Download Study notes of solid state chemistry and more Study notes Chemistry in PDF only on Docsity!
The solids are the substances which have definite volume and definite shape. In terms of kinetic molecular model, solids have regular order of their constituent particles (atoms, molecules or ions). These particles are held together by fairly strong forces, therefore, they are present at fixed positions. The properties of the solids not only depend upon the nature of the constituents but also on their arrangements.
Types and Classification of solids
(1) Types of solids Solids can be broadly classified into following two types, (i) Crystalline solids/True solids, (ii) Amorphous solids/Pseudo solids
Crystalline solids Amorphous solids They have long range order. They have short range order. They have definite melting point Not have definite melting point They have a definite heat of fusion Not have definite heat of fusion They are rigid and incompressible Not be compressed to any appreciable extent They are given cleavage i.e. they break into two pieces with plane surfaces
They are given irregular cleavage i.e. they break into two pieces with irregular surface They are anisotropic because of these substances show different property in different direction
They are isotropic because of these substances show same property in all directions There is a sudden change in volume when it melts.
There is no sudden change in volume on melting. These possess symmetry Not possess any symmetry. These possess interfacial angles. Not possess interfacial angles.
(2) Crystalline and amorphous silica( SiO 2 )
Silica occurs in crystalline as well as amorphous states. Quartz is a typical example of crystalline silica. Quartz and the amorphous silica differ considerably in their properties. Quartz Amorphous silica It is crystalline in nature It is light (fluffy) white powder All four corners of SiO^44 tetrahedron are shared by others to give a network solid
The SiO^44 tetrahedra are randomly joined, giving rise to polymeric chains, sheets or three-dimensional units It has high and sharp melting point (1710° C)
It does not have sharp melting point
(3) Diamond and graphite Diamond and graphite are tow allotropes of carbon. Diamond and graphite both are covalent crystals. But, they differ considerably in their properties. Diamond Graphite It occurs naturally in free state It occurs naturally, as well as manufactured artificially It is the hardest natural substance known.
It is soft and greasy to touch
It has high relative density (about 3.5) Its relative density is 2. It is transparent and has high refractive index (2.45)
It has black in colour and opaque
It is non-conductor of heat and electricity.
Graphite is a good conductor of heat and electricity It burns in air at 900° C to give CO 2 It burns in air at 700° C to give CO 2 It occurs as octahedral crystals It occurs as hexagonal crystals
(4) Classification of crystalline solids Table : 5.1 Some characteristics of different types of crystalline solids Types of Solid
Constituents Bonding Examples Physical Nature
M.P. B.P. Electrical Conductivity
Solid State
Chapter
Ionic Positive and negative ions network systematically arranged
Coulombic NaCl, KCl, CaO, MgO, LiF, ZnS, BaSO 4 and K 2 SO 4 etc.
Hard but brittle High (≃ 1000 K) High (≃2 000 K) Conductor (in molten state and in aqueous solution)
Covalent Atoms connected in covalent bonds
Electron sharing
SiO 2 (Quartz), SiC, C (diamond), C(graphite) etc.
Hard Hard Hard
Very high (≃ 4000 K) Very high (≃5 000 K)
Insulator except graphite
Molecular Polar or non-polar molecules
(i) Molecular interactions (intermolecu- lar forces) (ii) Hydrogen bonding
I 2 , S 8 , P 4 , CO 2 , CH 4 ,
CCl 4 etc.
Starch, sucrose, water, dry ice or drycold (solid CO 2 ) etc.
Soft
Soft
Low (≃3 00 K to 600K )
Low (≃ 400 K)
Low (≃ 450 to 800 K)
Low (≃373 K to 500K )
Insulator
Insulator
Metallic Cations in a sea of electrons
Metallic Sodium , Au, Cu, magnesium, metals and alloys
Ductile malleable
High (≃ 800 K to 1000 K)
High (≃15 00 K to 2000K)
Conductor
Atomic Atoms London dispersion force
Noble gases Soft Very low Very low Poor thermal and electrical conductors
Crystallography
“ The branch of science that deals with the study of structure,
geometry and properties of crystals is called crystallography”.
