Solid State. S.K.Sinha. Resonance, Kota.

Transcription

1 Solid State By S.K.Sinha Resonance, Kota

2 Solid State 1.Concept of Solid 2.Concept of crystalline Solid : 3.Solids and lattice 4. Type of Solids (Force of attraction) 5. The closest packing 6. Packing Metallic Crystals 7. Packing Ionic Solids 8. Example of Ionic Solids 9. Defect in Crystals

3 1 Solid State 1.Concept of Solid A large majority of substances around us are solids. The distinctive features of solids are: 1. They have a definite shape. 2. They are rigid and hard. 3. They have fixed volume. These characteristics can be explained on the basis of following facts: 1. The constituent units of solids are held very close to each other so that the packing of the constituents is very efficient. Consequently solids have high densities. 2. Since the constituents of solids are closely packed, it imparts rigidity and hardness to solids. 3. The constituents of solids are held together by strong forces of attraction. This results in their having define shape and fixed volume. Information regarding the nature of chemical forces in solids can be obtained by the study of the structure of solids, i.e. arrangements of atoms in space. There are two types of solids: Amorphous and crystalline.

4 2 2.Concept of crystalline Solid : Note 1:There are 7 crystal systems,defined on the basis of axis of symmetry. Note 2: It was shown by A. Bravais in 1848 that all possible three dimensional space lattice are of fourteen distinct types. These fourteen lattice types are derived from seven crystal systems CRYSTAL SYSTEM POSSIBLE VARIATION EDGE LENGTHS AXILE ANGLE EXAMPLES Primitive body Body-centered α = β = γ Cubic Face-Centered a=b=c = 90 NaCl, Zinc blende, Cu Primitive, α = β = γ White tin, SnO 2,TiO 2, Tetragonal Body-centered a=b c = 90 CaSO 4 Primitive, Body-centered, Face-centered, α = β = γ Rhombic sulphur, Orthorhombic End-centered a b c = 90 KNO 3, BaSO 4 Hexagonal Primitive a=b c Rhombohedral or trigonal Primitive a=b=c α = β = 90 γ = 120 α = β = γ 90 Graphite, Zno,Cds Calcite (CaCO 3 ), HgS(cinnabar) Primitive, α = γ =90 Monoclinic Monoclinic End-centered a b c β 120 sulphur,na 2 SO 4.10H 2 O Triclinic Primitive a b c α β γ 90 K 2 Cr 2 O 7, CuSo 4.5H 2 O, H 3 BO 3 Table: Seven Primitive Unit Cells and their Possible Variations as Centred Unit Cells

5 3 3.Solids and lattice 1. As already mentioned crystalline solids consist of regular arrangement of atoms dimensions. in three 2. If atoms are considered known as space lattice. as points, the arrangement of an infinite set of points is 3. Each point in the lattice is so chosen that its environment is the same as that of any other point. One example each of one dimensional, two dimensional and a threee dimensional space lattice is shown in the figure. It may be understood here that it is the arrangement of the point which is a lattice and not the line which are joining them. 4. The smallest repeating motif (pattern) is known as a Unit cell. If this motif is repeated in different directions it should be able to regenerate the entire lattice. The unit cell is so chosen as to fulfil the following conditions: It should possess the same symmetry as the crystal structure. If there is a choice between more than one repeating arrangements, the one which has the smallest number of atoms (i.e., smallest volume) is chosen as the unit cell. Such a unit cell is often labelled as the primitive ( or simple) unit cell representation. The nature of a solid is determined by the size, shape and contents of its unit cell. The size and the shape of a unit cell are characterized by the distance (a, b, c) of three intersecting edges and the angles (α, β, γ) between these axes.

