Crystallography: The Monoclinic System
Last Updated: 24th Jul 2018By Donald Peck & Alfred Ostrander
According to the International Union for Crystallography
The monoclinic crystal system embraces nearly 1,400 different mineral species (2018), or approximately 27% of all known minerals. That population is, by far, the largest of the seven crystal systems. The system is comprised of three crystal classes: the prismatic class, the sphenoidal class, and the domatic class. With more than 1,200 mineral species in the prismatic class alone it is worthwhile to become thoroughly acquainted with the symmetry of the class. The remaining two classes each hold slightly more than 80 different minerals.
The monoclinic crystal system is characterized by a 2fold axis of rotational symmetry coincident with the baxis; or a mirror plane that includes the caxis and the aaxis; or both. Usually, it is both. The prismatic class shows the 2fold axis perpendicular to the mirror plane and it has a center of symmetry. The sphenoidal class has only the 2fold axis (no mirror plane and no center of symmetry). And the domatic class has the mirror plane, but no 2fold axis and no center of symmetry. The monoclinic crystal system is one of low symmetry. The only system with lower symmetry is the triclinic system.
The symmetry of the monoclinic system generates a three axis model (The axes are a result of the symmetry, not viceversa). The axes are designated a, b, and c. The b and c axes are in the same plane and intersect at a 90^{o} angle. The a axis is usually inclined to the c axis and makes an angle of 90^{o} to the b axis. By custom, the positive end of the a axis (a^{+}) pitches downward relative to the c axis. The angle between the a and c axes is designated as β (beta) and is usually greater than 90^{o}. (Beta is the angle of rotation of the a^{+} axis from the c^{+} axis around the b axis.) In some references, the a axis is often referred to as the clino axis and the b axis as the ortho axis.
Symmetry determines the direction of the b axis, which is the standard unit. A prominant sloping face is usually considered to be parallel to the a axisl And if the crystal is elongated in the plane of the a and c axes, the longer of the two axes is usually chosen as c.
There are approximately 80 monoclinic minerals where β equals 90^{o}. You may well ask how this can be. Recall that the symmetry determines the axes, so if the symmetry is monoclinic, the a axis may be perpendicular to the c axis. Two with which you may be familiar are mesolite, in the sphenoidal class, and neptunite, in the domatic class. In both cases β is 90^{o} but α is unequal to 90^{o}.
Angular observations must be made carefully, as there are another 100, or so, species where β is between 91^{o} and 93^{o}.
There are two types of forms, general forms and special forms.
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 red forms, {111} and {221}, are general forms. 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. The same is true for {221}.
Special forms have Miller Indices like {100}, {110}, {111),{102}, etc. Special forms may be found on crystals in any crystal class of the system.
Forms Found on Monoclinic Crystals
The Generalized Monoclinic figure,at the right indicates the relative position of the faces for each form on the crystal.
Prism
A prism is an open form with three or more similar faces surrounding an axis (the ends are not closed by a face of the same form).
In the monoclinic system, a prism is comprised of four faces. The {hkl} prism is a 4th order prism. There is a positive 4th order prism in which the two faces on the upper half of the crystal intercept the positive end of the aaxis. And there is a negative 4th order prism in which the two faces on the upper half of the crystal intercept the negative end of the aaxis. They are not interchangeable. The {hkl} prism shown above is 4th order positive. The positive and negative forms, taken together, comprise a dipyramid that has eight faces. Together they make a closed form. That is, extended, they completely enclose space. Either the positive form or the negative form, or both, may be present on a monoclinic crystal.
The {0kl} prism is the 1st order prism (it surrounds the aaxis); the {hk0} prism is 3rd order (it surrounds the caxis). There is no 2nd order prism because the system's symmetry (and inclination of the aaxis) does not permit four similar and parallel faces to surround the b axis.
A Dome is "half a prism". It consists of two intersecting faces, parallel to an axis, and separated by a mirror plane. Domes parallel to the caxis are possible.
Pinacoids
A pinacoid is a pair of parallel faces. It is an open form, not closed on the sides or ends by faces of the same form.
The {100} pinacoid is parallel to the the plane of the b and c axes and constitutes the "front" and "back" of the crystal. Similarly {010} is the "sides" and {001) the "top" and "bottom". It is important to note that the plane of {001) is parallel to the plane of the a and b axes, and not perpendicular to the c axis.
