Solid State / Crystalline State Chemistry

Solid State

By

S.K.Sinha Resonance, Kota www.openchemistry.in

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

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Solid State

1.Concept of Solid A large majority of substances around us are solids. The distinctive features of solids are: 1. 2. 3.

They have a definite shape. They are rigid and hard. They have fixed volume.

These characteristics can be explained on the basis of following facts: 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. 1.

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.

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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 AXILE LENGTHS ANGLE

EXAMPLES

Primitive body Body-centered Cubic

Face-Centered

α=β=γ a=b=c

Primitive, Tetragonal

Body-centered

a=b≠c

= 90°

NaCl, Zinc blende, Cu

α=β=γ

White tin, SnO2,TiO2,

= 90°

CaSO4

α=β=γ

Rhombic sulphur,

= 90°

KNO3, BaSO4

Primitive, Body-centered, Face-centered, Orthorhombic

End-centered

a≠b≠c

α=β= 90° Hexagonal

Primitive

a=b≠c

Rhombohedral or trigonal

Primitive

a=b=c

Primitive, Monoclinic

End-centered

γ = 120°

Graphite, Zno,Cds

α=β=γ

Calcite (CaCO3),

≠ 90°

HgS(cinnabar)

α = γ =90° Monoclinic a≠b≠c

β ≠ 120°

sulphur,Na2SO4.10H2O

α ≠ β ≠ γ ≠ K2Cr2O7, CuSo4.5H2O, Triclinic

Primitive

a≠b≠c

90°

H3BO3

Table: Seven Primitive Unit Cells and their Possible Variations as Centred Unit Cells

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3.Solid ds and latttice 1. As already a menntioned crysstalline soliids consist of o regular arrangemen a nt of atoms in three dimensiions. 2. If attoms are considered c as points,, the arran ngement off an infinitte set of points p is known as space laattice. ny other 3. Eachh point in thhe lattice is so chosen that its environment iss the same aas that of an point. One O examplle each of one dimensioonal, two diimensional and a threee dimension nal space lattice is shown in the figure.

It may be b understoood here thaat it is the arrrangement of the poinnt which is a lattice and d not the line whhich are joinning them. 4. The smallest reppeating mottif (pattern)) is known as a Unit ceell. If this m motif is rep peated in differennt directionss it should be b able to reegenerate th he entire latttice. The un nit cell is so o chosen as a to fulfil th he followin ng conditio ons: 1. It should possess p the e same sym mmetry as the t crystall structure. b m more than one o repeating arrang gements, the t one 2. If there is a choice between which hass the smalllest numbe er of atomss (i.e., smallest volu ume) is cho osen as the unit ce ell. Such a unit cell iss often labe elled as the e primitive e ( or simp ple) unit cell repressentation. The natture of a soolid is deterrmined by thhe size, shaape and conntents of itss unit cell. The T size and thee shape of a unit cell are a characteerized by th he distance (a, b, c) oof three inteersecting edges and a the angles (α, β, γ) between b theese axes.

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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. 2. 3. 4.

Ionic solids Metallic solids Covalent solids 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.

Crystal type

Bonding force

Ionic

Ionic

Electrostatic attraction between +ve Metallic ions and sea of electrons Sharing electron pairs Molecular interaction forces

Units that Physical property occupy Melting lattice Hardness Brittleness point sites Ions

Very low Quite Relatively (high in NaCl, hard and Very high high molten CaO brittle state)

Positive ions in Variable Very low Variable electron gas

of Covalent Atoms

Electrical Examples conductivity

Very hard

Medium

Molecular Molecules Very soft Low

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Very high

Cu, Ag

Fe,

Very high Very low

Diamond, SiC, SiO2

Very low Very low

Ice, I2 , Fullerene

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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

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5. Thee closest packing p 1. studyy the most efficient waay of packing of hard spheres of equal size in three dirrection’s called thhe closest packing. p 2. The structures of crystalliine solid caan be assum med as sim mple conseqquence of th he most efficiennt packing of o the units involved. This T units may m be eitheer atoms, ioons or moleecules of approxiimately spherical shapee, 3. If a large l numbber of spherres of equaal size are put p in a coontainer andd shaken, th hey will arrangee themselvess in a mannner so as to occupy o vollume. The arrangement a t of such sp pheres in a plane are showinng the figuree.

