GROUP 1 | GROUP 2 | SYSTEM |

Isotropic | Cubic | |

Anisotropic | Uniaxial(2RIs) | Hexagonal |

Tetragonal | ||

Biaxial(3RIs) | Orthorhombic | |

Monoclinic | ||

Triclinic |

Note: 'Group' refers to type of optical properites. First observe:

- Is the crystal always dark under crossed polars ?
If yes - isotropic; If no - anisotropic (GROUP 1)

- If light passes through the crystal under cross polars, can one (uniaxial) or two (biaxial) orientations be found where the crystal appears dark? (GROUP 2)

Shapes of unit cells are determined by the crystal system, with the following results:

CRYSTAL SYSTEM | AXES LENGTHS | AXIAL ANGLES |

CUBIC | All equal | All 90 |

TETRAGONAL | a=b not = c | all 90 |

HEXAGONAL | two are equal | 2 are 90, one 120 |

ORTHORHOMBIC | all unequal | all are 90 |

MONOCLINIC | all unequal | two are 90 |

TRICLINIC | all unequal | none are 90 |

Example showing how optical properties that provide information about the crystal system can help distinguish similar looking gems!:

Blue sapphire - hexagonal - thus uniaxial.

Blue colored cubic zirconia (looks like sapphire) - cubic thus isotropic

Tanzanite (blue like sapphire) - orthorhombic thus biaxial.