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Crystals bent to logarithmic spirals have been used in applications where large acceptance of divergent x rays from a small source is needed. Small acceptances can be easily handled with cylindrically bent crystal. In cases where larger acceptances are needed differential bending may be adequate. However, the largest acceptance is obtained from a flat crystal plate when bent into the logarithmic spiral shape that allows the crystal to present the same angle of incidence to the beam emanating from a point source. The bending of such crystals generally can be accomplished by forcing the crystal into the required shape with a metal frame. A preliminary theoretical study of crystal shapes that when bent will naturally form logarithmic spiral shapes has been done. This study was done for the case of a cantilever beam with fixed end and a normal force applied to a point at the other end. A fixed thickness-variable width beam was considered. The crystal profile in width (direction perpendicular to the diffraction plane) can be spatially varied to achieve this spiral shape. Equations for both cases will be given. © 2002 American Institute of Physics.