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Message ID: 114     Entry time: Thu Sep 15 15:15:10 2016
Author: Gabriele 
Type: General 
Category: General 
Subject: Edge effect on losses 

I made a COMSOL model that can compute the distribution of elastic energy for each mode, dividing it into:

  • bulk and shear energies (integrated over the entire volume)
  • edge energy (integrated over the edge surface only)
  • surface energy (integrated over the top and bottom surfaces)

Then I used the measured Q values for the MO_101 disk and tried to see if I could reproduce it with the energy distribution. The first plot here shows that the loss angle of the disk (inverse of the Q) has a trend that is already quite well reproduced by the ratio on edge energy over total energy:

In particular the edge energy distribution is enough to explain the splitting of the modes in families. This fit is obtained assuming that the edge losses are uniform along the entire edge, and frequency independent. If we assume a "thickness" of the edge of the order of 1 micron, the loss angle is about 3.5e-3, which seems resonable to me since the edge is not polished.

Then I tried to improve the fit by adding also bulk, shear and surface losses. It turns out that shear is not very important, while bulk and surface are almost degenerate. The following plot shows a fit using only edge and surface losses:


The result is improved, expecially for the modes with lower loss angle. Again, assuming a surface thickness of 1 micron, the main surfaces have a loss angle of 1.3e-5, while the edge is 2.3e-3.

Including all possible losses gives a fit which is basically as good as the one above:

However, the parameters I got are a bit differentL: the surface losses are reduced to zero, while bulk dominates with a loss angle of 1.4e-4, and shear is not relevant. 

In conclusion, I think the only clear message is that the Q of our disks are indeed limited by the edge. The remaining differences are difficult to ascribe to a paritcular source. Since th disks are thin, I tend to ascribe them to the surface, which would imply that we are far from being able to see the bulk/shear losses. If I use only edge and surface losses, I found as expected that the polished main surfaces have much lower loss angle by a factor 200 or so.


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