Solid State Chemistry IPE

Solid state

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Prepared by V. Aditya vardhan adichemadi @ gmail.com

SOLID STATE Characteristic Characteristic properties of solid state 1) Solids S olids have definite definite mass, volume and shape. 2) They are ar e incompressible incompressible and rigid. 3) Their constituent part pa rticle icless (atoms (at oms or ions or molecules) are arranged very closely closely and the attracatt ractions between them are strong. 4) Their constituent particles pa rticles have fixed fixed positions po sitions and can only oscillate oscillate about their t heir mean positions. positions. Translatory Translatory and rotatory rotat ory motions are restricted. Crystalline and amorphous solids Solids can be classified classified into crystalline and amorphous on the t he basis of the nature natur e of order ord er present in the arrangem arr angement ent of thei t heirr constituent particles. Crystalline solids Crystalline Crystalline solids have definite definite characteristic charact eristic geometrical geometr ical shape. shape. They have long range order or der which means that there is a rregular egular pattern patte rn of arrangement of particl part icles es which is is repeated over the entire ent ire crystal. They possess definite definite and characteristic charact eristic melting points and heats of fusion. They show anisotropic anisotro pic nature. nature. Anisotropic Anisotro pic substances exhibit exhibit different values for some so me physical physical properties proper ties like refractive refract ive index, index, electrielectr ical resistance etc., in different directions. E.g.., Sodium chloride, chloride, crystalline crystalline quartz etc., Amorphous solids Amorphous Amorphous solids have irregular shape. They possess only short range r ange orders i.e., the regular patter patt ern n of arrangement is repeated over o ver short distance only o nly.. They do not possess p ossess definite definite and characteristi character isticc melting points and heats of fusion. They show isotro pic nature as a s they exhibit exhibit same values for for some so me physical propert pro perties ies in different different directions. directio ns. These are actually actu ally considered as super co cooled oled liquids or pseudo pseu do solids. E.g.., Glass, rubber, rubber, amorphous quartz, plastics (organic polymers) polymers) etc., etc. ,

N A H E y b D L E G d R L e r A O a p V C L e R A P r O I G A N N U Y A J R I T V A I E W D D G A A A V . V

Distinction between Crystalline and Amorphous Solids Property Crystalline solids Amorphous solids S ha pe Definite ch characteristic geometrical sh shape Irregular sh shape Meltin Melting g point point Melt Melt at a sharp sharp and char charact acteri eristi stic c Gradually soften over a range of temperature temperature Cleavage When cut with a sharp edged tool, they split When cut with a sharp edged tool, they cut property into two pieces and the newly generated into two pieces with irregular surfaces. surfaces are plain and smooth Heat of fusion fusion They have have a definite definite and characteri characteristic stic They do not have definite heat of fusion heat of fusion Anisotropy Anistropic in nature Isotropic in nature Nature True solids Pseudo solids or super cooled liquids Order Long range order Only short range order

Classification of solids based on nature of attractions Crystalline solids are classified classified based on nature of attract at tractions ions between constituent const ituent particle part icless in them them into four categories cat egories viz.,1) molecular, molecular, 2) ionic, ionic, 3) metallic metallic and 4) covale co valent nt solids 1) Molecular solids : Molecules (or rarely rare ly noble gas atoms ) are the constituent particles. part icles. They are attracted attract ed by weak van der wall's wall's forces of attractions att ractions or by hydrogen hydrogen bonds. Based on the nature of these intermolecular forces, fo rces, molecular solids are again subdivided into i) van der wall's crystals : In these solids, the intermolecular intermolecular forces for ces of attraction attr action are very weak van der wall's forces (Like London dispersion forces or o r dipole-dipole attractions). att ractions). These T hese solids solids have very very low melting points and relatively soft. E.g., Solid H2, N2, CO2, SO2 etc.,

