According to the law of nature

nothing is perfect, and so crystals need not be perfect. They always found to have some defects in the arrangement of their constituent particles. These defects affect the physical and chemical properties of the solid and also play an important role in various processes. For example, a process called doping leads to a crystal imperfection and it increases the electrical conductivity of a semiconductor material such as silicon. The ability of ferromagnetic material such as iron, nickel etc., to be magnetized and demagnetized depends on the presence of imperfections. Crystal defects are classified as follows

1. Point defects

2. Line defects

3. Interstitial defects

4. Volume defects

In this portion, we concentrate on point defects, more specifically in ionic solids. Point defects are further classified as follows

Point defects

1. stiochiometric defects
   1. Schottky defect
   2. Frenkel defect
2. non- stiochiometric defects
   1. metal excess defect
   2. metal deficiency defect
3. impurity defects

Stoichiometric defects in ionic solid:

This defect is also called intrinsic (or) thermodynamic defect. In stoichiometric ionic crystals, a vacancy of one ion must always be associated with either by the absence of another oppositely charged ion (or) the presence of same charged ion in the interstitial position so as to maintain the electrical neutrality.

Schottky defect arises due to the missing of equal number of cations and anions from the crystal lattice. This effect does not change the stoichiometry of the crystal. Ionic solids in which the cation and anion are of almost of similar size show schottky defect. Example: NaCl.

Presence of large number of schottky defects in a crystal, lowers

Schottky Defect

its density. For example, the theoretical density of vanadium monoxide (VO) calculated using the edge length of the unit cell is 6.5 g cm-3, but the actual experimental density is 5.6 g cm-3. It indicates that there is approximately 14% Schottky defect in VO crystal. Presence of Schottky defect in the crystal provides a simple way by which atoms or ions can move within the crystal lattice.

Frenkel defect arises due to the dislocation of ions from its crystal lattice. The ion which is missing from the lattice point occupies an interstitial position. This defect is shown by ionic solids in which cation and anion differ in size. Unlike Schottky defect, this defect does not affect the density of the crystal. For example AgBr, in this case, small Ag+ ion leaves its normal site and occupies an interstitial position as shown in the figure.

Metal excess defect arises due to the presence of more number of metal ions as compared to anions. Alkali metal halides NaCl, KCl show this type of defect. The electrical neutrality of the crystal can be maintained by the presence of anionic vacancies equal to the excess metal ions (or) by the presence of extra cation and electron present in interstitial position.

For example, when NaCl crystals are heated in the presence of sodium vapour, Na+ ions are formed and are deposited on the surface of the crystal. Chloride ions (Cl-) diffuse to the surface from the lattice point and combines with Na+ ion. The electron lost by the sodium vapour diffuse into the crystal lattice and occupies the vacancy created by the Cl- ions. Such anionic vacancies which are occupied by unpaired electrons are called F centers. Hence, the formula of NaCl which contains excess Na+ ions can be written as Na Cl1+ x .

Frenkel Defect

Ag+

Ag+ Missing

Ag+ Missing

 Br-

Ag+ in interstitial position

Ag+ in interstitial position

e

F center Metal Excess Defect

Na+

Cl

ZnO is colourless at room temperature. When it is heated, it becomes yellow in colour. On heating, it loses oxygen and thereby forming free Zn2+ ions. The excess Zn2+ ions move to interstitial sites and the electrons also occupy the interstitial positions.

Metal deficiency defect arises due to the presence of less number of cations than the anions. This defect is observed in a crystal in which, the cations have variable oxidation states.

For example, in FeO crystal, some of the Fe2+ ions are missing from the crystal lattice. To the maintain the electrical neutrality, twice the number of other Fe2+ ions in the crystal is oxidized to Fe3+ ions. In such cases, overall number of Fe2+ and Fe3+ ions is less than the O2- ions. It was experimentally found that the general formula of ferrous oxide is FexO, where x ranges from 0.93 to 0.98.

