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Wulff, Georg (Yuri Viktorovich)


(b. Nezhin, Russia, [now Ukrainian S.S.R.], 10 June 1863; d. Moscow, U.S.S.R., 25 December 1925)


Wulff’s father, Viktor Konstantinovich, was director of the boy’s Gymnasium in Nezhin. Wulff received his secondary education in Warsaw and entered the natural sciences section of the Faculty of Physics and Mathematics at Warsaw in 1880, specializing in mineralogy and crystallography with A. E. Lagorio and N. G. Egorov. His interest in crystallography was reflected in two student publications, on the morphology (1883) and physical properties of crystals (1884); and he was awarded a gold medal by the university for his research on the physical properties of quartz. After graduating in 1885, he was retained to prepare for a professorship in the department of mineralogy.

Wulff’s growing interest in physical crystallography and the structure of crystals led him to investigate the optical anomalies of crystals and the cause of rotation of the plane of polarization in crystals, as well as the piezoelectrical properties of quartz. From 1889 to 1892 he visited E. S. Fyodorov and V. 1. Vernadsky at St. Petersburg, P. Groth at Munich, and M. A. Cornu at Paris, becoming acquainted with the most recent developments in crystallography. He was the first to win recognition outside of Russia for Fyodorov’s classical research on the theory of the structure of crystals.

After defending his master’s dissertation in 1892 at Warsaw, Wulff became lecturer in the department of mineralogy there. Four years later he defended his doctoral dissertation at the University of Odessa and was appointed professor of mineralogy at the University of Kazan, where he remained for three semesters. In 1898 he became head of the department of mineralogy at the University of Warsaw; and in 1908, at Vernadsky’s invitation, he began teaching crystallography, crystal chemistry, and crystal optics at the University of Moscow. He transferred to the Shanyavsky University in 1911, heading the laboratory of crystallography, and in 1916 became director of the department of mineralogy and crystallography at the Moscow University for Women. From 1918 until his death he was professor at the University of Moscow. He started teaching and research in crystallography at the Faculty of Physics. His teaching chiefly concerned questions of geometrical crystallography, the growth of crystals and crystallophysics. He became a corresponding member of the Academy of Sciences of the U.S.S.R. in 1921, was president of the P. N. Lebedev Physical Society, and was a member of the All–Union Mineralogical Society.

Pierre Curie’s discovery of piezoelectricity in quartz (1880) and his work on the equilibrium morphology of crystals (1885) stimulated Wulff to investigate false pyroelectrical quartz (1886) and the velocity of growth and dissolution of crystals (1896, 1901). The results of this work led to the formulation of the Curie–Wulff principle (1916). Curie had demonstrated an inverse proportion between the sizes of crystal faces and their specific surface energies (Ki). In his 1895 thesis Wulff showed that for a constant volume, total surface energy would be minimized when the specific surface energies for each face (Ki) were proportional to the perpendicular distances (ni or Wulff vectors) from a central point (the Wulff point) to each face–K1 : K2 : K3:…: = n1 : n2: n3:…In modern studies of crystal growth the equilibrium form derived from the theorem is known as the Wulff construction.

Wulff also conducted detailed studies of the influence of concentration currents on the morphology of growing crystals (1895), investigated liquid crystals (1909), and invented a rotating crystallizer that, by removing the influence of concentration currents, made possible the formation of perfectly formed crystals. Fyodorov’s and Arthur Schönflies’ theoretical investigations of crystal symmetry and structure were incorporated in Wulff’s works on the theory of crystal habit (1908) and on the structure of quartz, and in optical research on pseudosymmetric crystals (1887-1890). One of the first to recognize the superiority of the Fyodorov–Goldschmidt theodolitic goniometry (the two–circle goniometer), Wulff developed methods of measuring and computing for it. In 1909 he proposed the Wulff net, the stereographic projection of a sphere with its meridians and parallels, oriented with polar axis horizontal; it is still widely used in optical, X–ray, and morphological crystallography. Wulff’s goniometric research showed an essential deviation between ideal theory and the real crystal.

In 1896 Wulff presented crystal symmetry in an original manner, by using consecutive reflection only in planes, which was incorporated in his subsequent textbooks (1923, 1926). Laue’s discovery of X–ray diffraction in 1912 drew Wulff’s attention to X–ray structural research on crystals. Concurrently with W. H. and W. L. Bragg (1913), he independently developed the diffraction relationship nλ = 2d sin θ (the Bragg–Wulff equation), the basis for the structural analysis of crystals. Wulff founded the first X–ray laboratory in Russia and conducted X–ray diffraction research there on crystal structure.

