Investigation of strain on diamond crystal mounted on two parallel wires Brent Evans, University of Connecticut (presented by Richard Jones)

Brent Evans September 12, Bending and Shearing in the Diamond Radiator  Fluctuations in the position of the coherent bremsstrahlung peak were seen during g8 test runs with a thin radiator.  One proposed explanation: bending of the diamond radiator by its mount.  The 20  m-thick crystal is mounted on two parallel tungsten wires with 25  m  diameters. çIf the wires were twisted when the diamond was glued on, they would exert torques on the crystal.  Can twists of a few degrees on the wires between the mount and the crystal produce enough warping of the crystal to explain the observation?

Brent Evans September 12,    5mm x 5mm x 20  m  diamond wafer 25  m dia. tungsten wire The Diamond Mount y x

Brent Evans September 12, Torques Produced by the Diamond Mount  There are two contributions to torque in the tungsten wires, that are distinguished by imagining the wire to be a bundle of fibers.  Shear: fibers shift parallel to each other but do not change length.  Stretch: fibers change length but do not shift parallel to each other. where  is the shear modulus, Y is Young’s modulus,  the angular twist, R the wire radius and L the wire length.  Since the radius is small, we ignore the stretch part, which is nonlinear.

Brent Evans September 12, Warping Effects in the Crystal  Next, we calculated the vertical displacement of the crystal at a position x as a function of the torques exerted by each wire.  As with the wires, there is shearing, where fibers stay parallel, and bending, where they do not.  Combining the two, the solution is where l is the spacing between the wires (x direction), w its width along the wires (y direction), h its thickness (z direction),  its shearing modulus, and Y its Young’s modulus.

Brent Evans September 12, Warping Effects in the Crystal  Consider the case where the torsions on the wire are equal and opposite in sign, so that the crystal deforms to an arc, not an S-shape. The maximum vertical displacement occurs at x = l /2, and is, as a function of wire twist,  z max is about 30  m for a 10-degree twist.

Brent Evans September 12, Warping Effects in the Crystal 1.Animation: 20mm crystal (local applet)20mm crystal local applet 2.Animation: 50mm crystal (local applet)50mm crystal local applet