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Chapter 2-
Atoms are made of protons, neutrons andelectrons
me=0.00091094x10-27= 9.1094x10-31kg = 0.511MeV
mp= 1.6726 x 10-27kg = 938.272 MeV
mn= 1.6749 x 10-27kg = 939.566 MeV =
mn= mp+ 1.293 MeV
proton & electron charge 1.6022 x 10-19C Howeverpare +ve and eareve
Atomic number (Z) describes the number ofprotons in the nucleus
Atomic mass (A) of an element isapproximately equal to the number of neutronsand protons the element has
Remember elements have isotopeselements canhave different numbers of neutrons (e.g. 12C, 13C,14C)
Atomic weight is the weighted average of theelement based on the relative amounts of itsisotopes (e.g. 1 mol/carbon = 12.0107 g/mol,NOT 12 g/mol!)
Basic concepts
Chapter 2-
Fundamental Concept
Atomic Weight
Weighted average of the atomic masses of an atom's
naturally occurring isotopes Atomic Mass Unit (amu)
Measure of atomic mass
1/12 the mass of C12atom
Mole
Quantity of a substance corresponding to 6.022X1023atoms
or molecules
1 amu/ atom (or molecule) = 1g/mol
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Chapter 2-
How many grams are there in one amu of a material?
The two major isotopes of carbon:
98.93% of 12C with an atomic weight of 12.00000 amu, and
1.07% of 13C with an atomic weight of 13.00335 amu.
Confirm that the average atomic weight of C is 12.011 amu.
Sum the product of the isotope atomic weight and the percent abundance.
(12 amu)*(.9893)+(13.00335 amu)*(.0107) = 12.011 amu
Examples
Chapter 2-
Electrons In Atoms
Bohr Atomic Model (old view)
Early outgrowth of
quantum mechanics
Electrons revolve aroundnucleus in discrete orbitals
Electrons closer to nucleus
travel faster then outer
orbitals
Principal quantum number
(n); 1stshell, n=1; 2ndshell,
n=2; 3rdshell, n=3
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Chapter 2-
c02f02
Quantum NumbersHydrogen atom
Chapter 2-
c02f03
Bohr AtomWave-mechanical atom
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Chapter 2-
Atomic Models
Wave-Mechanical
Model
Electron exhibits bothwave-like and particle-like
characteristics
Position is now considered
to be the probability of an
electron being at various
locations around the
nucleus, forming an
electron cloud
Chapter 2-
Atomic ModelsQuantum numbers
The size, shape, and spatial orientation of an
electrons probability density are specified by
three of these quantum numbers.
Principal quantum number n, represents a
shell
K, L, M, N, O correspond to n=1, 2, 3, 4,
5....
Quantum number l, signifies the subshell
Lowercase italicsletters, p, d, f; related to
the shape of the subshell
Quantum number ml, represents the
number of energy state
s, p, d, f have 1, 3, 5, 7 states respectively
Quantum number ms, is the spin moment
Each electron is a spin moment (either up
or down)
(+1/2) and (-1/2)
Each state can hold no more than 2
electrons which must have opposite spins
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Chapter 2-
Electron Configuration
Electron configuration
represents the manner in
which the states areoccupied
Valence electrons
Occupy the outermost
shell
Available for bonding
Tend to control chemical
properties
Ex. Silicon (Si)
Chapter 2-
Energy
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Chapter 2-
c02tf02
When some elements covalently
bond, they formsphybrid bonds,
e.g., C, Si, Ge
Chapter 2-
Examples
Give the electron configurations for the following:C
1s2 2s2 2p2
Br1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5
Mn+2
1s2 2s2 2p6 3s2 3p6 3d5
F-
1s2 2s2 2p6
Cr
1s2 2s2 2p6 3s2 3p6 4s1 3d5
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Chapter 2 - 15
Electronic Structure Electrons have wave-like and particle-like (old view)
properties.
We can better say that the wave-particle nature is the real
thing; individual wave and particle states are limiting cases;usually observed in measurements (collapse of the wave
function) To better understand electronic structure, we assume
Electrons reside in orbitals.
