CRYSTALLOGRAPHY

What is a crystal?

Something is crystalline if the atoms or ions that compose it are arranged in a regular way (i.e, a crystal has internal order due to the periodic arrangement of atoms in three dimensions). 

Gems are described as amorphous if they are non-crystalline.

 

Crystals characterized by well developed crystal faces (external surfaces) are described as euhedral . Crystals do not always show well developed crystal faces seen on euhedral examples.

 

A crystal is built up by arranging atoms and groups of atoms in regular patterns, for example at the corners of a cube or rectangular prism.

 

The basic arrangement of atoms that describes the crystal structure is identified. This is termed the unit cell.

 

Crystals must be charge balanced.  This means that the amount of negative charge must be compensated by the same amount of positive charge.

Example:

Al 3+ and O 2-:  These are combined as Al2O3 (two aluminums per three oxygens). Make sure you understand why it is not AlO (one aluminum per one oxygen!)

 

1       Morphological Crystallography

1.1     Unit Cell

1.2     Faces

1.3     Symmetry

 

 

 

 

 

 

 

 

Symmetry Operations and Elements

This symbolism will be used for a 2-fold rotation axis throughout the lectures and in your text.

 

 

 

 

Centre of Symmetry

1.4     Classes

The 32 Crystal Classes

The 32 crystal classes represent the 32 possible combinations of symmetry operations.  Each crystal class will have crystal faces that uniquely define the symmetry of the class.  These faces, or groups of faces are called crystal forms.  Note that you are not expected to memorize the crystal classes, their names, or the symmetry associated with each class.  You will, however, be expected to determine the symmetry content of crystal models, after which you can consult the tables in your textbook, lab handouts, or lecture notes.  All testing on this material in the lab will be open book.

 

In this lecture we will go over some of the crystal classes and their symmetry.  I will not be able to cover all of the 32 classes.  You will, however, see many of the 32 classes during your work in lab.  I also want to point out that it is often not easy to draw a crystal of some classes where the symmetry can be represented without adding more symmetry or that can be easily seen in a two dimensional drawing. 

1.5     Axes

·       The crystallographic axes are imaginary lines we can draw within the crystal lattice. These will define a coordinate system within the crystal.  For three dimensional space lattice we need three and in some cases four crystallographic axes that define directions within the crystal lattices. Depending on the symmetry of the lattice, the directions may or may not be perpendicular to one another, and the divisions along the coordinate axes may or may not be equal along the axes.

1.6     Form

 

Open Forms and Closed Forms

 

 

 

 

 

 

Pedions

Pinacoids

 

Domes

 

Sphenoids

 

Prisms

Pyramids

Dipyramids

Trapezohedrons

Scalenohedrons

 

Rhombohedrons

 

Disphenoids

 

Hexahedron

 

Octahedron

 

Dodecahedron

 

Tetrahexahedron

 

Trapezohedron

 

Tetrahedron

Gyroid

 

Pyritohedron

 

Diploid

 

Tetartoid

1.7     Habits and Surface Markings and their use in ID

In nature perfect crystals are rare. The faces that develop on a crystal depend on the space available for the crystals to grow. If crystals grow into one another or in a restricted environment, it is possible that no well-formed crystal faces will be developed. However, crystals sometimes develop certain forms more commonly than others, although the symmetry may not be readily apparent from these common forms. The term used to describe general shape of a crystal is habit.

Some common crystal habits are as follows (discussed previously):

Individual Crystals

Groups of Distinct Crystals

Some minerals characteristically show one or more of these habits, so habit can sometimes be a powerful diagnostic tool.

 

2       Vectorial Properties of Crystals

Tulane: Crystal form, Zones and habit p. 12

Although a crystal structure is an ordered arrangement of atoms on a lattice, as we have seen, the order may be different along different directions in the crystal.  Thus, some properties of crystals depend on direction.  These are called vectorial properties, and can be divided into two categories: continuous and discontinuous.

 

Continuous Vectorial Properties

 

Continuous vectorial properties depend on direction, but along any given the direction the property is the same.  Some of the continuous vectorial properties are:

Hardness - In some minerals there is a difference in hardness in different directions in the crystal. Examples: Kyanite, Biotite, Muscovite.  This can become an important identifying property and/or may lead to confusion about the hardness if one is not aware of the directional dependence.

