When the clay coating process is done, the blade is heated again until it reach it’s critical temperature, which depends on the kind of steel that is used but will have an average of 750 – 800°C.
Once the blade reached the 750-800°C, the structure of steel changes to austenite. Now, when the blade is quickly cooled by quenching (in water), austenite changes to martensite, the hardest type of steel. However, because of the clay application, the blade will cool more slowly where the clay is thick (on the back of the blade), turning not into martensite but instead forming ferrite and pearlite, which are softer and more flexible. So as result, you will get martensite on the edge and ferrite & pearlite on the back which gives the sword a ‘flexible construction’.
This hardening process also creates a visible change in the surface of the metal. It mainly depends on how the clay mixture was applied, but variety of effects can be produced and seen without looking ‘inside’ the blade. This pattern is called the hamon, and is one of the most important aspects in the aesthetic appearance of the Japanese sword. Like the jihada ( the surface pattern of the blade ), each of these hamon patterns has a specific name. Sugu, for example, is a very straight hamon, Gunome a zigzag pattern, Notare a wave pattern,etc.
Once the blade is successfully hardenend ( and in most cases, 50% or more of the blades are failing and does show cracks along the blade ) it’s not totally done. In most of the info your read, they talk about the forging, the hardening and that they continue with the polishing, mounting, etc but they all forget 1 important step, the tempering of the blade.
During the tempering process, the blade is heated again but this time to a much lower temperature and re-quenched. Since the temperature is far below the critical temperature (that is needed to harden the blade and change the structure of the steel), it won’t change the molecular structure of the steel anymore . Instead, it will simply help to relieve any internal stresses which the hardening process have built up.