LAVES, FRITZ H.

(b. Hannover, Germany, 27 February 1906; d. Laigueglia, Italy, 12 August 1978)

chemical crystallography, structural inorganic chemistry, metallurgy, mineralogy.

Fritz Henning Emil Paul Berndt Laves was the son of Georg Ludwig Eduard Laves, a judge, and Margarethe Hoppe. His father claimed descent from Georg Ludwig Friedrich Laves (1788–1867), court architect of the elector of Hannover (later George I of England). In 1938 Laves married Melitta Druckenmüller, an architect who frequently drew structural diagrams for her husband. The couple had three daughters, Gracia, Charlotte, and Katarina.

Laves was a piano student and built up a large collection of Beethoven and Mozart piano scores. He read literature extensively and particularly admired the works of Hermann Hesse and Thomas Mann. Evidently the young Laves brothers were fascinated by natural history; the two elder brothers collected butterflies and beetles while Fritz dabbled in spiders, rocks, and minerals. Perhaps the experience of discovering an attractive specimen, which Professor Otto Mügge at the University of Göttingen identified as orthoclase feldspar (KAISi₃O₈), was responsible for Laves’ interest in this perplexing family of major rock-forming minerals.

Laves’scientific activity can be divided into three professional phases: German (1929–1948), American (1948–1954), and Swiss (1954–1978). In all three phases order-disorder in crystals was his leitmotiv. His German phase focused principally on alloys and intermetallic compounds; the American phase on the order-disorder in, and crystallochemical definition of, feldspars; and the Swiss phase on more elaborate probings into order-disorder in general through infrared absorption, nuclear magnetic resonance, electron spin resonance, and the microscopies. In the last decade of his life, he studied A1, Ga, V, Nb, and Ta alloys with respect to superconductivity.

Laves studied at the Universities of Innsbruck and Göttingen. He received his Ph.D. in 1929 after studying with Paul Niggli at Zurich. Niggli, the foremost proponent of theoretical crystallography, introduced the “lattice complex” in 1919, extending this to Bauverbände (building units). Intrinsic in each of the 230 crystallographic space groups is a set of equivalent points that are related to each other under the symmetry or equivalence operations of the equivalent points that are related to each other under the symmetry or equivalence operations of the space group. Connecting these equivlent points together gave, among other topogeometric objects, polyhedra. It was Niggli’s objective to arrange the space groups according to each of the derived lattice complexes, and from this to evolve a catalog of crystal structures. Although Laves initially planned to study petrology, Niggli’s crystallography pleased him more and he was soon deep into the study of lattice complexes with respect to sphere packings. A strict definition of coordination number was wanting, and Laves pursued Wirkungsbereiche (spatial partitionings or domains such as Voronoy polyhedra or Dirichlet domains) and the newly published Wigner-Seitz cells.

Laves remained as a doctoral candidate and assistant at Zurich until 1930, then was assistant and Privatdozent at Göttingen until 1944, initially under Victor Moritz Goldschmidt. He remained Privatdozent because the Hitler regime suspected Laves, a principled man, of protecting Jews. Out of a sense of justice, in 1933 he tried to rally support from the science faculty to keep Goldschmidt. But Goldschmidt, a Jew, had to leave Germany in 1935, returning to his former position in Oslo, Norway, only to be later imprisoned several times by the Nazis.

Laves was assigned to a group under Reich Marshal Hermann Goering to develop an alloy “stronger than steel and lighter than air,” and this was perhaps why much of his research at that time involved alloys of magnesium. His strong background in theoretical crystallography and crystal chemistry, gained from Niggli, led to the study of alloys and intermetallic compounds. In 1934 and 1935 he studied the structure of AB₂ compounds.

The Laves phases play a pivotal role in the chemical crystallography of alloys and intermetallic compounds. In such compounds, of which over 220 discrete types are presently known, the relative sizes of the metal atoms are of key importance. The determination of atomic size usually proceeded from the estimation of interatomic distances from X-ray diffraction experiments. For predominantly ionic structures, such as Mg²⁺ O^2-, the procedure was relatively straightforward and ionic radius was governed by coordination number and ionic formal charge. From arrays of large numbers of bond distances, effective ionic radii could be established with remarkable replicability for different structures. For alloys the problem was, and still is, more difficult; formal charge as such does not exist and coordination number is frequently confounded by a range of interatomic distance values. Initially, metallic radii were determined from the metals themselves (e.g., Mg, Cu, Au Pb), and an additivity rule was applied with corrections for coordination number. Laves contributed significantly to retrieving such distances and subsequent metallic radii.

The Laves phases are AB₂ compounds, such as those found in MgZn₂, MgCu₂, and MgNi₂, studied by Witte and Laves. Note here that A has two valence electrons and B belongs to the first transition series of elements. The Laves phases are allied to the o phases. The coordination number for A is based on 12B+4A. Laves recognized their structural basis on dense-packing, the selected omission of nodes that leads to a tetrahedral tridy mite-like net (such a net figured heavily in his later work on silica polymorphs). With A corresponding to the central cavity in the tridymite net and B corresponding to the tridymite framework, the desired arrangement was obtained. Although the ideal radius ratio for such arrangements implicit in close-packings, the radius ratios observed in real crystals range from 1.05 to 1.67. demonstrating the wider flexibility of geometrical factors in alloys compared with ionic crystals.

