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Pair distribution function
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Pair distribution function : ウィキペディア英語版
Pair distribution function
The pair distribution function (PDF) describes the distribution of distances between pairs of particles contained within a given volume. Mathematically, if ''a'' and ''b'' are two particles in a fluid, the PDF of ''b'' with respect to ''a'', denoted by g_(\vec) is the probability of finding the particle ''b'' at the distance \vec from ''a'', with ''a'' taken as the origin of coordinates.
== Overview ==
The pair distribution function is used to describe the distribution of objects within a medium (for example, oranges in a crate or nitrogen molecules in a gas cylinder). If the medium is homogeneous (i.e. every spatial location has identical properties), then there is an equal probability density for finding an object at any position \vec:
:p(\vec)=1/V,
where V is the volume of the container. On the other hand, the likelihood of finding ''pairs of objects'' at given positions (i.e. the two-body probability density) is not uniform. For example, pairs of hard balls must be separated by at least the diameter of a ball. The pair distribution function g(\vec,\vec) is obtained by scaling the two-body probability density function by the total number of objects N and the size of the container:
:g(\vec, \vec') = p(\vec,\vec') V^2 \frac.
In the common case where the number of objects in the container is large, this simplifies to give:
:g(\vec, \vec') \approx p(\vec,\vec') V^2.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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