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Haüy, Ren

Haüy, René-Just

(b. St.-Just-en-Chaussée, Oise, France, 28 February 1743; d. Paris, France, 1 June 1822)

crystallography, mineralogy.

The son of a poor weaver, Haüy received a classical and theological education through a scholarship to the Collège de Navarre in Paris, where, in 1764, he became a régent. In 1770 he was ordained a priest and was assigned a similar teaching post at the Collège Cardinal Lemoine. Encouraged by his friend Lhomond, he undertook botanical studies, but Daubenton’s lectures on mineralogy at the Jardin du Roi soon turned his interest to mineralogy.

Haüy’s first publications, presented to the Academy in 1781, on the crystal forms of garnet and calcspar (Iceland spar, calcite) were favorably reviewed by Daubenton and Bezout and led to his election as an associate member of the botanical class of the Academy in February 1783. In 1784 he published Essai d’une théorie sur la structure des cristaux, which laid the foundation of the mathematical theory of crystal structure. He left his teaching post and henceforth devoted himself entirely to the elaboration of his crystal theory and its application to mineralogical classification.

During the Revolution, Haüy showed great flexibility in response to the rapidly changing political situation; but he staunchly refused to take the oath required by the Civil Constitution of the Clergy. In 1792 he and many other members of the clergy were arrested, but he was soon released through the efforts of Étienne Geoffroy Saint-Hilaire, who had been his pupil. Having been a member of an Academy commission concerned with the metric system, Haüy became, after the dissolution of the royal academies, a secretary of the Commission on Weights and Measures. In this capacity he tried in 1793, together with Borda, to obtain the release of their fellow member Lavoisier. In 1795 Haüy began teaching courses in physics and mineralogy at the École des Mines and became a member of the newly founded Institut National des Sciences et des Arts, in the natural history and mineralogy section. In 1801 he published his main work, Traité de minéralogie, the first volume of which presented his crystal theory; in the three subsequent volumes he expounded his system of mineral classification. In this work he revised the nomenclature of minerals.

Haüy also did work in physics. In 1787 he published Exposition raisonnée de la théorie de l’éléctricité et du magnétisme, d’après les principes d’Aepinus. In contrast with Aepinus, he refrained from mathematical calculations and added Coulomb’s recent results. Like Franklin and Aepinus, Haüy assumed one hypothetical electric fluid and one magnetic fluid, although in his later works he adhered to the two-fluid theory.

Napoleon, who in 1802, while first consul, had nominated Haüy an honorary canon of Notre Dame, in the next year ordered him to write a textbook of physics for the newly instituted lycées. This book was outstanding for its clear, methodical exposition of physics, although mathematical treatment of problems was again lacking. Like most of his contemporaries, Haüy adhered to Newton’s corpuscular theory of light and to the theory that heat was caused by a “caloric matter.” His own contribution to physics consisted in his researches on double refraction in crystals, on pyroelectricity in crystals (especially tourmaline and boracite), and on piezoelectricity. Haüy’s Traité de physique brought him appointment to the Legion of Honor in 1803.

After the death of Dolomieu, Haüy became in 1802 professor of mineralogy at the Muséum d’Histoire Naturelle, where he enlarged the mineral collection (Haüy’s own collection has belonged to the Muséum since 1848). In 1809 he was also appointed to the newly created chair of mineralogy at the Sorbonne. In his Tableau comparatif (1809) Haüy compared the results of the crystallographic and chemical determinations of mineral species. In his stubborn opposition to the notions of indefinite compounds, mixed crystals, isomorphism, and polymorphism Haüy showed that, despite his mild and pliable character, he was adamant when his deepest convictions were at stake. In 1822 he published Traité de cristallographie, which contained the last version of his theory and was immediately followed by the second edition of the Traité de mineralogie, limited to the portion on systematics. In the same year his rather uneventful life came to its end.

Haüy corresponded with many mineralogists and chemists of his time. He did no field research and avoided the problems of mineral genesis. Using the large collections at his disposal, he worked primarily in descriptive, physical, and theoretical mineralogy. He lived very frugally, supporting his brother Valentin (well-known for his activities in care of the blind), after the latter’s return from Russia, and his niece and nephew. Brongniart was his successor at the Muséum and F. S. Beudant at the Sorbonne. Delafosse, who had become his assistant in 1817, gave his theory of crystal structure a more mathematical character, which was developed further by Bravais in his theory of crystal lattices.

