The revolutionary who became the foremost Russian crystallograph

Joint project of St.-Petersburg Mining museum and Forpost Nord-West.
евграф федоров
© Общественное достояние

All of St. Petersburg knew the story of the escape from prison of the anarchist theorist Pyotr Kropotkin. People were telling it again and again as an action-packed novel, adding to the story and thinking out the details. One of the participants of the adventure was young Evgraf Fedorov, the man, whose scientific accomplishments in the field of crystallography today are compared with the periodic system of Mendeleyev.

Fedorov was born in 1853 in Orenburg into the family of a military engineer. A couple of years later, the parents moved to St. Petersburg, where they focused their efforts on the education of their offspring. By the age of five, Evgraf could to read, write, and knew the multiplication table. At seven, he came across a textbook on geometry from his older brother, a high school student, and literally without non-stop read the entire book. Although later the young man changed his occupation more than once, it was his passion for geometric shapes that eventually became his fortune.

In the period from 1867 to 1877, he managed to study at the military gymnasium (dropped out, not wanting to waste time on getting a certificate), the St. Petersburg Military Engineering School (graduated in the rank of sub-lieutenant), Medical and Surgical Academy (was expelled due to lack of school certificate), and Technological Institute (left after studying two courses at the Department of Chemistry).

For the next few years, politics became his main devotion. Dissatisfaction with the existing regime caused the young man to join the secret organization "Land and Freedom". However, then among active student youth this was not uncommon. On the party’s commission, in 1877 Fedorov went to Europe to establish contacts with foreign revolutionary organizations. For example, in Germany he met prominent figures of the international labor movement: Wilhelm Liebknecht and Augustin Bebel. Back in St. Petersburg, in his own apartment he published an illegal newspaper The Beginning and even took part in organizing the escape of the famous throughout Russia revolutionary Pyotr Kropotkin.

евграф федоров
Фото © Набросок побега (рисунок карандашом Петра Кропоткина)

While in the prison of the Peter and Paul Fortress, the prominent populist fell seriously ill. He was transferred to the prison department of a military hospital, where he was allowed to walk in the courtyard under the supervision of officers. Then everything was like in a movie: a beautiful lady in an open cab drove up to the gate, a “random” passer-by distracted the guard, and as a sign the violin began to play a cheerful mazurka. Kropotkin threw off his hospital gown, under which he had put on the suit that had been handed over beforehand, and ran to the gate. A sentry and several soldiers rushed after him, but too late - the carriage was darting off along the street ... To implement this plan, it took about twenty loyal people who helped the "father of Russian anarchy" flee abroad.

All organizers and participants of the "rescue" operation were put on the wanted list. Fedorov narrowly escaped arrest and subsequently decided to end his political career: he was categorically against the terror, which his associates were increasingly talking about.

Evgraf Fedorov came to the conclusion that his future was exclusively about scientific work. He chose a university with the most complex curriculum and in 1880 enrolled to the third grade of the Mining Institute.

горный университет
© Общественное достояние

At the age of 16 in 1869, Evgraf Fedorov began writing his first work: "The Beginning of Theory of Figures", which he completed only in 1879 and published in 1885. Looking at the table of contents, one would be surprised at the concepts that teenager was fascinated with. Gonohedrons, isogons, typical isohedra and other words that are difficult to perceive. The most interesting thing is that the young man invented some of them on his own, imitating the ancient Greek mathematicians. In this work, he gave a classification of polyhedra, presented a derivation of all types of symmetry for finite figures, described parallelotopes (convex polyhedrons, by parallel transfer of which the space can be completely covered so that they do not enter each other and do not leave voids between them).

The last section of the book was devoted to crystals. He finished it already at the age of 27, while studying at the Mining University at the Department of Mineralogy. It was here that Fedorov finally decided on the scientific path. Geometric crystallography became Evgraf Fedorov's passion.

евграф федоров
Фото © Форпост Северо-Запад /

In 1883, Fedorov graduated from the Institute first on the list, and according to the tradition of the educational institution, his name was inscribed on the marble plaque. However, unlike his fellow students, who got good positions, the leader of course got no job offer. According to one of the versions, the dean found out about the graduate's revolutionary past. At that time, several years after the assassination of Alexander II, that could have cost a career.

