By
S.K.Sinha
Resonance, Kota
www.openchemistry.in
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
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.
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 CRYSTA L SYSTEM POSSIBLE VARIATI ON EDGE LENGT H S AXILE ANGLE EXAMPLES Cubic Primitive body Body-centered Face-Centered a=b=c α = β = γ= 90° NaCl, Zinc blende, Cu
Tetragonal
Primitive,
Body-centered a=b≠c
α = β = γ = 90°
White tin, SnO2,TiO2,
CaSO4 Orthorhombic Primitive, Body-centered, Face-centered, End-centered a≠b≠c α = β = γ = 90° Rhombic sulphur, KNO3, BaSO4
Hexagonal Primitive a=b≠c
α = β = 90°
γ = 120° Graphite, Zno,Cds Rhombohedral
or trigonal Primitive a=b=c
α = β = γ ≠ 90° Calcite (CaCO3), HgS(cinnabar) Monoclinic Primitive, End-centered a≠b≠c α = γ =90° β ≠ 120° Monoclinic sulphur,Na2SO4.10H2O Triclinic Primitive a ≠ b ≠ c α ≠ β ≠ γ ≠ 90° K2Cr2O7, CuSo4.5H2O, H3BO3
3.Solid
1. As a dimensi 2. If at known 3. Each point. O lattice i It may b line wh 4. The differen The un 1. 2. The nat and the edges ads and lat
already men ions. toms are c as space la h point in th One exampl s shown in be understo hich are join smallest rep nt directions nit cell is so It should p If there is which has the unit ce cell repres ture of a so e shape of a and the anglttice
ntioned crys considered attice. he lattice is le each of o the figure.ood here tha ning them. peating mot s it should b o chosen a possess the a choice b s the small ell. Such a sentation. olid is deter a unit cell a es (α, β, γ) b stalline soli as points, so chosen ne dimensio at it is the ar tif (pattern) be able to re as to fulfil th e same sym between m lest numbe unit cell is rmined by th are characte between the ids consist o , the arran
that its env
onal, two di rrangement ) is known egenerate th he followin mmetry as t more than o er of atoms s often labe he size, sha erized by th ese axes. of regular a ngement of ironment is imensional of the poin as a Unit ce he entire latt ng conditio the crystal one repea s (i.e., sm elled as the
ape and con he distance arrangemen f an infinit s the same a and a three nt which is a ell. If this m tice. ons: l structure. ting arrang allest volu e primitive ntents of its (a, b, c) o nt of atoms te set of p as that of an e dimension a lattice and motif is rep gements, t ume) is cho e ( or simp s unit cell. T of three inte in three points is ny other nal space d not the peated in the one osen as ple) unit The size ersecting
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
Ionic Ionic Ions Quite hard and
brittle
Very high Relatively high Very low (high in molten state) NaCl, CaO Electrostatic attraction between +ve ions and sea of electrons Metallic Positive ions in electron gas
Variable Very low Variable Very high Cu, Fe,
Ag Sharing of
electron pairs
Covalent Atoms Very hard Medium Very high Very low Diamond, SiC, SiO
2
Molecular interaction
forces Molecular Molecules Very soft Low Very low Very low
Ice, I2,
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
5. The
1. study called th 2. The efficien approxi 3. If a l arrange a plane 4.The p the cor arrange The cen 5. The ncoordi
arrange 6. There 7.3 D a layers o of secon of holloe closest p
y the most he closest p structures nt packing o imately sph large numb e themselves are showin packing is c rners of a ement is in ntres of each number ofination nu
ed in a close e is only on arrangemen on top of th nd layer ma ows which apacking
efficient wa packing. of crystalli of the units erical shape ber of spher s in a mann ng the figure closest whe n equilate contact with h of these si spheres whumber
of e packed arr ne way of cl nt or Arrang he first layer ay be place are marked ay of packi ine solid ca involved. T e, res of equa ner so as to o e. en the spher ral triangl h six other s ix spheres a hich are actu f that sphere rangement in losest packin gement of r, spheres m d either on as C ng of hard an be assum This units m al size are p occupy vol res arrange le (see figu spheres as s are arranged ually in con e. The coor n one plane ng in 2D. O layers in 3 marked A, ( the hollow spheres of med as sim may be eithe put in a co lume. The a themselves ure) Each shown in th d hexagonal ntact with a rdination nu e. One sphere i 3D: Now if next figure) ws which are equal size mple conseq er atoms, io ontainer and arrangement s so that th sphere in t e following lly. particular s umber is six in contact w f we start b ), we soon e marked B in three dir quence of th ons or mole d shaken, th t of such sp heir centre the closest g figure. sphere is ca x when sph with 6 others building suc realize that or on the o rection’s he most ecules of hey will pheres in s are at packed alled the heres are s. ccessive spheres other set. Sites cr C. It m hollows B. Coveri occupan Howeve way: 7. ABA indefini possess packed next fig hexago reated by lay may be note s B and C. A ing of all B ncy by close