(1) Symmetry in Crystal : A crystal possess following three types of symmetry,
(i)Plane of symmetry : It is an imaginary plane which passes
through the centre of a crystal can divides it into two equal portions which are exactly the mirror images of each other.
(ii)Axis of symmetry : An axis of symmetry or axis of rotation is an
imaginary line, passing through the crystal such that when the crystal is rotated about this line, it presents the same appearance more than once in
one complete revolutioni.e., in a rotation through 360°. Suppose, the same
appearance of crystal is repeated, on rotating it through an angle of 360°/n,
around an imaginary axis, is called ann-fold axis where,n is known as the
order of axis. By order is meant the value of n in 2 / n so that rotation
through 2 / n ,gives an equivalent configuration.
(iii)Centre of symmetry : It is an imaginary point in the crystal that
any line drawn through it intersects the surface of the crystal at equal distance on either side.
Only simple cubic system have one centre of symmetry. Other system do not have centre of symmetry. The total number of planes, axes and centre of symmetries possessed by a crystal is termed as elements of symmetry. A cubic crystal possesses total 23 elements of symmetry. Plane of symmetry ( 3 + 6) = 9 Axes of symmetry ( 3 + 4 + 6) = 13 Centre of symmetry (1) = 1 Total symmetry = 23 (2) Laws of crystallography : Crystallography is based on three fundamental laws.
(i)Law of constancy of interfacial angles : This law states that angle
between adjacent corresponding faces is inter facial angles of the crystal of a particular substance is always constant inspite of different shapes and sizes and mode of growth of crystal. The size and shape of crystal depend upon the conditions of crystallisation. This law is also known as Steno's Law.
(ii)Law of rational indices : This law states that the ratio of
intercepts of different faces of a crystal with the three axes are constant and can be expressed by rational numbers that the intercepts of any face of a crystal along the crystallographic axes are either equal to unit intercepts
(i.e., intercepts made by unit cell)a,b,c or some simple whole number
multiples of them e.g.,na,n'b,n''c, wheren,n' andn'' are simple whole
numbers. The whole numbersn,n' andn'' are called Weiss indices. This law
was given by Hauy. Axis of four fold symmetry^ Axis of six fold symmetry
Plane of symmetry Rectangular plane of symmetry
Diagonal plane of symmetry Fig. 5.
Y
Centre of symmetry of a cubic crystal
X
Z Fig. 5.
Fig. 5.
Axis of two fold symmetry Axis of three f old symmetry
Fig. 5.4. Constancy of interfacial angles
Orthorhombic (Rhombic) a b c^ , 90 o
Simple: Points at the eight corners of the unit cell.
End centered : Also called side centered or base centered. Points at the eight corners and at two face centres opposite to each other.
Body centered : Points at the eight corners and at the body centre
Face centered: Points at the eight corners and at the six face centres.
KNO 3 , K 2 SO 4 ,
PbCO 3 , BaSO 4 , rhombic sulphur, MgSO (^) 4. 7 H 2 O etc.
Rhombohedral or Trigonal a b c , 90
Simple : Points at the eight corners of the unit cell , , NaNO 3 CaSO 4 calcite, quartz, As , Sb , Bi etc.
Hexagonal a b c ,
90 o
120 o
Simple : Points at the twelve corners of the unit cell out lined by thick line.
or Points at the twelve corners of the hexagonal prism and at the centres of the two hexagonal faces.
ZnO , PbS , CdS , HgS , graphite, ice, Mg , Zn , Cd etc.
Monoclinic a b c^ , 90 o^ , 90 o
Simple : Points at the eight corners of the unit cell End centered : Point at the eight corners and at two face centres opposite to the each other.
Na 2 SO 4. 10 H 2 O , Na 2 B 4 O 7. 10 H 2 O , CaSO 4. 2 H 2 O , monoclinic sulphur etc.
