Solid State: Class 12 Chemistry

Introduction to Solid State

• Solid State is the first chapter of Physical Chemistry for Class 12th, characterized as straightforward, with formula-based questions.
• Typically, one question from this chapter appears in the JEE Main exam each year.
• It is recommended for students who have already studied the chapter and are looking for a quick revision of concepts and important formulas.

Classification of Solids

• Solids can be classified into two main types: crystalline and amorphous.

Crystalline Solids

• Feature a fixed arrangement of particles that repeats over long distances.
• Have sharp and defined melting points.
• Exhibit anisotropic nature, meaning physical properties vary with direction.
• Produce sharp and smooth edges when cut with a knife.
• Possess a definite heat of fusion.

Amorphous Solids

• Lack a fixed particle arrangement over long distances.
• Exhibit diffused melting points, softening before melting over a range.
• Are isotropic in nature, meaning physical properties are the same in all directions.
• Produce irregular edges when cut with a knife.
• Do not have a definite heat of fusion.
• Also known as pseudo solids or super-cooled liquids due to their tendency to flow.
• Examples include glass, rubber and plastic.

Further Classification of Crystalline Solids

• Crystalline solids can be further classified into molecular, ionic, metallic, and covalent solids.

Molecular Solids

• Constituent particles are molecules.
• Can be further classified as non-polar, polar, and hydrogen-bonded.

Non-polar Molecular Solids

• Held together by London dispersion forces.
• Soft, insulators, with low melting points.
• Examples include hydrogen, iodine, carbon dioxide.

Polar Molecular Solids

• Held together by dipole-dipole interactions.
• Soft insulators with low melting points.
• Examples include sulfur dioxide and ammonia.

Hydrogen-bonded Molecular Solids

• Held together by hydrogen bonding.
• Somewhat harder than other molecular solids and are also insulators with low melting points.
• Example include ice.

Ionic Solids

• Constituent particles are ions held together by electrostatic forces.
• Hard and brittle, generally insulators in the solid state but conductive in molten or aqueous states due to ion formation.
• Have high melting points.
• Example NaCl.

Metallic Solids

• Consist of metal ions (metal cores) and a sea of electrons.
• Held together by metallic bonding.
• Hard, malleable, and ductile.
• Conductive in both solid and molten states.
• Have high melting points.

Covalent or Network Solids

• Constituent particles are atoms linked by covalent bonds.
• Generally hard but can be soft like graphite (exception).
• Typically insulators but can be conductors like graphite (exception).
• Have very high melting points.
• Examples include diamond, aluminum nitride, quartz, and graphite.

Crystal Lattices and Unit Cells

• A crystal lattice is a 3D arrangement of constituent particles (atoms, molecules, or ions).
• The smallest repeating unit of a crystal lattice is called a unit cell.

Unit Cell Parameters

• Unit cells are defined by axial distances (a, b, c) and interaxial angles (α, β, γ).

Types of Unit Cells

• Unit cells can be primitive or non-primitive (centered).

Primitive Unit Cells

• Lattice points are located only at the corners.

Centered Unit Cells

• Lattice points are at the corners and other positions.
• Include body-centered cubic (BCC), face-centered cubic (FCC), and end-centered unit cells.

Body-Centered Cubic (BCC)

• Lattice points at corners and one in the center of the body.

Face-Centered Cubic (FCC)

• Lattice points at corners and at the center of each face.

End-Centered Unit Cell

• Constituent particles are present at corners and any two opposite face centers.

Crystal Systems and Bravais Lattices

• There are seven possible crystal systems based on variations in axial distances and interaxial angles.
• Variations in unit cell types within crystal systems lead to 14 Bravais lattices.

Atomic Contribution in a Unit Cell

• Atoms at corners contribute 1/8 to a unit cell.
• Atoms at the body center contribute fully (1).
• Atoms at face centers contribute 1/2.
• Atoms at edge centers contribute 1/4.

Number of Atoms in Different Unit Cells

• Primitive Unit Cell: 1 atom (8 corners x 1/8).
• BCC: 2 atoms (8 corners x 1/8 + 1 body center).
• FCC: 4 atoms (8 corners x 1/8 + 6 face centers x 1/2).
• End-Centered: 2 atoms (8 corners x 1/8 + 2 face centers x 1/2).

Packing in One Dimension

• Involves arranging atoms in a row.
• Coordination number (number of nearest neighbors) is 2.

Packing in Two Dimensions

• Achieved by stacking one-dimensional rows.
• Occurs in two forms: square close packing and hexagonal close packing.

Square Close Packing

• Atoms are aligned horizontally and vertically.
• Coordination number is 4, forming a square when connecting the centers of touching atoms.
• Known as AAA type of packing.

Hexagonal Close Packing

• Atoms in the second row are placed in the depressions of the first row.
• Atoms are diagonally aligned.
• Coordination number is 6, forming a hexagon when connecting the centers of touching atoms.
• Known as ABAB type of packing.

Packing in Three Dimensions

• Achieved by stacking two-dimensional layers.
• Can result in simple cubic lattices or more complex structures depending on the type of layer and how they are stacked.

Simple Cubic Lattice

• Formed by stacking square close-packed layers directly on top of each other.
• Unit cell is primitive.
• Coordination number is 6.

Hexagonal Close-Packed (HCP) and Cubic Close-Packed (CCP) Structures

• Formed by stacking hexagonal close-packed layers. Results in voids (empty spaces) like tetrahedral and octahedral voids.