A general method of introducing defects in ionic solids is by adding impurity ions. If the impurity ions are in different valance state from that of host, vacancies are created in the crystal lattice of the host. For example, addition of CdCl2 to AgCl yields solid solutions where the divalent cation Cd2+ occupies the position of Ag+. This will disturb the electrical neutrality of the crystal. In order to maintain the same, proportional number of Ag+ ions leaves the lattice. This produces a cation vacancy in the lattice, such kind of crystal defects are called impurity defects.

_

Metal Deciency Defect

Energy harvesting by piezoelectric crystals:

Piezoelectricity (also called the piezoelectric effect) is the appearance of an electrical potential across the sides of a crystal when you subject it to mechanical stress. The word piezoelectricity means electricity resulting from pressure and latent heat. Even the inverse is possible which is known as inverse piezoelectric effect.

If you can make a little amount of electricity by pressing one piezoelectric crystal once, could youmake a significant amount by pressing many crystals over and over again? What happens if we bury piezoelectric crystals under streets to capture energy as vehicles pass by?

Summary

„ Solids have definite volume and shape.

„ solids can be classified into the following two major types based on the arrangement of their constituents. (i) Crystalline solids (ii)Amorphous solids.

„ A crystalline solid is one in which its constituents (atoms, ions or molecules), have an orderly arrangement extending over a long range.

„ In contrast, in amorphous solids (In Greek, amorphous means no form) the constituents are randomly arranged.

„ Crystalline solid is characterised by a definite orientation of atoms, ions or molecules, relative to one another in a three dimensional pattern. The regular arrangement of these species throughout the crystal is called a crystal lattice.

„ A crystal may be considered to consist of large number of unit cells, each one in direct contact with its nearer neighbour and all similarly oriented in space.

„ A unit cell is characterised by the three edge lengths or lattice constants a ,b and c and the angle between the edges α, β and γ

„ There are seven primitive crystal systems; cubic, tetragonal, orthorhombic, hexagonal, monoclinic, triclinic and rhombohedral. They differ in the arrangement of their crystallographic axes and angles. Corresponding to the above seven, Bravis defined 14 possible crystal systems

„ In the simple cubic unit cell, each corner is occupied by an identical atoms or ions or molecules. And they touch along the edges of the cube, do not touch diagonally. The coordination number of each atom is 6.

„ In a body centered cubic unit cell, each corner is occupied by an identical particle and in addition to that one atom occupies the body centre. Those atoms which occupy the corners do not touch each other, however they all touch the one that occupies the body centre. Hence, each atom is surrounded by eight nearest neighbours and coordination number is 8.

„ In a face centered cubic unit cell, identical atoms lie at each corner as well as in the centre of each face. Those atoms in the corners touch those in the faces but not each other.The coordination number is 12.

This idea, known as energy harvesting, has caught many people’s interest. Even though there are limitations for the large-scale applications, you can produce electricity that is enough to charge your mobile phones by just walking. There are power generating footwears that has a slip-on insole with piezoelectric crystals that can produce enough electricity to charge batteries/ USB devices.`

„ X-Ray diffraction analysis is the most powerful tool for the determination of crystal structure. The inter planar distance (d) between two successive planes of atoms can be calculated using the following equation form the X-Ray diffraction data 2dsin = nθ λ

„ The structure of an ionic compound depends upon the stoichiometry and the size of the ions.generally in ionic crystals the bigger anions are present in the close packed arrangements and the cations occupy the voids. The ratio of radius of cation and anion (–r/r–) plays an important role in determining the structure

„ Crystals always found to have some defects in the arrangement of their constituent particles.

„ Schottky defect arises due to the missing of equal number of cations and anions from the crystal lattice.

„ Frenkel defect arises due to the dislocation of ions from its crystal lattice. The ion which is missing from the lattice point occupies an interstitial position.

„ Metal excess defect arises due to the presence of more number of metal ions as compared to anions.

„ Metal deficiency defect arises due to the presence of less number of cations than the anions.