4.The packing p is closest c wheen the spherres arrange themselvess so that th heir centres are at the corrners of an equilateral trianglle (see figu ure) Each sphere in tthe closest packed arrangeement is in contact withh six other spheres s as shown s in the followingg figure.

The cenntres of eachh of these siix spheres are a arranged d hexagonallly. 5. The number n of spheres whhich are actuually in con ntact with a particular ssphere is caalled the coordiination nu umber off that spheree. The coorrdination nuumber is sixx when sphheres are arrangeed in a closee packed arrrangement inn one planee. 6. Theree is only onne way of cllosest packinng in 2D. One O sphere in i contact w with 6 otherss. 7.3 D arrangemen a nt or Arranggement of layers in 3D: 3 Now iff we start bbuilding succcessive layers on o top of thhe first layerr, spheres marked m A, (next figure)), we soon realize that spheres of seconnd layer maay be placed either on the hollow ws which aree marked B or on the other o set of holloows which are a marked as C

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. ayer 1 and available a too accept atoms in layerrs 2 either oon the hollo ows B or Sites crreated by lay C. It may m be noted that whille building the second d layer, we cannot placce spheres both on hollowss B and C. As A shown inn the figuree, we may build the seccond layers on hollows marked B.

 

Coveriing of all B sites by atoms a in thhe second la ayer makinng the C sittes unavaillable for occupanncy by closee-packed attoms. Howeveer, for buildding the third layer wee have a cho oice of arraanging spherres in two different d way: 



The third laayer of spheeres may bee placed on n the hollow ws of the seccond layerss, so that each spheree of the thiird layer liees strictly above a a sphhere of firsst layer. In such an arrangemennt the first and the third layers arre exactly identical. i T This arrangeement of close packiing of spherres is referreed to as ABA arrangem ment of packking of spheeres. Alternativeely, the thirdd layers mayy be placed d on the secoond set of hhollows whiich were marked C in i the first layer. Thesse hollows were left uncovered u w while arrang ging the second layer of spherres. This arrrangement of packingg is denoteed as ABC type of packing.

7. ABA ABABA... Arrangemen A nt: When thee ABABAB BA... arranggement of paacking is co ontinued indefiniitely, the syystem posseesses hexaggonal symm metry. This would w implly that the structure s possessses a six-foold axis of symmetry which is perpendicul p lar to the pplanes of th he close packed spheres. Suuch an arranngement of three dimen nsional packking of spheeres is show wn in the next figgure. Because of its hexagonall symmetry y, this arrrangement is referred to as hexagoonal close packing of spheres s ofteen abbrevia ated as hcp p.

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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 4fold 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.

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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. 2. 3.

Cubic close packed (face centered cubic) Hexagonal close packed Body centered cubic

The distribution of these structures among the s- and d-block metals is shown in the table. Li b

Be h

Na b Kb

Mg h

c = cubic close packed h = hexagonal close packed b = body centered cubic Al c

Ca c Sc c h Ti h b h Rb Sr c Yh Zr h b b Cs b Ba b La c Hf h h b

Vb

Cr b

Co c Ni c Cu h h c Mo b Tc h Ru c Rh c Pd c Ag c Nb b h h Ta b W b Os c h Ir c Pt c Re Au h c Mn

Fe c b

Zn h Cd h 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

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packingg of atoms. Each atom in this arraangement haas also 12 nearest n neighhbours as shown in the figuure

6.3 Bod dy Centereed Cubic: This arranngement of spheres (or atoms) iss not exactly close packed.. This struccture can be b obtainedd if spheress in the first layer (m marked A) of o close packingg are slightlly opened up. u As a ressult none of these sphheres are inn contact with each other. Such S an arraangement iss show in the abone.figu ure. The seccond layer of o spheres ( marked B) B may be placed p on thhe top of thhe first layerr, so the layer beelow it. Succcessive buuilding of thhe third layeer will be exactly e like the first lay yer (i.e., on top of o A). If this pattern off building laayers is repeeated infinittely we get aan arrangem ment bcc as show w in the figuure.

