Are you sure this photo is of Sam Alexander? The CSA TN 16th was an infantry unit. The soldier in the pic holds a carbine, and wears a sword; these are the tools of a cavalryman. The details of the pic are faint, the carbine might be a Smith, but I can't be sure. The pic seems to be from a magazine? If so, can you provide the magazine details. I found other records for a Samuel Alexander in a cavalry unit; any possibility they are one and the same?

Interestingly, there was another TN Samuel H. Alexander. With the US, he applied for a pension in 1890, his wife,Manerva, applied for one in 1897, the year of his death. He is buried in Cleveland County, OK.

I did not find record for the named soldier in either the US or CS records in the National Archives. The above info came from www.civilwardata.com.