Basically they work like a sword. You, simply put, clobber people with it. Or you skewer them with it. You do not saw them with it. You need teeth for proper sawing.
And I don't think that, even with adamantine, you could cut people in twain. It's amusing, yeah, but not very viable. There's more to it than just the sharpness/wobbliness of the blade. Maybe you could cut someone in half if you held them taut on something like a vertical torture rack.
Also, having a "razor" edge on a sword is a waste and useless.
Alsoalso I doubt it is possible to have anything "a" molecule thick. But then I'm not a scientastic person. How thick is a molecule?
A katana is a sawing weapon, Really. It has microscopic serrations.
Much like every cutting implement, yeah. I know you said microscopic but I'd also like to mention it's not something to brag about if you can either see or feel serrations on your blade.
And really, are you suggesting your dwarves try sawing goblins in half? Not even a stark raving mad goblin would allow you to do that.
*snip, adressed above* Katana are not used to strike one another in the fashion that a western fencing sword is.
Woof, that's really rather far too broad to say. And inaccurate. Swords, not even fencing swords, were ever intended to strike one another. Parrying happened, ofcourse, but the point there is that you a) keep your opponents blade away from you and b) that you do not turn your own blade into a decorative chunk of metal. Parrying with the edge is a bad idea for the quality of your blade and its edge.
Regardless, the enemy's sword isn't your enemy. Your enemy is. Hit him, not his sword.
Katana have 2 distinct types of metal used in construction, and the cutting edge is VERY VERY FRAGILE. (A curse from feudal japan is "May your sword shatter and break") Katana have only 1 cutting edge. The other is blunt, and made of mild, low carbon steel. When using the katana to deflect a blow, this blunt side is offered to the incoming blade, in the attempt to shatter the enemy blade. This 2 metal composition is what causes the sword's unique bowed shape. (The two metals have different modulus of elasticity, and different rates of thermal contraction.)
1. Every cutting edge is fragile. Comparatively so anyway. It's why things need sharpening once every so much time.
Scissors have this problem, for chrissakes.
2. I'm not an expert but AFAIK it really isn't all that clear-cut. I don't know (or really care, sorry) where you got the information from that the blunt side is offered to the incoming blade but a) yeah, that makes sense. Doing otherwise is a good ticket to bluntsville for your own sword too and b) shatter? Really? Blunt, sure, I can see that, but a swordedge isn't a pane of glass attached to spun sugar. It's not going to break that easy.
3. I rather think the shape is due to the heat treatment. Two different kinds of metal, fine, but that's not going to pull it out of shape all by itself. You'd need substantial heat for the differences to have any effect.
Due to the fragility of high carbon steels, a katana needs to be "Folded" and "Laminated". Basically, this means that part of the structural integrity of the blade is maintaned by the softer, mild steel in the back part of the blade, because it is folded in with the high carbon, fragile steel in layers. The mild steel bulks up the blade, but makes it so that it wont shatter if it strikes poorly, and gives it a little flexibility it otherwise wouldn't have.
The Japanese didn't fold metal so much due to the fragility of high carbon steel or whatever but rather because their iron ores were rather poor and they needed a hell of a lot of work to produce anything useful. The Celts in europe had been using it for over a thousand years before the Japanese came up with it, the Byzantines used it and europe had pretty much already discarded it by the time Katana-forging reached its zenith; Europe could reliable produce high-grade steels by that time which was both better and cheaper.
To put it really bluntly, it's like polishing a turd. You can go through all the effort and unleash an enormous level of craftsmanship at it but it's still a turd.
(note to self: feces-based weaponry in DF? Worth a thought.)
Imaginary Adamantine does not suffer a high fragility, like high carbon steel. As such, it wouldnt need lamination, could be made absurdly thin, and could be used absurdly fast. It would be like giving "Super paper cuts" rather than "Chopping".
I thought you wanted your enemies to die. Bleeding someone to death via paper cuts, super or otherwise is going to take ages. And they won't appreciate your honest effort. This is more of an issue of technique than material anyway.
Basically, a super paper-thin nano-serrated razorblade that never goes dull, and is 5ft long. Due to not needing to be laminated, and not needing a deflecting edge because the cutting edge cant shatter, it would\could be a 2-edged straight sword.
Sounds fun. A katana is a bit shorter though. And if you ignore the folding, the laminating, the deflecting edge, the material and the shape then yeah you could end up with a 2-edged straight sword. Which wouldn't be a katana anymore.
At five foot you essentially have a slightly oversized standard-fantasy longsword. Well done.
(Though curved would permit easier use.)
Eh, I'm not sure if it is by definition "easier" use. A curved blade is a bit more forgiving for slashes and
automatically imparts a drawing motion though, so it might help. An inversely-curved blade (imagine a sickle, a khopesh or a kukri) allows for a greater concentration of force in one spot which makes for better chopping and a straight sword is a good balance between the two with, in addition, being the best for stabbing. What could be awesome is a weighted adamantine blade with an inverse curve.