This page last updated on 10-Jan-2011 EENS 2110 MineralogyTulane University Prof. Stephen A. NelsonCrystal Form, Zones, Crystal Habit Crystal Forms As stated at the end of the last lecture, the next step is to use the Miller Index notation to designate crystal forms. A crystal form is a set of crystal faces that are related to each other by symmetry. To designate a crystal form (which could imply many faces) we use the Miller Index, or Miller-Bravais Index notation enclosing the indices in curly braces, i.e. {101} or {11 1} Such notation is called a form symbol. An important point to note is that a form refers to a face or set of faces that have the same arrangement of atoms. Thus, the number of faces in a form depends on the symmetry of the crystal. General Forms and Special Forms A general form is a form in a particular crystal class that contains faces that intersect all crystallographic axes at different lengths. It has the form symbol {hkl} All other forms that may be present are called special forms. In the monoclinic, triclinic, and orthorhombic crystal systems, the form {111} is a general form because in these systems faces of this form will intersect the a, b, and c axes at different lengths because the unit lengths are different on each axis. In crystals of higher symmetry, where two or more of the axes have equal length, a general form must intersect the equal length axes at different multiples of the unit length. Thus in the tetragonal system the form {121} is a general form. In the isometric system a general form would have to be something like {123}. Open Forms and Closed Forms A closed form is a set of crystal faces that completely enclose space. Thus, in crystal classes that contain closed forms, a crystal can be made up of a single form. An open form is one or more crystal faces that do not completely enclose space. z Example 1. Pedions are single faced forms. Since there is only one face in the form a pedion cannot completely enclose space. Thus, a crystal that has only pedions, must have at least 3 different pedions to completely enclose space. z Example 2. A prism is a 3 or more faced form wherein the crystal faces are all parallel to the same line. If the faces are all parallel then they cannot completely enclose space. Thus crystals that have prisms must also have at least one additional form in order to completely enclose space. Crystal Form, Zones, & Habit1/10/2011Page 1 of 15z Example 3. A dipyramid has at least 6 faces that meet in points at opposite ends of the crystal. These faces can completely enclose space, so a dipyramid is closed form. Although a crystal may be made up of a single dipyramid form, it may also have other forms present. In your textbook on pages 139 to 142, forms 1 through 18 are open forms, while forms 19 through 48 are closed forms. There are 48 possible forms that can be developed as the result of the 32 combinations of symmetry. We here discuss some, but not all of these forms. Pedions A pedion is an open, one faced form. Pedions are the only forms that occur in the Pedial class (1). Since a pedion is not related to any other face by symmetry, each form symbol refers to a single face. For example the form {100} refers only to the face (100), and is different from the form { 00} which refers only to the face ( 00). Note that while forms in the Pedial class are pedions, pedions may occur in other crystal classes. Pinacoids A Pinacoid is an open 2-faced form made up of two parallel faces. In the crystal drawing shown here the form {111} is a pinacoid and consists of two faces, (111) and ( ). The form {100} is also a pinacoid consisting of the two faces (100) and ( 00). Similarly the form {010} is a pinacoid consisting of the two faces (010) and (00), and the form {001} is a two faced form consisting of the faces (001) and (00 ). In this case, note that at least three of the above forms are necessary to completely enclose space. While all forms in the Pinacoid class are pinacoids, pinacoids may occur in other crystal classes as well. Domes Domes are 2- faced open forms where the 2 faces are related to one another by a mirror plane. In the crystal model shown here, the dark shaded faces belong to a dome. The vertical faces along the side of the model are pinacoids (2 parallel faces). The faces on the front and back of the model are not related to each other by symmetry, and are thus two different pedions. Crystal Form, Zones, & Habit1/10/2011Page 2 of 15Sphenoids Sphenoids are2 - faced open forms where the faces are related to each other by a 2-fold rotation axis and are not parallel to each other. The dark shaded triangular faces on the model shown here belong to a sphenoid. Pairs of similar vertical faces that cut the edges of the drawing are also pinacoids. The top and bottom faces, however, are two different pedions. Prisms A prism is an open form consisting of three or more parallel faces. Depending on the symmetry, several different kinds of prisms are possible. z Trigonal prism: 3 - faced form with all faces parallel to a 3 -fold rotation axis z Ditrigonal prism: 6 - faced form with all 6 faces parallel to a 3-fold rotation axis. Note that the cross section of this form (shown to the right of the drawing) is not a hexagon, i.e. it does not have 6-fold rotational symmetry. z Rhombic prism: 4 - faced form with all faces parallel to a line that is not a symmetry element. In the drawing to the right, the 4 shaded faces belong to a rhombic prism. The other faces in this model are pinacoids (the faces on the sides belong to a side pinacoid, and the faces on the top and bottom belong to a top/bottom pinacoid). Crystal Form, Zones, & Habit1/10/2011Page 3 of 15z Tetragonal prism: 4 - faced open form with all faces parallel to a 4-fold rotation axis or . The 4 side faces in this model make up the tetragonal prism. The top and bottom faces make up the a form called the top/bottom pinacoid. z Ditetragonal prism: 8 - faced form with all faces parallel to a 4-fold rotation axis. In the drawing, the 8 vertical faces make up the ditetragonal prism. z Hexagonal prism: 6 - faced form with all faces parallel to a 6-fold rotation axis. The 6 vertical faces in the drawing make up the hexagonal prism. Again the faces on top and bottom are the top/bottom pinacoid form. z Dihexagonal prism: 12 - faced form with all faces parallel to a 6-fold rotation axis. Note that a horizontal