6 4 4. Type of Solids (Force of attraction) Classification of crystals on the basis of bond type We have earlier discussed the classification of crystals on the basis of symmetry elements and in terms of interrelation of lengths (a, b and c) and angles (α, β and γ) between different crystal axes. It is equally useful to classify solids by the units that occupy the lattice sites and in terms of the bond type. Solids may be occupy the lattice sites and in terms of the bond type. Solids may be distinguished and classified in four different bond type, each representing different type of force between their constituent units in the crystal lattice: 1. Ionic solids 2. Metallic solids 3. Covalent solids 4. Molecular solids These are the main groups in which solids can be broadly classified. Examples of solid substances are, however, known which exhibit properties characteristic of more than one of these groups. This type of intermediate behaviour may be observed either due to the presence of two different types of bonds in these solids or these solids may consist of bonds which are intermediate in character. Some of the physical properties associated with these solids are summarized in the following table. Bonding force Crystal type Units that occupy lattice sites Physical property Hardness Brittleness Melting point Electrical conductivity Examples Very low Quite Ionic Ionic Ions hard and Very high Relatively (high in high molten brittle state) Electrostatic Positive attraction ions in between +ve Metallic Variable Very low Variable Very high electron ions and sea gas of electrons Sharing of Very electron Covalent Atoms Medium Very high Very low hard pairs Molecular interaction forces Molecular Molecules Very soft Low Very low Very low NaCl, CaO Cu, Ag Fe, Diamond, SiC, SiO 2 Ice, I 2, Fullerene

7 5 4.1 Ionic solids: The force of attraction between the ions is purely electrostatic. Examples of ionic solids are: NaCl, CsCl and ZnS. Since these ions are held in fixed positions, there, ionic solids do not conduct electricity in the solid state. They conduct electricity in the fused state. 4.2 Metallic solids The constituent units of metallic solids are positive ions. This array of positive ions are held together by the free moving electron charge cloud.. Examples of metallic solids include Cu, Ag, Au, Na, K etc. 4.3 Covalent solids The structural units of covalent solids is the atom. These solids are formed when a large number of the atoms are held by strong covalent bonds. This bonding extends throughout the crystal and as covalent bond is directional, it results in a giant interlocking structure. For example, in diamond each carbon atom is attached to for other carbon atoms covalent bonds. 4.4 Molecular solids The constituent units of molecular solid are the molecules (either polar or non-polar ) rather than atoms or ions, except in solidified noble glasses where the units are atoms. These solids have relatively high coefficients of expansion. They melt at low temperatures and have low heat of fusion. The bonding within the molecules is covalent and strong whereas the forces which operate between different molecules of the crystal lattice are the weak van der Waals forces. As result of these weak forces, the molecular solids are soft and vaporize very readily. These solids do not conduct electricity. The electrons are localized in the bonds in each molecule. They are, therefore, unable to move from one molecule to another on the application of electric field. Examples of these solids are iodine, sulphur, phosphorus (non polar) and water, sugar (polar) etc

8 6 5. The closest packing 1. study the most efficient way of packing of hard spheres of called the closest packing. equal size in three direction s 2. The structures of crystalline solid can be assumed as simple consequence of the most efficient packing of the units involved. This units may be either atoms, ions or molecules of approximately spherical shape, 3. If a large number of spheres of equal size are put in a container and shaken, they will arrange themselvess in a manner so as to occupy volume. The arrangement of such spheres in a plane are showing the figure. 4.The packing is closest when the spheres arrange themselvess so that their centres are at the corners of an equilateral triangle (see figure) Each sphere in the closest packed arrangement is in contact with six other spheres as shown in the following figure. The centres of each of these six spheres are arranged hexagonally. 5. The number of spheres which are actually in contact with a particular sphere is called the coordination number of that sphere. The coordination number is six when spheres are arranged in a close packed arrangement in one plane. 6. Theree is only one way of closest packing in 2D. One sphere in contact with 6 others. 7.3 D arrangement or Arrangement of layers in 3D: Now if we start building successive layers on top of the first layer, spheres marked A, ( next figure) ), we soon realize that spheres of second layer may be placed either on the hollows which are marked B or on the other set of hollows which are marked as C

