solid state chemistry ipe

1Solid state

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SOLID STATE

Characteristic properties of solid state1) Solids have definite mass, volume and shape.2) They are incompressible and rigid.3) Their constituent particles (atoms or ions or molecules) are arranged very closely and the attrac-

tions between them are strong.4) Their constituent particles have fixed positions and can only oscillate about their mean positions.

Translatory and rotatory motions are restricted.

Crystalline and amorphous solidsSolids can be classified into crystalline and amorphous on the basis of the nature of order present in

the arrangement of their constituent particles.Crystalline solids

Crystalline solids have definite characteristic geometrical shape. They have long range order whichmeans that there is a regular pattern of arrangement of particles which is repeated over the entire crystal.They possess definite and characteristic melting points and heats of fusion. They show anisotropic nature.Anisotropic substances exhibit different values for some physical properties like refractive index, electri-cal resistance etc., in different directions.

E.g.., Sodium chloride, crystalline quartz etc.,Amorphous solids

Amorphous solids have irregular shape. They possess only short range orders i.e., the regular patternof arrangement is repeated over short distance only. They do not possess definite and characteristicmelting points and heats of fusion. They show isotropic nature as they exhibit same values for somephysical properties in different directions.

These are actually considered as super cooled liquids or pseudo solids.E.g.., Glass, rubber, amorphous quartz, plastics (organic polymers) etc.,

Property Crystalline solids Amorphous solidsShape Definite characteristic geometrical shape Irregular shapeMelting point Melt at a sharp and characteristic

temperatureGradually soften over a range of temperature

Cleavage property

When cut with a sharp edged tool, they split into two pieces and the newly generated surfaces are plain and smooth

When cut with a sharp edged tool, they cut into two pieces with irregular surfaces.

Heat of fusion They have a definite and characteristic heat of fusion

They do not have definite heat of fusion

Anisotropy Anistropic in nature Isotropic in natureNature True solids Pseudo solids or super cooled liquidsOrder Long range order Only short range order

Distinction between Crystalline and Amorphous Solids

Classification of solids based on nature of attractionsCrystalline solids are classified based on nature of attractions between constituent particles in them

into four categories viz.,1) molecular, 2) ionic, 3) metallic and 4) covalent solids1) Molecular solids : Molecules (or rarely noble gas atoms ) are the constituent particles. They areattracted by weak van der wall's forces of attractions or by hydrogen bonds. Based on the nature of theseintermolecular forces, molecular solids are again subdivided into

i) van der wall's crystals : In these solids, the intermolecular forces of attraction are very weak vander wall's forces (Like London dispersion forces or dipole-dipole attractions). These solids have verylow melting points and relatively soft.

E.g., Solid H2, N2, CO2, SO2 etc.,

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ii) Hydrogen bonded Crystals : In these solids, the constituent molecules are attracted by hydrogenbonds. These are usually hard.

E.g., Ice (Solid H2O), solid HF, solid NH3 etc.,Usually the melting points of molecular solids are below room temperature. They are bad conductors

of electricity.

2) Ionic Solids : Ions are the constituent particles. The cations and anions are arranged regularly in threedimensions and strongly held together by electrostatic attractions. These solids are rigid with high meltingpoints. But they are brittle and non elastic. As the ions are not free to move, ionic solids are electricalinsulators in solid state.

E.g., NaCl, KCl etc.,

3) Metallic Solids : Metallic crystals constitute orderly arranged metal atom in a sea of free electrons.These electrons held the metal atoms together.

Metals are rigid and possess high melting points due to strong metallic bonds. Due to the presence offree electrons, they are good electrical and thermal conductors. They are also lustrous, opaque, malleableand ductile.

E.g., Cu, Al, Fe etc.,

4) Covalent Crystals : The entire crystal is considered as a giant molecule. It is a three dimensionalnetwork of atoms bonded covalently.

These solids are very hard with extremely high melting points. They do not conduct electricity (exceptgraphite).