The first job of the young specialist was the modest position of a clerk of the Geological Committee. He spent the summer months as part of the expedition to the Northern Urals as an ordinary geologist, and then, due to material difficulties, he moved there altogether, receiving in 1894 the position of the head of exploration work at the Turinsky mines in the Bogoslovsky Mining District.

Фото © Didier Descouens, Википедия

This period was marked with the most significant works of Fedorov; those raised crystallography to a fundamentally new level. If earlier the description of the external forms of crystals prevailed in the science, Fedorov looked took an insight of the materials and presented the laws of their construction.

Any crystal consists of groups of atoms repeating in space. In his work Symmetry of Regular Systems of Figures, for the first time in the history of science, he established 230 ways of arranging elementary particles in crystals and called them space groups (or Fedorov groups). The scientist predicted all possible structures of matter, all of its probable symmetry. Today, information has been accumulated on the structure of hundreds of thousands of crystalline substances. Some of the spatial groups are very common, others are extremely rare, and still others have not yet been found in nature. But whatever the newly studied structure turned out to be, it was based on one of the 230 groups predicted by Fedorov. Only in 1982 new types of structures were discovered that did not fit into classical crystallography (quasicrystals and modulated crystals).

евграф федоров
Фото © Форпост Северо-Запад /

Two devices designed by the mineralogist have also become epochal. In 1889, he proposed a project for a two-circle goniometer for measuring angles in crystals, and in 1891 he came up with a "universal" stage, placed in a microscope for optical examination of thin sections of minerals, which reduced the time required for their measurement tenfold. With these two discoveries, Evgraf Fedorov laid the foundation for a new theodolid method, which expanded the field of microscopic study of crystalline matter in many times.

федоровский столик
Фото © Вадим Смальков

An extensive cycle of scientific works written by Fedorov during expeditions to the Northern Urals and during geological exploration of the Bogoslovsky Mining District were quite successful. Already in 1895, the scientist became a professor of geology at the Moscow Agricultural Institute (now the Timiryazev Academy). In parallel, he taught at the Mining Institute, for which he traveled by train to the capital twice a week.

In 1901, he became a doctor of mineralogy and geognosy.

In 1905, the crystallographer received an offer from the Academic Council of the Petersburg Mining Institute to become its director. He accepted and became the first elected head of the Institute. Over the years of work as a rector, he opened an exploration and geological department and founded the journal Notes of the Mining Institute, which today remains one of the most authoritative Russian scientific publications in its field.

Despite the fact that Evgraf Fedorov was unanimously elected for a second term, the ministry interfered: Timashev, who headed it at that time, saw Fedorov as an "unreliable" person. Revolutionary activity in his youth "backfired" on the scientist for the second time. Until the end of his days he remained at the institute as a professor of crystallography and petrography, but concentrated on his own work: he was engaged in crystal chemical analysis and "new" geometry, in which, instead of a point, circles, balls, vectors, planes and other geometric images are taken as the main element.

евграф федоров
Фото © Форпост Северо-Запад /

Towards the end of his life, Fedorov’s theoretical prediction of the existence of 230 crystallographic structures found practical confirmation in experiments. In 1912, German scientist Max Laue proved in practice the lattice structure of crystals. Evgraf Fedorov gained worldwide fame, and his works and discoveries were broadly known and recognized. One after another, foreign Academies of Sciences and Mineralogical Societies offered him their membership. However, he was elected a full member of the national Academy of Sciences only in 1919. And five months later, he died from the effects of pneumonia.

The greatest minds of mankind thought about the laws of symmetry that underlie the world. For example, Plato described five regular polyhedra, Archimedes discovered thirteen semiregular polyhedra, Kepler and Poinsot considered four regular stellate polyhedra. Fedorov established that there are only five parallelotopes, and that alone made his name immortal. Achievements in the field of crystallography ranged him with the golden names of world science.