Triclinic a b c , 90 o
Simple : Points at the eight corners of the unit cell. CaSO 4. 5 H 2 O , K 2 Cr 2 O 7 , H 3 BO 3 etc.
Analysis of cubic system
(1) Number of atoms in per unit cell The total number of atoms contained in the unit cell for a simple cubic called the unit cell content.
The simplest relation can determine for it is, 8 2 1
nc (^) nf n i
Where nc Number of atoms at the corners of the cube=
nf Number of atoms at six faces of the cube = 6
ni Number of atoms inside the cube = 1
Cubic unit cell nc nf ni Total atom in per unit cell Simple cubic ( sc) 8 0 0 1 body centered cubic ( bcc) 8 0 1 2 Face centered cubic ( fcc) 8 6 0 4
(2) Co-ordination number (C.N.) : It is defined as the number of nearest neighbours or touching particles with other particle present in a crystal is called its co-ordination number. It depends upon structure of the crystal.
For simple cubic system C.N. = 6.
For body centred cubic system C.N. = 8
For face centred cubic system C.N. = 12.
(3) Density of the unit cell ( ): It is defined as the ratio of mass
per unit cell to the total volume of unit cell.
0 a^3 N
Z M
WhereZ = Number of particles per unit cell
M = Atomic mass or molecular mass
N 0 Avogadro number( 6. 023 1023 mol ^1 )
a Edge length of the unit cell= a pm a 10 ^10 cm
a^3 volume of the unit cell
i.e. 30 3
0 a^3 N 10 g / cm
Z M
^
c
a
b
The density of the substance is same as the density of the unit cell. (4) Packing fraction (P.F.) : It is defined as ratio of the volume of the unit cell that is occupied by spheres of the unit cell to the total volume of the unit cell.
Let radius of the atom in the packing =r
Edge length of the cube =a
Volume of the cubeV = a^3
Volume of the atom (spherical)^3 3
r
Packing density 3
3 3
a
r Z
V
Z
Structure r related to a
Volume of the atom ( )
Packing density % of void
Simple cubic 2
a r
3 3 2
a 6 ^0.^52
Face-centred cubic 2 2
a r
3
(^322)
(^) a 6 0.^74
Body- centred cubic^4
3 a r
3
4
(^) a 8 0.^68
^100 –^68
X -ray study of crystal structure
Study of internal structure of crystal can be done with the help of X- rays. The distance of the constituent particles can be determined from diffraction value by Bragg’s equation.
n 2 d sin
where, = Wave length of X-rays, n = order of reflection,
Angle of reflection,d = Distance between two parallel surfaces
The above equation is known as Bragg’s equation or Bragg’s law.
The reflection corresponding ton = 1 (for a given family of planes) is called
first order reflection; the reflection corresponding ton = 2 is the second
order reflection and so on. Thus by measuringn (the order of reflection of
the X-rays) and the incidence angle , we can knowd/ .
2 sin
d n
From this,d can be calculated if is known and vice versa. In X-ray
reflections,n is generally set as equal to 1. Thus Bragg’s equation may
alternatively be written as
2 d sin = 2 d hkl sin
Where d hkl denotes the perpendicular distance between adjacent planes
with the indiceshkl.
Close packing in crystalline solids
In the formation of crystals, the constituent particles (atoms, ions or molecules) get closely packed together. The closely packed arrangement is that in which maximum available space is occupied. This corresponds to a state of maximum density. The closer the packing, the greater is the stability of the packed system.
(1) Close packing in two dimensions : The two possible arrangement of close packing in two dimensions.
(i)Square close packing : In which the spheres in the adjacent row
lie just one over the other and show a horizontal as well as vertical alignment and form square. In this arrangement each sphere is in contact with four spheres.
(ii)Hexagonal close packing : In which the spheres in every second
row are seated in the depression between the spheres of first row. The spheres in the third row are vertically aligned with spheres in first row. The similar pattern is noticed throughout the crystal structure. In this arrangement each sphere is in contact with six other spheres.
