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Crystallography: The Orthorhombic System

Last Updated: 13th Aug 2018

By Donald Peck & Alfred Ostrander

According to the International Union for Crystallography

Barite Orthorhombic Dipyramidal Class
Natrolite: Orthorhombic Dipyramidal Class
Euchroite: Orthorhombic Disphenoidal Class
Enargite: Orthorhombic Pyramidal Class
Barite Orthorhombic Dipyramidal Class
Natrolite: Orthorhombic Dipyramidal Class
Euchroite: Orthorhombic Disphenoidal Class
Enargite: Orthorhombic Pyramidal Class
Barite Orthorhombic Dipyramidal Class
Natrolite: Orthorhombic Dipyramidal Class
Euchroite: Orthorhombic Disphenoidal Class
Enargite: Orthorhombic Pyramidal Class

There are 970 (2018) minerals in the orthorhombic crystal system. That is about 18% of all minerals. And it makes the Orthorhombic system the second largest crystal system, second only to the monoclinic system in population. Of the orthohombic minerals, 577 are in the Orthorhombic dipyramidal class, 88 are in the Orthorhombic disphenoidal Class, and 172 are considered to be orthohombic but the crystallographic class to which they belong is either unknown or uncertain.

Unique Symmetry of the Orthorhombic System


The Orthorhombic system is unique in having a 2-fold axis of rotational symmetry coincident with the c axis of the crystal without the presence of a 3-fold axis of rotational symmetry (which would place it in the isometric system).

When viewed from the termination, nearly all orthorhombic mineral crystals show a 2-fold axis of rotational symmetry. The axis is coincident with the c axis and lies in two perpendicular mirror planes.


Crystallographic Axes

Crystallographic Axes: Orthrhombic System


In any crystal system, the axes of a crystal are determined by the symmetry of the particular system, not visa versa.

The orthorhombic is a three axis system with the three axes mutually at 90o angles to each other and with the b axis taken as left to right and the longest, the c axis as being vertical and the shortest, and with the a axis intermediate in length and front to back. In some texts the a axis is referred to as the brachy-axis, and the b axis as the macro-axis.

Crystallography and crystal drawings have undergone different conventions and interpretations over time. Other conventions made the c axis longest, and another the a axis longest. The International System used here has the b > a > c ratio based on the unit cell with the axial ratio derived from the unit cell. However, in the world of crystals, the c axis usually appears to be longest. It is the axis of elongation. Due to differences between atomic point densities and resulting variation in forces of attraction in the crystals, growth is usually faster in this direction, and slower in the a direction.

In early descriptions, if there was a long dimension to the crystal it was often described as the the c axis. A single cleavage was designated as the "basal cleavage". A crystal with a pair of large pinacoidal faces perpendicular to the short axis, was termed tabular.

General and Special Forms


There are two types of forms, general forms and special forms.

Any form which is not a general form is a special form. Most often, the general form is the form for which the crystal class is named. It usually appears only in that crystallographic class or in classes of higher symmetry. A general form has the maximum number of faces of any form in its crystal class. Special forms may appear in any crystal class of the system.


The general form intercepts all three axes, each at a different distance. It is the form for which the mineral class is named and which generates the maximum number of faces relative to other forms in the crystal class. It is not always expressed on the crystal. In the Generalized Monoclinic figure (below, right) the purple form, {111}, is the general form. Because all three axes have different unit lengths, the axial lengths for the intercepts, at one, on each axis is different, meeting the requirement for different length intercepts.

In this system, the orthorhombic dipyramid is the general form in the Dipyramidal Class, the Orthorhombic pyramic is the general form in the Pyramidal Class, and the Orthorhombic disphenoid is the general form in the Sphenoidal Class.

Orthorhombic Forms (Click a figure to enlarge it)

Dipyramid & Pyramids
Orthorhombic dipyramid
Orthorhombic Pyramid {hkl}
Orthorhombic Pyramid {hk_l}
Prisms & Domes
Orthorhombic Prism {0kl};1st Order
Orthorhombic Prism {h0l};2nd Order
Orthorhombic Prism {hk0}; 3rd Order
Orthorhombic Dome {0kl}
Pinacoids & Pedions
Orthorhombic Pinacoid {100}
Orthorhombic Pinacoid {101}
Orthorhombic Pinacoid {001}
Pedion
Disphenoid & Sphenoid
Orthorhombic Disphenoid
Orthorhombic Sphenoid


Dipyramid: Comprised of eight triangular faces. each of which intercepts all three axes. The orthorhombic dipyramid is a closed form (It can totally enclose space). The symmetry of the dipyramidal Class (3 mutually perpendicular 2-fold axis of rotation, each perpendicular to a mirror plane, and a center of symmetry) requires the dipyramid. If one dipyramidal face forms on the crystal, all eight should be there. The dipyramid is the general form for the Dipyramical Class.

