Engineering Materials ME Chapt 2 10th Ed Aoh 20211004 [相容模式]

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Engineering MaterialsChapter 2

Atomic Structure and Interatomic bonding

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Prof. J.N. Aoh CCU ME 09.16.2021

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Bionics (also known as biomimicry, biomimetics, bio-inspiration, biognosis, and close to bionical creativity engineering) is the application of biological methods and systems found in nature to the study and design of engineering systems and modern technology

Geckos’ feet

Bionics

Chap. 2 Atomic Structure and Interatomic bonding

extremely fine hair

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Proceedings of the National Academy of Sciences of the United States of America (2008)

• Gecko tapes

Secret to the sticking of gecko’s toe to any surface:Van der Waal force betweenHair molecules and surface molecules.

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Atomic force microscope (AFM) reveals the gold atoms arrangement on the crystal surface.note the scale is in the nanometer (nm) range.

How large is a gold atom?

3 nm11 atoms

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Atomic Structure (Review on Freshman Chemistry)• Atom – electrons – 9.11 x 10-31 kg

protons – 1.67 x 10-27 kg neutrons (N)– 1.67 x 10-27 kg

• Atomic number Z= No. of protons in nucleus of atom= No. of electrons of neutral species

• A =atomic mass unit ( amu)原子質量單位= 1/12 atomic mass of 12C = 1.67 x 10-27 kg

A=Z+N

Atomic weight (atomic mass) = wt of 6.023 x 1023

molecules or atoms 1 amu/atom = 1g/mol

C 12.011H 1.008 etc.

}

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EXAMPLE PROBLEM 2.1Average Atomic Weight Computation for Cerium

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2.3 Electrons in Atoms• Electrons have wavelike and particulate properties —Duality .

– This means that electrons are in orbitals (軌域) defined by a probability.

– Each orbital at discrete energy level determined by quantum numbers.

• Bohr atom model and wave mechanical model

Bohr atom modelwave mechanical model

(a) The first 3 electron energy states for the Bohr Hydrogen

(b) The electron energy states for the first 3 shell of the wave-

mechanical Hydrogen atom

Bohr atom model

波粒二像性

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2.3 Electrons in AtomsQuantum Numbers DesignationN = principal (energy level-shell) K, L, M, N, O (N=1, 2, 3, etc.) size of an electrons orbital 主量子數相當於殼層L = subsidiary (orbitals) s, p, d, f (correspond to 0, 1, 2, 3,…, n -1)s=0, p=1, d=2, f=3, g=4…..subshell次量子數表示亞層 (determines angular momentum)Ml = magnetic 1, 3, 5, 7 (- L to + L) 原子軌域的伸展方向Ms = spin +½, -½

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Quantum numbers n, l, mland No. of electrons

L

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Subsidiary quantum number or azimuth (角) quantum number

• s, p, d, f represent orbitals

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Each orbital contains max. 2 electrons.

s1, s2

m l = 0

S- orbitals, l=1

1S2S

Sphere

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p- orbitals, l=1


Each orbital contains max. 2 electrons.p1 …p6 m l = -1, 0, +1

dumbbelm l = -1 m l = +1 m l = 0

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d- orbitals, l= 2



d1 …d10ml = -2, -1, 0, +1, +2

m l = +1 m l = +2

m l = -2

m l = 0

m l = -1

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f- orbitals



f1 …f14

ml = -3, -2, -1, 0, +1, +2, +3

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Electron Energy States

1s

2s2p

K-shell n = 1

L-shell n = 2

3s3p

M-shell n = 3

3d

4s

4p4d

Energy

N-shell n = 4

ml

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Electron Energy States

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1

2

3

4

5

6

7

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Energy level sequence of s, p, d, f


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

• Most elements: Electron configuration not stable.

SURVEY OF ELEMENTS

Electron configuration

(stable)

...

... 1s22s22p 63s23p 6 (stable)... 1s22s22p 63s23p 63d 10 4s24p 6 (stable)

Atomic #

18...36

Element1s11Hydrogen1s22Helium1s22s13Lithium1s22s24Beryllium1s22s22p 15Boron1s22s22p 26Carbon

...1s22s22p 6 (stable)10Neon1s22s22p 63s111Sodium1s22s22p 63s212Magnesium1s22s22p 63s23p 113Aluminum

...Argon...Krypton

Adapted from Table 2.2, Callister 7e.