The {hol} intercepts the a and c axes and is parallel to the b axis. The form is positive if the intercept of the face on the upper half of the crystal is on the positive end of the a axis. The form is negative if the intercept of the face on the upper half of the crystal is on the negative end of the a axis. Some texts refer to these forms as clinodomes. Together they may resemble a 2nd order prism, but they are not.
Monoclinic crystals are generally prismatic or acicular. Occasionally they will be tabular. Crosssections range from nearly square to rectangular or rhombic; and may appear nearly octagonal or hexagonal.
In a view of the termination, down the c axis, there is almost always a mirror plane that includes the aaxis and caxis. Generally, the faces of the upper termination above the a^{+} axis are distinctly different than those above the a^{} axis. The absence of a second mirror plane, perpendicular to the first usually, but not always, will differentiate monoclinic symmetry from orthorhombic symmetry (The orthorhombic disphenoidal class does not have mirror planes that include the caxis).
The angle, β, often is readily visible. A view along the baxis usually shows β as asymmetry in the termination. The inclined face, (001), is parallel to the plane of the aaxis and baxis. {It is not perpendicular to the caxis.} β, then, is the larger of the angles that the plane (001) makes with the caxis (usually parallel to the vertical edge of the crystal). A measured angle less than 90^{o} must be subtracted from 180^{o} in order to obtain beta.
Although there are three crystal classes in the monoclinic crystal system, only the prismatic class is commonly encountered. Mineral that crystallize in the sphenoidal and domatic classes are relatively rare and few in number. The sphenoidal class is important in other scientific fields, particularly chemistry, for its optical properties.
The monoclinic crystal classes, listed below, are in order of decreasing population, not in decreasing symmetry as they are sometimes listed in other references. The prismatic class holds, by far, the largest number of species of any class in any of the seven crystal systems. The sphenoidal and domatic classes have lower symmetry and hold comparatively few mineral species.
2/m (read as a 2fold axis of rotation perpendicular to a mirror plane. An axis of rotational symmetry perpendicular to a mirror plane always produces a center of symmetry).
Symmetry Elements
1A_{2},1P, C (One 2fold axis of rotational symmetry, 1 plane of symmetry, a center of symmetry).
Holohedral (The highest symmetry class of its system)
General Form
The general form, if present, is always a monoclinic 4th order prism{ hkl} where h≠k≠l≠h and h≠0≠k≠0≠l. In the Prismatic Crystal Class it is expressed as two faces modifying the corners above the >a^{+} axis and two faces below the a^{} axis.
Special Forms
Any of the following forms may be present:
Pinacoids: {100}, {010}, {001}, {h0l}+, {h0l}^{}
Prisma: {0kl}, {hk0}, {hkl}_{+}, {hkl}_{}
Look For
A vertical mirror plane that includes the a and c axes. The absence of a vertical mirror plane that includes the b and c axes. A (001) face inclined to the c axis.
Problems
1. Most often, we deal with crystals that are on matrix. In such cases, the lower termination is not available and the 2fold axis can be inferred, but not observed. The inclined a axis, with the inclined (001) face, is likely the first observation to indicate a monoclinic crystal. With the single mirror plane visible from the front, back, and especially the upper termination and the absence of a second mirror plane perpendicular to the first, the prismatic class becomes almost certain.
2. When the beta angle is 90o, or very close to it, the (100) face does not appear to be inclined when viewed along the b axis. Then one must rely on the observation of the single mirror plane, which is probable for the monoclinic prismatic class, but is not certain.
The crystal depicted above is of diopside, a typical mineral in the monoclinic prismatic class. Turn on the axes.
Symmetry
1 Axis of 2fold Rotational Symmetry: Coincident with the baxis
1 Mirror Plsne, vertical, the plane of the a and caxes.
Forms:
Prisms:
2 1st Order, (110} & {313}
1 4th Order, 211, Negative, (Upper half intercepts negative end of aaxis)
Pinacoids: 3, a {100}, b {010}, c {001}
1 2nd Order Pinacoid, 101, Negative, (Upper half intercepts negative end of aaxis)
Representative Minerals Acinolite, Azurite, Clinoclase, Hydromagnesite, Monazite(Ce), Orthoclase, Realgar,Staurolite
2 Only a 2fold axis of symmetry. There is no mirror plane and no center of symmetry.
Symmetry Elements1 A_{2} (which is 1 2fold axis of rotational symmetry {the b axis}). Prisms become sphenoids
Crystals in this class are enantiomorphic (showing left or right handedness; crystals are very similar, but one cannot be superimposed on the other.)
Forms
{100} and {h0l} pinacoids may be present.
