APPLIED PHYSICS Bonding in Solids by CHARIS ISRAEL ANCHA

8/9/2019 APPLIED PHYSICS Bonding in Solids by CHARIS ISRAEL ANCHA

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APPLIEDAPPLIEDAPPLIEDAPPLIED

PHYSICSPHYSICSPHYSICSPHYSICS

2008-2009

1

PREPARED BY

Mr. A.CHARIS ISRAEL. M.Sc., B.Ed., (Ph.D.)

Asst. Professor of PHYSICS

Mobile No: +91-9866934653

SECUNDERABAD


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UNIT I (PART A) BONDING IN SOLIDS 2008-2009

For Downloads visit: www.charis-ancha.blogspot.com [email protected] +91-9866934653 Page 2

Contents

DEFINITIONS: .................................................................................................................................... 3TYPES OF BONDING IN SOLIDS: .................................................................................................... 4FORCES BETWEEN TWO INTERACTING ATOMS ...................................................................... 8POTENTIAL ENERGY: .................................................................................................................... 10ESTIMATION OF COHESIVE ENERGY AND DISSOCIATION ENERGY ...................... ............ 11COHESIVE ENERGY OF IONIC CRYSTALS (NACL): ................................ .......................... ........ 13SOLVED PROBLEM: ........................................................................................................................ 15MADELUNG CONSTANT: ............................................................................................................... 16QUESTIONS ...................................................................................................................................... 17


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UNIT I PART - A

BONDING IN SOLIDS

DEFINITIONS:

Electro-positive atoms:

The atoms which readily give-up electrons are called Electro-positive atoms, usually

metal atoms.Ex: Group I & II elements i.e., Na, K, Ca, Cs etc.

Among all elements most electropositive element is Cesium (Cs).

Electro-negative atoms:

The atoms which readily take-up electrons are called Electro-negative atoms, usually

non-metallic atoms.Ex: Group VI & VII elements i.e., O, F, Cl, Br etc.

Among all elements Fluorine (F) is the most electronegative element.

Electronegativity is used to predict the type of bonding in a molecule:

If the electronegativity difference between two elements is greater than 1.9, then the bond

formed is ionic. If the electronegativity difference between two elements is less than 1.9, then thebond formed is covalent.

For example: The electronegativity difference between Na (0.9) and Cl (3.0) is 2.1 in NaCl.

So the bond in NaCl is ionic.

Ionization potential or Ionization Energy1:

The energy necessary to remove the electron from an atom i.e. creating a positive ion is

called ionization energy.

The element with highest ionization potential value is Helium (He) and Cesium (Cs) hasthe least.

Electron affinity:

The energy given up when a neutral atom gains an electron and becomes a negative ionis called electron affinity.

Among all elements Chlorine (Cl) has highest electron affinity and inert gases have zeroelectron affinity.

Ionic Size:

Al3+ is smaller than Mg2+

Al3+

and Mg2+

both have 10 electrons. But Al3+

has 13 protons while Mg2+

has 12 protons. Hence

effective nuclear charge in Al3+

is more, which leads to shrinkage of ionic size.For example, the order of ionic radii varies as Na

+> Mg

2+> Al

3+> Si

4+.

1 Ionization potential and Ionization energy are used synonymously. Ionization potential refers to single atom while ionizationenergy refers to 1 mole of atoms.


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TYPES OF BONDING IN SOLIDS:

Differentcharge distributions2

between the atoms gives rise to different types of bonding

and can be classified into five types. Also, basing on the bond strengths, atomic bonding can begrouped into primary andsecondary bonding. Primary bondings have the bond energies in the

range of0.1 - 10 eV/bond and Secondary bondings have the bond energies in the range of

0.01 - 0.5 eV/bond.

PRIMARY BONDINGS3:

(i) Ionic Bonding(ii) Covalent Bonding(iii) Metallic BondingSECONDARY BONDINGS

4:

(iv) Hydrogen Bonding(v) Van der Waals Bonding

IONIC BONDING:

The bond formed by the complete transfer of valance electrons from one atom to

another atom, in order tostabilize their outer electronic configurations is called ionic bond5

.

An ionic bonding is the Coulomb electrostaticattractive force6 between a positive ion

(cation) and a negative ion (anion) when they are brought closer to each other. This type ofbonding occurs between electro-positive and electro-negative atoms. The source of cohesive

energy that binds the ionic crystals together is thecoulomb electrostatic interaction7

between theoppositely charged ions.

