Distance Geometry: A Viewing Help for the Solid-Liquid Phase Transition in Small Systems

TL;DR

This paper explores using distance geometry to analyze phase transitions in small atomic clusters, providing new insights into their thermodynamics and a general mathematical result for N-body problems.

Contribution

It introduces a novel application of distance geometry to thermodynamics of small clusters and derives a general Jacobian determinant result for N-body coordinate transformations.

Findings

Distances explain features of caloric curves in small clusters

Distance geometry offers new insights into phase transitions

Derived a general Jacobian determinant formula for N-body systems

Abstract

Distance geometry is the study of the arrangements of points in space using only the mutual distances between them. The basic idea in this letter is to use distance geometry for thermodynamics studies of small clusters in the microcanonical ensemble. There are constraints on these distances, which are shown to explain some characteristic features of the caloric curve in very small clusters containing 3 or 4 atoms. We anticipate that this approach could give a novel insight into the phase transitions in larger clusters as well. During these studies, we have established a very general and rather simple result for the Jacobian determinant of the change of variables from Cartesian coordinates to mutual distances, which is of wide applicability in the N-body problem.