 

 

Velocity of Light (Refractive Index) - For all minerals except those in the isometric system, the velocity of light is different as the light travels along different directions in the crystal.  We will use this directional dependence of light velocity as an important tool in the second half of the course.  Refractive Index is defined as the velocity of light in a material divided by the velocity of light in a vacuum.  Because the velocity of light depends on direction, the refractive index will also depend on direction.

 

 

Thermal Conductivity - The ability of a material to conduct heat is called thermal conductivity.  Like light, heat can be conducted at different rates along different directions in crystals.

 

 

Electrical Conductivity-  The ability of a material to allow the passage of electrons is called electrical conductivity, which is also directionally dependent except in isometric crystals.

 

 

Thermal Expansion - How much the crystal lattice expands as it is heated is referred to as thermal expansion.  Some crystals expand more in one direction than in others, thus thermal expansion is a vectorial property.

 

 

Compressibility - Compressibility is a measure of how the lattice is reduced as atoms are pushed closer together under pressure.  Some directions in crystals may be more compressible than others.

 

 

Discontinuous Vectorial Properties

 

Discontinuous vectorial properties pertain only to certain directions or planes within a crystal.  For these kinds of properties, intermediate directions may have no value of the property.  Among the discontinuous vectorial properties are:

Cleavage -  Cleavage is defined as a plane within the lattice along which breakage occurs more easily than along other directions.   A cleavage direction develops along zones of weakness in the crystal lattice.  Cleavage is discontinuous because it only occurs along certain planes.

 

 

Growth Rate - Growth rate is defined as the rate at which atoms can be added to the crystal. In some directions fewer atoms must be added to the crystal than in other directions, and thus some directions may allow for faster growth than others.

 

 

Solution Rate - Solution rate is the rate at which a solid can be dissolved in a solvent.  In this case it depends on how tightly bonded the atoms are in the crystal structure, and this usually depends on direction.

3       Crystal Systems

3.1     Isometric

3.2     Hexagonal

3.3     Trigonal

Characterized by a single 4-fold or 4-fold rotoinversion axis.

Tetragonal-pyramidal Class, 4, Symmetry content - 1A4

 

Since this class has a single 4-fold axis and no mirror planes, there are no pyramid faces on the bottom of the crystal.  Wulfinite is the only mineral known to crystallize in this class.

           

Tetragonal-disphenoidal Class, , Symmetry content - 14

 

With only a single 4-fold rotoinversion axis, the disphenoid faces consist of two identical faces on top, and two identical faces on the bottom, offset by 90o.  Note that there are no mirror planes in this class.  Only one rare mineral is known to form crystals of this class.

           

Tetragonal-dipyramidal Class, 4/m, Symmetry content - 1A4, 1m, i

 

This class has a single 4-fold axis perpendicular to a mirror plane.  This results in 4 pyramid faces on top that are reflected across the mirror plane to form 4 identical faces on the bottom of the crystal.  Scheelite and scapolite are the only common minerals in this class.

 

           

Tetragonal-trapezohedral Class, 422, Symmetry content - 1A4, 4A2

 

This class has a 4 fold axis perpendicular to 4 2-fold axes.  There are no mirror planes.  Only one rare mineral belongs to this class.

           

 

Ditetragonal-pyramidal Class, 4mm, Symmetry content - 1A4, 4m

 

This class has a single 4-fold axis and 4 mirror planes.  The mirror planes are not shown in the diagram, but would cut through the edges and center of the faces shown.  Note that the ditetragonal pyramid is a set of 8 faces that form a pyramid on the top of the crystal. Only one rare mineral forms in the crystal class.

           

 

Tetragonal-scalenohedral Class, 2m, Symmetry Content - 14, 2A2, 2m

 

This class has a 4-fold rotoinversion axis that is perpendicular to 2 2-fold rotation axes.  The 2 mirror planes a parallel to the  and are at 45o to the 2-fold axes.  Chalcopyrite and stannite are the only common minerals with crystals in this class.

           

Ditetragonal-dipyramidal Class, 4/m2/m2/m, Symmetry content - 1A4, 4A2, 5m, i

 

This class has the most symmetry of the tetragonal system.  It has a single 4-fold axis that is perpendicular to 4 2-fold axes.  All of the 2-fold axes are perpendicular to mirror planes.  Another mirror plane is perpendicular to the 4-fold axis.  The mirror planes are not shown in the diagram, but would cut through all of the vertical edges and through the center of the pyramid faces.  The fifth mirror plane is the horizontal plane.  Note the ditetragonal-dipyramid consists of the 8 pyramid faces on the top and the 8 pyramid faces on the bottom.  

