The Alpha Particle X-ray Spectrometer (APXS) on the Mars Exploration Rovers possesses the ability to detect carbon and oxygen within martian samples via Rutherford backscattering principles. Several consecutive measurements of the martian atmosphere by Spirit, paralleled by Monte Carlo simulations, provided an energy calibration to mitigate the absence of an alpha-mode calibration pre-flight. Data from a pre-flight thermal acceptance test agreed with this energy calibration, confirming the presence of an unexpected offset. Correcting a bug in the APXS firmware resulted in a temperature-independent energy scale. A model was developed and applied to all atmospheric data illustrating a dip in atmospheric peak areas, potentially arising from a week-long weather event on Mars. An early expansion of this model to solid samples has not yet been able to detect any hydrated minerals or carbonates. Preliminary investigations into determining martian atmospheric pressure and potential elemental layering within samples shows promise.