Chapter 6

The Solid ste

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Although crystalline solids have short range as well as long range order in arrangement of their constituent particles, yet crystals are not perfect. Usually a solid consists of an aggregate of large number of small crystals. These small crystals have defects in them. This happens when crystallization process occurs at fast or moderate rate. Single crystals are formed when the process of crystallization occurs at extremely slow rate. Even these crystals are not free of defects. The defects are basically irregularities in the arrangement of constituent particles. The defects are of two types.

  1. Point defects
  2. Line defects

Point defects are irregularities or deviations from ideal arrangement around a point or an atom in a crystalline substance.
Line defects are irregularities or deviations from ideal arrangement in the entire rows of lattice points.


Point defects are classified into three types :

  1. Stiochiometeric defects
  2. Impurity defects
  3. Non-stiochiometric defects


These are the point defects that do not disturb the stiochiometry of the solid. They are also called intrinsic or thermodynamic defects . Basically these are of two types , vacancy defects and interstitial defects .

a) Vacancy Defects

When some of the lattice sites are vacant , the crystal is said to have vacancy defect (Fig). This results in decrease in density of the substance. This defect can also develop when a substance is heated.

b) Interstitial Defect

When some constituent particles (atoms or molecules) occupy an interstitial site , the crystal is said to have interstitial defect(Fig). This defect increases the density of the substance. The vacancy and interstitial defects can be shown by non-ionic solids. Ionic solids must always maintain electrical neutrality. Rather than simple vacancy or interstitial defects they show these defects as Frenkel and Schottky defects.

This defect is shown by ionic solids. The smaller ion(usually cation) is dislocated from its normal site to an interstial site (Fig). It creates a
vacancy defect , at its original site and an interstitial defect at its new location.

Frenkel defect is also called dislocation defect . It does not change the density of the solid. Frenkel defect is shown by ionic substance in which there is a large difference in the size of ions, for example, ZnS, AgCl, AgBr and AgI due to small size of Zn2+ and Ag+ ions.


It is basically a vacancy defect in ionic solids. In order to maintain electrical neutrality, the number of missing cations and anions are equal (Fig).

(a) Frenke kel defects (b) Schottky defects

Like simple vacancy defect, Schottky defect also decreases the density of the substance. Number of such defects in ionic solids is quite significant. For example in NaCl there are approximately 106 Schottky pairs per cm3 at room temperature. In 1 cm3 there are about 1022 ions. Thus there is one Schottky defect per 1016 ions. Schottky defect is shown by ionic substances in which the cation and anion are of similar sizes. For example, NaCl, KCl , CsCl and AgBr. It may be noted that AgBr shows both, Frenkel as well as Schottky defects.

Consequences of Schottky and Frenkel defects

Schottky and Frenkel defects in crystals leads to the following consequences :

  1. Because of the presence of these defects, the electrical conductivity of crystals increases.
  2. Due to the presence of holes in the crystal, its density decreases. However, the density decreases only for crystals having Schottky defects.
  3. The presence of 'holes' also decreases the lattice energy or the stability of the crystal.
  4. The Frenkel defects tend to increase the dielectric constant of the crystals.

Difference between Schottky and Frenkel defects


Schottky defect

Frekel defect

It is due to equal number of cations and anions missing from the lattice sites.

It is due to missing of ions (usually cations) from the lattice sites and these occupy the interstitial sites.

This results in the decrease in the density of the crystal.
It has no effect on the density of the crystal.


This type of defect is found in highly ionic compounds with high co-ordination number and having cations and anions of similar sizes , e.g. NaCl, CsCl etc.
This type of defect is found in crystals where the difference in the size of cations and anions is very large e.g. AgCl, AgBr, ZnS etc.


If molten NaCl containing a little amount of SrCl2 is crystallized , some of the sites of Na+ ions are occupied by Sr2+ (Fig).

Each Sr2+ replaces two Na+ ions. It occupies the site of one ion and other site remains vacant. The cationic vacancies thus produced are equal in number to that of Sr 2+ ions. Another example is solid solution of CdCl2 and AgCl.