Pyramid: The orthorhombic pyramid consists of four trianglar faces that intercept all three axes either in the upper half or the lower half. It is an open form (does not enclose space). The orthorhombic pyramid can not exist if there is a center of symmetry (which is the same as a mirror plane perpendicular to an axis of rotational symmetry). There is a positive pyramid with all four faces intercepting the c+ axis and a negative pyramid with the intercept at the c- axis. The two pyramids are separate forms. The Pyramid is the general form for the Pyramidal Class.

Prisms: There are three prisms in the orthorhombic system. A prism has four faces parallel to and surrounding an axis. Each face intercepts the two remaining axes. It is an open form (open on the ends. 1st, 2nd, and 3rd order surround respectively the a, b, and c axes.

Domes: A dome has two faces. It is "half a prism" and can exist when there is no center of symmetry. The two faces are always separated by a mirror plane. The orthorhombic system has 1st and 2nd order domes. In some texts theY are referred to as the macrodome (parallel to the a-axis)) and the brachydome (parallel to b-axis).

Pinacoids: The pinacoid, an open form, is a pair of faces each intercepting a different end of the same crystallographic axis. In the Orthorhombic system there is an a or front pinacoid, a b or side pinacoid, and a c or basal pinacoid. In some texts the front pinacoid is called the macro-pinacoid, the side inacoid is named the brachy-pinacoid, and the top pinachoid is the basal pinachoid.

Pedion: A pedion is a single face without a similar face opposite it on the crystal. If there is no center of symmetry, pedions are possible.

Disphenoid: A disphenoid is a closed form consisting of four scalene tringles. They occur as a pair of faces at opposite ends of the c axis in the Disphenoidal Class, where they are the general form. There is a positive and a negative disphenoid and they are not interchangeable. Thus the class is enantiomorphous.

Sphenoid: The sphenoid is half of the disphenoid, comprised of two scalene triangles. It is an open form, always with a 2-fold axis extending through and perpendicular to the common edges of the triangles. [This is included to illustrate a sphenoid and its distinction from a dome.]

General Morphology

Generalized Orthorhombic Crystal
Symmetry: Termination View

Orthorhombic symmetry generally results in blocky crystals. However, other common habits are long prismatic, tabular, platy, acicular, radiating, and filamentous. In cross-section, crystals tend toward rectangular or rhomboid, often with modified corners.

The figure at far right shows a generalized crystal with dipyramidal symmetry. The forms are shown in the same color as those in the table above.

The figure at near right shows the plan of the termination view for the general crystal at far right. It shows a 2-fold axis of rotational symmetry that is the c axis. If the crystal were rotated 180o it would fill exactly the same space. Rotated another half turn, it would be in its original position, thus the "2-fold axis of rotational symmetry". Also, the top edge of two mirror planes is shown by the dashed red lines. The left half of the crystal is a mirror image of the right half; so is the front half a mirror image of the rear half. Since any crystal in either the dipyramidal or pyramidal class (and that is nearly all orthorhombic crystals) that has a habit and size to show crystallographic forms can be seen in termination view looking for these elements can be diagnostic.

For crystals possibly in the dipyramiidal or pyramidal classes, always check, at least visually, the angles between the upper pinacoid and the front pinacoid; and between the upper pinacoid and the side pinacoid. If there are edges instead of pinacoids, use the edges. The angles should be 90o. Alternatively compare the angle between both side pinacoids and the faces of the 1st order prism if there is one above them. The angles on both sides of the crystal should be equal. Similarly, compare the angles between the 2nd order prism faces and the front and back pinacoids. They also should be equal.

