Lindemann melting criterion ($\sqrt{⟨x^2⟩}=c_{L}d$)

Frederick Lindemann's heuristic associates melting with vibrational displacement reaching a specified fraction of the nearest-neighbor distance $d$. The displacement convention must be stated: one-coordinate variance and full three-dimensional variance differ by a factor of three. With the high-temperature Einstein mean-square displacement, the displayed convention gives $T_m=c_L^2{d}^{2}m{k}_B{T}_E^2/{\hslash }^2$. Neither $c_L$ nor the independent-oscillator approximation is universal.