Each orbital at discrete energy level is determined by
quantum numbers.c
Quantum # Designation
n= principal (energy level-shell) K, L, M, N, O (1, 2, 3, etc.)
l= angular (orbitals) s,p, d, f (0, 1, 2, 3,, n-1)
ml= magnetic 1, 3, 5, 7 (-lto +l)
ms= spin , -Chapter 2 - 16
Electron Configurations
Valence electronsthose in unfilled shells
Filled shells more stable
Valence electrons are most available for
bonding and tend to control the chemicalproperties
example: C (atomic number = 6)
1s2 2s22p2
valence electrons
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Chapter 2 - 17
Electronic Configurationsex: Fe - atomic # = 26
valence
electrons
Adapted from Fig. 2.4,Callister & Rethwisch 3e.
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 3s23p6 3d6 4s2
Chapter 2-
Periodic Table
Elements classified according to electron configuration
Elements in a given column or group have similar valence electron
structures as well as chemical and physical properties
Group 0inert gases, filled shells and stable
Group VIIA halogen
Group IA and IIA - alkali and alkaline earth metals
Groups IIIB and IIB transition metals
Groups IIIA, IVA and VAcharacteristics between the metals and
nonmetals
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Chapter 2-19
The Periodic Table Columns: Similar ValenceStructure
Adapted fromFig. 2.6,Callister &
Rethwisch 8e.
Electropositive elements:Readily give up electronsto become + ions.
Electronegative elements:Readily acquire electronsto become - ions.
give
up
1e-
gi
ve
up
2e-
give
up
3e-
inertgases
ac
cept1e-
ac
cept2e-
O
Se
Te
Po At
I
Br
He
Ne
Ar
Kr
Xe
Rn
F
ClS
Li Be
H
Na Mg
BaCs
RaFr
CaK Sc
SrRb Y
Chapter 2 - 20
Atomic Bonding
Valence electrons determine all of the
following properties
1) Chemical2) Electrical
3) Thermal
4) Optical
5) Deteriorative
6) etc.
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Chapter 2-
tomic Bonding in Solids
Chapter 2-
Bonding in Solids
Bonding forces and energies
Far apart: atoms dont know about each other
As they approach one another, exert force on one another
Forces are Attractive (FA)slowly changing with distance
Repulsive (FR)typically short-range
Net force is the sum of these
FN= FA+ FR
At some point the net force is zero; at that position a state of
equilibrium exists
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Chapter 2-
Bonding Forces and
Energies
FN= FA+
FR
EN= EA+
ER
When 0 = FA+ FR,
equilibrium exists.
The centers of theatoms will remain
separated by the
equilibrium spacing
ro.
This spacing also
corresponds to the
minimum of the
potential energycurve. The energy
that would be
required to
separate two
atoms to an infiniteseparation is Eo
Figure 2.8
Chapter 2-
Bonding in Solids
Bonding forces and energies We are more accustomed to thinking in terms of potential energy
instead of forces in that case
RAN
r
R
r
AN
EEE
drFdrFE
The point where the forces are zero also corresponds to the minimumpotential energy for the two atoms (i.e. the trough in Figure 2.8), whichmakes sense because dE/dr = F =0 at a minimum.
The interatomic separation at that point (ro) corresponds to the potentialenergy at that minimum (Eo,it is also the bonding energy) The physical interpretation is that it is the energy needed to separate the atoms
infinitely far apart
FdrE
Setting our ZERO ENERGY reference at infinite
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Chapter 2-
Bonding Forces and Energies
A number of material properties depend on Eo,
the curve shape, and bonding type
Material with large Eotypically have higher melting
points
Mechanical stiffness is dependent on the shape of its
force vs. interatomic separation curve
A materials linear coefficient of thermal expansion
is related to the shapeof its Eovs. rocurve
Chapter 2-
ExamplesCalculate the force of attraction between ions X+and an Y-, the
centers of which are separated by a distance of 2.01 nm.
&
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Chapter 2-
Types of primary bonds found in solids
Ionic
Covalent
Metallic
As you might imagine, the type of bonding influences
propertieswhy?
Bonding involves the valence electrons!!!
Primary Interatomic Bonds
Chapter 2 - 28
Occurs between + and - ions.
Requires electron transfer.
Large difference in electronegativity required.
