Evgraf Stepanovich Fedorov

Born Dec. 10 (22), 1853, in Orenburg; died May 21, 1919, in Petrograd. A founder of contemporary structural crystallography, geometer, petrologist, mineralogist, and geologist. Academician of the Russian Academy of Sciences (1919).

The son of a military engineer, Fedorov graduated from the Military Engineering School in 1872. In 1874, after brief service in a sapper unit, he audited courses at the Medical and Surgical Academy and then enrolled as a student in the chemistry section at the Technological Institute. After developing an interest in crystallography, he entered the Mining Institute in St. Petersburg in 1880, graduating in 1883. Fedorov joined the staff of the Geological Committee in 1885 and carried out geological research in the Northern Urals from 1885 to 1890. In 1894 he was a mining engineer at Tur’inskie Rudniki in the Urals. In 1895 he was appointed professor at the Moscow Agricultural Institute. After the revolutionary events of 1905, Fedorov became the first elected director of the Mining Institute in St. Petersburg. His reelection in 1910 was nullified by the government, which feared the development of revolutionary sentiments among the students and believed that Fedorov promoted such development. He was elected a member of the Bavarian Academy of Sciences in 1896 and an adjunct of the Imperial St. Petersburg Academy of Sciences in 1901. He resigned from the Imperial St. Petersburg Academy of Sciences in 1905 after failing to obtain support for the establishment of a mineralogical institute.

Fedorov began writing his first major work, Principles of the Theory of Figures (1885), when he was 16 years old. This fundamental work contained the ideas of most of Fedorov’s subsequent discoveries in geometry and crystallography. In particular, this work introduced parallelohedrons, that is, the convex polyhedrons upon which Fedorov based his theory of crystal structure. From 1885 to 1890 he wrote a series of papers on the structure and symmetry of crystals, culminating in the classic work The Symmetry of Regular Systems of Figures (1890). This work presented the first derivation of the 230 space groups known as Fedorov groups. The groups were derived at almost the same time by the German mathematician A. Schoenflies. Correspondence between Fedorov and Schoenflies contained mutual consultations on the derivation of the space groups, and Schoenflies later published a letter in which he confirmed that Fedorov’s derivation was the first.

While studying fundamental aspects of crystallography, Fedorov also developed a universal theodolite method in goniometry and crystal optics. In 1889 he proposed both a design for a two-circle (theodolite) goniometer for measuring angles in crystals and a new method of depicting crystals with the aid of a stereo-graphic reference system. In 1891 he invented the universal stage, which made it possible to examine a crystal under an optical microscope in different directions and to measure the crystal’s optical constants. Fedorov first described the universal theodolite method in the monograph The Theodolite Method in Mineralogy and Petrology (1893), and the method won worldwide recognition.

Fedorov’s later research in crystallography dealt with the development of crystal chemical analysis, which is a method of determining the composition of crystalline substances from the results of goniometric studies. Fedorov’s research in crystallography was summarized in his Courses in Crystallography (1891, 1897, and 1901).

In the last years of his life, Fedorov studied certain aspects of a “new geometry,” in which circles, spheres, vectors, planes, and other geometric forms replace the point as the fundamental element. Fedorov used a special feature of the new geometry, namely, the existence of n-dimensional systems, to depict, for example, crystal structures and the multicomponent composition of complex chemical compounds.

In theoretical petrology and mineralogy, Fedorov derived the relationship between the gross chemical composition of plutonic rocks and the minerals contained in the rocks. He also developed a classification and nomenclature for rocks and devised a method for the graphical representation of the chemical compositions of rocks and such complex minerals as micas, chlorites, and tourmalines with the aid of the Fedorov chemical tetrahedron. Fedorov studied and described many natural and synthetic crystals, identified several new mineral species and rocks, and proposed the idea of the magmatic segregation of minerals with sorting by specific weight (1896–99).

Fedorov’s works also dealt with the descriptive and physical geology and ore deposits of the Urals, the coast of the White Sea, and other regions, as well as with other topics in geology.

Fedorov’s ideas were developed in the works of his students, who included V. V. Nikitin, A. K. Boldyrev, and A. N. Zavaritskii. Fedorov had the rare pleasure of seeing his theoretical ideas realized in practice. The atomic structures of crystalline substances (especially minerals), as determined by means of X-ray structural analysis, strictly conformed to Fedorov’s symmetry groups.

The Academy of Sciences of the USSR established the E. S. Fedorov Prize in 1944.