What is or what characterize the thermodynamic state of metal (structure of metal)?

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In the solid state, metals have a crystalline structure made of metal atoms, which are drawn together by low force vanderwaals interactions. The electrons form a cloud around the atom structure and migrate from one point to the other constantly.

The structured state of the atoms allows for low entropy in this state. Depending on the metal, several different structures may form, and one metal may have more than one structure at different temperatures, since its entropy depends on atom vibration as well, which is connected to the internal energy, reflected as temperature.

Crystalline structures have, usually, a straight correlation of stress in the elastic region. When traction stress is applied, the atoms are forced away from each other, up to a point where it, theoretically, should loose coherence by breaking all interactions at once and forming new surfaces. This energy level is so high that other mechanisms of energy dissipation happen first, usually connected to defects and dislocations in the crystalline structure. These mechanisms allow for the inducing of surface cracking, or plastic deformation.
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