MACHATSCHKI, FELIX KARL LUDWIG

(b. Arnfels, Styria, Austria, 22 September 1895; d. Vienna, Austria, 17 February 1970)

mineralogy, crystal chemistry.

Felix Karl Ludwig Machatschki was the third child of adjunct judge Felix Machatschki and his wife. Christine, née Schalmun. He was baptized a Roman Catholic. After attending primary school in Greifenburg (Carinthia) and Feldbach (Styria), Machatschki spent eight years at the classical secondary school I. Staatsgymnasium in Graz, where he graduated in 1941 with distinction. At this institution he acquired a good knowledge of classical languages, a subject he was very interested in.

In the winter term 1914–1915 he enrolled at the University of Graz to study natural sciences, intending to become a secondary school teacher. But because of World War I his studies were far from regular. From March 1915 to November 1918 he was in the military, serving in the south and at the eastern front. He was slightly wounded several times and was awarded military decorations. He left the army as a lieutenant. During his military service Machatschki had only one three-month leave for studies. Even the end of the war did not bring a normal student life, up to the end of 1919 he took part in the defense of territory in Styria and Carinthia against Yugoslavia.

But since he was gifted with intelligence and energy, he was able to finish his studies very quickly. In 1920 he passed the state examination for secondary school teachers, with natural sciences as the main subject and mathematics and physics as subsidiary subjects. He intended to specialize in botany and had begun preliminary work for a thesis in this field when in 1920 R. Scharizer offered him a job as assistant at the Institute for Mineralogy and Petrography at the University of Graz. Machatschki accepted, and though he never regretted this decision, a love for botany remained with him all his life. In 1921 he married Dr. Bertha Josepha Laurich, a botanist; their only child, Kurt, was born in 1923.

On 12 April 1922 Machatschki submitted a thesis on the chloritoid schists of the glein-alpe, and, having passed examinations in mineralogy, petrography, chemistry, and philosophy, the Ph.D. was conferred on him by the University of Graz on 2 June 1922.

He continued as Scharizer’s assistant until 1927, although initially, he claimed, not with much en thusiasm for mineralogy. But he acquired an excellent knowledge of classical mineralogy and rock analysis, mineralogy and petrography, crystallography, and mineral and rock analysis. Eventually he became interested in this field of science, especially in mineral chemistry. In 1925 he qualified as lecturer in mineralogy and petrography. His early publications show him to have been a very good and diligent young scientist, but they do not hint at his later scientific excellence.

The great break in Machatschki’s career occurred in 1927 when he obtained a Rockefeller scholarship to work in Oslo with V. M. Goldschmidt, one of the most famous mineralogists and petrographers of his time and a founder of modern geochemistry and crystal chemistry.

In 1928 Machatschki published what was probably his most important paper, even though it was only eight pages long. “Zur Frage der Struktur and Konstitution der Feldspate (Gleichzeitig vorläufige Mit teilung über die Prinzipien des Baues der Silikate).” To be able to appreciate the importance of this work it is necessary briefly to recall the situation of silicate mineralogy and crystal chemistry in 1927. At that time the chemical bulk composition of the more common silicate minerals was already rather well known, but the transformation of the analytical re sults into chemical formulas was often difficult. For example, scientists observed continuous series be tween end-members containing chemically quite different elements, for one, the olivine group, the composition of which was known to vary continuously from Mg₂SiO₄ to Fe₂SiO₄. More serious were cases where a continuous transition was observed between end-members that seemed to be salts of quite different silicic acids. A famous example was the plagioclases, one of the most common mineral groups in the earth’s crust, the chemical composition of which was known to vary from NaAlSi₃O₈ to CaAl₂Si₂O₈. In such cases it was often assumed that the corresponding silicic acids had, in spite of their different chemical formula, a similar shape on a molecular basis. In a number of cases it was almost impossible to derive for a mineral a reasonable chemical formula; this was the case for the tourmalines.

