Clear The Cookies
In browsers with a good UI you usually get an option to clear the cookies for a specific domain. So clearing the cookies will erase logged-in status from your browser.
In Chrome you can do that by clicking the small icon on the left of the URL in web address -> click "Show cookies and site data" -> And clear the cookies for
Clearing cookies aren't a great deal, though doing this many times would require you to verify yourself or should I say the device, as without those cookies Facebook would forget that you even logged in from that device. So it may once in a while require you to either verify by email or phone - just a small code verification.
Using Mobile Site
No offence, but if the desktop site of Facebook is too heavy for IE11 to handle you could alternatively use
mbasic.facebook.com which takes you to a lightweight version of Facebook for mobile (meant for phones from the Jurassic age ;) ) and log-out from their. I am pretty much sure it IE11 wouldn't crash for that small page. The logout button is at the bottom of the page.
Say no to "Keep Me Logged In"
While you log-in uncheck the "Keep Me Logged In" checkbox so that when you close your browser your session would end with it.
All you have to do to log out is close your browser and done! (Though I have seen this thing fail, it most of the times never clears the session and I would still be logged in, might be some conflict with the cookies)