Solids 24-25 - 2. Ionic Solids

Ionic Solids

Definition: Ionic solids (salts) like NaCl consist of closed-shell anions and cations held together by electrostatic interactions.
Formation: They form from combinations of highly electronegative elements (anions) and highly electropositive elements (cations).
Size Comparison: Anions are generally larger than cations because anions gain electrons and cations lose electrons, affecting their size and electron mobility.
Structure: Thought of as close-packing of anions with cations occupying tetrahedral or octahedral holes.

Cation-Anion Radius Ratio: Ratio of the ionic radius of cation to anion (rc/ra).
Instability: If the cation is too small, anions come too close, causing instability due to anion-anion repulsion (-ve/-ve).
Critical Limits: A radius ratio below 0.155 leads to instability; a ratio between 0.225-0.414 favors tetrahedral holes, while 0.414-0.732 favors octahedral holes.

Chloride Size: Cl- is relatively large, enabling close packing of anions.
Hole Types: Presence of octahedral (1 per lattice point) and tetrahedral (2 per lattice point) holes in the structure.
Radii:
- Chloride: 1.81 Å
- Octahedral holes: 0.75 Å
- Tetrahedral holes: 0.41 Å
- Sodium cation (Na+): 1.02 Å (ra/rc = 0.56)
Placement: Na+ can occupy all octahedral holes, forming a 6:6 structure, with tetrahedral holes remaining empty.

Composition: Materials can have double the number of cations compared to anions (e.g., Li2O).
Anion Radius: Oxide (O2-) has a radius of 1.40 Å and forms a close-packed arrangement.
Cation Radius: Lithium (0.76 Å) occupies the tetrahedral holes, leaving octahedral holes empty.
Structure Type: Alkali-metal oxides (M2O) follow this anti-fluorite structure (M = Li, Na, K, Rb).

Anion Size: Fluoride is a small anion (0.133 nm) and possesses inverse structures due to the small size of the anions relative to cations.
Arrangement: In CaF2, Ca2+ close packs while F- occupies tetrahedral holes (2:1 stoichiometry).
Coordination: Each cation is eight coordinated (shared between cells), each anion is four coordinated.
Common Structures: Other compounds like BaCl2 and f-block dioxides (e.g., CeO2) share this arrangement.

Size Increase: As the periodic table progresses, cation and anion sizes increase.
Cation Radius: Cs+ (0.174 nm) is too large for octahedral/tetrahedral holes, leading to a non-close-packed structure using 54% of space with cations positioned in the center of eight anions.
Structure Type: Referred to as an 8:8 structure due to cation-anion coordination; contributes to CsCl’s unique properties, including solubility in various solvents and lower lattice energy (-661 kJ/mol vs. -788 kJ/mol for NaCl).

Definition: Some ionic solids can exhibit polymorphism (exist in different structural forms) like zinc sulfide (ZnS).
Forms of ZnS:
- Zinc blende: Close-packed S2- ions with Zn2+ occupying half of the tetrahedral holes.
- Wurtzite: More complex hexagonal structure as the zinc and sulfurs are stacked in an ABBABBABB pattern.

Perfect Lattices Assumption: All solid-state lattices are not perfect; they contain defects. The energy to create a defect is compensated by increased entropy.
Types of Defects:
- Schottky Defect: Atom or ion vacancies while maintaining electroneutrality.
- Frenkel Defect: An ion or atom occupies a normally vacant site.

Size Dynamics: Anions are usually larger than cations; structures based on close-packed arrays with cations in the holes.
Stability and Radius Ratio Rules: Importance of maximizing attractive and minimizing repulsive interactions based on tetrahedral (0.225r) and octahedral (0.414r) hole sizes.
Limitations of Models: Not all structures comply; different arrangements needed when cations become larger or similar in size to anions (e.g., CsCl).
Significance of Defects: Understanding defects is crucial for potential material applications and behaviors.