Phonon Thermal Conductivity — the Umklapp Peak

Every crystalline solid's thermal conductivity κ(T) traces the same shape: it rises steeply at low temperature, peaks, then slowly falls as temperature keeps climbing. This simulator renders the two competing mechanisms behind that curve — a phonon gas whose heat capacity grows with temperature via the Debye model, and a mean free path that starts long (limited only by the crystal's grain boundaries) and collapses as Umklapp phonon-phonon scattering takes over. Pick a real material preset (diamond, silicon or rock salt), drag the temperature and grain-size sliders, and watch a single phonon's schematic random walk through a spring-coupled atomic chain while the live κ(T) chart traces out the conductivity peak in real time.