Hi adam,
Just right-click on the avast icon and select the "Close and exit" at the bottom of the menu. This stops all resident providers, which are all you'd have problems with. Don't forget to start them again afterwards.
Actually all you really need to do is (in that same menu) Pause the Standard shield -- none of the other providers should interfere with degragging. Again, don't forget to resume it afterwards.
Sliightly off-topic, but closely related -- if you happen to also use Javacool's SpywareGuard. While I don't think this is mentioned anywhere in its Help, Javacool recommends you shut that down too while defragging because of a history of problems. Select Options, untick all three boxes, and Save Settings (your SG icon will become x'd-out), then Exit Program from its menu.
When you're done defragging, restart SG (from the deskton icon, or from the Start Menu), re-tick the 3 categories and save settings again, then close its window and it's back to normal.
Best,
Mike