NASA's next generation of x-ray observation missions require x-ray calorimeters with superior energy resolution. Semimetallic HgTe has already proven itself as an excellent soft x-ray absorber material due to its low heat capacity. The alloy Hg0.834Cd0.166Te is predicted to also have zero energy gap at T=0 K and a heat capacity even less that that of HgTe due to: (i) a greater Debye temperature (resulting in a lower lattice heat capacity), and (ii) a smaller electron effective mass (resulting in a lower electronic heat capacity). Thus Hg0.834Cd0.166Te-based microcalorimeter arrays are expected to have an energy resolution superior to that of HgTe-based ones. We propose the growth of single crystal Hg0.834Cd0.166Te layers by molecular beam epitaxy on Si substrates. Mercury vacancies will be filled after growth to reduce the possibility of them acting as acceptors and introducing a significant electronic heat capacity. The Hg0.834Cd0.166Te layers will be characterized by x-ray diffraction to asses their structural quality and crystallinity, FTIR mapping to confirm the uniformity of their energy gaps and alloy compositions, Hall measurements to assess their electrical transport properties, etch pit density counts to determine dislocation densities, transmission electron microscopy to determine microscopic structural information, and heat capacity measurements at mK temperatures to test their promise as high energy resolution quantum calorimeters.