(2) Close packing in three dimensions : In order to develop three dimensional close packing, let us retain the hexagonal close packing in the first layer. For close packing, each spheres in the second layer rests in the hollow at the centre of three touching spheres in the layer as shown in figure. The spheres in the first layer are shown by solid lines while those in second layer are shown by broken lines. It may be noted that only half of the triangular voids in the first layer are occupied by spheres in the second
layer (i.e., either b or c). The unoccupied hollows or voids in the first layer
are indicated by (c) in figure.
There are two alternative ways in which species in third layer can be arranged over the second layer,
(i)Hexagonal close packing : The third layer lies vertically above the
first and the spheres in third layer rest in one set of hollows on the top of the second layer. This arrangement is called ABAB …. type and 74% of the available space is occupied by spheres. This arrangement is found in
Be, Mg, Zn, Cd, Sc, Y, Ti, Zr, Tc, Ru.
(ii)Cubic close packing : The third layer is different from the first
and the spheres in the third layer lie on the other set of hollows marked ‘C’
Fig. 5.6. Square close packing
Fig. 5.7. Hexagonal close packing
a
a
a
a
a
a
a^ a^ a
a a
b b b
a a a
c c^ c
a
Fig. 5.8. Close packing in three dimensions
Fig. 5.9. Hexagonal close packing ( hcp) in three dimensions
A
B A
B A
A
B
A
B
A
A
are mainly governed by the ratio of the radius of cation ( r )to that of
anion ( r ).The ratio r to r ( r (^) / r )is called as radius ratio.
r
r Radius ratio
Table : 5.4 Limiting Radius ratios and Structure
Limiting radius ratio ( r+ )/( r– ) C.N. Shape
< 0.155 2 Linear
0.155 – 0.225 3 Planar triangle 0.225 – 0.414 4 Tetrahedral 0.414 – 0.732 6 Octahedral 0.732 – 0.999 or 1 8 Body-centered cubic
Effect of temperature and Pressure on C.N.
On applying high pressure NaCl structure having 6 : 6 co-
ordination changes toCsCl structure having 8 : 8 co-ordination. Thus,
increase in pressure increases the co-ordination number.
Similarly,CsCl structure on heating to about 760K, changes to
NaCl structure. In other words, increase of temperature decreases the co-
ordination number.
( 6 : 6 )
NaCl (8:8)
CsCl
Structure of ionic crystals
Table : 5.5 Types of ionic crystal with description Crystal structure type
Brief description Examples Co-ordination number
Number of formula units per unit cell
Type AB
Rock salt (NaCl)
type
It has fcc arrangement in which Cl ions
occupy the corners and face centres of a cube while Na ions are present at the body and edge of centres.
Halides of Li, Na, K, Rb, AgF,
AgBr, NH 4 Cl, NH 4 Br, NH 4 I etc.
Na 6
Cl 6
Zinc blende (ZnS)
type
It has ccp arrangement in which S^2 ions
form fcc and each Zn^2 ion is surrounded
tetrahedrally by four S^2 ions and vice versa.
CuCl , CuBr , CuI , AgI , BeS Zn^2 4
S^2 4
Type AB 2
Fluorite (CaF 2 ) type
It has arrangement in which Ca^2 ions form
fcc with each Ca^2 ions surrounded by 8 F
ions and each F ions by 4 Ca2+ ions.
BaF 2 , BaCl 2 , SrF 2 SrCl 2 , CdF 2 , PbF 2
Ca^2 8
F 4
Antifluorite type Here negative ions form the ccp arrangement
so that each positive ion is surrounded by 4 negative ions and each negative ion by 8 positive ions
Na 2 O Na 4
O^2 8
Caesium chloride
(CsCl) type
It has the bcc arrangement with Cs at the
body centre and Cl ions at the corners of a cube or vice versa.
CsCl , CsBr , CsI , CsCN ,
TlCl , TlBr , TlI and TlCN
Cs 8
Cl 8
Defects or Imperfections in solids
Any deviation from the perfectly ordered arrangement constitutes a defect or imperfection. These defects sometimes called thermodynamic defects because the number of these defects depend on the temperature.
