describe crystallographic axes with diagram and symmetry of the mineral rutile drawba table showing simple forms withtheir no.of faces and miller symbols of the crystal class in which this mineral crystallizes?
Answers
Answer:
The symmetry of a crystal is the geometrical relationship between its faces and edges.
Crystal symmetry is a reflection of internal atomic symmetry.
If a crystal has symmetry, the symmetry is common to all of its properties.
By studying crystal symmetry, we can make inferences about internal atomic order.
Crystals may have any of an infinite number of shapes, but the number of possible symmetries is limited.
Crystal symmetry is the basis for dividing crystals into different groups and classes.
10.1 Symmetry
10.1.1 Introduction
The external shape of a crystal reflects its internal atomic arrangement. Of most importance is a crystal’s symmetry. As defined by the ancient Greek philosopher Aristotle, symmetry refers to the relationship between parts of an entity. Zoltai and Stout (1984) give an excellent practical definition of symmetry as it applies to crystals: “Symmetry is the order in arrangement and orientation of atoms in minerals, and the order in the consequent distribution of mineral properties.”
Figure 7.54 (Chapter 7) showed the atomic arrangement in halite. Halite, like all minerals, is built of fundamental building blocks called unit cells. In halite crystals, the unit cells have a cubic shape. Fluorite, too (Figure 7.55, Chapter 7) has a cubic unit cell. Figures 10.2, 10.3, 10.4, and 10.5, below, show other minerals with an overall cubic arrangement of their atoms. Diamond’s atomic arrangement is quite simple because it only contains carbon. Cuprite is a bit more complicated because copper and oxygen atoms alternate. Sodalite and garnet are even more complicated. But, all these minerals have cubic unit cells. The unit cells have what is called cubic symmetry.
10.2 Diamond, C
10.3 Figure 10.3 Cuprite, Cu2O
10.4 Sodalite, Na4(Si3Al3)O12Cl
10.5 Garnet, Fe3Al2Si3O12
Unit cells may have any of six fundamental shapes with different symmetries. For example, some unit cells have the shape of a shoe box instead of being cubes. Minerals with a cubic unit cell may form cubic crystals because atoms within them are arranged in a cubic pattern with identical structure in three perpendicular directions. So crystals with six identical faces (a cube) are possible. Minerals with shoe-box shaped unit cells cannot form cubic crystals. In the next chapter we will look closer at the possible unit cell shapes and the crystals they may form.
10.6 Some crystal shapes
Although the relationship between a cubic arrangement of atoms and a cube-shaped crystal may seem clear, things are not always so simple. Euhedral halite crystals are generally cubes. And, cuprite crystals (Figure 10.3) may be cubes, too, but they are also sometimes octahedra. Notice that octahedra are equivalent to cubes with their corners removed. The atomic arrangement in an octahedral crystal is the same in three perpendicular directions, just like the arrangement in a cubic crystal.