Crystallography
The systematic study of crystals or “crystallography” first named by Maurice Capeller(1685–1769) was realized as a modern scientific rationalism during the Enlightenment in the 17th century. One of the pioneers at the time was Johannes Kepler(1571–1630), who studied snow crystals and their symmetry in his pamphlet “Strena Set de Nive Sexangular” ( A New Year’s Gift of Hexagonal Snow). His work included other subject matters related to the study, such as the arrangement of matters. More specifically, he conjectured that the densest and most stable form of arrangement would be the cubic and hexagonal close packings, which was an answer to the old question of stacking of cannonballs on the deck of a ship. We can now see similar packings of oranges or apples in a grocery shop. However, this seemingly simple statement has not been mathematically proven until 2003.
As many discoveries in scientific history are said to be by accidents, one of the most defining events for crystallography was also a mishap. A Parisian priest, Rene-Just Haüy mistakenly dropped a precious prismatic calcite crystal of his friends to the floor, where it shattered into pieces. When he was examining the fragments, Haüy noticed that it “had a single fracture along one of the edges of the base…I tried to divide it in other directions, and I succeeded, after several attempts, in extracting its rhomboid nucleus.” What he discovered is that crystals always fracture along their intrinsic crystallographic planes. Also, it was known from previous discoveries that in a given crystal species the interfacial angles always have the same value. With these two pieces of knowledge combined, Haüy concluded that crystals had a periodic characteristic and made a model of composed stacks of little polyhedra which he called “molécules intégrantes.” His discovery was an important event in the crystallographic history because until then, the study was mainly about the superficial morphology of crystals. Haüy’s theory led to the today’s law of rational indices, which can explain the reason why small rational numbers connect to ask crystal planes, and it is also substantially similar to the modern periodicity. In this sense, Haüy’s theory is considered a masterpiece of imagination.
Nevertheless, the theory has been questioned about outer morphology and the exact nature of the molécules intégrantes. When it comes to the complete list of symmetries that a crystal can possess, Haüy’s laws can be associated with only 2, 3, 4 and 6-fold rotational axes. Eventually, Moritz Frankenheim (in 1826) and Johann Hessel (in 1830) pointed out that this limitation produces 32 possible crystal classes. In addition to outer morphology, the second question is regarding the nature of the molécules intégrantes. Since the molécules intégrantes look like small bricks, it cannot demonstrate the observation that crystals are elastic and the concept of a space lattice was missing.
Ludwig Seeber in 1824 and Gabriel Delafosse in 1840 came up with the fact that a crystal is defined by an array of discrete points generated by determined translational operations. Later, in 1850 August Bravais developed all 14 possible lattice symmetries. Because the 14 lattices could not explain all 32 crystal classes, Bravais tried to solve this discrepancy but could not consider their combination with rotations and reflections as well as pure translations. The combination then took geometrical group theory in order to elaborate all possible combinations.
In 1879, Leonhard Sohncke presented 65 space groups but ended up ruling out certain symmetry operations. Extending Sohncke’s result, two scientists, Arthur Shoenflies and Evgraf Fedorov, started a lively correspondence agreeing on a catalog of 230 space groups in 1891. These concepts appeared to be an unnecessary complication compared with the 32 crystal classes, and it was impossible to test the concept of a space lattice or space groups. However, Fedorov was able to determine that the distribution of atoms would be identified in the first X-ray diffraction experiments and, by the help of Max von Laue and the Braggs, the notions of the space lattice and space groups were found out earlier than Fedorov had expected.
References
Glazer, Anthony Michael. Crystallography: A Very Short Introduction. Vol. 469. Oxford University Press, 2016.
Montoya, Michelle, Alberto Moscatelli, and Andrea Taroni. “Nature Milestones in Crystallography.” Nature (2014): n. pag. Web.
