Crystal Symmetry And Classification PDF

CRYSTAL SYMMETRY AND Hurlbut and HM Notations CLASSIFICATION ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO Crystallography has developed a descriptive terminology which is applied to crystals and crystal features in order to describe their structure...

CRYSTAL SYMMETRY AND Hurlbut and HM Notations CLASSIFICATION ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO Crystallography has developed a descriptive terminology which is applied to crystals and crystal features in order to describe their structure, symmetry, and shape. This terminology defines the crystal lattice which provides a mineral with its ordered internal structure. It also describes various types of symmetry. By considering what type of symmetry a mineral species possesses, the species may be categorized as a member of one of seven crystal systems and one of thirty-two crystal classes. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO TERMS TO REMEMBER Symmetry describes the periodic repetition of structural features Two general types of symmetry exist: translational symmetry and point symmetry Translational symmetry describes the periodic repetition of a motif across a length or through an area or volume. Point symmetry, on the other hand, describes the periodic repetition of a motif around a point. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO TERMS TO REMEMBER A specified motif which is translated linearly and repeated many times will produce a lattice. A lattice is an array of points which define a repeated spatial entity called a unit cell. The unit cell of a lattice is the smallest unit which can be repeated in three dimensions in order to construct the lattice. The corners of the unit cell serve as points which are repeated to form the lattice array; these points are termed lattice points. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO POINT SYMMETRY OPERATIONS 1. Reflection 2. Rotation 3. Inversion 4. Rotoinversion ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO A REFLECTION OCCURS WHEN A MOTIF ON ONE SIDE OF A PLANE PASSING THROUGH THE CENTER OF A CRYSTAL IS THE MIRROR IMAGE OF A MOTIF WHICH APPEARS ON THE OTHER SIDE OF THE PLANE. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ROTATIONAL SYMMETRY ARISES WHEN A STRUCTURAL ELEMENT IS ROTATED A FIXED NUMBER OF DEGREES ABOUT A CENTRAL POINT BEFORE IT IS REPEATED. An object has rotational symmetry if there is a center point around which the object is turned (rotated) a certain number of degrees and the object looks the same. The number of positions in which the object looks exactly the same is called the order of the symmetry. When determining order, the last rotation returns the object to its original position. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO INVERSION If a crystal possesses inversion symmetry, then every line drawn through the center of the crystal will connect two identical features on opposite sides of the crystal. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ROTOINVERSION Rotoinversion is a compound symmetry operation which is produced by performing a rotation followed by an inversion. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO In the plane only five different lattices may be produced by translation. The French crystallographer Auguste Bravais (1811-1863) established that in three-dimensional space only fourteen different lattices may be constructed (termed the Bravais lattices.) ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO Every crystal class is a member of one of the seven crystal systems: 1. Cubic/Isometric 2. Hexagonal 3. Trigonal (Rhombohedral) 4. Tetragonal 5. Orthorhombic 6. Monoclinic 7. Triclinic Every crystal class which belongs to a certain crystal system will share a characteristic symmetry element with the other members of its system. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO  CUBIC/ISOMETRIC CRYSTAL SYSTEM The crystallographic axes used in this system are of equal length and are mutually perpendicular, occurring at right angles to one another. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO  All crystals of the isometric system possess four 3-fold axes of symmetry, each of which proceeds diagonally from corner to corner through the center of the cubic unit cell. Crystals of the isometric system may also demonstrate up to three separate 4-fold axes of rotational symmetry. These axes, if present, proceed from the center of each face through the origin to the center of the opposite face and correspond to the crystallographic axes. Furthermore crystals of the isometric system may possess six 2-fold axes of symmetry which extend from the center of each edge of the crystal through the origin to the center of the opposite edge. Minerals of this system may demonstrate up to nine different mirror planes. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO GARNET Fe3Al2(SiO4)3 ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO HALITE NaCl ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO FLUORITE CaF2 ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO PYRITE FeS2 ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO  HEXAGONAL Minerals of the hexagonal crystal system are referred to three crystallographic axes which intersect at 120° and a fourth which is perpendicular to the other three. This fourth axis is usually depicted vertically. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO SYMMETRY NOTATIONS Symmetry Notations Sets of symbols denoting the symmetry elements present in a crystal are termed as symmetry notations. There are two sets of conventional notations we are going to use for our purpose. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO SYMMETRY NOTATION HURLBUT’S NOTATION HERMANN-MAUGUIN NOTATION P - denotes a plane of symmetry m - denotes a mirror plane C - denotes a center of symmetry C - denotes a center of symmetry 1, 2, 3, 4, 6 -denote axes of symmetry equivalent to An - denotes an axis of symmetry where An of Hurlbut and are in themselves indicative of the n (period of the axis) indicates the period. number of times a motif repeats around 1, 2, 3, 4, 6, - (read one bar, two bar, and so on...); the axis. There are only five of these- denote axes of rotoinversion A1, A2, A3, A4, and A6. n/m, where n = 1, 2, 1, 2.., - denotes an axis of An + C - denotes a rotoinversion axis. A1 symmetry perpendicular to a mirror plane. + inversion is equivalent to a center of nm, where n denotes an axis of symmetry and m symmetry. denotes a mirror plane parallel to the axis of symmetry, n ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO With the symmetry elements as basis, crystals are classified into classes with common characteristic symmetry features. These classes are then grouped into crystal systems each having unique symmetry feature and crystallographic parameters. Following Hurlbut's classification, the following table shows the 32 crystal classes and their symmetry elements. ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO CRYSTAL FORM Any grouping of crystal faces or facets that are arranged in the same symmetry is referred to as a crystal form. There are two types of crystal forms: 1) Open forms: An open 2) Closed forms: A closed form is one or more crystal form is a set of crystal faces faces that do not that completely enclose completely enclose space. space. Thus, in crystal classes that contain closed forms, a crystal can be made up of a single form ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO ELEMENTS OF MINERALOGY | ENGR. CARYLL JOY C. FRANCO