Single crystal neutron and high-energy x-ray diffraction have identified the phase lines corresponding to transitions between the ambient-pressure tetragonal (T), the antiferromagnetic orthorhombic (O) and the nonmagnetic collapsed tetragonal (cT) phases of CaFe2As2. We find no evidence of additional structures for pressures up to 2.5 GPa (at 300 K). Both the T-cT and O-cT transitions exhibit significant hysteresis effects and we demonstrate that coexistence of the O and cT phases can occur if a non-hydrostatic component of pressure is present. Measurements of the magnetic diffraction peaks show no change in the magnetic structure or ordered moment as a function of pressure in the O phase and we find no evidence of magnetic ordering in the cT phase. Band structure calculations show that the transition results in a strong decrease of the iron 3d density of states at the Fermi energy, consistent with a loss of the magnetic moment.PACS numbers: 61.50. Ks, 61.05.fm, 74.70.Dd The discovery 1,2 of pressure-induced superconductivity in CaFe 2 As 2 has opened an exciting new avenue for investigations of the relationship between magnetism, superconductivity, and lattice instabilities in the iron arsenide family of superconductors. Features found in the compositional phase diagrams of the iron arsenides, 3 such as a superconducting region at low temperature and finite doping concentrations, are mirrored in the pressure-temperature phase diagrams. Superconductivity appears at either a critical doping, or above some critical pressure in the AFe 2 As 2 (A=Ba, Sr, Ca) or '122' family of compounds, raising questions regarding the role of both electronic doping and pressure, especially in light of the recent observation of pressure induced superconductivity in the related compound, LaFeAsO.4 Does doping simply add charge carriers, or are changes in the chemical pressure, upon doping, important as well? What subtle, or striking, modifications in structure or magnetism occur with doping or pressure, and how are they related to superconductivity? Similar to other members of the AFe 2 As 2 (A=Ba, Sr) family, 5,6,7,8 at ambient pressure CaFe 2 As 2 undergoes a transition from a non-magnetically ordered tetragonal (T) phase (a = 3.879(3)Å, c = 11.740(3)Å) to an antiferromagnetic (AF) orthorhombic (O) phase (a = 5.5312(2)Å, b = 5.4576(2)Å, c = 11.683(1)Å) below approximately 170 K.9,10 In the O phase, Fe moments order in the so called AF2 structure 11 with moments directed along the aaxis of the orthorhombic structure.10 Neutron powder diffraction measurements 12 of CaFe 2 As 2 under hydrostatic pressure found that for p>0.35 GPa (at T=50 K), the antiferromagnetic O phase transforms to a new, non-magnetically ordered, collapsed tetragonal (cT) structure (a = 3.9792(1)Å, c = 10.6379(6)Å) with a dramatic decrease in both the unit cell volume (5%) and the c/a ratio (11%). The transition to the cT phase occurs in close proximity to the pressure at which superconductivity is first observed. 1 Total energy calculations based on this cT s...