Chapter 2: Atomic
Structure and Interatomic
Bonding (updated)
These notes have been prepared by Jorge Seminario from the textbook material
Chapter 2 - 1
ISSUES TO ADDRESS...
• What promotes bonding?
• What types of bonds are there?
• What properties are inferred from bonding?
Chapter 2 - 2
Basic concepts
– Atoms are made of protons, neutrons and
electrons
•
•
•
•
me=0.00091094x10-27= 9.1094x10-31kg = 0.511MeV
mp = 1.6726 x 10-27 kg = 938.272 MeV
mn = 1.6749 x 10-27 kg = 939.566 MeV =
mn = mp + 1.293 MeV
• proton & electron charge 1.6022 x 10-19 C
• However p are +’ve and e are –’ve
– Atomic number (Z) describes the number of
protons in the nucleus
– Atomic mass (A) of an element is
approximately equal to the number of neutrons
and protons the element has
• Remember elements have isotopes – elements can
have different numbers of neutrons (e.g. 12C, 13C,
14C)
– Atomic weight is the weighted average of the
element based on the relative amounts of its
isotopes (e.g. 1 mol/carbon = 12.0107 g/mol,
NOT 12 g/mol!)
Chapter 2-
2.2 Fundamental Concept

Atomic Weight


Atomic Mass Unit (amu)



Weighted average of the atomic masses of an atom's
naturally occurring isotopes
Measure of atomic mass
1/12 the mass of C12 atom
Mole


Quantity of a substance corresponding to 6.022X1023 atoms
or molecules
1 amu/ atom (or molecule) = 1g/mol
Chapter 2-
Examples
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
Chapter 2-
2.3 Electrons In Atoms
Bohr Atomic Model (old view)




Early outgrowth of
quantum mechanics
Electrons revolve around
nucleus in discrete orbitals
Electrons closer to nucleus
travel faster then outer
orbitals
Principal quantum number
(n); 1st shell, n=1; 2nd shell,
n=2; 3rd shell, n=3
Chapter 2-
Quantum Numbers—Hydrogen atom
Chapter 2c02f02
Bohr Atom
Wave-mechanical atom
c02f03
Chapter 2-
Atomic Models

Wave-Mechanical
Model


Electron exhibits both
wave-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 Models
Quantum numbers

Principal quantum number n, represents a
shell


Quantum number l, signifies the subshell


Lowercase italics letter s, p, d, f; related to
the shape of the subshell
Quantum number ml , represents the
number of energy state


K, L, M, N, O correspond to n=1, 2, 3, 4,
5....
s, p, d, f have 1, 3, 5, 7 states respectively
Quantum number ms, is the spin moment


Each electron is a spin moment
(+1/2) and (-1/2)
Chapter 2-
Electron Configuration


Electron configuration
represents the manner in
which the states are
occupied
Valence electrons




