Calcite crystals are semi-transparent but turn white when crushed. I used to think that it has something to do with the scattering of all wavelengths of light from small particles. But that cannot be the whole story. By that explanation crushed carbon should also appear white (which is not the case).
So my question is why do some substances appear white when crushed while others do not.
It depends if the substance in bulk is transparent, highly reflective (metallic) or highly absorptive.
Carbon in its graphite allotrope is highly absorptive, and even finely divided is still black.
Carbon as diamond is transparent. Crushed diamonds are white -- look at a diamond file or abrasive disk. What happens is that incident light is scattered as it encounters particle after particle, refracted or reflected repeatedly, based on particle size, shape and index of refraction (nD). A higher nD increases the amount of light reflected from particles. For that reason, titanium dioxide, $\ce{TiO2}$, which has a comparatively high index of refraction (~2.5), makes an excellent white pigment.
Metals reflect light because the "cloud" of electrons on the surface return a reflected wave out of phase with the incident wave. However, finely-divided metals have fewer electrons to share, and electrons start behaving as discrete, localized charges. Finely divided silver appears black, for example. This is the basis for traditional silver halide photography. Powdered $\ce{AgCl}$ appears white, but where hit by light, it yields metallic silver nanoparticles, which appear black (as a negative image).
If your interested, look up the effect of surface plasmons on metallic reflectivity, which can yield surprising colors, such as gold in ruby glass.