The Orthorhombic Crystal Classes


There are three crystal classes in the orthorhombic system. The Orthrhombic dipyramidal class is holohedral. (exhibits the highest symmetry in the system). The Orthorhombic disphenoidal class, which is hemihedral and enantiomorphic (lower symmetry than the holohedral class, exhibiting only half as many faces) and (exhibiting left and right handedness). And the Orthorhombic dipyramidal which has the lowest symmetry and is hemimorphic (opposite ends of the axis of symmetry exhibit different forms; no transverse mirror plane and no center of symmetry).

Orthorhombic Dipyramidal Class: the Holohedral Class

Herman-Mauguin Symbol
2/m 2/m 2/m (The a axis is a 2-fold axis of symmetry perpendicular to a mirror plane; the b axis a 2-fold axis perpendicular to a mirror plane; and the c axis is a 2-fold axis perpendicular to a mirror plane.)

Symmetry Elements3A2, 3P, c (3 2-fold Axes of rotational symmetry, 2 Mirror Planes, and a Center of symmetry)

The General Form
The General Form is the Orthorhombic Dipyramid. Since the inequality of the three orthorhombic axes assure that absolute distances on the three axes will be different, form {111} is a general form. So to are {123}, [431}, or any indices that do not include a 0 (zero/zed).

Special Forms
Prisms: 1st order prism {0kl}; 2nd order prism {k0l}; 3rd order prism {hk0}
Pyramids: Dipyramid {111},
Pinacoids: a or front pinacoid {100}; b or side pinacoid {010}; c or basal pinacoid {001}

Look For
1. Crystals are usually blocky, prismatic, or tabular.
2. From a termination view: cross-section may be rectangular, diamond shaped, nearly octagonal, or approaching hexagonal. A 2-fold axis coincident with the c axis is usually evident, as are two mutually perpendicular mirror planes (i.e. the left half of the crystal is a mirror image of the right half; so too, the front half and the rear half.)
3. The angle between vertical faces and termination faces on opposite sides of the crystal should be equal. And the angle between all vertical edges of the crystal and the upper c pinacoid (or the edge of a horizontal prism) should be 90o.

Problems
1. Most often we see crystals based in matrix. This precludes observation of the lower termination, the horizontal mirror plane, and the two horizontal 2-fold axes. In such cases, observation of even partial faces on the lower termination can be confirmatory.
2. Angles between the termination and the vertical forms must be observed carefully. The axial angles for many monoclinic and triclinic minerals vary from ninety degrees by less than two degrees (In fact, for 80 or so monoclinic crystals there is no variation.)

Representative Minerals (Click a name to access its photo gallery)
Aragonite, Baryte, Brookite,Celestine, Danburite, Fayalite, Natrolite, Staurolite, Topaz

Topaz: Orthorhombic Dipyramidal Class

Toggle
Edge Lines | Miller Indices | Axes

Transparency
Opaque | Translucent | Transparent

View
Along a-axis | Along b-axis | Along c-axis

{120}, {001}, {011}, modified
Locality: Alabaschka, Mursinsk
Kokscharow, 1854. In: V.M. Goldschmidt, Atlas der Krystallformen, 1913-1923.
.
Symmetry & Forms Shown on the Model:
Symmetry:
.. 2-fold axis: coincident with c-axis;
.. 2-fold axis: coincident with a-axis;
.. 2-fold axis: coincident with b-axis;
.. 3 mirror planes: mutually at 90o to each other. 1 (vertical) contains a & c-axes, 1 (vertical) contains c & b-axes, 1 (horizontal) contains a & b-axes.
Forms:
..General Form: Dipyramid {112}
..Special Forms:
....Prisms: 1st Order {011}, 3rd Order {110} & {120}
....Pinacoids: Basal {001}

Orthorhombic Pyramidal Class: The Hemimorphic Class



Herman-Mauguin Symbol
mm2 (Two mirror planes parallel to a 2-fold axis. The 2-fold axis is coincident with the c axis and is located in both planes)

Symmetry Elements1A2 2P One 2-fold axis of rotational symmetry; 2 vertical mirror planes at 90o to each other and coincident with the 2-fold and c-axis.)

The General Form
The general form is the pyramid {hkl}. It is located at the positive end of the C axis. Because the symmetry is hemimorphic the forms at the positive end of the c axis are different from those at the negative end.

