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MSE 280: Introduction to Engineering Materials

Reading: Chapter 2Atomic structure and Bonding

g p

Overview•Electrons, protons and neutrons in atoms (Bohr and QM models).•IP, EA, χ, and periodic trends.

MSE280© 2007, 2008 Moonsub Shim, University of Illinois1

•Bonding between atoms.•Intermolecular forces.•Relation to macroscopic properties.

Electrons in atomsorbital electrons:

n = principal quantum number

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Nucleus: Z = # protons

Adapted from Fig. 2.1, Callister 6e.

Electrons in discrete orbitals.Bohr atom:

n=3 2 1

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N = # neutrons

Atomic mass A ≈ Z + N

1) electrons are particles that revolve around the nucleus.

2) quantized angular momentum.Quantum Mechanics:

Wave or matrix mechanics→ Probability.

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Comparison of Bohr and QM models

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Figs. 2.2 and 2.3 from Callister 6 ed.

Atomic orbitals

dyzdxy

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s px py pz dz2dx2-y2dxz

• have discrete energy states (Quantized).• tend to occupy lowest available energy state.

Electrons...

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Quantum numbers• Principal: n = 1, 2, 3, 4…• Angular momentum: l = 0, 1, 2, 3…, n – 1 = s, p, d, f…

s = sharp, p = principal, d = diffuse, f = fundamental• Magnetic: ml = 0, ±1, ±2, ±3… , ±l

Determines the number of states in a given l subshell (2l +1 total)

• Spin: ms = ±1/2

e g

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e.g.

1s n = 1, l = 0, ml = 0, ms = 1/2 n = 1, l = 0, ml = 0, ms = -1/2

2s n = 2, l = 0, ml = 0, ms = 1/2 n = 2, l = 0, ml = 0, ms = -1/2

Which atom is this? Be

Electron Configuration- Shorthand notation to represent which states electrons occupy in an atom (without specifying electron spin).

e.g. Carbon

1s

2s

Electron configuration: 1s22s22p2

2p

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Note- each energy level can only hold two electrons of opposite spin (Pauli exclusion principle).- for degenerate levels (e.g. 2p-orbitals), each orbital is filled with one electron before electrons are paired up.

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Electron configuration1 electron in the s-orbital: Alkali metals

Li, Na, K, Rb…

2 electrons in the s-orbital: Alkaline earthsBe, Mg, Ca…

Filled s-orbital and 4 electrons in p-orbital: ChalcogensO, S, Se…

Filled s-orbital and 5 electrons in p-orbital: HalogensF Cl Br

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F, Cl, Br…

Partially filled d-orbital: Transition metalse.g. Mn, Fe, Co…

Valence electrons determine which group atoms belong to.

Stable configuration

• have complete s and p subshellst d t b i t

Stable electron configurations...

• tend to be inert.

Z Element Configuration 2 He 1s 2 10 Ne 1s 22s 22p 6 18 Ar 1s 2 2s 22p 63 s 23p 6

Adapted from Table 2.2, Callister 6e.

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36 Kr 1s 2 2s 22p 63 s 23p 63d 10 4 s 24p 6

Noble gases

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Valence electrons

2p

3s

2p

3s

Filled shell}

Valence electron

1s

2sp

Na

1s

2s

Na+

Filled shell leads to stability.

}Lose an electron

33p

3s3p Filled shell }

Valence electrons

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Gain an electron

1s

2s2p

3s

Cl1s

2s2p

3s

Cl-

leads to stability.

How much energy does it require to take an electron out of an atom?

Energy of an electron in vacuum

Ene

rgy

Valence electron

IP

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• Ionization potential (IP): Energy required to pull out a valence electron (in vacuum).

By convention, IP is positive (i.e. need to put in energy to pull out the electron).

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How much energy does it require to place an electron in an atom?

Energy of electron in vacuum

Ener

gy

Valence electrons

EA

Lowest available state

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• Electron Affinity (EA): Energy gained by putting an electron in (from vacuum).

By convention, EA is negative (i.e. electron goes from higher energy state in vacuum to lower energy state in atom).

