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  • 7/30/2019 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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    Van der waals interaction occurs generally between atoms whichhave noble gas configuration.

    van der waals

    bonding

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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    Comparison of Ionic and

    Covalent Bonding

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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL

    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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    PHY 3201 FIZIK KEADAAN PEPEJAL