# Hermann, Carl Heinrich

# Hermann, Carl Heinrich

(*b*. Lehe, near Bremerhaven, Germany, 17 June 1898; *d*. Marburg, Germany, 12 September 1961)

*solid-state physics, crystallography*.

Hermann’s work was done in the period during which modern crystallography and solid-state theory gathered momentum after the interruption of their beginnings by World War I. In this early period his significant contributions helped to guide the development along sound mathematical lines. Much of his work is based on the structure theory developed by Arthur Schönflies and E. S. Fedorov. This theory calls for the investigation of all possible spatially periodic arrangements of matter which differ in their internal symmetry. Any of the 230 “space groups” thus determined can serve as the repeat scheme for the arrangement of atoms in a crystal.

At the time (1925) when Hermann became interested in it, the structure theory was more than thirty years old. It had remained in a dormant, and to most physicists and crystallographers highly hypothetical, state until 1912, when Max von Laue, Walter Friedrich, and Paul Knipping gave it a realistic basis through their discovery of the diffraction of X-rays traversing a crystal. Even in the early years of crystal structure analysis by W. H. and W. L. Bragg formal structure theory was disregarded. That it is now commonly used as a major tool in crystal structure determination is to no small extent the result of the simplified notations of the symmetry elements and the space groups invented simultaneously and independently by Charles Mauguin and Hermann. A combined Hermann-Mauguin nomenclature, which is well adapted to the techniques of X-ray crystal analysis, received the approval of a small international group of crystallographers meeting at Zurich in 1930 to plan the standard *Internationale Tabellen zur Bestimmung von Kristallstrukturen*. The *Tabellen*, divided into a volume on symmetry and one containing numerical tables of essential functions, appeared in 1935 with Hermann as both contributor and editor.

Another project of general benefit to crystallographers was the preparation of *Strukturberichte*, on which Hermann worked from 1925 to 1937. The first volume, written with P. P. Ewald, appeared in 1931 and covered the crystal structures known by 1928; a second volume of this series (which has been continued by others) covered structures determined between 1928 and 1932 and was published by Hermann, O. Lohrmann, and H. Philipp in 1937.

To Hermann spatial symmetry seemed to present no greater difficulty of visualization than the simpler requirements of plane geometry presented to less gifted people. In writing out the coordinates of symmetrically equivalent positions in a space group, he hardly ever took the trouble of looking them up in the tables, preferring to jot them down on the basis of internal inspection.

At the inaugural meeting of the International Union of Crystallography at Harvard in 1948, Hermann contributed an important paper on four-dimensional space groups; this was to be followed by studies of space groups in more than four dimensions. Unfortunately, these further papers were never published for lack of proof of a basic theorem which seemed reasonable and could be shown to hold in special cases but could not be established generally.

Hermann also extended Paul Niggli’s notion of “Gitterkomplexe”—that is, the occurrence of the same groups of symmetrically equivalent positions in different space groups—in an attempt to establish a systematic geometrical, and chemically significant, classification of actual crystal structures (in which, of course, different atomic species cannot occupy symmetrically equivalent positions). Hermann’s first attempt to list all lattice complexes in three-dimensional space groups was made in the *Internationale Tabellen*; he derived a simple nomenclature of univariant lattice complexes in 1960 from the symbols used for nonvariant complexes. This work is being continued by one of Hermann’s former students, E. Hellner, and his co-workers at Marburg.

Hermann attended the Gymnasium in his hometown and then studied mathematics and physics at Göttingen. He obtained his Ph. D. under Max Born in 1923 with a thesis in which Born’s newly developed theory of the optical rotatory power of crystals containing screw axes was applied to sodium chlorate. Although the numerical work was marred by wrong factors *π* in the transition from rational (Heaviside) to conventional charge units, this first calculation of its kind proved that the rotation of the plane of polarization of light passing through the crystal had at least one main cause in the screwlike arrangement of the atoms.

After a short period of work with Herman Mark and then with R. O. Herzog at the Kaiser Wilhelm Institut für Faserstoffe in Berlin, Hermann became assistant (and later lecturer) at the Institute of Theoretical Physics of the Technische Hochschule at Stuttgart. In this period, 1925–1937, he produced not only the *Strukturberichte* and the *Internationale Tabellen* but also papers on the effects of symmetry on higher-order tensorial properties and a study of the various kinds of statistical symmetry in noncrystalline and semicrystalline (mesomorphic) substances.