Types of Voids

• Tetrahedral voids are surrounded by 4 atoms.
• Octahedral voids are surrounded by 6 atoms.
• If there are N close-packed atoms, there are N octahedral voids and 2N tetrahedral voids.

Covering Voids

• Covering tetrahedral voids leads to ABAB type packing, forming a hexagonal close-packed (HCP) structure.
• Covering octahedral voids leads to ABCABC type packing, forming a cubic close-packed (CCP) structure or face-centered cubic (FCC) lattice.

Coordination Number in Three-Dimensional Structures

• Both HCP and CCP structures have a coordination number of 12.

Radius Relationship

• Relationship between the radius of atom (R) and radius of tetrahedral void is 0.225R.
• Relationship between the radius of atom (R) and radius of octahedral void is 0.414R.

Tetrahedral Voids in CCP Lattices

• Located on body diagonals at a distance of √3/4 from each corner.
• There are eight tetrahedral voids in total.

Octahedral Voids in CCP Lattices

• Located at the body center and edge centers.
• One octahedral present at body center and three on edge centers.
• Also given by N, for CCP structures with N atoms.

Packing Efficiency

• Defined as the percentage of total space filled by particles.
• Calculated as (Volume of particles / Volume of unit cell) x 100.
• Helps measure how tightly the atoms in a crystal structure fill the available space.

Packing Efficiency in Simple Cubic

• 52.4%.
• Relation between edge length (a) and radius (r): a = 2r.

Packing Efficiency in FCC

• 74%.
• Relation between edge length (a) and radius (r): √2a = 4r.

Packing Efficiency in BCC

• 68%.
• Relation between edge length (a) and radius (r): √3a = 4r.

Packing Efficiency in Hexagonal Close Packing(HCP)

• 74%.
• Relation between height (h) of hexagon and radius (r) of item: h = 4r * √(2/3)

Density of Unit Cell

• Formula: d = (Z x M) / (Na x a^3), where:
  • Z is the number of atoms in the unit cell.
  • M is the molar mass of the atom.
  • Na is Avogadro's number.
  • a is the edge length of the unit cell.
• If 'a' is in centimeters and 'M' in grams, density is in g/cm^3.

Radius Ratio Rule

• Applicable for ionic compounds.
• Ratio of cation radius to anion radius (r+ / r-).

Radius Ratio and Coordination Number

• Coordination Number of 3: Radius ratio between 0.155 and 0.225, with trigonal planar geometry.
• Coordination Number of 4: Radius ratio between 0.225 and 0.414, with tetrahedral geometry.
• Coordination Number of 6: Radius ratio between 0.414 and 0.732, with octahedral geometry.
• Coordination Number of 8: Radius ratio between 0.732 and 1, with cubic geometry.

Structures of Ionic Compounds

• Structures of ionic compounds include:

Rocksalt structure (NaCl)

• Cl- ions in FCC lattice and Na+ ions in octahedral voids, each having a coordination number of 6.

Cesium Chloride Structure (CsCl)

• Cl- in a simple cubic lattice and Cs+ in the cubic void at the center, each ion has a coordiation number of 8.

Zinc Blende Structure (ZnS)

• S2- in CCP and Zn2+ in tetrahedral voids, each ion has a coordination number of four.

Fluorite Structure (CaF2)

• Ca2+ in CCP lattice and F- in tetrahedral voids. Co-ordination number of Ca^2+ is 8 and F- is 4.

Anti-Fluorite Structure (Na2O)

• O2- in CCP lattice and Na+ in tetrahedral voids. Co-ordination number of O^2- is 8 and Na+ is 4.

Effect of Pressure and Temperature on Coordination Number

• Increase in pressure can increase coordination number.
• Increase in temperature generally decreases coordination number.

Defects in Solids

• Irregularities in the arrangement of particles.

Atomic Defects

• Caused by differences in the arrangement of atoms.

Electronic Defects

• Caused by differences in the arrangement of electrons.

Types of Atomic Defects

• Point defects, line defects.

Point Defects

• Involve defects around a single atom.

Line Defects

• Involve entire lines of atoms with irregular arrangements.

Types of Point Defects

• Stoichiometric Defects, Impurity Defects, and Non-Stoichiometric Defects.

Stoichiometric Defects

• Do not change the stoichiometry of the compound.
• Include Vacancy Defects, Interstitial Defects, Schottky Defects and Frenkel Defects.

Schottky Defect

• Occurs in ionic compounds where equal numbers of cations and anions are missing from the lattice.
• Decreases density.
• Found in compounds with similar cation and anion sizes and high coordination numbers.

Frenkel Defect

• Occurs when an ion leaves its position and occupies an interstitial site.
• Does not affect density.
• Found in compounds with large differences in ion sizes.

Impurity Defects

• Occur due to the presence of foreign atoms in the lattice.
• This creates cation vacancies.
• Number of cationic vacancies is equal to number of impurity added.

Non-Stoichiometric Defects

• Alter the stoichiometry of the compound.
• Include Metal Excess Defects and Metal Deficiency Defects.

Metal Excess Defects

• Occur when there is an excess of metal ions.
• Anionic vacancies (F-centers) or extra cations in interstitial sites can cause this.
• F-centers impart color to the lattice.

Metal Deficiency Defects

• Occur when there is a deficiency of metal ions.
• Commonly found in compounds with variable oxidation states, where a lower oxidation state ion is replaced with a higher oxidation state ion to maintain charge balance.