E.g., diamond, graphite, SiC, SiO2 etc.,The differences between above types of solids is summarized below

Type of solidConstituent

particles Attractive Forces ExamplesPhysical Nature

Electrical Conductivity

Melting point

(1) Molecular solids(i) van der wall's solids

Molecules van der wall's forces

Ar, CCl4,H2, I2, CO

Soft Insulator Very low

(ii) Hydrogen bonded

Hydrogen bonding H2O (ice) Hard Insulator Low

(2) Ionic solids Ions Coulombic or electrostatic

NaCl, MgO,ZnS, CaF

Hard but brittle

Insulators in solid state but conductors in molten state.

High

(3) Metallic solids Positive ions in a sea of delocalised electrons

Metallic bonding Fe, Cu,Ag, Mg,

Hard but malleable and ductile

Conductors in solid state as well as in molten stste

Fairly high

(4) Covalent or network solids

Atoms Covalent bonding SiO2

(quartz), SiC, C (diamond), AlN,

Hard Insulators Very high

C(graphite) Soft Conductor (exception)

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Metalling bondingThe bonding in metals can be explained by using following theories.

1) Electron sea model (Drude-Lorentz theory)According to this theoryi) A metal lattice comprises of rigid spheres of metal ions in a sea of free electrons.ii) Metal atoms contribute their valence electrons to the sea of free electrons.iii) These electrons move freely through the interstices.iv) The attraction between metal ions and free electrons is called metallic bond.v) This theory could explain the electrical and thermal conductivity of metal. But it fails in explaining thelattice energies quantitatively.

+ + + + +

+ + + + +

+ + + + +

- - - - - -

- - - - - -

- - - - - -

- - - - - -

- Free electron

+ Metal ion2) Valence bond theory

This theory was proposed by Linus Pauling. According to this theory, metallic bond is consideredas a highly delocalized covalent bond between metal atoms. Metal can exhibit several resonancestructures due to the delocalization of one electron and electron pair covalent bonds. These resonancestructures confer stability to the metallic crystal. Various resonance forms in sodium metal are shownbelow.

Na Na

Na Na Na

Na

Na

Na

Na NaNa

+Na

- Na NaNa

+Na

-Na

-

Na

Na

Na+

Na-

Na

Na

Na+

etc.,

This theory could not explain metallic lustre, heat conduction by metals and retention of metallicproperties in molten and solution state of metals.

Crystal lattice and unit cellCrystal lattice: The regular three dimensional arrangement of lattice points in space is called crystallattice.

The points at which the constituent particles (atoms or ions or molecules) of crystal are found arecalled lattice points.

Unit cell : The smallest part of the crystal lattice which generates entire crystal when repeated in threedimensions is known as unit cell.

Crystal parametersThe three edges of unit cell are denoted by a,b and c and the angles between these edges are

denoted by , and

between b & c between a & c between a & b

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z-axis

y-axis

x-axis

ab

c

Note: a,b,c, α,β and γ are called crystal parameters.

Types of unit cells1) Primitive or simple unit cell: The constituent particles are only present at the corners of the unitcell.

2) Body centered unit cell: It contains particles at all the eight corner as well as at the centre of theunit cell.

3) Face centered unit cell: In this unit cell, all the eight corners and six faces are occupied bythe constituent particles in the unit cell.

4) End centre unit cell: In this unit cell, one constituent particle is present at the centre of any twoopposite faces besides those present at the corners.

Crystal systems and Bravais lattices:Based on crystal parameters, crystal systems are divided into seven types by considering only primi-

tive arrangements. But there are 14 crystal lattices possible with all types of unit cell arrangements whichare called Bravais lattices. The requirement of this classification is that the geometric shape of the crystal

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lattice must be same as that of the solid crystal itself.The seven crystal systems and Bravais lattices are summarized below.