Romé de l’Isle had deduced the various forms of the same crystal species by truncating the edges or the solid angles of the rather arbitrarily selected primitive form. Haüy established a more rigorous mathematical relationship between primary and secondary forms of the same species, and his choice of the primary form was founded on more physical grounds. The basic idea of his theory is that the primitive form of crystals of a certain species results as a nucleus from the cleavage of all their secondary forms. If mechanical division proves to be impossible, there are other phenomena—particularly striation—that reveal the nucleus. In 1793 Haüy proposed six types of primary forms: parallelepiped, rhombic dodecahedron, hexagonal dipyramid, right hexagonal prism, octahedron, and tetrahedron.

Further mathematical division of the primary forms ultimately led to the molécules intégrantes (which he had previously called molécules constituantes), the constituent molecules of the substance. These may have the shape of the primary form-as in the case of the parallelepiped—or they may differ from it-as when the octahedral nucleus of fluorite is divided into tetrahedrons with octahedral empty spaces, or when the right hexagonal prism is divided into six trigonal prisms with equilateral triangles as their bases. The values of the interfacial angles of the primitive form and the constituent molecule are characteristic and invariable for each kind of mineral, and it is assumed that the dimensions of the edges of the molecules are also constant and characteristic. Only highly symmetrical forms, such as the cube, may be common to different species: their angles and their relative dimensions are known a priori. For calcspar, too, Haüy knew the relative dimensions (1: 1: 1) of the cleavage rhombohedron a priori; and he calculated its angles on the assumption that its faces make a 45° angle with a horizontal plane when the axis is vertical.

Since the cleavage form of a crystal reveals only a definite value of the dihedral angles, which are fixed, according to the law of constancy of angles, but not the relative dimensions—cleavage of a crystal of sea salt, which ideally has a cube as its nucleus, will lead in most cases to an oblong rectangular prism—Haüy introduced the additional principle of symmetry. Faces that are crystallographically identical will show their equivalence when secondary faces are developed.

Whereas the primary forms were derived from the secondary ones by the physical procedure of cleavage, the reverse occurred when Haüy theoretically derived the secondary forms by stacking layers of contiguous molecules on the faces of the nucleus. Subsequent layers recede by one or two (rarely by three-six) rows of molecules in relation to the edges of the previous layer. When, for instance, the primary form is a cube and on each of its faces are superposed layers one (cubical) constituent molecule thick, each of which falls short of the edge of the preceding layer by one row of molecules, a dodecahedron with rhombic faces is formed. If each layer has two (or three or four) rows of molecules less than the previous layer on each edge, the ensuing pyramids will be less steep and a tetrahexahedron (twenty-four faces), in which each face of the cube has developed into a tetragonal pyramid, will emerge.

Similar laws of decrement may operate on the solid angles or parallel to the diagonals of the faces of the nucleus. Haüy’s fundamental law of decrement states that subtractions are confined to a small number of

rows of molecules, usually one or two. This statement led his successors directly to the law of rational indices (the law of rationality of intercepts), which, together with the law of constancy of angles, is fundamental to modern crystallography.

The laws of decrement are subject to the law of symmetry, which requires that the same kind of decrement be simultaneously repeated on all identical faces of the nucleus, that is, those parts of it which may be substituted for each other “without the nucleus ceasing to present the same aspect” (1815). If one face of the cube is changed, all six will undergo the same change; in a rectangular parallelepiped, however, either the two bases or the four lateral faces undergo the same change. Hemimorphic forms, such as tourmaline, caused Haüy great difficulties.

In order to discover the laws of decrement, Haüy started with regular forms: the cube of sea salt and the rhombohedron of calcspar, which have relative dimensions of 1: 1: 1. He pointed out that in all other cases observation gave information only on the angles

and not on the dimensions, the determination of which required the theory established by the more regular forms. In order to find the relative dimensions of the edges of the molecules, a definite assumption about the decrement connected with a certain secondary form had to be made.

