When you warm a metal rod, where does the heat you put in go? It goes into the vibrations of the atoms. The atoms are connected by springs, and their vibrations become waves running through the whole crystal — phonons. In ①, we take a two-dimensional crystal with periodic boundary conditions and actually make it shake as the temperature is raised. The amplitude follows the formula for the atomic displacement parameter ADP exactly, so the vibration does not stop even when the temperature is set to 0. In ②, we plot the constant-volume specific heat per atom as a function of temperature. Classical theory says it stays at 3kB regardless of T (the Dulong–Petit law), but in reality it drops to 0 as T → 0. In ③, we see why. Vibrational energy can be exchanged only in quanta of ħω, and a mode whose quantum is larger than kBT stays asleep.
The Debye temperature ΘD, atomic weight, lattice constant, metallic radius, and melting point are standard literature values. The ADP and the specific heat come from the (three-dimensional) Debye model; only the appearance of the waves in ① follows the dispersion of a two-dimensional square lattice.