The defects so far discussed does not disturb the stoichiometry of the crystalline substance. However a large number of non-stiochiometric inorganic solids are known which contain the constituent elements in non-stiochiometric ratio due to defects in their crystal structures. These defects are of two types.
i ) Metal Excess Defect    ii) Metal Deficiency Defect.
Metal Excess Defect

i) Metal excess defect due to anionic vacancies

Alkali halides like NaCl and KCl show this type of defect. When crystals of NaCl are heated in atmosphere of sodium vapour. the sodium atoms are deposited on the surface of the crystal. The Cl ions diffuse to the surface of crystals and combine with sodium atoms to give NaCl. This happens by the loss of electrons by sodium atoms to form Na+ ions. The released electrons diffuse into the crystal and occupy anionic sites (Fig). As a result the crystal now has an excess of sodium. The anionic sites occupied by unpaired electrons are called F-centres
( farben : colour ). They impart yellow colour to crystals of NaCl. The colour results by excitation of these electrons when they absorb energy from the visible light falling on the crystals. Similarly excess of lithium makes LiCl crystals pink and excess of potassium makes KCl crystals violet (or lilac).

ii) Metal excess defect due to the presence of extra cations at the interstitial sites

Zinc oxide is white in colour at room temperature. On heating it loses oxygen and turns yellow.
                                                                              ZnO      Zn2+ +  ½ O2 +  2 e
Now there are excess of zinc in the crystal and its formula becomes Zn1 + x O. The excess of Zn2+ions move to interstitial sites and the electrons to the neighbouring interstitial sites.

Consequences of Metal excess defects

  1. The crystals with excess defects conduct electricity due to the presence of free electrons. These compounds are also called n-type semi-conductors, since the current is carried by electrons in the normal way.
  2. The crystal with metal excess defects are generally coloured. This is due to the presence of free electrons. For example, non-stoichiometric sodium chloride is yellow, non-stoichiometric potassium chloride is lilac.


There are many solids which are difficult to prepare in stiochiometric composition and contain less amount of the metal as compared to the stiochiometric proportion. A typical example of this type is FeO which is mostly found with composition Fe0.95O. It may actually range from Fe0.93O
to Fe0.96O. In crystals of FeO some Fe2+ cations are missing and the loss of positive charge is made up by the presence of required number of
Fe3+ ions.

Consequences of Metal deficiency defects

Crystals with metal deficiency defects can be semi-conductors. This property arises from the movement of an electron from one ion to another ion. In this way, the ion, say A+, changes into A2+ ion. This is called movement of positive ‘hole' and substances permitting this type of movement is known as p-type semi-conductors.


Solids exhibit an amazing range of electrical conductivities , extending over 27 orders of magnitude ranging from 10−20 to 107 ohm−1 m−1 . Solids can be classified into three types on the basis of their conductivities.

  1. Conductors : The solids with conductivities ranging between 104 to 107 ohm−1 m−1 are called conductors. Metals have conductivities in the order of 107 ohm−1 m−1 are good conductors.
  2. Insulators : These are solids with very low conductivities ranging between 10−20 to 10−10 ohm−1 m−1 .
  3. Semiconducors : These are solids with conductivities in the intermediate range from 10−6 to 104 ohm−1 m−1 .


A conductor may conduct electricity through the movement of electrons or ions. Metallic conductors belong to the former category and electrolytes to the latter . Metals conduct electricity in solid as well in molten state. The conductivity of metals depend upon the number of valence electrons available per electron. The atomic orbitals of metal atoms form molecular orbitals which are so close in energy to each other as to form a band . If this band is partially filled or it overlaps with a higher energy unoccupied conduction band , then electrons can flow easily under an applied electric field and the metal shows conductivity (Fig a).

Distinction among   (a) Metal    (b)   Insulator    (c) Semiconductor

If the gap between the filled valence band and next higher unoccupied band (conduction band) is large, electrons cannot jump to it and such a substance has very small conductivity and it behaves as an insulator(Fig b).

Conduction of Electricity in Semiconductors

In case of semiconductors , the gap between the valence band and conduction band is small (Fig c). Therefore, some electrons may jump into conduction band and show some conductivity. Electrical conductivity of semiconductors increases with rise in temperature, since more electrons can jump to conduction band. Substances like silicon and germanium show this type of behaviour and are called intrinsic semiconductors .

The conductivity of this intrinsic semiconductors is too low to be of practical use. Their conductivity is increased by adding an appropriate amount of suitable impurity. This process is called doping . Doping can be done with an impurity which is electron rich or electron deficient as compared to intrinsic semi conductor silicon or germanium. Such impurities introduce electronic defects in them.

