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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?
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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
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Discontinuous emission spectra cannot be understood.
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Bohr’s Model
To resolve the discontinuous emission spectra...
Assumptions : Quantum conditionFrequency condition
Bohr, Niels (1885-1962)
electron
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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
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Atomic mass A = Z + N
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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
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1 amu/atom (or molecule) = 1 g/mol
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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 ...
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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
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a probability distribution or electron cloud.
into electron sub-shellsdescribed by quantum numbers.
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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
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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 ...
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Eψ ψΗ = 228
hm
φπ
Η = − ∇ +where
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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
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3. Zero-point energy, cf. Heisenberg uncertainty principle
4. Suitable in describing small mass in small space, e.g. electrons in atom
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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
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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
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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
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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.
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Meaning of quantum numbers
n determines the size
l determines the shape
3s2 3p6 3d10
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3s 3p 3d
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Atomic structure of sodium (Na)
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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
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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)
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Why? Valence (outer) shell usually not filled completely
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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:
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Readily give up electrons
to become + ions.
Electronegative elements:Readily acquire electrons
to become - ions.
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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
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Smaller electronegativity Larger electronegativity
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Bonding
Primary bondingIonic bonding
l b dCovalent bonding
Metallic bondingg
Secondary bonding d W lvan der Waals
Hydrogen bonding
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y g g
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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
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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+ - + -
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-ex: liquid HCl H Cl H Clsecondary bonding
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Bonding
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Bonding (Table 2-3)
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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
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e e
eee
belonging to neighbor atoms.
Covalent bonding
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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
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p f f pp gIonic bonding
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Bonding Forces & Energies(Fig. 2-8)
ForceForce
EnergyEnergy
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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
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Tm is larger if Eo is larger.gy
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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
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Properties from Bonding: α
Thermal expansion asymmetric nature of the energy wellp y gyBroad well (generally more asymmetric) larger expansion
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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
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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
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Give up electrons Acquire electrons
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Ionic Crystal(Fig. 2-9)
ClNa
Each positive ion is surrounded by several negative ions and
vice versa.
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When voltage is applied to an ionic material, entire ions must move to cause a current to flow Ion movement is slow and
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move to cause a current to flow. Ion movement is slow and the electrical conductivity is poor.
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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
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must be formed.
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Covalent Bonding
The tetrahedral structure of silica (Si02) contains
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The tetrahedral structure of silica (Si02) contains
covalent bonds between silicon and oxygen atoms.
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Covalent Bonding
Covalent bonds are directional. In silicon, a tetrahedral structure is formed with angles of 109 5° required between each
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structure is formed, with angles of 109.5 required between each covalent bond.
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Covalent Bonding Electron sharing
Directional
CH4Cl2 CH4Cl2
SiO 2diamondSiO4
2-
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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
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elemental solids
compound solidsStrong directional nature of bonding
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Ionic vs. Covalent Bonding
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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
+ + +
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Primary bond for metals and their alloys.
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Metallic Bonding delocalized electron
Free electrons act as a
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“glue” to hold the ion core.
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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.
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electrons.
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Metallic Bonding
When voltage is applied to a metal, the electrons in the
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When voltage is applied to a metal, the electrons in the electron sea can easily move and carry a current.
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Metallic BondingMechanical properties
brittlebrittle
ductile
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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
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Van der Waals Bonding
Induced dipole Permanent dipole(polar molecule)(polar molecule)
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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
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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.
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Hydrogen Bonding
H2O Ice
open structureopen structure- lower density
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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
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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
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Types of Adsorption Modes
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http://bp.snu.ac.kr
- 2009-09-16