Transcript Part I

Brief Quantum Mechanics, Quantum Chemistry
& Molecular Physics Review
Note!! The following uses excerpts (with changes) from a lecture posted
by Engineering Prof. McCoy at Sweet Briar College, Sweet Briar, VA.
Issues & Ideas to Discuss
1. What causes chemical bonding between atoms?
2. What types of chemical bonds are there?
In crystalline solids,
3. What properties of a material can be inferred
from understanding the bonding between atoms?
An understanding of many of the physical
properties of materials is predicated on a
knowledge of the interatomic forces that
bind the atoms together.
We’ll start with a quick quantum mechanics &
atomic-molecular physics (& chemistry!) review.
Quantum Mechanics Review
• In order to understand Chemical
Bonding in Solids, we first need to have
at least a qualitative understanding of
Chemical Bonding in molecules.
• In order to understand Chemical Bonding
in molecules, we first need to review some
basic Quantum Mechanics of atoms.
• Then, we need to have a quick overview of
Quantum Chemistry &
Molecular Physics
The Bohr Model of the Atom
• We know that this model is wrong in detail,
but it gives a qualitative understanding of
electron orbits in atoms.
Nucleus
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ENGR 215, September 2, 2008 – Page 5
What is an Electron? Diffraction & Wave/Particle Duality
Young’s Double Slit
Experiment - Light
Young’s Double Slit
Experiment – Electrons!
N
ENGR 215, September 2, 2008 – Page 6
What is an Electron? Diffraction & Wave/Particle Duality
Typical Diffraction
Pattern for Waves
N
ENGR 215, September 2, 2008 – Page 7
What is an Electron? Diffraction & Wave/Particle Duality
Electron
Probability
Density
Electron
Orbit
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Electron Orbitals: – Probability Waves
ENGR 215, September 2, 2008 – Page 8
• The Quantum Mechanics of the atom (Schrödinger’s
Equation) describes electrons in terms of probability
distributions that can have only discrete values of energy.
Atomic Orbital Shapes
The Shapes of the atomic s, p, & d orbitals are predicted
by Quantum Mechanics (Schrödinger’s Equation)
ENGR 215, September 2, 2008 – Page 9
Atomic Structure
An s orbital holds
2 electrons with
opposite spins
Each p orbital
holds 2e- with
opposite spins
Each d orbital
holds 2e- with
opposite spins
Orbitals & the Periodic Table
The s sub-orbitals fill
Orbitals & the Periodic Table
The p sub-orbitals fill
Orbitals & the Periodic Table
The d sub-orbitals fill
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Discrete Electron Energy Levels
ENGR 215, September 2, 2008 – Page 15
The Discrete Energies of the atomic s, p, & d electrons are
well-predicted by Quantum Mechanics (Schrödinger’s Equation)
Quantum
Mechanics
Bohr
Model
(Schrödinger’s
Equation)
N
Discrete Electron Energy Levels
ENGR 215, September 2, 2008 – Page 16
The Discrete Energies of the atomic s, p, & d electrons are
well-predicted by Quantum Mechanics (Schrödinger’s Equation)
Quantum
Mechanics
Bohr
Model
Later, we’ll see that in
solids, the energy levels
merge & broaden into
bands & also shift,
Leaving some gaps of
forbidden energy.
(Schrödinger’s
Equation)
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Electronic Energy States
ENGR 215, September 2, 2008 – Page 17
Note!!!
The 4s state has a lower
energy than the 3d state, so
the N shell begins to fill
before the M shell is filled.
N
Atomic Electron Configurations for Some Elements
In most elements, the electron configuration is not stable.
ENGR 215, September 2, 2008 – Page 18
Adapted from
Table 2.2,
Callister 6e.
Why? Their Valence (outer) shell is usually not filled completely.
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ENGR 215, September 2, 2008 – Page 19
The Periodic Table
The atoms in each column have similar
Valence Electron Structure
Adapted from Fig.
2.6, Callister 6e.
Electropositive Elements:
Readily give up electrons
to become + ions.
Electronegative Elements:
Readily acquire electrons
to become - ions.
• Electronegativity is a concept first introduced by Pauling as a
dimensionless measure of an atom’s chemical reactivity. Its values
range from 0.7 to 4.0. Larger Values  A larger tendency to
acquire electrons in a reaction.
Smaller Electronegativity
Larger Electronegativity
Adapted from Fig. 2.7, Callister 6e. (adapted from Linus Pauling, The Nature of the
Chemical Bond, 3rd ed, Copyright 1939 & 1940, 3rd edition. Copyright 1960, Cornell U.).
• Why have we been discussing all of this about electrons?
• Because the
Electron configurations determine how
(& if) various atoms will bond.
• The type and strength of the atomic bonds
determines material properties.
A goal of this discussion:
Understand why materials have
the properties that they have.
• So, we’ll now look at different ways that atoms can form
interatomic bonds, & consider the implications for
material properties.
Bonding
Force
Bonding
Energy
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Examples: Ionic Bonding
ENGR 215, September 2, 2008 – Page 23
1 or 2 (or more) electrons are transferred from an atom
that has extra valence electrons to one that lacks them.
