ZACHARIASEN, (FREDRIK) WILLIAM HOULDER

(b. Langesund, Norway, 5 February 1906; d. Los Alamos, New Mexico, 24 December 1979)

chemical crystallography, X-ray diffraction.

Zachariasen was born near Brevik, Norway, the center of the now classic nepheline-syenitic and foyaitic rock occurrences that have yielded over thirty new mineral species. Many of these mineral species contain essential light elements (such as hydrogen, beryllium and boron) and the heavy lanthanides (lanthanum through lutetium) and natural actinides (actinium through uranium). These elements and their chemical crystallography occupied much of Zachariasen’s thoughts in later years, and one suspects that the environs of his youth left a permanent imprint.

Zachariasen’s father, Johannes, a ship captain, and his mother, Vissa, had three sons (of whom Fredrik was the youngest) and a daughter. Fredrik early dropped his first name and was thereafter called William or Willie. He received the Ph.D. in 1928 under Victor Moritz Goldschmidt at the University of Oslo, then did further study on crystal structures of minerals with Sir Lawrence Bragg at Manchester. In 1930 Zachariasen married Ragni (“Mossa”) Durban-Hansen, granddaughter of Wal-demar Christopher Brøgger, a leading authority on nepheline-syenite mineralogy, especially of Langesundfjord. They had a daughter, Ellen, and a son, Fredrik, who is a physicist. That same year Zachariasen joined the department of physics at the University of Chicago, where he went on to serve as chairman (1945–1949, 1956–1959) and dean of the Division of Physical Sciences (1959–1962). He was the Ernest DeWitt Burton Distinguished Service professor from 1962 to 1974. An intense, outspoken man with strong convictions, he always sought excellence and high qualities in candidates, thereby furthering a strong scientific foundation at the university. He became professor emeritus in 1974.

Zachariasen’s more than two hundred scientific publications cover crystal structures of inorganic substances (mostly minerals), anionic groups, the glassy state, actinide crystal chemistry, and X-ray diffraction theory. Crystal structure determinations before vector set techniques (especially the Patterson function) and the advent of artificial intelligence, that is, before World War II, was largely simply algebraic, intuitive, and trial-and-error in its approach. Zachariasen solved many structures, especially between 1930 and 1950, by these relatively tedious methods, and it is a credit to his genius that these structure solutions stand to this day as basically correct. Structures and mineral chemistries during this period include hambergite, meliphanite, titanite (sphene), eudidymite, epididymite, and eudialyte, phases characteristic of the Langesundfjord nepheline-syenite paragenesis.

Anionic groups (such as borates, carbonates, sulfates, and sulfites) occupied Zachariasen’s attention during the early 1930’s. He deciphered and interpreted a large body crystal structures. We should recall that at that time neither reliable atomic coordinate parameters nor bond distances were known for most groups or radicals. Zachariasen undertook a series of studies on sulfur-oxygen groups, and he established sulfate [SO₄]²⁻, sulfite [SO₃ψ]²⁻,

(ψ = lone pair; present author’s designations), and others. These studies culminated in a 1931 paper in which Zachariasen discussed two classes of XO₃ “groups” in crystals: Class 1 included (NO₃)¹⁻, and (BO₃)³⁻; Class 2 included (PO₃)³⁻, (SO₃)²⁻, (CIO₃)¹⁻, (AsO₃)³⁻, (SeO₃)²⁻, (BrO₃)¹⁻, and (SbO₃)³⁻, Class 1 possessed oxygens coplanar to the central cation, while in Class 2 the oxygens are pyramidally displaced above the central cation. Zachariasen recognized the duality of two different explanations, the one of shared electron pairs (the quantum mechanical treatment), the other of ions and their deformation in the field of surrounding ions. Today we would probably refer to Zachariasen’s “(3 × + 2) electron rule” of Class 2 as groups that possess a lone pair of electrons on the cations. Along with G.N. Lewis and his evolution of the rule of octets in the first decade of the twentieth century, it appears that Zachariasen anticipated our modern notion of lone electron pairs in crystal structures by about six years.

Speculations on the glassy state can be dated to the Old Testament, but a scientifically sensible model was achieved relatively recently, in the form of the famous Zachariasen glass model. Zachariasen was the first scientist to advance a model for the atomic arrangement in glassy substances that agreed with all the observations at hand. He argued that a small difference in energy between a symmetry-repeating crystalline substance and its glassy counterpart could be observed for cations in triangular, trigonal pyramidal, or tetrahedral coordination by oxygens such as B³⁺, Si⁴⁺, P³⁺, P⁵⁺, As³⁺, As⁵⁺, and Ge⁴⁺, which tend to form glassy oxides from a quenched liquid. He further noted that the need for maximal separation of like ions owing to electrostatic repulsion forced arrangements based on sheets or networks composed of structural rings or loops of varying sizes. Large cations of low charge would fill the spaces in the loops. Where an equal number of cations are surrounded by anions, and vice versa, a glass would not form because its energy content would be about the same as or identical to that of a crystal. Zachariasen proposed a general formula A_mB_nO, where B is the cations in triangular, pyramidal, or tetrahedral coordination by oxygen that define the framework, and A is the large cations of low charge. The condition for most favorable glass formation is n ˜ 0.4–0.5. The ultimate condition for a glass is the formation of an extended three–dimensional network that lacks periodicity and has energy content comparable with but not equal to the corresponding crystal network.