9 7. Sites created by layer 1 and available to accept atoms in layers 2 either on the hollows B or C. It may be noted that while building the second layer, we cannot place spheres both on hollows B and C. As shown in the figure, we may build the second layers on hollows marked B. Covering of all B sites by atoms in the second layer making the C sites unavailable for occupancy by close-packed atoms. However, for building the third layer we have a choice of arranging spheres in two different way: The third layer of spheres may be placed on the hollows of the second layers, so that each spheree of the third layer lies strictly above a sphere of first layer. In such an arrangement the first and the third layers are exactly identical. This arrangement of close packing of spheres is referred to as ABA arrangement of packing of spheres. Alternatively, the third layers may be placed on the second set of hollows which were marked C in the first layer. These hollows were left uncovered while arranging the second layer of spheres. This arrangement of packing is denoted as ABC type of packing. 7. ABABABA... Arrangement: When the ABABABA... arrangement of packing is continued indefinitely, the system possesses hexagonal symmetry. This would imply that the structure possesses a six-fold axis of symmetry which is perpendicul lar to the planes of the close packed spheres. Such an arrangement of three dimensional packing of spheres is shown in the next figure. Because of its hexagonal symmetry, this arrangement is referred to as hexagonal close packing of spheres often abbreviated as hcp.

10 8 8. ABCABC Arrangement: : When the ABCABC.. arrangement of packing is continued (1.e., every fourth layer is situated directly above the first layer) the system then possesses cubic symmetry. The arrangement is show in the next figure. The structure now has three 4- fold axes of symmetry. The arrangement is called cubic close packing of spheres and is often abbreviated as ccp. 9.ccp is equivalent to fcc: In this arrangement we have a sphere at the center of each face of the unit cube. This arrangement of spheres is also known as face centered cubic (fcc). 10 Coordination No :- In the both these arrangements, i.e., hcp and ccp, it is obvious that each sphere is surrounded spheres. There are six spheres which are in contact in the same plane and three each in adjacent layers, one just above, and the other just below. The coordination number of each sphere in both these close packed arrangement is twelve. These are shown in previous figures. 11. In both these type of close packed arrangements, maximum volume of space, i.e., 74% is actually occupied by the spheres. 12.Strictly all arrangements are not closest :-It may also be understood here that any irregular arrangement like ABABC-ABABC etc possesses neither cubic nor hexagonal symmetry. 13.Strictly all arrangements are not closest :- Arrangement in which atoms forming the layers are not in direct contact donot form the closest packing.

11 9 6. Packing Metallic Crystals The structure of most the metals (from s and d Blocks of the periodical chart) belong either to on or more of the three simple type of structures: 1. Cubic close packed (face centered cubic) 2. Hexagonal close packed 3. Body centered cubic The distribution of these structures among the s- and d-block metals is shown in the table. Li b Be h c = cubic close packed h = hexagonal close packed b = body centered cubic Na b Mg h Al c K b Ca c h Sc c h Ti h b V b Cr b Mn Fe c b Co c h Ni c h Cu c Zn h Rb b Sr c Y h Zr h b Nb b Mo b h Tc h Ru c h Rh c Pd c Ag c Cd h Cs b Ba b La c h Hf h b Ta b W b Re h Os c h Ir c Pt c Au c Hg 6.1 Cubic close packed (face centered cubic) In this structure atoms are arranged at the corners and at the centres of all six faces of a cube. In this structure each atom has 12 nearest neighbours as shown in figure. For example, the atom at the center of the middle face has four nearest neighbours at the corners of that face and eight more at the same distance at the center or four faces of adjoining cubes. 6.2 Hexagonal close packed In this arrangement, atoms are located at the corners and the center of two hexagons which are placed parallel to each other and three more atoms in a parallel plane midway between these two planes. This arrangement is obtained when we have ABABA... type of close