Occupy the outermost
shell
Available for bonding
Tend to control chemical
properties
Ex. Silicon (Si)
Chapter 2-
Energy
Chapter 2-
When some elements covalently
bond, they form sp hybrid bonds,
e.g., C, Si, Ge
c02tf02
Chapter 2-
Examples
Give the electron configurations for the following:
C
1s2 2s2 2p2
Br
1s2 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
Chapter 2-
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)
l = angular (orbitals)
ml = magnetic
K, L, M, N, O (1, 2, 3, etc.)
s, p, d, f (0, 1, 2, 3,…, n-1)
1, 3, 5, 7 (-l to +l)
ms = spin
½, -½
Chapter 2 - 15
Electron Configurations
• 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 (atomic number = 6)
1s2 2s2 2p2
valence electrons
Chapter 2 - 16
Electronic Configurations
ex: Fe - atomic # = 26 1s2 2s2 2p6 3s2 3p6 3d 6 4s2
4d
4p
N-shell n = 4 valence
electrons
3d
4s
Energy
3p
3s
M-shell n = 3
Adapted from Fig. 2.4,
Callister & Rethwisch 3e.
2p
2s
L-shell n = 2
1s
K-shell n = 1
Chapter 2 - 17
2.4 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 0 – inert 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 VA – characteristics between the metals and
nonmetals
Chapter 2-
2.4
Chapter 2-
Atomic Bonding
• Valence electrons determine all of the
following properties
1)
2)
3)
4)
5)
6)
Chemical
Electrical
Thermal
Optical
Deteriorative
etc.
Chapter 2 - 20
Atomic Bonding in Solids
Chapter 2-
When 0 = FA + FR,
equilibrium exists.
The centers of the
atoms will remain
separated by the
equilibrium spacing
r o.
This spacing also
corresponds to the
minimum of the
potential energy
curve. The energy
that would be
required to
separate two
atoms to an infinite
separation is Eo
2.5 Bonding Forces and
Energies
FN = FA +
FR
Figure 2.8
EN = E A +
ER
Chapter 2-
2.5 Bonding Forces and Energies
• A number of material properties depend on Eo,
the curve shape, and bonding type
– Material with large Eo typically have higher melting
points
– Mechanical stiffness is dependent on the shape of its
force vs. interatomic separation curve
– A material’s linear coefficient of thermal expansion
is related to the shapeof its Eo vs. ro curve
Chapter 2-
Bonding in Solids
• 2.5 Bonding forces and energies
– Far apart: atoms don’t 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
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
E   Fdr
Setting our ZERO ENERGY reference at infinite
r
r


E N   FA dr   FR dr
E N  E A  ER
•
The point where the forces are zero also corresponds to the minimum
potential energy for the two atoms (i.e. the trough in Figure 2.8), which
makes sense because dE/dr = F =0 at a minimum.
•
The interatomic separation at that point (ro) corresponds to the potential
energy at that minimum (Eo, it is also the bonding energy)
•
The physical interpretation is that it is the energy needed to separate the atoms
Chapter 2infinitely far apart
Examples
Calculate the force of attraction between ions X+ and an Y-, the
centers of which are separated by a distance of 2.01 nm.
&
Chapter 2-
2.6 Primary Interatomic Bonds
• Types of chemical bonds found in solids
– Ionic
– Covalent
– Metallic
• As you might imagine, the type of bonding influences
properties – why?
• Bonding involves the valence electrons!!!
Chapter 2-
2.6 Primary Interatomic Bonds
• Ionic Bonding
– Compounds composed of metallic and nonmetallic
elements
– Coulombic Attractive Forces: positive and negative ions,
by virtue of their net electrical charge, attract one another
• EA = -A/r
• ER = -B/rn
Coulombic bonding Force
A, B, and
Cl
Na
n are
constants the magnitude of the bond is
– Bonding is nondirectional:
+
equal in all directions around an ion
– Properties: generally large bonding energies (600-1500
kJ/mol) and thus high melting temperatures, hard, brittle,
and electrically and thermally insulative
Chapter 2-
2.6 Primary Interatomic Bonds
Chapter 2c02f09
2.6 Primary Interatomic Bonds
• Ionic bonding
– Prototype example – sodium chloride (NaCl)
• Sodium gives up one its electrons to chlorine – sodium becomes
positively charged, chlorine becomes negatively charged
– The attraction energy is electrostatic in nature in ionic solids
(opposite charges attract)
– The attractive component of the potential energy (for 2 point
charges) is given by
EA 
 Z1eZ 2e 1

4 o
r
– The repulsive term is given by
B
ER  n , n ~ 8  12
r
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 600 – 1500 kJ/mol
– Often hard, brittle materials, and generally insulators
Chapter 2-
Ionic bond:
metal
+
donates
electrons
nonmetal
accepts
electrons
Dissimilar electronegativities
ex: MgO
Mg
1s2 2s2 2p6 3s2
[Ne] 3s2
Mg2+ 1s2 2s2 2p6
[Ne]
O
1s2 2s2 2p4
O2- 1s2 2s2 2p6
[Ne]
Chapter 2 - 32
•
•
•
•
Ionic Bonding
Occurs between + and - ions.
Requires electron transfer.
Large difference in electronegativity required.
Example: NaCl
Na (metal)
unstable
Cl (nonmetal)
unstable
electron
Na (cation)
stable
-
+
Coulombic
Attraction
Cl (anion)
stable
Chapter 2 - 33
Ionic Bonding
• Energy – minimum energy most stable
– Energy balance of attractive and repulsive terms
EN = EA + ER =

