lecture+7+mak crystalbinding
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PHY 3201 FIZIK KEADAAN PEPEJAL
From Last Class
All of the mechanisms which cause bonding between the atomsderive from electrostatic interaction between nuclei and electrons.
The differing strengths and differing types of bond are determined by
the particular electronic structures of the atoms involved.
The existence of a stable bonding arrangement implies that thespatial configuration of positive ion cores and outer electrons has lesstotal energy than any other configuration (including infinite separationof the respective atoms).
The energy deficience of the configuration compared with isolatedatoms is known as cohesive energy, and ranges in value from 0.1eV/atom for solids which can muster only the weak van der Waals to7ev/atom or more in some covalent and ionic compounds and somemetals.
Interatomic Binding
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The potential energy of either atom will be given by:
or simply:
V= decrease in potential energy+increase in potential energy
(due to attraction) (due to repulsion)
( )m n
a bV r
r r
V(r):the net potential energy of interaction as function of r
r : the distance between atoms, ions, or molecules
a,b: proportionality constant of attraction and repulsion,respectively
m, n: constant characteristics of each type of bond and type of
structure
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VAN DER WAALS BONDING It is a weak bond, with a typical strength of 0.2 eV/atom.
It occurs between neutral atoms and molecules.
The explanation of these weak forces of attraction isthat there are natural fluctuation in the electron
density of all molecules and these cause smalltemporary dipoles within the molecules. It is thesetemporary dipoles that attract one molecule toanother. They are called van der Waals' forces.
The bigger a molecule is, the easier it is to polarise (toform a dipole), and so the van der Waal's forces getstronger, so bigger molecules exist as liquids or solidsrather than gases.
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Van der waals interaction occurs generally between atoms whichhave noble gas configuration.
van der waals
bonding
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Ionic Bonding
In an ionic crystal, an electron is essentially
transferred from one type of atom to another. The ionic bond results from the electrostatic
interaction of oppositely charged ions.
e.g. Na + Cl Na+ + Cl-
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Ionic bonding in NaCl
3s1
3p7
Sodium
Atom
Na
Chlorine
Atom
Cl
Sodium IonNa+
Chlorine Ion
Cl -
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Example
The transfer of an electron from Na atom to Cl atom to form a
Na+-Cl- ion pair =ionization energy of Na electron affinity of Cl=
5.1-3.6 = 1.5 eV
The cohesive energy of NaCl molecule due to the interaction
potential = -7.9
Total cohesive energy per NaCl molecule = -7.9 + 1.5 =-6.4 eV
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An ion i at a particular lattice site is considered and its
interaction with all its neighbouring ions are added.
The energy is written as;
The Coulomb term for both like and unlike charges
j
iji UU
ij
CoulombrqU
2
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The repulsive term due to overlap of electrons clouds
Therefore
Since the repulsive term is effective only at very shortdistances, Uij can be split into two parts
ij
repulsive
rU exp
ij
ij
ijr
qrU
2
exp
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For nearest neighbours, where R is the nearest
neighbour
and for other ions
expressing rij aspijR
R
qRUij
2
exp
ij
ijr
qU
2
Rp
qU
ij
ij
2
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Therefore
wherezis the number of nearest neighbour. Define the
Madelung constant as
j ijj
ijiRp
qRzUU
2' 1exp
j ijp
1
RqRzUU
j
iji
2'exp
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The total energy of the crystal is given by
Utotal=(2NUi)
N is the total number of molecules. The number of
ions is 2N. The term occurs because we must count
each pair of interaction only once. Therefore
R
qezNNUU Ritotal
2/
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To calculate the equilibrium distance between the
nearest neighbors, we use the fact that the derivative
dU/dR=0
00
2
0
2
2
0
2
2/2
0
2
0
2/
1
0
0
0
RR
Nq
R
Nq
R
qNU
z
qeR
R
qez
total
R
R
R
qRzUU
j
iji
2'
exp
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Evaluation of Madelung
constantExample- a one-dimensional lattice of ions of
alternating sign as shown in the Figure below
R
2,2ln
....
