Macroscopic bodies in solid state when they touch each other do not connect in one monolithic body, because of electrostatic repulsion of their electron clouds. Okay.

Say, have two iron ingot, we make them touch each other, and nothing happens. Now we melt them - they connect in one fluid. Then we cool it and it becomes being a single object.

I understand, that the heat is the atomic vibration, and if the amplitude of vibration is too high, connection among them loses. 

And I even understand intuitively, that when the body is solid “the doors are closed”, and the more we heat it the more “doors open - new guests can come in, current can come out”.

But how to explain it more scientifically? What do atoms of already melted body have, to connect with another bodies atom, that solid state body atoms don’t have?

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I think it’s because, when the body is melted, its energy levels are “blured” a lot, so the list of energies, atom can accept is more larger. But, at the same time, electrons of another body have(about) the same energies. Why can’t they be attracted then? I’m confused