Give up electrons
Acquire electrons
A large electronegativity difference is required
for 2 atoms to form an ionic bond.
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ENGR 215, September 2, 2008 – Page 24
Ionic Bonding
This electron transfer leaves both atoms ionized, with
opposite charges. They are then strongly attracted to
each other through the Coulomb attraction:
Example: NaCl
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Ionic Bonding – Large Scale Structure (Solid)
ENGR 215, September 2, 2008 – Page 25
Since a number of oppositely-charged ions are together,
each ion of one charge will try to surround itself with
atoms of the opposite charge. This causes ionic solids to
form a 3-dimensional structure with alternating positive &
negative ions, held together by relatively strong bonds:
We would like to understand
the strength, hardness,
ductility, electrical
conductivity, & other
properties that result from
this structure (as well as
similar structures).
Covalent Bonding
• Requires shared electrons
Note! This depiction is very
Example: CH4 –
misleading! Electrons are NOT
in Bohr like orbits but are waves
−
C: has 4 valence e , needs 4 more
spread out over the molecule!!!
−
H: has 1 valence e , needs 1 more
Their electronegativities
are comparable.
In a covalent bond, atoms
share electrons so that both
can assume states with a stable
number of valence electrons.
This is the primary bonding mechanism
in many materials.
N
ENGR 215, September 2, 2008 – Page 27
Examples: Covalent Bonding
3.5
An atom with N valence electrons can bond with, at
most, 8−N other atoms. Why?
N
ENGR 215, September 2, 2008 – Page 28
Metallic Bonding
Metal atoms have 1,2,or 3 valence electrons that are loosely
bound. Each metal atom will “give up” these electrons to all of
the other atoms to form a “sea of free electrons” in the metal
The structure thus becomes a a group
of ionized metal atom cores embedded
in the “electron sea”. The “free”
electrons bind the cores together and
shield them from each other. We’re
interested in how this structure affects:
Electrical conductivity
Thermal conductivity
Ductility, Strength
Any other measurable properties.
Secondary Bonding
When atoms are covalently bonded, the resulting molecule will
often have a positive end & a negative end (i.e. it forms a dipole).
Molecules that are dipoles will be attracted to other dipoles through
“Van der Waals” Bonding.
These secondary, Van der Waals bonds tend to be weak compared to
the primary bonds, but they can play an important role in determining
the properties of polymeric materials & other molecular solids.
General
Case:
Example:
Liquid HCl
Example:
Polymer
Adapted from
Fig. 2.14,
Callister 6e.
N
ENGR 215, September 2, 2008 – Page 30
Aside: Win bets (?), impress your friends (?) & astound
strangers (?) by knowing the answer to this question:
Why does water expand when it freezes (unlike most
materials, which contract when they freeze)?
A water molecule is a strong
dipole. Water molecules attract
each other by “hydrogen
bonding” - a special case of
Van der Waals bonding.
When water freezes, the lattice structure
that minimizes the potential energy due
to hydrogen bonding has more space
between atoms than liquid water (where
the atoms are all jumbled together).
Summary: Bonding Types
Bond Type Bond Energy
Ionic
Covalent
Metallic
Material Type
Large
Variable
Ceramics, Salts
Large in Diamond
Small in Bismuth
Semiconductors
Variable
Polymers
Metals
Large in Tungsten
Small in Mercury
Secondary
(Van der Waals,
Hydrogen)
Smallest
Solid Inert Gases
Polymers
Properties From Bonding:
Melting Temperature, Tm
Look at the data & observe how the melting temperature
varies with bonding energy. Why does it behave this way?
Melting Temperature, Tm
Tm is larger if |Eo| is larger.
N
Properties From Bonding:
ENGR 215, September 2, 2008 – Page 33
Elastic Modulus, E
How would you expect
Young’s modulus to vary
with the shape of the
potential energy curve?
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Properties From Bonding:
ENGR 215, September 2, 2008 – Page 34
Thermal Expansion Coefficient, a
How would you expect
Coefficient of thermal
expansion to vary
with the shape of the
potential energy curve?
N
ENGR 215, September 2, 2008 – Page 35
Summary: Primary Bond Categories
Ceramics
Large bond energy
Ionic &
Covalent bonding
large Tm, large E
small a
Metals
Variable bond energy
Metallic bonding
variable Tm, variable E
moderate a
Polymers
Directional Properties
Covalent & Secondary
Bonding
Secondary bonding
dominates: small Tm
small E, large a
Summary: Bonding Types
Bond Type Bond Energy
Ionic
Covalent
Metallic
Material Type
Large
Variable
Ceramics, Salts
Polymers
Large in Diamond
Small in Bismuth
Semiconductors
Variable
Metals
Large in Tungsten
Small in Mercury
Secondary
(Van der Waals,
Hydrogen)
Smallest
Solid Inert Gases
Polymers
Summary: Primary Bonding Categories
Material Type Bond Type
Properties
Ceramics
Ionic & Covalent Large Bond Energy
Large E
Large Tm, Small α
Metals
Metallic
Variable Bond Energy
Variable E
Variable Tm,
Moderate α
Polymers
Covalent &
Van der Waals
(Van der Waals
dominates)
Directional Bonds
Small E, Small Tm,
Large a