introduction to materials science and engineeringocw.snu.ac.kr/sites/default/files/note/5900.pdf ·...

Introduction toMaterials Science and Engineering

Chapter 2. Atomic Structure and Interatomic BondingInteratomic Bonding

What promotes bonding?What promotes bonding?

What types of bonds are there?

What properties are inferred from bonding?

1 http://bp.snu.ac.kr

Limitations in Early Atomic ModelLimitations in Early Atomic Model

slit

Geisslertube prism

screen

Electromagnetic Wave

Circumferential motion of charged particles should emit EM wave.

Discontinuous emission spectra cannot be understood


Discontinuous emission spectra cannot be understood.

Bohr’s Model

To resolve the discontinuous emission spectra...

Assumptions : Quantum conditionFrequency condition

Bohr, Niels (1885-1962)

electron

3 http://bp.snu.ac.krorbit nucleus

Bohr Atom

orbital electrons: i i l

(Fig. 2-1)n = principal quantum number

3 2 1n=3 2

Nucleus: Z = # protons 1 f h d t 94 f l t i= 1 for hydrogen to 94 for plutonium

N = # neutrons


Atomic mass A = Z + N

Bohr Atom

electrons & protons are electrically charged: 1.60 x 10-19 C

mass-proton = mass-neutron = 1.67 x 10-24 g

mass-electron = 9.11 x 10- 28 g

atomic number (Z) = # protons

atomic mass = mass-protons + mass-neutrons

# of protons: same for all atoms of an element

# of neutrons is variable

“isotopes” (elements with 2 or more atomic masses)

atomic weight = weighted average of the atom’s isotopes

the atomic weight of an element may be specified as mass/mole of material1 amu = 1/12 atomic mass of carbon 12 (12C)

1 mole = 6.023 x 1023 (Avogadro’s number) atoms or molecules

1 / ( l l ) 1 / l


1 amu/atom (or molecule) = 1 g/mol

Limitations in Bohr’s Model... Classic mechanical theory was employed ...

2pmr

... What if there are more than two electrons ? ...

2ke

mr... Quantum condition fails ...

Self contradiction in terms of Heisenberg uncertainty principle2r... Self-contradiction in terms of Heisenberg uncertainty principle ..

( )( )4hp xπ

Δ Δ ≥4π

... Therefore, in discussing the motion of an electron of known energy or momentum about a electron of known energy or momentum about a nucleus, it is necessary to speak only in terms of the probability of finding that an electron at any

6 http://bp.snu.ac.krHeisenberg, Werner (1901-1976)

particular position ...

Bohr vs. Wave-Mechanical Model(Fig 2-2)(Fig. 2-2)

(Fig. 2-3)

Bohr model

Wave mechanical

model

Bohr model

Wave mechanical

d lmodel

Electron position is described by b bilit di t ib ti

Bohr energy levels to be separatedi t l t b h ll


a probability distribution or electron cloud.

into electron sub-shellsdescribed by quantum numbers.

dual nature of light, dual nature of matterg

i ht i t f ti l ll di ht i t f ti l ll dLight consists of particles called Light consists of particles called

photonsphotons with with energyenergy equal toequal to

E = hv E = hv E = hv .E = hv .

E hchν= =8 http://bp.snu.ac.kr

λ-2009-09-09

Description of the motion of a particlein terms of quantum mechanics

h hDual nature of matters states ... 2 k

h hEmp

λ = =

It i t l t thi k th t th ‘ t ff t’ t

h = 4.1357 × 10-15 eV·sec... It is natural to think that the ‘quantum effect’ gets significant when the Planck’s constant matters ...

... Therefore, any moving particle can be described as a wave function …

2h

by Schrodinger equation, especially when the mass of the matter is small enough ...


Eψ ψΗ = 228

hm

φπ

Η = − ∇ +where

A particle in-a-box... A hypothetical system containing only a small particle in one-dimensional box ...