12 10 packing of atoms. Each atom in this arrangement has also 12 nearest neighbours as shown in the figure 6.3 Body Centered Cubic: This arrangement of spheres (or atoms) is not exactly close packed. This structure can be obtained if spheress in the first layer (marked A) of close packing are slightly opened up. As a result none of these spheres are in contact with each other. Such an arrangement is show in the abone.figure. The second layer of spheres ( marked B) may be placed on the top of the first layer, so the layer below it. Successive building of the third layer will be exactly like the first layer (i.e., on top of A). If this pattern of building layers is repeated infinitely we get an arrangement bcc as show in the figure. In a body centered cubic arrangement, the atoms occupy corners of a cube with an atom at its center. In this arrangement each sphere is in contactt with eight other spheres (four spheres in the layer just above and four spheres in the layer just below) and so the coordination number in this type of arrangement is only eight. The structure is known as body centered cubic (bcc). As has already been mentioned, this arrangement of packing is not exactly close packed,, and only 68% of the total volume is actually occupied.

13 Some Other Characteristics It has been observed that those metals which crystallize in cubic form are more malleable and ductile that those which crystallize in the hexagonal system. Since and ductility are related to deformation in crystals, it may be said that crystals with cubic symmetry are easily deformed. Deformation in crystals may mean sliding of on plane of atoms over other planes. Since the cubic close packed structure contains four sets of parallel close packed layers, therefore, metals with this structure will have more opportunities for slipping of one layers over the other. Examples of metals with cubic structure which are easily deformed are copper, silver, gold, iron, nickel, platinum, etc. Hexagonal close packed structure contains only one set of parallel close packed layers. Therefore, the chances of slipping of planes in hexagonal close packed structure are very little. Metals which show this structure, e.g., chromium, molybdenum, magnesium, zinc etc., are les malleable, harder and more brittle. Since iron can adopt both these type of arrangements depending upon temperature, therefore, this is the reason why iron can exhibit a wide variety of properties. No. Structure Cubic close Hexagonal close packed Body centered Property packed cubic 1 Arrangement of close packed close packed not close packed packing 2 Volume occupied 74% 74% 68% 3 Type of packing ABACABC... ABABABAB Coordination number 5 Other characteristics Malleable and ductile Less malleable, hard and brittle Malleable and ductile 6 Examples Cu, Ag, Au, Pt Cr, Mo, V, Zn alkali metals, Fe

14 12 7. Packing Ionic Solids The ionic solids consist of positive and negative ions arranged in a manner so as to acquire minimum potential energy. This can be achieved by decreasing the cation-anion distance to a minimum and reducing anion-anion repulsions. 7.1 structures of ionic solids: The structures of ionic solids can be described in terms of large anions/cations forming a close packed arrangement and the small cations/anions occupying one or the other type of interstitial sites. It was discussed earlier that the arrangement is close packed only when the centres of three spheres are at the vertices of an equilateral triangle. Since the spheres touch each other only at one point, there must be some empty space between them. This empty space (hole or void) is called a triangular site. tetrahedral hole: Similarly, it is observed that when a sphere in the second layer is placed upon three other touching spheres a tetrahedral arrangement of spheres is produced. The centres of these four spheres lie at the apexes of regular tetrahedron. Consequently, the space at the center of this tetrahedron is called a tetrahedral site. It may be mentioned here that it is not the shape of the void which is tetrahedral, but that the arrangement of the spheres which is tetrahedral. In a close packed arrangement each sphere is in contact with three spheres in the layer above it and three other spheres below it. As result there are two tetrahedral sites associated with each spheres. We may also observe that the size of the empty space is much smaller than the size of the spheres. But as the size of the spheres increases, the size of the empty space shall also increase. Octahedral hole :Another type of empty space in close packed arrangement is created by joining six spheres whose centres lie at the apexes of a regular octahedron. The creation of such an empty space in close packed arrangement may be visualized as shown in the figure.

