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Ionic Crystal Structures

Note:

This Page is for Students Preparing for IIT Advanced by S.K.Sinha, Kota.

Introduction to Ionic Crystals

Ionic Crystal Structures are three-dimensional arrangements of cations and anions held together by electrostatic (Coulombic) forces. The structure adopted depends on the size ratio of ions, charge balance, and the need to maximize attractive forces while minimizing repulsive interactions.

Radius Ratio Rules

Radius Ratio (ρ) is the ratio of smaller ion radius to larger ion radius (ρ = r_small/r_large). This ratio determines the coordination number and crystal structure that provides optimal packing and stability.

🔍 Radius Ratio Guidelines

Radius Ratio (ρ) Coordination Number Coordination Geometry Typical Structure Examples
0.155 - 0.225 3 Triangular Layer structures B₂O₃ layers
0.225 - 0.414 4 Tetrahedral Zinc Blende, Wurtzite ZnS, CuI, GaN
0.414 - 0.732 6 Octahedral Rock Salt, Rutile NaCl, MgO, TiO₂
0.732 - 1.000 8 Cubic Cesium Chloride CsCl, CsBr, CsI
> 1.000 12 Cuboctahedral Rare in binary ionic Complex structures

🧮 Radius Ratio Calculation Example

NaCl: r(Na⁺) = 1.02 Å, r(Cl⁻) = 1.81 Å

ρ = r(Na⁺)/r(Cl⁻) = 1.02/1.81 = 0.564

Prediction: 0.414 < ρ < 0.732 → Coordination = 6 → Rock Salt Structure ✓

CsCl: r(Cs⁺) = 1.67 Å, r(Cl⁻) = 1.81 Å

ρ = r(Cs⁺)/r(Cl⁻) = 1.67/1.81 = 0.923

Prediction: 0.732 < ρ < 1.000 → Coordination = 8 → Cesium Chloride Structure ✓

Major Ionic Crystal Structures - Interactive 3D Models

1. Fluorite Structure
CaF₂

🔷 Calcium Fluoride Structure

Structure Description:

  • FCC arrangement of Ca²⁺ ions
  • F⁻ ions in tetrahedral holes (all occupied)
  • Coordination: 8:4 (Ca²⁺:F⁻)
  • Formula unit per cell: 4

Examples: CaF₂, SrF₂, BaF₂, PbF₂, UO₂

Coordination Environment

Ca²⁺: Surrounded by 8 F⁻ in cubic geometry

F⁻: Surrounded by 4 Ca²⁺ in tetrahedral geometry

Ratio: 2:1 anion:cation ratio accommodated

Explore Interactive 3D Model →
2. Rock Salt Structure
NaCl

🧂 Table Salt Structure

Structure Description:

  • FCC arrangement of Cl⁻ ions
  • Na⁺ ions in octahedral holes
  • Coordination: 6:6 (Na⁺:Cl⁻)
  • Formula unit per cell: 4

Key Features:

  • Two interpenetrating FCC lattices
  • Edge length: a = 2(r₊ + r₋)
  • Highly symmetric structure

Examples: NaCl, KCl, MgO, CaO, FeO

Coordination Environment

Na⁺: Surrounded by 6 Cl⁻ in octahedral geometry

Cl⁻: Surrounded by 6 Na⁺ in octahedral geometry

Lattice Energy: High due to 6:6 coordination

Explore Interactive 3D Model →
3. Niccolite Structure
NiAs

🔶 Hexagonal Structure

Structure Description:

  • HCP arrangement of As atoms
  • Ni in octahedral holes (all occupied)
  • Coordination: 6:6 (Ni:As)
  • Hexagonal unit cell

Key Features:

  • Metal-metal bonding along c-axis
  • Metallic properties
  • Common for transition metal compounds

Examples: NiAs, FeS, CoS, NiS

Coordination Environment

Ni: Surrounded by 6 As in octahedral geometry

As: Surrounded by 6 Ni in trigonal prismatic geometry

Bonding: Significant metal-metal interactions

Explore Interactive 3D Model →
4. Quartz Structure
SiO₂

💎 Framework Silicate

Structure Description:

  • 3D network of SiO₄ tetrahedra
  • Corner-sharing tetrahedra
  • Coordination: 4:2 (Si:O)
  • Trigonal crystal system

Key Features:

  • Helical chains of tetrahedra
  • Enantiomorphic forms exist
  • Most common SiO₂ polymorph

Examples: α-Quartz, β-Quartz

Coordination Environment

Si: Surrounded by 4 O in tetrahedral geometry

O: Bridging between 2 Si atoms

Structure: Continuous 3D framework

Explore Interactive 3D Model →
5. Wurtzite Structure
ZnS (Hexagonal)

🏠 Hexagonal ZnS Polymorph

Structure Description:

  • HCP arrangement of S²⁻ ions
  • Zn²⁺ in tetrahedral holes (1/2 occupied)
  • Coordination: 4:4 (Zn²⁺:S²⁻)
  • Hexagonal unit cell

Key Features:

  • Hexagonal polymorph of zinc blende
  • Polar structure
  • Piezoelectric properties

