TheLindemann index^[1] is a simple measure of thermally drivendisorder in atoms or molecules.

The local Lindemann index is defined as:^[2]

${\displaystyle q_i=\frac{1}{N-1}\sum _{j\ne i}\frac{\sqrt{⟨r_{ij}^2⟩-⟨r_{ij}{⟩}^2}}{⟨r_{ij}⟩}}$ 

where angle brackets indicate a time average. The global Lindemann index is a system average of this quantity.

Incondensed matter physics

a departure fromlinearity in the behaviour of the global Lindemann index or an increase above a threshold value related to the spacing betweenatoms (ormicelles, particles, globules, etc.) is often taken as the indication that a solid-liquidphase transition has taken place. SeeLindemann melting criterion.

Biomolecules

often possess separate regions with different order characteristics. In order to quantify or illustrate local disorder, the local Lindemann index can be used.^[3]

Care must be taken if the molecule possesses globally defined dynamics, such as about a hinge or pivot, because these motions will obscure the local motions which the Lindemann index is designed to quantify. An appropriate tactic in this circumstance is to sum ther_ij only over a small number of neighbouring atoms to arrive at eachq_i. A further variety of such modifications to the Lindemann index are available and have different merits, e.g. for the study ofglassy vscrystalline materials.^[4]