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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
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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
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Each orbital contains max. 2 electrons.
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
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Each orbital contains max. 2 electrons.
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.
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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 =
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Electronic Configurations
-1/2
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Example: Al (z= 13)
• 1s 2s 2p 3s 3p
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l=0 l=1 l=2 l=3
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Example: Fe+2 (z= 26-2)
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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
Adapted from Fig. 2.6, Callister 6e.
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
Adapted from Fig. 2.13, Callister 6e.
Adapted from Fig. 2.14, Callister 6e.
Adapted from Fig. 2.14, Callister 6e.
SECONDARY BONDING
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Primary Bonding – mixed bonding
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Primary Bonding – mixed bonding
• 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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Primary Bonding – mixed bonding
• 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