Alloy and solid solution

Everyday term

In plain words

A crystal in which two similar kinds of atom share the same sites at random – some molybdenum sites taken by tungsten, say, or some sulfur sites by selenium – so that one crystal structure holds a mixture. By choosing the mix, its properties can be set almost anywhere between those of the two pure compounds, much as mixing two paints gives any shade between them. Chemists call it a solid solution; alloy is the everyday word.

Going deeper

In a solid solution two kinds of atom share one set of sites at random, so the crystal stays one crystal while its composition changes. Its band gap then moves smoothly between those of the two parents – a dial that pure compounds do not have.

Mixing on the atomic scale

In a solid solution the mixing happens site by site: a MoS₂ crystal in which a fraction of the sulfur sites hold selenium instead is still one crystal with one structure, not a patchwork of MoS₂ and MoSe₂ grains. It works when the two kinds of atom are similar enough in size and chemistry to stand in for each other, and when the parent compounds share a structure. Molybdenum and tungsten, or sulfur and selenium, mix across the whole range; CrCl₃ and RuCl₃ form a solid solution because both build the same layers.

The spacing of the crystal changes smoothly with composition, close to a straight line between the two parents – a rule of thumb known as Vegard’s law – and so, roughly, do many of its other properties.

Tuning a gap by composition

The most common reason to make a 2D alloy is to set the . of MoS₂ and MoSe₂ emit light at about 1.87 and 1.55 eV; alloys between them emit anywhere in between, following the composition with only a slight sag below the straight line, called bowing. The same idea sets the colour of the in LEDs and lasers, where alloys such as indium gallium nitride are chosen for a particular wavelength.

Alloys can also tune a , which makes it easier to match a layer to its neighbour or to its , and mixing a magnetic compound with a non-magnetic one dilutes the magnetism in a controlled way.

Alloy or something else?

Mixed does not always mean random. The atoms may order into a regular pattern, separate into regions rich in one or the other, or – when one element sits on one face of a layer and the other on the opposite face – form a layer, a different material with a different symmetry. Composition alone cannot tell these apart; diffraction, spectra and atom-resolved microscopy can.

A random alloy also pays a price for its . The varying surroundings of each atom scatter electrons and broaden optical lines, so alloys rarely match the or the sharp emission of the pure compounds. The composition, measured rather than assumed, belongs in any report on one.

For specialists

A single-phase crystal in which two or more species share a sublattice at random, such as Mo_1−xW_xS₂ or MoS_2(1−x)Se_2x, with lattice constants close to Vegard’s law and band gaps that vary continuously with x, often with a small bowing. Complete miscibility needs similar radii, the same structure type and favourable mixing energetics; otherwise the mixture separates into phases or orders. Random disorder adds alloy scattering and inhomogeneous broadening.

Where this comes from

Synthesis of micro- and nanosheets of CrCl₃–RuCl₃ solid solution by chemical vapour transport Froeschke et al. · Nanoscale 14, 10483 (2022) cited by 7
Controlled nanoplatelet deposition of 2D chromium trihalide solid solutions Froeschke et al. · Chemistry of Materials 35, 4136 (2023) cited by 5

Honeycomb lattice

A flat net of hexagons, like a beehive, with an atom at every corner. Graphene is the famous example, but the same pattern gives boron nitride its band gap, gives graphene its massless electrons, and gives some magnets interactions that cannot all be satisfied at once.

A triangular Bravais lattice with a two-site basis, so every site has three nearest neighbours on the other sublattice. Equivalent sublattices with nearest-neighbour hopping give Dirac cones at K and K′ (graphene); inequivalent ones open a gap with valley-contrasting Berry curvature (hBN, TMDC monolayers seen from above); buckling mixes in spin–orbit coupling (the Xenes); and bond-dependent exchange on the same geometry gives the exactly solvable Kitaev model behind the α-RuCl₃ spin-liquid programme.

Full explanation

Substrate

The base a thin film or flake sits on – often a polished slice of silicon, glass or sapphire. For a crystal one atom thick, the substrate is not just a table: its bumps, stray charges and vibrations reach right into the sheet and change how it conducts and glows. That is why the same material can behave differently on two substrates, and why the flattest, cleanest one – boron nitride – gives the best results.

The material beneath a 2D layer. It acts on the layer through surface roughness, charged impurities, surface optical phonons, dielectric screening, strain and charge transfer, and during growth it sets orientation through epitaxy. Replacing SiO₂ with hexagonal boron nitride, which is atomically flat and nearly free of dangling bonds and charge traps, improved the mobility and charge homogeneity of graphene by close to an order of magnitude.

Full explanation

Janus 2D material

A single layer whose two faces are made of different atoms – selenium on top and sulfur underneath, for example – named after the two-faced Roman god. Because top and bottom differ, the sheet carries a built-in electric field from one face to the other, which a symmetric layer cannot have. That lopsidedness allows effects a symmetric sheet forbids, such as producing a voltage when it is squeezed from above.

A monolayer in which the two outer atomic planes are different elements, as in MoSSe, where one chalcogen sheet is S and the other Se. Mirror symmetry through the metal plane is broken (D₃h → C₃v for the 1H structure), giving an intrinsic out-of-plane dipole, out-of-plane piezoelectricity, Rashba-type spin splitting and an out-of-plane second-harmonic response. Most are made by replacing one face of a parent monolayer; RhSeCl is a rare bulk crystal whose layers are Janus by nature.

Full explanation

Disorder and localisation

Every real crystal has some disorder: missing or misplaced atoms, impurities, stray charges in the substrate, a random mixture of elements in an alloy. Electrons moving through it scatter off these imperfections, which raises the resistance. If the disorder is strong enough, electron waves become trapped in small regions – localised – and the material stops conducting, even if it would be a metal when perfect. In a sheet one atom thick, disorder in its surroundings matters especially.

Deviations from perfect periodicity – point defects, substitutional or alloy disorder, interface roughness, charged impurities and strain variations in the substrate – that scatter carriers and, beyond a threshold, localise their wavefunctions through interference (Anderson localisation). Scaling theory predicts that non-interacting electrons in two dimensions without spin–orbit coupling are localised by any disorder; its precursor, weak localisation, appears as a logarithmic rise of resistance at low temperature that a magnetic field suppresses, while strong spin–orbit coupling gives weak antilocalisation. In graphene on SiO₂, charged impurities break the sheet near charge neutrality into electron–hole puddles, which hBN encapsulation reduces. Strong disorder leads to hopping conduction, broadens optical lines and smears phase transitions; in frustrated magnets and correlated oxides, structural or cation disorder can mimic exotic states.

Full explanation