A very important addition to Haüy’s original theory was his introduction of the notion of molecules soustractives (1793). Constituent molecules which do not possess the parallelepipedal form are combined to form parallelepiped units: two triangular prisms form a rhombic prism with angles of 120° and 60° on their basic faces; an octahedral space together with two adjoining tetrahedral molecules (fluorite) forms a parallelepiped. In this way all crystals may be conceived of as consisting of parallelepipedal units packed together in parallel positions so as to fill space, and all secondary forms are derived by stacking layers of molecules, according to laws of decrement, on primitive nuclei of the same form as these molecules. All crystals, then, possess a threefold periodicity along the edges of parallelepipeds. The agreement between Haüy’s measurements of angles and the values calculated from the application of a certain law of decrement gave proof of the correctness of these laws as well as of the numerical value of the angles and ratios of the dimensions of the subtractive molecule.

Haüy considered the subtractive molecules to be geometrical fictions, introduced for the sake of simplification of the theory. Similarly, although the nucleus was found by physical means, he emphasized as early as 1782 that the derivation of secondary forms from the primary form did not represent the physical process of crystal growth, since even the smallest crystal may show these secondary forms (the smallest fluorite crystals are cubes, although the cleavage form is an octahedron). Moreover, he stressed that the nucleus should not be conceived of too literally, for it is found throughout the crystal. This means that his crystal theory is fundamentally static and mathematical, however much physical data and physical claims about the constituent molecules may be involved. It is at the base of the modern lattice theory developed by Delafosse, Bravais, Sohncke, Fyodorov, and Schönflies.

Haüy’s belief in simplicity had some awkward consequences. He rigidly maintained, for instance, that the faces of the cleavage rhombohedron of calcspar are inclined at exactly 45° to the axis, which led to a ratio of the diagonals of the rhombic faces of . He rejected the more exact measurements made by Wollaston with the reflecting goniometer in 1809, because these data would imply a less simple ratio of the diagonals () than did his theoretical values. Haüy always used the less precise contact goniometer, which made it easier to make the data conformable to the “simplicity of nature.” Other crystallographers, such as H. J. Brooke (1819), inevitably criticized “the imaginary simplicity... supposed to exist naturally in the ratios of certain lines either upon or traversing a crystal” and the disposition to regard “the disagreement of an observed measurement” with this simplicity “rather as an error of the observation than a correction of his theoretic determination.”

According to Haüy himself, he started from the observation of a hexagonal prism of calcspar which was detached from a group of crystals along a plane of the cleavage rhombohedron. Further division led him to assume rhombohedral molecules. This story masks his debt to the work of Bergman. Haüy’s first publications of 1782 (on garnet and on calcspar), although correcting some errors in Bergman’s publications of 1773 and 1780 on these minerals, bear the stamp of his theory, as Romé de l’Isle pointed out in 1783. Like Bergman, Haüy superposed “integrant lamellae,” not “molecules,” on a nucleus. On a rhombic dodecahedron of garnet he stacked rhomboidal lamellae of the same form as the faces of the nucleus, and on the rhombohedron of Iceland spar he stacked steadily decreasing lamellae, forming a scalenohedron. Bergman tried to derive both the rhombic dodecahedron of garnet and the scalenohedron of calcspar from the Iceland spar crystal, which Haüy clearly recognized in 1781–1782 as totally wrong. Nevertheless, in Haüy’s theory, as in Bergman’s, the lamellae decreased continuously (and not by steps), so that the laws of decrement of the superposed layers were not put forward and a rigorous deduction of secondary forms from the primary one was still lacking. Moreover, Bergman’s article of 1773 had been mentioned in the 1781 manuscript of which Haüy’s 1782 publication was an extract. On the other hand, although starting from the same principles, Haüy’s publications of 1782 far surpassed Bergman’s in the application of those principles.

In 1784, in his Essai d’une théorie sur la structure des cristaux, Haüy criticized Bergman’s deduction of the calcite scalenohedron from the primitive form as being too vague. He proposed the notion of the crystal molecule and the laws of decrement and the constancy not only of the angles but also of the dimensions of the crystal units. He then clearly recognized the discontinuity principle: not all angles and not all inclinations of faces are possible, thus limiting the number of varieties of a crystal species. Instead of the “demi-rhombs” of his lamellar theory of 1782 he now admitted empty spaces half the size of a rhombohedral unit, since there was now at least one row less of molecules on the edges of subsequent layers.

