Captain R. Dennistown Buchanan was appointed an Ensign by purchase on 19 Jan 1849; promoted to Lieutenant by purchase 2 Aug 1850; promoted to Captain by purchase 1 Dec 1854. Buchanan "served in the Eastern campaign of 1855, including the expedition to Kertch, the siege and fall of Sebastopol, and the attack of 18th June (Medal and Clasp)--taken from Hart's Army List July 1856, p. 174, and Note 5 on page 175. His Crimean Medal entitlement appears on page 435 (and also on page 456) of the 72nd's Medal Rolls; the award of the Sebastopol Clasp (barely legible) is recorded on page 476.
Buchanan does not appear in Hart's for 1860, so it is a good guess he left the service before then.
Best of luck in your researches,
Lawrence Crider Author, In Search of the Light Brigade Editor, The War Correspondent: journal of the Crimean War Research Society