A
r

B
rn
Repulsive energy ER
Interatomic separation r
Net energy EN
Adapted from Fig. 2.8(b),
Callister & Rethwisch 3e.
Attractive energy EA
Chapter 2 - 34
Examples: Ionic Bonding
• Predominant bonding in Ceramics
NaCl
MgO
CaF 2
CsCl
Give up electrons
Acquire electrons
Adapted from Fig. 2.7, Callister & Rethwisch 3e. (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.
Chapter 2 - 35
2.6 Primary Interatomic Bonds
• Covalent Bonding
– Stable electron configurations are assumed by
the sharing of electrons between adjacent atoms
– Bonding is directional: between specific atoms
and may exist only in the direction between one
atom and another that participates in electron
sharing
– Number of covalent bonds for a particular
molecule is determined by the number of
valence electrons
– Bond strength ranges from strong to weak
• Rarely are compounds purely ionic or
covalent but are a percentage of both.
Sharing
4
electrons
Sharing
2
electron
s
%ionic character = {1 – exp[-(0.25)(XA-XB)2]} x 100
XA and XB are electronegatives
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!
– Number of covalent bonds possible is guessed by the
number of valence electrons
• Typically is 8 – N, where N is the number of valence
electrons
• Carbon has 4 valence e’s – 4 bonds (ok!)
Chapter 2-
EXAMPLES: COVALENT BONDING
H2
H
2.1
Li
1.0
Na
0.9
K
0.8
Rb
0.8
Cs
0.7
Sr
1.0
Ba
0.9
Fr
0.7
Ra
0.9
•
•
•
•
C(diamond)
SiC
Be
1.5
Mg
1.2
Ca
1.0
column IVA
H2O
Ti
1.5
Cr
1.6
Fe
1.8
F2
He
O
2.0
C
2.5
Ni
1.8
Zn
1.8
Ga
1.6
Si
1.8
Ge
1.8
As
2.0
Sn
1.8
Pb
1.8
F
4.0
Cl
3.0
Ne
-
Br
2.8
Ar
Kr
-
I
2.5
Xe
-
At
2.2
Rn
-
Cl2
GaAs
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.
Molecules with nonmetals
Molecules with metals and nonmetals
Elemental solids (RHS of Periodic Table)
Compound solids (about column IVA)
Chapter 2- 11
Covalent Bonding
• similar electronegativity  share electrons
• bonds determined by valence – s & p orbitals
dominate bonding
• Example: CH4
H
C: has 4 valence e-,
needs 4 more
CH 4
H: has 1 valence e-,
needs 1 more
H
Electronegativities
are comparable.
C
H
shared electrons
from carbon atom
H
shared electrons
from hydrogen
atoms
Adapted from Fig. 2.10, Callister & Rethwisch 3e.
Chapter 2 - 39
Bonding in Solids
• Many materials have bonding that is both ionic and
covalent in nature (very few materials actually exhibit pure
ionic or covalent bonding)
• Easy (empirical) way to estimate % of ionic bonding
character:



% ioniccharacter 1  exp  (0.25)( X A  X B )2 x100
XA, XB are the electronegativities of atoms A and B involved
Notice: this is a very very very empirical formula
Chapter 2-
Primary Bonding
• Ionic-Covalent Mixed Bonding
% ionic character =

