The Lindemann index is a simple measure of thermally driven

disorder Disorder may refer to randomness, non-order, or no intelligible pattern. Disorder may also refer to: Healthcare * Disorder (medicine), a functional abnormality or disturbance * Mental disorder or psychological disorder, a psychological pattern a ...

in atoms or molecules. The local Lindemann index is defined as:

q_i = \frac \sum_ \frac

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

condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the sub ...

: a departure from

linearity Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear r ...

in the behaviour of the global Lindemann index or an increase above a threshold value related to the spacing between

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...

s (or

micelle A micelle () or micella () (plural micelles or micellae, respectively) is an aggregate (or supramolecular assembly) of surfactant amphipathic lipid molecules dispersed in a liquid, forming a colloidal suspension (also known as associated collo ...

s, particles, globules, etc.) is often taken as the indication that a solid-liquid

phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...

has taken place. See Lindemann melting criterion. ;

Biomolecule A biomolecule or biological molecule is a loosely used term for molecules present in organisms that are essential to one or more typically biological processes, such as cell division, morphogenesis, or development. Biomolecules include large ...

s : often possess separate regions with different order characteristics. In order to quantify or illustrate local disorder, the local Lindemann index can be used. 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 the r_ij only over a small number of neighbouring atoms to arrive at each q_i. A further variety of such modifications to the Lindemann index are available and have different merits, e.g. for the study of glassy vs

crystalline A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macrosc ...

materials.

References

Molecular physics Condensed matter physics Dimensionless numbers {{CMP-stub