Crystal System Bravais Lattices

Axes or edge length

parameters Angles Examples

1. Cubic 3 (P, I, F) a = b = c = 900 NaCl, Zinc blende,

Cu

2. Tetragonal 2 (P, I ) a = b c = 900 White tin, SnO2,

TiO2, CaSO4

3. Orthorthombic 4 (P, I, F, C) a b c = 900 Rhombic sulphur,

KNO3, BaSO4

4. Rhombohedral (OR) Trigonal

1 (P)

a = b c

900 Calcite (CaCO3),

HgS (cinnabar) 5.Hexagonal 1 (P) a = b = c = 900 ; = 1200 Graphite, ZnO,

CdS,

6. Monoclinic 2 (P, C) a b c = = 900 ; 900 Monoclinic sulphur,

Na2SO4.10H2O 7. Triclinic 1 ( P) a b c 900 CuSO4

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a

aa

c

aa

c

ab

a120o

c

a

aa a

c

ab

a

c

b

simple(P)

BodyCentred

(I)

FaceCentred

(F)

EndCentred

(C)

90o a b c

90o a b c

90o

a b c

90o a b c

90 ; 120o o

a b c

90 ; 90o o

a b c

90o a b c

1. Cubic

2. Tetragonal

3. Ortho rhombic

4. Rhombohedralor

Trigonal

5. Hexagonal

6. Monoclinic

7. Triclinic

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Packing in metallic solidsMetal atoms in metallic crystal can be packed closely in four different arrangements as described

below.1) Simple cubic arrangement

Simple cubic arrangement of metallic crystal is obtained when two dimensional square closepacked layers are arranged over each other such that the spheres in the second layer are presentexactly over the spheres of first layer.

The coordination number of each sphere in this arrangement is six. The packing fraction is only52%.

E.g., Polonium

2) Body centered cubic (BCC) arrangementIn this arrangement, the two dimensional square close packed layers are arranged such that the

spheres in every next layer are arranged over the voids of the first layer.The coordination number is eight and packing fraction is 68% in this arrangement.E.g., Na, K, Rb, Cs, ba, Cr, Mo, W etc.,

3) Hexagonal close packed (HCP) arrangementIn this arrangement, the closest packed layers are arranged in ABAB pattern. There are two types

of closest packed layers in which the spheres in every second layer (B) are present over the voids ofone type in first layer (A).

The coordination number is twelve and packing fraction is 74%.E.g., Be, Mg, Cd, Co, Zn, Ti, Tl etc.,

4) Cubic close packed arrangement (CCP) or Face centered cubic (FCC) arrangementIn this arrangement, the closest packed layers are arranged in ABCABC pattern. The spheres in

the second layer (B) are arranged over one type of voids in the first layer (A). Whereas the spheres inthe third layer (C) are placed over the second type of voids of first layer (A).

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The coordination number is twelve and packing fraction is 74%.E.g., Al, Cu, Au, Pt, Pb, Pd, Ni, Ca etc.,

Packing fractionIt indicates how much of space is occupied by constituent spheres in a crystal lattice.

volumeof all thespheresPacking fraction =volumeof thecrystal

Coordination number : The number of closest atoms surrounding an atom in a metallic crystal isknown as coordination number of that crystal.

Number of atoms (z) present in a unit cellThe atoms at the corners of a unit cell contribute only 1/8th part of them to the unit cell.The atoms at the centre of a face of unit cell contribute only 1/2 part of them.The atoms on the edges of unit cell contribute 1/4th part of them.

In simple cubic unit cell: z = 8 x 1/8 = 1

In Body centered unit cell: z = (8 x 1/8 ) + (1) = 2

In Face centered unit cell: z = (8 x 1/8 ) + ( 6 x 1/2) = 1+3 = 4

Density ( ) of the crystalIt is possible to calculate the density of crystal from the dimensions of unit cell and mass of atoms in

it.

3

mass of atomsin unit celldensity ρ =volume of unit cell

Zma

whereZ = no. of atoms in a unit cell

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m = mass of one atom

A

Molar mass M=

Avogadro number N

a = edge length

3A

Z.Mρ =N .a

Types of voidsTrigonal void :The empty space between adjacent three spheres in a layer of closely packed crystals iscalled trigonal void .

trigonal void

If the number of atoms in closely packed crystals ( hcp or ccp) is 'X' then the number of trigonal voids inthem is '8X'.Tetrahedral void : The three dimensional empty space formed in between closely spaced three spheresin a layer and another sphere in the next layer is called tetrahedral void.

tetrahedral void

There are two types of tetrahedral holes in closely packed crystals ( hcp or ccp) . The total number oftetrahedral holes containing 'X' atoms in hcp or ccp crystal is equal to '2X'.Octahedral void : The empty space between three spheres of one layer and three spheres of next layeris called octahedral void.

octahedral void

In hcp and ccp arrangements, the number of octahedral voids is equal to number of atoms in the crystal.