As for the crystal structure, the atomic arrange ment was known of the SiO₂ polymorphs quartz, tridymite, and cristobalite; olivine (Mg₂SiO₄), zircon (ZrSiO₄), garnet (Ca₃Al₂[SiO₄]₃), beryl (Be₃Al₂[Si₆O₁₈]), and essentially also of phenakite (Be₂SiO₄). All these minerals contained SiO₄ tetra hedra, that is, units in which four oxygen atoms occupy the corners of a (possibly slightly distorted) tetrahedron that houses a silicon atom at its center. The edge length of the tetrahedron is about 2.70 Å (angstroms), the distance Si-O about 1.65 Å. The SiO₄ tetrahedra were known to occur isolated in olivine, zircon, and garnet, polymerized via each two oxygen corners to Si₆O₁₈ rings in beryl and polymerized via all four oxygen corners in the SiO₂ polymorphs quartz, tridymite, and cristobalite.

In the field of crystal chemistry generally, the atomic arrangement in quite a number of chemically simple compounds was known, due largely to the pioneering work of the Braggs. The concept of effective ionic radii was well developed. Goldschmidt and his co-workers were active in this field and based on Wasastjerna’s value r(O^-2) = 1.32 Å, systematically derived the effective ionic radii of a large number of elements in their different states of valency. Goldschmidt’s aim was to obtain a better insight into the laws governing the distribution of the elements in the earth.

The general building principles of the silicates beyond the state discussed above were, however, unknown. Even a scientist of the rank of Goldschmidt wrote in 1926, when dealing with the silicates in his Geochemische Verteilungsgesetze der Elemente VII. Die Gesetze der Krystallochemie:

The so-called metasilicates MgSiO₃ (enstatite and po lymorphous modifications) and CaSiO₃ (wollastonite) correspond in crystal chemistry to none of the structure types of compounds ABX₃.

Therefore, the so-called magnesium metasilicate MgSiO₃ is evidently magnesium orthosilicate + “crystal silicon dioxide,” that is Mg₂SiO₄·1SiO₂, corresponding to a formula already used by P. Niggli in his textbook. The incongruent melting behavior of enstatite with its decomposition into orthosilicate and silicic acid does indeed remind one of the decomposition of a salt con taining water of crystallization. (p. 111)

And, some few lines further:

One could interpret orthoclase, which like anstatite has an incongruent melting point, as leucite +crystal silicon dioxide, or KAlSi₂O₆·1SiO₂; leucite as kalio philite plus crystal silicon dioxide, or KAlSiO₄·2SiO₂.

Such dissections of formulas may in many cases be mere idle play. However, in connection with what I have said on the analogy between the ions SiO₄ and SO₄, the new formulas seem to offer a means to study the constitution of silicates. That is to say, it should be possible to prepare, so to speak, “structural models” of these silicates that are sulfates.

Machatschki’s 1928 paper contains two pioneering concepts on the constitution of crystallized silicates. First, with the exception of some simple cases like the orthosilicates with their SiO₄ tetrahedra, he broke from the concept that crystallized silicates contain finite radicals of silicic acids; second, he postulated that Si can be substituted by Al⁺³ in the silicates.

Considering the silicates as salts of silicic acids of finite size was a widespread view at that time, and a publication of W. Wahl in 1927 along these lines was the immediate motivation for Machatscki’s paper. Wahl drew analogies between organic acids and silicic acids and, for example, formulated orthoclase (KAlSi₃O₈) as

where SiO₃ and Si₂O₅ are finite radicals and the expressions in the square brackets symbolize com plex but finite radicals (in which aluminum is fourfold coordinated). Machatschki, however, argued that “as a rule it is useless to speak of a molecule in connection with silicates.”

The next important item he addressed in this paper is the coordination number of oxygens around aluminium in silicates. Evidently, only crystal structures in which Al is coordinated to six oxygens were known at the time. But it was well known that the effective ionic radius of Al⁺³ is larger than that of Si⁺⁴, although smaller than that of Mg⁺². Gold-schmidt considered the following values to be the most reliable: r(Si⁺⁴) = 0.39 Å, r(Al⁺³) = 0.57 Å, and r(Mg⁺²) = 0.78 Å. The brilliant idea of Ma chatschki was to assume that Al⁺³ could also be 4coordinated in the silicates:

For the structure of silicate crystals it is of further importance that the ion Al⁺³ as a consequence of its size relative to that of O^-2, is on the borderline between 4 and 6 as to its coordination number toward O^-2 and, therefore, is likely to occur in silicates with both co ordination numbers toward O^-2. Where it has coordination number 4, it replace Si⁺⁴ at the centers of O^-2 tetrahedra, whereby these should expand somewhat.