Examples:NaCl8, KCl, etc

9.

The magnitude of this cohesive energy is about 5-10 eV per molecule, for NaCl it is 7.95 eV.Properties of Ionic Solids:

1) Ionic solids arecrystalline10 in nature.2) They arephysicallyhard11 andbrittle.3) They havehighmelting andboilingpoints.

2 Transfer of electrons, sharing of electrons, electrons surrounding the positive ion core and formation of dipoles are thedifferent types of charge distributions.3 Primary bonds are also called as Interatomic Bonds.4 Secondary bonds are also called asIntermolecular Bonds.

5 Ionic bond is formed betweenhighly electropositive andhighly electronegative elements.6 In spite of electrostatic attraction there exists a repulsive force between the negatively charged electron clouds which becomeoperative when the two ions try to overlap.7 The ions arrange themselves in such a way that the coulomb attraction between ions of opposite sign is stronger than thecoulomb repulsion between ions of the same sign.8 Crystal structure of NaCl is Face centered cubic with coordination number 6.9 KBr, MgO, KOH, Al2O3, (all alkali halides, alkaline oxides) are the few more examples of ionic solids.10 They usually crystallize in relatively close-packed structures. The structure (simple, body-centered, face-centered etc.,)actually depends upon theradius ratio of the two ions.11 On account of strong binding energies the ionic crystals are physically hard, brittle and have a relatively high melting andboiling points.


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4) They are quite poor electrical conductors12 at normal temperatures and at elevatedtemperaturesionic conductivity

13 results.

5) They aresolublein polar solvents and insolublein non-polar solvents.6) They are usuallytransparentto visible light.7) The ionic bonds arenon-directional14.

COVALENT BONDING:

The bond formed by sharing of valance electron pairs between two or more similar ordissimilar atoms such that no net charge is associated with any of the atoms is called covalent

bond15

.

The attractive force between the atoms participating in thecovalent bonding is due to the

anti-parallel spins16

of the sharing electrons. In covalent crystals, the total cohesive energy or binding energy will not only include the energy of bonds but also the energy of interaction

between different bonds. However, in many cases the binding energy is quite close to the sum ofbond energies; this is particularly true for diamond.

Examples:Hydrogen molecule (H2),HCl, etc.17

The binding energy of carbon in diamond is 7.4eV.

Properties of Covalent Solids:

1) The covalent bonds are stronglydirectional18in character.2) Different covalent solids have different bond strengths, hence they exhibit varying19

physical properties.

3) They arehardandbrittle, and possesscrystalline structures withhigh20melting andboiling points.

4) Electrical conductivity is normally not possible and so these crystals are insulatorsatordinary temperatures.

5) They aresoluble innon-polar solvents.6) When they aredopedwith certain impurities they become semi-conductors.7) They are transparent to long-wavelength radiation, but opaque to shorter

wavelengths.

12 Because the valence electrons are bound quite tightly to the ionic nuclei and .hence all ionic solids are electrically neutral.13 At elevated temperatures however, the ions themselves become mobile and ionic conductivity results. (Conductivity in ionicsolids is due to ions).14 In ionic crystals, the ions are held together with strong electrostatic forces which have no specific direction and thus the ionicbonds are non- directional.15 Since the valence of the atoms forming this bond is the same, it is also called as valence bond. Since the atoms taking part in

covalent bond are identical, this bond is also called asHomopolar bond.16 As the spin is the intrinsic property in Quantum Mechanics, hence the covalent bonding is the quantum mechanical

phenomenon..17 S, I, Ge, Si, Diamond, Graphite, H2O,CO2, NH3 etc., are the few more examples of covalent solids and molecules.18 Covalent bond is formed by the overlapping of orbitals with unpaired electrons. But this overlapping takes place only in thedirection of maximum electron density. Hence covalent bonds are directional.19 For example,diamondis the hardest substance having high melting points and is best electrical insulator. Tin which is very

soft with low melting point is a good electrical conductor. Silicon andGermanium which are hard with high melting points aresemi-conductors.20Ionic compounds have higher melting and boiling points than covalent compounds. This is because ionic solids are heldtogether by strong electrostatic attractive forces while covalent solids are held by weak van der waals' forces.


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METALLIC BONDING:

The bond formed by sharing a number of valence electrons21 with a number of atoms22in a solid is calledmetallic bond.