(1) Electronic imperfections : Generally, electrons are present in fully occupied lowest energy states. But at high temperatures, some of the electrons may occupy higher energy state depending upon the temperature.
For example, in the crystals of pureSi orGe some electrons are released
thermally from the covalent bonds at temperature above 0 K. these electrons are free to move in the crystal and are responsible for electrical conductivity. This type of conduction is known as intrinsic conduction. The
electron deficient bond formed by the release of an electron is called a hole. In the presence of electric field the positive holes move in a direction opposite to that of the electrons and conduct electricity. The electrons and holes in solids gives rise to electronic imperfections. (2) Atomic imperfections/point defects : When deviations exist from the regular or periodic arrangement around an atom or a group of atoms in a crystalline substance, the defects are called point defects. Point defect in a crystal may be classified into following three types.
(i)Stoichiometric defects : The compounds in which the number of
positive and negative ions are exactly in the ratios indicated by their chemical formulae are called stoichiometric compounds. The defects do not
Coordination number decreases from 6 to 4
r+/ r–^ = 0.414^ r+/^ r–^ < 0.
Fig. 5.17. Effect of radius ratio on co-ordination number
r+/ r–^ > 0. Coordination number increases from 6 to 8
Pressure Temp
disturb the stoichiometry (the ratio of numbers of positive and negative ions) are called stoichiometric defects. These are of following types,
(a) Interstitial defect : This type of defect is caused due to the presence of ions in the normally vacant interstitial sites in the crystals. (b) Schottky defect : This type of defect when equal number of cations and anions are missing from their lattice sites so that the electrical neutrality is maintained. This type of defect occurs in highly ionic compounds which have high co-ordination number and cations and anions
of similar sizes.e.g.,NaCl, KCl, CsCl andKBr etc.
(c) Frenkel defect : This type of defect arises when an ion is missing from its lattice site and occupies an interstitial position. The crystal as a whole remains electrically neutral because the number of anions and cations remain same. Since cations are usually smaller than anions, they occupy interstitial sites. This type of defect occurs in the compounds which have
low co-ordination number and cations and anions of different sizes.e.g.,
ZnS, AgCl andAgI etc. Frenkel defect are not found in pure alkali metal
halides because the cations due to larger size cannot get into the interstitial
sites.In AgBr both Schottky and Frenkel defects occur simultaneously.
Consequences of Schottky and Frenkel defects
Presence of large number of Schottky defect lowers the density of the crystal. When Frenkel defect alone is present, there is no decrease in density. The closeness of the charge brought about by Frenkel defect tends to increase the dielectric constant of the crystal. Compounds having such defect conduct electricity to a small extent. When electric field is applied, an ion moves from its lattice site to occupy a hole, it creates a new hole. In this way, a hole moves from one end to the other. Thus, it conducts electricity across the crystal. Due to the presence of holes, stability (or the lattice
energy) of the crystal decreases.
(ii) Non-stoichiometric defects : The defects which disturb the
stoichiometry of the compounds are called non-stoichiometry defects. These defects are either due to the presence of excess metal ions or deficiency of metal ions.
(a)Metal excess defects due to anion vacancies : A compound may
have excess metal anion if a negative ion is absent from its lattice site,
leaving a ‘ hole’, which is occupied by electron to maintain electrical
neutrality. This type of defects are found in crystals which are likely to possess Schottky defects. Anion vacancies in alkali metal halides are reduced by heating the alkali metal halides crystals in an atmosphere of alkali metal
vapours. The ‘ holes’ occupy by electrons are called F-centres (or colour
centres).
(b)Metal excess defects due to interstitial cations : Another way in
which metal excess defects may occur is, if an extra positive ion is present in an interstitial site. Electrical neutrality is maintained by the presence of an electron in the interstitial site. This type of defects are exhibit by the
crystals which are likely to exhibit Frenkel defectse.g., whenZnO is heated,
it loses oxygen reversibly. The excess is accommodated in interstitial sites, with electrons trapped in the neighborhood. The yellow colour and the
electrical conductivity of the non-stoichiometricZnO is due to these
trapped electrons.