This theory allowed Machatschki to postulate that the arrangement of the building units in the feldspars must correspond principally to a pure SiO₂ structure with part of the silicon ions replaced by Al⁺³ and with the ions K⁺, Na⁺, Ca⁺², and Ba⁺² in the interstices. He further recognized from the effective ionic radii r(Na⁺) = 0.98 Å, r(Ca⁺²) = 1.06 Å, r(K⁺) = 1.33 Å, and r(Ba⁺²) = 1.43 Å that complete solid solutions are to be expected between albite (NaAlSi₃O₈) and anorthite (CaAl₂Si₂O₈) on the one side, and between potassium feldspar (KAlSi₃O₈) and barium feldspar (BaAl₂Si₂O₈) on the other side. He gave to this main type of silicate the preliminary name “feldspar type”; later he spoke of Geruest silikate (framework silicates). H. Strunz introduced the expression Tektosilikate (tectosilicates).

In his 1928 paper Machatschki also presented the essential building principles of the metasilicates, the pyroxenes, of which a chemically simple repre sentative is enstatite (MgSi₃). He predicted that in this class of silicates each SiO₄tetrahedron has to share two oxygen ions with neighboring tetrahedra, probably to form chains.

Machatschki’s postulates were later confirmed by crystal structure determinations: on the feldspars by W. H. Taylor (1933), W. H. Taylor, J. A. Dar byshire, and H. Strunz (1934, and others; on the pyroxenes by B. Warren and W. L. Bragg (1928) and others.

Machatschki was always fully aware of how much he owed to others, especially to Goldschmidt and to Bragg. In his speech accepting the Roebling Medal he said:

I became acquainted [in Graz] with the work of V. M. Goldschmidt and his co–workers on the crystal structure of simple compounds. By means of a Rokefeller fellowship I was able to go to the laboratory of Goldschmidt in Oslo. Here I studied the early pub lications of Sir William L. Bragg and his co–workers on the crystal structure of some silicates. Now it was merely a synthesis of all these results which made it inevitable to abandon the assumption of discrete mol ecules in the silicates and other groups of inorganic compounds. Instead, the replacement of tetravalent Si by trivalent Al was assumed, as well as other non isovalent substitutions.

In 1928 Machatschki published two important pa pers on the crystal structure of the fahlores, a group of chemically complex minerals essentially consisting of copper, antimony (or arsenic), and sulphur. At that time the atomic arrangement in several simple crystallized sulfides was known: galena (PbS), sphalerite (cubic ZnS), wurtzite (hexagonal ZnS), pyrite (cubic FeS₂), and a few others. But the atomic arrangement was not known on anything with the chemical complexity of the fahlores. The chemical formulas given for the antimony fahlore, tetrahedrite, varied between Cu₃SbS₃ and Cu₃SbS₄.

The essential clue for the determination of struc ture was the similarity of the X–ray powder diagrams of the fahlores and of sphalerite. It was known that the atomic arrangement of sphalerite can be described by a unit cell in the form of a small cube with edge length (= lattice constant) 5.41 Å, containing four Zn and four S atoms in such a way that when the cell is continued, each Zn atom is tetrahedrally surrounded by four S atoms, and vice versa.

The unit cell of tetrahedrite also has the shape of a cube, but, as a consequence of weak reflections, with the lattice constant doubled in comparison to sphalerite; in sphalerite such a cell would contain twenty–four Zn and twenty–four S atoms (being three fourths of 4 × Z³).

For tetrahedrite Machatschki assumed first the idealized formula Cu₃SbS₃, of which the cell contains eight units, that is, it contains twenty–four Cu, eight Sb, and twenty He showed that the essential relationship between the sphalerite and the tetrahedrite structure can be described as follows: of the thirty–two Zn atoms in the sphalerite, twenty four are replaced in tetrahedrite by Cu and the remaining eight by Sb (in an ordered way); of the thirty–two atoms in sphalerite, only twenty–four are occupied (again by S), and the rest are vacancies. He further showed that the antimony atoms are not exactly at the same locations as the corresponding Zn atoms in sphalerite but are shifted by ∼ 0.5Å. All this results in Sb forming a SbS₃ pyramid with three S neighbors; eight pyramids are contained in the unit cell. One half of the Cu atoms have a tetrahedral coordination of S atoms, the other half has a one–sided coordination of only two S atoms.

