No, it was "volume per mass" = lower density. Density and volume are inverts. Density decreases when volume increases. My example is always feathers vs lead, "A pound of feathers occupies more volume than a pound of lead. It has higher volume per mass and lower density".
I did have one part slightly wrong and adjusted the wording. I edited it. Here is the better explanation:
The blade is all austenite at austenitization temp ... even under the clay. Upon quench the edge cools quicker than the clayed spine.
Because the edge cools rapidly enough to not transform into pearlite, it misses the pearlite nose and stays as super-cooled austenite (which is very soft). As the clayed spine drops below 1000°F if stays within the pearlite nose and converts to pearlite. Thus, the spine expands causing the downward curve. When the steel at the edge then transforms into martensite at 400°F it becomes less dense than the pearlite spine, so it expands greatly, causing the backwards curvature. As the structure changes from soft super-saturated austenite to martensite it becomes very brittle and can tear itself apart as the curvature changes.
Here is an in-depth thread about it. Kevin Cashen and I both posted longer explanations of the reasons for curvature.
I just forged a Japanese style short sword (wakizashi?) and I'm wondering how straight it should be prior to heat treat. From what I've read, it sounds like water makes it curve one way, and oil the other. So I'm wondering if a fast oil like Parks #50 will make it curve the same as water...
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They are the same basic reasons that warp happens in a billet of two different steels. One thing that is a common misunderstanding is the confusion with thermal expansion/shrinking caused by heating and cooling vs structural expansion/shrinking caused by a change in the atomic arrangement of the structure. FCC is denser than BCC. Austenite is FCC and martensite is BCC (technically BCT in high carbon steel). While thermal changes are there, the largest factor is structural.
Just to finish up this tech talk:
In the conversion from austenite to pearlite, the spine gets harder. The pearlite is not as hard as martensite, but it is harder than the austenite it used to be. While harder, the spine is also less tough. The edge is soft, rubbery, super-cooled austenite so it doesn't care about the change in curvature. So, when the edge expands as it becomes brittle martensite the spine does not want to change its shape. It will lose the battle and curve, but this causes extreme stress between the two areas, and something has to give. If all goes right the spine curves upward and the edge hardens. A quick temper removes the stresses, and all is well. Sometimes they fight it out until one of the two strictures can't take the stress anymore. It is usually the brittle edge. I have seen a blade split lengthwise along the transition area following the hamon line due to this phenomenon. This is what shears a san-mai billet down the spine.