Consequences of Metal excess defects
The crystals with metal excess defects are generally coloured due to the presence of free electrons in them. The crystals with metal excess defects conduct electricity due to the
presence of free electrons and aresemiconductors. As the electric transport
is mainly by “excess” electrons, these are called n-type (n for negative)
semiconductor. The crystals with metal excess defects are generally paramagnetic due to the presence of unpaired electrons at lattice sites. When the crystal is irradiated with white light, the trapped electron absorbs some component of white light for excitation from ground state to
the excited state. This gives rise to colour. Such points are calledF-centres.
(German word Farbe which means colour) such excess ions are accompanied by positive ion vacancies. These vacancies serve to trap holes in the same way as the anion vacancies trapped electrons. The colour
centres thus produced are calledV-centres.
(c)Metal deficiency defect by cation vacancy : In this a cation is
missing from its lattice site. To maintain electrical neutrality, one of the nearest metal ion acquires two positive charge. This type of defect occurs in
compounds where metal can exhibit variable valency.e.g., Transition metal
compounds likeNiO,FeO,FeS etc.
(d)By having extra anion occupying interstitial site : In this, an extra
anion is present in the interstitial position. The extra negative charge is balanced by one extra positive charge on the adjacent metal ion. Since anions are usually larger it could not occupy an interstitial site. Thus, this structure has only a theoretical possibility. No example is known so far.
Consequences of metal deficiency defects
Due to the movement of electron, an ion A+ changes to A+2 ions. Thus, the movement of an electron from A+ ion is an apparent of positive hole and
the substances are calledp-type semiconductor
(iii)Impurity defect : These defects arise when foreign atoms are
present at the lattice site (in place of host atoms) or at the vacant interstitial sites. In the former case, we get substitutional solid solutions while in the latter case, we get interstitial solid solution. The formation of the former depends upon the electronic structure of the impurity while that of the later on the size of the impurity.
Properties of solids
Some of the properties of solids which are useful in electronic and magnetic devices such as, transistor, computers, and telephones etc., are summarised below,
A+^ B–^ A+^ B–
B–^ A+^ B–^ A+
A+^ B–^ A+^ B–
Fig. 5.20. Metal excess defect due to extra cation
A+
A+^ B–^ A+^ B–
B–^ A+^ B–^ A+
A+^ e–^ A+^ B–
Fig. 5.21. Metal excess defect due to anion vacancy
A+^ B–^ A+^ B–
B+^ A–^ A+
B–^ A+^ B–
Fig. 5.18. Schottky defect
A+^ B–
B–^ A+
B–^ A+^ B–
Fig. 5.19. Frenkel defect
A+
B–^ A+
A+ B–
A+^ B–^ A+^ B–
B–^ B–^ A+
B–^ A+^ B–^ A+
A+^ B–^ A+^2 B–
Cation vacancy
Metal having higher charge
Fig. 5.
ferroelectric crystal. Example, Potassium hydrogen phosphate ( KH 2 PO 4 ),
Barium titanate ( BaTiO 3 ).
(iv) Antiferroelectricity : In some crystals, the dipoles in
alternate polyhedra point up and down so that the crystals does not
possess any net dipole moment. Such crystals are said to be
antiferroelectric. Example, Lead zirconate ( PbZrO 3 ). Ferroelectrics
are used in the preparation of small sized capacitors of high
capacitance. Pyroelectric infrared detectors are based on such
substances. These can be used in transistors, telephone, computer
etc.
The reverse of crystallization is the melting of the solid.
The slower the rate of formation of crystal, the bigger is the crystal.
The hardness of metals increases with the number of electrons
available for metallic bonding. Thus Mg is harder than sodium.
Isomorphism is applied to those substances which are not only
similar in their crystalline form, but also possess an equal number of atoms united in the similar manner. The existence of a substance in more than one crystalline form is known as polymorphism.