Pinacoids perpendicular to the b axis become pedions (A single faced form resembling half a pinacoid). The 1st, 3rd, and 4th order prisms alter to sphenoids which are enantiomorphic. A sphenoid is an open form that has two faces related to each other by a 2fold axis and that are not parallel to each other (think of clipping two diagonal corners off the top of a shoebox).
Problems
The minerals in this class tend to be fibrous, radiating, and acicular. About the best that one can hope for is to find radiating crystals large enough so the inclined {001} face is observable as a termination of the crystal. Recognizing the class is difficult.
Representative MineralsHalotrichite, Pickeringite, Uranophane, Wallastonite2M
m = 2
Forms
This class has extremely low symmetry. Pinacoids that are on opposite sides of the mirror plane become pedions (i.e. The two faces are no longer mirror images of each other). Domes (two intersecting (possibly by extension) faces that lie on opposite sides of the mirror plane. Domes are an open form.
Symmetry Elements
P (1 mirror plane.) The Holohedral class (The lowest symmetry of any class in its system.) Also, minerals in this class are hemimorphic (the forms at one end of the principal axis are different from those at the other end). Prisms become domes. that is, two adjacent faces of the prism remain forming a dome, while the other two faces are not expressed.
Look For
Look for the inclined {001} face and the single mirror plane in the plane of the a and c axes.
If both ends of the c axis are visible, look for the hemimorphism. In the stereophoto at the right, the(001) face is uppermost with the mirror plane running left to right.
Problems
If the crystal is on matrix, differentiating this class from the prismatic class is virtually impossible. The minerals in this class are not common.
.
Symmetry
1 Mirror Plane: the plane of the a and c axis.
Forms
Prism: 3rd Order {110}; 3rd Order {120}; 4th Order {131}
Domes: 3rd Order (320); 4th OrderNegative (551}; 4th OrderNegative {531}
Pinacoid: {010}
Representative MineralsClinohedrite, Neptunite, Scolecite
Links to the Crystallography Series
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.
Our thanks to Erin Delvinthal, who helped with the formatting.
The monoclinic crystal system embraces nearly 1,400 different mineral species (2018), or approximately 27% of all known minerals. That population is, by far, the largest of the seven crystal systems. The system is comprised of three crystal classes: the prismatic class, the sphenoidal class, and the domatic class. With more than 1,200 mineral species in the prismatic class alone it is worthwhile to become thoroughly acquainted with the symmetry of the class. The remaining two classes each hold slightly more than 80 different minerals.
Unique Symmetry of the Monoclinic System
The monoclinic crystal system is characterized by a 2fold axis of rotational symmetry coincident with the baxis; or a mirror plane that includes the caxis and the aaxis; or both. Usually, it is both. The prismatic class shows the 2fold axis perpendicular to the mirror plane and it has a center of symmetry. The sphenoidal class has only the 2fold axis (no mirror plane and no center of symmetry). And the domatic class has the mirror plane, but no 2fold axis and no center of symmetry. The monoclinic crystal system is one of low symmetry. The only system with lower symmetry is the triclinic system.
The 2fold axis of rotational symmetry as the principal axis of symmetry, coincident with the baxis, is unique to the monoclinic crystal system. All others have the caxis as the principal axis of rotational symmetry (or the vertical aaxis in the isometric system).
Crystallographic Axes
The symmetry of the monoclinic system generates a three axis model (The axes are a result of the symmetry, not viceversa). The axes are designated a, b, and c. The b and c axes are in the same plane and intersect at a 90^{o} angle. The a axis is usually inclined to the c axis and makes an angle of 90^{o} to the b axis. By custom, the positive end of the a axis (a^{+}) pitches downward relative to the c axis. The angle between the a and c axes is designated as β (beta) and is usually greater than 90^{o}. (Beta is the angle of rotation of the a^{+} axis from the c^{+} axis around the b axis.) In some references, the a axis is often referred to as the clino axis and the b axis as the ortho axis.
Symmetry determines the direction of the b axis, which is the standard unit. A prominant sloping face is usually considered to be parallel to the a axisl And if the crystal is elongated in the plane of the a and c axes, the longer of the two axes is usually chosen as c.
There are approximately 80 monoclinic minerals where β equals 90^{o}. You may well ask how this can be. Recall that the symmetry determines the axes, so if the symmetry is monoclinic, the a axis may be perpendicular to the c axis. Two with which you may be familiar are mesolite, in the sphenoidal class, and neptunite, in the domatic class. In both cases β is 90^{o} but α is unequal to 90^{o}.
