Fajans' Rules: When Ionic Bonds Become Covalent

Aluminium fluoride is a hard, high-melting solid that stays put when you heat it far past the point where most salts have melted. Aluminium chloride, made from the same metal and a halogen from the same group, turns straight into a vapour at around 180 °C, and in that vapour it exists as neat Al₂Cl₆ molecules. On paper both are “metal + non-metal = ionic compound”. In practice one of them behaves like a salt and the other behaves a lot like a molecular substance.

The idea that explains this kind of mismatch is called Fajans’ rules, after the Polish-American chemist Kazimierz Fajans, who set them out in the 1920s. They do not replace the ionic model. Instead, they tell you when and why a compound that “should” be ionic picks up a good deal of covalent character.

The starting picture: perfect spheres

The simple ionic model treats every ion as a hard, perfectly round ball of charge. A cation and an anion attract each other, the lattice builds up, and the electrons stay firmly on whichever ion they belong to. In that picture there is no sharing at all.

Real ions are not billiard balls. An anion’s outer electrons sit in a cloud, and that cloud can be pushed around. When a small, strongly charged cation sits next to it, the cation’s positive charge pulls the anion’s electron cloud towards itself. The cloud bulges into the space between the two nuclei.

Electron density piling up between two nuclei is exactly what a covalent bond looks like. So a strongly distorted (chemists say polarised) anion is partway to sharing its electrons. The more the distortion, the more covalent the bond.

Two words matter here, and they are easy to mix up:

• Polarising power belongs to the cation. It measures how strongly the cation can distort a neighbouring electron cloud.
• Polarisability belongs to the anion. It measures how easily its electron cloud can be distorted.

Covalent character is highest when a strongly polarising cation meets a highly polarisable anion.

An analogy: a magnet and a water balloon

Imagine the anion as a water balloon and the cation as a small, very strong magnet (pretend the balloon’s skin is attracted to it). A big, floppy balloon deforms easily; a small, tightly filled one hardly changes shape. A weak magnet held nearby barely dents either. A powerful, tiny magnet pressed right up against a big floppy balloon drags a lobe of it sideways.

That lobe is the covalent contribution. Fajans’ rules are really just a list of what makes the magnet strong and the balloon floppy.

Rule 1: small cations polarise more

A cation’s charge is concentrated in a smaller volume when its radius is small, so its electric field near its surface is stronger. Lithium, beryllium and aluminium ions are all tiny. Approximate six-coordinate ionic radii show the trend:

Cation	Charge	Radius (pm, approx.)
Na⁺	+1	102
Li⁺	+1	76
Mg²⁺	+2	72
Al³⁺	+3	54

Compare lithium chloride with sodium chloride. Both are ionic solids, but LiCl dissolves noticeably in organic solvents such as ethanol and acetone, which is a sign of covalent character. The small Li⁺ distorts the chloride ion more than Na⁺ does. For more on how ionic sizes are measured and why they change across the table, see ionic radius explained.

Rule 2: highly charged cations polarise more

Doubling or tripling the charge on a cation multiplies its pull on nearby electrons. Many textbooks combine rules 1 and 2 into a single quantity, charge density: roughly the charge divided by the size. High charge density means high polarising power.

This is why the chlorides across period 3 slide from ionic to covalent. NaCl is a classic ionic lattice. MgCl₂ is still ionic but with a layer structure that hints at some distortion. AlCl₃, with the small, triply charged Al³⁺, has so much covalent character that it forms discrete molecules in the vapour. Going on to SiCl₄ and PCl₃ you are in fully molecular territory. The aluminium element page is a good place to compare aluminium’s properties with its neighbours.

Beryllium follows the same logic. Be²⁺ is smaller still than Mg²⁺, and BeCl₂ is widely described as a covalent compound: in the solid it forms chains in which each beryllium is bridged to its neighbours by chlorine atoms.

Rule 3: large anions are more polarisable

On the anion side, size is everything. A large anion holds its outermost electrons far from its nucleus and shielded by many inner shells, so they are loosely held and easily pulled. The halide ions increase steadily in size from F⁻ to I⁻, so iodide is far more polarisable than fluoride.

That brings us back to the opening puzzle. The same Al³⁺ ion meets a small, “stiff” F⁻ in AlF₃ and a larger, softer Cl⁻ in AlCl₃. The fluoride cloud barely moves, so AlF₃ stays largely ionic with a high melting point. The chloride cloud distorts, so AlCl₃ becomes largely covalent. Aluminium iodide goes further still.

Rule 4: highly charged anions are more polarisable

An anion carrying extra negative charge has more electrons than protons, and the surplus is held less tightly. So O²⁻ is more polarisable than F⁻, and N³⁻ more again. Large, multiply charged anions such as S²⁻ are especially easy to distort, which is one reason many metal sulfides behave more covalently than the corresponding oxides.