In a boddy centeredd cubic arranngement, thhe atoms occcupy cornerrs of a cubee with an ato om at its center. In this arranngement eaach sphere is in contactt with eight other spherres (four sp pheres in the layeer just abovve and four spheres s in the t layer jusst below) annd so the cooordination number in this type of arrrangement is only eigh ht. The stru ucture is knnown as boody centereed cubic A has alreeady been mentioned,, this arran ngement of packing iss not exacttly close (bcc). As packed,, and only 68% 6 of the total t volumee is actually y occupied.

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6.4 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 → Property ↓ 1 Arrangement of packing 2 Volume occupied 3 Type of packing 4 Coordination number 5 Other characteristics 6 Examples

Cubic close packed close packed

Hexagonal close packed close packed

Body centered cubic not close packed

74% ABACABC... 12

74% ABABABAB.... 12

68% 8

Malleable and ductile Cu, Ag, Au, Pt

Less malleable, hard and brittle Cr, Mo, V, Zn

Malleable and ductile alkali metals, Fe

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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.

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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 0.155 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

1-0.732

8

Smaller ion in Cubic holes

CsCl

0.732-0.414

6

Smaller ion in Octahedral

NaCl

0.414-0.225

4

Smaller ion in Tetrahedral

ZnS

0.225-0.155

3

Smaller ion in Triangular

Boron oxide

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Proof:11

Lim miting Radiius Ratio fooe Triangullar hole

Let rc and a ra the raadii of the caation and annion, respecctively. In an eqquilateral triiangle ABC C AD=ra and AE=ra+rc

cos ( EAD) = AD A / AE

i.e.

s we gett On inveerting both side,

Thus inn order to occupy o a trrigonal voidd without disturbing d thhe close paacked structture, the radius of o small sphhere should not be greaater than 0.155 times thhan of largee spheres. Only O B3+ ion can be thought to fit into such s a smalll site in its oxide. o

Proof:22

Lim miting Radiius Ratio foor Tetrahed dral hole

Let "a" be the lenggth of side of o cube (say AB)

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Face diagonal Since thhe two anionns are touchhing each otther, BC=2 2ra (where ra is the radiuus of the an nion) or

Body diiagonal

Also boody diagonaal = 2ra+2rc (where rc iss the radius of the catioon)

Substituuting the vaalue of a wee get

Dividinng both sides by 2 ra, we w get

Proof:33

Lim miting Radiius Ratio foor Octahed dral hole

The sizze of an octahedral sitte may accoordingly be calculated if we consiider a crosss-section throughh an octaheddral site as shown s in following figu ure.

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ABCD is a square CD = BD = 2ra (where ra is the raadius of the anion)

Moreovver BC = 2rra + 2rc In otherr words, wee may write

Dividinng both sides by 2r_a, we w get

Thus inn order to occcupy an occtahedral vooid, in a clo ose packed lattice, the radius of th he small sphere should s not be b greater thhan 0.414 tiimes that th he large spheeres. Proof:44

Lim miting Radiius Ratio foor Cubic ho ole

Let thee legth off each sidde of a cube c = a so the leength of tthe face diagonal d

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Legth of the boody diagonnal AC which w contaains the body b centeer ion hass length <

Let rc annd ra be the radius of cation and annion, respecctively.

Divide both side byy 2ra

The em mpty space at a the centerr of the cube, formed by b eight idenntical spherres is called d a cubic interstiitial site. The T largest void v and caan accomm modate a sphhere of radiius 0.732 tiimes the radius of o the large sphere Structurre of variouus substancees can be modified m by the introduuction of other ions off varying sizes innto differentt interstitiall sites. Exaamples may y include thhe introduction of smalll atoms (such as a non metaals like carbbon, boron, etc.) into the t interstittial sites off metals wh hich will change their properties.

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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 (CaF2) (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. 2. 3. 4.

5.

6.

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. 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. As there is only one octahedral site for every chloride ion, the stoichiometry is 1 : 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 0.414. The actual radius ratio 0.525 exceeds this limit. To accommodate large sodium ions, the arrangement of chloride ions has to slightly open up. 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. The structure of sodium chloride consists of eight ions in one unit cell, four Na+ ions and four Cl- ions.

