(1)

Atomic Structure and Interatomic Bonding

Nucleus: Z = # protons

2

orbital electrons: n = principal quantum number

n=3 2 1

= 1 for hydrogen to 94 for plutoniumN = # neutrons

Atomic mass A ≈ Z + N

Adapted from Fig. 2.1, Callister 6e.

BOHR ATOM

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

3

Inc

rea

sin

g e

ne

rgy

n=1

n=2

n=3

n=4

1s2s

3s2p

3p

4s4p

3d

Electrons...

Adapted from Fig. 2.5, Callister 6e.

ELECTRON ENERGY STATES

4

• have complete s and p subshells• tend to be unreactive.

Stable electron configurations...

Z Element Configuration

2 He 1s2

10 Ne 1s22s22p6

18 Ar 1s22s22p63s23p6

36 Kr 1s22s22p63s23p63d104s24p6

Adapted from Table 2.2, Callister 6e.

STABLE ELECTRON CONFIGURATIONS

5

• Why? Valence (outer) shell usually not filled completely.

• Most elements: Electron configuration not stable.Element Hydrogen Helium Lithium Beryllium Boron Carbon ... Neon Sodium Magnesium Aluminum ... Argon ... Krypton

Atomic # 1 2 3 4 5 6

10 11 12 13

18 ... 36

Electron configuration 1s1

1s2 (stable) 1s22s1 1s22s2 1s22s22p1 1s22s22p2 ...

1s22s22p6 (stable) 1s22s22p63s1 1s22s22p63s2 1s22s22p63s23p1 ...

1s22s22p63s23p6 (stable) ...

1s22s22p63s23p63d104s246 (stable)

Adapted from Table 2.2, Callister 6e.

SURVEY OF ELEMENTS

6

• Columns: Similar Valence Structure

Electropositive elements:Readily give up electronsto become + ions.

Electronegative elements:Readily acquire electronsto become - ions.

He

Ne

Ar

Kr

Xe

Rn

ine

rt g

ase

s a

cc

ep

t 1

e a

cc

ep

t 2

e

giv

e u

p 1

e

giv

e u

p 2

e

giv

e u

p 3

e

F Li Be

Metal

Nonmetal

Intermediate

H

Na Cl

Br

I

At

O

S Mg

Ca

Sr

Ba

Ra

K

Rb

Cs

Fr

Sc

Y

Se

Te

Po

Adapted from Fig. 2.6, Callister 6e.

THE PERIODIC TABLE

METALS

CERAMICS

POLYMERS

SEMICONDUCTOR

7

• Ranges from 0.7 to 4.0,

Smaller electronegativity Larger electronegativity

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

• Large values: tendency to acquire electrons.

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.

ELECTRONEGATIVITY

Na (metal) unstable

Cl (nonmetal) unstable

electron

+ - Coulombic Attraction

Na (cation) stable

Cl (anion) stable

8

• Occurs between + and - ions.• Requires electron transfer.• Large difference in electronegativity required.• Example: NaCl

IONIC BONDING

9

• Predominant bonding in 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

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.

EXAMPLES: IONIC BONDING

10

• Requires shared electrons• Example: CH4

C: has 4 valence e, needs 4 more

H: has 1 valence e, needs 1 more

Electronegativities are comparable.

shared electrons from carbon atom

shared electrons from hydrogen atoms

H

H

H

H

C

CH4

Adapted from Fig. 2.10, Callister 6e.

COVALENT BONDING

11

• Molecules with nonmetals• Molecules with metals and nonmetals• Elemental solids• Compound solids (about column IVA)

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

co

lum

n IV

A

Sn 1.8Pb 1.8

Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 isadapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.

EXAMPLES: COVALENT BONDING

12

• Arises from a sea of donated valence electrons (1, 2, or 3 from each atom).

• Primary bond for metals and their alloys

+ + +

+ + +

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

METALLIC BONDING

13

Arises from interaction between dipoles

• Permanent dipoles-molecule induced

• Fluctuating dipoles

+ - secondary bonding + -

H Cl H Clsecondary bonding

secondary bonding

HH HH

H2 H2

secondary bonding

ex: liquid H2asymmetric electron clouds

+ - + -secondary

bonding

-general case:

-ex: liquid HCl

-ex: polymer

Adapted from Fig. 2.13, Callister 6e.

