User:GreatStellatedDodecahedron/History of crystallography before x-rays

The story of crystallography begins in the 17th century with the work of Kepler on the structure of snowflakes and Nicolas Steno's discovery that the angles between corresponding faces in a crystalline substance are always the same. Some sources state that the history of crystallography started with the investigation of the diffraction of x-rays by Max von Laue in 1912 but that ignores the previous three centuries of scientific work in the field.

References to be used:

• Burke
• CSIC
• Authier
• Ewald
• Lima-de-Faria.

17th Century

• 1669 - In his book De solido intra solidum naturaliter contento Nicolas Steno asserted that, although the number and size of crystal faces may vary from one crystal to another, the angles between corresponding faces are always the same. This was the original statement of the first law of crystallography (Steno's law).

Conceptual developments

Drawing of square (A) and hexagonal (B) packing from Kepler's work, Strena seu de Nive Sexangula.

The hexagonal symmetry of snowflakes results from the tetrahedral arrangement of hydrogen bonds about each water molecule.

Crystals, though long admired for their regularity and symmetry, were not investigated scientifically until the 17th century. Johannes Kepler hypothesized in his work Strena seu de Nive Sexangula (A New Year's Gift of Hexagonal Snow) (1611) that the hexagonal symmetry of snowflake crystals was due to a regular packing of spherical water particles. The Danish scientist Nicolas Steno (1669) pioneered experimental investigations of crystal symmetry. Steno showed that the angles between the faces are the same in every exemplar of a particular type of crystal. René Just Haüy (1784) discovered that every face of a crystal can be described by simple stacking patterns of blocks of the same shape and size. Hence, William Hallowes Miller in 1839 was able to give each face a unique label of three small integers, the Miller indices which remain in use for identifying crystal faces. Haüy's study led to the idea that crystals are a regular three-dimensional array (a Bravais lattice) of atoms and molecules; a single unit cell is repeated indefinitely along three principal directions. In the 19th century, a complete catalog of the possible symmetries of a crystal was worked out by Johan Hessel, Auguste Bravais, Evgraf Fedorov, Arthur Schönflies and (belatedly) William Barlow (1894). Barlow proposed several crystal structures in the 1880s that were validated later by X-ray crystallography; however, the available data were too scarce in the 1880s to accept his models as conclusive.

Before the development of X-ray diffraction and X-ray crystallography (see below), the study of crystals was based on physical measurements of their geometry using a goniometer. This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question. The position in 3D space of each crystal face is plotted on a stereographic net such as a Wulff net or Lambert net. The pole to each face is plotted on the net. Each point is labelled with its Miller index. The final plot allows the symmetry of the crystal to be established.