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THn AvrERrcAN MruERAI,ocrsr JOURNAL OF TIIE MINERALOGICAL SOCIETY OF AMERICA Vol. 56 MARCH-APRIL Nos. 3 and 4 THE LOW-KEY CRYSTALLOGRAPHYI'2 W. F. Bnaor.ou, Department of Chemical Engineering Unhersity of Teras at Ausl,in, Aust'in, Teros 787 12 Over past years our Society has been honored by Presidential ad- dresses delivered by proponents of best informed aspects of their various areas of interest. Later today we will enjoy a Roebling medal acceptance by an individual who will perform this function for my area. I will there- fore try today to give recognition to some of the scattered collateral benefits that accrue to mineralogy and crystallography by virtue of the adaptation of information deduced by the good practitioners from ade- quate data to materials from which collectable data is not definitive. The remarkable successes that have accumulated in the 58 years of X- ray diffraction analyses have attracted an ever-growing number of scientists, providing an ever-increasing fund of facts on which to draw. Currently, the availability of computer programs makes possible the solution of crystal structures from massive data collections with only limited time demands and assures a continuing proliferation of additional facts. The neglected area is that populated by the large number of crystalline solids too imperfectly constituted to provide the massive data collections. For their characterization recourse must be had to empirical-based principles. Professor Linus Pauling was earliest to exploit extensively the recog- nition that complex stable structures were based on arrangements of relatively few coordinated polyhydral groupings and their articulations with each other. Any such polyhedron has a calculable transform that represents its potential to scatter radiation in any given direction and the same is equally true of any articulated assemblage of polyhedra. This potential amplitude then either is or is not delivered to observed in- tensities, depending on the disposition in space and dimensional corre- spondences with periodic repetition of such assemblages with respect to l Presidential address to the Mineralogical Society of America, 12 November, 1970. 2 Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support for several of the illustrations reviewed. 375 J / O W. F. BRADLEY each other. Our present Roebling medalist is among those who have pro- vided abundant examples of alternative arrangements with respect to each other of entire macro-areal Iayers of the various micaceous minerals. As one who has habitually been faced with poorly organized mineral matter, and limited diffraction data, I have followed the course of seeking what advantages may be taken by borrowing from the better established principles. The few examples that I can cite here today can not possibly be comprehensive, nor can they include proper coverage of the many successes of other investigators who have faced similar situations. Three little related sources from which borrowing is productive can be chosen as illustrative. They are: peculiar aspects of geometry, the utility of transforms of rigid bodies, and collateral information from specialized auxiliary instrumental methods. GnouBrnv It was originally observed ...

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