whensizeofionincreases.Multiplebonding electronsincreaselatticeenergy.

Example:‐NaCl Latticeenergy=766KJ/mol

Meltingpoint=801oCCsCl Latticeenergy=649KJ/mol

MeltingPoint=646oCBaO Latticeenergy=3127KJ/mol

Meltingpoint=1923oC

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Bonding Energy Consider production of LiF: result in the release of about 617 kJ/mole.

Step 1. Converting solid Li to gaseous Li (1s22s1): 161 kJ/mole of energy.

Step 2. Converting the F2 molecule to F atoms: 79.5 kJ/mole.

Step 3. Removing the 2s1 electron of Li to form a cation, Li+: 520 kJ/mole.

Step 4. Transferring or adding an electron to the F atom to form an anion, F-: -328 kJ/mole.

Step 5. Formation of an ionic solid from gaseous ions: lattice energy , unknown=-617 kJ – [161 kJ + 79.5 kJ + 520 kJ – 328 kJ] = -1050 kJ

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Hess law △H0= △H1+△H2+△H3+△H4+△H5

△H5= △H0- △H1+△H2+△H3+△H4=-1050 kj

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Covalent Bonding

In covalent bonding, outer s and p electrons are shared between two atoms to obtain noble gas configuration.

Takes place between elements

with small differences in

electronegativity and close by

in periodic table.

In Hydrogen, a bond is formed between

2 atoms by sharing their 1s1 electrons

H + H H H

1s1

Electrons

Electron

Pair

Hydrogen

Molecule

Overlapping Electron Clouds

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45

Covalent Bonding - Examples

In case of F2, O2 and N2, covalent bonding is formed by sharing p electronsFluorine gas (Outer orbital – 2s2 2p5) share one p electron to attain noble gas configuration.

Oxygen (Outer orbital - 2s2 2p4) atoms share two p electrons

Nitrogen (Outer orbital - 2s2 2p3) atoms share three p electrons

F + F F FH

F FBond Energy=160KJ/mol

O + O O O O = OBond Energy=28KJ/mol

N + N Bond Energy=54KJ/mol

N N N N

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Formation of covalent bonds:

Cooperative sharing of valence electrons

Can be described by orbital overlap

Covalent bonds are HIGHLY directional

Bonds - in the direction of the greatest orbital overlap

Covalent bond model: an atom can covalently bondwith

at most 8-N’, N’ = number of valence electrons

Covalent Bonding

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47

Carbonhaselectronicconfiguration1s2 2s2 2p2

Hybridization causesoneofthe2sorbitalspromotedto2porbital.Resultfoursp3orbitals.

Ground State arrangement

1s 2s 2p

Two ½ filed 2p orbitals

Indicates

carbon

Forms two

Covalent

bonds

1s 2pFour ½ filled sp3 orbitals

Indicates

four covalent

bonds are

formed

Covalent Bonding in Carbon

48

Structure of Diamond

Foursp3 orbitals aredirectedsymmetrically towardcornersofregulartetrahedron.Thisstructuregiveshighhardness,highbondingstrength(711KJ/mol)andhighmeltingtemperature(3550oC).

Carbon Atom Tetrahedral arrangement in diamond

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Carbon Containing Molecules

InMethane,CarbonformsfourcovalentbondswithHydrogen.(hydrocarbons)

Moleculesareveryweeklybondedtogetherresultinginlowmeltingtemperature(‐183oC).Intramolecularbonding:1650kl/mole;intermolecularbonding:8kj/mole

Carbonalsoformsbondswithitself. Moleculeswithmultiplecarbonbondsaremorereactive.–unsaturatedbond

Examples:‐

C CH

H

H

HEthylene

C CH H

Acetylene

Methane

molecule

50

Covalent Bonding in Benzene

ChemicalcompositionofBenzeneisC6H6.TheCarbonatomsarearrangedinhexagonalring.Singleanddoublebondsalternatebetweentheatoms.

CC

CC

C

CH

H

H

H

H

HStructure of Benzene Simplified Notations

Figure 2.23

26

51

Atoms in metals are closely packed in crystal structure.Loosely bounded valence electrons are attracted towards nucleus of other atoms.Electrons spread out among atoms forming electron clouds.These free electrons are reason for electric conductivity and ductility

Since outer electrons are shared by many atoms,metallic bonds areNon‐directional

Positive Ion

Valence electron charge cloudFigure 2.24

Metallic Bonding

52

Metallic Bonds (Cont..)

Overall energy of individual atoms are lowered by metallic bonds

Minimum energy between atoms exist at equilibrium distance a0

Fewer the number of valence electrons involved, more metallic the bond is.

Example:- Na Bonding energy 108KJ/mol,

Melting temperature 97.7oC

Higher the number of valence electrons involved, higher is

the bonding energy.

Example:- Ca Bonding energy 177KJ/mol,

Melting temperature 851oC

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53

Ionic‐CovalentMixedBonding

%ioniccharacter =

whereA & B arePaulingelectronegativities

(1 e

(A B )2

4 ) 100%

ionic 70.2% (100%) x e1 characterionic % 4)3.15.3(

2

Ex: MgO XMg = 1.3XO = 3.5

Mixed Bonding

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55

Secondary Bonding

Secondarybondsareduetoattractionsofelectricdipoles inatomsormolecules.Dipolesarecreatedwhenpositiveandnegativechargecentersexist.

Theretwotypesofbondspermanentandfluctuating.

-q

Dipole moment=μ =q.d

q= Electric charge

d = separation distance

+q

dFigure 2.26

Fluctuating Dipoles

Weak secondary bonds in noble gasses.

Dipoles are created due to asymmetrical distributionof electron charges.

Electron cloud charge changes with time.

Symmetrical

distribution

of electron charge

Asymmetrical

Distribution

(Changes with time)

Figure 2.27

29

Permanent Dipoles

Dipoles that do not fluctuate with time are called Permanent dipoles.

Examples:-

Symmetrical

Arrangement

Of 4 C-H bonds

CH4

No Dipole

moment

CH3ClAsymmetrical

Tetrahedral

arrangement

Creates

Dipole

Hydrogen Bonds

HydrogenbondsareDipole‐Dipoleinteractionbetweenpolarbondscontaininghydrogenatom.

Example:‐ Inwater,dipoleiscreatedduetoasymmetricalarrangementofhydrogenatoms.

Attractionbetweenpositiveoxygenpoleandnegativehydrogenpole.

105 0O

H

H

Hydrogen

Bond

Figure 2.28