Machatschki was fully aware that reliable analyses of tetrahedrite indicated a somewhat higher S content than required by the formula Cu₃SbS₃. He recognized that the formula given by G. Tschermak in 1903, SbS₃Cu₃•SbS₄CuZn₂, fit the analyses best. It can be rewritten Cu₁₀Zn₂Sb₄S₁₃, of which the cell contains two units, that is, the cell contains twenty–four Cu, Zn; eight Sb; and twenty–six S atoms (instead of the twenty–four in Machatschki’s idealized structure). In his first paper he gives a possible location for the two excess S atoms in an ordered structure, while in the second he writes; “The excess sulphur atoms can enter the structure at those places where in the fahlore the S atoms are missing in comparison with the sphalerite structure.” This would require a statistical distribution of these two S atoms. An experimental decision between the two models would have been impossible with the only roughly estimated intensities.

L. Pauling and E. W. Neuman, working on arsenic fahlore in 1934, became convinced that Machat schki’s first proposal was the correct one. The final experimental proof of this view was given for tet rahedrite by B. Wuensch in 1964.

In 1928 and 1929 Machatschki worked with Sir William L. Bragg in Manchester, and from this laboratory in 1929 he published another paper, “Die Formeleinheit des Turmalins.” The tourmalines are the most widespread borosilicates in nature, but their chemical composition is so complex that no agreement on a chemical formula had yet been reached, and the proposals varied widely. By putting ions of similar size (independent of their valence state and chemical properties) into groups, he proposed the formula XY₉Si₆B₃H_xO₃₁ for this mineral, with X for large ions (mainly Na⁺ and Ca⁺²) and Y for medium-size ions that were expected to have an octahedral oxygen coordination (mainly Al⁺³ Mg⁺², Fe⁺², and Li⁺). His suggestion was first confirmed by a structure determination of tourmaline by G. E. Hamburger and M. J. Buerger in 1948.

In Manchester Machatschki also worked on the experimental determination of the structure of danburite (CaB₂Si₂O₈), which according to his principles, should belong to the feldspar type, that is, the frame work structure. But according to Bragg (1965). “it proved to be a refractory structure to analyze,” and Machatschki’s usually high spirits were sometimes replaced by intervals of deepest despair when the crystal just would not ’come out.‴ The structure was published by C. Dunbar and F. Machatschki in 1931 and showed the expected features, although the B atom seemed to be rather strongly displaced from the center of the oxygen tetrahedron. A much later structure refinement by G. Johansson (1959) showed, however, that the BO₄ tetrahedron in danburite is quite normal.

Machatschki spent the winter term 1929-1930 in Göttingen, Where Goldschmidt was now professor. His suggestion that the arsenate mineral berzeliite has the same structure type as the garnets dates from this time. In 1930 he received invitations to the university of Graz and also to Tubingen. Because Graz could not afford the X-ray equipment he required, he went to Tubingen, where he was full professor of mineralogy and petrology until 1941 and dean from 1931 to 1933. He had now found his style of work, and his institute developed into an international center of research. He continued to work on minerals with complicated chemical compositions, while maintaining an interest in analogies of silicates with phosphates and arsenates and in other fields of mineralogy and petrography.

In 1941 he moved to Munich, but his home and institute were soon destroyed by air attacks. In 1944 Machatschki went to Vienna to succeed the late A. Himmelbauer as professor of mineralogy and petrography at the university. Soon this institute was also damaged, although work continued until the early spring of 1945. Machatschki spent the very end of the war in Styria, but he soon returned to Vienna, and in 1945 resumed his teaching and research. He went on to build the institute’s international reputation. He wrote three books covering the whole field of mineralogy, including raw materials, and served as editor of Tschermaks Mineralogische and Petrographische Mitteilung until his retirement in 1967.

Machatschki received many honors. The Bavarian Academy of Sciences elected him a member in 1943, followed by the academies in Austria, Sweden, Italy, Gottingen, the Deutsche Akademie der Naturforscher Leopoldina, and the academies in Norway and Yugoslavia. He was elected honorary member or correspondent of several scientific societies. In 1958 he received the Schrodinger Prize of the Austrian Academy of Science, in 1959 the Roebling Medal of the Mineralogical Society of America, and in 1965 the Becke Medal of the Mineralogical Society of Austria. In the same year a special Machatschki volume of Tschermaks Mineralogische and Petrographische Mitteilungan appeared. In 1961 he was awarded the Österreichisches Ehrenzeichan für Wissenschaft und Kunst, and in 1962 he became honorary citizen of his native town, Arnfels.