(X A X B )2 



4
1 e
 x (100 %)




where XA & XB are Pauling electronegativities

Ex: MgO
XMg = 1.3
XO = 3.5

(3.5 1.3 )2


4
% ionic character  1  e




 x (100%)  70.2% ionic


Chapter 2 - 41
2.6 Primary Interatomic Bonds
• Metallic Bonding
– Found in metals and their alloys
– 1 to 3 valence electrons that form a
“sea of electrons” or an “electron
cloud” because they are more or
less free to drift through the entire
metal
– Nonvalence electrons and atomic
nuclei form ion cores
– Bonding energies range from weak
to strong
– Good conductor of both electricity
and heat
– Most metals and their alloys fail in
a ductile manner
Ion
Cores
+
+
-
-
+
+
+
+
+
-
+
Sea of Valence
Electrons Chapter 2-
+
METALLIC BONDING
• Arises from a sea of donated valence electrons
(1, 2, or 3 from each atom).
Adapted from Fig. 2.11, Callister 6e.
• Primary bond for metals and their alloys
Chapter 2- 12
Bonding in Solids
• Metallic bonding
– Most metals have one, two, or at most three valence electrons
– These electrons are highly delocalized from a specific atom – have
a “sea of valence electrons”
– Free electrons shield positive core of
ions from one another (reduce ER)
– Metallic bonding is also nondirectional
– Free electrons also act to hold
structure together
– Wide range of bonding energies,
typically good conductors (why?)
Chapter 2-
2.7 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 symmetric
Chapter 2 -
2.7 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 point
Atomic nucleus
Atomic nucleus
Instantaneous
Electron
cloud
Electron
cloud
Fluctuation
Chapter 2 -
2.7 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
-
Atomic nucleus
Electron Cloud
Induced
Dipole
Chapter 2 -
2.7 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: exists
between molecules that have hydrogen as one of the
constituents
Hydrogen Bond
H
Cl
H
Cl
Chapter 2 -
Bonding in Solids
• Permanent dipoles
(hydrogen bonds)
– Van der Waals
interactions between
polar molecules
– Best known example –
hydrogen bonding
• These interactions are
fairly strong, very
complex, and
surprisingly not well
understood!
Chapter 2-
c02tf03
Chapter 2-
MATERIAL OF IMPORTANCE
Water
c02f16
Many molecules do not have a
symmetric distribution/arrangement
of positive and negative charges
(e.g. H2O, HCl)
Chapter 2-
Chapter 2c02uf01
Properties From Bonding: Tm
• Bond length, r
• Melting Temperature, Tm
Energy
r
• Bond energy, Eo
ro
Energy
r
smaller Tm
unstretched length
ro
r
Eo =
“bond energy”
larger Tm
Tm is larger if Eo is larger.
Chapter 2 - 53
Properties From Bonding : a
• Coefficient of thermal expansion, a
length, L o
coeff. thermal expansion
unheated, T1
DL
= a (T2 -T1)
Lo
DL
heated, T2
• a ~ symmetric at ro
Energy
unstretched length
ro
Eo
Eo
r
a is larger if Eo is smaller.
larger a
smaller a
Chapter 2 - 54
PROPERTIES FROM BONDING: E
• Elastic modulus, E
Elastic modulus
F
DL
=E
Ao
Lo
E ~ dF/dr|ro elastic modulus
Chapter 2- 16
Summary: Primary Bonds
Ceramics
(Ionic & covalent bonding):
Metals
(Metallic bonding):
Polymers
(Covalent & Secondary):
Large bond energy
large Tm
large E
small a
Variable bond energy
moderate Tm
moderate E
moderate a
Directional Properties
Secondary bonding dominates
small Tm
small E
large a
Chapter 2 - 56
Summary: Bonding
Comments
Type
Bond Energy
Ionic
Large!
Nondirectional (ceramics)
Covalent
Variable
large-Diamond
small-Bismuth
Directional
(semiconductors, ceramics
polymer chains)
Metallic
Variable
large-Tungsten
small-Mercury
Nondirectional (metals)
Secondary
smallest
Directional
inter-chain (polymer)
inter-molecular
Chapter 2 - 57