EVALUATION

Choose the best answer:

1. Graphite and diamond are

a) Covalent and molecular crystals b) ionic and covalent crystals c) both covalent crystals d) both molecular crystals

2. An ionic compound AxBy crystallizes in fcc type crystal structure with B ions at the centre of each face and A ion occupying corners of the cube. the correct formula of AxBy is

a) AB b) AB3 c) A3B d) A8B6

3. The ratio of close packed atoms to tetrahedral hole in cubic packing is

a) 1:1 b) 1:2 c) 2:1 d) 1:4

4. Solid CO2 is an example of

a) Covalent solid b) metallic solid c) molecular solid d) ionic solid

5. Assertion : monoclinic sulphur is an example of monoclinic crystal system

Reason: for a monoclinic system, a≠b≠c and α γ β= = ≠90 900 0,

a) Both assertion and reason are true and reason is the correct explanation of assertion.

b) Both assertion and reason are true but reason is not the correct explanation of assertion.

c) Assertion is true but reason is false.

d) Both assertion and reason are false.

6. In calcium fluoride, having the flurite structure the coordination number of Ca2+ ion and F- Ion are (NEET)

a) 4 and 2 b) 6 and 6 c) 8 and 4 d) 4 and 8

7. The number of unit cells in 8 gm of an element X ( atomic mass 40) which crystallizes in bcc pattern is (NA is the Avogadro number)

a) 6.023 X 1023 b) 6.023 X 1022 c) 60.23 X 1023 d) —-6 023 10

8. In a solid atom M occupies ccp lattice and (1 / 3) of tetrahedral voids are occupied by atom N. find the formula of solid formed by M and N.

a) MN b) M3N c) MN 3 d) M3N2

9. The ionic radii of A+ and B− are 0 98 10 10. m× − and 1 81 10 10. m× − . the coordination number of each ion in AB is

a) 8 b) 2 c) 6 d) 4

10. CsCl has bcc arrangement, its unit cell edge length is 400pm, its inter atomic distance is

a) 400pm b) 800pm c) 3 100× pm d) 3—

11. A solid compound XY has NaCl structure. if the radius of the cation is 100pm , the radius of the anion will be

a) 100 0 414.– b) 0 732 100 . c) 100 0 414× . d) 0 414 100 .

12. The vacant space in bcc lattice unit cell is

a) 48% b) 23% c) 32% d) 26%

13. The radius of an atom is 300pm, if it crystallizes in a face centered cubic lattice, the length of the edge of the unit cell is

a) 488.5pm b) 848.5pm c) 884.5pm d) 484.5pm

14. The fraction of total volume occupied by the atoms in a simple cubic is

a) π 4 2

b) π 6

c) π 4

d) π

15. The yellow colour in NaCl crystal is due to

a) excitation of electrons in F centers

b) reflection of light from Cl- ion on the surface

c) refraction of light from Na+ ion

d) all of the above

16. if ‘a’ stands for the edge length of the cubic system; sc , bcc, and fcc. Then the ratio of radii of spheres in these systems will be respectively.

a) 1 2

b) 1 3 2_a a a_: :( )

c) 1 2

d) 1 2

17. If ‘a’ is the length of the side of the cube, the distance between the body centered atom and one corner atom in the cube will be

a) 2 3

b) 4 3

c) 3 4

d) 3

18. Potassium has a bcc structure with nearest neighbor distance 4.52 A0 . its atomic weight is 39. its density will be

a) 915 kg m-3 b) 2142 kg m-3 c) 452 kg m-3 d) 390 kg m-3

19. Schottky defect in a crystal is observed when

a) unequal number of anions and cations are missing from the lattice

b) equal number of cations and anions are missing from the lattice

c) an ion leaves its normal site and occupies an interstitial site

d) no ion is missing from its lattice.

