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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