Example: NaCl
Ionic Bonding
Na (metal)unstable
Cl (nonmetal)unstable
electron
+ -CoulombicAttraction
Na (cation)stable
Cl (anion)stable
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Chapter 2 - 29
Ionic bond: metal + nonmetal
donates accepts
electrons electrons
Dissimilar electronegativities
ex: MgO Mg 1s22s22p63s2 O 1s22s22p4
[Ne] 3s2
Mg2+ 1s22s22p6 O2- 1s22s22p6
[Ne] [Ne]
Chapter 2-
Primary Interatomic Bonds
Ionic bonding Sodium chloride (NaCl)
Sodium gives up one its electrons to chlorine sodium becomespositively charged, chlorine becomes negatively charged
The attraction energy is electrostaticin nature in ionic solids
(opposite charges attract) The attractive component of the potential energy (for 2 point
charges) is given by
r
eZeZE
o
A
1
4
21
The repulsive term is given by
128~, nr
BE
nR
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Chapter 2-
c02f09
Primary Interatomic Bonds
Chapter 2-
IONIC BONDING
Ionic bonding is non-directional magnitude of the bond is equal in
all directions around the ion
Many ceramics have an ionic bonding characteristic
Bonding energies typically in the range of 6001500 kJ/mol
Often hard, brittle materials, and generally insulators
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Chapter 2 - 33
Ionic Bonding
Energyminimum energy most stable
Energy balance of attractiveand repulsiveterms
Attractive energy EA
Net energy EN
Repulsive energy ER
Interatomic separation r
r
A
nr
BE
N= E
A+ E
R=
Adapted from Fig. 2.8(b),Callister & Rethwisch 3e.
Chapter 2 - 34
Predominant bonding in Ceramics
Adapted from Fig. 2.7, Callister & Rethwisch 3e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of theChemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.
Examples: Ionic Bonding
Give up electrons Acquire electrons
NaCl
MgO
CaF2CsCl
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Chapter 2-
Covalent bonding
Sharing of electrons between adjacent atoms
Most nonmetallic elements and molecules containing
dissimilar elements have covalent bonds
Polymers!
Bonding is highly directional! : between specific atomsand may exist only in the direction between one atom
and another that participates in electron sharing
Number of covalent bonds possible is guessed by the
number of valence electrons
Typically is 8N, where N is the number of valence
electrons
Carbon has 4 valence es 4 bonds (ok!)
Chapter 2 - 36
C: has 4 valence e-,
needs 4 more
H: has 1 valence e-,
needs 1 more
Electronegativities
are comparable.
Adapted from Fig. 2.10, Callister & Rethwisch 3e.
Covalent Bonding similar electronegativityshare electrons
bonds determined by valences&porbitals
dominate bonding
Example: CH4
shared electronsfrom carbon atom
shared electronsfrom hydrogenatoms
H
H
H
H
C
CH4
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Chapter 2- 11
Molecules with nonmetals Molecules with metals andnonmetals Elemental solids (RHS of Periodic Table) Compound solids (about column IVA)
He-
Ne-
Ar-
Kr-
Xe-
Rn-
F4.0
Cl3.0
Br2.8
I2.5
At2.2
Li1.0
Na0.9
K0.8
Rb0.8
Cs0.7
Fr0.7
H2.1
Be1.5
Mg1.2
Ca1.0
Sr1.0
Ba0.9
Ra0.9
Ti1.5
Cr1.6
Fe1.8
Ni1.8
Zn1.8
As2.0
SiC
C(diamond)
H2O
C2.5
H2
Cl2
F2
Si1.8
Ga1.6
GaAs
Ge1.8
O2.0
columnIVA
Sn1.8
Pb1.8
Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 isadapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.
