Transcript File

ME 330 Engineering Materials
Lecture 4
Atomic Structure and Interatomic Bonding
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Chemistry review
Interatomic bonding in solids
Crystalline vs. Amorphous
Crystals and crystallographic planes
Read Chapters 2 and 3
Why Atomic Structure?
• Atomic level structure can strongly influence
material performance
– Modulus, melting point, coefficient of expansion all
depend on interatomic forces
• Will now demonstrate how to understand properties based
on bonding potentials
• Different bond types have different potentials
• Constructionist approach
– Look at most basic level to begin our understanding
– Today we’ll look (in detail) at:
• How atoms pack together
• How atoms bond together
• See how these effect macroscopic properties
ATOMIC STRUCTURE AND BONDING
Why study it?
Carbon (Diamond & Graphite)
Many properties of materials depend on
(i)
bonds between atoms
(ii)
atomic packing (arrangement)
ATOM
NUCLEUS = PROTONS + NEUTRONS
+
ELECTRONS ( = no. of protons for neutrality)
Protons: + charge, neutrons: neutral charge, electrons: negative charge
Quantum mechanics – establishment of a set of
principles and laws that govern systems of atomic and
subatomic entities.
Models of atomic behavior:
Bohr atomic model – electrons revolve around
atomic nucleus in discrete orbitals.
Wave-mechanical model – electron exhibits both
wave-like and particle-like behavior. Position of
electron is defined by probability of electron’s being at
various locations around nucleus.
Nucleus 10-14m. diameter surrounded by electron
cloud. Atomic diameter  10-10 m
~ 99.98% of mass is in nucleus & most of volume is
electron cloud.
Bohr atomic model –
electrons are assumed to revolve
around nucleus in discrete orbitals
Electrons in ORBITALS or shells, characterized by four
QUANTUM numbers
– Size (K,L,M…) (shells; specified by a principal quantum
number n=1,2,3,…)
- Shape (s,p,d,f) (subshells – different shapes of electron
orbits in a shell; second quantum numbers)
- Spatial orientation (ml) (number of energy states for each
subshell; third quantum number)
- Spin (ms) (spin moment, oriented either up or down; fourth
quantum number)
See Table 2.1
Outermost shell contains VALENCE electrons (bonding,
chemical, electrical and thermal properties). These are of
most importance to us.
If outer shell is complete, i.e. the S &
P orbitals are full (S2P6 = 8 electrons)
then element is very stable and very
un-reactive - Noble gases (helium,
neon, argon, krypton). Some other
elements gain or lose electrons to try
and attain this stable configuration
through bonding.
Note: s, p, d, f subshells can accommodate
the total of 2, 6, 10, and 14 electrons, respectively
SURVEY OF ELEMENTS
• Most elements: Electron configuration not stable.
Electron configuration
1s1
1s2
(stable)
1s22s1
1s22s2
1s22s22p1
1s22s22p2
...
1s22s22p6
(stable)
1s22s22p63s1
1s22s22p63s2
1s22s22p63s23p1
...
1s22s22p63s23p6
(stable)
...
1s22s22p63s23p63d10 4s246
(stable)
• Why? Valence (outer) shell usually not filled completely.
PERIODIC TABLE
Table of elements (types of atoms)
Atomic Number -
number of protons
Hydrogen 1 proton
Helium 2
“
etc.
Atomic Mass - relative atomic mass
- mass of 6.023 x 1023 atoms of that element
(6.023 x 1023 of something is 1 mole)
1 mole of aluminium atoms (i.e. 6.023 x 1023
atoms) has a mass of 26.98 g etc.
THE PERIODIC TABLE
• Columns: Similar Valence Structure
Adapted
from Fig. 2.6,
Callister 6e.
