Groth, Paul Heinrich von

(b. Magdeburg, Germany, 23 June 1843; d. Munich, Germany, 2 December 1927)

mineralogy, crystallography.

Following a trip to St. Petersburg in 1840 Groth’s father, Philipp Heinrich August Groth, lived in Magdeburg and then, from 1845, worked in Dresden as a portrait painter. His mother, Marie Steffen, was a daughter of a businessman in Frankfurt an der Oder. After attending the Kreuzschule in Dresden from 1855 to 1862, Groth studied at the Freiberg Mining Academy and at the Dresden Polytechnical School. In 1865 he entered the University of Berlin to study physics and mineralogy. He received his doctorate in 1868 and until 1870 was an assistant to the physicist Gustav Magnus. He qualified as a lecturer at the University of Berlin in 1870 and from 1870 to 1872 taught mineralogy and geology at the mining academy in Berlin. In April 1872 he assumed the new professorship of mineralogy at the University of Strasbourg, where he established a mineral collection whose catalog (1878) was considered a model of the type. On 1 September 1883 he succeeded F. von Kobell as professor of mineralogy at the University of Munich and as director of the Bavarian State Collection, which he enlarged primarily in the areas of Alpine minerals and of mineral deposits. He retired on 1 April 1924 and devoted his time to the history of science.

Groth’s first mineralogical work (1866) dealt with the titanite he discovered in the Plauenscher Grund, near Dresden, a substance that J. D. Dana named grothite in 1867. (A silicate probably related to harstigite was named grothine by F. Zambonini in 1913.) As a student of F. A. Breithaupt, Groth paid particular attention to paragenesis of minerals. In 1885, in Dauphiny, he accounted for the dependence of axinite-epidote occurrences in amphibole schists and of anatase-turnerite occurrences in gneiss by the leaching of the surrounding rock. His Topographische Übersicht der Minerallagerstätten (1917) was one of the best surveys in its time.

Groth’s most important contribution to science was his explanation of the connections between chemical composition and crystal structure. Although he did not succeed in determining the optical properties of potassium permanganate through interpolation from isomorphic mixtures with potassium perchlorate, he did recognize the crystallographic peculiarities of mixed crystals. Comparison of the analogies between crystals of the same system with similar interfacial angles led him to a new definition of isomorphism (1874) as requiring the capacity to form homogeneous mixed crystals (isomorphic mixtures) as well as the growth of crystals of each end member in solution with the other.

Systematic measurements of the influences on the crystal form of benzene derivatives with the substitution of hydroxyl, nitro, and ammonia groups, or halides or alkali metals led Groth to call this influence “morphotropy” (1870) and to conceive of, for example, mononitrophenol, dinitrophenol, and trinitrophenol as a morphotropic series. In this regard he also spoke of the morphotropic force of an element or a group of atoms, asserting that the manifestation of such a force depended on the specific morphotropic force of the atom or group of atoms (or both) that is being substituted on (1) the chemical nature of the compound in which the substitution takes place, (2) the crystal system of the compound being altered, and (3) the position of the entering group relative to the other atoms in the molecule. Sometimes the elastic deforming force changes only an axial length, but it may also cause a predictable change in the crystal system. The deforming effect is necessarily greater in regular crystals than in other crystal systems, because in the former a change of angle is not possible without a change in the system.

In 1870 Groth began the lectures that he published in 1876 as the textbook Physikalische Krystallographie. With his students he systematically investigated the optical, thermal, elastic, magnetic, and electrical properties of crystals. In 1871 Groth improved the polariscope, the stauroscope, the axial-angle instrument, and the goniometer and combined them into a universal instrument. In 1890 he simplified the reflecting goniometer and modified Koch and Emil Warburg’s device for determining the coefficients of elasticity in circular plates. His most important finding came in 1876, when he determined that crystallographically equivalent orientations are also always physically equivalent and hence that every geometric plane of symmetry of a crystal is also a physical plane of symmetry.

In 1895, in the third edition of Physikalische Krystallographie, Groth presented for the first time a derivation based on Leonard Sohncke’s ideas of the crystal forms from the simplest to the highest symmetry and discussed the theory of the space lattice. In 1904 he provided this definition:

A crystal consists of regular systems of points, placed within each other, each of which is formed of similar atoms; each of these systems of points belongs to a number of lattices, placed within each other, each of which is formed of similaratoms in parallel position; all the lattices of such a structure are congruent, that is, their elementary parallelepiped is the same [Zeitschrift für Krisrallographie, 54 (1915), 67].

During the period in which other physicists and mineralogists showed scant interest in the space lattice theory, Groth “maintained, through his teaching in Munich, the Sohnckian tradition” (Max von Laue, Geschichte der Physik [1947], p. 119).

