SOLID STATE notes

 SOLID STATE

A solid is defined as the matter which has definite shape and volume. They are classified as Amorphous and Crystalline.

Crystalline solids: - the constituting particles such as atoms, ions or molecules are arranged in a definite regular geometrical pattern within the solid.(Long range order).

Amorphous solids; - If the constituting particles are not arranged in a definite pattern within the molecule (short range order) are called amorphous solids. Eg. Glass, silica, and plastics….etc

Types of solids: - Ionic, molecular, Network solids, and Metallic solids.

Solids are also classified as true solids and pseudo solids. Pseudo solids possess the following properties

1. they can easily be distorted by applying force and have tendency to flow under their own weight and lose shape
2. They do not have sharp melting point, they first softens and then melts over a range and the examples of such solids are Pitch and Glass. Sometimes they are referred as super cooled liquids.

Space lattice or crystal lattice the constituting particles are arranged in a regular geometry in space…such a arrangement of atoms, ions, or molecules in 3-D space is called crystal lattice.

Unit Cell the smallest 3-D portion of a complete space lattice which is repeated over and over again in different directions to form a space lattice is called a unit cell.(Wall=lattice & brick =unit cell).

Types of unit cells There are called seven types of unit cells or crystal system which are as follows:-Cubic, tetragonal, orthorhombic, monoclinic, triclinic, trigonal and hexagonal.

Similarly there are different types of lattices…these are made-up of different types of unit cells depending upon the positions of particles in that unit cell. The types of unit cells in which particles are present only at the corners are called primitive unit cell or simple unit cells. These simples unit cells are further divided into Three types:- 
Face centered, End centered, and Body centered.

Face Centered:- Particles are available at the corners and at the each face of unit cell.

End Centered:- Particles are available at the corners as well as at the centres of end faces.

Body Centered the particles are available at the corners as well as one particle is present at the centre of the body of the unit cell.

The all above given unit cells form lattices and a crystal system. Every crystal system does not have all the four types of unit cells (simples, face centered, end centered and body centered).

There is also cubic system (part of seven crystal system) which have simple, face centered, and body centred

Unit cells are the part of lattices and they are the building blocks of crystals, in other words we can say that these unit cells form lattices and then crystals are formed.

In class XII we shall study the cubic system and the unit cells associated with it.

Cubic system:- It is the system in which axial lengths of the unit cells are equal i.e. a=b=c and the axial angles are=90⁰. Unit cells are represented by the points which are connected by lines and the points are considered to be spheres (atoms, ions, or molecules). The spheres (atoms) at the corners of the face centered and the body centered cubes do not touch each other, instead they all touch the central sphere. Similarly in face centered cubic the spheres at the corners touch all the spheres present at each face of the cubic. Similarly In the face centered cube, each sphere at the corner touches 3 spheres present at the faces of 3 adjoining faces. This arrangement extends in all the 3-D space and the number of spheres touching a particular sphere is called the co-ordination number of the cube or crystal. In ionic crystals the number of oppositely charged ions surrounding the particular ion is called its co-ordination number.

CALCULATION OF NUMBER OF PARTICLES PER UNIT CELL OF A CUBIC CRYSTAL SYSTEM.

The number of particles per unit cell can be calculated by keeping the following points in mind. Actually each particle at the corner, edge, or at the centre has a definite contribution(shared) in its own cell and with the surrounding cell in 3-D space (we have to imagine it). Hence the contribution is different for an atom present at the corner, edge, on the face and within the body. Remember that, in a cubic system it is presumed that the atoms are always available at the corners so we have to consider these atoms for the sake of calculation of contribution of these atoms. Hence….

Contribution of the particles (atoms) present at the on the corner of the unit cell = (atom is shared by 8 unit cells)

Contribution of the particles (atoms) present at the face of the unit cell = (atom is shared by 2 unit cells)

Contribution of the particles (atoms) present within the body of a unit cell = (atom is shared by no unit cells)

Contribution of the particles (atoms) present on the edge of the unit cell = (atom is shared by 4 unit cells)

The ratio of the number of particles present per unit cell gives the formulas of the compound.

Question:- Calculate the number of atoms present in the unit cell of a monoatomic substance of a) simple cubic lattice b) body centre cubic c) face centered cubic.

CLOSE PACKING IN CRYSTALS:- In solids atoms are considered to be hard spheres and they pack themselves in different manners depending upon the type of crystal. They pack in such a way that they occupy maximum space available to them and to gain maximum density. This type of packing is called CLOSE PACKING. The different spheres of equal sizes pack inn one dimension (horizontal row) as a result an edge of crystal is formed. Similarly in two dimensional packing (row over another row horizontally) the atoms can pack themselves in a manner so that they give rise to two types of packings i.e. square close packing & hexagonal close packing. .