Electropositive elements:
Readily give up electrons
to become +ve ions.
Electronegative elements:
Readily acquire electrons
to become -ve ions.
Most elements in Periodic Table are METALS. e.g.
Mg, Zn, Fe, Ti, Pd.
Few gases and non-metals and some in between.
CERAMICS are usually compounds based on mixtures
of elements Cr2O3 , Al2O3, Si3N4, SiC.
POLYMERS are usually based on CARBON chains /
networks.
Sizes of atoms can be important, i.e. Diffusion in Solids.
ELECTROPOSITIVE metallic elements
give up outer electrons to form positive ions CATIONS
Mg  Mg2+ + 2e-
ELECTRONEGATIVITY
• Ranges from 0.7 to 4.0,
• Large values: tendency to acquire electrons.
Smaller electronegativity
Larger electronegativity
ATOMIC BONDING
ATOMS bond to each other to reduce their overall
energy, i.e. to become more stable.
Everything tends towards a state of lower free
energy.
Bonding Forces and Energies
Inter-atomic spacing is caused by balance between
REPULSIVE and ATTRACTIVE forces.
Attractive force depends on type of bond trying to form
between atoms;
Repulsive force occurs when atoms get close together.
Net force between atoms is balance of two forces and
depends on inter-atomic distance.
FN = FA + FR
FN = 0 when FA = FR
FN : net force
FN = FA + FR
Equilibrium is reached when: FA + FR = 0
Atoms happily sit this distance apart (r0) (often ro  0.3nm)
Also considered in energy terms: EN = EA + ER
In this case, equilibrium is reached when overall energy is
a minimum.
Bonding energy, E0 (binding energy) is the energy required
to break the bond (separate two atoms).
Higher bonding energy  Stronger bonds  higher
strength & Melting point, (Tm)
Also Stiffness (slope (dF/dr) at r0 and thermal expansion
(trough of E curve)
PRIMARY ATOMIC BONDS
(Chemical) - STRONG
IONIC
COVALENT
METALLIC
SECONDARY BONDS
(Physical) - WEAK
Van Der Waals bonds/forces
Fluctuating + permanent dipoles
IONIC BONDS
Form between electropositive (metallic) and electronegative
(non-metallic) elements,
eg. CERAMICS NaCl, Al2O3,MgO
• Na looses outer electron to be more stable  Na+.
• Chlorine accepts extra electron to be more stable  Cl(Note: there is a size change when atoms form ions.)
After such a transfer, the chlorine atom has net negative
charge, while sodium atom has net positive charge. In sodium
chloride (NaCl), all sodium and chloride atoms exist as ions.
IONIC BONDS (cont)
Form between electropositive (metallic) and electronegative
(non-metallic) elements,
• Na loses outer electron to be more stable  Na+.
• Chlorine accepts extra electron to be more stable  Cl-
Opposite charges attract so get:
ELECTROSTATIC (coulombic) BONDING
A
B
EA  
and ER  n
r
r
EA = Attractive energy, ER = Repulsive energy,
A, B and n are constants that depend on system (n  8).
THE PERIODIC TABLE
• Columns: Similar Valence Structure
Adapted
from Fig. 2.6,
Callister 6e.
Electropositive elements:
Readily give up electrons
to become +ve ions.
Electronegative elements:
Readily acquire electrons
to become -ve ions.
Example: NaCl
Ionic Bonding
Metal
Nonmetal
Na
Cl
Atomic
Structure
Cl-
Na+
Ions
Ionic
Bond
NaCl
Notes on Ionic Bonding
Repulsion Curve
•
•
A  
1
r
– Repulsive force:
R 
•
•
•
ER 
To be stable, all positive ions must
be near negative ions
Bond strength is equal in all
0
directions (nondirectional)
Energy considerations
– Coulombic attractive force
1
(n  8)
n
r
Generally, very high bonding
energies
Typically hard, brittle, thermally
and electrically insulative
Ceramics
Energy (r)
•