er, for build The third la each sphere arrangemen close packi Alternative marked C i second lay packing. ABABA... A itely, the sy ses a six-fo spheres. Su gure. Beca onal close p ayer 1 and a d that whil As shown in B sites by a e-packed at
ding the thi ayer of sphe e of the thi nt the first ing of spher ely, the third
in the first er of spher Arrangemen ystem posse old axis of uch an arran use of its acking of s available to le building n the figure atoms in th toms. rd layer we eres may be ird layer lie and the thi res is referre d layers may layer. Thes res. This ar nt: When the esses hexag symmetry ngement of hexagonal spheres ofte o accept ato the second e, we may b he second la e have a cho e placed on es strictly a rd layers ar ed to as AB y be placed se hollows rrangement e ABABAB gonal symm which is p three dimen l symmetry en abbrevia ms in layer d layer, we uild the sec
ayer makin oice of arra n the hollow above a sph re exactly i A arrangem d on the seco were left u of packing BA... arrang metry. This w perpendicul nsional pack y, this arr ated as hcp rs 2 either o cannot plac cond layers ng the C sit anging spher ws of the sec here of firs identical. T ment of pack ond set of h uncovered w g is denote gement of pa would impl lar to the p king of sphe rangement p. on the hollo ce spheres on hollows tes unavail res in two d cond layers st layer. In This arrange king of sphe hollows whi while arrang ed as ABC acking is co ly that the s planes of th eres is show is referre ows B or both on marked lable for different s, so that such an ement of eres. ich were ging the type of ontinued structure he close wn in the d to as
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.
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
packing the figu 6.3 Bod packed. packing other. S The sec layer be on top o as show In a bod center. the laye in this (bcc). A packed, g of atoms. ure dy Centere . This struc g are slightl Such an arra cond layer o
elow it. Suc of A). If thi w in the figu dy centered In this arran er just abov type of arr As has alre , and only 6 Each atom ed Cubic: cture can b ly opened u angement is of spheres ( ccessive bu s pattern of ure. d cubic arran ngement ea ve and four s rangement eady been 68% of the t in this arra This arran be obtained up. As a res s show in th ( marked B uilding of th f building la ngement, th ach sphere i spheres in t is only eigh mentioned, total volume angement ha ngement of d if spheres sult none of e abone.figu B) may be p he third laye ayers is repe he atoms occ s in contact the layer jus
ht. The stru , this arran e is actually as also 12 n spheres (o s in the fir of these sph ure. placed on th er will be e eated infinit cupy corner t with eight st below) an ucture is kn ngement of y occupied. nearest neigh r atoms) is st layer (m heres are in he top of th exactly like tely we get a rs of a cube other spher nd so the co nown as bo packing is hbours as s s not exact marked A) o n contact w he first layer the first lay an arrangem e with an ato res (four sp oordination ody centere s not exact hown in ly close of close ith each r, so the yer (i.e., ment bcc om at its pheres in number ed cubic tly close
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 ↓ Cubic close packed Hexagonal close packed Body centered cubic
1 Arrangement of
packing
close packed close packed not close packed
2 Volume occupied 74% 74% 68%
3 Type of packing ABACABC... ABABABAB.... -
4 Coordination number 12 12 8 5 Other characteristics Malleable and ductile
Less malleable, hard and brittle
Malleable and ductile
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.