In square close packing each sphere is in contact with 4 other spheres whereas in hexagonal close packing each sphere is in contact with 6 other spheres. Hexagonal packing is more efficient that square close packing because of more space is occupied with this kind of packing.

THREE DIMENSIONAL PACKING:- During two dimensional packing more efficient packing is hexagonal so during hexagonal packing there is a space between the spheres which are touching each other. This small space(unoccupied) is called VOID OR A HOLE. There are different types of voids created during packing depending upon the type of packing hence mainly these voids are of 2 types tetrahedral voids and octahedral voids. A simple triangular void surrounded by four spheres is called (tetrahedral void) and a double triangular void is called (octahedral void) which is surrounded by six spheres. The formation of tetrahedral and octahedral voids is a result of two layers of spheres. When a third layer is placed then a new geometry is formed such as AB.AB.AB.AB called hexagonal close packing (hcp) and when ABC . ABC . ABC layers are introduced is called CUBIC CLOSE PACKING (ccp) [whereas A, B, C are different layers of spheres (atoms)] .

Molybdenum, magnesium and Beryllium crystallise in hcp structures. whereas Nickel, copper, silver, gold and aluminium crystallises as ccp structures.

Further in both ccp and hcp a sphere is always in contact with 6 spheres in its own layer and it touches 3 spheres directly in above layer and 3 spheres directly in layer below. Hence a sphere has total of 12 neighbours therefore the co-ordination number is 12. The common co-ordination number are 4, 6,8,12.

In crystals with directional bonds the co-ordination number is lower than that of crystals with directional bonds.

In addition to the above two types of arrangements a third possible arrangement is bcc which is commonly found in metals such as lithium, potassium, rubidium, and cesium. They occupy 68% of space and the co-ordination number in bcc is 8. The space occupied by hcp and ccp is about 74%.and 52% in simple cubic unit cell.

SIZE OF TETRAHEDRAL AND OCTAHEDRAL VOIDS:- Voids are of different sizes depending upon the size of the sphere present. If R is the radius of the sphere in the closed packed arrangement then the Radius Tetrahedral void = 0.225R whereas Radius of octahedral void = 0.414R. the tetrahedral void is much smaller than the octahedral void, further the maximum size of the spheres occupying the void is 0.414R. if the smaller spheres to occupy the voids have size larger than this, the arrangement will no longer be closed packed. the sizes are important in the formation of the transition metals hydrides, borides, carbides, and nitrides. The non metals such as H, B, C, N occupy these voids and that is why these are called interstitial

Compounds.

NUMBER AND LOCATION OF VOIDS IN A CRYSTAL:- In a closed pack structure (ccp or hcp) if there are N spheres (atoms or ions) in the packing, then

Number of octahedral voids = N therefore

Number of tetrahedral voids = 2N.

In ccp i.e. (fcc) unit cell there are 4 atoms or ions, per unit cell, therefore there are 4 octahedral voids and 8 tetrahedral voids. These are located at the different positions.

Octahedral void:- is present at the body center of the cube and 12 octahedral voids are present on the centers of 12 edges of the cube, but each void on the edge is shared by the 4 unit cells. Hence, its contribution in the cell = ¼ . Therefore effective number of octahedral voids in the ccp structure =1+12 ×1/4 = 1+3 = 4.

Tetrahedral voids:- the reason for 8 tetrahedral voids present in the ccp is due to the fact that there are 8 spheres present at the corners of the unit cell and each sphere touches 3 other spheres on the face centered of the adjoining faces, each giving rise to 1 tetrahedral void . These voids are found to be at the body diagonals, two on each body diagonal at one-fourth of distance from each end.

Examples:- CCP structures Nobel gases(ccp) except He which has hcp structure.

Metals: - Be, Cd, Co, Mg, and Zn have hcp whereas Al, Ag, Au, Cu, Ni, and Pt have ccp structure.

Molecular substances:- Solid H₂ has hcp whereas solid CH₄, HCI, and H₂S have ccp structures.

Ionic substances:- NaCI ----- CI^- ions (fcc) and Na⁺ ions in all octahedral voids

ZnS ------ S^2- ions (fcc) and Zn⁺² ions in alternate tetrahedral voids

CaF₂------ Ca⁺² ions (fcc) and F^- ions in all tetrahedral voids.

IMPORTANT:- No. of octahedral voids = No. of atoms present in closed packed structure

No. of tetrahedral voids = 2 × No of octahedral void = 2 × No of atoms.