r8
Separate Ions
Atoms
Electrostatic Attraction
EA  
“Stable”
 

r


r8

r
r
Cl-
Na+
Cl-
Na+
Cl-
Na+
Cl-
Na+
Cl-
EXAMPLES: IONIC BONDING
• Predominant bonding in Ceramics
NaCl
MgO
CaF2
CsCl
H
2.1
Li
1.0
Be
1.5
Na
0.9
Mg
1.2
K
0.8
Rb
0.8
Ca
1.0
Sr
1.0
Cs
0.7
Ba
0.9
Fr
0.7
Ra
0.9
Ti
1.5
Cr
1.6
Give up electrons
Fe
1.8
Ni
1.8
He
-
Zn
1.8
As
2.0
O
F
3.5 4.0
Cl
3.0
Ne
-
Br
2.8
I
2.5
Kr
Xe
Rn
-
At
2.2
Acquire electrons
Ar
-
NON-DIRECTIONAL, electrical neutrality is most
important.
IONS pack to maintain neutrality.
Eg. For NaCl
For each Na+ ion there must also be a Cl- ion.
Likewise, for MgCl2 there must be two Chlorine
ions for every magnesium ion.
Ionic bonds tend to be strong bonds - high
bonding energy. (Table 2.3)
Ceramics are usually ionically bonded and have
high melting points, high hardness, brittle and
electrically and thermally insulative (atoms and
electrons cannot move easily).
COVALENT BONDING
Atoms SHARE outer electrons with each other to attain noble
gas electron configurations.
Atoms close to each other in periodic table and in
electronegativities (X) tend to form covalent bonds
Covalent bonds do not distort very easily - so can be very
strong (Diamond) but appear in "weak" materials as well
(polyethylene - covalently bonded carbon chain)
Some materials show mixed Ionic/Covalent bonding.



% ionicity  1  exp  0.25( X A  X B ) 2 x100
XA, XB electronegativities for respective elements
COVALENT BONDING
• Requires shared electrons
• Example: CH4
C: has 4 valence e,
needs 4 more
H: has 1 valence e,
needs 1 more
Electronegativities
are comparable.
Because atoms in covalent bonds have to share electrons
with other atoms, Direction is very important.
DIRECTIONAL BONDING e.g. DIAMOND
Covalent Bonding
Cl
H
H
C
H
CH4
Cl2
H
• Two atoms share electrons - extra electron belongs
to both
• Bonding is directional - between atoms being
bonded
• Many interatomic bonds are partially ionic and
covalent
– Wider separation in periodic table  more ionic
• Ceramics, Metals, Polymer backbones
EXAMPLES: COVALENT BONDING
H2
H
2.1
Li
1.0
Na
0.9
K
0.8
Be
1.5
Mg
1.2
Ca
1.0
Rb
0.8
Cs
0.7
Sr
1.0
Fr
0.7
Ra
0.9
•
•
•
•
Ba
0.9
column IVA
H2O
C(diamond)
SiC
Ti
1.5
Cr
1.6
Fe
1.8
Ni
1.8
Zn
1.8
Ga
1.6
C
2.5
Si
1.8
Ge
1.8
F2
He
O
2.0
As
2.0
Sn
1.8
Pb
1.8
GaAs
Molecules with nonmetals
Molecules with metals and nonmetals
Elemental solids (RHS of Periodic Table)
Compound solids (about column IVA)
F
4.0
Ne
-
Cl
3.0
Ar
Kr
-
Br
2.8
I
2.5
At
2.2
Xe
-
Rn
-
Cl2
• Widely variable
properties
– Diamond
Energy
(r)
Covalent Potential
Repulsion Curve
• Very soft
• Weak
• Tmelt = 270 ºC
– Based on m & n
rn
0
Atoms
• Hardest substance
known
• Very stiff, strong
• Tmelt = 3550 ºC
– Bismuth