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Solid state


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ii) Hydrogen bonded Crystals : In these solids, solids, the constituent co nstituent molecules are attract att racted ed by hydrogen hydrogen bonds. These are usually hard. E.g., Ice (Soli (So lid d H2O), solid HF, HF, solid NH 3 etc., Usually the melting points of molecular molecular solids are bel below ow room ro om temperature. temperat ure. They are bad conductors conducto rs of electricity. electricity. 2) Ionic Solids : Ions are the t he constituent particl part icles. es. The cations and anions are arranged regularly r egularly in three dimensions dimensions and strongly stro ngly held together toget her by electrostatic electrost atic attract att ractions. ions. These solids are rigid with high melting points. But they are brittle britt le and non elastic. As the ions are not free to move, ionic solids are electrical electrical insulators in solid solid state. stat e. E.g., NaCl, KCl etc., 3) Metallic Solids : Metallic crystals constitute constit ute orderly o rderly arranged metal atom in a sea of free free electrons. electro ns. These electrons held the metal atoms ato ms together. Metals are rigi r igid d and possess high melting melting points due to strong metallic metallic bonds. Due to the presence of free electrons, electro ns, they are good electrical electr ical and thermal conductors. conducto rs. They are also lustrous, lustro us, opaque, malleable and ductile. E.g., Cu, Al, Fe etc.,


4) Covalent Crystals : The entire crystal is considered as a giant molecule. It is a three dimensional dimensional network of atoms ato ms bonded covalently covalently.. These solids are very hard with extremely high melting melting points. They T hey do not conduct electricity (except (except graphite). E.g., diamond, graphite, SiC, SiO2 etc., The differences between above types t ypes of solids is summarized summarized below

Type of solid (1) Molecular solids (i) van der wall's solids (ii) Hydrogen bonded (2) Ionic solids

Constituent particles

Molecules

Ions

(3) Metallic solids Positive ions in a sea of delocalised electrons Atoms (4) Covalent or network solids

Attractive Forces

Examples

Physical Nature

Electrical Conductivity

Melting point

van der wall's forces

Ar, CCl4, H2, I2, CO

Soft

Insulator

Very low

Hydrog drogen en bond bondin ing g

H2O (ice)

Hard

Insulator

Low

Coulom bic or electrostatic

NaCl, MgO, Hard but ZnS, CaF brittle

Insulators High in solid state but conductors in molten state.

Metallic bonding

Fe, Fe, Cu,Ag, Mg,

Covalent bonding

SiO2 (quartz), SiC, C

Conductors in solid state as well as in molten stste Insulators

Hard but malleable and ductile Hard

Fairly high

Very high







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Metalling bonding The bonding in metals can be explained by using following theories. theo ries. 1) Electron sea model (Drude-Lorentz theory) According According to this theory i) Ametal lattice comprises co mprises of rigid spheres of metal ions in a sea of free electrons. electr ons. ii) Metal ato atoms ms contribute their valence electrons electrons to the sea of free electrons. iii) iii) These electrons electro ns move freely freely through the inter interstices. stices. iv) The attraction att raction between bet ween metal ions and free electrons electro ns is called called metallic metallic bond. v) This theory t heory could explain the electrical elect rical and thermal conductivity condu ctivity of metal. But it fails in explaining explaining the lattice energies quantitatively.

-

+ + +

-

-

+ + +

-

+ + +

-

-

- Free electro electron n

+ Metal ion

+

-

+

-


+ +

-

+ +

-

2) Valence Valence bond theory t heory This theory was proposed pr oposed by Linus Linus Pauling. According According to t o this theory theor y, metallic bond is considered as a highly delocalized delocalized covalent bond between metal atoms. at oms. Metal Met al can exhibit exhibit several resonance structures struct ures due to the delocalization of one electron electron and electron electro n pair covalent bonds. bonds. These resonance resonance structures confer stability to the metallic crystal. Various resonance forms in sodium metal are shown below. Na Na Na Na

Na Na Na Na

Na Na

+

-

Na Na

Na Na

Na Na

+

-

+

Na Na -

Na Na

-

Na Na +

etc.,

Na Na

This theory theor y could not explain metallic metallic lustre, heat conduction conduct ion by metals and retention retent ion of metallic properties propert ies in molten molten and solution solut ion state of o f metals. Crystal lattice and unit cell Crystal lattice: The regular three t hree dimensional dimensional arrangement of o f lattice points in space is called crystal lattice. The points at which the constituent particles par ticles (atoms or ions or molecules) molecules) of crystal are found are called lattice points. Unit cell : The smallest smallest part of the crystal lattice which generates entire crystal when repeated in three dimensions is known as unit cell. c ell. Crystal parameters The three edges ed ges of unit cell are denoted by a,b and c and the angles between these edges are

denoted by  ,  and 







Solid state


4 z-axis

c 

a



b



y-axis

x-axis

and γ are called Note: a,b,c, α,β and called crystal parameters. parameter s. Types of unit cells 1) Primitive or simple unit cell: The constituent particles par ticles are only present at the t he corners of the unit cell.