15 13 From this diagram, it is obvious that each octahedral site is generated by two set of equilateral triangles whose apexes point in opposite directions. We may also note that there is only one octahedral site for every sphere. This means that the number of octahedral site are half as many as there are tetrahedral sites. The size of an octahedral hole is larger than a tetrahedral hole which in turn is larger than a trigonal hole. But once again the size of an octahedral site will vary with the size of the spheres. The size of each empty space is fixed relative to the size of the spheres. The radius of the small sphere that may occupy the site can be calculated by simple geometry. For example, it may be shown that the radius of small sphere which can fit into a trigonal site is times the radius of large close packed spheres. Limiting ratio r+/r- C.N Structural arrangement/holes Example 1 12 Close packing (ccp and hcp) metals Smaller ion in Cubic holes CsCl Smaller ion in Octahedral NaCl Smaller ion in Tetrahedral ZnS Smaller ion in Triangular Boron oxide

16 14 Proof:1 Limiting Radius Ratio foe Triangular hole Let r c and r a the radii of the cation and anion, respectively. In an equilateral triangle ABC AD=r a and AE=r a a+r c cos ( EAD) = AD / AE i.e. On inverting both side, we get Thus in order to occupy a trigonal void without disturbing the close packed structure, the radius of small sphere should not be greater than times than of large spheres. Only B 3+ ion can be thought to fit into such a smalll site in its oxide. Proof:2 Limiting Radius Ratio for Tetrahedral hole Let "a" be the length of side of cube (say AB)

17 15 Face diagonal Since the two anions are touching each other, BC=2r a (where r a is the radius of the anion) or Body diagonal Also body diagonal = 2r a +2r c (where r c is the radius of the cation) Substituting the value of a we get Dividing both sides by 2 r a, we get Proof:3 Limiting Radius Ratio for Octahedral hole The size of an octahedral site may accordingly be calculated if we consider a cross-section throughh an octahedral site as shown in following figure.

18 16 ABCD is a square CD = BD = 2r a (where r a is the radius of the anion) Moreover BC = 2r a + 2r c In other words, we may write Dividing both sides by 2r_a, we get Thus in order to occupy an octahedral void, in a close packed lattice, the radius of the small sphere should not be greater than times that the large spheres. Proof:4 Limiting Radius Ratio for Cubic hole Let the legth of each side of a cube = a so the length of the face diagonal

19 17 Legth of the body diagonal AC which contains the body center ion has length < Let r c and r a be the radius of cation and anion, respectively. Divide both side by 2r a The empty space at the center of the cube, formed by eight identical spheres is called a cubic interstitial site. The largest void and can accommodate a sphere of radius times the radius of the large sphere Structure of various substances can be modified by the introduction of other ions of varying sizes into different interstitial sites. Examples may include the introduction of small atoms (such as non metals like carbon, boron, etc.) into the interstitial sites of metals which will change their properties.

20 18 8. Example of Ionic Solids A large number of ionic solids exhibit one of these five structures which are discussed here: (a) Sodium chloride (NaCl) (b) Zinc blend (ZnS) (c) Wurtzite (ZnS) (d) Fluorite (CaF 2 ) (e) Cesium chloride (CsCl) 8.1 The Sodium Chloride structure A unit cell representation of sodium chloride is shown in the following figure. The salient features of Sodium Chloride structure are: 1. Chloride ions are ccp type of arrangement, i.e., it contains chloride ions at the corners and at the center of each face of the cube. 2. Sodium ions are so located that there are six chloride ions around it. This is equivalent to saying that sodium ions occupy all the octahedral sites. 3. As there is only one octahedral site for every chloride ion, the stoichiometry is 1 : For sodium ions to occupy octahedral holes and the arrangement of chloride ions to be close packed the radius ratio, rna + /rcl -, should be equal to The actual radius ratio exceeds this limit. To accommodate large sodium ions, the arrangement of chloride ions has to slightly open up. 5. It is obvious from the diagram that each chloride ion is surrounded by six sodium ions which are disposed towards the corners of a regular octahedron. We may say that cations and anions are present in equivalent positions and the structure has 6 : 6 coordination. 6. The structure of sodium chloride consists of eight ions in one unit cell, four Na + ions and four Cl - ions.