Electron rich impurities

Germanium and silicon belong to Group 14 of the periodic table. These elements , in pure state, have very low electrical conductivity. However, on adding even traces of an element belonging to Group 13 or 15 , the electrical conductivity is greatly enhanced. This may be explained as under. Suppose , in the first instance , a group 15 element , like arsenic, is added to germanium crystal. As germanium atom is substituted by an atom of arsenic, four electrons in arsenic form covalent bonds with surrounding germanium atoms but the fifth electron remains free. In this way , an extra electron, over and above the number required for forming four covalent bonds, gets introduced into the crystal. This extra electron can serve to conduct electricity, i.e., it behaves like conductor-electron as in metals. Thus , germanium containing traces of arsenic (known as arsenic-doped germanium) begins to exhibit fairly high electrical conductivity. This type of conduction is known as extrinsic conduction . It is much greater than the intrinsic conduction. Since, in this type of conduction, current is carried by excess electrons in the normal way, it is n-type semi-conduction .

Electron deficient impurities

Silicon or germanium can also be doped with a group 13 elements like B, Al , or In which conntains only three valence electrons. The atoms of indium, evidently are not able to complete tetrahedral covalent structures because they have one electron short of the requirement. Hence, some of the sites normally occupied by electrons will be left empty. This give rise to electron-vacancies. The electron-vacant sites are known as ‘positive holes' because the net charge at these sites is positive. When electric field is applied, adjacent electrons move into the positive holes and in this way other electron-vacancies ( or positive holes) are formed. The migration of positive holes thus continues and current is carried thereby throughout the crystal. Thus , doping of germanium with traces of indium increases the electrical conductivity of germanium crystal. Since the current , in the present case is carried by positive holes, this type of conduction is
p-type semi-conduction

Applications of n-type and p-type semiconductors

Various combinations of n-type and p-type semiconductors are used to make electronic components, for example a diode is a combination of p- and n-type semiconductors and is used as a rectifier. Transistors which are pnp or npn sandwich ' semiconductor are used to detect or amplify radio or audio signals. The solar cell is essentially an efficient photo diode used for converting radiant (light) energy into electrical energy.

Germanium and silicon are group-14 elements and have therefore , a characteristic valence of four and form four bonds as in diamond. A large variety of solid state materials have been prepared by the combination of elements of group-13 and 15 or 12 and 16 to stimulate average valence of four as in Ge or Si. Typical of group 13-15 compounds are InSb, AlP and GaAs . Galium arsenide (GaAs) semiconductors have very fast responses and have revolutionised the design of semiconductor devices . ZnS, CdS. CdSe and HgTe are examples of group 12-16 compounds. In these compounds, the bonds are not perfectly covalent and the ionic character depends on the electronegativities of the two elements.

The transition metal oxides show marked differences in electrical properties. TiO, CrO2 and ReO3 behave like metals. Rhenium oxide, ReO3 is like metallic copper in its conductivity and appearance. Certain other oxides like VO, VO2 , VO3 , TiO3 show metallic or insulating properties depending on temperature.


The macroscopic (observable) magnetic properties of materials are due to the magnetic moments associated with individual electron. Each electron in an atom has magnetic moment which originates from two sources :

(i)   Orbital motion around the nucleus.   (ii)   Spin of electron around its own axis.

A moving electron may be regarded as a small current loop generating a small magnetic moment along its axis of rotation as shown in Fig 47 (a) . The magnetic moment which originates from electron spin is directed along the spin axis. The spin moments are generally shown by up and down direction as shown in Fig (b). Thus , each electron in an atom may be regarded as a small magnet having permanent orbital and spin magnetic moments . The fundamental magnetic moment is the Bohr magneton m B which is equal to 9.27 x 10−24 A m2 . For each electron in an atom , the spin moment is ± μB (depending upon two possibilities of the spin). The contribution of orbital magnetic moment is equal to mi μB where mi is the magnetic quantum number of the electron.

Demonstration of magnetic moment associated with
(a) an orbiting electron and (b) a spinning electron.

The magnetic properties of solids are also related to the electronic structures. Materials can be classified into different types depending upon their behaviour towards magnetic fields.

