Part VIII - Papers - Automatic Computer Plotting of Pole Figures and Axis Density Figures

A method is described by whichX-ray pole figures and axis density figures may be plotted automatically. The X-ray data are obtained using a Siemens texture gonionleter and the Schulz reflection method. Composite sampling methods are used to obtain a full quadrant of the pole figure. The contour lines of the pole figure and axis density figures are drawn using a computer-controlled x-y plotter. The computer program used to draw the contours was obtained from ZBM. POLE figures used to describe crystallographic orientations of poly crystalline sheet materials are usually plotted manually from X-ray diffraction output in the form of a strip chart recording of the intensity distribution of a given crystallographic pole in physical space. Today's computers and associated plotting equipment now make it possible to plot pole figures and axis density figures automatically. Inverse pole figures have been determined by mathematically "inverting" X-ray pole figure data.'-' In general, these methods require complicated, time-consuming numerical calculations. A more economical but less accurate method is to determine the axis densities of low-index crystallographic poles using an X-ray diffractometer. When these axis densities are plotted in a unit stereographic triangle contour lines can be drawn to represent the axis density distribution. This can now be done automatically. Computers were used to plot pole figures by a method developed by Holland, Engler, and powers.' In their method intensity ratios based on a random standard sample were obtained from a strip chart recording, and the stereographic (x, y) coordinates of these ratios were determined by a computer. Symbols characteristic of different intensity ratio levels were then plotted using an automatic x, y plotter and intensity contours were drawn manually. The present paper describes a method by which pole figures and axis density figures have been automatically plotted from digital data obtained from a Siemens X-ray unit. Plotting was accomplished using an IBM 1620 computer and a Calcomp 563 digital plotter. COMPUTER PROGRAM The computer program was obtained from IBM Systems Reference Library, No. 1620-CS-05X, and was designed to plot contour maps from randomly distributed data. It consists of a set of twelve separate subprograms, four of which were used in this work. The program takes a given distribution of data points and by a numerical method determines the values at mesh points of a square grid system superimposed over the input data. The output data from this program is in a form suitable for input to the contour plotting program. A smoothing program is also available which calculates new mesh point values from a continuous function fitted to neighboring mesh points. The degree of smoothing depends on the number of points around a given grid point which are used to adjust or smooth the grid value. The contour plotting program is designed to allow the user to specify the interval, scale, and annotation of the contours to be plotted. EXPERIMENTAL PROCEDURE Pole Figure Data Points. Diffracted X-ray intensities were determined using a Siemens texture goniometer and the schulzs reflection method. Due to geometric