2) Body centered unit cell: It contains particles at all the eight eight corner as well as at the centre of the t he unit cell.

3) Face centered unit cell: In this t his unit unit cell, all the eight cor corners ners and six faces are occupied occup ied by the constituent const ituent particles par ticles in in the unit cell.

4) End centre unit cell: In this unit cell, one constituent particle par ticle is present at the centre centr e of any two opposite faces besides besides those present at the corners. cor ners.







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lattice must be same as that of o f the solid crystal itself. itself. The seven crystal systems and Bravais lattices are summarized summarized below.

Crystal System 1. Cubic

2. Tetragonal

3. Orthorthombic

4. Rhombohedral (OR) Trigonal 5.Hexagonal

N A H E y b D L E G d R L e r A O a p V C L e R A P r O I G A N N U Y A J R I T V A I E W D D G A A A V . V Bravais Lattices

3 (P, I, F)

2 (P, I )

4 (P, I, F, C)

Axes or edge length parameters a=b=c

a=b

a



b



Examples









 = 900

NaCl, Zinc blende, Cu

c









 = 900

White tin, SnO2, TiO2, CaSO4

c









 = 900

Rhombic sulphur, KNO3, BaSO4











Calcite (CaCO3), HgS (cinnabar) Graphite, ZnO,



1 (P)

a=b

1 (P)

a=b=c



Angles

c







90

0

 = 900  = 1200







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simple (P)

1. Cubic

a 

 

b  c     90 o

Body Centred (I)

Face Centred (F)

a a

a

2. Tetragonal


abc 







  90

c

o

a

a

3. Ortho rhombic

abc 







c

  90 o

b

a

4. Rhombohedral or Trigonal

abc







  90o



a

a

5. Hexagonal

a

abc









c

o

90 ;   120

o a

o

120

a

6. Monoclinic

abc









c

90o ;   90 o b a

End Centred (C)









Solid state

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Packing in metallic solids Metal atoms at oms in metallic metallic crystal can be packed closely in in four different arrangements as described de scribed below. 1) Simple cubic arrangement arrangement Simple Simple cubic arrangement o off metallic crystal is obtained when two dimensional dimensional square close packed layers layers are arranged ar ranged over each other such that t hat the spheres in the second layer layer are present exactly over the t he spheres of first layer. The coordination coo rdination number number of each sphere in this arrangement is six. The packing fraction is only 52%. E.g., Poloni Po lonium um

N A H E b y D L E G d R L e r A O a C p e V R L r P O G A I A N N U Y A J R I T V A I E W D D G A A V A . V

2) Body centered cubic (BCC) (B CC) arrangement In this arrangement, the two t wo dimensional dimensional square close packed layers layers are arranged ar ranged such that the t he spheres in every next next layer are arranged arr anged over the voids vo ids of the first layer. layer. The coordination coor dination number number is eight and packing fraction is 68% in this t his arrangement. E.g., Na, K, Rb, Cs, ba, Cr, Mo, W etc.,

3) Hexagonal close packed (HCP) arrangement In this arrangement, tthe he closest packed layers are arranged in ABAB pattern. patter n. There are two t ypes of closest packed layers in which which the spheres in every second layer layer (B) are a re present prese nt over the t he voids of one type in first first layer layer (A). The coordination coo rdination number is twelve and packing fraction is 74%.







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The coordination coo rdination number is twelve and packing fraction is 74%. E.g., Al, Al, Cu, Au, Pt, Pb, Pd, Ni, Ca et c., Packing fraction It indicates indicates how ho w much of space is occupied by constituent spheres in a crystal lattice.

