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Historic Note No. 1: Gibbs’ Phase Rule

Historic Notes is a series of articles that explore the history of materials science, thermodynamics and other related fields through the scientists who made the discoveries.

This article was generously written by Prof. Mats Hillert from the Royal Institute of Technology (Stockholm). Thermo-Calc Software would like to thank Prof. Hillert for this contribution to our blog.


Josiah Willard Gibbs 1839-1903

Gibbs’ Phase Rule

Before 1900, few people who studied phase diagrams knew anything about thermodynamics. As a result, thermodynamically incorrect phase diagrams were sometimes published. It was not until 1875 that differences in composition were included in thermodynamics, when Gibbs, of Yale University, released a paper on it. Unfortunately, only a few experts appreciated his work, and those who did had little interest in such practical matters as phase diagrams. The fact that Gibbs, in his very long and theoretical paper, had presented a simple relation that could be directly applied to phase diagrams remained unnoticed for 25 years. But that changed in 1901 when Bakhuis Roozeboom in Holland finally started exploring the usefulness of Gibbs’ phase rule.

The very long delay may have been the result of the title of Gibbs’ paper: “On the Equilibrium of Heterogeneous Substances”. Practical people interested in phase diagrams could hardly expect to find any useful information in such a paper. However, it is interesting to note that Bakhuis Roozeboom was faithful to Gibbs and gave his treatise the title “Die Heterogenen Gleichgewichte” (The Heterogeneous Equilibria). Yet this time the work was quickly recognized because it presented numerous T,x phase diagrams, whereas Gibbs had only presented a few and all of them from isothermal sections of ternary systems, a kind of phase diagram rarely studied in those days.

Heterogeneous Equilibria simply means Phase Equilibria. It is intriguing to imagine how much quicker Gibbs’ phase rule could have been applied if Gibbs had used today’s language and given his paper the title “On Phase Equilibria”.

This article is the first in a three-part series tracing the evolution of CALPHAD from the Gibbs Phase Rule to the first lattice stabilities. Click the link below to read the next article in the series.

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