Modern thermodynamics originates from Clausius' work 160 years ago.
Simple energy distriburion curves help students grasp the idea of
thermodynamic stability from a statistical thermodynamic view point.

You may be interested in the Fortran program used to calculate
the Free Energy Curves in a 4x4 two-dimensional array with 16 atoms:
Here you find it in a text-file-style .f90 format.

An noticeable aspect of this calculation is described in the paper as follows:
In Figs. 4, 6, and 9, the distribution curves at 0 K are similar to those curves
that are seen in textbooks. This indicates that a layer of 4-atom thickness
may possibly reflect the properties of a bulk body, in fortuitous agreement with
experiences in electron diffraction of thin films.

Some noticeable results of the paper, based on the above facts, are:
Figure 7 Calculated order-disorder equilibrium temperatures for 4x4 arrays with EAA = -40, EAB = EBA = -41, and EBB = -38 kJ/mol.
Fig. 7. Calculated order-disorder equilibrium temperatures
for 4x4 arrays with E(A-A) = -40, E(A-B) = E(B-A) = -41, and E(B-B) = -38 kJ/mol.


Fig. 6. Energy distributions for a 4x4 array of 12 A atoms and 4 B atoms (XB = 0.25)
at 0 K with E(A-A) = -40, E(A-B) = E(B-A) = -41, and E(B-B) = -38 kJ/mol.


Fig. 9 Energy distributions for a 4x4 array of 8 A atoms and 8 B atoms (XB = 0.5)
at 0 K with E(A-A) = -40, E(A-B) = E(B-A) = -38, and E(B-B) = -41 kJ/mol.

 


Fig. 4. Free energy distributions for a 4x4 square array of
8 A atoms and 8 B atoms (XB = 0.5)
with E(A-A) = -40, E(A-B) = E(B-A) = -41, and E(B-B) = -38 kJ/mol.


The published version is available in
Journal of Materials Education, Volume 31, Numbers 3 - 4.



Abstract

When teaching thermodynamics to students in materials science, premature introduction of the term gentropyh
often makes it difficult for them to understand its essence and the role it plays in phase stability.
This paper starts from the physical stability that they feel when the gravitational energy is lowest,
describes the historical development of entropy within thermodynamics, and finally
shows a better way for students to understand the role that entropy plays in assessing the thermodynamic stability.