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Electron Configurations• Pauli exclusion principle

– it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers.

– Quantum numbers are unique for each electron.

• Valence electrons– those in unfilled shells

• Filled shells more stable• Valence electrons are most available for

bonding and tend to control the chemical properties

• Example: C (z= 6)1s2 2s2 2p2

valence electrons

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Electronic Configurationsex: Fe - atomic # = 26

valence electrons

Adapted from Fig. 2.4, Callister 7e.

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 3d6 4s2

ms= ± 1/2

Fill +1/2 first!!

ms= ± 1/2

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• What is 4s2 ?

• principal Q-no. n =

• azimuth Q-no.4s l =

• magnetic Q-no. ml= 0

• spin Q-no. ms= +1/2

• n, l, ml , ms are unique for each electron.


Electronic Configurations

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• What is 5f 13 ?

• principal Q-no. n =

• azimuth Q-no. 5f l =

• magnetic Q-no. ml = -3 -2 -1 0 +1 +2 +3

• __ __ __ __ __ __ __

• spin Q-no. ms =


Electronic Configurations

-1/2

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Example: Al (z= 13)

• 1s 2s 2p 3s 3p


l=0 l=1 l=2 l=3

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Example: Fe+2 (z= 26-2)


l=0 l=1 l=2 l=3

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From electron configurations to periodic table


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The Periodic Table

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• Columns: Similar Valence Structure

Electropositive elements: Readily give up electrons to become + ions. (Cation)

Electronegative elements: Readily acquire electrons to become - ions. (Anion)

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


THE PERIODIC TABLE

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• Ranges from 0.9 to 4.1,

Smaller electronegativity Larger electronegativity

• 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 Cornell University.

ELECTRONEGATIVITY

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ELECTRONEGATIVITY

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2.5 Bonding Force and Energy

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Bonding Force and Energy

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• Ionic Bonding• Covalent Bonding• Metallic Bonding

2.6 PRIMARY INTERATOMIC BONDS

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Ionic bond – metal + nonmetal

donates acceptselectrons electrons

Dissimilar electronegativities

ex: MgO Mg 1s2 2s2 2p6 3s2 O 1s2 2s2 2p4

[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

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Na (metal) unstable

Cl (nonmetal) unstable

electron

+ - Coulombic Attraction

Na (cation) stable

Cl (anion) stable

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

IONIC BONDING

• The bonding force is Coulumbic attraction.• The ionic bonding is nondirectional.

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No touch!

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• Predominant bonding in Ceramics

Examples of Ionic Bonding

Give up electrons Acquire electrons

NaClMgOCaF2CsCl

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Ionic Bonding

• Energy – minimum energy most stable– Energy balance of attractive and repulsive terms

Attractive energy EA

Net energy EN

Repulsive energy ER

Interatomic separation r

rA

nrBEN = EA + ER = −−

Adapted from Fig. 2.8(b), Callister 7e.

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table_02_03

Bonding Energies

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Example problems 2-2Calculate FA & FRbetween two ions

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Each H: has 1 valence e-,needs 1 more

Electronegativitiesare the same.

Fig. 2.12, Callister & Rethwisch 9e.

Covalent Bonding

• similar electronegativity ∴ share electrons• bonds determined by valence – s & p orbitals

dominate bonding• Example: H2

shared 1s electronfrom 2nd hydrogen atom

H

H2

shared 1s electronfrom 1st hydrogen atom

H

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• Requires shared electrons• Example: CH4

☺C: has 4 valence e, needs 4 more

☺ H: has 1 valence e, needs 1 more

☺ Electronegativities are comparable.

COVALENT BONDING

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• Molecules with nonmetals (e.g., F2, Cl2)• Molecules with metals and nonmetals (e.g., H20, CH4) • Elemental solids (RHS of Periodic Table, e.g., Ge, Si) • Compound solids (about column IVA, 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

co

lum

n IV

A

Sn 1.8Pb 1.8

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 Cornell University.