Radius ratio in ionic compoundsIn ionic compounds, the crystal lattice is considered to be formed by bigger ions (usually anions)

and the small sized ions (usually cations) occupy the vacancies formed by bigger ions.The geometry around each ion and coordination number of ion are decided by the limiting radius

ratio.

radius of small ionlimiting radius ratio = radius of large ion

small

big

r rr r

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Radius ratio s m a ll la rg e( r / r )

Geometric shape of the crystal formed

Coordination number of

the ion Upto 0.15 Linear 2 0.15 to 0.22 Trigonal planar 3 0.22 to 0.41 Tetrahedral 4 0.41 to 0.73 Square pyramidal 4 0.41 to 0.73 Octahedral 6 >0.73 Cubic 8

Defects in crystalsThe irregularities in the arrangement of constituent particles in crystals lead to several types of defects

in crystals.Defects in crystals affect density, heat capacity, entropy, mechanical strength, electrical conductivity,

catalytic activity etc., . Thermodynamically all the crystal have the tendency to become defective becausedefects increase the entropy of crystals.

Defects in crystals are broadly divided intoi) Point defects: which occur around a lattice point in a crystal.ii) Line or extended defects: which are present in one or more dimensions.

Defects can also be classified intoi) Intrinsic : which are present in pure crystals.ii) Extrinsic : which occur due to impurities in crystals

Point defects: These are of three types :i) Stoichiometric : Stoichiometry is maintained in the defected crystal.ii) Non stoichiometric : Stoichiometry of the defected crystal is not maintained.iii) Impurity defects : These defects otherwise known as extrinsic defects occur due to presence of

impurities in crystals.

Stoichiometric defects1. Schottky defect

The point defect which arises due to missing of ions at the lattice points of ionic crystal is calledschottky defect.

In order to maintain electrical neutrality, the number of missing cations and anions must be equal.Schottky defects are shown by ionic compounds in which cation and an ion sizes are equal. They

show high coordination numbers ( 6 or 8).Eg :- NaCl, KCl, CsCl etc.,

The density of crystal decreases with increase in number of schottky defects.It is a thermodynamic defect i.e., the number of defects increases with temperature.

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Frenkel defectIt is a point defect formed due to shifting of an atom or ion from its normal lattice point to an interstitial

site. It is also called dislocation defect.This defect is shown by ionic compounds in which there is a large difference in size of ions.

E.g., AgCl, Ag Br, AgI, ZnS etc.,In above compounds cations (Ag+, Zn2+ etc.,) are smaller in size when compared to anions ( like halides).

Frenkel defect does not change the density of the crystal.

Bragg's equation: Consider a crystal surface with planes of lattice points as shown below. Let the interplanar distance between them is 'd'. Now consider two X-rays , of wavelength ' ' ,which are incident onthe surface of the crystal and undergoing constructive interference.

1st plane

2nd plane

3rd plane

1st ray2nd ray

d

A

BCD

E

F

The first ray is reflected at point 'A' on the surface of 1st plane, where as the 2nd ray is reflected atpoint 'B' on the surface of 2nd plane, both at an angle of . This is called angle of reflection.

Both the rays travel the same distance till the wavefront 'AD'. The second ray travels an extra distanceof DB+BC and then interfere with first ray constructively. If the two waves are to be in phase, the pathdifference between the two rays must be an integral multiple of wavelength of X-ray ' '.i.e., n DB BC (where n= an integer and known as order of diffraction)and AB = d = inter planar distance

Now DB = BC = d sinor DB+BC = 2d sin

2n d Sin

Above equation is known as Bragg's equation.

Electrical properties: Based on electrical conductivity, solids are broadly divided into three types.

(i) Conductors: The solids with conductivities ranging between 104 to 107 ohm–1m–1 are called conduc-tors. Metals have conductivities in the order of 107 ohm–1m–1 and are good conductors.

