Fractal Analysis of the Microstructure of the Martian Soil at the Phoenix Landing Site

Introduction: The microscope station of the Phoenix Lander is able to image the dust and soil of Mars at unprecedented resolution, with a 4 ! m resolution for the optical microsope and less than 100 nm with the atomic force microscope [1]. Soil was delivered by the robot-arm scoop of Phoenix to a series of substrates for imaging by the two microscopes. We present here an analysis of the particle sizes of material collected on substrates which were intentionally not loaded with soil, a white calibration standard and a stitching standard. These substrates passively collected material over the course of the mission which was mobilized within the microscope station enclosure. Hence the particle population represents a integrated sample from the dig volume of Phoenix [2] with the selection criteria of sufficient adhesion between the particles and the substrates to prevent removal either during the vibrations induced by rotations and translations of the sample wheel or by gravity as the substrates were imaged vertically. The two substrates both accumulated particles between observations. A sequence of images from the white calibration substrate is shown in fig. 1(a d) from which it is evident that once particles adhered, they remained on the substrate. Larger particles were able to stick to the rougher surface of the macor of white calibration standard compared to the quartz of the stitching standard. The particles show very little variation in coloration, with the most likely provenance being the dominant orange-brown segment of the soil seen in all samples from the landing site [3]. Particle size distributions: Particle size distributions were determined from images (d) and (e) using a variety of segmentation approaches. These were converted to plots of accumulated mass (in arbitrary units) against particle diameter, with the assumption that the density of the material was constant and the particles are approximately spherical. The former is justified by the even colouration which is independent of particle size, while images of the particles in profile at the edges of the substrates formed the basis for approximate sphericity. Fig. 2 shows such a plot for the Sol 137 image using different segmentation approaches. The data shows a break in slope at about 15 ! m particle diameter. Fractal analysis: Such plots can be interpreted in terms of the fractal dimension of the fragmentation of the soil [4]. The slope can vary between a value of 3 and zero, with the slope given by 3 – D, where D is the fractal dimension of fragmentation. D is inversely related to the probability of fragmenation of a particle, with a high probability corresponding to an easily fragmented particle. Hence a steep slope corresponds to a size regime where the probability of particle fragmentation is low, while a shallow slope indicates that the particles easily break up in that size range. Breaks in the slope correspond to a change in the strength of the particles to fragmentation, for instance the transition from primary particles to agglomerates above a certain size. A good fit to the data is possible with the parameters as shown in fig. 2. corresponding to a fractal dimension of 0.23 for particles smaller than 15 ! m and 1.71 for larger particles. The very low value for the smaller particles, close