∞ ∞

φ φ

( )2 2

2 2

8 0d m Edx h

ψ π φ ψ+ − =

0φ =φ = ∞ φ = ∞

2 2

28nhE n

mL=

0 L1/ 22 sinn

n xL L

πψ ⎛ ⎞= ⎜ ⎟⎝ ⎠

What should be noted ...1. Quantization of energy

2. Probability & nodes

3 Z i f H i b i i i l


3. Zero-point energy, cf. Heisenberg uncertainty principle

4. Suitable in describing small mass in small space, e.g. electrons in atom

Orbital conceptImagine & take a picture of an electron confined in an atom with a single room for it ...

“ orbital ”which cannot be

Then, what if there are two available rooms

defined by a discrete line, but a region of a volume

for an electron ...region of a volume due to Heisenberg uncertainty principle


Wave equation to Hydrogen atom

Eψ ψΗ =

( ) ( ) ( )R Yψ θ φ θ φ

( ) ( ) ( ) ( )n l m R rψ θ φ= ⋅Θ ⋅Φ

( ) ( ) ( ), , ,r R r Yψ θ φ θ φ= ⋅

( ) ( ) ( ) ( ),, , n l l mn l m R rψ θ φ= ⋅Θ ⋅Φ

... From the solution of the wave function,three quantum numbers result three quantum numbers result ...

n, l, and ml


Quantum numbersi i l b 1 2 3 4 (K L M N )n principal quantum number 1, 2, 3, 4, --- (K, L, M, N, ---)

Determines the effective volume of an electron orbital

Distance of an electron from the nucleus position of an electronDistance of an electron from the nucleus, position of an electron

l azimuthal quantum number 0, 1, 2, 3, 4, ---, (n-1) (s, p, d, f)Determines the angular momentum of the electron Determines the angular momentum of the electron

Shape of electron subshell, shape of electron distribution

ml magnetic quantum number 0, ±1, ±2, ---, ±ll g qDetermines the orientation of the orbital

ms spin quantum number ½, -½

Pauli exclusion principleNo two interacting entities can have the same set of the quantum numbers ...

Each orbital will hold up to two electrons

There can never be more than one electron in the same quantum state


There can never be more than one electron in the same quantum state.

Only one electron can be in a particular quantum state at a given time.

Each electron state cannot hold more than two electrons with opposite spins.

Meaning of quantum numbers

n determines the size

l determines the shape

3s2 3p6 3d10

14 http://bp.snu.ac.krml determines the orientation

3s 3p 3d

Atomic structure of sodium (Na)


Electron Energy StatesElectrons...

Have discrete energy statesHave discrete energy states.

Tend to occupy lowest available energy state.(Fig 2 4)

rgy

4p

(Fig. 2-4)(Fig. 2-5)

ng

en

er

n=3

n=4

33p

4s4p

3d

cre

asi

n

n=2

n 3

2s

3s2p

p

Inc

n=1 1s


Survey of ElementsMost elements: Electron configuration is not stable.

Element Atomic # Electron configuration Hydrogen Helium Lithium B lli

1 2 3 4

1s1 1s2 (stable) 1s22s1 1 22 2 Beryllium

Boron Carbon

4 5 6

1s22s2 1s22s22p1 1s22s22p2

... Neon Sodium Magnesium

10 11 12

... 1s22s22p6 (stable) 1s22s22p63s1 1s22s22p63s2 Magnesium

Aluminum ... Argon

12 13

18

p1s22s22p63s23p1 ... 1s22s22p63s23p6 (stable) g

... Krypton

... 36

... 1s22s22p63s23p63d104s246 (stable)


Why? Valence (outer) shell usually not filled completely

Periodic TableColumns: Similar Valence Structure

ase

s 1

e

e

ert

ga

ep

t 1

e e

pt

2e

ve u

p u

p 2

ee

Metal

He

N

ina

cc

ea

cc

e

giv

giv

e

e u

p 3

Li

Nonmetal

Intermediate

H

Ne

Ar

Kr

giv

e F Li Be Intermediate

Na Cl

Br

O

S Mg

Ca K Sc Se

Xe

Rn

Br

I

At

Sr

Ba

Rb

Cs

Y

Se

Te

Po

Ra Fr

Electronegative elements:


Readily give up electrons

to become + ions.