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(ii) Insulators : These are the solids with very low conductivities ranging between 10–20 to 10–10 ohm–

1m–1.

(iii) Semiconductors : These are the solids with conductivities in the intermediate range from 10–6 to 104

ohm–1m–1.

A conductor may conduct electricity through the movement of electrons or ions. Metals conductelectricity in solid as well as molten state through the movement of electrons. The conductivity of metalscan be explained as follows.

The atomic orbitals of metal atoms form molecular orbitals which are so close in energy to each otherand form a band. There are two types of molecular orbitals possible. The molecular orbitals with lowenergy are referred to as bonding and with high energy are called anti-bonding orbitals. The band formedby bonding molecular orbitals is generally called valence band and that band formed by anti-bondingorbitals is called conduction band. If the valence band is partially filled or it overlaps with conductionband, then electrons can flow easily under an applied electric field and the metal shows conductivity. Theconductivity of metals decreases with increase in temperature due to increase in vibrations of atoms.

In case of insulators, the gap between valence and conduction bands is very large and hence theelectrons cannot jump from filled valence band to unoccupied conduction band. Hence these substancesexhibit poor electrical conductivity.

But in case of semiconductors, there is a small gap between valence and conduction bands. There-fore, some number of electrons can jump into conduction band and show some conductivity. The con-ductivity of semiconductors increases with raise in temperature as more number of electrons can jump toconduction band.

conductors(metals)

S

Insulators

S

Semiconductors

conduction band

valence band

forbidden zonelarge energy gap small

energy gap

SEne

rgy

overlapping bands

partially filledvalence band

Semiconductors can be divided into intrinsic and extrinsic types.Intrinsic semi conductors: The pure semiconductors are called intrinsic semiconductors. Their con-ductivity is too low to be of practical use.

Eg., pure silicon, germanium

Extrinsic semiconductors: The conductivity of semiconductors, can be greatly enhanced by addingsuitable impurity. The semiconductors containing impurity are called extrinsic semiconductors.

Doping: The process of addition of impurities (dopant) to enhance the conductivity of semiconductors iscalled doping.

Extrinsic semi conductors are divided into two types based on type of impurity (dopant) added viz.,n-type and p-type semi conductors.

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i) n-type semi-conductors: The extrinsic semi conductors which contain electron-rich impurities arecalled n-type semi conductors. The electrical conductivity is due to movement of electrons.

Eg., Silicon or germanium doped with phosphorus or arsenic (15th group elements)Mechanism: Silicon and germanium belong to group 14 of the periodic table and have four valenceelectrons each. In their crystals each atom forms four covalent bonds with its neighbors . When dopedwith a group 15 element like P or As, which contains five valence electrons, they occupy some of thelattice sites in silicon or germanium crystal . Four out of five electrons are used in the formation of fourcovalent bonds with the four neighboring silicon atoms. The fifth electron is extra and becomes delocal-ized. These delocalized electrons increase the conductivity of doped silicon (or germanium). Here theincrease in conductivity is due to the negatively charged electron, hence silicon doped with electron-richimpurity is called n-type semiconductor.

ii) p-type semiconductors: The extrinsic semi conductors which contain electron-deficit impurities arecalled p-type semi conductors. The electrical conductivity is due to electron holes.

Eg., silicon or germanium doped with boron or aluminium or gallium (13th group elements)Mechanism: Silicon or germanium doped with a 13th group element like B, Al or Ga which contains onlythree valence electrons. As they can form only three bonds, an electron vacant site called 'electron hole'on the dopant atom is formed. An electron from a neighboring atom can jump into this electron hole bycreating a new hole on the neighboring atom. Thus there is a movement of electron holes and electrons inopposite direction. As the conductivity is increased due to formation of positively charged holes, thesubstances are called p-type semi conductors.

Applications:1) Diode is a combination of n-type and p-type semiconductors and is used as a rectifier.2) Transistors are made by sandwiching a layer of one type of semiconductor between two layers of theother type of semiconductor.3) npn and pnp type of transistors are used to detect or amplify radio or audio signals.4) The solar cell is an efficient photodiode used for conversion of light energy into electrical energy.Magnetic properties :

Materials can be divided into three different classes viz., diamagnetic, paramagnetic and ferromag-netic substances, depending on their responses to an applied magnetic field.

