Crystalline vs Amorphous Solids | Class 12 Chemistry

A unit cell is the smallest repeating unit in a crystal that generates the entire lattice when repeated. Simple cubic has 1 particle (8 corners × 1/8), BCC has 2 particles (8 corners × 1/8 + 1 center), and FCC has 4 particles (8 corners × 1/8 + 6 faces × 1/2). Bravais lattices are the 14 distinct arrangements of lattice points in 3D space, grouped into 7 crystal systems: Triclinic (all unequal edges and angles), Monoclinic (unequal edges, two 90° angles), Orthorhombic (unequal edges, all 90° angles), Tetragonal (two equal edges, all 90° angles), Cubic (all equal edges, all 90° angles), Trigonal (all equal edges, equal angles <120°), and Hexagonal (two equal edges, α=β=90°, γ=120°). Density (ρ) equals mass divided by volume. For a unit cell, mass = n × m (number of particles × mass per particle), and volume = a³ for cubic cells. Mass per particle m = M/N_A (molar mass/Avogadro's number). Therefore, ρ = (n × M) / (N_A × a³). This relationship allows calculation of density from crystal structure parameters or vice versa.

There are 7 crystal systems (cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, rhombohedral) with 14 Bravais lattices. Unit cell calculations involve determining edge length from atomic radius: simple cubic (a=2r), BCC (a=4r/√3), FCC (a=4r/√2). Coordination numbers vary: HCP and FCC have 12, simple cubic has 6. These calculations form the foundation of crystal structure analysis.

The seven crystal systems contain 14 Bravais lattices, defined by lattice points at unit cell corners with additional off-corner points satisfying identical surrounding conditions. The cubic system contains three Bravais lattices: Simple Cubic (SC) with points at 8 corners, Body-Centered Cubic (BCC) with points at 8 corners plus one at body center, and Face-Centered Cubic (FCC) with points at 8 corners plus one at each of 6 face centers. Key parameters for studying crystal structures include: lattice point density (n/V), mass density ((n × M) / (V × N_A)), packing fraction (volume occupied by atoms / total unit cell volume), and coordination number (nearest neighbor atoms equidistant from a lattice point). The number of lattice points per unit cell is calculated by considering how many unit cells share each lattice point: SC = 1, BCC = 2, FCC = 4. Unit cell volume for orthogonal systems is V = a × b × c, and for cubic systems V = a³. A real crystal structure consists of a Bravais lattice plus a basis (group of atoms attached to each lattice point).

Crystal systems are classified by edge lengths and interaxial angles: Cubic (a=b=c, α=β=γ=90°), Tetragonal (a=b≠c, α=β=γ=90°), Orthorhombic (a≠b≠c, α=β=γ=90°), Monoclinic (a≠b≠c, α=γ=90°≠β), Triclinic (a≠b≠c, α≠β≠γ≠90°), Hexagonal (a=b≠c, α=β=90°, γ=120°), and Rhombohedral (a=b=c, α=β=γ≠90°). Cubic is most symmetric, triclinic least. Among 14 Bravais lattices, body-centered unit cells exist in only 3 systems (Cubic, Tetragonal, Orthorhombic). In FCC, octahedral voids are at body center and edge centers, with each edge center contributing 1/4 to a single unit cell. Molecular mass can be calculated from density using d = (Z × M) / (N_A × a³).

A crystal lattice is a regular three-dimensional arrangement of atoms, ions, or molecules in space, with 14 possible Bravais lattices named after August Bravais. A unit cell is the smallest repeating unit that represents the overall symmetry of a crystal and can be characterized by edge lengths a, b, c and interaxial angles alpha, beta, gamma. The entire crystal lattice can be built up by repeating the unit cell in three dimensions.

In close-packed structures, there are two types of voids: (1) Tetrahedral voids - formed by 4 atoms, coordination number = 4, shape is tetrahedral, (2) Octahedral voids - formed by 6 atoms, coordination number = 6, shape is octahedral. In FCC unit cell, there are 8 tetrahedral voids and 4 octahedral voids.

