The Lindemann index is a simple measure of thermally driven

disorder Disorder may refer to randomness, a lack of intelligible pattern, or: Healthcare * Disorder (medicine), a functional abnormality or disturbance * Mental disorder or psychological disorder, a psychological pattern associated with distress or disab ...

in atoms or molecules.

Definition

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 State of matter, phases, that arise from electromagnetic forces between atoms and elec ...

: a departure from

linearity In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a '' polynomial''. An example of a linear function is the function defined by f(x) ...

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

atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...

s (or

micelle A micelle () or micella () ( 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 colloidal system). ...

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

phase transition In physics, chemistry, and other related fields like biology, 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 Sta ...

has taken place. See Lindemann melting criterion. ;

Biomolecule A biomolecule or biological molecule is loosely defined as a molecule produced by a living organism and essential to one or more typically biological processes. Biomolecules include large macromolecules such as proteins, carbohydrates, lipids ...

s : often possess separate regions with different order characteristics. In order to quantify or illustrate local disorder, the local Lindemann index can be used.

Factors when using the Lindemann index

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

{{reflist Molecular physics Condensed matter physics Dimensionless numbers of physics