[email protected] ENGR-45_Lec-02_AtomicBonding.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Registered Electrical.

[email protected] • ENGR-45_Lec-02_AtomicBonding.ppt1

Bruce Mayer, PE Engineering-45: Materials of Engineering

Bruce Mayer, PERegistered Electrical & Mechanical Engineer

[email protected]

Engineering 45

Atomic StructureAtomic Structureandand

InterAtomic InterAtomic BondingBonding



Learning GoalsLearning Goals

Understand the Sources/Causes of Atom-Level Bonding

Understand The Number & Types of Bonding

Determine Which properties May be inferred from bonding trends



The Nuclear AtomThe Nuclear Atom

Current Best Model of the Atomic Structure• A Small & Dense

NUCLEUS surrounded by an Electronic Cloud

Nucleus Composition → Two Constituents• PROTONS → POSITIVE Electronic Charge

• NEUTRONS → UNcharged

Electronic Cloud Composed of NEGATIVELY Charged ELECTRONS



Atomic FactsAtomic Facts

ELEMENTS are Defined by the Atomic Number, Z• Z Number of Protons

– For NATURALLY Occurring Elements Z Ranges from 1 (H) to 92 (U)

By the Electronic Neutrality Requirement • [No. Protons] = [No. Electrons]

Electronic Charge = 1.6x10-19 Amp•sec• Note: 1 A•s = 1 Coulomb (C)



Atomic Facts contAtomic Facts cont

Since The No. of NEUTRONSAre not Constrained by ChargeNeutrality, Then The SAME Element May Have Different No.s of Nuetrons, N • Elemental Forms with Different Neutron

Counts are Called ISOTOPES– e.g,; Consider Oxygen with Z = 8

O Isotope Neutrons, N Abundance16O 16-8 = 8 99.7620%17O 17-8 = 9 0.0383%18O 18-8 = 10 0.2001% h

ttp://ie.lbl.gov/education/isotopes.htm



Recall the Periodic TableRecall the Periodic Table



Atomic Facts cont.2Atomic Facts cont.2

Atomic Weight/Mass, A Weighted Average of NaturallyOccurring Isotopes

SubAtomic Particle Masses • Electron, e- = 9.11x10-31 kg

• Proton, p+ , and Neutron, n = 16 700x10-31 kg

Since Mp+ & Mn >> Me-

• Then A (Z+N)Mn



amu & gMolamu & gMol

By SI DEFINITION 12.00000... grams of 12C contains ONE gram-Mol of Carbon• 1 Mol of Any element Contains 6.023x1023

Protons and/or Electrons– 6.023x1023 Avagrado’s Number

Atomic Mass Unit, amu• 1 amu/atom = 1 g/mol

– e.g.; Atomic Wt of Niobium = 92.91 amu/atom = 92.91 g/mol



Atomic ReactionsAtomic Reactions

Nuclear Reaction• Change in the Number of Neutrons, N, or

Protons, Z, in an Atom– Remember, Changing Z Changes the

ELEMENT TYPEe.g., a Nuclear Reaction can Change LEAD to GOLD

Chemical Reaction• Exchange or ReArrangement of

ELECTRONS– VAST Majority of Matl Sci Done with Chem Rcns



Electron Behavior → QuantaElectron Behavior → Quanta

Electronic Behavior Governed by Quantum (Energy) Mechanics (QE)• QE Studied in Advanced

Physics/Chemistry, and Some Branches of Engineering

Basic Principle of QE as Applied to Materials Science• Electrons can have ONLY DISCRETE

Quantities (quanta) of Energy– i.e., e- Energy Levels are QUANTIZED



Bohr AtomBohr Atom 1st

QuantumModel• Electrons Revolve Around

Nucleus at Discrete EnergyLevels Called Orbitals

A Refined Model Based on Wave Mechanics• e- Treated as Both a WAVE

and a PARTICLE– Position is Determined STATISTICALLY,

not Physically

orbital electrons: n = principal quantum number

n=3 2 1



Atom: Shells & ValenceAtom: Shells & Valence

Nucleus

Proton

Neutron

INNER Shell Electron

VALENCEElectron

VALENCEShell/Orbit



Atom Structure - ValenceAtom Structure - Valence Only the electrons

(e-) in the OUTERmost electron shell can participate in CHEMICAL Reactions

Adding or Removing an e- creates a CHARGED Atom Called an ION

Valence e- Behavior Governs the Atom’s Ability to combine with other elements



Valence eValence e-- Importance Importance

A CHEMICAL reaction is the restructuring of the VALENCE Electrons in two or more Elements

Valence electron structure determines all of the following properties

Composition Electrical

Thermal Optical



Electron Configuration of AtomsElectron Configuration of Atoms Four QUANTUM

NUMBERS Describe the Electronic Configuration of Atoms

1st

Shell2nd

Sub-shell3rd

# ElectronsPer Sub-shell

4th

Spin

1

2

3

n

dp

s

s

sp

1062

62

2

M

L

K

• 3rd Quantum No. Describes the Number of VALENCE Electrons



Electron Energy StatesElectron Energy States e- have DISCRETE energy states; tend to

occupy LOWEST available energy state.

