Published 2004
| Version v1
Publication
CLOSED-FORM EXPRESSION FOR THE POTENTIAL WITHIN A FACE-CENTRED CUBIC IONIC CRYSTAL
Creators
Contributors
Others:
Description
In this work we deal with the electrostatic potential generated by a periodical system of
charges in the space. Specifically, we consider a three-dimensional mesh having cubic cells,
whose nodes are occupied by point charges +Q or- Q; so that each positive (negative) charge
is surrounded by six negative (positive) charges at distances d: This system clearly models a
face centred cubic (FCC) ionic crystal that we further assume to extend to infinity in every
direction. Considering ions as point particles subject only to coulombic interactions, the
potential here concerned can be expressed by means of an alternating series that exhibits a very
slowconvergence, giving rise to computational difficulties.
In the following we illustrate an alternative formula for the potential, consisting in a closedform
expression involving the elliptic Jacobi Theta functions. Such formula provides either an
immediate interpretation from an analytical point of view, and a fast converging procedure for
numerical purposes.
Finally, we illustrate an application of our methodology concerning the calculus of the
Madelung constant in the case of an ideal FCC ionic crystal. Numerical accuracy and
computational costs are comparable with those of the most rapidly converging formulas
previously known.
Additional details
Identifiers
- URL
- http://hdl.handle.net/11567/206257
- URN
- urn:oai:iris.unige.it:11567/206257