Adapted from Fig. 2.14, Callister 6e.

Adapted from Fig. 2.14, Callister 6e.

SECONDARY BONDING

14

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large!

Variablelarge-Diamondsmall-Bismuth

Variablelarge-Tungstensmall-Mercury

smallest

Comments

Nondirectional (ceramics)

Directionalsemiconductors, ceramics

polymer chains)

Nondirectional (metals)

Directionalinter-chain (polymer)

inter-molecular

SUMMARY: BONDING

15

• Bond length, r

• Bond energy, Eo

F F

r

• Melting Temperature, Tm

Eo=

“bond energy”

Energy (r)

ro r

unstretched length

r

larger Tm

smaller Tm

Energy (r)

ro

Tm is larger if Eo is larger.

PROPERTIES FROM BONDING: TM

16

• Elastic modulus, E

• E ~ curvature at ro

cross sectional area Ao

∆L

length, Lo

F

undeformed

deformed

∆L F Ao

= E Lo

Elastic modulus

r

larger Elastic Modulus

smaller Elastic Modulus

Energy

ro unstretched length

E is larger if Eo is larger.

PROPERTIES FROM BONDING: E

17

• Coefficient of thermal expansion, α

• α ~ symmetry at ro

α is larger if Eo is smaller.

∆L

length, Lo

unheated, T1

heated, T2

= α (T2-T1) ∆L Lo

coeff. thermal expansion

r

smaller α

larger α

Energy

ro

PROPERTIES FROM BONDING: α

18

Ceramics(Ionic & covalent bonding):

Metals(Metallic bonding):

Polymers(Covalent & Secondary):

secondary bonding

Large bond energylarge Tm

large Esmall α

Variable bond energymoderate Tm

moderate Emoderate α

Directional PropertiesSecondary bonding dominates

small Tsmall Elarge α

SUMMARY: PRIMARY BONDS

2

• Non dense, random packing

• Dense, regular packing

Dense, regular-packed structures tend to have lower energy.

Energy

r

typical neighbor bond length

typical neighbor bond energy

Energy

r

typical neighbor bond length

typical neighbor bond energy

ENERGY AND PACKING

• atoms pack in periodic, 3D arrays• typical of:

3

Crystalline materials...

-metals-many ceramics-some polymers

• atoms have no periodic packing• occurs for:

Noncrystalline materials...

-complex structures-rapid cooling

Si Oxygen

crystalline SiO2

noncrystalline SiO2"Amorphous" = NoncrystallineAdapted from Fig. 3.18(b), Callister 6e.

Adapted from Fig. 3.18(a), Callister 6e.

MATERIALS AND PACKING

4

• tend to be densely packed.

• have several reasons for dense packing:-Typically, only one element is present, so all atomic radii are the same.-Metallic bonding is not directional.-Nearest neighbor distances tend to be small in order to lower bond energy.

• have the simplest crystal structures.

We will look at three such structures...

METALLIC CRYSTALS

5

• Rare due to poor packing (only Po has this structure)• Close-packed directions are cube edges.

• Coordination # = 6 (# nearest neighbors)

(Courtesy P.M. Anderson)

SIMPLE CUBIC STRUCTURE (SC)

6

APF = Volume of atoms in unit cell*

Volume of unit cell

*assume hard spheres

• APF for a simple cubic structure = 0.52

APF = a3

4

3π (0.5a)31

atoms

unit cellatom

volume

unit cellvolume

close-packed directions

a

R=0.5a

contains 8 x 1/8 = 1 atom/unit cell

Adapted from Fig. 3.19, Callister 6e.

ATOMIC PACKING FACTOR

• Coordination # = 8

7

Adapted from Fig. 3.2, Callister 6e.

(Courtesy P.M. Anderson)

• Close packed directions are cube diagonals.

--Note: All atoms are identical; the center atom is shaded differently only for ease of viewing.

