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Gems and Minerals: The science of minerals

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Malachite Calcite Rosasite, Aurichalcite, and Calcite

Calcite


The Science of Minerals


Both the physical properties of minerals and gemstones and their beauty are dependent on their chemical composition and atomic structure.  Physical properties can be useful in distinguishing between both mineral species and individual minerals within a group or series.  An understanding of basic crystallography is fundamental to an appreciation of the relationships between physical properties, chemical composition, and atomic structure.

Crystallography

A crystal is a solid material with a highly-ordered three-dimensional atomic arrangement or structure.  When conditions allow unimpeded growth of a crystal, its internal atomic arrangement is reflected in its exterior shape, producing a regular geometric shape bounded by smooth planar surfaces (referred to as crystal faces).  Crystallography is the study of crystalline solids and the principles that govern their growth, external shape and internal structure.  A few of the basic concepts of crystallography are explained here.  More detailed explanations of basic crystallography and crystal forms and symmetry classes are available on the web, or in Klein and Hurlbut's Manual of Mineralogy.

Irradiated Quartz Early crystallographers were able to deduced many things about the internal structure of crystals from their studies of crystal symmetry.  For example, in 1869, after studying numerous quartz crystals, Nicolaus Steno observed that although they varied in size and shape the angle between any two adjacent prism faces was always 120o.  This observation is known as the Law of Constancy of Interfacial Angles.

Further study eventually determined that all crystals can be organized into 32 crystal classes (also called point groups) based on the presence or absence of the following four symmetry elements:

 

An axis of rotation is an imaginary line drawn through the center of a crystal around which the crystal may be rotated so that it appears the same as it did before the rotation.  Depending on the number of degrees through which the crystal must be rotated to produce this effect, a crystal may look the same from 2, 3, 4, or 6 different positions; such a crystal is described as having n-fold symmetry (e.g.: "2-fold symmetry") along that axis of rotation.

A rotoinverison axis is similar to an axis of rotation, except that in addition to being rotated around an imaginary line the crystal must also be turned end to end around the center point of the axis.  A rotoinversion 3-fold or 4-fold axis is distinguished from a 3-fold or 4-fold rotoinversion axis by a horizontal line above the 3 or 4. That horizontal line is not supported on a computer and so the rotoinversion axis is indicated on these pages by highlighting the rotoinversion axis in yellow.  

A crystal is said to have a center of symmetry if for each and every crystal edge, crystal plane or point on its surface, there is another edge, plane, or point equidistant in the opposite direction from the center.  Another way of expressing this is to say that a mineral has a center of symmetry  if an imaginary line can be run from any point on the surface of a crystal through its center to an identical point on the opposite face which is the same distance beyond the center.

A mirror plane is an imaginary plane that divides a crystal into halves that are mirror images of each other.

A crystal may have more than one of these symmetry elements, and a given symmetry element may occur more than once in a given crystal.  All crystals can be grouped into one of 32 classes, based what symmetry elements are present and their relationship to each other.

Another concept that can be used to classify crystals is that of crystallographic axesThese are a set of imaginary lines drawn through the center of a crystal. The 32 mineral classes are  subdivided into six crystal systems, based on the number of crystallographic axes (always either 3 or 4), their relative lengths, and whether the angles between them are perpendicular or oblique.  Each system is briefly described below; the hyperlinks lead to more detailed descriptions.

Isometric system:  Three mutually perpendicular axes of equal lengths (a1, a2, a3).  

Tetragonal system:  Three mutually perpendicular axes (a1, a2, c), with axes a1 and a2 of equal length and  axis c of a different length.

Hexagonal system:  Four axes (a1, a2, a3, and c).  Axes a1, a2, and a3 are of equal length (a1 = a2 = a3) and intersect at 120o, while axis c is at right angles to the plane formed by the other three axes and may be of any length.  

Orthorhombic system:  Three mutually perpendicular axes (a, b, c), all of which are different lengths.

Monoclinic system:  Three axes (a, b, c) of different lengths, two  of which are inclined to each other at an oblique angle (an angle other than 90o), with the third axis perpendicular to the plane formed by the other two.

Triclinic system:  Three unequal axes (a, b, c) of different lengths, all intersecting at oblique angles

Crystal habit refers to the general shapes of individual crystals or aggregates of crystals, which are governed by the development of their faces.  Crystal habit depends not only on atomic structure and crystal symmetry, but also on on the environment in which the crystals grew, and so a given mineral species may exhibit different crystal habits at different localities.  Since conditions are seldom ideal for free, unimpeded crystal growth, beautiful, well-formed mineral crystals are rare.  Minerals that crystallize in open spaces filled with fluid or gas are much more likely to be well formed.  Some mineral species very rarely develop crystals bounded by well defined planar faces.

Terms used to describe the crystal habit of single crystals are listed below.  Click on the small images to see enlarged views.

Rutilated Quartz (Quartz and Rutile) Acicular  Elongated, thin, needlelike crystals.
Arsenopyrite Bladed  Elongated, flattened prisms shaped like a knife blade.  
Native Silver-Copper Mixture Dendritic  Arborescent, or shaped like a tree, having a branching form.
Natrolite (A Zeolite Group Mineral) Filiform or capillary  Hairlike crystals, thinner and more delicate than acicular crystals.
Covellite Platy  Thin plate-shaped or sheet-like crystals.
Epidote and Quartz Prismatic  A crystal with one dimension markedly longer than the other two, prism-shaped.