Packing Packing fraction fraction =

volum volumee of all all thespheres thespheres volum volumee of thecrysta thecrystall

Coordination number : The number of closest atoms surroundi surro unding ng an atom at om in a metallic metallic crystal is known as coordinati coord ination on number number of that t hat crystal. Number of atoms (z) present in a unit uni t cell The atoms at the corners cor ners of a unit unit cell contribute only 1/8th part of o f them to the unit cell. The atoms ato ms at the centre of o f a face of unit unit cell contribute only o nly 1/2 part of them. The atoms on the edges of unit cell contribute contr ibute 1/4th part of o f them.


In simple cubic unit cell: z = 8 x 1/8 = 1

In Body centered unit cell: z = (8 x 1/8 ) + (1) = 2

In Face centered unit cell: z = (8 x 1/8 ) + ( 6 x 1/2) = 1+3 = 4







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m = mass of one atom =

Molar mass  M  Avog vogadronu adronumb mbeer  N A 

a = edge length ρ=

Z.M N A .a 3

Types of voids Trigonal void :The empty space between adjacent adjacent three spheres in a layer of closely packed crystals is called trigonal trigo nal void .

N A H E b y D L E G d R L e r A O a C p e V R L r P O G A I A N N U Y A J R I T V A I E W D D G A A V A . V trigonal void

If the number of atoms at oms in closely closely packed crystals ( hcp or ccp) is 'X' then t hen the number of trigonal voids voids in them is '8X'. Tetrahedral void : The three dimensional empty empty space formed in b between etween closely spaced three spheres spher es in a layer layer and another anot her sphere in the next layer is called called tetrahedr te trahedral al void.

tetrahedral void

There are two types of tetrahedral tet rahedral holes in in closely packed packed crystals ( hcp or ccp) . The total t otal number of tetrahedral tet rahedral holes containing 'X' atoms in hcp hcp or ccp crystal cr ystal is equal to '2X'. '2 X'. Octahedral void : The empty space between three spheres of o f one layer layer and three thr ee spheres of next layer is called octahedral void.







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Radius ratio ( rs m a l l / r l a r g e )

Geometric shape of the crystal formed

Upto 0.15 0.15 to 0.22 0.22 to 0.41 0.41 to 0.73 0.41 to 0.73 >0.73

Linear Trigonal planar Tetrahedral Square pyramidal Octahedral Cubic


Coordinatio n number of the ion 2 3 4 4 6 8

Defects in crystals The irregularities irregularit ies in in the arrangement arr angement of constituent particles part icles in in crystals lead to several types t ypes ofdefects in crystals. Defects in crystals affect density densit y, heat capacity capac ity,, entropy, ent ropy, mechanical strength, str ength, electrical elect rical conducti condu ctivity vity,, catalytic activity act ivity etc., . Thermodynamically Thermodynamically all the crystal have the tendency t endency to become defective defect ive because because defects increase the entropy entrop y of crystals. crystals. Defects in crystals are broadly bro adly divided divided into i) Point defects: which occur around a lattice point in a crystal. ii) Line Line or extended e xtended defects: which are present in one or more dimensions. Defects can also a lso be classified classified into i) Intrins Intr insic ic : which are present in pure crystals. cr ystals. ii) Extrinsic : which occur due to t o impurities in crystals


Point defects: These are of three types t ypes : i) Stoichiometric Sto ichiometric : Stoichiometry Sto ichiometry is maintained maintained in the defected crystal. ii) ii) Non stoich sto ichiome iometr tric ic : Stoichiome S toichiometry try of the defected crystal is not maintain maintained. ed. iii) iii) Impurity defects defects : These defects otherwise ot herwise known as extrinsic extrinsic defects occur due to presence of impurities impurities in crystals. Stoichiometric defects 1. Schottky defect The point defect which arises due to missing of ions at the t he lattice points of ionic crystal is calle called schottky defect. In order or der to maintain electrical neutrality, neut rality, the number of missing missing cations and anions must be equal. Schottky Schott ky defects are shown by ionic compounds compounds in which cation and an ion sizes are equal. They







Solid state


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Frenkel defect It is a point po int defect formed due to t o shifting of an atom or ion from fro m its its normal nor mal lattice lattice point po int to an interst interstitial itial site. It is also also called dislocation defect. This defect is shown by ionic ionic compounds co mpounds in which there is a large difference in size of ions. E.g., AgCl, AgCl, Ag Br, Br, AgI, ZnS etc., In above compounds cations (Ag +, Zn2+ etc.,) etc.,) are smaller in size when compared to t o anions ( like halides). halides). Frenkel defect does not change the density of the crystal.