ER 
Electron Overlap Attraction
EA  
 

r
m


r
n
r
m  n 

rm
METALLIC BONDING- Found in metals and alloys.
Atoms of metal pack relatively closely together in
ordered arrangement - Ion cores
Valence electrons form "sea" in between cores "electron gas or cloud"
These electrons can move/drift - thermal/electrical
conduction. FREE electrons.
• Arises from a sea of
donated valence
electrons
(1, 2, or 3 from each
atom).
METALLIC BONDING
Non-directional
Not many restrictions on metallic bond (no charge
neutrality - ionic, or electron-pair sharing covalent) so if metal deformed, atom positions
can move relatively large amounts without
breaking bonds. (Ductility)
Bonding energies affect melting points and vary
from low (-39 C) to high (3410C) values.
• Primary bond for metals and their alloys
Metallic Bonding
e- M+ e M+
ee- e
e
M+ M+ M+
ee- eM+ M+ M+
e
e-
M+
•
•
•
•
•
•
•
M+
M+
M+
M+
M+
M+
M+
M+
M+
Ion Cores (M+)- net positive charge equal to total valence
Valence electrons (e-) drift through metal in “electron cloud”
– Electrically shield ion cores
– Physically hold cores together
Nondirectional bond
Metallic bonding potential similar to covalent (use same eqn.)
Wide variety of bonding energies and hence properties
Excellent conductors due to mobility of electron cloud
Metals and metallic alloys
SECONDARY BONDING - Van Der Waal's
forces (in biological systems)
Low energy - weak bonds
4 - 40 kJmol-1
(Primary 100  1500 kJmol-1)
Based on DIPOLES
When -ve and +ve charges are separated, an
electric dipole moment is set up.
FLUCTUATING INDUCED DIPOLE BONDS
Asymmetrical distribution of electron cloud
(vibrations etc)
e.g. noble gases - boiling, melting.
Van der Waals Bonding
H
H
•
•
•
•
•
O
H
O
 
H
H
O

r
6


r
n
(n  12)
H
Sometimes called physical bonds to contrast with chemical
(primary)
Much lower energy than primary bonds
Arise from electric dipoles – Separation of + and - portions of atom - much weaker than
ions
– Bonding from attraction of + from one dipole to - of other
dipole
Hydrogen bonding is special case when hydrogen is present
– Strongest secondary bonding type
Polymeric interchain bonds
POLAR MOLECULE-INDUCED DIPOLE BONDS
Asymmetric charge distribution in some molecules
(polar)
Eg. HCl molecule. Can attract non-polar molecules.
PERMANENT DIPOLE BONDS
Van der Waals forces will also exist between adjacent
polar molecules.
H-F, H-O and H-N bonds
Hydrogen end becomes very +ve.
One of strongest secondary bonds.
eg. H2O. (Hydrogen bonding - Reason for high boiling
point of water.)
Also between carbon chains in polymeric materials.
• Fluctuating dipoles
• Permanent dipoles-molecule induced
-general case:
-ex: liquid HCl
-ex: polymer
PROPERTIES FROM BONDING: TM
• Bond length, r
F
• Melting Temperature, Tm
F
r
• Bond energy, Eo
Tm is larger if Eo is larger.
PROPERTIES FROM BONDING: E
• Elastic modulus, E
Elastic modulus
F
L
=E
Ao
Lo
• E ~ curvature at ro
Energy
unstretched length
ro
r
E is larger if Eo is larger.
smaller Elastic Modulus
larger Elastic Modulus
PROPERTIES FROM BONDING: 
• Coefficient of thermal expansion, 
coeff. thermal expansion
L
= (T2-T1)
Lo
•  ~ symmetry at ro
 is larger if Eo is smaller.
SUMMARY: PRIMARY BONDS
Ceramics
(Ionic & covalent bonding):
Metals
(Metallic bonding):
Polymers
(Covalent & Secondary):
Large bond energy
large Tm
large E
small 
Variable bond energy
moderate Tm
moderate E
moderate 
Directional Properties
Secondary bonding dominates
small T
small E
large 
Summary - Atomic Bonding in Solids
• Primary
– Ionic
– Covalent
– Metallic
• Secondary
– Van der Waals
– Hydrogen
Force
F( r ) 
d
dr
ro
Energy
(r)
r
• Interatomic potential energies
– Function of separation, r
– Attractive - depends on bond
– Repulsive - atomic scale overlap
• Bonding energy (Eo) is strongly
dependent on bond type
– Effect on modulus ???
– Effect on thermal expansion ???
Eo
Atomistic Origins of Properties
dF 
E  

