You are talking to yourself.
It amazes me how no one here can grasp this simple concept. Combustibles smoldering in the debris pile will slow the cooling of the molten steel. They need not be as hot as the molten steel, they only need to raise the temperature of the debris significantly. Think of the pulverized debris as a blanket and the smoldering combustibles as turning it into an electric blanket.
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But the problem is, you have to exclude the possibility that the "electric blanket" didn't catch fire. It is within the realm of speculation that there was only enough energy to keep already-molten steel molten for weeks. But it would have to be a very narrow range of energies.
If there's not enough energy, then the puddle of molten steel cools and hardens from the outside in, and you would have to crack through the "eggshell" surrounding the liquid steel to get at it. That certainly isn't what the witnesses you've quoted described.
If there's more than enough energy, then there's enough to melt steel that wasn't melted, and there's no way to differentiate such steel from steel melted by thermite.
I have speculation of my own, but I don't think you'll like the conclusion I come to. And of course, it's only speculation. I have absolutely no way to prove it. It only had to be enough to satisfy me. I tell you what. I'll tell you about it, and then you can do the research to show me what an ignoramus I am.
The rubble pile was hot to begin with, because of the fires in it. It didn't have a free flow of oxygen, but it did have a fair amount of insulation, so that smoldering continued to keep it hot, much like the multi-year burning underground coal fires.
It did have an air supply, since there was a subway entrance in the lower levels. Within the "bathtub", of course, the air couldn't escape to the sides, so any air that came in (at a very slow rate, I imagine) would become heated and rise through the pile.
One of the things that happened was that fireboats pumped seawater over the pile to try to put out the fires. I'm sure that cooled off the top part of the pile, but to do that it had to heat the water. Some of it no doubt flashed into steam immediately. Some of it no doubt dripped, considerably hotter, further down into the pile.
Hot, salty water is a really good recipe for rusting steel. Hot, salty steam is even better.
When steel rusts, it's an exothermic reaction. It gives off heat. The rule of thumb I learned in high school chemistry is that in general, there's a doubling of reaction rate for every 10 degrees F rise in temperature. So if the heat can't be drawn away fast enough, it leads to a thermal runaway. It gets hot, the reaction happens faster, it gets hotter, which makes the reaction happen faster...
I think it's possible that, in spots, unlikely as it sounds, the steel caught fire.
This has been known to happen on ocean-going freighters carrying steel, and I assume they don't start with the cargo already hot, or have a vent on the bottom of the cargo hold to make a chimney. I imagine it can get seawater on it, though.
It wouldn't be a "fast" fire, because the oxygen was limited. But that was probably part of what made it so hot. The air wasn't moving fast enough to carry off the heat by convection, and the air that was coming into such a spot would already have been warmed by its slow trip through the lower hot parts of the pile. So a hot spot got hotter. There would be thermal energy coming into that spot, and nowhere for it to go quickly.
So it wouldn't really surprise me if while cleaning up, someone dug up a piece of metal that was plastic enough to bend under its own weight while being removed. Considering how stiff a big chunk of steel is at room temperature, it wouldn't surprise me to hear that piece of metal described as "melted", even it it wasn't liquid.
There were something like 100 acres of zinc-plated floor pan in each tower, and who knows how much lead from batteries and solder from electrical and electronic devices. So seeing metal, or glass, or metal mixed with glass in a liquid state wouldn't surprise me either.
All of this seems much more plausible to me than the idea that the configuration of the debris piles was such that it balanced on that knife edge of just enough energy in to maintain liquidity, yet not so much that previously un-melted steel would not melt. Also, there's the difficulty of proving that this knife-edge scenario is the ONLY one that could POSSIBLY have happened.
Now, I will admit right up front that much of this is personal lack-of-incredulity that things could have gotten really, really hot in the debris pile. So I don't really expect it to sway you in the least, and I'm not claiming it as a "debunking".
But the fact remains that to claim therm*te causing the collapse to be the
only possible explanation, you would have to show that a perfectly balanced energy budget with respect to energy in vs energy out existed in the debris pile. I don't think you can do that, so reports of liquid this and melted that during the cleanup, while interesting, are not evidence of much except that it was very hot in the debris pile.
I believe it was very hot in certain spots in the debris pile. I don't think that necessarily means there was therm*te involved in the collapse.
You may have that belief, but I don't see any way for you to prove that it is true.