Hello, What Victor is saying is not completely exact, the Luxembourg effectively was a state from germany between all the 300 + repertoried, but a part of Belgium was included in the Duchy of Luxembourg, we can sa all the province of Luxembourg was included in the Duchy. It only is when the Orange-Nassau kept thepower in 1838, the Great Duchy was separated from Germany and Belgium.
If you ancestor was coming in the U.S. in 1851, he was coming from Great Duchy. DIEKIRCH is a reknown name there as it is a city in the north of the country but also an excellent beer manufactured in the south of the country. It exists a forum which is treating of Great Duchy of Luxembourg, let me look if you always are interested.