What are the 6 crystal systems of minerals?

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This site has your answer.

http://dave.ucsc.edu/myrtreia/crystal.html#SYSTEMS

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The six crystal systems of minerals are:

1. Cubic System: In this system, the crystal lattice has three equal axes (a, b, c) that intersect at right angles. An example of a mineral in this system is halite, which forms cubic-shaped crystals.

2. Tetragonal System: Crystals in this system have three axes (a, b, c) that intersect at right angles. However, two of the axes are equal in length, while the third (c) is longer or shorter. An example of a mineral in this system is zircon.

3. Orthorhombic System: This system has three axes (a, b, c) that are mutually perpendicular and of unequal length. An example of a mineral in this system is topaz.

4. Monoclinic System: Crystals in this system have three axes (a, b, c), where two are of equal length, but they do not intersect at right angles. The third axis (c) is inclined to the other two. An example of a mineral in this system is gypsum.

5. Triclinic System: This system has three axes (a, b, c) of unequal length, and none of them intersect at right angles. An example of a mineral in this system is microcline.

6. Hexagonal System: Crystals in this system have four axes (a1, a2, a3, c), with three of them forming a hexagonal prism and the fourth (c) perpendicular to the prism axes. An example of a mineral in this system is quartz.

To determine the crystal system of a mineral, scientists observe the external shape of the mineral's crystal, measure its dimensions and angles, and then compare them to known crystal systems in mineralogy textbooks or databases. Additionally, X-ray diffraction techniques can be used to analyze the internal atomic arrangement of a crystal, which further confirms its crystal system.