Electronegative elements:Readily acquire electrons

to become - ions.

ElectronegativityRanges from 0.7 to 4.0

Large values: tendency to acquire electronsLarge values: tendency to acquire electrons

He -

Ne -

F 4.0

Li 1.0

H 2.1

Be 1.5

Ar -

Kr -

Cl 3.0

Br 2.8

Na 0.9

K 0.8

Mg 1.2

Ca 1.0

Ti 1.5

Cr 1.6

Fe 1.8

Ni 1.8

Zn 1.8

As 2.0

Xe -

Rn -

I 2.5

At 2.2

Rb 0.8

Cs 0.7

F

Sr 1.0

Ba 0.9

R Fr 0.7

Ra 0.9


Smaller electronegativity Larger electronegativity

Bonding

Primary bondingIonic bonding

l b dCovalent bonding

Metallic bondingg

Secondary bonding d W lvan der Waals

Hydrogen bonding


y g g

Two fundamental types of bondingP i b d t t t t S nd b nd : m h k It is th Primary bonds: strong atom-to-atom attractions produced by changes in electron position of the valence e–

Secondary bonds: much weaker. It is the attraction due to overall “electric fields,” often resulting from electron transfer in p

Example: Strong intramolecular covalent bond between two hydrogen atoms in H2

gprimary bonds

Example: intermolecular bond between

H2 molecules


Secondary BondingArises from interactions between

- Induced dipolesI d d di l d l l l- Induced dipoles and polar molecules

- Polar molecules

• Fluctuating dipoles (He-He)asymmetric electron

clouds H2 H2ex: liquid H2

clouds

+ - + -secondary

HH HH

H2 H2

secondary

• Permanent dipoles

secondary bonding

secondary bonding

m p-general case: secondary

bonding+ - + -


-ex: liquid HCl H Cl H Clsecondary bonding

Bonding


Bonding (Table 2-3)


Atomic BondingWhen more than two atoms get closer ... Especially in case of atoms of the kind ...

ee e

eWhen atoms with less valence electrons are brought together, each atom tends to form ‘ closed shell ’ structure by

3+Li

e3+Li

ee

to form closed shell structure by abandoning less bound free electrons.

Metallic bonding3+Li

e

e3+Li

e

eFree electron

Metallic bonding

Shared electrone

9

e

ee e

eWhen atoms with many valence electrons are brought together, each

9+F

e

ee

e

9+F

e

ee

e

e

e

g g ,atom tends to form ‘ closed shell ’ structure by sharing electrons belonging to neighbor atoms


e e

eee

belonging to neighbor atoms.

Covalent bonding

Atomic bondingWhen atoms of far- & near-closed shell structure are brought together ...

ee e

ee e

3+Li

e

ee 9+F

e

ee

e

e

3+Li

e

e9+F

e

eee

e

eee e

ee

At f f l d h ll t t & l d t d t l & i Atoms of far-closed shell structure & near-closed one tend to lose & gain electrons, respectively

Electronegativity by L PaulingElectronegativity by L. Pauling

Excess charge induced by the transfer of electrons are compensated by the presence of ions of opposite sign


p f f pp gIonic bonding

Bonding Forces & Energies(Fig. 2-8)

ForceForce

EnergyEnergy


Properties from Bonding: Tm

Bond length, r0Melting Temperature, Tm

- Depth of energy wellF

F

r Energy (r)

