 
Summary: Structural and entropic insights into the nature of the randomclosepacking limit
A. V. Anikeenko and N. N. Medvedev
Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russia
T. Aste
Department of Applied Mathematics, The Australian National University, 0200 Canberra, ACT, Australia
Received 14 September 2007; revised manuscript received 27 November 2007; published 3 March 2008
Disordered packings of equal sized spheres cannot be generated above the limiting density fraction of
volume occupied by the spheres of 0.64 without introducing some partial crystallization. The nature of this
"randomclosepacking" limit RCP is investigated by using both geometrical and statistical mechanics tools
applied to a large set of experiments and numerical simulations of equalsized sphere packings. The study of
the Delaunay simplexes decomposition reveals that the fraction of "quasiperfect tetrahedra" grows with the
density up to a saturation fraction of 30% reached at the RCP limit. At this limit the fraction of aggregate
"polytetrahedral" structures made of quasiperfect tetrahedra which share a common triangular face reaches it
maximal extension involving all the spheres. Above the RCP limit the polytetrahedral structure gets rapidly
disassembled. The entropy of the disordered packings, calculated from the study of the local volume fluctua
tions, decreases uniformly and vanishes at the extrapolated limit K 0.66. Before such limit, and precisely
in the range of densities between 0.646 and 0.66, a phase separated mixture of disordered and crystalline
phases is observed.
DOI: 10.1103/PhysRevE.77.031101 PACS number s : 05.40. a, 45.70. n, 45.70.Cc, 81.05.Rm
I. INTRODUCTION