Diamagnetic materials : Diamagnetic materials are weakly repelled by the applied magnetic fields. It isbecause all the electrons are paired.Eg., NaCl; ZnO2; Benzene.

Molecular polarity alignment in Diagmagnetic substance

Paramagnetic materials : There are permanent magnetic dipoles due to the presence of unpairedelectrons on atoms, ions or molecules.Eg., O2, NO, Na atoms, Ti2O3, VO2.

These materials are attracted into the applied magnetic fields. They lose their magnetism when theapplied magnetic fields are removed.

Ferromagnetic materials : Ferromagnetic substances show permanent magnetism even after the ap-plied magnetic field is removed.Eg., Fe, CrO2.

In these substances there are domains of magnetization, which direct their magnetic moments in thesame direction. A spontaneous alignment of magnetic moments in the same direction gives rise to ferro-magnetism. Fe, Co, Ni are the only three elements which show ferromagnetism at room temperature.

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Molecular polarity alignment in Ferromagnetic substance

Ferrimagnetism arises when the magnetic moments are aligned in parallel and anti parallel direction inunequally resulting in a net moment.

Eg., Fe3O4, Ferrites of the general formula MII (Fe2O4) where M = Mg, Cu, Zn etc.,In case of anti ferromagnetism, the magnetic moments of domains are cancel out each other so as to

give zero net moment.Eg., MnO

Molecular polar alignment in Anti ferromagnetic substance

All these magnetically ordered solids transform to the paramagnetic state at elevated temperaturesdue to the randomization of spins.

Eg., V2O3, NiO change from anti-ferrimagnetic phase to paramagnetic phase at 150K and 523Krespectively.

Problems :1) A Metal crystallizes in fcc lattice. It the edge length of unit cell is 0.56 A0. Calculate the nearestneighbour distance in Al.2) Na metal crystallizes in body centered cubic lattice the edge length of unit cell is 0.424 nm at 298 Kcalculate the density of Na metal .3) An ionic compound contains two elements X and Y. If the atoms of X occupy the corners of unit cellwhat is the formula of that compound.4) An X-ray beam of wave length 70.93 pm was scattered by a crystalline solid. The angle (2 ) ofdiffraction for a second order reflection is 14.660. Calculate the distance between parallel planes ofatoms from which the scattered beam appears to have been reflected.5) A crystal when examined by the Bragg's technique using X-rays of wave length 2.29A0 gave an X-rayreflection at an angle of 23020'. Calculate the inter-planar spacing ; With another X-ray source, thereflection was observed at 15026'. What was the wave length of the X-rays of the second source.6) X-rays of wave length 5460A0 are incident on a grating with 5700 lines per cm. Find the angles ofreflection for the 1st and 2nd order diffraction maximum.

TEST YOUR UNDERSTANDINGState whether the following statements are true or false.1) Molecular solids posess high melting points as the attractions between the constituent particles arevery strong covalent bonds.2) The empty space in simple cubic packing is 48%.3) The unit cell parameters in case of hexagonal crystal system are 0 0; 90 , 120a b c

4) Bragg's equation can be written as sin = 2n

d

5) The number of atoms belonging to body centered unit cell is equal to two.6) The coordination number in cubic close packing is 6.7) The destructive interference occurs when the order of diffraction 'n' is a non integer.8) K2Cr2O7 belongs to triclinic crystal system.9) CsCl crystal show Frenkel defect.10) Stoichiometric compounds are called daltonides, whereas non stoichiometric compounds are calledberthollides.

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11) The density of crystal with Schottky defects is less than that of perfect crystal.12) The dopant used in p-type semi conductors belongs to VI A group.13) Mg(Fe2O4), a ferrite, exhibits ferrimagnetism.14) If the limiting radius ratio of an ionic compound is 0.71, then the cation will occupy the octahedralvoid formed by anions.15) The number of tetrahedral voids found in a crystal of one mole of magnesium metal is equal to N(Avogadro number).

solid state chemistry ipe

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