1s

2s2p

K-shell n = 1

L-shell n = 2

3s3p M-shell n = 3

3d

4s

4p4d

Energy

N-shell n = 4



Shell Filling RulesShell Filling Rules

Following Quantum Mechanics1. Electrons Fill Shells/Orbitals to MINIMIZE

the Overall Atom Energy

2. Only TWO e- can Occupy a Single Orbital– Must Have OPPOSITE “SPINS”: ↑ and ↓

3. Electrons Stay as Widely Separated in physical space as Possible

– Favors EMPTY Orbitals as opposed to Half-Filled Orbitals of the SAME Energy

Leads to apparently “NONsequential” Filling; e.g. Ca (20) and Sc (21)



Electronic ConfigurationElectronic Configuration

42622 33221 pspssS Principal

Quantum No. SubShell ElectronsPer SubShell

Number of VALENCE Electrons

The Normal Fill Sequence• 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p

→ 5s → 6s → 4f → 5d → 6p → 7s → 5f →6d → 7p

For a Given Shell Structure We can Write a ShortHand for an Element’s Electronic Structure; e.g., Sulfur



Stable Electron ConfigurationsStable Electron Configurations Stable Electron Configurations

• Have COMPLETE s & p SubShells– i.e., The VALENCE SubShell is FULL

• Are VERY Unreactive

Z Element Configuration

2 He 1s2

10 Ne 1s22s22p6

18 Ar 1s22s22p63s23p6

36 Kr 1s22s22p63s23p63d104s24p6

“OCTET”RULE:Ns2Np6



PeriodicPeriodicTableTable

Structure Structure

n=1 (1sn=1 (1s11))n=2 (2sn=2 (2s11))n=3 (3sn=3 (3s11))n=4 (4sn=4 (4s11))R

ow

s(v

ale

nce s

hells)

Columns(valence electron structure)



Periodic Table Structure cont.Periodic Table Structure cont. Rows: Same OUTER Shell (Primary Quantum No.) Column: SAME Number Of Valence Electrons

Similar Properties Trends: Atomic Radii, Electronegativity (tendency

to acquire electrons)

META

LS

NO

NM

ETA

LS

Radii

More ElectroNegLess ElectroNeg



Periodic Table StructurePeriodic Table Structure Organized by Quantum No., Valence

(or Group), and SubShell



Metals, SemiMetals, NonMetalsMetals, SemiMetals, NonMetalss p

d

f

Qu

antu

m N

o.



Metals, SemiMetals, NonMetalsMetals, SemiMetals, NonMetals METALS

• Solid at Room Temperature– Except Hg

• Maleable & Ductile

• Conduct Electricity

NonMetals (17)• Poor Heat

Conductors

• Brittle and Fracture Easily

SemiMetals• 6 or 7 (Astatine

is the Wobbler)

• Have Some Metal-Like Properties– Solids at Rm Temp

– Can Conduct Electricity

• Have Some NonMetal-Like Props– Hard & Brittle

At



Refined Shell Model for NitrogenRefined Shell Model for Nitrogen

Valence SHELL(L or 2)

Valence SUBShell(2p)



Molecular BondingMolecular Bonding

Molecules (2+ units of SAME atom) and Compounds (2+ DIFFERENT atoms) are Formed by CHEMICAL Bonding

CHEMICAL Bonds Result from ELECTRON Configuration Rearrangement• STRONG Bonds → Ionic, Metallic,

Covalent

• WEAK Bonds → Van Der Waals – DiPole, Polar, H-Bond



Bond-Energy Bond-Energy CurveCurve

Balance Between Atoms’ REPULSIVE and ATTRACTIVE Forces• ZERO Net Force

• LOWEST System Energy

Bond Distance Equilibrium InterAtomic Distance, or LATTICE Constant

Bond STRENGTH ↑• Melting Temperature ↑

• Stiffness ↑

too close → Repulsion

too far → Attaction

“just right”:r0 - equilibrium bond distance

Forc

eEn

erg

y

Min U



Ionic BondingIonic Bonding Ion An Atom That Has Gained/Lost e-(s)