Radius Ratio:- Foe the stability of ionic compounds, each cation should be surrounded by maximum No. of anions and vice-versa (for max. electrostatic forces). Since ionic bonds are Non-directional, therefore arrangements of ions are determined by size of the ions.

Radius Ratio = Radius of the cation (r⁺)

Radius of the anion (r^-)

Greater the ratio larger is the size of the cation, therefore greater is co-ordination number.

If the radius ratio comes out to be 0.155 - 0.225 ( planner triangular) ---------3 (co-ordination number) 0.225 - 0.414 ( tetrahedral) ---------4 (co-ordination number 0.414 - 0.732 (Octahedral) --------- 6 (co-ordination number)

0.732 - 1 (Body centered cubic) ---------- 8(co-ordination number)

CALCULATION OF DENSITY OF CUBIC CRYSTALS FROM ITS EDGE:-

THE FOLLOWING FORMULA IS USED TO CALCULATE THE DENSITY:-

M = atomic mass, N₀ = Avogadro’s number, a = volume of the unit cell, Z = no. of atoms present per unit cell.

DEFECTS IN SOLIDS:- There is a perfect periodic arrangement of atoms in crystals at 0⁰K.(∆S = 0), but with rise of temperature deviations take place and results into the departure of atoms take place within the crystals. The presence of impurities also results in disorder arrangement of atoms. This departure of atoms is called imperfection in solids or defect. These defects alter the properties of solids such as electrical conductivity and mechanical strength in terms of structure alone. Sometimes they create new properties in the solids and also effect their melting point, boiling point, and density also.

At 0⁰K, in a covalent crystal(Si) or in a pure ionic crystals (NaCI), the electrons are in lowest energy levels, so the arrangement of electrons depends upon the nature of the chemical bond, hence as the temperature rises above 0⁰K, the electrons occupy higher energy levels and these electrons are mobile which are responsible for electrical conductivity.

When an electron is thermally removed it creates a electron deficient site called a hole, these holes also impart electrical conductivity and these holes also move in electrical field but opposite to the direction of flow of electrons, hence electrons and these holes impart electronic imperfections in a solid.

POINT DEFECTS OR ATOMIC IMPERFECTIONS:- When there are deviations existing apart from the regular arrangement around an atom or group of atoms, such defects are called point defects. These are of following types:- Stoichiometric defects, Non Stoichiometric defects, and Impurity Defects.

Stoichiometric defects:- if imperfections are such that the ratio between the cations and anions remain the same as represented by the molecular formula, is called Stoichiometric defects. These are further of two types:- SCHOTTKY DEFECT & FRENKEL DEFECT.

SCHOTTKY DEFECT:- if in an ionic crystal of the type A⁺ B^-, if equal number cations and anions are missing from the lattice sites so that the electrical neutrality is maintained, it is called schottky defect. It contains one pair of holes. This type of defect is shown by the highly ionic compounds which have high co-ordination number, small difference in size of cations and anions.(NaCI, KCI, KBr, CsCI). 
During this defect the density of the solid decreases due decrease in number of ions, but volume remains the same.

Frenkel Defect:- if an ion (usually cation) is missing from its lattice site and it occupies the interstitial site, then it is called Frenkel Defect, the electrical neutrality and the stoichiometry of the compound is still maintained, since the cations are smaller ,it is common to find the cations occupying the interstitial sites.

The Schottky and Frenkel defects are also called thermodynamic defects or intrinsic defects.

Frenkel defects are shown by the compounds which have high co-ordination number, and large differences in Size of cations and anions. They are found in silver halides due to small size of Ag⁺ ions. AgBr shows both schottky and Frekel defect.

During this defects no ions are missing from the crystal, therefore density of the solid remains the same. Solids which show these defects conduct less electricity and lattice energy of the solid also decreases due to the presence of holes. In Frenkel defect similar charges come closer which increases the dielectric constant of the crystals.

NON STOICHIOMETRIC DEFECTS:- Theses defects are of three types:- Metal excess, Metal deficiency,

And Impurity defect. Non Stoichiometric defects those defects in which the ratio between the cations and anions is different.

Metal Excess:- It occurs in two ways— 
 i) anion vacancies 
ii) by the presence of extra cation in the interstitial site.

Anion vacancy: - A negative ion may be missing from the lattice site, creating a hole which is occupied by the electron, thereby maintaining the electrical balance. These electrons which are trapped in anion vacancy are called F- centers. These are responsible for imparting color to the crystal. This defect is similar schottky defect and is found in crystals having schottky defects.

By the presence of extra cation in the interstitial site.:- Metal excess can also be caused by the extra cation present in interstitial site, electrical neutrality is still maintained by the electron present in another interstitial site. This defect is similar to Frenkel defect, hence found in crystals having Frenkel defect.

