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The Day plot was initially developed to delineate the domain states of magnetite grains based on saturated magnetic properties and has since become a standard method in rock magnetic studies. Because most natural magnetic systems are "dirty", meaning they may contain a combination of non-stoiciometric magnetite, partially oxidized magnetite, other magnetic minerals, and/or complicated grain-size distributions, Day plots can be difficult to interpret and may not even be applicable to these systems. Furthermore there is a tendency for many natural systems to have similar magnetic parameters, and thus fall in the same field of a Day plot, even though they have distinctly different magnetic compositions and grain sizes. We aim to overcome some of these limitations by using the trajectories of unsaturated magnetic properties in a Day plot. Below saturation, rock magnetic parameters are highly variable with respect to the maximum applied field, B$_{max}$, though surprisingly little work has been done to utilize this variability as a rock magnetic tool. The magnetic moment, the magnetic remanance, the coercivity, and the coercvity of remanance were measured as a function of B$_{max}$, from 10 mT (unsaturated) to 1400 mT (saturated for magnetite). These four parameters were then plotted on a Day plot, which gave a trajectory of points as a function of B$_{max}$, instead of a single point. These trajectories are useful for discriminating grain-size distributions and compositions as illustrated for several pure and mixed synthetic samples of magnetite and hematite, all diluted in vacuum grease to minimize interactions. The technique was also applied to NIST standards 1633 (Fly Ash), 1649 (Urban Dust), and 1650 (Diesel PM) and revealed that all three samples contained at least two magnetic components, each of which has different coercivities and grain-size distributions. This information would not have been discernable with most conventional magnetic measurements.
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