CROSSWORD SIMPLE-CAPITAL LETTER PROBLEM?

I filled a crossword in for an exercise, I got all the words correct but I'm not sure whether to use capital or simple letters because the words involve scientific terms like elements, radians, tan etc. for example Archimedes crosses with Eco and IR so then it's spelled "ArchImEdes". Simple - Capital really matters for this puzzle. What's the correct way to fill it.