Special Forms
The absence of the center of symmetry prevents 1st or 2nd order prisms. Instead they are replaced by domes.
.. Domes: 1st and 2nd order
.. Prisms: 3rd order prism
.. Pinacoids: a of front pinacoid, b or side pinacoid
.. Pedions: (001) and others

To Look For
1. A vertical 2-fold axis of rotation; two vertical mirror planes mutually perpendicular and both containing the c axis.
2. Any indication of hemimorphism (e.g. an exposed negative pyramid.
3. 90#o angles between the upper pedion (or the edge in its place) and the plane of the side pinacoids.

Problems
1. The negative pypramid is likely not developed because of the matrix.
2. The principle mineral in this class is hemimorphite, and crystals tend to be small.

Representative MineralsHemimorphite

Hemimorphite: Orthorhombic Pyramidal Class

Toggle
Edge Lines | Miller Indices | Axes

Transparency
Opaque | Translucent | Transparent

View
Along a-axis | Along b-axis | Along c-axis

{010}, {100}, {031}, {12-1}, modified
Lewis, 1899. In: V.M. Goldschmidt, Atlas der Krystallformen, 1913-1923.
.
Symmetry & Forms Shown on the Model:
Symmetry
..2-fold axis: coincident with c-axis.
..2 Mirror planes: vertical, both containing c-axis and at 90o to each other.
General Form:
..The General Form is the Orthorhombic Pyramid (negative) {121}.
Special Forms
..Domes: {101}, {031) (both positive)
..Prism: 3rd Order Prism {110}
..Pinacoids: {100}, {010}
..Pedion: {100}

Orthorhombic Disphenoidal Class: The Enantiomorphic Class



Herman-Mauguin Symbol
222 (Three 2-fold axes of rotational symmetry. They are coincident with the a, b, and c crystallographic axes.)

Symmetry Elements3A2 ( Three 2-fold axes of rotational symmetry. There are no mirror planes and no center of symmetry.)

The General Form
As with any crystal system where the axes are all unequal in length to each of the others, the general form may have the indices {111}. The general form is the orthorhombic disphenoid: {hkl}, right handed; or { h_kl }, left handed. The closed form has four scalene triangles as faces. It usually shows as 2 scalene triangles at each terminus of the c axis.

Special Forms
Prisms: 1st, 2nd, and 3rd order prisms are possible; {0kl}. {h0l}. and {hk0}.
Pinacoids: a or front, b or side, c or basal.

To Look For
Mineral crystals in this class are rare. Virtually all minerals of the class are filimentous, acicular, or radiating. When prismatic crystals are found, they are usually poorly formed. If reasonably well formed micro crystals are discovered, the defining feature is the disphenoid.

Problems
Mineral crystals with observable forms are almost never encountered.

Representative Minerals (Click on a name to view its Photo Gallery)
Austinite, Chonichalcite, Epsomite, Euchroite,

Epsomite: Orthorhombic Disphenoiddal Class

Toggle
Edge Lines | Miller Indices | Axes

Transparency
Opaque | Translucent | Transparent

View
Along a-axis | Along b-axis | Along c-axis

{110}, {111}, modified
Locality: Staßfurt
Milch, 1892. In: V.M. Goldschmidt, Atlas der Krystallformen, 1913-1923.
.

symmetry & Forms Shown on the Model:

Symmetry
..3 2-fold axes: coincident with the a b & c-axes.
..No mirror planes
..General Form:
....Disphenoid {111}
....Special Forms:
....Prisms: 2nd Order {101}, 3rd Order {110}




References


Mason, Brian and Berry, L.G. (1968) Elements of Mineralogy. W. H. Freeman and Company, San Francisco.
Smith, Jennie R. (1991) Understanding Crystallography. The Rochester Mineralogical Symposium.
Peck, Donald B. (2007) Mineral Identification: A Practical Guide for the Amateur Mineralogist. Mineralogical Record, Tucson, Arizona.
http://www.tulane.edu/~sanelson/eens211/forms_zones_habit.htm: A good explanation and depiction of crytallographic forma
https://en.wikipedia.org/wiki/Monoclinic_crystal_system , Short explanation of lattices, space groups, hemimorphic & enantiomorphic structure.

Acknowledgements


We are indebted to Erin Delvenfhal for suggesting the use of the 3D rotating crystal models and for working to make it happen.





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