Cleavage notation is the systematic, crystallographic shorthand used to identify the precise orientation of planes along which a mineral will preferentially break. Expressed using Miller indices — a set of three integers enclosed in curly braces, such as {001}, {110}, or {111} — cleavage notation encodes the geometry of a crystal's internal lattice into a compact, universally understood symbol. For the practising gemologist, this notation is far more than academic: it predicts how a rough stone will behave under the lapidary's wheel, where a faceted gem may cleave if struck, and how a cutter should orient the rough to minimise the risk of catastrophic splitting.

Miller Indices and the Unit Cell

To understand cleavage notation, one must first grasp the concept of the unit cell — the smallest repeating structural unit of a crystal lattice, defined by three axes (conventionally labelled a, b, and c) and the angles between them. Miller indices describe a crystallographic plane by recording the reciprocals of the fractional intercepts that plane makes with each of the three axes, reduced to the smallest integers. The curly-brace notation {hkl} denotes not a single plane but the entire family of equivalent planes related by the crystal's symmetry — a distinction that matters because cleavage, being governed by symmetry, typically occurs on all planes of an equivalent set simultaneously.

For example, the notation {001} describes planes perpendicular to the c-axis (the plane intercepts the c-axis at unit distance and runs parallel to both a and b). The notation {110} describes planes that intercept both a and b axes at unit distance while running parallel to c. The notation {111} describes planes that intercept all three axes equally — the octahedral planes of a cubic crystal. These conventions are codified in standard mineralogical references, most notably Cornelius Hurlbut and Cornelius Klein's Manual of Mineralogy, which remains a foundational text in gemmological education.

Common Cleavage Notations in Gem Minerals

A handful of cleavage notations recur throughout gemmology, each associated with characteristic gem behaviour:

• {001} — Basal cleavage. A single plane of cleavage perpendicular to the principal axis. Topaz exhibits perfect basal cleavage on {001}, which is why a blow to the base of a topaz gem can shear it cleanly. Mica's famously easy splitting is also basal cleavage on {001}.
• {110} — Prismatic cleavage. Planes parallel to the c-axis and intersecting the a and b axes. Spodumene (the parent mineral of kunzite and hiddenite) has perfect cleavage on {110} in two directions, making it notoriously difficult to cut and wear. Feldspar minerals, including moonstone and labradorite, also display prominent prismatic cleavage.
• {111} — Octahedral cleavage. The signature of diamond. Because diamond crystallises in the cubic system, the {111} family comprises four equivalent planes, each parallel to a face of the octahedron. Diamond's perfect octahedral cleavage — the basis of the traditional art of diamond cleaving — allows a skilled cutter to split a rough crystal along these planes with a single, precisely directed blow. The same cleavage, however, makes a mounted diamond vulnerable to a sharp impact at the right angle.
• {010} — Pinacoidal cleavage. Seen in orthoclase and other monoclinic feldspars, this plane is perpendicular to the b-axis and contributes to the two-directional cleavage characteristic of the feldspar group.
• {1011} — Rhombohedral cleavage. Calcite's near-perfect rhombohedral cleavage in three directions produces the characteristic rhombohedra when the mineral is broken. While calcite itself is rarely faceted for jewellery, understanding its cleavage is important when it occurs as an inclusion in other gems.

Cleavage Quality and Its Notation

Cleavage notation specifies direction but not quality. Mineralogical convention separately grades cleavage quality on a descriptive scale — perfect, good, distinct, indistinct, and none — based on the smoothness and ease of the resulting surface. A complete description of a mineral's cleavage therefore pairs the Miller index with the quality descriptor: topaz is said to have perfect cleavage on {001}, while orthoclase has perfect cleavage on {001} and good cleavage on {010}. The number of cleavage directions a mineral possesses (one, two, three, four, or six) is equally significant: minerals with cleavage in multiple directions — such as fluorite with four directions on {111} — are especially challenging to cut and polish.

Practical Implications for Cutting and Setting

A gemologist's ability to read cleavage notation translates directly into practical decisions at the cutting wheel and the jeweller's bench. When orienting rough for faceting, the cutter must consider whether any cleavage plane runs at a shallow angle to a proposed table facet; if so, polishing across that plane may be difficult or may produce a surface that appears hazy. More critically, a cleavage plane running nearly parallel to the girdle of a finished stone creates a latent weakness that could cause the gem to split during setting or wear.

For stones with pronounced cleavage — topaz, kunzite, tanzanite (which has perfect cleavage on {010}), and moonstone — gemologists routinely advise bezel or protective settings rather than prong settings, and caution against ultrasonic cleaning, which generates vibrations capable of propagating along cleavage planes. Knowledge of the relevant Miller index allows the gemologist to explain precisely why a particular stone is vulnerable and in which direction.

In the assessment of rough, cleavage notation informs yield calculations. A parcel of rough spodumene with prominent {110} cleavage traces visible on the surface signals that the cutter must plan around those planes, potentially accepting a lower yield or a different cut shape to avoid cleaving through the finished stone.

Cleavage Notation in Laboratory Reports

Major gemmological laboratories do not typically reproduce Miller indices on standard grading reports, but the underlying crystallographic data informs the laboratory's assessment of inclusions, fractures, and potential durability concerns. When a laboratory notes a "cleavage" as a clarity characteristic — distinct from a fracture, which follows no crystallographic plane — the notation in the mineralogical literature provides the precise geometric context. Gemologists cross-referencing a laboratory report with mineralogical data can, for instance, confirm whether a reported cleavage in a sapphire (corundum has no true cleavage, only parting on {0001} and {1011}) is correctly identified or whether it is in fact a fracture or a parting plane.

Further Reading

• GIA Gems & Gemology — Clarity Characteristics
• International Gem Society — Cleavage, Fracture, and Tenacity