After establishing the foundations of his crystal theory, Haüy applied it to mineralogical classification. Both Rome de l’Isle and Haüy held that the characteristic form of the constituent molecule of a compound is due to the forms, the definite proportions, and the definite arrangement of the constituent elementary particles. That is, before Proust they proposed a priori the chemical law of fixed proportions. For Haüy the mineral species was defined by a geometrical type (the form of the constituent molecule) and a chemical type (the composition of the constituent molecule); the crystallographic molecule and the chemical molecule were identical. Molecules of different species, except those of the isometric or regular system, have different forms and different composition. These ideas enabled Haüy to unite in one species minerals hitherto considered different, such as beryl and emerald, and to divide groups that had been considered varieties of the same species, such as zeolites.

Haüy’s survey of the results of crystallography and chemical analysis in relation to the classification of minerals (1809) gave a detailed exposition of the successes and difficulties his method encountered. Chemical composition decided the four traditional classes in mineralogy—acidiferous (salts), earthy, nonmetallic combustible, and metallic-and the orders and genera; the form of the constituent molecule determined the species. Only with the formes limites (the isometric forms which may be common to different species) were the physical properties—hardness, specific weight, optical behavior—and/or the chemical composition indispensable for definition of the species.

A series of mixed crystals of calcium-iron carbonate was considered as a group of subspecies of calcium carbonate, the latter assumed to have impressed its form on the whole mixture. Haüy became involved in a controversy with Berthollet, who supposed compounds to have a variable composition. In his Tableau comparatif (1809), Haüy emphasized the invariability of the form and the composition of the constituent molecule of a species but was forced to admit that the definite proportions were often blurred by heterogeneous materials accidentally mixed with the compound: “Only for geometry are all crystals pure.” He did not take up the problem of locating alien particles in crystals in which the polyhedral molecules normally left no interstices between them, as is the case with parallelepipedal molecules. He recognized that chemical analysis cannot decide which components are accidental and which essential, since even a small percentage of a substance may impress its form on a large percentage of “accidental” impurities: such was the case with the mixed crystals made by Beudant (1817), in which 10 percent iron sulfate “gave its form” to 90 percent copper sulfate.

Mitscherlich’s discovery of isomorphism (1819) was rejected by Haüy. Like Romé de l’Isle, Haüy considered pure iron spar (FeCO3) to be a pseudomorph of calcspar, and its own molecular form was considered still unknown. Consequently, he did not admit the difference of 2° between the interfacial angles of the rhombohedrons of iron carbonate and calcium carbonate found by Wollaston, although this difference would have supported in a more natural way his belief that each species has its unique characteristic form. In other cases he denied the identity of angles of substances that were believed by other scientists to be isomorphic.

Haüy admitted the polymorphism of calcium carbonate (aragonite and calcite) only reluctantly; after the discovery of the chemical identity of carbon and diamond, he concluded that geometry and physics (crystal form and properties such as specific weight and hardness) gave better criteria for distinguishing different species than did chemistry (1822). Yet in the case of two forms of titanium oxide, he said (1809, 1822) that he would regard them as different species “until new investigations... have unveiled the lack of agreement here existing between chemistry and crystallography.”

In 1784 Haüy believed that chemistry was to play a dominant role in determining mineral species. Like his friend Dolomieu, who in 1801 considered the mineralogical species to be wholly defined by one constituent molecule, Haüy in his theory always rigidly maintained that “constant composition” defined a mineral species. Yet in practice he completely changed his view, using geometrical rather than chemical data for this purpose. The results of chemical analysis allowed divergent interpretations, all the more so since their accuracy, especially in the case of the silicates, was unsatisfactory. Consequently, in his mineralogical nomenclature Haüy could not always follow the examples of Linnaeus and Lavoisier, who had introduced a rational binomial nomenclature in their respective disciplines. With the “earths” it was impossible to establish beyond doubt the chemical type because the number and proportion of the elements essential to the constituent molecule were uncertain; and only the geometrical type (the molecular form) was known with certainty. Haüy had to resort to trivial names and omitted the division of his second class into genera. In the first and fourth classes, he classified according to Lavoisier’s chemistry, although he deemed the metallic component more important than the acid part (which in Lavoisier’s nomenclature decided the generic name). Instead of Lavoisier’s carbonate de chaux there was Haüy’s chaux carbonateé; the genus copper contained the species native copper, copper oxide, copper carbonate, and so on.

