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1 Materials Science and Engineering I Chapter Outline Review 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 2

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  • 1

    Materials Scienceand

    Engineering I

    Chapter OutlineReview of Atomic StructureElectrons, Protons, Neutrons, Quantum numberof atoms, Electron states, The Periodic TableAtomic Bonding in SolidsBonding Energies and Forces

    Periodic TablePrimary Interatomic BondsIonic, Covalent, Metallic

    Secondary Bonding (Van der Waals)Three types of Dipole Bonds

    Molecules and Molecular SolidsUnderstanding of interatomic bonding is the first stepTowards understanding/explaining materials properties

    2

  • 2

    Structure of Atoms

    3

    ATOM

    Basic Unit of an Element

    Diameter : 10 –10 m.

    Neutrally ChargedNucleus

    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) + electronsCharges:

    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

  • 4

    7

    8

    MaxPlanck,discoveredthatatomsandmoleculesemitenergyonlyincertaindiscretequantities,calledquanta.

    JamesClerkMaxwellproposedthatthenatureofvisiblelightisintheformofelectromagneticradiation.

    E=hυ =hc/λ Energyisalwaysreleasedinintegermultiplesofhυ

    8

    Planck’s Quantum Theory

  • 5

    Electron Structure of AtomsElectron 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 lightλ = Wavelength of

    light

    hc

    Emit

    Energy

    (Photon)

    Absorb

    Energy

    (Photon)

    Energy levels

    9

    Energy in Hydrogen AtomHydrogen atom has one proton and one electronEnergy 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

    23 22

    2-7 10

  • 6

    Energy-Level diagram for the line spectrum of hydrogen

    11

    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

    13

    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.

    14

  • 8

    15

    S, p and d Orbitals

    16

    Solutionofthewaveequationisintermsofawavefunction,ψ (orbitals).

    Thesquareofthewavefunctionrepresentselectrondensity.

    Boundarysurfacerepresentation.

    Totalprobability

    0.05 nm

    0.1 nm

    16

    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

    17

    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

  • 10

    19

    Elementsareclassifiedaccordingtotheirgroundstateelectronconfiguration.

    Orbital Box Diagram

    20

  • 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.

    22

  • 12

    23

    Atomic Structure

    Valence electrons determine all of the following properties

    1) Chemical2) Electrical 3) Thermal4) 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

    24

  • 13

    25

    Trends in Ionization Energy Energyrequiredtoremoveanelectronfromitsatom. Firstionizationenergy playsthekeyroleinthechemicalreactivity.

    Astheatomicsizedecreasesittakesmoreenergytoremoveanelectron.

    asthefirstoutercoreelectronisremoved,ittakesmoreenergytoremoveasecondoutercoreelectron

    26

    Electronegative elementsacceptelectronsduringchemicalreaction.Someelementsbehaveasbothelectronegativeandelectropositive.Electronegativity isthedegreetowhichtheatomattractselectronstoitself

    Measuredonascaleof0to4.1 Example:‐ Electronegativity ofFluorineis4.1

    Electronegativity ofSodiumis1.

    0 1 2 3 4K

    Na N O Fl

    W

    Te

    SeHElectro-

    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

  • 15

    29

    Trends in Electron Affinity Electronaffinity:Tendencytoacceptoneormoreelectronsandreleaseenergy.

    Electronaffinityincreases(moreenergyisreleasedafteracceptinganelectron)aswemovetotherightacrossaperiodanddecreasesaswemovedowninagroup.

    Groups6Aand7Ahaveingeneralthehighestelectronaffinities.

    30

    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 -H2Metallic: 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...)

  • 16

    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 chargeAnion

    -ve charge

    IONIC BOND

    Electrostatic

    Attraction

    32

    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]

  • 17

    33

    Ionic Bonding - Example

    3s13p6

    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 ionsFigure 2.11

  • 18

    35

    Ion Force for Ion Pair (Cont..)

    Z1,Z2 =Numberofelectronsremovedoraddedduringionformation

    e=ElectronChargea=Interionic seperation distanceε=Permeabilityoffreespace (8.85x10‐12c2/Nm2)

    (nandbareconstants)

    a

    eZZaZZF

    eeattractive 2

    0

    221

    2

    0

    21

    44

    aF nrepulsive

    nb1

    aaeZZF nnet nb12

    0

    221

    4

    Attraction

    Force

    Repulsion

    Force

    36 36

    • 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 2CsCl

  • 19

    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/Nm2a0 = 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

    221 1002.3

    m) 10x /Nm2)(2.76C 10x 8.85(4)1060.1)(1)(1(

    4

    Na+ Cl-

    a0

    38

    Interionic Energies for Ion PairsNetpotentialenergyforapairofoppositelychargedions=

    Enet isminimumwhenionsareatequilibriumseperation distancea0

    aaeZZE nnet b 0

    221

    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

  • 22

    43

    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

    43

    Hess law △H0= △H1+△H2+△H3+△H4+△H5

    △H5= △H0- △H1+△H2+△H3+△H4=-1050 kj

    44

    Covalent Bonding

    In covalent bonding, outer s and p electrons are shared between two atoms to obtain noble gas configuration.Takes place between elementswith small differences in electronegativity and close by in periodic table.

    In Hydrogen, a bond is formed between2 atoms by sharing their 1s1 electrons

    H + H H H1s1

    Electrons

    Electron

    Pair

    Hydrogen

    Molecule

    Overlapping Electron Clouds

  • 23

    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/molN N N N

    46

    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

  • 24

    47

    Carbonhaselectronicconfiguration1s2 2s2 2p2

    Hybridization causesoneofthe2sorbitalspromotedto2porbital.Resultfoursp3orbitals.

    Ground State arrangement

    1s 2s 2pTwo 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

  • 25

    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 HAcetylene

    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 cloud Figure 2.24

    Metallic Bonding

    52

    Metallic Bonds (Cont..)Overall energy of individual atoms are lowered by metallic bondsMinimum energy between atoms exist at equilibrium distance a0Fewer 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

  • 27

    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

    54

  • 28

    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

    CH4No Dipole

    moment

    CH3ClAsymmetrical

    Tetrahedral

    arrangement

    Creates

    Dipole

    Hydrogen BondsHydrogenbondsareDipole‐Dipoleinteractionbetweenpolarbondscontaininghydrogenatom.

    Example:‐ Inwater,dipoleiscreatedduetoasymmetricalarrangementofhydrogenatoms.

    Attractionbetweenpositiveoxygenpoleandnegativehydrogenpole.

    105 0O

    H

    H

    Hydrogen

    Bond

    Figure 2.28