The metallic bonding is the Coulomb electrostatic force of attraction between the

negative electron cloud23

and the positive ions24

. Metallic bond is also called as incompleteorunsaturated

25covalent bond

26. The source of cohesive energy or binding energy in metals isthe same as in electron pair bonds with a difference that there is an additional property of finding

the electrons in the low potential energy regions between the ions. Metallic bonds are weakerthan ionic and covalent bonds, but stronger than Van der Waals bonds.

Examples:Sodium (Na),Aluminum (Al), etc.27

The binding energies of sodium and aluminum are 1.3eV and 3.23eV respectively.

Properties of Metallic Solids:

1) Metallic solids arecrystalline in nature.2) They possess ahigh degree ofcrystal symmetry28.3) They possesshighelectrical and thermalconductivities29.4) Unlike ionic and covalent solids, the metallic solids aresoft, malleable30and ductile.5) The metals are opaque to all electromagnetic radiations from very low frequency to

the middle ultraviolet frequencies, beyond which they aretransparent.

6) They arenot soluble inpolarand non-polar solvents.HYDROGEN BONDING:

The bond formed between two similar atoms31 with the hydrogen atom in-between32

asthepositive endof the dipole is calledhydrogen bond.

OR

The weak intermolecular forces of attraction (electrostatic) that exists between H atomof one molecule and a more electronegative atom of another molecule is called hydrogen bond.

Inhydrogen bonding, the hydrogen atom with its single 1s orbital cannot form more thanone pure covalent bond; hence the attraction of two atoms must be largely due to electrostatic

forces.

21 No valence electron is associated with a specific atom and hence these electrons do not promote the formation of anypermanent bond between the atoms.22 The bonding in metals must be thought in terms of all the atoms in the solids taken together.23 The free electrons in metals are also termed asfree electron gas orasea of mobile electrons.24 Positive ions are also termed askernels.

25 It is unsaturated because of many vacancies in their outermost electron shells and hence their bonds do not exhibit directionalpreferences.26 According to L. Pauling, metallic bond is considered as highly delocalized covalent bond.27 Potassium, copper, silver, gold, iron, nickel, tungsten, titanium etc., are few more examples of metallic solids.28 This symmetry is due to the symmetrical arrangements of positive ions.29 This is due to the enormous number of free electrons present in the metals.30 Unlike other crystals, metallic crystal can be deformed without fracture since the electron gas behaves as a lubricant which

permits the atoms to slide on one another.31 The atoms involved are electro-negative atoms such as Oxygen, Fluorine and Nitrogen.32 Under certain circumstances, the hydrogen atom appears to beattracted simultaneously by rather strong forces to two otheratoms, which serves as a bridge between two species and is considered as a basis for the bond between two atoms.


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Examples:Water molecule in theform ofice,Hydrogen difluoride (HF2-), etc.

33

Thebinding energy of hydrogen atom in hydrogen bonding is of the order 0.1eV.

Properties of Hydrogen bonded Solids:

1) The hydrogen bonds aredirectional.2) Hydrogen bonded solids can becrystalline ornon-crystalline in nature.3) They possess lowmelting points.4) They are very goodinsulators of electricity.5) They aretransparent to visible light.6) They aresoluble in polar and non-polar solvents.

No table of contents entries found. The bond formed between the atoms or molecules34

due tothedipolar forces35 is calledmolecular orvan der waals bond.

Themolecular bonding is the instantaneous dipole interactions36

between the atoms ormolecules in the solids. Van der waals bonding is typically an order of magnitude weaker than

the hydrogen bonding.Examples:Solid Neon, solid methane (CH4) andsolid Argon are the best examples of this class.

Properties of Solids with Van der Waals bonding:

1) Van der waals bonds arenon-directional.2) Van der waals bonded solids are electrical insulators because the electrons are

localized.3) Due to the presence ofweak forces they aresoft andmechanically weak.4) They have low melting points.5) They aresoluble in bothpolarand non-polar solvents.6) They are usuallytransparent to light.

33 potassium dihydrogen phosphate (KH2PO3), H2O, NH3 (ammonia molecules) are the other few examples of hydrogen bondingmolecules.34 These atoms or molecules have no tendency to lose or even share their valence electrons with other atoms or molecules in thesolid.35 The dipole moment is the source of an electrostatic dipole field which in turn may induce a dipole moment in another atom or

molecule. The interaction between original and induced dipole moment is attractive and is called as dipolar forces or van derwaals forces.36 These interactions are primarily due to non-uniformities in the electrostatic charge distributions which are caused by themomentary shifts of the electrons and nuclei towards the opposite ends of the atom, producing so calleddipoles.