21 19 In this structure, each cornerr ion is shared between eight unit cells, each ion on the face of the celll is shared by two cells, and each ion on the edge is shared by four cells and the ion inside the cell belongs entirely to that unit cell. Most of the alkali halides, alkaline earth oxides, and sulphidess exhibit this type of structure. Other compounds which crystallize in sodium chloride type of structure are NH 4 Cl, NH 4 Br, NH 4 I, AgF, AgCl and AgBr. 8.2 The Zinc Blend structure A unit cell representation of zinc blend is shown in the figure. Figure. Unit cell representation of zinc blend structure. The salient features of Zinc Blende structure The zinc atoms are ccp type of arrangement, i.e., zinc atoms at the corners and at the center of each face of the cube. Sulphur atoms are so located that there are four zinc atoms around it. Or it may be said that sulphur atoms occupy tetrahedral sites and their coordination number is four. As there are eight tetrahedral sites available; four sulphur atoms occupy only half of tetrahedral sites. So the stoichiometry of the compound is 1:1. Only alternate tetrahedral sites are filled by sulphur atoms. Each zinc atom is surrounded by four sulphur atoms and in turn each sulphur atom is also surrounded by four zinc atoms which are also disposed towards the corners of a

22 20 regular tetrahedron. We may say that cations and anions are present in equivalent positions and the coordination of zinc blende structure is described as 4:4. 5. For the arrangement of sulphur atoms to be truly close packed and zinc atoms to occupy tetrahedral voids, the radius ratio (rzn 2+ /zs 2- ) should be This value is greater than and so we may say that the arrangement of sulphur atoms is not actually close packed. This structure is found in 1:1 compounds in which the cation is smaller than the anion. Examples : Copper(I) halides (CuCl, CuBr, CuI), silver iodide and beryllium sulphide. 8.3 The Wurtzite structure It is an alternative form in which ZnS occurs in nature. Its unit cell representation is shown in the figure Figure. Unit cell representation of Wurtzite structure. The salient features of Wurtzite structure : 1. Sulfur atoms form the hcp type of arrangement and are yellow spheres in the diagram. 2. Zinc atoms are violet spheres and are located that there are four sulphur atoms around each zinc atom. It may be said that zinc atoms occupy tetrahedral sites. 3. As there are two tetrahedral sites available for every sulphur atom, zinc atoms occupy only half of tetrahedral sites. The alternate tetrahedral sites remain vacant. The stoichiometry of the compound is 1:1. 4. Each zinc atom is surrounded by four sulphur atoms and in turn each sulphur atom is also surrounded by four zinc atoms (which are also disposed towards the corners of a regular tetrahedron). The coordination of the compound is 4:4. Again we may say that cations and anions are in equivalent positions. 5. It may be concluded that the structure of Wurtzite is very similar to the structure of zinc blende. The only difference is in the sequence of the arrangement of close packed

23 21 layers of sulphur atoms. In zinc blende, sulphur atoms follow the sequence ABCABC... etc. whereas in wurtzite the sequence is ABABAB... etc. Examples : ZnO, CdS, and BeO. 8.4 The CaF 2 (fluorite) structure A unit cell representation of fluorite structure is shown in the figure. Figure. Unit cell representation of CaF 2 structure. The calcium ions are marked as green spheres, and fluoride ions are marked as light blue sphere. The salient features of CaF 2 structure : 1. The calcium ions form the ccp arrangement, i.e., these ions occupy all the corner positions and the center of each face of the cube. 2. Fluoride ions are so located that there are four calcium ions around it. It may be said that the fluoride ions occupy tetrahedral sites and the coordination number of fluoride ion is As there are two tetrahedral sites available for every calcium ion, the fluoride ions occupy all the tetrahedral sites. The stoichiometry of the compound is 1:2. 4. Each fluoride ion is surrounded by four calcium ions whereas each calcium ions is surrounded by eight fluoride ions which are disposed towards the corners of a cube. The coordination of the compound is 8:4 Examples: SrF 2, BaF 2, SrCl 2, CdF 2, HgF 2, and PbF The Cesium Chloride structure

