The X-ray optics of singly and doubly curved crystals are studied using a vector procedure and rotation matrices and general relations for the angular deviation from the Bragg angle over the crystal surface with a source aligned or misaligned on the Rowland circle. Hence, the effective scattering area, collection solid angle and diffracted X-ray intensity profile on the crystal surface are derived. The effective areas and the diffracted X-ray intensity profiles on the crystal surface for both aligned and misaligned source cases are plotted and compared. It is argued that the introduced point-focusing crystal configuration confirms the radii that have been obtained previously by a trial and error method by optimizing the crystal collection solid angle.
AbstractMulti-welled energy landscapes arising in shells with nonzero Gaussian curvature typically fade away as their thickness becomes larger because of the increased bending energy required for inversion. Motivated by this limitation, we propose a strategy to realize doubly curved shells that are bistable for any thickness. We then study the nonlinear dynamic response of one-dimensional (1D) arrays of our universally bistable shells when coupled by compressible fluid cavities. We find that the system supports the propagation of bidirectional transition waves whose characteristics can be tuned by varying both geometric parameters as well as the amount of energy supplied to initiate the waves. However, since our bistable shells have equal energy minima, the distance traveled by such waves is limited by dissipation. To overcome this limitation, we identify a strategy to realize thick bistable shells with tunable energy landscape and show that their strategic placement within the 1D array can extend the propagation distance of the supported bidirectional transition waves.
Study of the collection solid angle of doubly curved crystals