How do we determine when an atom will accept an electron or give one up?

y EA IP

Vacuum level

• Electronegativity (χ): a measure of how likely an atom will take up or give up an electron

EAIP +

Ene

rgy

Valence electrons

EA

Lowest available state

IPχ

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A simple (and intuitive) definition:

-When two atoms are brought together, the atom with larger χ will have higher electron density around its nucleus.

-Larger Δχ more ionic bond.

2~ EAIPx +

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BondingPrimary

Ionic ECovalentMetallic

SecondaryDipole-dipoleH bonds

E

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H-bondsDipole-induced-dipoleFluctuating dipoles

Equilibrium bond length

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Ionic Bonding• Occurs between + and - ions.• Requires electron transfer.

Na (metal) unstable

Cl (nonmetal) unstable

electron

• Large difference in electronegativity required.• Example: NaCl

3s3p

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electron

+ - Coulombic Attraction

Na (cation) stable

Cl (anion) stable

Na(χ = 0.9)

3s3p

Cl(χ = 3.0)

Ionic BondingNa (metal) unstable

Cl (nonmetal) unstable

electron

+Na (cation) Cl (anion)

ezzEA 4

221=

+ - Coulombic Attraction

Na (cation) stable

Cl (anion) stable ro

A πε4

Since z1 = +1 for Na+ and z2 = -1 for Cl-

rA

reE

oA −=−=

πε4

2Negative energy means attraction only.Will the atoms collapse on themselves?

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No, there is also repulsive energy (e.g. e-e repulsion)

nR rBE = B and n depend on atoms involved.

In many cases n ~ 8.

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Ionic BondingE

rAE

nR rBE =

Bond energy

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rEA −=

Equilibrium bond length

gy

Note: Other types of bonds can also be described in a similar manner

Ionic Bonding: examples• Predominant bonding in Ceramics

M ONaCl

He -

Ne -

Ar -

Kr -

Xe -

F 4.0Cl

3.0Br

2.8I

2.5

Li 1.0Na 0.9K

0.8Rb 0.8

H 2.1

Be 1.5Mg 1.2Ca 1.0Sr 1.0

Ti 1.5

Cr 1.6

Fe 1.8

Ni 1.8

Zn 1.8

As 2.0

Cs Cl

MgOCaF 2

O 3.5

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Give up electrons Acquire electrons

Rn -

At2.2

Cs 0.7Fr

0.7

Ba 0.9Ra 0.9

Adapted from Fig. 2.7, Callister 6e. (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 CornellUniversity.

From Callister 6e resource CD.

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Covalent Bonding

1s 1s

HH

Molecular orbitals

• “Sharing” of electrons• Why do some atoms want to share electrons?

• Example2: CH4

C: has 4 valence e,needs 4 more

• Example1: H2

shared electrons from carbon atomH

CH4

H HHH

Atomic orbitals

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H: has 1 valence e,needs 1 more

Electronegativitiesare same or comparable.

Adapted from Fig. 2.10, Callister 6e.

shared electrons from hydrogen atoms

HH

H

C

an s-orbital three p orbitalsAtomic Orbitals

atomic orbitals for carbon:

1s

2s2p 4 valence electrons but

two different types orbitals.H’s on CH4 should be equivalent.

xy

zpx py pz

an s-orbital p

Hybridization sp3 hybridization for C in CH4

MSE280© 2007, 2008 Moonsub Shim, University of Illinois20x

y

z1s + 2p = sp2-orbitals 1s + 3p = sp3-orbitals

60°

60°x

y

z

y

xy

z1s + 1p = sp-orbitals

sp3 hybridization for C in CH4

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EXAMPLES: COVALENT BONDING

He -

H 2 1 SiC

C(diamond)

H2OH2

Cl2

F2

colu

mn

IVA

Ne -

Ar -

Kr -

Xe -

Rn -

F 4.0Cl

3.0Br

2.8I

2.5At

2.2

Li 1.0Na 0.9K

0.8Rb 0.8Cs 0.7Fr

0.7

2.1Be 1.5Mg 1.2Ca 1.0Sr

1.0Ba 0.9Ra 0.9

Ti 1.5

Cr 1.6

Fe 1.8

Ni 1.8

Zn 1.8

As 2.0

SiCC

2.5

Cl2

Si 1.8

Ga 1.6

GaAs

Ge 1.8

O 2.0

c

Sn 1.8Pb 1.8

Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is

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• Molecules with nonmetals• Molecules with metals and nonmetals• Elemental solids (RHS of Periodic Table)• Compound solids (about column IVA)

0.9 p g , ( gadapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.