BODY CENTERED CUBIC STRUCTURE (BCC)

aR

8

• APF for a body-centered cubic structure = 0.68

Close-packed directions: length = 4R

= 3 a

Unit cell contains: 1 + 8 x 1/8 = 2 atoms/unit cell

Adapted fromFig. 3.2,Callister 6e.

ATOMIC PACKING FACTOR: BCC

APF = a3

4

3π ( 3a/4)32

atoms

unit cell atomvolume

unit cell

volume

9

• Coordination # = 12

Adapted from Fig. 3.1(a), Callister 6e.

(Courtesy P.M. Anderson)

• Close packed directions are face diagonals.--Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing.

FACE CENTERED CUBIC STRUCTURE (FCC)

APF = a3

4

3π ( 2a/4)34

atoms

unit cell atomvolume

unit cell

volume

Unit cell contains: 6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell

a

10

• APF for a body-centered cubic structure = 0.74

Close-packed directions: length = 4R

= 2 a

Adapted fromFig. 3.1(a),Callister 6e.

ATOMIC PACKING FACTOR: FCC

11

• ABCABC... Stacking Sequence• 2D Projection

A sites

B sites

C sitesB B

B

BB

B BC C

CA

A

• FCC Unit CellA

BC

FCC STACKING SEQUENCE

12

• Coordination # = 12

• ABAB... Stacking Sequence

• APF = 0.74

• 3D Projection • 2D Projection

A sites

B sites

A sites Bottom layer

Middle layer

Top layer

Adapted from Fig. 3.3, Callister 6e.

HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)

13

• Compounds: Often have similar close-packed structures.

• Close-packed directions --along cube edges.

• Structure of NaCl

(Courtesy P.M. Anderson) (Courtesy P.M. Anderson)

STRUCTURE OF COMPOUNDS: NaCl

14

Example: Copper

ρ = n AVcNA

# atoms/unit cell Atomic weight (g/mol)

Volume/unit cell

(cm3/unit cell)Avogadro's number

(6.023 x 1023 atoms/mol)

Data from Table inside front cover of Callister (see next slide):• crystal structure = FCC: 4 atoms/unit cell• atomic weight = 63.55 g/mol (1 amu = 1 g/mol)• atomic radius R = 0.128 nm (1 nm = 10 cm)-7

Vc = a3 ; For FCC, a = 4R/ 2 ; Vc = 4.75 x 10-23cm3

Compare to actual: ρCu = 8.94 g/cm3Result: theoretical ρCu = 8.89 g/cm3

THEORETICAL DENSITY, ρ

15

Element Aluminum Argon Barium Beryllium Boron Bromine Cadmium Calcium Carbon Cesium Chlorine Chromium Cobalt Copper Flourine Gallium Germanium Gold Helium Hydrogen

Symbol Al Ar Ba Be B Br Cd Ca C Cs Cl Cr Co Cu F Ga Ge Au He H

At. Weight (amu) 26.98 39.95 137.33 9.012 10.81 79.90 112.41 40.08 12.011 132.91 35.45 52.00 58.93 63.55 19.00 69.72 72.59 196.97 4.003 1.008

Atomic radius (nm) 0.143 ------ 0.217 0.114 ------ ------ 0.149 0.197 0.071 0.265 ------ 0.125 0.125 0.128 ------ 0.122 0.122 0.144 ------ ------

Density (g/cm3) 2.71 ------ 3.5 1.85 2.34 ------ 8.65 1.55 2.25 1.87 ------ 7.19 8.9 8.94 ------ 5.90 5.32 19.32 ------ ------

Crystal Structure FCC ------ BCC HCP Rhomb ------ HCP FCC Hex BCC ------ BCC HCP FCC ------ Ortho. Dia. cubic FCC ------ ------

Adapted fromTable, "Charac-teristics ofSelectedElements",inside frontcover,Callister 6e.