Rule 5: cations without a noble-gas core polarise more

This rule surprises many students. Compare two cations of almost the same size and the same charge:

• Ca²⁺ has the electron configuration of argon: a complete noble-gas core.
• Hg²⁺ has a filled d¹⁰ shell outside its core.

The d electrons are spread out and do a poor job of shielding the nucleus. So the nucleus of Hg²⁺ “shows through” more strongly than you would expect from its charge and radius, and it polarises neighbouring anions more. The result: calcium chloride is a typical ionic salt with a high melting point (772 °C), while mercury(II) chloride melts below 300 °C and dissolves in ethanol, behaving much more like a molecular compound.

The same effect appears with Cu⁺, Ag⁺, Zn²⁺ and Cd²⁺, all of which have d¹⁰ configurations.

Evidence you can see: the silver halides

The silver halides make Fajans’ rules visible. Ag⁺ is a d¹⁰ cation, so it is quite polarising, and the anion gets bigger down the group:

Compound	Solubility in water
AgF	very soluble
AgCl	very slightly soluble (white solid)
AgBr	less soluble still (cream solid)
AgI	least soluble (yellow solid)

As the anion grows more polarisable, covalent character rises. Covalent character lowers solubility in water, because water is very good at pulling apart ions but much less effective at breaking genuinely shared electron density. The deepening colour is linked to the same distortion: electrons in a strongly polarised bond can be excited by lower-energy visible light. (You should not treat colour as a general test for covalency, though; many coloured compounds are coloured for other reasons, such as d–d transitions.)

The solubility rules you learn for precipitation reactions contain several quiet examples of the same effect.

Evidence from heat: carbonates of group 2

A carbonate ion is large and fairly polarisable. When a group 2 carbonate is heated, it decomposes into the metal oxide and carbon dioxide. A small cation such as Mg²⁺ distorts the carbonate cloud strongly, weakening one of the C–O bonds and making it easier for CO₂ to break away. Larger cations such as Ba²⁺ distort it much less.

So thermal stability rises down the group: MgCO₃ decomposes at a much lower temperature than BaCO₃. The same reasoning explains why group 2 nitrates decompose more easily near the top of the group.

How Fajans’ rules fit the wider picture

It helps to stop thinking of “ionic” and “covalent” as two boxes. Every real bond between different atoms sits somewhere on a spectrum, and the article on the bonding continuum walks through that idea in detail. Electronegativity difference gives you one way to place a bond on the spectrum. Fajans’ rules give a second, complementary view, starting from the ionic end and asking how much the ions deform each other.

The two approaches usually agree. Where they differ, Fajans’ rules often do better for real solids, because they account for the size and charge of the actual ions rather than for neutral atoms. For a numerical estimate using electronegativity, see percentage ionic character.

One more place covalent character shows up is in lattice energy. A lattice energy calculated from a purely ionic model (the Born–Haber cycle gives the experimental value) often matches experiment well for the alkali halides. For the silver halides the experimental value is noticeably larger than the ionic model predicts. That extra stability is the covalent contribution the simple model left out.

Common mistakes

Swapping the roles. The cation does the polarising; the anion is polarised. Writing “the chloride ion has high polarising power” gets the direction backwards.

Thinking a bigger cation polarises more. A bigger cation has its charge spread out, so its field is weaker. Small and highly charged is what you want for strong polarisation.

Forgetting the d¹⁰ rule. If an exam compares Ca²⁺ with Hg²⁺, or Na⁺ with Cu⁺, the answer depends on electron configuration, not just size and charge.

Treating “some covalent character” as “covalent”. AgCl still has a lot of ionic character. Fajans’ rules describe a shift along a spectrum, not a switch from one type to the other.

Using Fajans’ rules as exact predictions. They are qualitative. They tell you which of two compounds is more covalent, not a precise percentage, and crystal structure and other factors can override them.

Mixing up the cause of low melting points. AlCl₃ vaporises easily because it forms discrete molecules held together only by weak intermolecular forces, not because its Al–Cl bonds are weak.

Key takeaways

• Fajans’ rules explain why many “ionic” compounds show covalent character: the cation distorts the anion’s electron cloud towards itself.
• Covalent character increases with a small, highly charged cation, a large, highly charged anion, and a cation with a non-noble-gas (often d¹⁰) configuration.
• AlF₃ versus AlCl₃, CaCl₂ versus HgCl₂, and the trend from AgF to AgI are the classic examples.
• Signs of covalent character include lower melting points, solubility in organic solvents, lower solubility in water and, in some cases, deeper colour.
• Fajans’ rules are qualitative and work alongside electronegativity: both place bonds on a single ionic-to-covalent continuum.