Angular observations must be made carefully, as there are another 100, or so, species where β is between 91^{o} and 93^{o}.
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 red forms, {111} and {221}, are general forms. 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. The same is true for {221}.
Special forms have Miller Indices like {100}, {110}, {111),{102}, etc. Special forms may be found on crystals in any crystal class of the system.
Forms Found on Monoclinic Crystals
Monoclinic Forms  

The Generalized Monoclinic figure,at the right indicates the relative position of the faces for each form on the crystal.
Prism
A prism is an open form with three or more similar faces surrounding an axis (the ends are not closed by a face of the same form).
In the monoclinic system, a prism is comprised of four faces. The {hkl} prism is a 4th order prism. There is a positive 4th order prism in which the two faces on the upper half of the crystal intercept the positive end of the aaxis. And there is a negative 4th order prism in which the two faces on the upper half of the crystal intercept the negative end of the aaxis. They are not interchangeable. The {hkl} prism shown above is 4th order positive. The positive and negative forms, taken together, comprise a dipyramid that has eight faces. Together they make a closed form. That is, extended, they completely enclose space. Either the positive form or the negative form, or both, may be present on a monoclinic crystal.
The {0kl} prism is the 1st order prism (it surrounds the aaxis); the {hk0} prism is 3rd order (it surrounds the caxis). There is no 2nd order prism because the system's symmetry (and inclination of the aaxis) does not permit four similar and parallel faces to surround the b axis.
A Dome is "half a prism". It consists of two intersecting faces, parallel to an axis, and separated by a mirror plane. Domes parallel to the caxis are possible.
Pinacoids
A pinacoid is a pair of parallel faces. It is an open form, not closed on the sides or ends by faces of the same form.
The {100} pinacoid is parallel to the the plane of the b and c axes and constitutes the "front" and "back" of the crystal. Similarly {010} is the "sides" and {001) the "top" and "bottom". It is important to note that the plane of {001) is parallel to the plane of the a and b axes, and not perpendicular to the c axis.
The {hol} intercepts the a and c axes and is parallel to the b axis. The form is positive if the intercept of the face on the upper half of the crystal is on the positive end of the a axis. The form is negative if the intercept of the face on the upper half of the crystal is on the negative end of the a axis. Some texts refer to these forms as clinodomes. Together they may resemble a 2nd order prism, but they are not.
General Morphology
Monoclinic crystals are generally prismatic or acicular. Occasionally they will be tabular. Crosssections range from nearly square to rectangular or rhombic; and may appear nearly octagonal or hexagonal.
In a view of the termination, down the c axis, there is almost always a mirror plane that includes the aaxis and caxis. Generally, the faces of the upper termination above the a^{+} axis are distinctly different than those above the a^{} axis. The absence of a second mirror plane, perpendicular to the first usually, but not always, will differentiate monoclinic symmetry from orthorhombic symmetry (The orthorhombic disphenoidal class does not have mirror planes that include the caxis).
The angle, β, often is readily visible. A view along the baxis usually shows β as asymmetry in the termination. The inclined face, (001), is parallel to the plane of the aaxis and baxis. {It is not perpendicular to the caxis.} β, then, is the larger of the angles that the plane (001) makes with the caxis (usually parallel to the vertical edge of the crystal). A measured angle less than 90^{o} must be subtracted from 180^{o} in order to obtain beta.
Although there are three crystal classes in the monoclinic crystal system, only the prismatic class is commonly encountered. Mineral that crystallize in the sphenoidal and domatic classes are relatively rare and few in number. The sphenoidal class is important in other scientific fields, particularly chemistry, for its optical properties.
The Crystal Classes
The monoclinic crystal classes, listed below, are in order of decreasing population, not in decreasing symmetry as they are sometimes listed in other references. The prismatic class holds, by far, the largest number of species of any class in any of the seven crystal systems. The sphenoidal and domatic classes have lower symmetry and hold comparatively few mineral species.
The Prismatic Class
HermanMauguin Symbol2/m (read as a 2fold axis of rotation perpendicular to a mirror plane. An axis of rotational symmetry perpendicular to a mirror plane always produces a center of symmetry).
Symmetry Elements
1A_{2},1P, C (One 2fold axis of rotational symmetry, 1 plane of symmetry, a center of symmetry).
Holohedral (The highest symmetry class of its system)
General Form
The general form, if present, is always a monoclinic 4th order prism{ hkl} where h≠k≠l≠h and h≠0≠k≠0≠l. In the Prismatic Crystal Class it is expressed as two faces modifying the corners above the >a^{+} axis and two faces below the a^{} axis.
