The thin empty slot between two neighbouring layers of a layered crystal, bridged only by weak attraction. It is why the layers slide and peel apart, and it is room into which atoms, ions and even whole molecules can be slipped.
Going deeper
No covalent bond crosses the gap between layers, only van der Waals attraction of roughly 20 meV per square ångström. That is weak enough for layers to be peeled apart or slid over one another, and it leaves room for ions and molecules to be inserted.
What holds the layers together
Within a layer, atoms are held by or ionic bonds worth several electronvolts. Between layers there is only the van der Waals interaction: fluctuating charge distributions in one layer induce matching ones in the next. Density-functional calculations that treat this attraction properly find that the binding energy per unit area is similar across chemically very different layered crystals, around 20 meV per square ångström, corresponding to roughly 0.3 nm of empty space between the outer atoms.
That near-universal value explains why the same sticky-tape trick works for graphite, MoS2, hBN and many other compounds, and why calculations of energy are a useful screen for which bulk crystals could yield .
A gap with degrees of freedom
The gap is not just empty space. Because nothing pins the layers laterally, they can slide and rotate relative to each other at little cost, which is what makes twisted stacks and possible, and what gives graphite its lubricating behaviour. itself lives in the gap: 2H, 3R and twisted arrangements differ only in how neighbouring layers sit.
Sliding also has consequences for symmetry. Two layers stacked in parallel rather than antiparallel break , and a small slide reverses a tiny out-of-plane polarisation – . Interlayer , the shear and seen at low frequencies, are the vibrations of this soft direction.
Room for guests
Ions and molecules can be inserted into the gap, which is . Lithium in graphite is the reaction behind batteries; in MoS2 it can convert the layers to the 1T form; and organic molecules large enough to stand between layers push them several ångströms apart.
When the spacing grows enough, the layers stop talking to each other electronically – a stack of monolayers separated by molecular spacers behaves like many isolated monolayers, a molecular superlattice. Intercalation also dopes the layers, so conductivity, and magnetism can be tuned by what is placed in the gap. The signature is structural: the interlayer spacing grows, and peaks from planes parallel to the layers move to lower angle.
For specialists
The region between adjacent layers that no covalent bond crosses, typically about 0.3 nm from the outer atoms of one layer to the next. Interlayer binding energies across very different layered compounds fall in a narrow range around 20 meV per Å2, which sets the exfoliation energy. The gap carries the stacking and sliding degrees of freedom and hosts intercalants – from lithium ions to organic molecules large enough to push the layers apart and decouple them electronically.