Dr Helen Lang Dept of Geology Geography West Virginia University FALL 2005 GEOLOGY 284 MINERALOGY External Shape of Crystals reflects Internal Structure External Shape is best described by Symmetry Symmetry Repetitive arrangement of features faces corners and edges of a crystal around imaginary lines points or planes Reflects internal ordering of atoms in the mineral structure Mirror Symmetry reflection across a mirror plane Exists if two halves of an image or figure are identical Mammals have Bi lateral Symmetry a mirror plane Rotational Symmetry Rotation of x degrees with respect to a line called a rotation axis leaves the image or shape unchanged 60o Rotational Symmetry If an object looks the same after rotation of 360o n that object is said to have n fold rotational symmetry or an n fold axis Called n fold because it takes n rotations to return to its original position Only certain angles folds of rotational symmetry are possible in minerals Rotational Symmetry in Minerals Name Short hand Angle 1 fold 1 360o 2 fold 2 180o 3 fold 3 120o 4 fold 4 90o 6 fold 6 60o Symbol Only these five are possible 5 fold 7 fold and other symmetries are not possible in crystals because you can t fill space with 5 sided objects 6 fold rotation illustrated 60o 60o 60o 60o 60o Rotational Symmetry of 3 D Objects 4 fold 90o rotation 90o Rotational Symmetry of 3 D Objects 6 fold 60o rotation 60o 6 fold Rotation Axis of Beryl Crystal To test for rotational symmetry Hold a wooden block or crystal with your index finger and thumb on two opposite corners opposite faces or opposite edges Rotate the block or crystal 60o 90o 120o 180o and check to see if it looks the same Grasp it in other orientations to check for additional rotation axes All symmetry elements must intersect at the center of the crystal Many Crystal shapes have several Rotation Axes that cross at the center Cube Octahedron Inversion or a Center of Symmetry symbol is 1 For every point or face on one side of the center of symmetry there is similar point or face at an equal distance on the opposite side of the center Inversion Centers in Crystals Inversion Center Only No other symmetry Inversion Center with other symmetry Some Crystals or blocks have no Center of Symmetry Trigonal pyramid pedion Rotoinversion combined rotation and inversion 4 4 bar 90o rotation plus inversion Note 2 faces or pairs of faces on top and 2 faces on the bottom off set by 90o Rotoinversion combined rotation and inversion 3 3 bar 120o rotation plus inversion Note 3 faces or pairs of faces on top and 3 faces on the bottom off set by 60o rhombohedron Dogtooth Spar also has 3 symmetry 3 axis in Rhodochrosite Rhombohedron Types of symmetry possible in Minerals 1 2 3 4 6 m 1 4 3 proper rotations mirror planes center of symmetry rotoinversion rotoinversion These can be combined in 32 ways to make crystal shapes