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
Proof:1 Let rc a In an eq AD=ra i.e. On inve Thus in radius o ion can Proof:2 Let "a" 1 Lim and ra the ra quilateral tri a and AE=ra erting both s n order to o of small sph be thought 2 Lim be the leng miting Radi adii of the ca iangle ABC a+rc side, we get occupy a tr here should to fit into s miting Radi gth of side o ius Ratio fo ation and an C t rigonal void not be grea such a small ius Ratio fo of cube (say oe Triangul nion, respec cos d without d ater than 0. l site in its o or Tetrahed AB) lar hole ctively. ( EAD) = A disturbing th 155 times th oxide. dral hole AD / AE he close pa
Face di Since th Body di Also bo Substitu Dividin Proof:3 The siz through agonal he two anion iagonal ody diagona uting the va ng both side 3 Lim ze of an oct h an octahed ns are touch or al = 2ra+2rc alue of a we s by 2 ra, w miting Radi ahedral sit dral site as s hing each ot (where rc is e get we get ius Ratio fo te may acco shown in fo ther, BC=2 s the radius or Octahed ordingly be llowing figu 2ra (where ra of the catio dral hole calculated ure. a is the radiu on) if we consi us of the an ider a cross nion) s-section
ABCD Moreov In other Dividin Thus in sphere s Proof:4 Let the is a square ver BC = 2r r words, we ng both side n order to oc should not b 4 Lim e legth of CD = BD = ra + 2rc e may write s by 2r_a, w ccupy an oc be greater th miting Radi f each sid = 2ra (wher we get ctahedral vo han 0.414 ti ius Ratio fo de of a c e ra is the ra oid, in a clo imes that th or Cubic ho cube = a adius of the ose packed he large sphe ole so the le anion) lattice, the eres. ength of t radius of th the face d he small diagonal
Legth Let rc an Divide The em intersti radius o Structur sizes in (such a change of the bo nd ra be the both side by mpty space a itial site. T of the large re of variou nto different as non meta their prope ody diagon < radius of c y 2ra at the center The largest v sphere us substance t interstitial als like carb
rties. nal AC w ation and an r of the cub void and ca es can be m l sites. Exa bon, boron, which conta nion, respec e, formed b an accomm modified by amples may etc.) into t ains the b ctively. by eight iden modate a sph the introdu y include th the interstit body cente ntical spher here of radi uction of ot he introduct tial sites of er ion has res is called ius 0.732 ti her ions of ion of smal f metals wh s length d a cubic imes the f varying ll atoms hich will
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. 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 : 1.
4. 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.
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
In this the cell inside th Most of Other c NH4I, A 8.2 The A unit c Figure. The sal 1. 2. 3. 4. structure, e l is shared b he cell belo f the alkali compounds AgF, AgCl a e Zinc Blen cell represen Unit cell re lient featur The zinc at center of ea Sulphur ato said that su As there ar tetrahedral tetrahedral Each zinc a also surrou ach corner by two cell ongs entirely halides, alk which crys and AgBr. nd structure ntation of z epresentatio res of Zinc toms are ccp ach face of t oms are so ulphur atoms re eight tetr sites. So sites are fil atom is surr unded by fou r ion is shar s, and each y to that uni kaline earth stallize in so e inc blend is on of zinc bl Blende stru p type of ar the cube. located tha s occupy tet rahedral site the stoich led by sulph rounded by ur zinc atom red between h ion on the it cell. h oxides, an odium chlor s shown in t lend structu ucture rrangement at there are trahedral sit es available iometry of hur atoms. four sulphu ms which a n eight unit edge is sh nd sulphides ride type of the figure. ure. , i.e., zinc a four zinc a tes and thei e; four sulph
f the comp ur atoms an are also disp
t cells, each ared by fou s exhibit thi f structure a atoms at the atoms aroun r coordinati hur atoms o pound is 1 nd in turn ea posed towar h ion on the ur cells and is type of st are NH4Cl, e corners an nd it. Or it ion number occupy only :1. Only a ach sulphur rds the corn e face of d the ion tructure. NH4Br, nd at the may be r is four. y half of alternate r atom is ners of a
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 :
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
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 :
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 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
Examples: SrF2, BaF2, SrCl2, CdF2, HgF2, and PbF2.
