What characteristic or property of Earth material is used to classify layers as lithosphere or asthenosphere, as well as the inner and outer core?

The lithosphere is composed of both the crust and the portion of the upper mantle that behaves as a brittle, rigid solid. The asthenosphere is partially molten upper mantle material that behaves plastically and can flow. This animation by Earthquide shows the layers by composition and by mechanical properties.

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Lithosphere                                                      

Has a lower density than the asthenosphere

Allows for conductive heat transfer

Asthenosphere

Asthenosphere is denser than the lithosphere

Allows for advective heat transfer

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not sure if this helps much, but if need i can go further into detail. happy studying!

it would be a gas formation