• Resulting Ion has +/- CHARGE

Ionic Bonding Ocurrs Between + & - Ions• Requires Electron TRANSFER; e.g. NaCl

Na (metal) Unstable

1s22s22p63s1

Na (cation) Stable

1s22s22p6

Cl (nonmetal) Unstable

1s22s22p63s23p5

electron

Coulombic Attraction

Cl (anion) Stable

1s22s22p63s23p6

+ -

X



Ionic Bonding ExamplesIonic Bonding Examples Dominant Bonding Type for CERAMICS

Give up electrons Acquire electrons

He -

Ne -

Ar -

Kr -

Xe -

Rn -

F 4.0

Cl 3.0

Br 2.8

I 2.5

At 2.2

Li 1.0

Na 0.9

K 0.8

Rb 0.8

Cs 0.7

Fr 0.7

H 2.1

Be 1.5

Mg 1.2

Ca 1.0

Sr 1.0

Ba 0.9

Ra 0.9

Ti 1.5

Cr 1.6

Fe 1.8

Ni 1.8

Zn 1.8

As 2.0

CsCl

MgO

CaF2

NaCl

O 3.5



CoValent BondingCoValent Bonding Requires SHARED

Electrons (Co-Valent)

Example is CH4 (methane)

• C: has 4 valence e-’s, needs 4 more

• H: has 1 valence e-, needs 1 more

Characteristics• If A compound, Then

Electronegativities are comparable

• ≥4 valence e-’s

Cl2



CoValent Bonding ExamplesCoValent Bonding Examples NonMetallic Elemental

Molecules; e.g. F2

Hydrogen Compounds; e.g., HF, HNO3

Elemental Solids; e.g., C, Si, Ge

Near Group-IVA Solid Compounds; e.g. GaAs

He -

Ne -

Ar -

Kr -

Xe -

Rn -

F 4.0

Cl 3.0

Br 2.8

I 2.5

At 2.2

Li 1.0

Na 0.9

K 0.8

Rb 0.8

Cs 0.7

Fr 0.7

H 2.1

Be 1.5

Mg 1.2

Ca 1.0

Sr 1.0

Ba 0.9

Ra 0.9

Ti 1.5

Cr 1.6

Fe 1.8

Ni 1.8

Zn 1.8

As 2.0

SiC

C(diamond)

H2O

C 2.5

H2

Cl2

F2

Si 1.8

Ga 1.6

GaAs

Ge 1.8

O 2.0

col IV

A

Sn 1.8Pb 1.8



Mixed Ionic+Covalent BondingMixed Ionic+Covalent Bonding

Many Compounds Exhibit Ionic-Covalent Mixed Bonding

1

%1001 Ionic-% 4

2

BA XX

e

• where XA & XB are Pauling ElectroNegativities

Example MgO: XMg = 1.3, XO = 3.5

%2.701

%1001 Ionic-% 4

5.33.1 2

e



Metallic BondsMetallic Bonds

Ne config

Electrons Shared By All Atoms• “sea of electrons” around

“ion cores”

Ion Cores• Atoms Give Up Valence-e-

to the “sea”, leaving remaining Atoms with a Positive Ionic Charge– The Ion contains the Large

& Heavy Nucleus and is thus FIXED in Space

Generally Applies to Electro-Positive Elements• e.g.; Transition Metals such

as Ti, Ni, Zn, Cu



Secondary BondingSecondary Bonding Arises from Atomic or

Molecular DIPOLES What’s a DiPole?

• Separation of the + & - Charge-Centers– Generates an

ELECTRIC Field within the Entity

Fluctuating DiPoles• Charge Centers Due to

SHORT-LIVED Charge Asymmentry

E-Field

asymmetric electron clouds

+ - + -secondary bonding

Liquifying Force for Electrically Neutral and Symetrical Molecules such as H2, N2



Secondary Bonding cont.Secondary Bonding cont. Ionic Bonding in some

Molecules results in a PERMANENT Dipole

The +/- End of These Polar Molecules can Then Attract the -/+ Ends of Other Polar Molecules

