S2.4.1 Bonding as a continuum

Bonding and Material Properties

Imagine holding a piece of copper wire in one hand and a crystal of table salt in the other. One is malleable, shiny, and conducts electricity, while the other is brittle and forms a lattice of tiny cubes. Why do these materials behave so differently?

The answer lies in their bonding.

Bonding as a Continuum

You’ve likely learned about the three primary types of chemical bonds: ionic, covalent, and metallic. While these categories are helpful, most bonds don’t fit neatly into one type—they exist on a spectrum.

Example

Aluminium chloride $A l C l_{3}$ exhibits both ionic and covalent characteristics, while silicon shows a mix of covalent and metallic properties.

This idea of bonding as a continuum is elegantly captured in the bonding triangle, first developed by van Arkel and Ketelaar.

The Bonding Triangle

Definition

Bonding triangle

The bonding triangle is a triangular diagram that represents the relative contributions of ionic, covalent, and metallic bonding to a material.

Each corner of the triangle corresponds to a "pure" bonding type:

Ionic Bonding: Found in compounds like NaCl, where electrons are transferred from one atom to another.
Covalent Bonding: Found in molecules like $H_{2}$ or $S i O_{2}$ , where electrons are shared between atoms.
Metallic Bonding: Found in metals like Cu or Fe, where electrons are delocalized and free to move.

The sides of the triangle represent intermediate bonding types:

Ionic–Covalent Continuum: Bonds with partial ionic and covalent character, such as in AgCl.
Covalent–Metallic Continuum: Bonds with partial covalent and metallic character, such as in silicon.
Metallic–Ionic Continuum: Bonds with partial metallic and ionic character, such as in alloys.

The position of a material in the bonding triangle is determined by two key parameters:

Electronegativity Difference (Δχ): This measures the ionic–covalent character of the bond.
Mean Electronegativity ( $\bar{χ}$ ): This measures the metallic–covalent character of the bond.

Tip

To locate a bond on the bonding triangle, calculate both Δχ and $\bar{χ}$ using the electronegativity values of the atoms involved.

Applications of Bonding Models: Explaining Material Properties

Understanding bonding as a continuum allows us to explain the properties of materials, such as melting points, conductivity, and hardness, in terms of their position on the bonding triangle.

Melting and Boiling Points

The strength of bonding interactions determines a material’s melting and boiling points:

Ionic Compounds: High melting and boiling points due to strong electrostatic forces between ions (e.g., NaCl).
Covalent Molecular Substances: Low melting and boiling points because only weak intermolecular forces need to be overcome (e.g., $C O_{2}$ .
Covalent Network Solids: Extremely high melting points due to strong covalent bonds throughout the structure (e.g., diamond, $S i O_{2}$ .
Metallic Substances: Variable melting points depending on the strength of metallic bonding (e.g., mercury melts at -39°C, while tungsten melts at 3422°C).

Example

Consider the melting points of silver halides (AgCl, AgBr, AgI) and potassium halides (KCl, KBr, KI).

Silver halides have greater covalent character, so their melting points increase with stronger London dispersion forces.
In contrast, potassium halides are more ionic, and their melting points decrease as the size of the anion increases, weakening electrostatic attractions.

Electrical Conductivity

Electrical conductivity depends on the presence of mobile charged particles:

Metals: Excellent conductors due to the sea of delocalized electrons.
Ionic Compounds: Conduct electricity when molten or dissolved in water, as ions are free to move.
Covalent Molecular Substances: Poor conductors because they lack free-moving charged particles.
Covalent Network Solids: Generally poor conductors, except for graphite and graphene, which have delocalized electrons.

Common Mistake

Don’t confuse ionic compounds with covalent network solids! While both have high melting points, ionic compounds conduct electricity when molten, whereas covalent network solids generally do not.

Hardness and Brittleness

The arrangement of atoms or ions and the type of bonding determine whether a material is hard, brittle, or malleable:

Metals: Malleable and ductile because metallic bonds are non-directional, allowing layers of atoms to slide past each other.
Ionic Compounds: Brittle because the rigid ionic lattice shatters when like-charged ions are forced together.
Covalent Network Solids: Hard and brittle due to the strong, directional covalent bonds.

Analogy

Think of metals as a flexible net where the "knots" (metal cations) can slide without breaking the overall structure, while ionic compounds are like a stack of magnets that shatter when misaligned.

Mixed Bonding Types

Magnesium Iodide $M g I_{2}$

Magnesium iodide lies on the border between ionic and covalent bonding in the bonding triangle. Its properties reflect this mixed character:

High Lattice Enthalpy: Due to significant ionic bonding.
Low Solubility in Water: Due to covalent character.

Aluminium Chloride $A l C l_{3}$

Aluminium chloride exhibits both ionic and covalent properties:

Low Melting Point: $A l C l_{3}$ forms covalent dimers $A l_{2} C l_{6}$ in the liquid phase.
Solubility in Non-Polar Solvents: Unusual for an ionic compound, explained by its covalent character.

Note

The bonding triangle is a useful guide but isn’t perfect. Some compounds, like $A l C l_{3}$ , defy simple categorization due to their mixed bonding nature.

Reflection and Broader Implications

Theory of Knowledge

The bonding triangle helps us classify and predict the properties of materials, but it also raises deeper questions:

How do we define the "boundaries" between bonding types?
What role do exceptions play in refining our models?

Self review

Using the bonding triangle, can you explain why silicon is a semiconductor or why alloys like steel are stronger than pure metals?

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