Examples: ZnS, ZnO, BeO, SiC, GaN

Coordination Environment

Zn²⁺: Surrounded by 4 S²⁻ in tetrahedral geometry

S²⁻: Surrounded by 4 Zn²⁺ in tetrahedral geometry

Polarity: Non-centrosymmetric structure

Explore Interactive 3D Model →
6. Zincblende Structure
ZnS (Cubic)

💎 Diamond-like Arrangement

Structure Description:

  • FCC arrangement of S²⁻ ions
  • Zn²⁺ in tetrahedral holes (1/2 occupied)
  • Coordination: 4:4 (Zn²⁺:S²⁻)
  • Formula unit per cell: 4

Key Features:

  • Related to diamond structure
  • Tetrahedral coordination
  • Covalent character possible

Examples: ZnS, CuI, GaAs, InP, SiC

Coordination Environment

Zn²⁺: Surrounded by 4 S²⁻ in tetrahedral geometry

S²⁻: Surrounded by 4 Zn²⁺ in tetrahedral geometry

Bonding: Significant covalent character

Explore Interactive 3D Model →
7. Cesium Chloride Structure
CsCl

🎯 Simple Cubic with Center

Structure Description:

  • Simple cubic of Cl⁻ ions
  • Cs⁺ ion at cube center
  • Coordination: 8:8 (Cs⁺:Cl⁻)
  • Formula unit per cell: 1

Key Features:

  • Two interpenetrating simple cubic lattices
  • Body diagonal: 2(r₊ + r₋)
  • Higher coordination than rock salt

Examples: CsCl, CsBr, CsI, TlCl, NH₄Cl

Coordination Environment

Cs⁺: Surrounded by 8 Cl⁻ in cubic geometry

Cl⁻: Surrounded by 8 Cs⁺ in cubic geometry

Stability: Requires large cation for stability

Explore Interactive 3D Model →
8. Spinel Structure
MgAl₂O₄

🔮 Complex Oxide Structure

Structure Description:

  • CCP of O²⁻ ions
  • Mg²⁺ in 1/8 tetrahedral holes
  • Al³⁺ in 1/2 octahedral holes
  • Formula: AB₂O₄ type

Key Features:

  • Cubic close-packed oxide framework
  • Normal vs inverse spinel structures
  • Important magnetic materials

Examples: MgAl₂O₄, Fe₃O₄, CoFe₂O₄

Coordination Environment

Mg²⁺ (A-site): 4 O²⁻ in tetrahedral geometry

Al³⁺ (B-site): 6 O²⁻ in octahedral geometry

Applications: Magnetic materials, gemstones

Explore Interactive 3D Model →
9. Perovskite Structure
CaTiO₃

🔲 Complex Oxide Structure

Structure Description:

  • Ca²⁺ at cube corners
  • Ti⁴⁺ at cube center
  • O²⁻ at face centers
  • Formula: ABX₃ type

Key Features:

  • Corner-sharing octahedra
  • Tolerance factor important
  • Many important properties

Examples: CaTiO₃, BaTiO₃, SrTiO₃, LaAlO₃

Coordination Environment

Ti⁴⁺ (B-site): 6 O²⁻ in octahedral geometry

Ca²⁺ (A-site): 12 O²⁻ in cuboctahedral geometry

Applications: Ferroelectrics, superconductors

Explore Interactive 3D Model →

Structure Comparison Summary

Structure Formula Type Coordination Anion Arrangement Cation Sites Key Feature
Fluorite MX₂ 8:4 FCC (cations) Tetrahedral holes All tetra holes filled
Rock Salt MX 6:6 FCC Octahedral holes High symmetry
Niccolite MX 6:6 HCP Octahedral holes Metal-metal bonding
Quartz MX₂ 4:2 Framework Corner-sharing 3D network
Wurtzite MX 4:4 HCP Tetrahedral holes Polar structure
Zinc Blende MX 4:4 FCC Tetrahedral holes Covalent character
Cesium Chloride MX 8:8 Simple cubic Cube center Large cation
Spinel AB₂X₄ 4:6 CCP Tetra & octa holes Magnetic materials
Perovskite ABX₃ 12:6 Face centers Corner/center Complex oxide

Problem-Solving Strategies

Common Problem Types:

1. Structure Identification
  • Given ionic radii → Calculate radius ratio → Predict structure
  • Given coordination numbers → Identify structure type
  • Given density and composition → Determine structure
2. Lattice Parameter Calculations
  • Rock salt: a = 2(r₊ + r₋)
  • Cesium chloride: Body diagonal = 2(r₊ + r₋)
  • Zinc blende: Face diagonal = 2√2(r₊ + r₋)
3. Density and Formula Unit Calculations
  • Count effective ions per unit cell
  • Calculate unit cell volume
  • Apply density formula: ρ = (Z × M)/(N_A × V)
4. Coordination Number Problems
  • Use radius ratio rules
  • Consider geometric constraints
  • Apply Pauling's electrostatic valence rule
Structure Lattice Relation Formula Units/Cell Coordination
Fluorite a = 2(r₊ + r₋) 4 8:4
Rock Salt a = 2(r₊ + r₋) 4 6:6
Cesium Chloride a√3 = 2(r₊ + r₋) 1 8:8
Zinc Blende a√2 = 2√2(r₊ + r₋) 4 4:4