Polarization-dependent Imaging Contrast (PIC) Mapping in 2018

Abstract

Ten years after Polarization-dependent Imaging Contrast (PIC) mapping was first introduced (1,2), it has changed and advanced significantly: it now measures the orientation of the crystallographic c-axis of crystals in three dimensions (3), and quantitatively displays it in color (4-10). PIC mapping is based on x-ray linear dichroism, a natural effect occurring in any non-cubic crystal, first discovered by Joachim Stöhr in molecular monolayers (11-13) and later observed in magnetic materials (14-18), organic molecules (19), and liquid crystals (20). All these were human-made systems, whereas Metzler et al. first observed it in a natural sample, nacre from an abalone shell (1). For PIC mapping a PhotoEmission Electron spectroMicroscope (PEEM)(21-26) is used to acquire images at the photon energy position of the most dichroic peaks. Those first observations in nacre (1,2) and sea urchin teeth (27-30) were obtained by the digital ratio of two images, displayed in black and white, and they were not quantitative. See (31) for a comprehensive review. More recently, however, a much more sophisticated and informative method was introduced, in which the angle of the linear polarization from the elliptically polarizing undulator (EPU°) source is rotated by 90°, in 5° increments. In the resulting stack of 19 images each pixel is fit to a Malus law: f(EPU°) = a + b cos 2 (EPU°-c') where a, b, and c' are fit parameters. In the Malus law c' represents the in-plane angle of the crystal's c-axis, and b/a is the off-plane angle. These are displayed as hue and brightness, respectively, in Figure 1. Notice that these in-plane and off-plane angles are referred to the polarization plane, which is not the image plane. Since the beam illuminates the sample surface from the right at 30° grazing incidence, the polarization plane is 60° from the surface. Hue in PIC maps displays the c' angle, that is, the angle between the projection of the crystal c-axis onto the polarization plane, termed c'-axis, and the vertical in the laboratory and in the images. When the c'-axis is vertical, the angle is 0° and the color is cyan, when the c'-axis is-30° (left from the vertical) the color is blue, at +30° is green, and so on as shown in the color legend in Figure 1. Brightness in PIC maps displays the off-plane angle of the crystal c-axis: bright colors indicate in-plane c-axes, darker colors are off-plane, and black is 90° off-plane, that is, the c-axis points directly into the x-ray beam (4). All PIC maps presented here use the default parameter values in the software used to produce them: angle minimum =-90, maximum +90, scale bar colors 0°-360°, brightness set to max B = 200. The software is called GG Macros and it is distributed free of charge to any interested users (32). Figure 1 shows PIC maps from aragonite, calcite, and vaterite in space-filling (30) marine biominerals. These are three polymorphs of calcium carbonate (CaCO3) with orthorhombic, trigonal-rhombohedral, and hexagonal crystal structures, respectively. The PEEM resolution in Figure 1 is 20 nm, and the pixel sizes vary between 10 nm and 60 nm. All these PIC maps were obtained at the oxygen K-edge in PEEM.