20. The cation leaves its normal position in the crystal and moves to some interstitial position, the defect in the crystal is known as

a) Schottky defect b) F center

c) Frenkel defect d) non-stoichiometric defect

21. Assertion: due to Frenkel defect, density of the crystalline solid decreases.

Reason: in Frenkel defect cation and anion leaves the crystal.

a) Both assertion and reason are true and reason is the correct explanation of assertion.

b) Both assertion and reason are true but reason is not the correct explanation of assertion.

c) Assertion is true but reason is false.

d) Both assertion and reason are false

22. The crystal with a metal deficiency defect is

a) NaCl b) FeO

c) ZnO d) KCl

23. A two dimensional solid pattern formed by two different atoms X and Y is shown below. The black and white squares represent atoms X and Y respectively. the simplest formula for the compound based on the unit cell from the pattern is

a) XY8 b) X4Y9

c) XY2 d) XY4

Answer the following questions:

1. Define unit cell.

2. Give any three characteristics of ionic crystals.

3. Differentiate crystalline solids and amorphous solids.

4. Classify the following solids a. P4 b. Brass c. diamond d. NaCl e. Iodine

5. Explain briefly seven types of unit cell.

6. Distinguish between hexagonal close packing and cubic close packing.

7. Distinguish tetrahedral and octahedral voids.

8. What are point defects?

9. Explain Schottky defect.

10. Write short note on metal excess and metal deficiency defect with an example.

11. Calculate the number of atoms in a fcc unit cell.

12. Explain AAAA and ABABA and ABCABC type of three dimensional packing with the help of neat diagram.

13. Why ionic crystals are hard and brittle?

14. Calculate the percentage efficiency of packing in case of body centered cubic crystal.

15. What is the two dimensional coordination number of a molecule in square close packed layer?

16. What is meant by the term “coordination number”? What is the coordination number of atoms in a bcc structure?

17. An element has bcc structure with a cell edge of 288 pm. the density of the element is 7.2 gcm-3. how many atoms are present in 208g of the element.

18. Aluminium crystallizes in a cubic close packed structure. Its metallic radius is 125pm. calculate the edge length of unit cell.

19. if NaCl is doped with 10-2 mol percentage of strontium chloride, what is the concentration of cation vacancy?

20. KF crystallizes in fcc structure like sodium chloride. calculate the distance between K+ and F−

in KF.( given : density of KF is 2 48 3. _g cm_− )

21. An atom crystallizes in fcc crystal lattice and has a density of 10 3 _gcm_− with unit cell edge length of 100pm. calculate the number of atoms present in 1 g of crystal.

22. Atoms X and Y form bcc crystalline structure. Atom X is present at the corners of the cube and Y is at the centre of the cube. What is the formula of the compound?

23. Sodium metal crystallizes in bcc structure with the edge length of the unit cell 4 3 10 8. × − cm . calculate the radius of sodium atom.

24. Write a note on Frenkel defect.

Solids

Crystalline solid Amorphous solid

Ionic crystals

Covalent crystals

Molecular crystals Crystalline structure

Crystal lattice Close packing

Packing fraction

Unit cell

Imperfection in crystals

Schottky defect

Frenkel defect

Metal excess defect

Metal deciency defect

Simple Cubic

Body Centered Cubic

Face Centered Cubic

Sc

Bcc

Hcp

Ccp

XII U6 Solid State - Jerald.indd 202 2/19/2020 4:42:45 PM

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CRYSTAL SYSTEMS

Steps

• Open the Browser and type the URL given (or) Scan the QR Code. In the webpage click physical science tab and then click solid state virtual lab. Then go to crystal structure and then click simulator.

Note: One time sign up is needed to access this webpage. Login using your username and password. Once logged in click the simulator tab.

• Now the using the menu (box 1) select any one of the seven crystal systems and the lattice type. Now the unit cell of the selected crystal system will appear on screen (box 2) and the unit cell parameters will also be displayed in the measurement tab (box 3)

By using this tool, you will be able to visualize different crystal systems and know their unit cell parameters.

Please go to the URL http://vlab.amrita.edu (or) Scan the QR code on the right side