In 1943 Zachariasen was senior physicist on the Manhattan Project. Elucidating the nature and chemistry of the synthesized actinides is among his most celebrated work. From 1943 to 1948 Zachariasen characterized the crystal chemistries of over 150 discrete compounds of Group 5f elements, and elevated the tool of X-ray crystallography to the level of ultramicrochemical analysis where microgram quantities could be studied. His technique proved far more reliable than any chemical analytical technique at that time. In 1925 Goldschmidt had demonstrated lanthanide contraction of the ionic radii for the Grou 4f elements by techniques of X-ray diffraction. Zachariasen demonstrated the same effect for the Group 5f elements. In addition, he solved numerous crystal structures and showed that formal valences vary from 2⁺ to 5⁺, with uneven charge distributions, from actinium to americium. He attributed this to mixing between the closely spaced 5f-6d electronic shells. Detailed accounts of these studies appeared after 1948, when such studies were declassified.

In 1931, Zachariasen published a set of empirical crystal radii for ions with inert gas configuration. Such crystal radii form the basis of crystal chemistry because bond distances, problems in radius ratio and solid solution, and variation of bond lengths with variation in formal charge for some given ion all are derived from these radii. Today reliable tables of effective ionic radii exist because a large number of precisely refined crystal structures became available after 1950. In 1931 the problem was far more difficult because only the data of simple oxides and fluorides, with few, if any, variable atomic parameters, were available.

An X-ray diffraction experiment allows only the determination of a diffracted intensity from some crystallographic plane. Since the intensity is a product of a structure factor amplitude and its complex conjugate, the associated phase information is lost. This is the famous phase problem in X-ray crystallography. Zachariasen (1952) utilized an identity from which the Schwarz inequality follows. In a metaboric acid crystal, 12HBO₂, the coordinates of nine unique atoms, each with three degrees of freedom, were determined by this direct method. Today many kinds of “direct methods” have been studied and tested; most of them involve inequalities between and among sets of reflections with strong relative intensity and usually proceed with the assistance of artificial intelligence.

In 1945 Zachariasen published Theory of X-ray Diffraction in Crystals. Although many books of varying depth have recently been published on crystals and X-ray diffraction, this self-consistent and rigorous work is still eminently suitable. Dyadics (second-order tensors) and group theory play a central role in this tome. From crystal symmetry and X-ray diffraction in ideal crystal, there follow more contemporary problems in a real crystals, such as disordered crystal structures, temperature diffuse scattering, and crystal mosaicity. Several papers published between 1960 and 1965, including the problem of power loss during the course of diffraction in mosaic crystals (secondary extinction) and multiple diffraction in imperfect crystals, round out Zachariasen’s studies in X-ray diffraction theory.

BIBLIOGRAPHY

I. Original Works. Zachariasen’s writings include “A Set of Empirical Crystal Radii for Ions with Inert Gas Configuration,” in Zeitschrift für Kristallographie, 80 (1931), 137-153 “The Structure of Groups XO₃ in Crystals,” in journalsof the American Chemical Society, 53 (1931), 2123–2130; “The Atomic Arrangement in Glass,” ibid., 54 (1932), 3841–3851; Theory of X-ray Diffraction in Crystals (New York, 1945); “The Crystal Chemistry of the 5f-Series of Elements,” in Record of Chemical Progress, 10 (1949), 47–51; “A New Analytical Method for Solving Complex Crystal Structures,” in Acta Crystalographica, 5 (1952), 68–73.

A bibliography of Zachariasen’s professional papers and his books, on microfiche, is available as Document AM-81-177 from the Business Office, Mineralogical Society of America, 2000 Florida Avenue, N.W., Washington, D.C. 20009.

II. Secondary Literature. A short and more personal account is Paul B. Moore, “Memorial of Fredrik William Houlder Zachariasen, February 5, 1906–December 24, 1979,” in American Mineralogist, 66 (1981), 1097–1098. For a longer tribute, see Robert A. Penneman, “Chapter 2: William H. Zachariasen,” in D. McLachlan, Jr., and J.P. Glusker, eds., Crystallography in North America (1983), 108–111. An extended memorial concluding with over 200 titles has been submitted to the National Academy of Sciences by Mark G. Inghram.

Paul Brian Moore