EXAMPLES: COVALENT BONDING
Chapter 2-
Bonding in Solids
Many materials have bonding that is both ionic andcovalent in nature (very few materials actually exhibit pure
ionic or covalent bonding)
Easy (empirical) way to estimate % of ionic bondingcharacter:
XA, XBare the electronegativities of atomsA and Binvolved
100x))(25.0(exp1characterionic% 2BA
XX
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Chapter 2-
Primary Interatomic Bonds Metallic Bonding
Found in metals and their alloys
1 to 3 valence electrons that form asea of electrons or an electroncloud because they are more orless free to drift through the entiremetal
Nonvalence electrons and atomicnuclei form ion cores
Bonding energies range from weakto strong
Good conductor of both electricityand heat
Most metals and their alloys fail ina ductile manner
Ion
Cores
Sea of Valence
Electrons
+
+
+
+
+
+
+
+
+
- -
- -
Chapter 2-
Bonding in Solids
Metallic bonding
Most metals have one, two, or at most three valence electrons
These electrons are highly delocalized from a specific atomhavea sea of valence electrons
Free electrons shield positive core ofions from one another (reduce ER)
Metallic bonding is also non-
directional
Free electrons also act to holdstructure together
Wide range of bonding energies,typically good conductors (why?)
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Chapter 2 -
Secondary Bonding or van der
Walls Bonding Also known as physical bonds
Weak in comparison to primary or chemical
bonds Exist between virtually all atoms and molecules
Arise from atomic or molecular dipoles
bonding that results from the coulombic attraction
between the positive end of one dipole and the
negative region of an adjacent one
a dipole may be created or induced in an atom or
molecule that is normally electrically symmetricChapter 2 -
Secondary Bonding or van der
Waals Bonding Fluctuating Induced Dipole Bonds
A dipole (whether induced or instantaneous)
produces a displacement of the electron distribution
of an adjacent molecule or atom and continues as a
chain effect
Liquefaction and solidification of inert gases
Weakest Bonds
Extremely low boiling and melting pointAtomic nucleus
Atomic nucleus
Electron
cloud
Electron
cloud
Instantaneous
Fluctuation
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Chapter 2 -
Secondary Bonding or van der Waals Bonding
Polar Molecule-Induced Dipole Bonds
Permanent dipole moments exist by virtue of an
asymmetrical arrangement of positively and negatively
charged regions
Polar molecules can induce dipoles in adjacent nonpolar
molecules
Magnitude of bond greater than for fluctuating induced
dipoles
+ -
Polar
Molecule
Induced
Dipole
Atomic nucleus
Electron Cloud
Chapter 2 -
Secondary Bonding or van der
Waals Bonding Permanent Dipole Bonds
Stronger than any secondary bonding with induced
dipoles
A special case of this is hydrogen bonding: existsbetween molecules that have hydrogen as one of the
constituents
H Cl H Cl
Hydrogen Bond
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Chapter 2-
c02tf03
Chapter 2-
c02f16
Many molecules do not have asymmetric distribution/arrangementof positive and negative charges(e.g. H2O, HCl)
MATERIAL OF IMPORTANCE
Water
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Chapter 2-
c02uf01
Chapter 2 - 48
Bond length, r
Bond energy, Eo
Melting Temperature, Tm
Tmis larger if Eois larger.
Properties From Bonding: Tm
ror
Energy
r
larger Tm
smaller Tm
Eo =
bond energy
Energy
ro r
unstretched length
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Chapter 2 - 49
Coefficient of thermal expansion, a
a~ symmetric at ro
ais larger if Eois smaller.
Properties From Bonding : a
= a (T2-T1)DL
Lo
coeff. thermal expansion
DL
length, Lo
unheated, T1
heated, T2
ror
smaller a
larger a
Energy
unstretched length
Eo
Eo
Chapter 2- 16
Elastic modulus, E
DLFAo
= ELo
Elastic modulus
PROPERTIES FROM BONDING: E
E ~ dF/dr|ro elastic modulus
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Chapter 2 - 51
Ceramics
(Ionic & covalent bonding):
Large bond energylarge Tmlarge E
small a
Metals(Metallic bonding): Variable bond energymoderate Tmmoderate E
moderate a
Summary: Primary Bonds
Polymers(Covalent & Secondary):
Directional PropertiesSecondary bonding dominates
small Tmsmall Elarge a
Chapter 2 - 52
Type
Ionic
Covalent
Metallic
Secondary
Bond Energy
Large!
Variablelarge-Diamondsmall-Bismuth
Variablelarge-Tungstensmall-Mercury
smallest
Comments
Nondirectional (ceramics)
Directional(semiconductors, ceramicspolymer chains)
Nondirectional (metals)
Directional
inter-chain (polymer)inter-molecular
Summary: Bonding