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FORCES BETWEEN TWO INTERACTING ATOMS

There exist two types of forces37

between interacting atoms.

(i) Attractive force(ii) Repulsive force Resultant force = attractive force + repulsive force

Attractive force:

The atoms with less stable electronic configuration, try to have stable electronicconfiguration. In this attempt, they will attract other atoms to form a stable compound where

attractive forces begin to act. This attractive force exists only when the atoms are at far distancesand is electrostatic in nature.

Attractive Forcem

A

r=

Repulsive force:

When atoms approach each other, their negatively charged electron shells come much

closer than their positive nuclei. Thus repulsive force between the two atoms is due to theoverlapping of the electron shells.

Repulsive forcen

B

r=

Resultant force:

The two atoms approach each other to a stable condition and have minimum energy. Nowthe bonding force, F(r) between two atoms may be represented by the general equation

Resultant force, ( ) ( )m n

A BF r = n m

r r >

38

where A, B, m and n are constants that depend on the type of bond and r is centre-to-centre spacing betweentwo atoms.

At larger separation, the attractive force predominates and the two atoms approach untilthey reach equilibrium spacing ro. If they continue to approach further, the repulsive force

predominates, tending to push them back to their equilibrium spacing ro.

At the equilibrium spacingro, the resultant force F(r) is Zero.39

i.e., ( ) 0oF r =

ro is of the order 10-10

m i.e. 1Ao. For different bonds ro varies between 1 A

oand 4 A

o.

37 Just by casual thinking we may draw two conclusions from the very existence of solids: Firstly, there must act attractive forcebetween the atoms or molecules in a solid which keep them together and secondly, there must also be the repulsive forcesbetween them since large external pressures are required to compress a solid to any appreciable extent.38 Since the attractive forces in interatomic bonds are largely electrostatic, m is usually 2 following Coulombs inverse squarelaw of electrostatics. The value of n is not so easy to approximate, but it takes values from 7 to 10 for metallic bonds and10 to 12 for ionic and covalent bonds.39 the attractive and repulsive forces are equal in magnitude.


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Variation of interatomic force F(r) with interatomic spacing r:

F

Attractive Force, mA

r

Resultant Force, ( )m n

A BF r =

r r

or

O r

( ) 0o

F r = maxF

Repulsive Force,n

B

r

Fig. 1

The above figure shows the variation of resultant force between atoms. To separate the

atoms completely from the structure, a force maxF is to be applied. This force corresponds to the

cohesive strength of the material.

Equilibrium spacing, ro:

The general expression for the bonding force between two atoms is

( ) ( )m n

A BF r = n m

r r >

At equilibrium spacing ,or = r ( ) 0oF r =

Hence,

m no o

A B

r r=

n m

o

B

Ar

=

1

n m

o

B

Ar

=

The above equation represents the equilibrium spacing between two atoms.


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POTENTIAL ENERGY:

Variation of Potential Energy U(r) with interatomic distance r:

U Fig. 2

Repulsive Energy, nb

r

Potential Energy, ( ) m na b

U rr r

= +

or r=

O r

0U=

minU

Attractive Energy, mar

When two atoms approach other, some work is said to be done either on the system or by

the system. This work done is stored in the form of potential energy. Basing on the work done,potential energy is divided into two types

i) Attractive Potential Energyii) Repulsive potential energy

Total Potential Energy = Attractive Energy + Repulsive Energy

Attractive Potential Energy:

During their approach, the atoms do the work of attraction. This work done by the atomsis stored in the form of attractive potential energy. At large separations this energy is zero, but

decreases gradually at shorter distances according to the expressionm

a

r

Repulsive Potential Energy:

When the atoms are so close to each other, such that the outer electrons of each atom caninteract, repulsive forces begin to act. Hence some external work must be done to bring the

atoms together, when they repel each other. This external work done is stored in the form ofrepulsive potential energy. At shorter distances this increases more rapidly

40than the attractive

potential according to the expressionn

b

r

Hence thetotal potential energy is given by

( ) ( )m n

a bU r n m

r r= + >

At equilibrium position i.e. at ,or = r the total potential energy is minimum i.e. min( )oU r U= .

40 This is because, the positive charges on the nuclei repel each other very strongly when r becomes small.


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Cohesive EnergyorBinding Energy and Bond dissociation energy:

The energy released when a molecule is formed from two atoms is called cohesiveenergy.