Bragg's equation: Consider a crystal surface with planes of lattice points as a s shown below. below. Let the inter planar distance distance between them is 'd'. Now consi co nsider der two t wo X-rays , of wavelength wavelength '  ' ,which are incident on the surface of the t he crystal and undergoing constructive interference. 1 s t r 2 a n d y r a y

F



1st plane

d

2nd plane

E

D

A

 



C

B

3rd plane

The first ray is reflected at point 'A' on the t he surface of 1st plane, where as the 2nd ray is reflected reflected at point 'B' on the surface of 2nd plane, both bot h at an angle of  . This is called angle of reflection. Both Both the rays travel the t he same distance till the wavefront 'AD'. The second ray ttravels ravels an extra distance distance of DB+BC and then interfere interfere with first ray constructively constr uctively.. If the two waves are to t o be in phase, the path difference difference between the t he two rays must must be an integral multiple of wavelength wavelength of X-ray X-r ay ' '. i.e.,

 DB

diffraction) BC BC (where n= an integer and known as order of diffraction)









Solid state

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(ii) Insulators : These are the solids with very low conductivities conduct ivities ranging ranging between betwee n 10–20 to 10–10 ohm– 1 –1 m . (iii) Semiconductors : These are the solids so lids with with conductivities co nductivities in the intermediate range from 10–6 to 104 ohm–1m–1.

A conductor may conduct electricity through throug h the movement movement of electrons or ions. Metals conduct electricity electr icity in in solid as well as molte molten n state throu t hrough gh the movement of electrons. electro ns. The conductivity conduct ivity of metals metals can be explained as follows. The atomic ato mic orbitals of metal meta l atoms form molecular orbitals which are so close in energy to each other and form a band. There are two t wo types t ypes of molecular molecular orbitals possible. The molecular molecular orbitals with low energy are referred referre d to as bonding and with with high energy are called anti-bonding orbitals. The band formed formed by bonding molecular orbitals is generally called valence band and that band formed by anti-bonding orbitals is called conduction band. If the valence band is partially filled or it overlaps with conduction band, then t hen electrons can c an flow easily under an applied ap plied electric field and the metal shows conduct c onductivit ivity y. The conductivity of metals decreases with increase in temperature temperatur e due to increase increase in vibrations of atoms at oms.. In case of insulators, tthe he gap between valence and conduction bands is very large and hence the electrons cannot jump from filled valence band to unoccupied conduction band. Hence these substances exhibit exhibit poor p oor electrical conductivity conduct ivity.. But in case of semiconductors, semiconducto rs, there t here is a small small gap between valence and conduction conductio n bands. Therefore, some s ome number number of electrons electr ons can jump jump into conduction co nduction band and show some conductivity condu ctivity.. The conductivity of semiconductors semiconducto rs increases with raise in temperature temperat ure as more number of electrons elect rons can jump to conduction band.

N A H E y G b D L E d R L e r A O a p V C L e R A P r O I G A N U A N Y J I A R T V I