Bond energy, Eor

Energy (r) r

smaller T

ro

ro r

unstretched length

larger Tm

smaller Tm

Eo=

밷ond energy Tm is larger if Eo is larger.Bond energy


Tm is larger if Eo is larger.gy

Properties from Bonding: α

Coefficient of thermal expansion, αlength, Lo coeff. thermal expansion

ΔL

g , o

unheated, T1

= α (T2-T1) ΔL L

coeff. thermal expansion

heated, T2 ( 2 1)

Lo

1 dlαα ~ symmetry at ro

Energy

th l dTα =

α is larger if Eo is smaller.r ro

α is larger if Eo is smaller.r

larger α

30 http://bp.snu.ac.krsmaller α

Properties from Bonding: α

Thermal expansion asymmetric nature of the energy wellp y gyBroad well (generally more asymmetric) larger expansion


-2009-09-14

Ionic BondingOccurs between + ions and – ions.

An ionic bond is created between two unlike atoms with different electronegativities.gWhen Na donates its valence electron to Cl, each becomes an ion;

attraction occurs, and the ionic bond is formed.,Na (metal) unstable

Cl (nonmetal) unstable

l t electron

+ - C l bi

Na (cation) stable

Cl (anion) stable Coulombic

Attraction stable stable


Example: Ionic BondingPredominant bonding in Ceramics

MgONaCl

He -

Ne F 4 0

Li 1 0

H 2.1

Be 1 5 CsCl

MgO

CaF2O

3 5 -

Ar -

Kr

4.0

Cl 3.0

Br 2 8

1.0

Na 0.9

K 0 8

1.5

Mg 1.2

Ca 1 0

Ti 1 5

Cr 1 6

Fe 1 8

Ni 1 8

Zn 1 8

As 2 0

CsCl 3.5

-

Xe -

Rn -

2.8

I 2.5

At 2 2

0.8

Rb 0.8

Cs 0 7

1.0

Sr 1.0

Ba 0 9

1.5 1.6 1.8 1.8 1.8 2.0

-2.20.7

Fr 0.7

0.9

Ra 0.9


Give up electrons Acquire electrons

Ionic Crystal(Fig. 2-9)

ClNa

Each positive ion is surrounded by several negative ions and

vice versa.


When voltage is applied to an ionic material, entire ions must move to cause a current to flow Ion movement is slow and


move to cause a current to flow. Ion movement is slow and the electrical conductivity is poor.

Covalent Bonding (Fig. 2-10)

Requires shared electrons

Example: CH4

shared electronfrom carbon atoH

CH4

C: has 4 valence e, needs 4 more.

H: has 1 valence e, needs 1 more.shared electron

HH C

Electronegativities are comparable. shared electronfrom hydrogen atoms

H

Covalent bonding requires that electrons be shared between electrons be shared between atoms in such a way that each atom has its outer sp orbital pfilled. In silicon, with a valence of four, four covalent bonds


must be formed.

Covalent Bonding

The tetrahedral structure of silica (Si02) contains


The tetrahedral structure of silica (Si02) contains

covalent bonds between silicon and oxygen atoms.

Covalent Bonding

Covalent bonds are directional. In silicon, a tetrahedral structure is formed with angles of 109 5° required between each


structure is formed, with angles of 109.5 required between each covalent bond.

Covalent Bonding Electron sharing

Directional

CH4Cl2 CH4Cl2

SiO 2diamondSiO4

2-


Example: Covalent Bonding

C(diamond)

H2OH2 F2

mn

IVA

He -

Ne F 4 0

Li 1 0

H 2.1

Be 1 5

SiC

C(diamond)

C 2 5

Cl2O

2 0

co

lum

-

Ar -

Kr -

4.0

Cl 3.0

Br 2 8

1.0

Na 0.9

K 0.8

1.5

Mg 1.2

Ca 1 0

Ti 1 5

Cr 1 6

Fe 1 8

Ni 1 8

Zn 1 8

As 2 0

2.5

Si 1.8

Ga 1 6

Ge 1 8

2.0

-

Xe -

Rn -

2.8

I 2.5

At 2.2

0.8

Rb 0.8

Cs 0.7

1.0

Sr 1.0

Ba 0.9

1.5 1.6 1.8 1.8 1.8 2.01.6 1.8

Sn 1.8Pb 1.8

molecules with nonmetals

.

