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Crystallographic axes

Crystallographic axes are the imaginary lines, which we can draw within the crystal lattice. In order to describe the faces and symmetry of crystals, a set of three or four reference axes are established.  These imaginary reference axes are established. These imaginary reference lines are called ”crystallographic axes” and are generally taken parallel to the intersection edges of major crystal faces. In fact, crystallographic axes are the reference lines which rin parallel to the edges of the unit cell and their lengths are proportional to the lengths of the unit cell edges. Thus when we say that the three edges of the cubic unit cell are equal and mutually perpendicular. The lengths of the unit cell edges measured in the direction of crystallographic axes, are called ”unit lengths” and are generally expressed as a, b, and c.

The lettering/naming of Crystallographic Axes: 

Normally the vertical crystallographic axis is labeled as ‘c’, the left to the right axis as ‘b’, and the front to back axis as ‘a’. If the axes are of equal length, they are all labeled as ‘a’. For example, in the cubic system the three equal axes are referred to as a1, a2, and ay.

One end of each axis is designated as plus and the other end as a minus. The front end of the a-axis, the right-hand end of the b-axis, and the upper end of the c-axis are positive while the opposite ends are negative.

When the crystallographic axes are not at right angles, the angle between the positive ends of b and c is referred to as α (alpha), between +a and +b as β (beta), and between +a and +b as γ (gamma).

Axial Ratio: 

The ”unit lengths” of crystallographic axes are length of the unit ell edges. These are expressed as a, b, and c. For example, for the orthorhombic mineral sulfur, the unite cell dimensions are: a=10.47 A°, b=12.87A°, and c=24.29°. Taking b as a unit of measure, we can determine the lengths a and c in terms of b. The ratio determined in this way is a:b:c = 0.813 : 1 : 1.903. This ratio which expresses the relative lengths of the unit cell edges along crystallographic axes is called ”axial ratio”.

(A) A crystal face PQR, crystallographic axes and intercepts, (B) Miller indices.

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