Lab Module #12
Noon, Tuesday, December 8
Submit via Blackboard’s Digital Drop Box
The purpose of this lab module is to use Virtual Substance to compare the short-range
and long-range order (or disorder) of solid argon with its liquid counterpart.
Can the structures of solids and liquids be quantitatively modeled by
How do the long-range and short-range orders differ between a solid
structure and that if its liquid counterpart?
The organization of particles in a liquid is qualitatively different from the solid state.
zero, particles are at rest in a regular crystal lattice structure that extends infinitely in every
This perfect crystalline lattice is said to have infinite long-range order.
temperature is raised, the particles gain kinetic energy and vibrate about their rest positions, but
they remain locked in the lattice structure.
The long-range order is maintained.
At a certain
temperature, the motion reaches a critical level and the ordered structure breaks down abruptly.
This occurs at the melting point.
In the liquid state, the particles have competing influences between the intermolecular forces,
which tend to reproduce the ordered structure of the crystal lattice, and the kinetic energy, which
tends to overcome the IM forces and work against the ordered structure.
In liquids, the long-
range structure is lost altogether. Despite this, a visible short-range order still exists in the liquid
The strength of this remnant of the crystalline structure depends on the IM forces in the
Choosing a center particle in the liquid, one sees that the nearest neighbors are not randomly
oriented about it; rather, they resemble, to some extent, the structure of the solid.
nearest neighbors demonstrate a smaller, yet visible, degree of order with respect to the center
At great distance, of course, there is no evidence of structure.
Thus, liquids are said to
exhibit some short-range order but no long-range order.
The distance over which short-range
order can be observed is on the order of particle diameters; this distance decreases as the
temperature is raised because the particles have greater kinetic energy.
The radial distribution function, g(r), is one method of quantifying the degree of long- and short-
range order in a condensed phase system. The physical significance of g(r) can be visualized
as follows: pick an atom in system, e.g. the red atom in the figure above.
Then, the number of
atoms N(r) in a spherical shell between r and r+
r away from the central atom, i.e. the red atom,
is the bulk density and (4πr
dr) is the volume of the shell. If there was no spatial order,
then the number of atoms inside the spherical shell would essentially be the bulk density (