Special Forms
Any of the following forms may be present:
Pinacoids: {100}, {010}, {001}, {h0l}+, {h0l}^{}
Prisma: {0kl}, {hk0}, {hkl}_{+}, {hkl}_{}
Look For
A vertical mirror plane that includes the a and c axes. The absence of a vertical mirror plane that includes the b and c axes. A (001) face inclined to the c axis.
Problems
1. Most often, we deal with crystals that are on matrix. In such cases, the lower termination is not available and the 2fold axis can be inferred, but not observed. The inclined a axis, with the inclined (001) face, is likely the first observation to indicate a monoclinic crystal. With the single mirror plane visible from the front, back, and especially the upper termination and the absence of a second mirror plane perpendicular to the first, the prismatic class becomes almost certain.
2. When the beta angle is 90o, or very close to it, the (100) face does not appear to be inclined when viewed along the b axis. Then one must rely on the observation of the single mirror plane, which is probable for the monoclinic prismatic class, but is not certain.
The crystal depicted above is of diopside, a typical mineral in the monoclinic prismatic class. Turn on the axes.
Symmetry
1 Axis of 2fold Rotational Symmetry: Coincident with the baxis
1 Mirror Plsne, vertical, the plane of the a and caxes.
Forms:
Prisms:
2 1st Order, (110} & {313}
1 4th Order, 211, Negative, (Upper half intercepts negative end of aaxis)
Pinacoids: 3, a {100}, b {010}, c {001}
1 2nd Order Pinacoid, 101, Negative, (Upper half intercepts negative end of aaxis)
Representative Minerals Acinolite, Azurite, Clinoclase, Hydromagnesite, Monazite(Ce), Orthoclase, Realgar,Staurolite
The Sphenoidal Class
HermanMauguin Symbol2 Only a 2fold axis of symmetry. There is no mirror plane and no center of symmetry.
Symmetry Elements1 A_{2} (which is 1 2fold axis of rotational symmetry {the b axis}). Prisms become sphenoids
Crystals in this class are enantiomorphic (showing left or right handedness; crystals are very similar, but one cannot be superimposed on the other.)
Forms
{100} and {h0l} pinacoids may be present.
Pinacoids perpendicular to the b axis become pedions (A single faced form resembling half a pinacoid). The 1st, 3rd, and 4th order prisms alter to sphenoids which are enantiomorphic. A sphenoid is an open form that has two faces related to each other by a 2fold axis and that are not parallel to each other (think of clipping two diagonal corners off the top of a shoebox).
Problems
The minerals in this class tend to be fibrous, radiating, and acicular. About the best that one can hope for is to find radiating crystals large enough so the inclined {001} face is observable as a termination of the crystal. Recognizing the class is difficult.
Representative MineralsHalotrichite, Pickeringite, Uranophane, Wallastonite2M
The Domatic Class
HermanMauguin Symbolm = 2
Forms
This class has extremely low symmetry. Pinacoids that are on opposite sides of the mirror plane become pedions (i.e. The two faces are no longer mirror images of each other). Domes (two intersecting (possibly by extension) faces that lie on opposite sides of the mirror plane. Domes are an open form.
Symmetry Elements
P (1 mirror plane.) The Holohedral class (The lowest symmetry of any class in its system.) Also, minerals in this class are hemimorphic (the forms at one end of the principal axis are different from those at the other end). Prisms become domes. that is, two adjacent faces of the prism remain forming a dome, while the other two faces are not expressed.
Look For
Look for the inclined {001} face and the single mirror plane in the plane of the a and c axes.
If both ends of the c axis are visible, look for the hemimorphism. In the stereophoto at the right, the(001) face is uppermost with the mirror plane running left to right.
Problems
If the crystal is on matrix, differentiating this class from the prismatic class is virtually impossible. The minerals in this class are not common.
Symmetry
1 Mirror Plane: the plane of the a and c axis.
Forms
Prism: 3rd Order {110}; 3rd Order {120}; 4th Order {131}
Domes: 3rd Order (320); 4th OrderNegative (551}; 4th OrderNegative {531}
Pinacoid: {010}
Representative MineralsClinohedrite, Neptunite, Scolecite
Links to the Crystallography Series
 Determining Symmetry of Crystals: An Introduction
 Miller Indices
 HermannMauguin Symmetry Symbols
 Crystallography: The Monoclinic System
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
Our thanks to Erin Delvinthal, who helped with the formatting.
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