The energy necessary to dissociate the molecule into isolated neutral atoms is called

dissociation energy.These energies are equal in magnitude but with opposite signs. These energies are of the

order ofa few electron volts (eV) in magnitude.

ESTIMATION OF COHESIVE ENERGY AND DISSOCIATION ENERGY

Expression for the equilibrium spacing of two atoms for which the potential energy is

minimum:

Let us consider a general situation of two identical atoms. These two atoms comes closer

to each other in accordance with the force relation

( ) ( )NM

A BF r = N M rr

> (1)

The work done in moving through a small distance dr, due to this force is stored in the form ofpotential energy ( )du r given by

( ) ( )du r F r dr =

Hence the potential energy of the molecule is

( ) ( ) ( )U r du r F r dr = =

M N

A Bdr

r r

=

1 1

1 1

1 1

M N

A BC

M r N r

= + +

( )m n

a bU r C

r r

= + + (2)

where 1 11 1

, , andA B

a b m M n N M N

= = = =

.

We know that at infinite distance the potential energy is zero i.e. when , 0r U= =

substituting ' ' ' 'r and U in eq(2), we have 0C =

Therefore eq(2) can be written as,

( )m n

a bU r

r r

= + (3)

where the first term is theattractive energy and the second term is therepulsive energy.

We know that the condition for the potential energy to have minimum value is


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0dU

dr=

This happens at equilibrium position ,or = r i.e. 0

or r

dU

dr=

=

from eq(3),

1 10

m n

or r

dU am bn

dr r r + +=

= = (4)

1 1

m n

am bn

r r+ +

=

n m

o

b nr

a m

=

(5)

1

n m

o bnram

= (6)

This is the expression for the equilibrium spacing of two atoms for which the potential

energy is minimum.

The cohesive energy and dissociation energy can be calculated as below:

Using eq(3) at ,or = r we have

( )o m n

o o

a bU r

r r

= + (7)

Rearranging the eq(5), we get

1 1

n m

o o

a m

b nr r

=

Substituting this equation in the above eq(6), we have

1( )o m m

o o

a a mU r b

b nr r

= +

( ) 1 ( )o mo

a mU r n m

nr

= >

(8)41

This energy corresponding to the equilibrium position i.e. ,r = ro is called Cohesive energy.

Thedissociation energy of the molecule is given by

1 1( ) ( )o m mo o

a m a mU r n m

n nr r

= = >

(9)

41 The negative sign indicates that the total binding energy is essentially attractive in nature. Since m n the attractive andrepulsive energies are not equal though the attractive and repulsive forces are equal in equilibrium.


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To show that n m> :

Since U is minimum at ,or = r U must also satisfy the condition,

2

20

or r

d U

dr =

>

(10)

Differentiating Eq. (4) and applying the condition given by Eq.(10), we get2

2 2 2

1 1- ( ) ( )= + 0

m n

o oor r

d U am m bn n

dr r r + +=

+ +>

2 21 1( ) ( ) 0n mo oam m r bn n r

+ +

+ + + >

2 21 1( ) ( )m no obn n r am m r

+ +

+ > +

1 1( ) ( ) n mobn n am m r

+ > +

Substituting for or from Eq. (6), we get

1 1( ) ( )b n

bn n am ma m

+ > +

1 1( ) ( )n m+ > +

i.e. n m> (11)42

COHESIVE ENERGY OF IONIC CRYSTALS (NaCl):

The attractive potential energy of ionic crystals is

2

1 2

04

AZ Z e

r

(1)

where A is Madelung constant

43

, Z1, Z2 are valencies of corresponding ions, e is the electroniccharge.

The repulsive energy between the ions is nB

r (2)

where n is called Born repulsive exponent.

Therefore the total energy of ionic crystals is2

1 2

0

( )4

n

AZ Z e BU r

r r= +

(3)

For Uni-valent crystals (such as NaCl), Z1 = Z2 = 1.

For 1 Kilo mole Eq. (1) can be written as2

0

( ) N4 nAe B

U rr r

= +

(4)

where N is the Avagadro number.

42 This indicates that the forces between the atoms are mostly electrostatic in nature.43 The value of madelung constant A purely depends on the geometrical arrangement of ions in the crystal(i.e. structure of the crystal).


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At equilibrium position i.e.