It is an irony of history that Haüy’s geometrical definition of mineral species, especially in the case of the silicates, has acquired great importance in twentieth-century mineralogy through acquiring the opposite sense, that of substitution of “vicarious,” isomorphic constituents.

BIBLIOGRAPHY

I. Original Works. An extensive bibliography of Haüy’s writings, as well as a list of his biographies and portraits, are in A. Lacroix, “La vie et l’oeuvre de l’abbé René-Just Haüy,” in Bulletin de la Société française de minéralogie, 67 (1944), 15–226, esp. 95–112.

Extracts of his first memoirs, presented to the Academy, are “Extrait d’un mémoire sur la structure des cristaux de grenat,” in Journal de physique, 19 (1782), 366–370; and “Extrait d’un memoire sur la structure du spath calcaire,” ibid, 20 (1782), 33–39.

Besides some 130 articles, almost all on geometrical and physical crystallography and mineralogy, Haüy wrote the following longer works: Essai d’une théorie sur la structure des cristaux appliquée à plusieurs genres de substances cristallisées (Paris, 1784); Exposition raisonnée de la théorie de l’électricité et du magnetisme, d’apres les principes d’Aepinus (Paris, 1787); Traité de minéralogie, 4 vols. and atlas (Paris, 1801; 2nd ed., rev. and enl., 1822); Traité élémentaire de physique..., 2 vols. (Paris, 1803; 2nd ed., 1806; 3rd ed., 1821); Tableau comparatif des résultats de la cristallographie et de d’analyse chimique relativement à la classification des minéraux (Paris, 1809); Traité des caracterés physiques des pierres précieuses, pour servir à leur détermination lorsqu’elles ont été taillées (Paris, 1817); Traité de cristallographie, suivi d’une application des principes de cette science à la détermination des espèces minérales, 2 vols. and atlas (Paris, 1822).

Seventy-two letters by Haüy may be found in Lacroix (see above), pp. 113–226. More letters are in R. Hooykaas, “La correspondance de Haüy et van Marum,” in Bulletin de la Société française de minéralogie, 72 (1949), 408–448.

II. Secondary Literature. Several articles on Haüy’s life and work are in American Mineralogist, 3 (1918), and in Bulletin de la Société française de minéralogie, 67 (1944). For example, see C. Mauguin, “La structure des cristaux d’apres Haüy,” ibid., 227–262; and J. Orcel, “Haüy et la notion d’espece en mineralogie,” ibid., 265–335.

Articles by R. Hooykaas dealing with Haüy’s work and the origin of his theory are “Kristalsplijting en kristalstructuur van kalkspaat I (Bergman),” in Chemisch weekhlad, 47 (1951), 297–302; “Kristalsplijting en kristalstructuur van kalkspaat II (R. J. Haüy 1782),” ibid., 537–543; “The Species Concept in 18th Century Mineralogy,” in Archives internationales d’histoire des sciences, 5 , no. 18–19 (1952), 45–55; “Torbern Bergman’s Crystal Theory,” in Lychnos (1952), 21–54; and “Les débuts de la théorie cristallographique de R. J. Haüy, d’apres les documents originaux,” in Revue d’histoire des sciences, 8 (1955), 319–337.

Books on the history of crystallography that treat Haüy’s work are J. G. Burke, Origins of the Science of Crystals (Berkeley-Los Angeles, 1966), chs. 4, 5; P. Groth, Entwicklungsgeschichte der mineralogischen Wissenschaften (Berlin, 1926), pp. 14–57; R. Hooykaas, La naissance de la cristallographie en France au XVIIIe siécle (Paris, 1953), pp. 12–29; C. M. Marx, Geschichte der Crystallkunde (Karlsruhe, 1825), pp. 132–175; and H. Metzger, La genése de la science des cristaux (Paris, 1918), pp. 80–87, 195–206.

R. Hooykaas

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