A large number of terms are used to describe the crystal habit of parallel or radiating groups of crystals.  Some of the most common ones are listed here.

Heulandite (A Zeolite Group Mineral) Amygdaloidal  Mineral-lined or mineral-filled cavities, typically gas holes, that occur in some extrusive volcanic rocks.  These crystals are secondary minerals, precipitated from aqueous solutions which circulated through cooling submarine lavas.
Chysotile (A Serpentine Group Mineral) Asbestiform or fibrous  An aggregate of thin fibers.
Goethite Botryoidal, reniform, mammillary   An aggregate composed of intergrown spherical shapes resembling the outside surface of a bunch of grapes.  The three terms differentiate between spheres of different sizes.  The specimen shown here is "botryoidal" (the smallest).  "Mammillary" is the largest.
Malachite Concentric  More or less spherical layers around a common center or centers.
Vanadinite Drusy  A layer or encrustation of small (less than 2 mm), fairly well-formed crystals. The tiny quartz crystals that line the cavity in the center of the blue agate at the bottom of this page are another example of drusy crystals.
Rhodonite (pink), Franklinite (black), and Calcite (white) Massive  A homogeneous texture or fabric characterized by an absence of layering, foliation, cleavage, or any other directional structure or preferred orientation of constituent minerals.  If a massive group of crystals has a preferred direction of cleavage, it is due to aligned fractures or other closely spaced planes of weakness produced by deformation or metamorphism.  Foliation is the planar structure that results from flattening and/or separation of the constituent minerals of a metamorphic rock into light quartz- and feldspar-rich layers and dark mica-rich layers.
Biotite mica Micaceous  An aggregate of very thin sheets, typically of the mica minerals (biotite, muscovite, phlogopite, chlorite).
Gypsum Radiating  Groups of elongated crystals that extend from a common central point.
Rhodochrosite Stalactitic  Icicle-like shapes that form through the precipitation of evaporating aqueous solutions in caves and large, air-filled solution cavitites.  Cutting through the stalactite perpendicular to the length typically reveals a concentric cross section, as shown in this rhodochrosite sample.
Wulfenite Tabular  A crystal form characterized by having one dimension markedly smaller than the other two.

Chalcedony (variety Agate)The Individual crystals in an monomineralic (composed of one mineral) aggregate may be so small that their crystalline nature can be determined only with the aid of a microscope (called microcrystalline) or by X-ray diffraction (called cryptocrystalline).  Jade, a highly prized gemstone, is an aggregate of microcrystalline jadeite (a pyroxene group mineral), or actinolite and tremolite (amphibole group minerals).  Chalcedony is a cryptocrystalline aggregate of quartz.  Agate (banded chalcedony), flint (dark colored and nonbanded), and chert (light colored and nonbanded) are common names for varieties of chalcedony.


Imaginery halite crystal plane Although all crystalline substances have a regular, ordered, internal structure, different planes and directions within the crystals have different atomic environments. The isometric mineral halite illustrates this observation.  The figure to the left is a diagram of an imaginary plane cutting through a halite crystal, showing the regular arrangement sodium (s) and chlorine (c) ions.  The lines marked 1, 2, 3 and 4 represent four of the many different paths that a ray of light traveling through the crystal might take.  The light ray would encounter many more ions of sodium and chlorine along Line 1 than it would along Lines 2, 3, and 4. These differences in atomic environment can lead to differences in index of refraction, hardness, heat and electrical conductivity, thermal expansion, growth and solution rates, and others.  The importance of these differences (called vectorial properties) will be discussed in more detail in later sections.

Twinned Microcline Feldspar, variety AmazoniteTwinning is the symmetrical intergrowth of two or more crystals of the same substance.  Three special symmetry elements are used to describe types of twinning:  1) reflection across a mirror plane referred to as the twin plane, 2) rotation about a twin axis that is common to both of the twinned individuals, and 3) inversion about a point referred to as the twin centerTwinned crystals can be described as contact twins or penetration twins.  The individual crystals in a contact twin meet along a plane referred to as the composition surface.  The individual crystals in a penetration twin pass through each other, and share a common twin axis.  The twinned microcline shown on the right is a penetration twin in which the c-axis is the twin element.

Repeated twinning is characteristic of some minerals, particularly plagioclase feldspar, calcite, rutile, and chrysoberyl.  In plagioclase and calcite, the multiple composition planes  parallel each other, producing polysynthetic twinning.  A cyclic twin results when the composition planes are not parallel, as in rutile and chrysoberyl.

Twinned Selenite Gypsum Twins are also classified by their cause.  Primary twinning occurs during crystal growth, and is thought to occur as a result of nucleation errors, due to the addition of a few atoms or ions in the wrong place on the surface of a growing crystal.  Transformation twinning occurs in response to changes in crystal structure and symmetry, as a result of falling temperature.  An example of transformation twinning is Dauphine twinning in quartz.  Deformation twinning results from the application of an applied mechanical stress.  Calcite and other carbonate minerals twins unusually easily under stress; the deformation produced caused by cutting and polishing thin sections of rocks for microscopic examination typically is enough to cause twinning in these minerals.

The notch on the end of the long bladed selenite gypsum crystal shown above is an example of primary twinning. This particular kind of twin in selenite gypsum is called a swallowtail twin because of its shape.  The swallowtail twin is a contact twin. The two individuals in the twinned crystal are on either side of a mirror plane


 

 

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