How exactly does a point-contact razor blade diode work?
Buried in the Wikipedia Article on Crystal Radio is an asseration that a cat's whisker detector is a form of Schottky Barrier Diode formed by the junction between a metal and a metal oxide semiconductor.  This would be in contrast to an "ordinary" diode formed by the junction between two semiconductors being relatively P-type vs N-type with respect to one another.

However, there was a lot of variation in materials used, and getting satisfactory results seemed to require a lot of manual adjustment to find a region with the right properties and suitable contact pressure, so it is at least worth considering if more than one phenomenon has been utilized - one might ask if there might also have been junctions between regions of different oxidation states, for example.  

A contrasting explanation is that of a point contact diode, where the migration of metal from the contact wire into the semiconductor serves to locally dope a region to differing properties than the surrounding bulk - apparently this is done in manufacturing by passing a large current through it to cause migration, so it's an interesting question if anyone ever "primed" their cat's whisker setup with a few electrochemical battery cells.  Jeri Ellsworth electro-forms such doped regions around a phosphor broze wire by discharging a capacitor through a resistor.

It so happens that if you want to make a crystal-radio like device today (or a diode power detector for measuring RF) a modern packaged Schottky Diode is a frequent choice, typically having a low forward voltage and often being more available and cheaper than a Germanium Diode.