Tetrahedral voids are formed by 4 spheres in contact, surrounded by 4 spheres with coordination number 4. Octahedral voids are formed by 6 spheres in contact, surrounded by 6 spheres with coordination number 6. In English, they are called 'Tetrahedral Voids' and 'Octahedral Voids' respectively.

- Tetrahedral voids: located at the body diagonals of the unit cell, coordination number = 4 - Octahedral voids: located at the body center and edge centers of the unit cell, coordination number = 6

Tetrahedral voids form when one atom sits above three atoms arranged in a triangular pattern, with coordination number 4. Octahedral voids form between two triangular layers of atoms, with coordination number 6. In any close-packed structure, the ratio of tetrahedral voids to atoms is 2:1, and the ratio of octahedral voids to atoms is 1:1.

Solids are rigid with constant particle positions that oscillate about mean positions. Amorphous solids have sharp melting points and are isotropic, while crystalline solids soften over temperature ranges and are anisotropic. Coordination number is the number of nearest neighbor atoms touching a central atom. In 1D close packing, coordination number is 2. In 2D, square packing has coordination number 4, and hexagonal packing has coordination number 6. In 3D, both cubic close packing (ABCABC...) and hexagonal close packing (ABAB...) have coordination number 12. Voids are empty spaces: trigonal (3 atoms), tetrahedral (4 atoms), octahedral (6 atoms), and cubic (8 atoms). In FCC, there are 8 tetrahedral voids and 4 octahedral voids.

(1) Schottky defect: Equal numbers of cations and anions missing from lattice sites. Stoichiometry unchanged, density decreases. Occurs when cation and anion sizes are similar and coordination number is high. (2) Frenkel defect: Ion leaves lattice site and occupies interstitial site. Stoichiometry unchanged, density unchanged. Occurs when significant size difference between cation and anion. (3) AgBr is the only compound showing both defects.

Crystal defects are deviations from perfect periodic arrangement. Stoichiometric defects maintain chemical formula: Schottky defect (equal cation/anion vacancies, density decreases, examples: NaCl, KCl, AgCl, AgBr, AgI, ZnS), Frenkel defect (small ion moves to interstitial, density unchanged, examples: AgCl, AgBr). AgBr uniquely shows both defects. Non-stoichiometric defects change formula: metal excess (N-type semiconductors, extra electrons), metal deficiency (P-type semiconductors, electron holes). F-center is electron trapped in anion vacancy, causing coloration.

Crystal defects are imperfections in ideal crystal structures. Stoichiometric defects maintain cation:anion ratio: vacancy defects (missing ions, reduced density), interstitial defects (extra ions, increased density), and Frenkel defects (ion moves to interstitial site). Non-stoichiometric defects change the ratio: metal excess defects (extra metal ions or F-centers causing coloration), metal deficiency defects (missing metal ions with higher oxidation states). Examples: NaCl heated in Na vapor shows yellow color due to F-centers; FeO becomes Fe0.95O with some Fe2+ replaced by Fe3+ to maintain neutrality.

Crystal defects are irregularities or imperfections in the regular arrangement of particles in a crystal lattice. A Schottky defect is a type of crystal defect where equal numbers of cations and anions are missing from the crystal lattice. This creates vacancies in the lattice. Schottky defects are common in ionic crystals where cations and anions have similar sizes. The density of the crystal decreases because mass is lost while volume remains the same. Examples include NaCl, KCl, and AgBr. A Frenkel defect is a type of crystal defect where an ion leaves its normal lattice position and occupies an interstitial site (a space between lattice particles). The ion does not leave the crystal but moves to a different position within it. Frenkel defects are common in ionic compounds where there is a large size difference between cations and anions. Examples include AgCl, AgBr, and ZnO. The overall density of the crystal remains unchanged because no particles leave the crystal. Silver bromide (AgBr) is unique because it can exhibit both Schottky and Frenkel defects.