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
Name Coordination number Fraction filled Examples
Rock salt (NaCl-type) NaCl-+ 6 6 1 Li, Na ,K, Bb halides, NHAgF, AgCl, AgBr. 4Cl, NH4Br, NH4I,
Zinc Blende
(ZnS-type) Zn
+2 4
S-2 4 ½ ZnS, BeS, CuCl, CuBr, CuI, AgI
Wurtzite (ZnS-type) Zn+2 4
S-2 4 ½ ZnS, ZnO, CdS, BeO
Fluorite (CaF2-type) Ca
+2 8
F- 4 1 CaF2, SrF2, BaF2, SrCl2, BaCl2, CdF2, HgF2 Cesium Chloride
(CsCl-type)
Cs+ 8
9. Defe
Real cry very reg this tem The fol of A+B Sto the mig Sch (a) acc the in t This d the ion predom lesser nect in Cry
ystals have gular. Ideal mperature a lowing disc B- units. Def Stoichiome Non-stoich oichiometri e ions in the gration of a hottky defec Schottky d companied e system. Th the followin defect is mo s (both cat minantly sho number of ioystals
always imp l crystals w all crystallin cussion is o fects in crys etric, and hiometric str ic Defects. I e lattice can an ion to s ct; (b) Frenk defect: This by a vacan he missing ng figure. ost predomi tions and a ow this defe ons in the la perfect stru with no impe ne solids co nly restricte stals may gi ructures. In stoichiom n occur due ome other kel defect. s defect con cy at an an cations and nant in com anions) areect are the a attice, the de uctures. The erfections a ontain some ed on simpl ive rise to metric comp e to a vacan interstitial nsists of a v nion site so d anions mo mpounds wi e of similar alkali halide ensity of so e arrangeme are possible e defects in le compoun pounds irre ncy at a cati site. These vacancy at as to maint ve to the su
ith high coo
r sizes. Som
es such as N lid will dec
ent of const e only at ab n the arrang nds are main gularity in ion and an a defects are a cation si tain the elec urface. The ordination n me of the NaCl and Cs rease. tituent units bsolute zero gement of i nly ionic co the arrange anion site o e of two ty ite and this
ctrical neut defect is ill numbers an compound sCl. Since t s are not . Above its units. onsisting ement of or by the ypes: (a) will be trality of lustrated nd where s which there are
(b) to a ani Th Ex Ag me So the def Sch for ) Frenkel D another pos ions. This is his defect is In compou coordinatio cation can e This defect In compou anion. xamples of c gBr etc. Th edium. the d lids general e other. The fects in a cr hottky defe r their forma Defect: This sition betwe s illustrated most predo unds which on numbers easily move is more com unds where compounds his type of density of th lly contain e crystal is rystal gener cts are easie ation. defect cons een the two d in the follo ominant: h have low the attractiv e into the in mmon in co we have h which show defects lea he medium, both these then said to rally increa er to form th sists of a va layers and i owing figure w coordinat ve forces be nterstitial sit ompounds w highly pola w this defec ads to an in however, r types of de o possess o ase with the han Frenke acancy at a is thus surro e. tion numbe eing less, ar te. which have i arizing catio ct are ZnS (b ncrease in emains unc efects, but o
nly that par e rise of tem l defects as cation site ounded by a ers. In com re easy to ov ons of differ on and an both zinc bl the dielectr changed. one is more rticular defe mperature. N the former . The cation a greater nu mpounds w vercome so rent sizes. easily pol lende and w ric constan e predomin fect. The nu Normally sp require less n moves umber of with low o that the larizable wurtzite), nt of the ant than umber of peaking, s energy
