lattice.notes
Reference — Terminology

Definitions: graphite, graphene & stacking order

Graphene terminology is easy to use loosely and easy to get wrong. The definitions below follow ISO/TS 80004-13, Nanotechnologies — Vocabulary — Part 13: Graphene and related/other two-dimensional (2D) materials (first edition 2017, second edition 2024), the international standard that sets common vocabulary for graphene and 2D materials. Definitions are quoted or closely adapted from the standard; explanatory notes are added for context.

Graphite ISO/TS 80004-13, 3.1.2.2

"Allotropic form of the element carbon, consisting of graphene layers stacked parallel to each other in a three-dimensional, crystalline, long-range order."

Graphite is the bulk, 3D stacked form of the same honeycomb carbon sheet that, isolated as a single layer, is called graphene. The standard's note distinguishes two primary allotropic forms based on how the layers stack: hexagonal (Bernal, AB) and rhombohedral (ABC).

ISO/TS 80004-13 also draws the line between "2D material" and "bulk": graphene stacks remain a two-dimensional material for electrical-measurement purposes up to roughly 10 layers thick; beyond that, electrical behavior converges with bulk graphite.

Related term — nanographite: a flake made of 11 or more graphene layers, with total thickness up to 100 nm — the standard's boundary case between few-layer graphene and bulk graphite.

Graphene ISO/TS 80004-13, 3.1.2.1

"Single layer of carbon atoms with each atom bound to three neighbours in a honeycomb structure."

Also termed graphene layer, single-layer graphene, or monolayer graphene, and abbreviated 1LG. It is the fundamental building block of the graphene/graphite family and of many other carbon nano-objects (nanotubes, fullerenes). Real graphene sheets have edges and can contain defects and grain boundaries where the ideal bonding is disrupted — the standard is explicit that "graphene" does not imply a defect-free crystal.

1LG — monolayer

A single honeycomb sheet, one atom thick.

2LG — bilayer

Two well-defined stacked graphene layers; stacking registry (Bernal or twisted) can be specified.

3LG — trilayer

Three stacked layers; can be Bernal (ABA) or rhombohedral (ABC).

FLG — few-layer

Three to ten well-defined stacked graphene layers.

The 2024 second edition adds graphene-related 2D material (GR2M): a carbon-based 2D material of 1–10 layers covering graphene, graphene oxide, reduced graphene oxide, and their functionalized variants — and deprecates the loose term "graphene-based material" in favor of precise terms like GR2M-based, GR2M-enhanced, and GR2M-modified.

Turbostratic (twisted) graphene ISO/TS 80004-13, 3.1.2.7 (2017) / 3.1.2.8 (2024)

"Twisted bilayer graphene / turbostratic bilayer graphene (tBLG, t2LG): two-dimensional material consisting of two well-defined graphene layers that are turbostratically stacked, with a relative stacking angle (θ), also known as commensurate rotation, rather than Bernal (hexagonal) or rhombohedral stacking."

In turbostratic stacking, one layer is rotated relative to the other by some twist angle θ instead of sitting in registry (atom-over-atom) with it. Because the layers are no longer aligned to a shared lattice, interlayer electronic coupling is weak — turbostratic/twisted stacks tend to behave electronically more like isolated monolayers than like Bernal-stacked bulk graphite. See sp² bonding for why it's van der Waals forces, not covalent bonds, holding these layers together in the first place.

A related term, twisted few-layer graphene (t(n+m)LG), describes a stack of n Bernal-stacked layers sitting at a relative twist angle on top of a separate block of m Bernal-stacked layers — i.e., internally ordered blocks that are twisted relative to each other.

Twisted bilayer graphene at the "magic angle" (~1.1°) is the structure behind twistronics and magic-angle superconductivity research — a direct application of this stacking definition.

A-B Bernal structure & rhombohedral (ABC) stacking ISO/TS 80004-13, 3.4.1.10–3.4.1.13

Bernal (AB) stacking: the registry in which the two triangular sublattices (A and B) of each graphene layer alternate so that the B sites of one layer sit directly above the A sites of the layer below — shown in the standard as "Bernal stacked bilayer graphene," contrasted against turbostratic stacking.

A graphene honeycomb lattice has two atomic sublattices, conventionally labeled A and B. In Bernal (AB) stacking, alternating layers are offset so that half the atoms in one layer sit directly over atoms in the layer below, and half sit over the centers of hexagons — this is the natural stacking order of ordinary graphite. It gives strong interlayer coupling and is the reference case the standard contrasts turbostratic/twisted stacking against.

ABA (Bernal) trilayer

Third layer repeats the registry of the first: A-B-A. The common, lower-energy stacking of natural graphite.

ABC (rhombohedral) trilayer

Each layer shifts further in the same direction: A-B-C. A metastable, less common allotropic stacking form.

Graphite itself (3.1.2.2) is defined as having two primary allotropic forms distinguished exactly by this choice of registry: hexagonal graphite (built from Bernal/AB stacking) and rhombohedral graphite (built from ABC stacking).

Fractal graphene not an ISO term

ISO/TS 80004-13 standardizes vocabulary for pristine layer count, stacking registry, chemistry, and production/characterization methods — it does not define "fractal graphene." The term comes from materials-science and nanotechnology literature rather than the ISO vocabulary, and is used to describe graphene-based structures that exhibit self-similar, scale-invariant geometry across multiple length scales, rather than a single uniform lattice or a simple stacked sheet.

How "fractal graphene" is used in practice

Sierpiński-type lattices: hexagons recursively removed from a graphene sheet in a self-similar pattern, producing scale-invariant electronic band structure that a uniform honeycomb lattice cannot reach.

Defect-engineered sheets: controlled vacancies or etch patterns introduce a non-integer (fractal) dimension into an otherwise chemically unchanged graphene lattice.

Hierarchical / diffusion-limited aggregates: graphene flakes or nanoplatelets assembled — often via diffusion-limited aggregation (DLA) — into branching, self-similar structures across micro- to macro-scale, rather than a dense, compact restack.

The common thread is surface accessibility: because a fractal aggregate's mass is distributed across branches rather than buried inside a compact block, far more of it is exposed surface for the same total mass — improving ion transport, effective capacitance, and catalytic/sensing activity per gram relative to bulk or restacked graphene. See the simulation results on this site for a worked example.