% ionic character

Most bonds between two different types of atoms are somewhere in between ionic and covalent.between ionic and covalent.

% ionic character = ]})(25.0exp[1{ 2BA χχ −−−

χj = electronegativity of atom j

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χj electronegativity of atom j

KEY POINT: Larger electronegativity difference more ionic

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Example problem

• Order the following semiconductors from t l t t t i imost covalent to most ionic.

1) ZnS, GaP, CuCl2) ZnS, ZnSe, ZnO

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What’s so important about ionicity of bonds?

• Chemical propertiesNaCl (highly ionic solid) dissolves readily in water but– NaCl (highly ionic solid) dissolves readily in water but Si (covalent solid) does not.

• Electronic properties– Ionicity of the bonds will have a strong influence on

the band gap and other electronic properties.• All properties of materials are largely determined

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All properties of materials are largely determined by the types and strength of bonds between the constituent atoms.

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Metallic Bonding• Arises from a sea of donated valence electrons

Fixed ion cores (nuclei+ + +

+ + +

Fixed ion cores (nuclei and inner electrons)

“sea” of electrons

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• Primary bond for metals and their alloys.• Large atomic radius and small IP will more likely lead to metallic bonding.

+ + + Adapted from Fig. 2.11, Callister 6e.

Secondary Bonds: Intermolecular Forces

• Dipole-dipole interaction: secondary bond between molecules with permanent dipole moments

Van der Waals

+ - secondary bonding + -

H Cl H Clsecondary bonding

secondary bonding

-general case:

-ex: liquid HCl

-ex: polymer

Adapted from Fig. 2.14,Callister 6e.

Adapted from Fig. 2.14,Callister 6e.

From Callister 6e resource CD.

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• Hydrogen bonding

HO

H

HO H

HO

H

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• Dipole-induced-dipole interaction: secondary bond between molecules with permanent dipole moments

+

-

+

- +

-

• Fluctuating dipoles

H2 H2ex: liquid H 2asymmetric electron

clouds

secondary bondingpolar

Nonpolar (e.g. atom)

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HH HH

H2 H2

secondary bonding

clouds

+ - + -secondary

bondingAdapted from Fig. 2.13, Callister 6e.

SUMMARY: BONDING

TypeIonic

Bond EnergyLarge!

CommentsNondirectional (ceramics)Ionic

Covalent

Large!

Variablelarge-Diamondsmall-Bismuth

Variable

Nondirectional (ceramics)

Directional(semiconductors, ceramics

polymer chains)

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Metallic

Secondary

large-Tungstensmall-Mercury

smallest

Nondirectional (metals)

Directionalinter-chain (polymer)

inter-molecularFrom Callister 6e resource CD.

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• Bond length, r

F F

• Melting Temperature, Tm

Energy (r)

PROPERTIES FROM BONDING: TM

• Bond energy, Eo

r

Energy (r)

unstretched length

r

larger T

smaller T m

r o

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Eo= “bond energy”

r o r

u st etc ed e gt larger T m

Tm is larger if Eo is larger.

From Callister 6e resource CD.

• Elastic modulus, E cross sectional area A o length, Lo

undeformed ΔLF

Elastic modulus

PROPERTIES FROM BONDING: E

• E ~ curvature at ro

ΔL

F

undeformed

deformed

ΔLFAo

= E Lo

Energy

unstretched length E is larger if curvature at

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r

larger Elastic Modulus

smaller Elastic Modulus

r o unstretched length E is larger if curvature at

ro is larger.

From Callister 6e resource CD.

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Ceramics(Ionic & covalent bonding):

Large bond energylarge Tm

large Esmall α

SUMMARY: BONDING and Materials’ properties

Metals(Metallic bonding):

Polymers

small α

Variable bond energymoderate Tm

moderate Emoderate α

Directional Properties

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Polymers(Covalent & Secondary):

secondary bonding

Directional PropertiesSecondary bonding dominates

small Tsmall Elarge α

From Callister 6e resource CD.