 

Common minerals that occur with this symmetry are anatase, cassiterite, apophyllite, zircon, and vesuvianite.

3.4     Orthorhombic

Characterized by having only two fold axes or a 2-fold axis and 2 mirror planes.

 

 

Rhombic -disphenoidal Class, 222, Symmetry content - 3A2

 

In this class there are 3  2-fold axis and no mirror planes.  The 2-fold axes are all perpendicular to each other.  The disphenoid faces that define this group consist of 2 faces on top of the crystal and 2 faces on the bottom of the crystal that are offset from each other by 90o.  Epsomite is the most common rare mineral of this class.

           

 

 

 

Rhombic-pyramidal Class, 2mm (mm2), Symmetry content - 1A2, 2m

 

This class has two perpendicular mirror planes and a single 2-fold rotation axis.  Because it has not center of symmetry, the faces on the top of the crystal do not occur on the bottom.  A pyramid, is a set of 3 or more identical faces that intersect at a point.  In the case of the rhombic pyramid, these would be 4 identical faces, labeled p, in the diagram. 

           

 

Hemimorphite is the most common mineral with this symmetry.

Rhombic-dipyramidal Class, 2/m2/m2/m, Symmetry content - 3A2, 3m, i

 

This class has 3 perpendicular 2-fold axes that are perpendicular to 3 mirror planes.  The dipyramid faces consist of 4 identical faces on top and 4 identical faces on the bottom that are related to each other by reflection across the horizontal mirror plane or by rotation about the horizontal 2-fold axes.

 

The most common minerals in this class are andalusite, anthophyllite, aragonite, barite, cordierite, olivine, sillimanite, stibnite, sulfur, and topaz.

3.5     Monoclinic

Characterized by having only  mirror plane(s) or a single 2-fold axis.

Sphenoidal Class,  2, Symmetry content - 1A2

 

In this class there is a single 2-fold rotation axis.  Faces related by a 2-fold axis are called sphenoids, thus this is the sphenoidal class. Only rare minerals belong to this class.

           

 

 

 

Domatic Class, m, Symmetry content - 1m

 

This class has a single mirror plane.  Faces related by a mirror plane are called domes, thus this is the domatic class.  Only 2 rare minerals crystallize in this class.

           

 

 

 Prismatic Class, 2/m. Symmetry content - 1A2, m, i

 

This class has a single 2-fold axis perpendicular to a single mirror plane.  This class has pinacoid faces and prism faces.  A prism is defined as 3 or more identical faces that are all parallel to the same line.  In the prismatic class, these prisms consist of 4 identical faces, 2 of which are shown in the diagram on the front of the crystal.  The other two are on the back side of the crystal.

           

 

The most common minerals that occur in the prismatic class are the micas (biotite and muscovite), azurite, chlorite, clinopyroxenes, epidote, gypsum, malachite, kaolinite, orthoclase, and talc.

3.6     Triclinic

Characterized by only 1-fold or 1-fold rotoinversion axis

 

Pedial Class,   1, Symmetry content - none

 

In this class there is no symmetry, so all crystal faces are unique and are not related to each other by symmetry.  Such faces are called Pedions, thus this is the Pedial Class.  Only a few rare minerals are in this class.

Pinacoidal Class,  , Symmetry content - i

 

Since in this class there is only a center of symmetry, pairs of faces are related to each other through the center.  Such faces are called pinacoids, thus this is the pinacoidal class.  Among the common minerals with pinacoidal crystals are: microcline (K-feldspar), plagioclase, turquoise, and wollastonite.

4       Outward Appearance

4.1     Twinning

Types of Twinning

Origin of Twinning

4.2     Polycrystalline, Microcrystalline, Cryptocrystalline

5       Metamict

Metamict minerals are minerals whose crystal structure has been partially destroyed by radiation from contained radioactive elements. The breakdown of the crystal structure results from bombardment of a particles emitted by the decay of U and Th radioactive isotopes.

The mineral zircon (ZrSiO4) often has U and Th atoms substituting for Zr in the crystals structure. Since U and Th have radioactive isotopes, Zircon is often seen to occur in various stages of metamictization.

6       Amorphous (Mineraloids)

By definition, a mineral has to have an ordered atomic arrangement, or crystalline structure. There are some Earth materials that fit all other parts of the definition of a mineral, yet do not have a crystalline structure. Such compounds are termed amorphous (without form).

Some of these amorphous compounds are called mineraloids. These usually form at low temperatures and pressures during the process of chemical weathering and form mammillary, botryoidal, and stalactitic masses with widely varying chemical compositions. Limonite [FeO.(OH).nH2O] and allophane ( a hydrous aluminum silicate) are good examples.