5
1
4
1
3
1
2
112
In this case
where we took into account the logarithm expansion into
series
2
1
11ln
n
nn
n
xx
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The cohesive energy for NaCl can be estimated by using
=1.75, Ro=a/22.8 Angstrom, q=e, =0.1Ro
This implies that the ionic bond is very strong.
Experimentally, this strength is characterized by therelatively high melting temperatures. For example, the
melting temperature of NaCl is about 1100o, while the
melting temperatures for the Na metal is about 400o
eV-8eV
09.276
8.11.01/ 0
0
0
2
0
0
RR
ae
aRNU
o
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Covalent bonding
The covalent bond between two atoms isusually formed by two electrons, one fromeach atom participating in the bond.
The electrons forming the bond tend to be
partly localized in the region between thetwo atoms joined by the bond.
Normally the covalent bond is strong: for
example, it is the bond, which couplescarbon atoms in diamond. The covalentbond is also responsible for the binding ofsilicon and germanium crystals
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In Covalent bonding, outer s and p electrons are
shared between two atoms to obtain noble gas
configuration.
Takes place between elements
with small differences in
electronegativi tyand close by
in periodic table.
In Hydrogen, a bond is formed between 2 atoms
by sharing their 1s1 electrons
H + H H H
1s1
Electrons
Electron
Pair
Hydrogen
Molecule
H H
Overlapping Electron Clouds
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The binding of molecular hydrogen
The strongest binding occurs when the
spins of the two electrons are antiparallel
This spin-dependent coulomb energy iscalled the exchange interact ion.
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In case of F2, O2 and N2, covalent bonding isformed by sharing p electrons
Fluorine gas (Outer orbital 2s2 2p5) share one p electronto attain noble gas configuration.
Oxygen (Outer orbital - 2s2 2p4) atoms share two pelectrons
Nitrogen (Outer orbital - 2s2 2p3) atoms share three pelectrons
H H
F + F F FH
F FBond Energy=160KJ/mol
O + O O O O = O
N + NBond Energy=54KJ/mol
N N N N
Bond Energy=28KJ/mol
C l t B di
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Carbon has electronic configuration 1s2 2s2 2p2
Hybridizat ioncauses one of the 2s orbitals
promoted to 2p orbital. Result four sp3
orbitals.
Ground State arrangement
1s 2s 2p
Two filed 2p orbitals
Indicates
carbon
Forms two
Covalent
bonds
1s 2pFour filled sp3 orbitals
Indicatesfour covalent
bonds are
formed
Covalent Bonding
in Carbon
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Four sp3 orbitals are directed symmetr ical ly
toward corners of regular tetrahedron. This structure gives high hardness, high bonding
strength (711KJ/mol) and high melting
temperature (3550oC).
Carbon Atom Tetrahedral arrangement in diamond
Structure of Diamond
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Comparison of Ionic and
Covalent Bonding
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Atoms in metals are closely packed in crystalstructure.
Loosely bounded valence electrons are attractedtowards nucleus of other atoms.
Electrons spread out among atoms formingelectron clouds.
These free electrons arereason for electric
conductivity and ductility
Since outer electrons are
shared by many atoms,metallic bonds are
Non-direct ional
Positive Ion
Valence electron charge cloud
Metallic Bonding
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Hydrogen Bonds
Hydrogen bonding arises because a hydrogen
atom is usually a somewhat positive chargedregion of a molecule. This can, by electrostaticattraction, form a weak bond to a negativelycharged region of another molecule
e.g. the water molecule, H2O, the shared
electrons shared between the oxygen andhydrogen atoms tend to stay closed to the oxygenatom than the hydrogen atom because of theelectronegativity of oxygen. As a results, oxygen
act as the negative end of the dipole andhydrogen act as the positive ends.
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Hydrogen bonds are Dipole-Dipole
interact ionbetween polar bondscontaining hydrogen atom.
Example :-
In water, dipole is created due to
asymmetrical arrangement of hydrogen
atoms.
Attraction between positive oxygen pole and
negative hydrogen pole.
105 0O
H
HHydrogen
Bond
Hydrogen Bonds
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