Characteristics of Selected Elements at 20C

ρmetals ρceramics ρpolymers

16

ρ (g

/cm

3)

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

1

2

20

30Based on data in Table B1, Callister

*GFRE, CFRE, & AFRE are Glass, Carbon, & Aramid Fiber-Reinforced Epoxy composites (values based on 60% volume fraction of aligned fibers

in an epoxy matrix). 10

3 4 5

0.3 0.4 0.5

Magnesium

Aluminum

Steels

Titanium

Cu,Ni

Tin, Zinc

Silver, Mo

Tantalum Gold, W Platinum

Graphite Silicon

Glass-soda Concrete

Si nitride Diamond Al oxide

Zirconia

HDPE, PS PP, LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE*

CFRE*

GFRE*

Glass fibers

Carbon fibers

Aramid fibers

Why? Metals have... • close-packing (metallic bonding) • large atomic mass Ceramics have... • less dense packing (covalent bonding) • often lighter elements Polymers have... • poor packing (often amorphous) • lighter elements (C,H,O) Composites have... • intermediate values Data from Table B1, Callister 6e.

DENSITIES OF MATERIAL CLASSES

17

• Some engineering applications require single crystals:

• Crystal properties reveal features of atomic structure.

(Courtesy P.M. Anderson)

--Ex: Certain crystal planes in quartz fracture more easily than others.

--diamond single crystals for abrasives

--turbine bladesFig. 8.30(c), Callister 6e.(Fig. 8.30(c) courtesyof Pratt and Whitney).(Courtesy Martin Deakins,

GE Superabrasives, Worthington, OH. Used with permission.)

CRYSTALS AS BUILDING BLOCKS

18

• Most engineering materials are polycrystals.

• Nb-Hf-W plate with an electron beam weld.• Each "grain" is a single crystal.• If crystals are randomly oriented, overall component properties are not directional.• Crystal sizes typ. range from 1 nm to 2 cm (i.e., from a few to millions of atomic layers).

Adapted from Fig. K, color inset pages of Callister 6e.(Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany)

1 mm

POLYCRYSTALS

19

• Single Crystals-Properties vary with direction: anisotropic.

-Example: the modulus of elasticity (E) in BCC iron:

• Polycrystals

-Properties may/may not vary with direction.-If grains are randomly oriented: isotropic. (Epoly iron = 210 GPa)-If grains are textured, anisotropic.

E (diagonal) = 273 GPa

E (edge) = 125 GPa

200 µm

Data from Table 3.3, Callister 6e.(Source of data is R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley and Sons, 1989.)

Adapted from Fig. 4.12(b), Callister 6e.(Fig. 4.12(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)

SINGLE VS POLYCRYSTALS

d=nλ/2sinθc

x-ray intensity (from detector)

θ

θc20

• Incoming X-rays diffract from crystal planes.

• Measurement of: Critical angles, θc, for X-rays provide atomic spacing, d.

Adapted from Fig. 3.2W, Callister 6e.

X-RAYS TO CONFIRM CRYSTAL STRUCTURE

reflections must be in phase to detect signal

spacing between planes

d

incoming

X-rays

outgoin

g X-ra

ys

detector

θλ

θextra distance travelled by wave “2”

“1”

“2”

“1”

“2”

21

• Atoms can be arranged and imaged!

Carbon monoxide molecules arranged on a platinum (111)

surface.

Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler. Reprinted with permission from International Business Machines Corporation, copyright 1995.

Iron atoms arranged on a copper (111)

surface. These Kanji characters

represent the word “atom”.

SCANNING TUNNELING MICROSCOPY

22

• Demonstrates "polymorphism" The same atoms can have more than one crystal structure.

DEMO: HEATING ANDCOOLING OF AN IRON WIRE

Temperature, C

BCC Stable

FCC Stable

914

1391

1536

shorter

longer!shorter!

longer

Tc 768 magnet falls off

BCC Stable

Liquid

heat up

cool down

• Atoms may assemble into crystalline or amorphous structures.

• We can predict the density of a material, provided we know the atomic weight, atomic radius, and crystal geometry (e.g., FCC, BCC, HCP).

• Material properties generally vary with single crystal orientation (i.e., they are anisotropic), but properties are generally non-directional (i.e., they are isotropic) in polycrystals with randomly oriented grains.

23

SUMMARY