The influence gof Niggli can be found throughout the crystallographic communications of Laves. The topology of crystallography, crystallographic networks, and structure systematology are themes of a publication that appeared during Laves’ early period at Göttingen.¹ It appeared after the classic work on silicate structures by W. L. Bragg, who organized them according to increasing condensation of the (SiO₄) tetrahedra through sharing corners with other (SiO₄) tetrahedra. It was already recognized that one oxide anion could receive at most two bonds from tetrahedrally coordinated silicon(4+) atoms, that is, (Si—O—Si). The known structures were arranged according to increasing condensations of the tetrahedra, such as insular units (SiO₄), clusters (Si₂O₇), and rings (Si₃O₉); chains (SiO₃); sheets (Si₂O₅); and frameworks (SiO₂). Laves inquired about the theoretical dimensionality that was possible for each of these stoichiometries. If dimensionality n = 0 corresponds to finite units, n = 1 to onedimensional chains, n = 2 to two-dimensional sheets, and n = 3 to three-dimensional frameworks, he derived for SiO₄, n = 0; for SiO₃, n = 0, 1; for Si₂O₅, n = 0, 1, 2, 3; and for SiO₂, n = 1, 2, 3 as topological possibilities. In short, this stimulating work was an alternative, more topological way of comprehending crystal structures both real and hypothetical.

A profound influence on Laves’ insights into the chemical crystallography of metals and alloys came from the brilliant studies conducted by Eduard Zintl (1898—1941) during his brief career. At Munich, Zintl perfected methods of potentiometric titration for analysis of elements in the periodic system. This was followed by the study of saltlike compounds of sodium and other metals in liquid ammonia at Freiburg, and finally the evolution of a remarkable chemical model among the elements while at Darmstadt. He concluded that a wall or boundary existed between elements of groups I-III (which formed intermetallic phases and alloys with each other) and elements of groups IV-VII (which formed saltlike compunds with groups I-III). This boundary is known to this day as the Zintl border. (Earlier, Friedrich Adolf Paneth recognized that elements to the right of the border formed liquid or gaseous hydrides, whereas those to the left of the border, with the exception of boron, did not.) Thus the compound Na₄Pb₉ prepared in liquid ammonia was in fact a polyanionic salt This “polyplumbide” formed the basis for the enumeration of many other polyanionic clusters comprising groups IV-V, such as polyplumbides, polystannides, polybismuthides, polyantimonides, and polyarsenides. Zintl’s discoveries had a profound influence on Laves. Both declared X-ray diffraction the tool of choice for unraveling their crystal chemistries and both sought a focused systematology. Furthermore, Laves drafted a far-reaching appraisal of Zintl’s work and the tasks of metallurgists in general.² It should be recalled that at that time formal crystal structure analysis on such compounds was hampered by gross differences among atomic numbers of the constituent atoms, and confronted problems that have become structurally solvable at the required level of accuracy only relatively recently, by the use of X-ray techniques.

In 1943 Laves was called to the faculty at Halle, and in 1945 he was made professor at Marburg. During this time he concentrated on problems in one-dimensional disorder. Shortly thereafter, however, began the second phase in his life. In 1948 he arrived at the University of Chicago as a “paper clip specialist” (code for scientists whisked out of Germany at their own consent). There he worked with J. R. Goldsmith on order-disorder in feldspars. Although feldspars are a far cry from alloys, the underlying principles of substructure-superstructure, order-disorder, and twinning in these seemingly very different classes of substances join at the level of the topology and geometry of crystal structure. In addition, interest in feldspars went back to Laves youth.

Order-disorder is a central theme in feldspar crystal chemistry. A good example is found in anorthite, CaAl₂Si₂O₈, and its synthetic gallium (Ga) and germanium (Ge) analogues: Ca(Al_{1, 25} Ga_.75)Si₂O₈, CaAl₂ (Si_1.25Ge_.75)O₈, and Ca(Al_1.75Ga₇₅)Si_1.25 Ge₇₅)O₈. Goldsmith and Laves deliberately studied such synthesized substitutions because the relative intensities of structure factors vary as atomic numbers of substituents over nonequivalent sites in a structure type.³ Three types of X-ray reflections occur in anorthite: so-called type a constitute the reflections of the average structure; type b are additional reflections, the ordering reflections over the (Si + Al) cations in the tetrahedral framework; type c are yet additional “diffuse” reflections. By comparing single crystal photographs of these various compositions, it was possible to conclude that the type b reflections were due to Si-Al ordering, based on the contrast patterns of equivalent reflections for various crystals with Al, Ga, and Ge substitutions. The type c reflections hardly varied at all among the different compositions. Since the Ca cation was an invariant in these compositions, it was concluded that the centroid of this relatively large cation was responsible for these diffuse reflections. Order-disorder in such feldspars can lead to structure cells with at least one axial multiple or with a space group of reduced symmetry, usually a subgroup of the parent space group.

