Graduation Year


Document Type




Degree Granting Department

Mechanical Engineering

Major Professor

Alex A. Volinsky Ph.D.


Thin films, Residual stress, X-Ray diffraction, Sin²psi technique


Silicon is used as a substrate for X-ray mirrors for correct imaging. The substrate needs to be mechanically bent to produce a certain curvature in order to condition and focus the X-ray beam. The X-rays impinge a mirror at very shallow angles, in order to reduce the amount of intensity loss in the diffraction process. The X-ray mirrors need to be bent to an extremely precise profile, and even small distortions from this profile can reduce the effectiveness of the X-ray mirrors. The X-rays that impinge on the mirror also produce large amounts of heat that can change the temperature of the substrate, resulting in its thermal expansion and distortion. By measuring the distortions in-situ caused by these temperature changes it may be possible to correct for these errors. A four-point bending fixture was designed for in-situ X-ray bending experiments in order to measure the distortions to the (100) silicon sample caused by the bending setup.

By being able to measure the distortion caused by the setup, in like manner it would be possible to measure distortion caused by thermal expansion. Several alignments were needed in order to obtain accurate results, including adding copper powder on top of the sample. The copper powder that was added is not under stress, and therefore will not shift its reflection peak when the sample is under bending stress, thus serving as a reference in order to make corrections. The strain results were then compared to values calculated from mechanical deflections from bending. Despite the efforts to control accuracy, a significant variation appeared in the values when the top surface was in compression. As an alternative an IONIC stress-gauge was used to measure the deflections of the sample rather than calculate them.

Another alternative was to calculate the deflection of the substrate by first determining the stress in the layer deposited onto the mirror's substrate by using sin²psi technique, then using Stoney's equation to determine the change in curvature of the substrate, with the stress in the layer being known. Several tests were performed to demonstrate the ability to measure these deflections.