Dear Colleagues,

Thermodynamics is a well-established materials characterization tool used extensively by materials researchers. Thermodynamic parameters including enthalpy and entropy for substances under consideration are calculated by standardized mathematical procedures and the stability range of the substances are discussed in terms of free energy.

The preface to a monumental classical monograph, “Thermodynamics” originally authored by Gilbert Newton Lewis and Merle Randall revised by Kenneth S. Pitzer and Leo Brewer, was started as follows by the revising authors, Pitzer and Brewer. The first paragraph is rather long but it is worth reproducing.

“There are ancient cathedrals which, apart from their consecrated purpose, inspire solemnity and awe. Even the curious visitor speaks of serious things, with hushed voice, and as each whisper reverberates through the vaulted nave, the returning echo seems to bear message of mystery. The labor of generations of architects and artisans has been forgotten, the scaffolding erected for their toil has long since been removed, their mistakes have been erased, or have become hidden by the dust of centuries. Seeing only the perfection of the completed whole, we are impressed as by some superhuman agency. But sometimes we enter such an edifice that is still partly under construction; then the sound of hammers, the reek of tobacco, the trivial jests bandied from workman to workman, enables us to realize that these great structures are but the result of giving to ordinary human efforts a direction and a purpose.”

Thermodynamics is without doubt one of cathedrals of science. We, as ordinary science workers, must feel happy and proud to be able to contribute its continued improvement and amendment of the structural detail. From this standpoint, this Special Issue of Entropy must provide as a convenient forum for researchers working on thermodynamic and statistical thermodynamic aspects in materials research.

Thermodynamics is a powerful tool to evaluate phase boundaries between neighboring phases and especially useful for the characterization of stoichiometric compounds, but is not necessarily adequate for non-stoichiometric interstitial compounds including primary solution in the low concentration range. The devaluation of thermodynamic parameters does not demand elaboration for details of the substance to be characterized (atomic configuration pattern, whether the substance is ionic or metallic, whether the substance is organic or inorganic, etc.). This makes conventional thermodynamics very powerful as the standardized materials characterization tool to evaluate the relative stability of a substance in a given environmental condition. However, this same advantage makes thermodynamics a somewhat problematic materials characterization tool.

In contrast, statistical thermodynamics demands plausible modelling for the atomic configuration of the substance to be analyzed. When statistical thermodynamic analysis is carried out on the basis of a non-realistic atom configuration model, the derived parameters become meaningless non-sense showing irrational variation with composition. Further, unlike conventional thermodynamics, statistical thermodynamics is powerless to define the boundaries of neighboring phases, whereas atomistic interaction parameters in a given phase are evaluated by statistical thermodynamics.

As such, thermodynamics and statistical thermodynamics must be considered complementary tools of materials characterization.

It was demonstrated in the statistical thermodynamic analysis of a hypo-stoichiometric Cr₂N phase reported in 1974 that the free energy of formation of the Cr₂N phase might be drawn approximately from evaluated statistical thermodynamic parameters. Similar comparisons were also attempted later for other cases.

Therefore, it would be beneficial if efforts were invested to check compatibility between atomistic interaction parameters drawn by statistical thermodynamic analysis and macroscopic thermodynamic parameters. We hope that manuscripts submitted to this Special Issue will discuss this aspect.

Dr. Nobumitsu Shohoji
Dr. José Brito Correia
Guest Editors

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• thermodynamics
• statistical thermodynamics
• entropy
• enthalpy
• free energy
• substitutional alloy
• interstitial alloy
• lattice defect
• non-stoichiometry
• phase stability