Laves and his co-workers probed problems of order-disorder and substructure-superstructure in great detail among many oxides of fundamental importance to mineralogic, petrologic, and ceramic sciences. Included were the fundamental structure types corundum (Al₂O₃) and spinel (Al₂MgO₄), which are based respectively on principles of hexagonal and cubic close-packing, and quartz (SiO₂). Quartz displays many principles in chemical crystallography; over one dozen polymorphs of SiO₂ are known. Geologically important silica polymorphs include tridymite, cristobalite, chalcedony, low quartz, and high quartz. The last two are related by a groupsubgroup relationship in their space groups, and low quartz, owing to its relative hardness, is the most frequent constituent of beach sands.

In 1954 M.J. Buerger discussed the stuffed derivatives of the silica structures, thereby opening up an enormous field of applied crystallographic research. Stuffed derivatives of a fundamental structure. For example, nepheline, KNa₃ (Al₄Si₄O₁₆), is a stuffed derivative of tridymite □□₃ (Si₄Si₄O₁₆, where vacancies (□) in the one are filled by alkalies in the other (also not that Al and Si can be ordered in nepheline). On structural grounds this may lead to an integral multiple of one or more of the crystallographic axes, a subgroup of the parent structure space group, or both. The most frequent cause of this phenomenon is order, or the sequential alternation of two or more ionic species over sites formerly occupied by only one ionic species. Ordering is usually temperature dependent; as atomic thermal vibrations increase with increasing temperature, the ordering or superstructure reflections on X-ray films will become weaker and vanish completely when perfect mixing of the two or more ionic species merges at a crystallographic site. This is one way to use single crystals of minerals as potential geothermometers. Laves and his co-workers assiduously studied stuffed derivatives of high quartz and vigorously pursued the possibility of using feldspars as geothermometers.⁴

The high quartz structure is a three-dimensional framework built of pairwise corner-linkages of (SiO₄) tetrahedral modules. Its symmetry is P 6 ₂22 or P 6₄ 22, space groups which are enantiomorphic, that is, right- or left-handed. Thus quartz is piezoelectric. In addition, linking just the Si⁴⁺ cations together results in the (6. 3. 6. 3)Kagomé 4-connected net. The hexagonal rings in the net are the largest channels in the structure and, like nepheline, can incorporate larger cations. Laves became interested in orderdisorder, solid-solution, defect, and ionic conduction problems in the channels. Electrolysis, electrical conductivity, color centers, and the presence of trace elements, particularly Ti⁴⁺, in quartz attracted his and his students’ attention.⁵

Order-disorder studies continued in the spirit of Laves’ research. Interaction with colleagues in physics led him to emphasize infrared spectroscopy, nuclear magnetic resonance, electron spin resonance, and other spectroscopies because these new techniques admitted new and more direct observations of previously inaccessible structural phenomena. Such studies constituted the bulk of his crystallographic research after he accepted the chair of mineralogy at the Eidgenössische Technische Hochschule in Zurich in 1954, succeeding Paul Niggli.

Laves served as chairman of the Deutsche Mineralogische Gesellschaft (DMG) (1956–1958) and was a member of the executive committee of the International Union of Crystallography (1960–1966). Among other honors, he received an honorary doctorate from the University of Bochum, the Abraham Gottlob Werner Medal of the DMG, and the Roebling Medal of the Mineralogical Society of America.

NOTES

1. “Zur Klassifikation der Silikate,” in Zeitschrift für Kristallographie, 82 (1932), 1–14.

2. “Eduard Zintls Arbeiten über die Chemie und Struktur von Legierungen,” in Die Naturwissenschaften, 29 (1941), 244– 255

3. “Cation Order in Anorthite (CaAl₂Si₂O₈) as Revealed by Gallium and Germanium Substitution,” in Zeitschrift Für Kristallographie, 106 (1955), 213–235, written with J. R. Goldsmith.

4. “On the Use of Calcic Plagioclases in Geologic Thermometry,” in Journal of Geology, 62 (1954), 405–408, written with J. R. Goldsmith.

5. “Eigenschaften von Elektrolyse-Farbzentren in Quartzkristallen,” in Die Naturwissenschaften, 48 (1961), 714, written with p. Schindler and H. E. Weaver.

BIBLIOGRAPHY

I. Original Works. A list over 230 professional papers of Laves’, and a select few by his former students, is in Zeitschrift für Kristallographie, 151 (1980), 9–20.

II. Secondary Literature. A short biographical sketch by J. R. Goldsmith is in American Mineralogist55 (1970), 541–546. For a detailed biographical account of Laves’ life, see the memorial by E. Hellner in Zeitschrift für Kristallographie, 151 (1980), 1–9.

Paul Brian Moore