The very purpose of the powdered steel mentioned by the previous poster is to improve this tradeoff between ductility and hardness. The simplest carbon steels

The very purpose of the powdered steel mentioned by the previous poster is to improve this tradeoff between ductility and hardness. The simplest carbon steels can be made very hard with an appropriate heat treatment, if they have high carbon content, but then, as you say, they chip too easily. The various kinds of alloyed steels that can be used instead of carbon steel attempt to improve the tradeoff between ductility and hardness, so that one may choose a heat treatment that results in greater hardness without making the blade as fragile as a blade made of carbon steel with the same hardness. The alloyed steels made using powder metallurgy are said to achieve the best tradeoff between hardness and ductility, but I have not tested this yet, because they are also the most expensive. In the past I have used softer German style steels, but I do not like having to sharpen them, so now I prefer to use only harder and sharper Japanese knives, which must be sharpened much less frequently.