Crystals: What is the Secret Underneath the Forms?


In the vernacular usage, the word ‘crystal’ resonates with purity, perfection, transparency and even durability. In ‘crystalore’, crystals are supposed to have special properties to energize and heal people. These exceptional attributes of crystals are stretched to the limit in expressions  like ‘crystal gazing’ and ‘looking at the crystal ball’ implying that crystals allow us to also see into the future.  From the emotional standpoint, a very special ‘crystal’ and the most prized of the gemstones, diamond, is also associated with pure and faithful love. What is then the ‘secret’ of crystals that makes them so intriguing to all of us, human beings, and for so many different reasons?

Origins. The word itself comes from the Greek (krystallos) and one can find several translations around the idea of ‘frozen ice’. The Greeks invented the term because the early quartz specimens were believed to be water frozen by the intense cold of distant, almost inaccessible mountains. Most likely, the remote sources of these specimens, produced by insurmountable forces in distant places added to the mystery of these geometrical objects. Pliny the Elder was the first compiler of the scientific terminology of the Greeks and perished in the eruption of Vesubius (74 A.D.) recording those events. He wrote in his Natural History: ‘crystal is only found in those high places where the winter snows have gathered in great quantity, and it is surely ice; and for this reason the Greek have given it its name.’ The geometric nature of these ‘crystals’ was also described by Pliny when he talks about ‘sexangulum’ in referring to the hexagonal cross-section of quartz, the mineral most commonly associated with the term ‘crystal’.

Linnaeus classification of the different classes of quartz.Photographed from the book by S.J. Gould.

Fig. 1. Linnaeus classification of the different classes of quartz.(Photographed from the book by S.J. Gould.[1]).

This observation relates to what is probably the most striking external property of crystals: their regular, conspicuous, geometric forms. The regularity of the common cubic common salt crystals and the ones of other minerals (i.e., pyrite) probably inspired Plato in exploring the constraints of regular polyhedra and the inferences that led to the construction of the ‘Platonic’ solids: tetrahedron, cube or hexahedron, octahedron, dodecahedron and icosahedron. These geometric forms have been the iconic representations of perfect solids for centuries in the Western world and have been used as references to classify the various geometric forms  present in crystals. However, the classification of crystals and minerals had always been rather difficult.

Classification. Even the most successful of the scientific taxonomists, Carolus Linnaeus (1707-1778), who succeeded in developing the binomial classification of living organisms (plants and animals) failed miserably in his attempts to classify the mineral world, including crystals.  S. J. Gould has argued in one of his inimitable essays that Linnaeus succeeded in the organic domain by a combination of detailed observations, dichotomic rules and possibly luck[1]. Gould also presents a page of Linnaeus’s seventh edition (1748) of Systema Naturae illustrating the master’s attempt to classify the various types of quartz using his binomial nomenclature (Fig.1).

For example, he used binomial ‘species-like’ description for the minerals of the ‘genus’ Quartzum, depending on the names of the rocks containing them: Quartzum aqueum (transparent), Quartzum album (white), Quartzum tinctum (colored) and others. Notice his attempts to classify all the varieties of this later ‘species’ referring to the common gemstones: topaz, ruby, amethyst, sapphire. However, having succeeded in the domain of animals and plants he extended indiscriminately his concepts to a different domain of the natural world. He thought that with the binomial system he could classify any object in the real word and even diseases. Minerals in their appearance, origin and formation do not share the same structural constraints as organisms do and so the classification failed to reveal the relationships among the different minerals and their different geometrical manifestations.

As more and more samples were found and characterized by their transparency, color, and especially geometrical regularity, the study of crystals faced the problem of getting a handle on the immense variety of crystal forms. A French ex-officer of the war of India (Jean–Baptiste Louis Romé de Lisle, 1736-1790) was to cut a clear trail through the jungle and introduce the right criteria to classify crystals.  Incidently, he was imprisoned by the English for five years and eventually was brought to France as a free man, where he developed a passionate interest in the study of minerals, developing catalogs for many of the private collections of the time.

A key instrument. In the history of science, many of the unsung heroes are instrument makers. We glorify the theoreticians who impose order on the kaleidoscope of shapes and forms with their platonic notions. However, we tend to ignore the craftsmen who created the instruments who made certain measurements possible; in due course, these measurements were critical to provide basis for the unifying ideas of the theoreticians. In this case, the manufacture and usage of a precision contact ‘goniometer’ (i.e. instrument to measure angles accurately) by his assistant Arnould Carangeot (ca. 1780) allowed Romé de Lisle the careful measurement of the angles between the faces (dihedral angles) of various geometrical forms of the same crystal specimen. A few years later,  the description and manufacture of a more accurate reflective instrument by William H. Wollaston  (published in 1809) permitted the measurements of dihedral angles in even smaller crystals. This parameter did indeed permit Romé de Lisle to establish and enunciate the law of constancy of angles: ‘in all crystals of the same substance the angles between corresponding faces have the same value (italics are mine)’.  The measurement and comparison of these angular parameters among different crystals allowed the correct classification of the various crystalline forms and establish, for the first time, a connection between the geometrical features of the crystals and the nature of the chemical substance forming them. Thus, although following also Linnaeus’s ideas, he initially tempted to classify crystals based only on external shapes and forms, Romé de Lisle eventually found that it was the constancy of angles what proved to be essential to organize the universe of crystal forms. 

