Brookite, TiO2 (titanium = grey, oxygen = red). An orthorhombic unit constructed by an octahedron of oxygen ions arranged about a single titanium ion. Each octahedron shares three edges with adjoining octahedra.
After returning from a trip to Europe in 1927, Linus Pauling was appointed to the position of Assistant Professor of Theoretical Chemistry at Caltech, and reinitiated his study of crystal structures in Pasadena. During this time, Pauling was focusing his attention on the crystal structures of silicate minerals. He and other scientists were utilizing X-ray analysis for crystal structure determinations, but the limitations of the technique were becoming more and more apparent as it was applied to increasingly complex crystal structures.
To overcome these difficulties, Pauling formulated a new theory which helped him to determine the structure of brookite, topaz and a number of other complex ionic crystals. The theory, and the work that resulted from it, comprised an important step in the development of his most cited and most used crystal structure work.
Pauling’s new development was called coordination theory, and served as a method for predicting the possible structures of ionic compounds. Pauling contrasted the new theory with another method used previously by crystallographers for similar crystal structure determinations. The previous method involved testing and eliminating all but one of the possible arrangements in order to determine the atomic arrangement of particular crystals. Pauling noted that this method was both very certain in its results, and extremely labor intensive, making it difficult to apply to more complex compounds.
Pauling’s new method utilized sets of rules to both dismiss unlikely potential chemical structures and to hypothesize an atomic arrangement that would likely match the crystal structure of the compound being examined. Pauling and his associates would then compare the hypothesized arrangement to experimental observations. The new theory closely resembled an earlier technique formulated by William Lawrence Bragg, which applied a method called close-packing. (In this letter, Pauling discusses his crystal structure work with Bragg, including his research on the structure of brookite.)
Pauling first used his extended version of the technique to successfully determine the structure of brookite. Brookite, or titanium oxide, is a minor ore of titanium and a polymorph with two other minerals. It shares a number of similarities with the minerals rutile and anatase, having the same chemistry but a different structure. The variety of similar structures largely results from exposure of the basic chemical components to different temperature variations. As such, when exposed to higher temperatures, brookite reverts to the chemical structure of rutile.
In their examination of brookite, Pauling and J. Holmes Sturdivant used spectral photographs to determine the dimensions of the possible unit cells, and Laue photographs to determine the smallest possible unit and space group symmetry criteria. Using Pauling’s new coordination theory, they predicted two possible structures for brookite. One of these hypothesized structures turned out to have a space-group symmetry and unit cell matching the spectral and Laue photograph observations. From there, Pauling and Sturdivant were able to determine that the basic unit of arrangement in brookite was that of an octahedron of oxygen ions around a titanium ion.
Following his examination of brookite, Pauling later used coordination theory to determine the structure of topaz. After these successful examinations, he was compelled to develop a set of principles which governed the structures of complex ionic crystals. The principles were described in a set of compiled documents known as the Sommerfeld festschrift papers, and would later be known as “Pauling’s Rules”. Pauling used his examinations of brookite and topaz, as well as the principles developed in their determinations, to write a paper that detailed this work. “The Principles Determining the Structure of Complex Ionic Crystals,” [J. Am. Chem. Soc. 51 (April 1929): 1010-1026.] published in 1929, became the most cited and most used of all of Pauling’s crystal structure papers.
For more on Pauling’s achievements in structural chemistry, see Linus Pauling and the Nature of the Chemical Bond: A Documentary History.