Dan McLachlan

A Versatile Projector for Assisting in Crystal Structure Determinations

In the determination of crystal structures from x‐ray data, mathematical equations are frequently used for which there are no physical analogs available. The introduction of physical analogs is advantageous because they assign a physical significance to the mathematics and, also, because they make possible the use of apparatus which either aids or replaces the long computations. In this paper a description is given of an optical device which produces as photographic records the results of the mathematical processes known as convolutions. Since there are several kinds of convolutions, and since the device is very versatile, the particular types of convolutions for which the apparatus is adaptable are the well‐known Patterson projection and, also, the mixed projections. The illustrations that are furnished should aid in the understanding of some of the more recently developed methods of structure determination. The apparatus is constructed of materials readily available in any laboratory.

A Multiple Projector for the Huggins Masks

The usual procedure for making two‐dimensional fourier projections of crystal structures by means of the Huggins masks requires the expenditure of time in the photographic darkroom during which errors may be made. These errors can be corrected only by a repetition of the entire laborious procedure of successive exposures of the plate. An apparatus is described whereby 144 Huggins masks are projected simultaneously on a screen and the result photographed. The projection is accomplished without lenses and the cost of production is thereby reduced considerably. Grooves are provided for changing the signs of the fourier coefficients at will. Rheostats on the projection lamps are provided for controlling the lumination in proportion to the magnitude of the fourier coefficients.

A Machine for Synthesizing Two‐Dimensional Fourier Series in the Determination of Crystal Structures

An electromechanical analog machine is described which performs a two‐dimensional Fourier synthesis for use primarily in x‐ray crystal structure calculations, ρ(xy)=Σ lim hΣ lim kFhkocos2π(hx+ky). The analog to a term in this summation is obtained through the use of a pair of selsyns as a synchro‐variable transformer somewhat similar to its use in servomechanisms. ρ(xy)hk is represented by the output voltage, Fhko by the input voltage, and 2πhx and 2πky are the angles of rotation of the primary and secondary rotors respectively. A system of crossed shaft and cascading gear trains turns the rotors to the appropriate angles for each selection of point (x, y) in the unit cell. The present machine handles h and k values up through 8, but provision is made for future extension through 16. Computations are shown for two known structures to indicate the results obtainable with the machine.