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Mineral
A naturally occurring crystalline solid with a highly ordered atomic structure and a definite (but not necessarily fixed) chemical composition.
What is not a mineral?
A mineral is not man made, but can be made by animals, as in the case of mollusk shells. Some things that lack internal order but meet other criteria for a mineral are called mineraloids, like volcanic glasses such as obsidian. A mineral made in a lab like lab grown rubies or diamonds are called synthetic minerals.
Symmetry element
The geometric feature that expresses the symmetry of an ordered arrangement is known as a
Reflection (mirror)
A mirror plane (m) is an imaginary line that divides a crystal into two halves, each of which, in a perfectly developed crystal, is the mirror image of the other. A reflection across a mirror plane produces a mirror image.
Center of symmetry (i)
is present in a crystal if an imaginary line can be passed from any point on its surface through its center and the same point is found on the line equidistant beyond the center on the opposite side. This is called an inversion.
Rotation
The presence of a rotation is established by rotating a motif about an imaginary axis that intersects the crystal center. When rotational symmetry is present, a specific face on a crystal is repeated n times in a complete rotation of the crystal. Each rotation is termed by an angle. A2,A3,A4,A6
Rotoinversion (A bar over A2/A3,etc)
There also exists rotoinversions, where the motif is rotated about an axis at a specific angle, and then inverted. There exists a rotoinversion for each of the angles of rotation discussed earlier.
Primitive Lattice (P)
Has nodes only at its corners
Face Centered (F)
nodes centered on all faces of the unit cell
Body Centered (I)
An extra node centered in the middle of the unit cell
Crystal System: Triclinic
a ≠ b ≠ c, alpha ≠ beta ≠ gamma ≠ 90 degrees, has only primitive lattices, 1 total
Crystal System: Monoclinic
a ≠ b ≠ c, alpha = gamma = 90 degrees ≠ beta, has primitive and body centered lattices, 2 total
Crystal system: Orthorhombic
a ≠ b ≠ c, alpha = beta = gamma = 90 degrees, it has primitive, face centered body centered, and c centered lattices, 4 in total
Crystal System: Tetragonal
a = b ≠ c, alpha = beta = gamma = 90 degrees, it has primitive and body centered lattices, 2 total
Crystal System: Hexagonal
a = b ≠ c, alpha = beta = 90 degrees, gamma = 120 degrees, it has primitive or rhombohedral lattices, 2 total
Crystal system: Isometric
a = b = c, alpha = beta = gamma = 90 degrees, it has primitive, face, and body centered lattices 3 in total