Crystallography

Crystallography - Crystallography A crystal is a solid...

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Crystallography A crystal is a solid object with a geometric shape that reflects a “long-range” regular internal structure (commonly with some element of symmetry). I- Space lattices Definition : The regular internal structure of a mineral is manifested by the existence of a space lattice , which is " an array of points in space that can be repeated indefinitely" . All "points" in a lattice have identical environments (Fig. 1). In the case of a mineral or crystal, these "points" (also known as motifs ) may be considered atoms, ions, or groups of atoms/ ions. Note that a lattice has no origin. A unit cell (Fig. 1) is the smallest number of "points" which completely define the space lattice. The repetition of those points or unit cells in a space lattice is performed by certain operations which build the space lattice. Criteria used for the selection of unit cells: 1- The smallest sized unit that retains the characteristics of the space lattice (Fig. 1b). 2- Edges of the cell should coincide with symmetry axes (see below). 3- Edges of the cell related to each other by the symmetry of the lattice. Building a space lattice: from motifs to lattices: Motif Line lattice Plane lattice Space Lattice Operations : (a) elements of symmetry; (b) translations; (c) glide planes; (d) screw axes A- Elements of symmetry : Types: i- Axes of rotation ( 1, 2, 3, 4 or 6 ) : If during the rotation of a crystal around an axis one of the faces repeats itself two or more times, the crystal is said to have an axis of symmetry. Symmetry axes may be two fold (digonal) if a face is repeated twice every 360°, three fold (trigonal) if it is repeated three times, four fold (tetragonal) if it is repeated four times, or six fold (hexagonal) if that face is repeated 6 times. Figure 2a shows these relations. ii- Center ( n or i ) : If two similar faces lie at equal distances from a central point, the crystal is said to have a centre of symmetry (Fig. 2e). iii- Planes ( m ) : When one or more faces are the mirror images of each other, the crystal is said to have a plane of symmetry (Fig. 2f). Motifs related to each other by mirror planes are known as “enantiomorphs” (Fig. 4). iv- Axes of rotary inversion ( 1 , 2 , 3 , 4 or 6 ) : When two similar faces are repeated 2, 3, 4 or 6 times when the crystal is rotated 360° around an axis, but in such a
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2 way that these faces appear inverted. Therefore, if the face is repeated 2 times during a full rotation, the axis is known as a 2-fold rotary inversion axis, 3 times 3-fold rotary inversion, . .... etc. Figure 3 shows the types of rotary inversion axes. Note that axes of rotary inversion can also produce “enantiomorphs” (Fig. 4). Equivalence of some symmetry elements:
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Crystallography - Crystallography A crystal is a solid...

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