I'm writing a fictional story with early industrial age technology where a chemist discovers not only that diamond and graphite are made of the same substance, but that they differ by crystalline structure (cubic vs hexagonal). However, I'd like this to be a realistic depiction if possible and the chemist does not have access to electron tunneling microscopy or advanced spectrographic methods. The farthest spectroscopy has gotten is Fraunhofer's spectroscope and John Herschel's evaporogram, with visible light and the beginnings of an understanding of infrared and ultraviolet. Would 1850's level spectroscopy or other technology of the time be able to demonstrate the crystal structures of carbon (specifically graphite and diamond) without a 1900's understanding of atomic structure?
Would 1850's level spectroscopy or other technology of the time be able to demonstrate the crystal structures of carbon (specifically graphite and diamond) without a 1900's understanding of atomic structure?
Yes, using visible light and petrographic microscopes. The field of optical mineralogy was mature enough by the mid-1800's for one to determine the crystal structure of minerals. In particular, the work of Sir William Nicol is worth investigating (thin but useful Wikipedia article).
I will add that there's a pretty simple way to determine whether or not the crystal structure of a mineral is the same or different than that of another mineral - the so-called crystal habit.
Finally, diamond exhibits conchoidal fracture, and graphite does not. This might be the easiest way to tell that the two minerals have different crystal structures.