EXAMPLES: COVALENT BONDING

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Bond Hybrization in Carbon

• Carbon can form s1p3

hybrid orbitals = s+p+p+p

Fig. 2.13, Callister & Rethwisch 9e.Fig. 2.14, Callister & Rethwisch 9e. (Adapted from J.E. Brady and F. Senese, Chemistry: Matter and Its Changes, 4th edition. Reprinted with permission of John Wiley and Sons, Inc.)

hybridization is the concept of mixing atomic orbitals into new hybrid orbitals (with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to form chemical bonds in valence bond theory

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C = 1s2 2s2 2p2

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Hybridization of Carbon

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Covalent Bonding: Carbon sp3

• Example: CH4

C: has 4 valence e-,needs 4 more

H: has 1 valence e-,needs 1 more

Electronegativities of C and Hare comparable so electrons are shared in covalent bonds.

Fig. 2.15, Callister & Rethwisch 9e.(Adapted from J.E. Brady and F. Senese, Chemistry: Matter and Its Changes, 4th edition. Reprinted with permission of John Wiley and Sons, Inc.)

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Formation of sp2 hybrid orbitals in Carbon

Fig_02_17

Fig_02_18

2s2p2

2sp3

2sp2

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Formation of sp2 + p hybrid orbitals in Carbon

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σ-bond and π-bond

• Single bond and double bond

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

• Primary bond for metals and their alloys

METALLIC BONDING

Fig_02_19

Metallic Bond -- delocalized as electron cloud

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SECONDARY BONDING OR VAN DER WAALS BONDINGSecondary bonding arises from atomic or moleculardipoles. Hydrogen bonding is a special example.

•FLUCTUATING INDUCED DIPOLE BONDS

•POLAR MOLECULE-INDUCED DIPOLE BONDS

•PERMANENT DIPOLE BONDS

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FLUCTUATING INDUCED DIPOLE BONDS

SECONDARY BONDING

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POLAR MOLECULE-INDUCED DIPOLE BONDS

SECONDARY BONDING

Fig_02_22b

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• Van der Waal and hydrogen bonding

SECONDARY BONDINGPERMANENT DIPOLE BONDS

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The arrangement of water molecules• (a) solid ice

Relatively open structure

• (b) liquid water

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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




SECONDARY BONDING

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Primary Bonding – mixed bonding

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• Metallic Bond -- delocalized as electron cloud

• Ionic-Covalent Mixed Bonding

% ionic character (IC) =

where XA & XB are Pauling electronegativities

%)100(x

Ex: MgO XMg = 1.3XO = 3.5

Ex. 2.3: %IC of C-H bond=3.9%CCU ME Aoh

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• Metallic Bond -- delocalized as electron cloud

• Ionic-Covalent Mixed Bonding

% ionic character (IC) =

where XA & XB are Pauling electronegativities

%)100(x

ionic 3.9% (100%) x e1 character ionic % 4)1.25.2(

2

=

−=−−

Ex. 2.3: %IC C & H XC = 2.5XH = 2.1

%IC of C-H bond=3.9% covalent bondingCCU ME Aoh

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TypeIonic

Covalent

Metallic

Secondary

Bond EnergyLarge!

Variable large-Diamond small-Bismuth

Variable large-Tungsten small-Mercury

smallest

CommentsNondirectional (ceramics)

Directional semiconductors, ceramics

polymer chains)

Nondirectional (metals)

Directional inter-chain (polymer)

inter-molecular

SUMMARY: BONDING

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• Bond length, r

• Bond energy, Eo

F F

r

• Melting Temperature, Tm

Eo=

ond 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

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• Elastic modulus, E

• E ~ curvature at ro

cross sectional area Ao

ΔL

length, Lo

F

undeformed

deformed

ΔL 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

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Ceramics(Ionic & covalent bonding):

Metals(Metallic bonding):

Polymers(Covalent & Secondary):

secondary bonding

Large bond energy large Tm

large E small α

Variable bond energy moderate Tm

moderate E moderate α

Directional Properties Secondary bonding dominates

small Tmsmall E large α

SUMMARY: PRIMARY & SECONDARY BONDS

Engineering Materials ME Chapt 2 10th Ed Aoh 20211004 [相容模式]

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