Why is it necessary for the spins of two electrons that occupy one orbital, to be in the opposite directions? What is that law called?

Since electrons cannot have the same set of quantum numbers, a maximum of two can be in the n = 1 level, and a third electron must reside in the higher-energy n = 2 level. If there are two electrons in the n = 1 level, their spins must be in opposite directions.

they begin to vibrate harder causing the material that was solid to turn into a liquid i.e gallium or ice

the role of the microscope world in creating new materials .