Not Scottish but Irish in origin, I gave it the Scottish tag temporarily as “from within the United Kingdom, but alien”.  It means, of course, “little smithers”, particles or atoms, and has not been observed as a singular in the wild.

• 12.101 in a jumble of smithereens,

“smithereens, n.” OED Online. Oxford University Press, March 2015. Web. 1 June 2015.

“ˈsmithers, n.” OED Online. Oxford University Press, March 2015. Web. 1 June 2015.