Wulff’s lectures on crystallography made extensive use of microprojection, which made possible the immediate reproduction and visual demonstration of phenomena arising in the growth and development of crystals. His students, included Sigmund Weiberg, A. V. Shubnikov, E. E. Flint, A. B.Mlodseevsky, and S.T.Konobeevsky.


I. Original Works. Some of Wulff’s writings on crystallophysics and crytallography were collected as lzbrannye raboty po kristallofizike i kristallografi (“Selected Works in Crystallophysics and Crystallography” Moscow, 1952). Separately published early works include, “Optnoe issledovanie elektricheskikh svoystv kvartsa” (“Experimental Investigation of the Electrical Properties of Quartz”), in Varshavskia universitetskia izvestia, no,3 (1886), 1–17; “O stroenii kristallov kvartsa” (“On the Structure of Quartz Crystals”) in Zapiski Imperatorskago mineralogicheskago obschestva, 2nd, ser, 25 (1889), 341–342; “Ob uproshchenii kristallograficheskikh vychisleny” (“On the Simplification of Crystallographic Computation”) ibid., 29 (1892), 58–64; “Svoystva nekotorykh psevdosimmetricheskikh kristallov v svyazi s teoriey kristallicheskogo stroenia veshchestva” (“Properties of Certain Pseudosymmetrical Crystals in Relation to the Theory of the Crystal Structure of Matter”) ibid.,29 (1892), 65–130, his master’s thesis; “K voprosu o skorostyakh rosta i rastvorenia kristallicheskikh graney” (“On the Question of the Velocity of Growth and Dissoulation of Crystal Faces”), in Varshavskia universitetskia izvestia,7 (1895), 1–40; 8 (1895), 41–56; n.s., 1 (1896), 57–88–2 (1896), 89–122, his doctoral dissl also in German in Zeitschrift für Kristallographie und Mineralogie,34 (1901), 449–530; “Die Symmetrieebene als Grundelement der Symmertrie,” ibid,,27 (1897),556–558; “Untersuchungen im Gebiete der optischen Eigenschaften isomorpher Krystalle,” ibid.,36 (1902), 1–28; “Ein Beitrag zur Theo–dolithmethode,” ibid.,37 (1903), 50–56; and “Untersuchungen über die Genauigkeitsgrenzen der Gesetze der geometrischen Krystalllographie,” ibid.,38 (1904),1–57; and Rukovodstvo po kristallografii (“Guide to Crystallography” Warsaw, 1904).

Subsequent works are Simmetria i ee proyavlenia v prirode “Symmetry and Its Appearance in Nature” ; Moscow, 1908); “Über die Krystallisation des Kaliumjodods auf dem Glimmer,” in Zeitschrift für kristallographie und Mineralogie,45 (1908), 335–345; “Zur Theorie des Krystallhabitus,” ibid., 433–472; “Über die Natur ‘flussiger’ und ‘fliessender’ Krystalle,” ibid.,46 (1909), 261–265; “Über die Kristallröntgenogramme,” in Physikalische Zeitschrift,14 (1913), 217–222; “O kapillyarnoy teorii formy kristallov” (“On the Capillary Theory of Crystal Forms”), in Zhurnal Russkago fiziko khimicheskago obshchestva pri Imperatorskom St–Peterburgskom universitete,48 (1916), 337–349; Kristally, ikh obrazovanie, vid i stroenie (“Crystals, Their Formstion, Appearance, and Structure” ; Moscow, 1917; 2nd ed., ed. and annotated by M.M. and S. Sabshnikov, 1926); Zhizn crystallov (“The Life of Crystals” ; Moscow, 1918); Osnovy kristallografii (“Principles of Crystallography” Moscow, 1923, 2nd ed., 1926); Praktichesky kurs geometricheskoy kristallografü so steregraficheskoy setkoy (“Practical Course in Geometrical Crystallography With a Stereographic Net” ; Moscow, 1924); and “O molekulyarnoy strukture muskovita” (“On the Molecular Structure of Muscovite”), in Trudy Instituta prikladnoi mineralogii i metallurgii,25 (1926), 22–29.

II. Secondary Literature. On Wulff and his work, see G. G. Leleyn and G. A. Kirsanov; “Khronologichesky ukazatel trudov Y. V. Vulfa” (“Chronological Guide to the Works of Y. V. Vulf”), in Trudy Instituta kristallografii. Akademiys nauk SSSR (1951), no. 6. 15–24; and M.von Laue, “Der Wulffsche Satz für die Gleichgewichtsform von Kristallen,” in Zeitschrift für kristallographie und Mineralogie,105 (1943), 124–133.

V. A. Frank–Kamenetsky

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