Two-dimensional 'crystal' created with an image of musical instruments on the stage repeated along the horizontal and vertical directions. (Copyrighted CAZ).

Fig. 2. Two-dimensional ‘crystal’ created with an image of musical instruments on the stage repeated along the horizontal and vertical directions. (Copyright CAZ). In a way, this image is like a ‘sheet’ of postal stamps from the past, using the stamp from Fig. 3 (below) as a ‘unit cell’.

The next hero in the history of crystallography is René-Just Haüy (1743-1822), the son of a poor French weaver who, like many in those times, was able to obtain an education only by joining the church. He studied the classics and the natural sciences of the time, namely botany and physics, reaching the level of abbot. Because of his religious affiliation he suffered persecution and was almost put to death during the French revolution. However, he was appointed a member of the Academy of Sciences during the reign of Napoleon and became recognized by scientific societies in France and all over Europe because of his contributions to mineralogy and the study of crystals. Yet, his modest persona never abandoned him.

An accident. Abbot Haüy discovered the study of crystals at the rather old age of thirty-five, most likely by accident.  The legend goes that he unintentionally dropped and naturally broke, a specimen of calcite crystals and noticed that the resulting fragments had the same shape and the same oblique angle of the original specimen. This is a commonplace observation for any person familiar with calcite crystals but in the case of Abbot Haüy, resulted in an idea that inspired all of his seminal contributions to crystallography. From this fortuitous observation, he concluded that crystals were built of a large number of smaller, simpler and basic units-so small that the resulting faces of the crystal looked smooth-, all of which had the same shape. This elementary unit he named ‘integrant element’ or ‘integrant molecule’. He refined this original hypothesis in two major works (Traité de minéralogie, 1801; and Treatise of Crystallography, 1822) and proposed that a limited number basic building blocks are needed to construct a crystal, much like bricks making up a house.

Fig. 3. An image of a set of musical instruments on the stage making the 'asymmetric unit' of the 2-D crystal of Fig. 2.

Fig. 3. An image of a set of musical instruments on the stage making the ‘unit cell” of the 2-D crystal of Fig. 2. (Copyright CAZ).

The secret. This is the key secret underneath the beauty and variety of forms encountered in crystals. The concept of identical repeating units forming a crystal provided the two critical elements which define a crystalline lattice in modern terms: i) the underlying repetition by symmetry of a motif in a geometrical array or points (i.e. a lattice); ii) the requirement for the building block or ‘brick’ to fill the space without internal voids or spaces. Fig 2 illustrates the basic notion of a crystal in two dimensions, using the motif of a musical arrangement of instruments on a stage. The motif is repeated on the horizontal (x) and vertical (y) directions to create a two-dimensional crystal formed by the ‘unit cell’ on Fig.3. Why this motif? If you continue to read these postings you will find out why I chose this particular ‘still life’ to make a two-dimensional crystal. Although much more elaborate and artistic, similar repetitive patterns can also be found on the design of wallpaper, textile fabrics and patently in decorative motifs using majolica tiles in many Islamic buildings, for instance  the Alhambra in Granada, Spain (Fig.4).

The notion of the underlying repetition or symmetry introduced above as the critical element of crystallographic forms needs further explanation but giving due respect to the blog format, I’ll finish this entry here with the promise of elaborating this concept with further examples and discussion in future postings. We will connect also with the history of crystallography and the contributions of Auguste Bravais (1811-1863) and others.

Fig. 4. An example of the intricate beauty of the decorative patterns of the majolica tiles in the Alhambra Palace of Granada, Spain. The rhombus outlines the 'unit' that repeating along the indicated directions can generate the complete pattern.

Fig. 4. An example of the intricate beauty of the decorative patterns of the majolica tiles in the Alhambra Palace of Granada, Spain. The green rhombus outlines the ‘unit’ that repeating along the indicated directions can generate the complete pattern (copyright CAZ).

In summary, the constraints imposed by the internal repetition of an underlying geometric lattice limits the forms and variety of crystals found in the real world, which although multiple and rich in form, color and texture, cannot compare with the myriad of forms and shapes present in organisms. Minerals and crystals are classified according to their own causes of order and regularity, distinctly different from the evolutionary and genealogical principles that interconnect the richness of the ‘tree of life’. In retrospect, we cannot blame Carolus Linnaeus, the greatest of scientific taxonomists, for missing this critical difference between the organismic and mineral worlds and for trying to extend his insightful binomial nomenclature to other domains of the natural world.


Parts of this essay have been excerpted from Chapter 1 of  ‘Crystals and Life: A Personal Journey‘ (Abad-Zapatero, IUL, 2002),  with permission from the publisher (



(1)  Gould, S.J.  Linnaeus’s Luck? In the collection of essays I Have Landed. Harmony Books. NY. 2002.