Pinacoid — A Crystal Form of Two Parallel Faces
Pinacoid — A Crystal Form of Two Parallel Faces
An open form fundamental to the morphology of many gem species
The pinacoid is an open crystal form consisting of two parallel faces, typically perpendicular to one of the crystallographic axes. As a crystal form it does not enclose space — it must combine with other forms to produce a complete crystal — but it is fundamental to the morphology of many gem species and is named explicitly in the descriptions of crystals from species including topaz, beryl, feldspar, and the various sulphates and carbonates relevant to mineral collecting and gemmology.
Definition
In crystallographic terminology, a form is the set of all faces related by the symmetry of the crystal. A pinacoid is a form consisting of two parallel faces; the two faces are related to each other by a centre of symmetry, by a mirror plane perpendicular to them, or by a two-fold rotation axis perpendicular to them, depending on the crystal class.
The pinacoid is one of seven open forms in the standard crystallographic classification, alongside the pedion (a single face), the dome (two non-parallel faces meeting at an edge), the sphenoid (two non-parallel faces related by two-fold rotation), and several others. Open forms must combine with closed forms or other open forms to produce a complete crystal capable of enclosing volume.
Types of pinacoid
The standard nomenclature distinguishes pinacoids by their orientation relative to the crystallographic axes. The basal pinacoid, perpendicular to the c-axis, is the most commonly named example and is encountered in topaz, beryl, apatite, and many other gem species where the basal termination of the crystal is recognisable. Front pinacoid, side pinacoid, and similar terms refer to pinacoids perpendicular to the a-axis or b-axis respectively.
In orthorhombic crystals, three distinct pinacoids — perpendicular to the three axes — are possible, and crystals showing all three are described accordingly. In monoclinic crystals, the situation is more complex because of the lower symmetry, and the pinacoidal forms are correspondingly more numerous and named with reference to the unique b-axis.
Pinacoids in gem species
Topaz crystals typically show prominent basal pinacoids combined with prism faces and pyramidal terminations. The basal pinacoid in topaz is often the dominant feature of the termination and is the surface most commonly encountered in faceted topaz, where it is sometimes used as the table of the cut stone. The cleavage in topaz, parallel to the basal pinacoid, is one of the species' principal cutting and care considerations.
Beryl crystals (including emerald, aquamarine, and morganite) commonly show basal pinacoids closing the prismatic crystal at the termination. The Mariposa-style hexagonal beryl crystal with basal pinacoid is a familiar form in the mineral specimen literature. Feldspar minerals — orthoclase, microcline, albite, and the broader plagioclase series — show pinacoidal forms as a routine part of their morphology, and the pinacoidal cleavages in the feldspars are the basis of their identification and their working properties.
Other gem species where pinacoidal forms are prominent include apatite, tourmaline (where the basal pinacoid is often present as a secondary form on the prismatic crystal), and the various sulphate gems including gypsum, celestite, and barite. Calcite and the carbonate gem materials similarly include pinacoidal forms as standard.
Pinacoidal cleavage
Cleavage parallel to a pinacoid is described as pinacoidal cleavage, and it is the controlling factor in the working properties of several gem species. Topaz's perfect basal cleavage, parallel to the basal pinacoid, requires careful orientation in cutting and setting; mica's perfect pinacoidal cleavage, while not relevant to gem use, is a well-known example of the effect; and the various feldspar cleavages similarly affect the working of moonstone and orthoclase gem material.
Cutters working with materials showing strong pinacoidal cleavage orient the rough so that the cleavage plane is at an oblique angle to the cabochon base or facet table, distributing any cleavage stress across multiple crystal directions and avoiding the catastrophic splitting that can occur when force is applied along the cleavage plane.
Pinacoids and crystal symmetry classes
The presence and orientation of pinacoidal forms is determined by the symmetry class of the crystal. In the triclinic system, with its low symmetry, every face is in principle a pinacoid because there is at most a centre of symmetry to relate parallel faces. In the monoclinic system, the unique b-axis allows pinacoids perpendicular to b as well as oblique pinacoidal pairs in the a-c plane. In the orthorhombic system, three orthogonal pinacoids are possible. In the tetragonal and hexagonal systems, the basal pinacoid (perpendicular to the principal axis) is standard, with the corresponding prism faces forming the lateral surfaces. In the cubic system, no faces qualify as pinacoids because the high symmetry relates more than two faces in any single form.
Understanding the symmetry-class context is helpful for reading mineralogical descriptions and for identifying the forms present on gem-quality crystals. The Hermann-Mauguin notation used in modern crystallography specifies the symmetry elements present and the corresponding allowed forms, including the pinacoidal forms relevant to each class.
Crystal habit and the prominence of pinacoids
The habit of a crystal — its overall shape, determined by the relative growth rates of the different faces — affects the visual prominence of the pinacoidal forms. In a tabular crystal habit, pinacoidal faces dominate the surface area and define the crystal's appearance; mica, gypsum, and certain calcite varieties are familiar examples. In a prismatic habit, the pinacoidal forms appear only as terminations and are often subordinate to the prism faces, as in beryl, tourmaline, and topaz.
For the gem cutter, the habit of the rough determines the practical approach to the material. Tabular rough is naturally suited to flat or shallow cuts that take advantage of the wide pinacoidal faces; prismatic rough is suited to elongated cuts that follow the prism axis and use the pinacoidal terminations as the table and culet positions.
Identification and crystal description
Mineralogical descriptions of crystal specimens routinely identify the pinacoidal forms present, using the standard Miller index notation to specify orientation. For gemmological purposes, the practical implications of pinacoidal forms are mainly in the cleavage behaviour and in the optical character of the cut stone (where the orientation of the table relative to the basal pinacoid affects pleochroism and the appearance of optical phenomena).
Historical terminology
The term pinacoid derives from the Greek pinax, meaning a board or tablet, reflecting the flat, board-like appearance of the parallel faces. The term was standardised in nineteenth-century crystallography and remains the preferred terminology in modern mineralogical literature, although the older synonyms parallelohedron and basal plinth still appear in occasional use. The standardisation followed the consolidation of crystallographic notation under Friedrich Mohs, William Hallowes Miller, and the broader nineteenth-century mineralogical community.