Matters of conscience were not taken lightly in Hermann’s family. His father, Gerhard, and his mother, the former Auguste Leipoldt, both came from a long line of Protestant clergy. of their six children Carl was the oldest; the next one, Grete, studied philosophy and mathematics, went into exile during the Hitler years, and later became principal of a teacher’s academy in Bremen. Wilhelm became a minister after being a businessman, and one of the three daughters married a clergyman. Hermann himself married Eva Lüddecke, daughter of a clergyman. He and his wife became very active members of the German group of the Society of Friends. When the Nazis took over, his position at the Technische Hochschule of Stuttgart became untenable. R. Brill, head of the X-ray laboratory at I. G. Farbenindustrie in Oppau, offered him a job; and it was there that the well-known study of the electron distribution in diamond and other simple crystals by Brill, H. G. Grimm, Hermann, and C. Peters was done. A later paper by Hermann in conjunction with W. Schlenk, Jr., was on the determination of the structure of urea adducts with hydrocarbons (1949); Hermann’s structure determination led to an entirely new concept of adduct products.

During the second half of World War II, Hermann and his wife were jailed for having listened to BBC broadcasts. After the war Hermann was appointed professor of crystallography at the University of Marburg, a post he held until his death.

## BIBLIOGRAPHY

I. Original Works. Hermann’s writings on symmetry are “Zur systematischen Strukturtheorie,” 4 pts.: I, “Eine neue Raumgruppensymbolik,” in *Zeitschrift für Kristallographie*, **68** (1928), 257–287; II, “Ableitung der 230 Raumgruppen aus ihren Kennvektoren,” *ibid*., **69** (1929), 226–249; III, “Ketten und Netzgruppen,” *ibid* 250–270; and IV, “Umergruppen,” *ibid*., 533–555: “Bemerkungen zu der vorstehenden Arbeit von Ch. Mauguin,” *ibid*., **76** (1931), 559–561; “Die Symmetriegruppen der amorphen und mesomorphen Phasen,” *ibid*. **79** (1931), 186–221, 337–343; “Kristallographie in Räumen beliebiger Dimensionszahl, I: Die Symmetrie-operationen,” in *Acta crystallographica***2** (1949), 139–145; “Translationsgruppen in *n* Dimensioned,” in *Struktur und Materia der Festkörper* (1952); and “Zur Nomenklatur der Gilterkomplexe,” in *Zeitschrift für Kristallographie*, **113** (1960). 142. 154.

Crystal physics and structures are discussed in “Über die natürliche optische Aktivität der regulären Kristalle NaCIO_{3} und NaBrO_{3}” (Göttingen, 1923), his diss., also in *Zeitschrift für Physik*, **16** (1923), 103–134; “Tensoren und Kristallsymmetrie,” in *Zeitschrift für Kristallographie*, **80** (1934), 32–45; “Anwendung der röntgenographischen Fourieranalyse aul Fragen der chemischen Bindung.” in *Annalen der Physik*, **34** (1939), 393–445, written with R. Brill, H. G. Grimm, and C. Peters; and “Die Hamstoff-Addition der aliphatischen Verbindungen,” in *Justus Liebigs Annalen der Chemie*, **565** (1949), 204–240, written with W. Schlenk, Jr., with Hermann’s crystal structure determination on pp. 212–216.

His books include *Strukturbericht 1913–1928*, supp. vol.1 to *Zeitschrift für Kristallographie* (Leipzig, 1931); *Internationale Tabellen zur Bestimmung von Kristallstrukturen*, 2 vols. (Berlin, 1935); and *Strukturbericht 1928–1932*, supp. vol. 2 to *Zeitschrift für Kristallographie* (Leipzig, 1937).

II. Secondary Literature. See P. P. Ewald, *Fifty Years of X-Ray Diffraction* (Utrecht, 1962), pp. 339, 357–360, 451, 461, 465, 689, 700; and Kathleen Lonsdale, “Obituary C. Hermann,” in *Nature*, **192** (1961), 604.

P. P. Ewald

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