 dr  r  r•o
Force
F(r)
Modulus
– Proportional to slope of
force-separation curve at
Atomic separation, r equilibrium separation
distance
• Melting Temperature
– Large Eo leads to high Tmelt
Energy
(r)
• Coefficient of thermal
expansion
E0
– Large Eo leads to small 
r – Deep narrow trough forces
large energy change for
small dimensional change
Potentials & Properties
Atomic Separation
0
0
2
4
6
8
-0.1
Ceramics
~~Potential
-0.2
-0.3
Material
E (GPa)
Silicon Carbide
475
Alumina
375
Glass
70
Steel
Brass
210
97
Aluminum
69
PVC
3.3
Epoxy
2.4
LDPE
0.23
10
Ionic
n=2,m=8
n = 2, m = 6
Secondary
Metals
-0.4
-0.5
Polymers
-0.6
Material
 (C-1x10-6)
Silicon Carbide
4.1-4.6
Alumina
7.6
Glass
9.0
Steel
Brass
12.0
20
Aluminum
23.
PVC
90-180
Epoxy
81-117
LDPE
180-400
-0.7
Relative differences in potential curves
Assumes  & are 1 - comparitive purposes only!
Ceramics
Metals
Polymers
From Callister, p. 22
Atomic Packing
• Crystalline:
– 3-D arrangement of atoms in which every atom has the
same geometrical arrangement of neighbors
– Long-range, periodic array over large length scales
– Most solids are crystalline (metals, most ceramics,
some polymers)
• Amorphous
–
–
–
–
Arrangement over which no long range order exists
Often clear - not enough order to diffract light
Rarely purely amorphous - have regions of crystallinity
Many polymers and some ceramics
Crystal Structure Definitions
• Unit cell: Smallest
repeating unit of the
crystal.
• Lattice: 3–D framework
of a crystal where atoms
are located
• Lattice parameters:
Dimensions (a,b,c) and
angles (,,) of the
lattice
c



b
a
Bravais Lattices
•
•
•
•
•
•
French Crystallographer Bravais (1848)
7 crystal systems using primitive unit
cells
Primitive - one lattice point at origin
14 distinguishable point lattices
– P - simple
– F - face centered
– I - body centered
– C - base centered
For now, interested in BCC, FCC, HCP
– Metallic crystal structures
– Metallic bond is non-directional
– No restriction on nearest neighbors
– Very dense packing
First need to collect some definitions
Tetragonal
FCC
Monoclinic
Rhombohedral
BCC
Cubic
Hexagonal Orthorhomic
HCP
Triclinic
Crystallographic Directions
•
Determining direction indices
z
– Start vector at crystal axis
– Draw to any point in the 3-D crystal
– Project vector on each xyz axes
•
•
•
measure a in x-direction
measure b in y-direction
measure c in z-direction
[001]
[111]
a=1
b=½
c=0
– Multiply by common factor to achieve
smallest integer value
x
– Enclose in [ ] without commas
•
•
•
y
[010]
[100]
[210]
[110]
Negative directions indicated with Family of directions indicated by < >
Hexagonal crystals have 4 indices
[100], [ 1 00], [010], [0 1 0], [001], [00 1 ]
In a cubic crystal,
all in the <100> family.
are
Crystallographic Planes
• Determining Miller indices
– Look at plane in unit cell which
does not pass through the origin
– Determine length of planar
intercept with each axes (again,
a,b,c)
– Take reciprocal of a,b,c
– Reduce to smallest integer value
– Enclose in ( ) without commas
• Any parallel planes are equivalent
z
z
y
x
-1
z
[001]
c = 1/3
b = 1/2
a=1
x
y
[010]
[100] (123)
z
1
Intercepts :  ,  1,
2
Re ciprocals: 0 , 1,2
Plane : 01 2 
x
(012)