In solid geometry (geometry of three dimensions) the position of lines planes are expressed with respect to three mutually intersecting rectangular references axes.
Since the crystals are also three-dimensional bodies bounded by flat faces, reference axes similar to those of solid geometry are also taken into consideration to designate different planes (faces) and lines (edges, zone axes etc) of crystals.
Unlike the axes of solid geometry, which are mutually perpendicular and extend indefinitely in all the three directions, crystallographic axes are of finite length and not always perpendicular to each other.
The crystals are classified into six systems each of which is characterized by a set of crystallographic axes having unique characters. The six systems are isometric, tetragonal, hexagonal, orthorhombic, monoclinic and triclinic. The axes are generally designated as lower case English alphabets ‘a’, ‘b’ and ‘c’.
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The c-axis is always vertical in position where as b-axis is perpendicular to c-axis (except triclinic system) and lies in vertical plane. The a-axis may or may not lie in horizontal plane containing b-axis. The angles between b- and c-axes, c- and a-axes and a- and b-axes are designated by ‘ P’ and ‘ Y ‘ respectively. The ratio of lengths of crystallographic axes is known as axial ratio.
Axes of isometric system: In case of isometric system all the three crystallographic axes are equal in length and they are mutually perpendicular to each other, i.e. a = b = c and a = (3 = Y=90°
Axes of tetragonal system: In case of tetragonal system the horizontal (a and b) crystallographic axes are equal in length; vertical axis (c) is either shorter or longer than the horizontal axes. All the three axes are mutually perpendicular to each other, i.e. a = b * c and a = (3 = Y = 90°
Axes of hexagonal system: The hexagonal system is characterized by three horizontal crystallographic axes of equal length, which are inclined to each other at 120°. The vertical axis is either shorter or longer than the horizontal axes and perpendicular to the horizontal crystallographic axes at the point of their intersection.
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Axes of orthorhombic system: The orthorhombic system has three crystallographic axes, which are unequal in length but perpendicular to each other i.e. a * b * c and a = (3 = Y = 90°. The a- and b-axes lie in the horizontal plane and are designated as brachy- and macro-axes respectively in old convention.
Axes of monoclinic system:
Three crystallographic axes of unequal length characterize this system. The c-axis is vertical, b-axis (ortho) is horizontal in position and perpendicular to the c-axis while a-axis (clino) is inclined to the vertical plane containing the b-c axes and slopes down towards the observer. In this case a* b* c, a=Y =90° and (3 * 90°.
Axes of triclinic system:
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In case of triclinic system all the crystallographic axes are unequal in length and inclined to each other i.e. amebic and a * (3 * Y * 90°. The c-axis is vertical, a-axis slopes to the front and right of the observer and b-axis is inclined to the right of the observer. In old convention, and b axes were designated as branchy- and macro-axes respectively.