Question

Importance of symmetry of elements in crystal structure

Answer 1

Our discussion of symmetry in crystallography should begin with a description of crystals. Crystals are defined as solids that have an atomic structure with long-range, 3-dimensional order. Unfortunately, this long-range order cannot be absolutely confirmed by any other method than some diffraction technique. However, there are several observations that can be made that will strongly suggest that a sample is crystalline before a diffraction experiment is undertaken.

Typically, crystals have flat faces and sharp edges. Also, many crystals will have one or more directions that can be cleaved cleanly. Samples with a naturally round shape, or samples that have a concoidal fracture pattern are nearly always described as a glass having no significant, long-range, 3-D order. Similarly, materials that can be gently poked with a probe, and retain the deformed shape are gels or plastic materials and hence have not long-range, 3-D order.

When you look at several crystals from one material, you will soon notice that, although the crystals may have different sizes, all crystals have the same shape or habit. In particular, the angles between certain pairs of faces of the different crystals will be the same. This observation was first made by Nicholas Steno in 1669.2 This observation became known as the law of constancy of interfacial angles.

Figure 1. Models of crystals showing constant angles.3

Steno and others in the 17th century were interested in the specific make up of crystals that would allow them to maintain the same angles between pairs of faces.4 These scientists believed that crystals must be made of some regularly-repeating components. Through these early studies,René-Just Haüy was able to postulate that if crystals of calcite and cubic garnets were built from many small blocks, then these blocks could easily be used to describe the faces of these crystals in terms of rational indices.5 This law of rational indices forms the basis of optical crystallography.