The Subhron Equation: A Shortcut for Estimating Atomic Deviation in Falling Crystalline Nanoparticles English / German

This paper introduces the Subhron Equation, a mathematical shortcut for estimating the microscopic deviation of a middle atom from the center-of-mass path in a falling crystalline nanoparticle. By separating macroscopic motion from microscopic lattice vibrations, the equation provides a fast, cost-effective pre-screening tool for computational physics. Unlike the static Crystallographic B-factor, it estimates dynamic deviation during free-fall, helping researchers decide if a full molecular dynamics simulation is necessary. Keywords: nanoparticle, atomic displacement, phonons, center of mass; free fall ,RMS displacement; Debye model