,or = r the potential energy equation can be written as

2

0

( ) N4

o n

o o

Ae BU r

r r

= +

(5)

To find the value of B:

To evaluate the repulsion constant B, let us consider the fact that at equilibrium separation

i.e. at ,or = r the potential energy is minimum.

Hence,

( )0

or r

dU r

dr=

=

22 1

0

( )N ( 1) ( ) 0

4

n

o o

or r

dU r Aer B n r

dr

=

= + =

2

2 1

0

N 04

n

o o

Ae Bn

r r+

=

(6)

In Eq. (6) N 0 hence,2

2 1

0

04

n

o o

Ae Bn

r r+

=

2 1

2

0

4

n

o

o

Ae r B

r n

+

=

2 1

0

4

n

oAe r Bn

=

(7)

Now, substituting the value ofB in Eq. (5), we get

2 12

0 04 4

( ) Nn

oo n

o o

Ae rAeU r

r nr

= +

2 2

0 04 4( ) No

o o

Ae AeU r

r r n

= +

2

0

1

14

N

( )oo

Ae

U r r n

= (8)

44

where A is madelung constant of ionic crystal.

The above Eq. (8) represents thecohesive energy per 1kilomole ofionic crystal.

44 The negative sign indicates that the energy isattractive in nature. The dissociation energy of ionic crystals is2

0

N 1( ) 1

4o

o

AeU r

r n

=


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SOLVED PROBLEM:

Calculate the cohesive energy of NaCl from the following data:

Equilibrium separation between the ion pair , ro = 0.281 nm

Ionization energy of Na = 5.14 eV

Electron affinity of Cl = 3.61 eV

Born repulsive exponent, n = 9

Madelung constant,A = 1.748

SOLUTION:

Cohesive energy per molecule of NaCl is

2

0

11

4( )o

o

AeU r

r n

=

We know,191.602 x 10e C=

128.85 x 10o

=

90.281 0.281 x 10 ,or nm m

= =

1.748A =

9n =

Hence cohesive energy per molecule of NaCl is

19 2

12 9

1.748 x (1.602 x 10 ) (8/ 9)

4 x 8.85 x 10 x 0.281 x 10=

38

21

3.98762 x 10

31.2632 x 10=

170.12755 x 10= J

17

19

0.12755 x 10

1.602 x 10= eV

7.96 eV=


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MADELUNG CONSTANT:

It is a function of crystal structure and can be calculated from the geometrical

arrangement of ions in the crystal.

Evaluation of madelung constant A for NaCl:

Na+

Cl-

r

C

Fig. 3

Consider the Sodium Chloride crystal as shown in the fig. 3. Let the distancebetween two successive ions in NaCl crystal lattice be r. Let us take a sodium ion named C,

which is surrounded by six chlorine ions at a distance r.

The coulomb energy due to these six chlorine ions is2

0

6

4

e

r

.

Further the coulomb energy due to twelve sodium ions at a distance 2ris

2

0

12

4 2

e

r .

Similarly, the coulomb energy due to eight chlorine ions which are at a distance 3ris

2

0

8

4 3

e

r

Further Na at C is surrounded by six sodium ions at a distance of 2rand so on.

Thus the total energy of Na at position C is given by2

0

6 12 8 6 24...

4 1 2 3 4 5

eU

r

= + +

In the above equation the bracketed term is a natural number whose value depends on thestructure of the crystal, calledMadelung Constant A.

Therefore, the value of madelung constant for NaCl crystal is

6 12 8 6 241.7475

1 2 3 4 5A

= + + =


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QUESTIONS

1) Explain the different types of bondings in solids with suitable examples.2) Explain the forces between the two interacting atoms when they are brought nearer to

form a molecule.

3) Plot and explain the variation of(i) Attractive potential energy(ii) Repulsive potential energy(iii) Resultant potential energy

with the interatomic distance, when two atoms are brought nearer.

4) Illustrate graphically the variation of(i) Attractive force(ii) Repulsive force(iii) Resultant force

with the spacing between two interacting atoms.

5) Derive the expression for the equilibrium spacing of two atoms for which the potentialenergy is minimum and hence obtain the dissociation energy.

6) What is cohesive energy? Assuming a suitable model for interatomic forces derive anexpression for the cohesive energy.

7) Derive an expression for the cohesive energy of an ionic crystal.8) Evaluate the value of madelung constant for NaCl crystal.

Documents

APPLIED PHYSICS Bonding in Solids by CHARIS ISRAEL ANCHA