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In this structure, each cornerr ion is sharred between n eight unitt cells, eachh ion on thee face of the celll is shared by b two cells, and eachh ion on the edge is shared by fou ur cells and d the ion inside thhe cell beloongs entirelyy to that uniit cell.

Most off the alkali halides, alkkaline earthh oxides, an nd sulphidess exhibit thiis type of sttructure. Other compounds c which crysstallize in soodium chlorride type off structure aare NH4Cl, NH4Br, NH4I, AgF, A AgCl and a AgBr. 8.2 Thee Zinc Blen nd structuree A unit cell c represenntation of zinc blend iss shown in the t figure.

Figure. Unit cell reepresentatioon of zinc bllend structu ure. The sallient featurres of Zinc Blende stru ucture The zinc attoms are ccpp type of arrrangement, i.e., zinc atoms a at thee corners an nd at the center of eaach face of the t cube. oms are so located thaat there are four zinc atoms a arounnd it. Or it may be 2. Sulphur ato said that suulphur atomss occupy tettrahedral sittes and their coordinatiion numberr is four. es availablee; four sulphhur atoms ooccupy only y half of 3. As there arre eight tetrrahedral site tetrahedral sites. So the stoichiometry off the comppound is 1:1. Only alternate a tetrahedral sites are filled by sulphhur atoms. a is surrrounded by four sulphu ur atoms annd in turn eaach sulphurr atom is 4. Each zinc atom also surrouunded by fouur zinc atom ms which are a also dispposed towarrds the corn ners of a 1.

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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 (rZn2+/zS2-) should be 0.40. This value is greater than 0.225 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 : Sulfur atoms form the hcp type of arrangement and are yellow spheres in the diagram. 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 1. 2.

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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 CaF2 (fluorite) structure A unit cell representation of fluorite structure is shown in the figure.

Figure. Unit cell representation of CaF2 structure. The calcium ions are marked as green spheres, and fluoride ions are marked as light blue sphere. The salient features of CaF2 structure : 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 4. 3. 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 1.

Examples: SrF2, BaF2, SrCl2, CdF2, HgF2, and PbF2. 8.5 The Cesium Chloride structure

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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 : The cesium ions from the simple cubic arrangement. 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. 1. 2.

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 Name

Coordination Fraction Examples number filled

Rock salt (NaCl-type)

Na+ Cl- 6

6

(ZnS- Zn+2 S-2 4

4

Wurtzite (ZnS-type)

Zn+2 S-2 4

4

Fluorite (CaF2-type)

Ca+2 F- 4

8

Cesium Chloride Cs+ (CsCl-type) Cl- 8

8

Zinc Blende type)

1

Li, Na ,K, Bb halides, NH4Cl, NH4Br, NH4I, AgF, AgCl, AgBr.

½

ZnS, BeS, CuCl, CuBr, CuI, AgI

½

ZnS, ZnO, CdS, BeO

1

CaF2, SrF2, BaF2, SrCl2, BaCl2, CdF2, HgF2

1

CsCl, HgBr, CsI

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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.

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(b)) Frenkel Defect: D This defect conssists of a vaacancy at a cation site. The cation n moves to another a possition betweeen the two layers and is i thus surroounded by a greater nu umber of aniions. This iss illustratedd in the folloowing figuree.

Thhis defect is most predoominant: 

 

In compouunds whichh have low w coordinattion numbeers. In com mpounds with w low coordinatioon numbers the attractivve forces beeing less, arre easy to ovvercome so o that the cation can easily e movee into the innterstitial sitte. This defect is more com mmon in coompounds which w have ions of differrent sizes. In compouunds where we have highly h pola arizing catioon and an easily pollarizable anion.

Exxamples of compounds c which show w this defecct are ZnS (bboth zinc bllende and wurtzite), w AggBr etc. Thhis type of defects leaads to an in ncrease in the dielectrric constan nt of the meedium. the density d of thhe medium, however, remains uncchanged. Solids generallly contain both these types of deefects, but one o is moree predominant than thee other. Thee crystal is then said too possess only that parrticular defe fect. The nu umber of deffects in a crrystal generrally increaase with thee rise of tem mperature. N Normally sp peaking, Schhottky defects are easieer to form thhan Frenkel defects as the former require lesss energy forr their formaation.

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