Crystal defects are imperfections in crystal structures. Frenkel defect occurs when a smaller ion (typically cation) leaves its lattice position and occupies an interstitial site, creating a vacancy. This defect is named after Yakov Frenkel (1926) and occurs due to low coordination number and large size difference between cation and anion. Properties include unchanged density, electrical neutrality, and decreased stability. Examples include AgCl, AgBr, AgI, and ZnS. Non-stoichiometric defects (berthollide defects) have unequal cation-anion ratios. Metal excess defect occurs when metal ions exceed stoichiometric ratio (e.g., ZnO turning yellow when heated). F-center (Farbe center) is where electrons are trapped after anions leave positions, causing coloration (NaCl yellow, LiCl pink, KCl violet). F-centers also cause decreased density, paramagnetism, and increased conductivity. Metal deficiency defect occurs when metal ions are deficient (e.g., FeO with 0.84-0.94 Fe content). Transition metals commonly exhibit these defects due to variable oxidation states.

Solids are classified by electrical conductivity: Conductors (10²-10⁷ S/m), Insulators (10⁻¹⁰-10⁻²⁰ S/m), Semiconductors (10⁻⁶-10⁻⁴ S/m). Band theory explains conductivity: Valence band contains bound electrons, conduction band contains free electrons, band gap is the energy difference. Metals have zero band gap. Semiconductors have intermediate band gaps. Intrinsic semiconductors are pure; extrinsic are doped. N-type (doped with phosphorus) has extra electrons; P-type (doped with boron) has holes. Magnetic properties include: Diamagnetism (weak repulsion, paired electrons), Paramagnetism (weak attraction, unpaired electrons), Ferromagnetism (strong attraction, permanent magnetization).

Solids are classified by conductivity: conductors (Ag, Cu, graphite) allow charge flow; insulators (rubber, diamond) block it; semiconductors (Si, Ge) have intermediate conductivity. Band theory explains this: conductors have overlapping or partially filled bands; insulators have large band gaps; semiconductors have small gaps allowing thermal excitation. Magnetic properties arise from electron orbital and spin magnetic moments (Bohr magneton = 9.27×10⁻²⁴ J/T). Materials exhibit paramagnetism (unpaired electrons attract to fields), diamagnetism (all paired electrons repel), ferromagnetism (aligned domains), antiferromagnetism (opposite domains cancel), or ferrimagnetism (unequal parallel/anti-parallel alignment).

Band theory explains the electrical properties of solids by describing how electrons occupy energy bands (valence band and conduction band) separated by an energy gap; conductors have overlapping or very small energy gaps allowing easy electron flow, semiconductors have moderate gaps that can be overcome with energy, and insulators have large energy gaps preventing electron movement.

Solids are classified by electrical conductivity: conductors (free electrons), insulators (no free electrons), and semiconductors (intermediate). Band theory explains this: in atoms, electrons occupy discrete energy levels; in solids, these split into valence and conduction bands. Conductors have overlapping bands allowing free electron movement. Insulators have large band gaps preventing electron flow. Semiconductors have small band gaps allowing limited conductivity.

Solids are classified into three types based on electrical conductivity: (1) Conductors - materials where electric current flows easily, with conductivity ranging from 10^4 to 10^14 ohm^-1 m^-1, such as aluminum, copper, and iron; (2) Insulators - materials where electric current flow is negligible, with conductivity ranging from 10^-20 to 10^-10 ohm^-1 m^-1, such as wood and plastic; (3) Semiconductors - materials that behave as insulators at absolute zero but conduct electricity when temperature increases or impurities are added, with conductivity ranging from 10^-6 to 10^4 ohm^-1 m^-1, such as silicon and germanium. Band theory explains these properties through two energy bands: Valence Band (where electrons are present) and Conduction Band (which is empty). The energy difference between these bands is called the band gap. In conductors, the valence band and conduction band overlap or are very close, resulting in a band gap of approximately zero, allowing electrons to easily move between bands. In insulators, the band gap is very large (approximately 6 electron volts), preventing electron movement. In semiconductors, the band gap is approximately 1 electron volt, allowing electron movement only when temperature increases.