Structure of Crystal Axis, Crystal System AND Crystal Field Symbols

Structure of Crystal Axis
In addition to determining or measuring the angle of the field of two large, then to be able to imagine the crystal shape we must also determine the position of the field-field coordinate axis arrangement.
In the known crystal there are seven kinds of arrangement of the different axes remember three things, namely:
The number of axes.
Judging from its axis otal there are 2 kinds:
a. Consists of 3 axis is the axis a, b, and c.
b.Terdiri of 4 axis is the axis a, b, c, and d.
The angle formed by the axis.
Viewed from the angle formed by the axis, there are 4 kinds, namely:
a. Three mutually perpendicular axes (90º).
b.Empat axis, 3 axis which lies in one plane and mutually angled 120º, being the fourth axis perpendicular to the axis of the last three.
c. Three axis, where the axis perpendicular to the other two axes. Being the last one to two axes are mutually angled between 90º and 120º and contained in one plane.
d. Three intersecting axes make an angle of more than 90º.

Parameter / unit length of the axis.
Judging from the parameters, known there are 3 kinds, namely:
a. Three axis with the same parameters.
b.Tiga axes with different parameters.
c. A single axis with different parameters with two or three other axes.

Crystal System
Based on the composition of the crystal axes that have been described above, then the world known crystal 6 (six) crystal system, namely:
1. The regular system / isometric / cubic.
This system consists of a three-axis arrangement axis having the same length and all three mutually perpendicular (a = b = c and a ┴ b ┴ c).
2. tetragonal system.
Consists of three axes where the two axes of equal length and perpendicular to one another, while the third axis or the c axis perpendicular to the axis had different lengths (a = b ≠ c and a ┴ b ┴ c).


3. hexagonal system.
Consists of four axis where the three axes have the same length and form 120º angles lie in one plane, while the fourth axis as the vertical axis and perpendicular to the axis of the other three had different lengths. The fourth axis is often called the c axis (a = b = d ≠ c and a, b, d ┴ c).
4. System ortorombis.
Consists of three axes with different length but the three mutually perpendicular axes (a ≠ b ≠ c and a ┴ b ┴ c).
5. monoclinic system.
Consists of three axes with different length, while the b-axis perpendicular to the axis of the other two, but the axis a is not perpendicular to the c (a ≠ b ≠ c and a ┴ ┴ b b and c).
6. System triklin
Consists of three axes with different length, whereas the angle formed by the third axis is not perpendicular different also.

Crystal Field Symbols
Crystal axes are straight lines that penetrate the center of the crystal. Its position is determined by the symmetry of the crystal. The crystal axes have parameters (unit of length) that can be the same or different. The parameters required for the calculation of the position of a crystal field.
For ease of illustration, the crystal field given symbol consisting of a series of round numbers and figures that show how the intersection of the field relative to the crystal axes.
In the literature there are various ways of writing the symbol of the crystal field, such as: Weiss, Miller, Nauman, Dana, and Goldschmidt.

According to Weiss in symbolism should not be any fractional number, then rounded to 2a: 3b: 6c. Meanwhile, according to Miller (Miller indeces) for ALM field will be:

1/1 A: 1/1 ½ b: 1/3 c then equated the denominator, becomes: 3/3 A: 2/3 b: 1/3 c. So that was written by Miller is the numerator is (321).