Chemical bond

Everyday term

In plain words

The glue that holds atoms together. In a covalent bond two atoms share electrons, as within a sheet of graphene; in an ionic bond one atom hands electrons to another and the resulting charges attract, as in table salt; in a metal the outer electrons are shared by all the atoms at once. Much weaker hold molecules and the layers of a layered crystal together. A is a crystal with strong bonds within its layers and only weak ones between them – which is why it can be peeled.

Going deeper

In a covalent bond two atoms share electrons; in an ionic bond one hands an electron to the other and the opposite charges attract. A layered crystal has strong bonds of a few electronvolts within each layer and only weak van der Waals binding of about 20 meV per square ångström between layers – which is why it can be peeled.

Sharing, handing over, pooling

Atoms bond because their electrons can lower their energy by rearranging. In a covalent bond the outer orbitals of two atoms overlap and a pair of electrons is shared between them; the bond is strong and points in a definite direction, which is why covalent crystals such as diamond and the sheets of graphene have fixed angles and are stiff. In an ionic bond one atom gives up an electron to another that holds it more tightly, and the two ions attract each other – as in table salt, or the iodides of CrI₃. In a metal, outer electrons leave their atoms altogether and move through the whole crystal, gluing the ions together.

Most real bonds are mixtures. How strongly each atom pulls on electrons – its electronegativity, a scale introduced by Linus Pauling – sets how ionic a bond is: the bond between boron and nitrogen in hBN is partly ionic, which helps give hBN its , while carbon–carbon bonds in graphene are purely covalent.

Strong within, weak between

Layered crystals are defined by their bonding. Within a layer, covalent or partly ionic bonds of several electronvolts each hold the atoms firmly; between layers there are no such bonds, only van der Waals attraction worth about 20 meV for every square ångström of contact – far weaker, atom for atom. That contrast is what lets tape peel a away, and it is the test computer screens apply to thousands of known crystals: those with low enough binding between their layers are flagged as candidates for , and about a thousand of them pass as easy to peel, and some eight hundred more as possibly peelable.

Some materials blur the picture. In the layers are held by surface groups and water; in spare electrons sit in the gaps between layers; and in some tellurides the layers are bonded more strongly than van der Waals forces alone would allow.

Bonds in the properties

Much of what a material does can be read from its bonds. Strong, short bonds give stiffness and high vibration frequencies, which is why graphene is among the stiffest materials known and conducts heat so well. The direction of the bonds sets the : black phosphorus, with its puckered bonds, conducts differently along and across its rows. Where bonds are broken – at an edge, a or a surface – appear, which trap charge and react with the air. And the weak bonds between layers set how easily layers slide, twist and can be stacked with others.

For specialists

The attractive interactions that hold atoms in molecules and solids, classified by how electrons are shared: covalent bonds, from overlapping orbitals holding shared electron pairs, strong and directional (sp² carbon, Mo–S in ); ionic bonds, from electron transfer and electrostatic attraction (, oxides); metallic bonding, with electrons delocalised in a partly filled band; and the weak, non-directional van der Waals interaction from correlated charge fluctuations, besides hydrogen bonds. Real bonds are mixtures, characterised by electronegativity differences and charge analyses. Layered crystals combine in-plane bonds of several electronvolts with interlayer binding of only about 20 meV per Å² (some 0.3 J/m²), the criterion high-throughput screens use to identify exfoliable compounds.

Where this comes from

The nature of the chemical bond. Application of results obtained from the quantum mechanics and from a theory of paramagnetic susceptibility to the structure of molecules Pauling · Journal of the American Chemical Society 53, 1367 (1931)
van der Waals bonding in layered compounds from advanced density-functional first-principles calculations Björkman et al. · Physical Review Letters 108, 235502 (2012) cited by 1,163
Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds Mounet et al. · Nature Nanotechnology 13, 246 (2018) cited by 1,875

Electride

A crystal in which some electrons belong to no atom at all. In table salt, each sodium atom hands an electron to a chlorine atom; in an electride the metal atoms give up electrons too, but there is no atom to take them, so they sit on their own in the empty space between the layers, playing the chlorine’s part. Electrons held that loosely leave easily, which makes such crystals unusually good at giving electrons to whatever touches them.

An ionic crystal whose anions are electrons confined in interstitial space – in the layered case a two-dimensional electron gas in the interlayer gallery. The anionic layer gives a low work function, a high carrier density and metallic conduction, and it survives exfoliation. Ca₂N was the first layered example; the same loosely bound electrons drive catalytic ammonia synthesis and electron-injection layers.

Full explanation

Point defect

A flaw in a crystal that involves a single atomic site: an atom missing (a vacancy), an atom of the wrong kind in a site (a substitution, or an antisite when the crystal’s own two kinds of atom swap places), or an extra atom squeezed in between (an interstitial). Every real crystal has some. In a sheet a few atoms thick each one sits at the surface, so a handful of them can change how the material conducts, glows or reacts far more than in a thick crystal.

A defect confined to one or a few lattice sites – vacancy, interstitial, substitutional impurity, antisite or adatom – or a small complex of them. What it does is set by the levels it introduces: shallow levels dope, deep levels trap carriers and act as non-radiative recombination centres, and an isolated deep level in a wide gap can emit single photons. Formation energies and charge states depend on the chemical conditions of growth and on the Fermi level. In 2D materials every defect is a surface defect, less screened and more exposed to the environment, and densities of 10¹² to 10¹³ per cm² are typical of TMDC monolayers.

Full explanation

Dangling bond

A bond left with nothing on the other end, on an atom at a surface that has lost the neighbour it was bonded to inside the crystal. Such bonds grab stray molecules and trap electrons, which is why ordinary surfaces are messy – and why layered crystals, whose sheets keep every bond inside themselves, split into faces that stay clean down to a single layer.

An unsaturated valence orbital at a surface, edge or defect where a covalent bond has been cut. In a bulk semiconductor such as silicon these states lie in the gap, trap charge and pin the Fermi level unless passivated by hydrogen or a grown oxide. The basal plane of a layered crystal has none, which is what allows van der Waals stacking without lattice matching and interfaces with few traps – and also why atomic layer deposition nucleates poorly on it. Edges, grain boundaries and vacancies do carry them, and are where 2D materials are chemically active.

Full explanation

Chalcogenide, halide and pnictide

Family names for compounds, taken from the element in them that carries the negative charge. Chalcogenides contain sulfur, selenium or tellurium; halides contain fluorine, chlorine, bromine or iodine; pnictides contain phosphorus, arsenic, antimony or bismuth. Most layered crystals belong to one of these families, and the catalogue groups many of them that way.

Compounds named for their most electronegative constituent: chalcogenides of group 16 (S, Se, Te; oxides are conventionally counted apart), halides of group 17 (F, Cl, Br, I) and pnictides of group 15 (P, As, Sb, Bi; nitrides usually keep their own name). Down each group the anion grows larger and less electronegative, so bonding turns more covalent, gaps shrink and spin–orbit coupling grows. Chalcogenides give the MX₂ semiconductors and metals, halides mostly ionic, often magnetic insulators built from edge-sharing octahedra, and pnictides many metals, semimetals and the parents of the iron-based superconductors; mixed-anion compounds such as oxychalcogenides and chalcohalides combine two.

Full explanation