A Point Focusing Monochromator for the Study of Low-Angle X-Ray Diffraction: Determining the Size Distributions of Carbon Blacks and a Precision Determination of the Size of Dow Latex Particles

Abstract

A point focusing x-ray monochromator was designed and constructed for low angle scattering studies. The anastigmatic point focus is achieved by means of two cylindrically bent quartz crystals whose focal circles are mutually perpendicular. The beam, emanating from the copper target of an x-ray tube, is reflected in succession, first from the crystal defining the horizontal focal circle and, second from the crystal defining the vertical focal circle following which it comes to a mono chromatic point focus of wavelength 1.537 A (Cu Ko(1). The sample to be studied is placed between the second crystal and the point focus, and the scattered beam is detected by means of a photographic plate placed at the point focus, at right angles to the undeviated beam, the latter being suppressed by means of an absorber. Mathematical analysis, in which a ray was traced through the two crystal system, revealed correctly the shape and size of the point focus, and the possibility of reducing the latter in size by stopping down the beam emerging from the target. The instrument and its lining up procedure is described in detail, particularly the latter since the orientation of the two crystals relative to each other and the x-ray tube involve twelve degrees of freedom. Suggestions for improving the intensity of the instrument are made . These consist of (1) substitution of topaz crystals for quartz, (2) use of helium atmosphere instead of air to surround the x-ray beam (3) reorientation of the x-ray tube to permit smaller angles of emergence of the beam. As a trial run for the instrument, the scattering patterns of two kinds of carbon black (good scatterers) were obtained from which the average particle sizes and size distributions were calculated