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What is a Crystal

Crystallography

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Crystallography

 

All minerals are crystalline. If a mineral is allowed to grow unhindered it will develop a characteristic three-dimensional shape, a crystal. A crystalline material is a solid in which the atoms, molecules, or ions it is composed of are arranged in a particular, repeating, three-dimensional microscopic pattern, forming a crystal lattice that extends in all directions (fractals). The crystal form reflects the arrangement of atoms in the molecule. This is expressed externally as flat faces arranged in geometric forms. When Quartz, for example, accumulates, the molecules of Silica will be positioned upon one another only in a way that the shape of the molecule permits. Thus, many millions of molecules will build up in a regular pattern which will show itself in the shape of the final crystal. Some crystals are large enough to see, even reaching dimensions measured in yards, and others so small they can be seen only with the most powerful microscopes. But from the tiniest to the largest, crystals of the same mineral are built to the same atomic pattern (even though their growth habits may vary). Crystallography- the study of the geometric properties and internal structures of crystals- is a fundamental part of mineralogy.

 Atomic Structure (Chemistry)

A crystal is built up of individual, identical, structural units of atoms or molecules called unit cells. The smallest group of elements in the material that constitutes the repeating pattern is the unit cell of the structure. A crystal can consist only of a few unit cells, or billions of them. The unit cell is reproduced over and over in three dimensions, constructing the larger scale internal structure of the crystal, which is called the lattice. The shape of the unit cell and the symmetry of the lattice determine the position and shape of the crystal’s faces. The crystals of many different minerals have unit cells that are the same shape but are made of different chemical elements. The final development of the faces that appear on any given crystal is determined to a large extent by the geological conditions at the time that the crystal is forming. Certain faces may be emphasized, while others disappear all together. The final form a crystal takes is known as its habit.

Crystal Symmetry

Because a crystal is built up of repeating geometric patterns, all crystals exhibit symmetry. The crystal shape is an important clue to the identification of a particular mineral, and geologist recognize patterns of crystal symmetry that fall into six main groups, called crystal systems. Each is based on the number of axes of symmetry developed. An axis in an imaginary line running through the crystal around which it can be turned to produce the same appearance from more than one side.

Faces

The sides of a crystal are termed faces, and these meet one another in interfacial angles. This gives us a valuable rule in crystallography. A crystal hardly ever grows evenly. Sometimes one face grows faster than another and so the final crystal looks nothing like the theoretical type for that mineral. However, the law of constancy of interfacial angles states that angles between the faces are always the same no matter how distorted the crystal may be. The angles can be measured on a device called a goniometer.

Cleavage

Related to the crystal structure is a property called the cleavage. Planes of weakness in the crystal lattice reveal themselves in the tendency for the crystal to split in a certain direction. A mineral like Mica, in which the silicate minerals are arranged in flat sheets, can flake away like the leaves of a book. Others, such as Calcite, have more than one cleavage plane, and upon shattering fragment into perfect mini-crystals.

Twin Crystals

A crystal may grown in two different directions from one face. Twinned crystals can be recognized by the presence of re-entrant angles - something not found in single crystals. When two or more crystals of the same species, such as gypsum or fluorite, form a symmetrical intergrowth, they are referred to as twinned crystals. Twins can form by contact (have a planar composition surface separating 2 individual crystals) or interpenetration (have an irregular composition surface separating 2 individual crystals). Penetration twinning may occur with the individual crystals at an angle to one another (as in the staurolite cross) or paralleled to one another, as in the Carlsbad twin of orthoclase. Contact twins can also occur as repeated or multiple twins, if the compositions surfaces are parallel to one another, they are called polysynthetic twins, if the composition surfaces are not parallel to one another, they are called cyclical twins.

If the twin law can be defined by a simple planar composition surface, the twin plane is always parallel to a possible crystal face and never parallel to an existing plane of symmetry (remember that twinning adds symmetry). If the twin law is a rotation axis, the composition surface will be irregular, the twin axis will be perpendicular to a lattice plane, but will never be an even-fold rotation axis of the existing symmetry.  For example twinning cannot occur on a new 2 fold axis that is parallel to an existing 4-fold axis. Sometimes during the growth of a crystal, or if the crystal is subjected to stress or temperature/pressure conditions different from those under which it originally formed, two or more intergrown crystals are formed in a symmetrical fashion.

If a twin involves three or more individual crystals, it is referred to as a multiple, or repeated, twin. Albite often forms multiple twins. Many minerals form twins, but they are particularly characteristic of some species (a group of minerals that are chemically similar), such as the “fishtail” contact twins of gypsum, or the penetration twins of fluorite.

What happens is that lattice points in one crystal are shared as lattice points in another crystal adding apparent symmetry to the crystal pairs.  Twinning, because it adds symmetry, never occurs in relation to the existing symmetry of the crystal.

Symmetry Operations that Define Twinning

Because symmetry is added to a crystal by twinning, twining can be defined by the symmetry operations that are involved.  These include:

  • Reflection across a mirror plane.  The added mirror plane would then be called a twin plane.

  • Rotation about an axis or line in the crystal.  The added rotation axis would then be called a twin axis.

  • Inversion through a point.  The added center of symmetry would then be called a twin center.

Three modes of formation of twinned crystals

  • Growth twins are the result of an interruption or change in the lattice during formation or growth due to a possible deformation from a larger substituting ion.

  • Transformation twins (Annealing twins) are the result of a change in crystal system during cooling as one form becomes unstable and the crystal structure must re-organize or transform into another more stable form.

  • Deformation or gliding twins are the result of stress on the crystal after the crystal has formed. 


    See more about crystal twinning at geologyin.com