Such crystals contain free electrons and act as semi-conductors.

Metal Deficiency:- This defect is normally present in metals which have variable valency such as transition elements, this defect arises due to missing of a cation from the lattice site and the presence of cation of higher charge (+2 instead of +1). For example in Fe0, FeS, NiO two mono valent cations are replaced by one divalent cation to maintain electrical neutrality.

IMPURITY DEFECTS:- This defect arise due to the presence of a foreign atom at the lattice site or at interstitial site. If the foreign atom is present at lattice site we get substitutional solid and if it is present at interstitial site we get interstitial solution.

DOPING:- Introduction of defects by incorporating small amount of foreign impurities in the crystal is called Doping.

For example group 13 elements such as B, Ga, AI and group 15 group 15 elements such as P, AS, or Ge or Si of group 14 can be doped. With 13 & 15 group elements which give rise to n-type or p- type semiconductors. Since the group 15 contain one extra valence electron compared to group 14 elements after forming four covalent bonds. The extra electron gives rise to electrical conduction. A group 13 element which has only three valence electrons forms electro deficient bond (hole). These holes can move across the crystals and also give rise to electrical conductivity, therefore Si-Ge act as semiconductors. Whose conductivity increases with rise in temperature unlike metals. Group 14 elements when doped with 15 group elements are called n-type semiconductors. The symbol n- indicates the negative charge flow in them. Whereas Group 14 elements when doped with 13 group elements are called p-type semiconductors. The symbol p- indicates the hole which moves across the crystal like a positive charge in a direction opposite to the flow of electrons.

IMPURITIES IN IONIC CRYSTALS: - in case of ionic solids, impurities are added in form of ions if the impurities are in different valence state than the host ions then vacancies are created. Suppose 2⁺ charged ions are introduced then for every 2⁺ ion introduced as impurity two 1⁺ ions are removed to maintain the neutrality. So 2⁺ ion occupies one of the lattice site and the other remains vacant, these vacancies increases the electrical conductivity of the ionic solid.(NaCl –SrCl₂) and (CdCl₂ AgCl).

PROPERTIES OF SOLIDS:- The three main properties of solids depend upon their structure and the composition. These properties are –(A) Electrical properties such as i) conductors, ii) insulators, iii) semi-conductors.

(B)Magnetic properties such as i) diamagnetic ii) paramagnetic, iii) ferromagnetic, iv) Anti-ferromagnetic

(C)Dielectric properties such as i) Piezoelectricity, ii) Piezoelectricity, iii) Ferroelctricity, iv) anti-Ferroelctricity.

Electrical properties: electrical properties of solids is due to motion of electrons or +ve holes. Or it is due to motion of ions. Conduction through ions or +ve holes is due to Electronic Imperfections. Conduction through electrons is n-type conduction (n for negative) or p-type conduction (p for positive)

Super conductivity :- It is the phenomena in which metals, alloys and compounds become perfect conductors with zero resistivity at temperature approaching absolute zero. Mercury becomes superconductor at 4K. The temperature at which a substance starts behaving as a superconductor is called Transition Temperature. It lies between 2 to 5K for most of metals. Super conductors are diamagnetic in nature.

Dielectric properties :- A substance through which there is no net flow of electric charge when placed under magnetic field is called dielectric substance. 
This is due to tightly packed electrons by atoms or ions in these substances. The electrical field polarizes these substances, as a result di pols are created with two equal and opposite charges. These electrical di poles interact with applied electrical field hence dipoles align themselves differently in the following manner, so that either there is no net dipole moment. If there is some value of the dipole moment then substances exhibits the following properties

Piezoelectricity :-Electricity is produced due to displacement of ions from their orderly arrangementby the application of mechanical stress. Such substances are used in record players.

Pyroelectricity :- on heating if the orderly arrangement of ions or atoms get displaced and produces electricity, this property is called Pyroelectricity.

Ferroelectricity :- some piezoelectric substances show permanent alignment of dipoles even in the absence of electrical field.

Anti-ferroelectricity :- if the crystal is having alternate electrical dipoles pointing in opposite direction then it shall not show ferroelectric properties. The net dipole moment in such solids is zero


Chemistry for class 12 ...........
biodegradable-polymers
electrochemistry
reaction-kinetics
functional-derivatives-of-carboxylic
enzyme-catalysis regulation
carboxylic-acids-and-their-derivatives
introduction-to-d-block-element
transition-metals
coordination-chemistry
solid-state-2
polymer
amino-acidspeptide-and-proteins
benzene-and-aromatic-compounds
solutions-questions
biomolecules

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