24 22 The structure of CsCl is shown in the figure at the left and its unit cell representation is shown in figure at the right. Figures. (left) Structure of CsCl and (right) unit cell representation of CsCl. The salient features of CsCl structure : 1. The cesium ions from the simple cubic arrangement. 2. Chloride ions occupy the cubic interstitial sites, i.e., each chloride ion has eight cesium ions as its nearest neighbours. 3. If we consider the figure at left it can be observed that each cesium ion is surrounded by eight chloride ions which are also disposed towards the corners of a cube. 4. It may be concluded that both type of ions are in equivalent positions, and the stoichiometry is 1:1. The coordination is 8:8. Examples : CsBr and CsI. This structure is observed only when the cations are comparable in size to the anions. 8.6 Summary on structure of ionic solids Coordination Name number Rock salt (NaCl-type) Na+ 6 Cl - 6 Zinc Blende (ZnStype) Wurtzite (ZnS-type) Fluorite (CaF 2 -type) Cesium (CsCl-type) Chloride Zn +2 4 S -2 4 Zn +2 4 S -2 4 Ca +2 8 F - 4 Cs + 8 Cl - 8 Fraction filled 1 ½ ½ Examples Li, Na,K, Bb halides, NH 4 Cl, NH 4 Br, NH 4 I, AgF, AgCl, AgBr. ZnS, BeS, CuCl, CuBr, CuI, AgI ZnS, ZnO, CdS, BeO 1 CaF 2, SrF 2, BaF 2, SrCl 2, BaCl 2, CdF 2, HgF 2 1 CsCl, HgBr, CsI

25 23 9. Defeect in Cryystals Real cryystals have always impperfect struuctures. Thee arrangemeent of consttituent unitss are not very reggular. Ideall crystals with w no impeerfections are a possiblee only at abbsolute zero. Above this tem mperature all a crystallinne solids coontain somee defects inn the arranggement of its i units. The following disccussion is only restricteed on simplle compounnds are mainnly ionic co onsisting of A+B B- units. Deffects in crysstals may giive rise to Stoichiomeetric, and Non-stoichhiometric strructures. Stooichiometriic Defects. In I stoichiom metric comp pounds irregularity in the arrangeement of thee ions in thee lattice cann occur duee to a vacan ncy at a catiion and an aanion site or o by the miggration of an a ion to some other interstitial site. These defects aree of two ty ypes: (a) Schhottky defecct; (b) Frenkkel defect. (a) Schottky defect: d Thiss defect connsists of a vacancy v at a cation siite and this will be acccompanied by a vacancy at an annion site so as to mainttain the elecctrical neuttrality of thee system. Thhe missing cations andd anions move to the suurface. The defect is illlustrated in the t followinng figure. This defect d is moost predominant in com mpounds wiith high cooordination nnumbers an nd where the ions (both cattions and anions) a aree of similarr sizes. Som me of the compounds which predom minantly shoow this defeect are the alkali a halidees such as NaCl N and CssCl. Since there t are lesser number n of ioons in the laattice, the deensity of solid will decrease.

26 24 (b) Frenkel Defect: This defect consists of a vacancy at a cation site. The cation moves to another position between the two layers and is thus surrounded by a greater number of anions. This is illustrated in the following figure. This defect is most predominant: In compounds whichh have low coordination numbers. In compounds with low coordination numbers the attractive forces being less, are easy to overcome so that the cation can easily move into the interstitial site. This defect is more common in compounds which have ions of different sizes. In compounds where we have highly polarizing cation and an easily polarizable anion. Examples of compounds which show this defect are ZnS (both zinc blende and wurtzite), AgBr etc. This type of defects leads to an increase in the dielectric constant of the medium. the density of the medium, however, remains unchanged. Solids generally contain both these types of defects, but one is more predominant than the other. The crystal is then said to possess only that particular defect. The number of defects in a crystal generally increase with the rise of temperature. Normally speaking, Schottky defects are easier to form than Frenkel defects as the former require lesss energy for their formation.