Analytical polarized energy-dispersive X-ray fluorescence (PEDXRF) spectrometry (PEDXRFS) represents a substantial advancement over conventional XRF. The higher signal-to-noise commensurate with background lowering and better energy resolution, permits trace analysis for elements with Z ≥ 11. Concomitantly, improvements in analytical software based on the fundamental parameters (FP) approach have improved accuracies and precisions for standard-less analysis (SLA). Two ceramic and soil standard reference materials (SRMs), 98a-Plastic Clay and GSS-1 powders, differed in their intrinsic matrix properties of grain size, bulk, and surface monolayer densities as well as the elemental concentrations. The SRMs were analyzed as powder and as pellets compacted under the same pressure conditions to double the bulk density. Different geometries represented by the sample cup (10, 15, and 24 mm) and pellet (10, 15, and 25 mm) diameters with the same sample thickness (with differing masses and aspect ratios), as well as (for powder samples only) identical low masses (0.5 g) but with varying thicknesses, were analyzed. PEDXRFS combined with TURBOQUANT® (TQ) as SLA-FP enables good quantitative analysis for powders (Z ≥ 13) even for masses significantly lower than recommended, for soil–ceramic samples. Pellets (Z ≥ 12) yielded the best accuracy factor (AF) at high aspect ratio and thicknesses of the matrix analytical depth. Binder in pellets depreciates the AF. TQ needs to adequately quantitate matrix interferences effects, to improve accuracy in the analysis of low atomic numbers, e.g. Na and Mg.