In accordance with this definition Groth treated structural change resulting from substitution of another atom or group of atoms (or both) as a homogeneous deformation and expressed the dimensions of the unit cell by the topical parameters ψ, χ, ω, of his co-worker W. Muthmann (1894), in the equations

where in the triclinic case a, b, c are the axial lengths (expressed as a ratio a: I: c) and a, β γ are the angles. V is molecular weight divided by density, or equivalent weight; and A is the angle opposite side a in the spherical triangle with sides a, β γ (Einleitung in die chemische Krystallographle, p. 26).

In his Chemische Krystallographie (1906–1919) Groth compiled crystallographic and physical data on more than 7,000 substances, thereby facilitating their positive identification; but his data did not enable him to give a complete explanation of the relationships between chemical composition and crystal form—and above all he could not explain atomic structures. There is a certain element of tragedy in the fact that the first X-ray structural analyses of diamond, sphalerite, rock salt, fluorite, pyrite, and calcite misled Groth (1914) into thinking that molecule’s could no longer be mentioned in connection with crystals and were confined to gases, liquids, and colloids. In crystallization, molecules necessarily assumed a reciprocal orientation, a parallel or “twin” position.

In the union of two or more molecules into a single crystal particle there emerge, in the place of the earlier, internal atomic bonds, bonds between the atoms of adjacent molecules.... That parts of the molecule’s internal bonds enter into the crystal structure is shown by the.... previously observed relationship between the structure of the chemical molecule and the crystal structure, that is, crystal form [Bericlzte der Deutschen chemischen Gesellschaft, 47 (1914), 2064].

Here Groth was thinking especially of the persistence of organic ring bonds. Earlier he had pointed out the limited tendency to crystallization of very large organic molecules and the preservation of enantiomorphic molecules in the crystal structure, but he was unwilling to accept a molecular lattice.

Groth’s importance to modern structural research and to chemistry has been aptly expressed by E. H. Kraus:

Many of his views on morphotropy and isomorphism, and on chemical crystallography in general have become firmly embodied in chemical literature. Furthermore, the remarkable advances in our knowledge of crystal structure as the result of the development of X-ray analysis, dating from 1912, are in large measure due to Groth’s long and enthusiastic advocacy of the point system theory of crystal structure [American Mineralogist, 13 (1928), 96].

Groth was a member of the academies of science of Munich, St. Petersburg, and Vienna, of the National Academy of Sciences of the United States, the Accademia dei Lincei of Rome, the Royal Society, and the Geological Society of London, whose Wollaston Medal he received in 1908. He was also an honorary member of the Mineralogical Society of London, the Mineralogical Society of America, the French Society of Mineralogy and Geology, the Chemical Society of London, and the German Chemical Society, and received honorary doctorates from the universities of Cambridge, Geneva, and Prague. Groth founded the Zeitschrist für Kristallographie und Mineralogie in 1877 and from that year until 1920 edited its first fifty-five volumes.

BIBLIOGRAPHY

I. Original Works. Groth’s writings include Tabellarische Übersicht der einfachen Mineralien (Brunswick, 1874; 2nd ed., 1882; 3rd ed., 1889; 4th ed., 1898); Physikalische Krystallographie (Leipzig, 1876; 2nd ed., 1885; 3rd. ed., 1895; 4th ed., 1905); Die Mineraliensammlung der Kaiser-Wilhelm-Universität Strassburg (Strasbourg, 1878); Grundriss der Edelsteinkunde (Leipzig, 1887); Führer durch die Mineraliensammlung des bayerischen Staates in München (Munich, 1891); Einleitung in die chemische Krystallographie (Leipzig, 1904); Chemische Krystallographie, 5 vols. (Leipzig, 1906–1919), also in photocopy (University Park, pa., 1959) Elemente der physikalischen und chemischen Krystallographie (Munich—Berlin, 1921); Mineralogische Tabellen (Munich, 1921), written with K. Mieleitner; Entwicklungsgeschichte der mineralogischen Wissenschaften (Berlin, 1926, repr. 1970); and “Vorgeschichte, Gründung und Entwicklung der Zeitschrift för Kristalographie in den ersten fünfzig Jahren,” in Zeitschrift für Kristallographie, 66 (1928), 1–21.

There is a full bibliography by K. Mieleitner, “Verzeichnis der Arbeiten P. H. von Groth’s” in Zeitschrift für Kristallographie, 58 (1923), 3–6, a special issue commemorating Groth’s eightieth birthday; and in Poggendorff.

II. Secondary Literature. On Groth or his work, see G. Menzer, in Neue deutsche Biographie, VII (1966), 167–168; and C. Schiffner, in Aus dem Leben alter Freiberger Bergstudenten (Freiberg, 1935), pp. 339–341. The numerous obituaries are listed by Menzer and Poggendorff.

Walther Fischer