Diamagnetic materials

Materials, which are weakly repelled by magnetic fields are called diamagnetic materials. Diamagnetism arises when all the electrons are paired. In other words, diamagnetic substances contain only filled orbitals, e.g., alkali metal halides, TiO2 , C6 H6 etc.

Paramagnetic materials

Materials which are weakly attracted by magnetic fields are called paramagnetic materials and the property thus exhibited is called paramagnetism. However, such substances lose their magnetism in the absence of a magnetic field. In such materials there are permanent magnetic dipoles due to the presence of atoms, ions or molecules with unpaired electrons.
Examples : O2 , NO, CuO, Ti2 O3 , VO2 etc.

Ferromagnetic materials

Materials which are strongly attracted by magnetic fields are called ferromagnetic materials and the property thus exhibited is called ferromagnetism. Such substances show permanent magnetism even after the magnetic field is removed. Only three elements (Fe, Co, Ni) show ferromagnetism at room temperature. The ferromagnetic character of these elements can be explained on the basis of their electronic configurations.
                                 Fe( Z = 26) : 1s2 2s2 2p 6 3s2 3p6 4s2 3d6
                                 Co( Z = 27) : 1s2 2s2 2p6 3s2 3p6 4s2 3d7
                                 Ni( Z = 28) : 1s2 2s2 2p6 3s2 3p6 4s2 3d8
From these configurations it is clear that the dipositive ions which exist in the metal lattice of these elements contain unpaired electrons. However, the magnetisation is so large and so persistent that it cannot be explained on the basis of number of unpaired electrons alone. The explanation is in these metals there are domains of magnetisation. Domains are regions of a millions or so ions, all of which co-operatively direct their individual magnetic effects in the same way. In an un-magnetised piece of metal these domains point randomly in all directions in such a way that , the sum of the magnetic effect cancels. When placed in a magnetic field, the domains are turned so that all point in the same direction giving rise to a large magnetic effect. If the metal is now removed from the field, it remains permanently magnetised unless the domain orientation is disorganised, as by heating.

The conditions for the formation of domains are satisfied only in case of these metals. The conditions are that the ions contain unpaired electrons and that the distance between ions be just exactly right in order that the interaction for lining up all the ions to form a domain may be effective. Manganese metal has most of the properties needed to be ferromagnetic, but the ions of the metal are too close. Addition of copper to manganese increases this average spacing, and the resulting alloy is ferromagnetic. Examples of ferromagnetic materials are Fe, Co, Ni, CuO, CrO2 etc. These are very important in technology. For example, CrO2 is used as the magnetic material in the magnetic recording tapes.

Schematic alignment of magnetic moments in
(a) Ferromagnetic (b) Antiferromagnetic and (c) Ferrimagnetic

The phenomenon of ferromagnetism depends on temperature. Ferromagnetic material, if heated above a particular temperature becomes paramagnetic. This temperature is called curie point . For example, 1023 K , 1373 K and 623 K are curie points for iron, cobalt and nickel respectively.

Antiferromagnetic materials

Materials which are expected to possess paramagnetism or ferromagnetism on the basis of unpaired electrons but actually have zero net magnetic moment are called antiferromagnetic materials. Antiferromagnetism is due to alignment of magnetic moments in a compensatory way
(i.e., equal number of magnetic moments in opposite directions) . e.g., V2O3 , Cr2O3 , MnO , Mn2O3 , FeO and Co3O4 .

Ferrimagnetic materials

Materials which are expected to possess large magnetism on the basis of unpaired electrons but actually possesses small net magnetic moment are called ferrimagnetic materials. In these materials , the magnetic moments are aligned in parallel and anti-parallell directions in unequal numbers such that there is net magnetic moment. e.g., Fe3O4 , MgFe2O4 , ZnFe2O4 and CuFe2O4 . The magnetic properties of some typical transition metal oxides are given in the TABLE.

Magnetic properties of typical transition metal oxides

TiO(p) VO(p) MnO(af) FeO (af)

Ti2O3 (p) , V2 O3 (af) , Cr2O3(af) , Mn2O3(af) , Fe2O3 (af)

TiO2(d) , VO2(p) , CrO2 (f) , MnO2 (af) , CoO (af)

V2O5 (p) , Fe3 O4 (fe)

CoI (af) , NiO(af) , CuO(p)

p = paramagnetic ; af = anti-ferromagnetic. fe = ferrimagnetic ; f = ferromagnetic d = diamagnetic .

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