General Case + - secondary bonding + -

H Cl H Clsecondary bonding

secondary bonding

e.g.; HCl Liquid

e.g.; PolymerSolid



Secondary Bonding, H BondSecondary Bonding, H Bond Recall that H has in

Only a Single Proton and Electron • NO Neutrons

When H forms an Ionic Bond, it Gives Up (for the most part) the e-

• This Leaves the Hydrogen’s p+ Ionic Core Unscreened by any e-’s

• This Forms a Molecule with a POSITIVE (and Negative) end

This Proton-Induced Dipole is quite Strong and Can Lead to relatively powerful Dipole Bonding• Classic Example = H2O

to Form Liquid or Solid



Summary: Chemical BondingSummary: Chemical Bonding

Bond Type Bond Energy Notes

Ionic LargeNonDirectionale.g.; Ceramics

Covalent

Variable• Large =>Diamond• Small => Bismuth

Directionale.g.: SemiConductors, Ceramics,

Polymer-Chains

Metallic

Variable• Large => Tungsten• Small => Mercury

NonDirectionale.g.; Metals

Secondary Smallest

DirectionalInterchain (PolyMer)

InterMolecular (Liq Water)



Properties From Bonding: TProperties From Bonding: TMeltMelt

Bond Length Melting Temperature, TM

Bond Energy, E0

General Relationship:|E0|↑ TM ↑

r

larger TM

smaller TM

Energy (r)

ro

r

Eo=

“bond energy”

Energy (r)

ro r

unstretched length



Properties From Bonding: EProperties From Bonding: E Modulus of Elasticity

Defined Modulus of Elasticity

Curvature of E vs r curve

Mathematically, E

General Relationship:|E0|↑ E ↑L F

Ao = E

Lo

Elastic modulus

r

larger E

Smaller E

Energy

ro unstretched length

cross sectional area Ao

L

length, Lo

F

undeformed

deformed



Properties From Bonding: Properties From Bonding: Coefficient of Thermal

Expansion, , Defined ~symmetry at r0

Mathematically,

General Relationship:|E0|↑ ↑

r

Larger

Smaller

Energy

ro L

length, Lo

unheated, T1

heated, T2

= (T2 -T1)LLo

coeff. thermal expansion



Summary: Primary BondsSummary: Primary Bonds

Ceramics(Ionic & covalent bonding):

Metals(Metallic bonding):

Polymers(Covalent & Secondary):

secondary bonding

Large bond energylarge Tm

large Esmall

Variable bond energymoderate Tm

moderate Emoderate

Directional PropertiesSecondary bonding dominates

small Tm

small Elarge



All Done for TodayAll Done for Today

α Superimposed

On PeriodicTable

GALLUIUM is the Tall Yellow one SODIUM is th Tall Blue one



WhiteBoard Work – P2.13WhiteBoard Work – P2.13

K+ & O2-

dipotassium oxide = K2Or0 = 1.5 nm



Problem TutorialProblem Tutorial

Let’s WorkText Problem

2.14

CalcuimOxide →



P2.13P2.13



P2.13P2.13



P2.13P2.13



P2.14P2.14



P2.14

P2.14



P2.15

P2.15

% Program E45_Prob_2_15_1101.m:

% Plot EA and ER vs r * Verify r0 numerically

% Bruce Mayer, PE • ENGR45 • 24Jan11

%% Calc r0 numerically using anonymous fcn for En

%* the eqn in text book is for r in nm

%A = 1.436;

B = 5.86e-6;

En = @(r) B/r^9 - A/r

%% find En,min at r = r0 us fminbnd command

[r0, Emin] = fminbnd(En, 0, 1);

disp('InterAtomic spacing for Min E, r0 in nm =')

disp (r0)

%% Calc En,min = En(r0)

En_min = En(r0);

disp('Min E, En_min in eV =')

disp (En_min)%

% Set Plotting Vector as 300 points

r_plt = linspace (0.1, .4, 300); % in nm

%% The Energy Functions

EA = -A./r_plt;

ER = B./r_plt.^8;

Etot = EA + ER;

%% Plot on Same Graph

plot(r_plt,EA, r_plt,ER, r_plt, Etot), xlabel('r (InterAtom

Spacing)'),...

ylabel('Energy'), title('ENGR45 Problem 2.14'), grid,...

legend('EA', 'ER', 'Etot'), axis([.1 .4 -8 8])

%% Compare to eqn 2.11 solution

n = 9;

disp('by eqn 2.11')

r0eqn = (A/(n*B))^(1/(1-n))

E0eqn = -A/(A/(n*B))^(1/(1-n)) + B/(A/(n*B))^(n/(1-n))



NaCl electron ExchangeNaCl electron Exchange



WhiteBoard Work – P2.13WhiteBoard Work – P2.13

Ca2+ & O2-

[email protected] ENGR-45_Lec-02_AtomicBonding.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Registered Electrical.

Documents

pe engineering

materials of engineering

atomic number

gmol slide

atomic structure

z z number of protons

z nm n slide

atomic weightmass