7       Polymorphism

Polymorphism means many forms or shapes. It is when minerals have the same chemical composition but different crystal structures resulting in different minerals. Diamond and graphite are both composed of carbon but obviously different minerals with vastly different physical and optical properties. Graphite is the soft pencil lead and used as a lubricant, while diamond is a hard gemstone and used as an abrasive for cutting in its industrial applications.

 

Polymorphism means "many forms". In mineralogy it means that a single chemical

composition can exist with two or more different crystal structures. As we will see when we look more closely at crystal structures, if a crystal is subjected to different pressures and temperatures, the arrangement of atoms depends on the sizes of the atoms, and the sizes change with temperature and pressure. In general, as pressure increases the volume of a crystal will decrease and a point may be reached where a more compact crystal structure is more stable. The crystal structure will then change to that of the more stable structure, and a different mineral will be in existence. Similarly, if the temperature is increased, the atoms on the crystal structure will tend to vibrate more and increase their effective size. In this case, a point may be reached where a less compact crystal structure is more stable. When the crystal structure changes to the more stable structure a different mineral will form.

The change that takes place between crystal structures of the same chemical compound are called polymorphic transformations.

8       Isomorphism

Isomorphism means one or the same form or shape. Isomorphic minerals have the same geometric structural arrangement, but with different atoms or ions in the sites that results in different minerals. Minerals with the same anion belong to isostructural groups, such as garnet and spinel groups. These groups have the same structural configuration but a wide diversity in chemical composition.

9       Pseudomorphism

Pseudomorphism means false form or shape. It is when a mineral crystal's chemical composition and/or crystal structure is changed, but the external form is preserved. An example is in the alteration of azurite crystals to malachite, and the replacement of wood by chalcedony to produce petrified wood. A common misconception is that tiger's-eye and hawk's-eye (blue tiger's-eye) are quartz pseudomorphs after the asbestos mineral crocidolite, that is the quartz replaced the asbestos fibers. This has recently been shown to be a false assumption. Heaney and Fisher (2003) have a new interpretation of the origin of tiger's-eye in that quartz crystal growth is synchronous with the crocidolite through a crack-seal vein-filling process (p. 323).

 

Pseudomorphism is the existence of a mineral that has the appearance of another mineral. Pseudomorph means false form. Pseudomorphism occurs when a mineral is altered in such a way that its internal structure and chemical composition is changed but its external form is preserved. Three mechanisms of pseudomorphism can be defined:

  1. Substitution. In this mechanism chemical constituents are simultaneously removed and replaced by other chemical constituents during alteration. An example is the replacement of wood fibers by quartz to form petrified wood that has the outward appearance of the original wood, but is composed of quartz. Another example is the alteration of fluorite which forms isometric crystals and is sometimes replaced by quartz during alteration. The resulting quartz crystals look isometric, and are said to be pseudomorphed after fluorite.
  2. Encrustation. If during the alteration process a thin crust of a new mineral forms on the surface of a preexisting mineral, then the preexisting mineral is removed, leaving the crust behind, we say that pseudomorphism has resulted from encrustation. In this case the thin crust of the new mineral will have casts of the form of the original mineral.
  3. Alteration. If only partial removal of the original mineral and only partial replacement by the new mineral has taken place, then it is possible to have a the space once occupied entirely by the original mineral be partially composed of the new mineral. This results for example in serpentine pseudomorphed after olivine or pyroxene, anhydrite (CaSO4) pseudomorphed after gypsum (CaSO4 .2H2O), limonite [FeO.(OH).nH2O] after pyrite (FeS2), and anglesite (PbSO4) after galena (PbS).

10  Bibliography and Supplementary Reading

Webster, Practical Gemmology, Lessons 1,2

Read, Gemmology, Chapters 1,2,3

Hurlbut, C. S., & Kammerling, R. C. (1991), Gemology, Chapters 1,2, NY: John Wiley & Sons, Inc.

Gemmological Association of Great Britain, FGA Foundation course materials, Chapters 1,2

GIA Colored Stones course materials

CGA Preliminary course materials, Chapters 1,2

Schumann, Walter. (1997) Gemstones of the World, NY: Sterling Publishing Co, Inc.

Harvey, Anne (1981). Jewels. London: Bellew & Higton Publishers Limited.

 

Kunz, G. F. (1971). The curious lore of precious stones. NY: Dover.