Fr 0.7

0.9

Ra 0.9 GaAs

m m

molecules with metals and nonmetals

elemental solids


elemental solids

compound solidsStrong directional nature of bonding

Ionic vs. Covalent Bonding


Metallic Bonding

Arises from a sea of donated valence electrons

(1 2 or 3 from each atom) (Fi 2 11)(1, 2, or 3 from each atom).

+ + +

(Fig. 2-11)

+ + +

+ + +

+ + +

Primary bond for metals and their alloys

+ + +


Primary bond for metals and their alloys.

Metallic Bonding delocalized electron

Free electrons act as a


“glue” to hold the ion core.

Metallic Bondingg

The metallic bond forms when atoms give up their valence electrons, which then form an electron sea.

The positively charged p y gatom cores are bonded by mutual attraction to the negatively-charged electrons.


electrons.

Metallic Bonding

When voltage is applied to a metal, the electrons in the


When voltage is applied to a metal, the electrons in the electron sea can easily move and carry a current.

Metallic BondingMechanical properties

brittlebrittle

ductile


Van der Waals bonding

e Although electrons have tendency of being separated as far as possible due to e e

2+Heseparated as far as possible due to e-e

repulsion, electrons are constantly in motion.

eIt follows that electrons could get close

δ +

It follows that electrons could get close enough to induce a “electric dipole

moment” at atomistic level.2+HeeThis tendency is expected to be more significant

as the number of electrons increases. eδ −Temporal bonding due to the induced electric dipole.

51 http://bp.snu.ac.krvan der Waals bonding

Van der Waals Bonding

Induced dipole Permanent dipole(polar molecule)(polar molecule)


Van der Waals BondingArises from interactions between

Induced dipolesInduced dipoles and polar moleculesPolar moleculesPolar molecules

Fluctuating Dipolesg p

H2 H2ex: liquid H2asymmetric electron

clouds

HH HHsecondary

bonding

+ - + -secondary

bonding

Permanent Dipoles

+ - secondary bonding + --general case: bonding

H Cl H Clsecondary bonding

general case:

-ex: liquid HCl


Hydrogen bondingWhen one of the components of covalent bonding is hydrogen ...

e e

+H e 9+F

e

ee

e

e

9+F

e

ee

e

e

+H ee

eee

e

eee

Since hydrogen atom has only one electron, there is no electron left for the formation of closed shell.

B p t n is xp s d ith ut b in shi ld d b l t ns Bare proton is exposed without being shielded by electrons ...Strong ionic character develops locally about hydrogen atom ...

δ − +δ −+ H2O, HF, NH3, etc.Strongest secondary bonding.

55 http://bp.snu.ac.kr... Strong bonding develops ...

Hydrogen Bonding

H2O Ice

open structureopen structure- lower density


Materials-Bonding ClassificationCeramics Large bond energyCeramics

(ionic & covalent)Large bond energylarge Tmsmall α

Metals(metallic)

Variable bond energymoderate Tmmoderate αmoderate α

Di i l P iPolymers

(covalent & secondary)Directional PropertiesSecondary bonding dominatessmall Tmlarge αlarge α


READING

Read Chapter 2 of Callister

Problems from CallisterProblems from Callisterhttp://bp.snu.ac.kr

Prob. 2-2 Prob. 2-4 Prob. 2-6

Prob. 2-7 Prob. 2-8 Prob. 2-11

Prob. 2-14 Prob. 2-18 Prob. 2-20

Prob 2 22Prob. 2-22


Types of Adsorption Modes


http://bp.snu.ac.kr

- 2009-09-16

introduction to materials science and engineeringocw.snu.ac.kr/sites/default/files/note/5900.pdf ·...

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