Crystal Symmetries: The Base of Crystallography

Many of the most fundamental discoveries about the basic properties of matter are closely connected with the study of crystal symmetry. The first major discovery about the true nature of crystals was made by the Danish scientist Nicolaus Steno (Niels Stensen).

In 1669, he postulated that the angles between corresponding faces of crystals are constant, regardless of the size or shape of the faces. This law became known as Steno's law, or the Law of Constancy of Interfacial Angles.

The French mineralogist Rene-Just-Hauy demonstrated why Steno's law worked. He was intrigued by the way certain minerals, notably calcite or halite, always split or cleaved into smooth-sided fragments of similar shape; he postulated that the shape of the fragments was the shape of the fundamental building block of the mineral.

He had many small blocks cut in the shape of calcite cleavage fragments and discovered that he could account for all the crystal faces of calcite by stacking these blocks in simple ways. He also found that he could account for the crystal forms of other minerals with other units, such as cubes.

Hauy not only discovered the unit cell and showed how it related to the crystal form, but also provided additional evidence that the matter was composed of discrete units, which further supported the emerging concept of atoms.

Later, scientists systematized the study of crystals. Between 1815 and 1825, the German scientists Christian Weiss and Friedrich Mohs identified the major crystal systems. In 1830, Johann Hessel , another German scientist, described thirty-two point groups.

Between 1880 and 1891, 230 crystallographic space groups were independently discovered by the Soviet mineralogist E. S. Fedorov, the German mathematician Arthur Schoenflies, and the British scientist William Barlow.

When X-rays were discovered in 1895, there was a great debate about their nature. The German scientist Max von Laue passed a beam of X-rays through a crystal and showed that they underwent diffraction, thus demonstrating that X-rays were very short wavelength electromagnetic radiation.

The father and son team of Sir William Henry and Sir Lawrence Bragg then used the diffraction of X-rays to determine the structures of unknown crystals. This technique is the basis of all modern crystal structure study.

Moseley showed that the atomic numbers were integers, that there were no undiscovered elements between adjacent elements, and established a physical basis for the periodic table.

In fact, all crystalline materials have a repeating arrangement of atoms called a lattice. This regularity and repetition of atomic patterns identifies a material as crystalline. Such familiar materials as concrete, most rocks, and nearly all metals are made of crystalline materials, despite their lack of outward crystalline form.

In fact, well-formed crystals are quite rare in nature. The geometrical rules that govern the close-packed arrangement of coins are called symmetry.

It is important to understand that the symmetry concepts can be applied to any object or pattern. Thus, the same geometrical concepts can describe coins on a table, atoms in crystals, tiles on a floor, or cells in a honeycomb.

Major types of crystal structures can be classified as the following:-
1. Triclinic
2. Monoclinic
3. Orthorhombic
4. Tetragonal
5. Cubic
6. Trigonal
7. Hexagonal

An understanding of crystal symmetry vastly simplifies the task of determining the atomic structure of materials. If the position of one atom in a crystal structure is known, the position of many other atoms may be determined automatically. In addition, almost every physical property of materials is closely related to their crystal structure and symmetry.

For example, quartz is widely used in electronics because it becomes electrically charged when it is stressed, and thus can be used to make oscillators for timing circuits. This property, called piezoelectricity, is found only in crystal classes that lack symmetry.

Optical properties of materials are also closely related to their crystal symmetries. The relationship is important to gem cutters. When light enters a crystal, it usually splits into two beams of light, a process called double refraction.

This phenomenon is exploited in some optical instruments, but is a nuisance to gem cutters, because it causes the internal reflections within the gem to appear fuzzy and dulls the luster of the gem.