In spite of all the honors. Machatschki remained a modest man to the end. He liked company and a glass of wine. During his time in Vienna he had little to do with his wife and son. For years he lived in the institute. His death was a great loss for mineralogists and solid-state chemists all over the world.

In 1977 K. Walenta named a secondary arsenate mineral in his honor, and on 11 May 1984 a commemorative bronze tablet was unveiled at the Institute for Mineralogy and Crystallography and at the University of Vienna.

BIBLIOGRAPHY

I. Original Works. “Zur Frage der Struktur and Konstitution der Feldspate (Gleichzeitig vorläufige Mitteilung über die Prinzipien des Baues der Silikate),” in Zentralblatts für Mineralogie, Geologie and Paläontologie, sec. A (1928), 97–104; “Formel und Kristallstruktur des Tetraedrites,” in Norsk geologisk tidsskrift, 10 (1928), 23–32; “Präzisionsmessungen der Gitterkonstanten verschiedener Fahlerze. Formel und Struktur derselben,” in Zeitschrift für Kristallographie, 68 (1928), 204–222; “Die Formeleinheit des Turmalins”, ibid., 70 (1929), 211–233; “Berzelit, ein Arsenat vom Formel-und Strukturtypus Granat (X₃Y₂Z₃O₁₂),” ibid., 73 (1930), 123–140; “Structure of Danburite, CaB₂Si₂O₈,” ibid., 76 (1931), 133–146, written with C. Dunbar; “Acceptance of the Roebling Medal of the Mineralogical Society of America,” in American Mineralogist, 45 (1960), 411–412.

II. Secondary Literature: Obituaries, with bibliographies, are by H. Heritsch in Almanach ŌsterreichischeAkademie der Wissenschaften. Wien, 120 (1970), 330–344;and by J. Zemann in Tschermaks mineralogische und Petrographische Mitteilungen, 3rd ser. 15 (1971), 1–13, and in American Mineralogist, 56 (1971), 698–706.

See also W. L. Bragg, “Introduction,” in Tschermaks Mineralogische und Petrographische Mitteilungen, 3rd ser. 10 (1965); I. Campbell, “Presentation of the Roebling Medal to Felix Machatschki,” in American Mineralogist, 45 (1960), 407–410; V. M. Goldschmidt, Geochemische Verteilungsgesetze der Elemente. VII. Die Gesetze der Krystallochemie (Olso, 1926); G. E. Hamburger and M. J. Buerger, “The Structure of Tourmaline,” in American Mineralogist, 33 (1948), 532–540; G. Johansson, “A Re finement of the Crystal Structure of Danburite,” in Acta Crystallographica, 12 (1959), 522–525; L. Pauling and E. W. Neuman,“The Crystal Structure of Binnite, (Cu Fe)₁₂As₄S₁₃and the Chemical Compostion and structure of minerals of the Tetrachedrite Group,” in Zeitschrift für Kristallographie, 88 (1934) 54–62.

W. H. Taylor. “The Structure of Sanidine and Other Feldspars.” ibid., 85 (1933), 425–442; W. H. Taylor. J. A. Darbyshire, and H. Strunz, “An X-ray Investigation of the Felspars.” ibid., 87 (1934), 464–498); W. Wahl. “Über die Konstitution der Silikate,” ibid., 66 (1927), 33–72; K. Walenta, “Machatschkiit, ein neues Arsenat aus der Grube Anton im Heubachtal bei Schiltach (Schwarzwald, Bundesrepublik Deutschland), in Tscher maks Mineralogische und Petrographische Mitteliungen, 3rd ser. 24 (1977), 125–132; B. Warren and W. L. Bragg. “The Structure of Diopside, CaMg (SiO₃)₂,” in Zeitschrift für Kristallographie, 69 (1928), 168–193; B. J. Wuensch, “The Crystal Structure of Tetrahedrite, Cu₁₂Sb₄S₁₃,” ibid., 119 (1964), 437–453.

Josef Zemann