On the tendency of solutions to tend toward ideal solutions at high temperatures

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62 Citations (Scopus)


The rule of Lupis and Elliott (LE rule) proposed for the first time in 1966 is reformulated in this article as, "Real solid, liquid and gaseous solutions (and pure gases) gradually approach the state of an ideal solution (perfect gas) as temperature increases at any fixed pressure and composition." This rule is rationalized through the heat expansion of phases and loss of any interaction with increased separation between the atoms. It is shown that the rule is valid only if the standard state is selected properly, i.e., if mixing does not involve any hidden phase changes, such as melting. It is shown that the necessary and sufficient practical conditions to obey the LE rule is the equality of signs of the heat of mixing and excess entropy of mixing and the nonequality of signs of heat of mixing and excess heat capacity of mixing of the same solution. It is shown that these two conditions are fulfilled for most of the experimentally measured high-temperature solutions. The LE rule is compared with the existing laws of thermodynamics. It is shown that the LE rule can be considered as a potential fourth law of materials thermodynamics.

Original languageEnglish
Pages (from-to)531-543
Number of pages13
JournalMetallurgical and Materials Transactions A: Physical Metallurgy and Materials Science
Issue number2
Publication statusPublished - Feb 1 2012

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Metals and Alloys

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