conduction band







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i) n-type semi-conductors: The extrinsic semi conductors conduct ors which contain electron-rich electron- rich impurities impurities are called called n-type semi conductors. conductor s. The electrical electr ical conductivity conductivity is due to t o movement movement of o f electrons. Eg., Silicon or germanium doped with phosphorus or arsenic (15th group gro up elements) elements) Mechanism: Mechanism: Silicon and germanium belong to group grou p 14 of the t he periodic table t able and have have four valence electrons electro ns each. In their crystals each atom ato m forms four covalent bonds with its neighbors . When doped with a group gr oup 15 element like P or As, which contains five five valence valence electrons, t hey occupy some some of the t he lattice sites in silicon silicon or germanium ge rmanium crystal . Four out of o f five five electrons electro ns are used in the formation of four covalent covalent bonds with the four neighboring neighboring silicon silicon atoms. ato ms. The fifth electron is extra and becomes delocaldelocalized. These delocalized electrons increase the conductivity co nductivity of doped silicon silicon (or (o r germanium). Here the increase in conductivity is due to the negatively charged electron, hence silicon doped with electron-rich impurity is called called n-type semiconduc semiconducto tor. r. ii) p-type semiconductors: The extrinsic semi conductors conduct ors which contain electron-deficit electro n-deficit impurities are called called p-type p-t ype semi semi conductors. conductor s. The electrical elect rical conductivity conductivity is due to t o electron electro n holes. Eg., silicon or germanium ger manium doped with wit h boron or aluminium or gallium (13th group gro up elements) Mechanism: Mechanism: Silicon or germanium doped with wit h a 13th group gro up element like B, A All or Ga which contains onl only y three valence electrons. As they can form only three bonds, an electron vacant site called called 'electron 'electro n hole' on the t he dopant atom at om is formed. An electron electro n from a neighboring atom can jump into into this electron hole by creating creat ing a new hole on the neighboring atom. Thus T hus there is a movement of electron electr on holes and electron electro ns in opposite direction. direct ion. As the conductivity is increased increased due to t o formation of positively charged charged holes, the substances are called p-type p-t ype semi conductors. conducto rs.


Applications: 1) Diode is a combination of n-type and p-type p-t ype semiconduct semiconductors ors and is used as a rectifie rect ifier. r. 2) Transistors are made by sandwichin sandwiching g a layer of one type t ype of semiconducto semiconductorr between betw een two layers of t he other type of semiconductor. semiconductor. 3) npn and pnp type of transistors transistor s are used to detect d etect or amplify radio or audio aud io signals. signals. 4) The solar cell is an efficient photodiode used for conversion of light energy into electrical energy.







Solid state

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Molecular polarity alignment in Ferromagnetic substance

Ferrimagnetism arises when the magnetic magnet ic moments are ar e aligned in parallel and anti parallel direction directio n in unequally resulting resulting in a net moment. Eg., Fe3O4, Ferrites of o f the general formula MII (Fe2O4) where M = Mg, Cu, Zn etc., In case of anti ferromagnetism, the magnetic moments moments of domains are cancel out each other so as to give zero net moment. Eg., MnO

Molecular polar alignment in Anti ferromagnetic substance

All these magnetically ordered solids transform to the paramagnetic state at elevated temperatures due to the randomization randomization of spin s pins. s. Eg., V2O3, NiO change from anti-ferrimagnetic phase to paramagnetic phase at 150K 1 50K and 523K respectively.


Problems : 1) A Metal crystallizes in fcc lattice. It I t the t he edge length of o f unit cell is 0.56 A0. Calculate the nearest neighbour distance dist ance in Al. Al. 2) Na metal crystallizes cr ystallizes in body body centered center ed cubic lattice latt ice the edge length lengt h of unit cell is 0.424 nm at 298 K calculate the density of Na metal . 3) An ionic ionic compound contains c ontains two elements elements X and Y. Y. If I f the atoms at oms of X occupy o ccupy the corners cor ners of unit cell what is the formula of that compound. 4) An X-ray beam of wave length length 70.93 pm was scattered scatt ered by a crystalline crystalline solid. The angle angle ( 2 ) of diffraction for a second order reflection is 14.660. Calculate the t he distance between parallel planes of atoms ato ms from which the scattered scatt ered beam appears to have been reflected.







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11) The density density of crystal with Schottky Schott ky defects defects is less than that of perfect crystal. 12) The dopant used in p-type semi semi conductors belongs to VI A group. 13) Mg(Fe2O4), a ferrite, exhibits exhibits ferrimagnetism. ferrimagnetism. 14) If the t he limiting limiting radius ratio of o f an ionic compound is 0.71, then t hen the cation will occupy the octahedral void formed by anions. 15) The number of tetrahedral tetr ahedral voids voids found in a crystal of one mole of magnesium magnesium metal is is equal to N (Avogadro (Avogadro number). number) .


Solid State Chemistry IPE

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