The extension of the phase rule to nano-systems and on the quaternary point in one-component nano phase diagrams

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Abstract

The phase rule of Gibbs has been extended to nano-systems in this paper. For that, first the total number of atoms or stable molecules (N) in the system is selected as a new independent thermodynamic variable to characterize the size of nano-systems. N is preferred to r (the radius of the system) as the volume and radius are functions of other independent variables (p, T, composition) and therefore r is not an independent variable. As follows from the extended phase rule, the maximum number of phases and the degree of freedom at a given number of phases is increased by 1 for nano-systems compared to macro-systems, due to the new independent thermodynamic parameter N. The extended phase rule can serve as the basis to work out topological details of nano phase diagrams. As an example, an existence of a quaternary point is predicted in one component nano phase diagram of thallium (in contrast to usual one component phase diagrams with triple points at most). At given values of p = 7.2E-12 bar, T = 544 K, and N = 1.2E5, HCP (hexagonal closely packed solid), BCC (body centered cubic solid), liquid and vapour phases of pure Tl are predicted to be in equilibrium.

Original languageEnglish
Pages (from-to)8164-8170
Number of pages7
JournalJournal of Nanoscience and Nanotechnology
Volume10
Issue number12
DOIs
Publication statusPublished - Dec 2010

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phase rule
Thermodynamics
Phase diagrams
phase diagrams
Thallium
thermodynamics
radii
thallium
Macros
solid phases
liquid phases
degrees of freedom
Vapors
vapor phases
Atoms
Molecules
Liquids
Chemical analysis
atoms
molecules

Keywords

  • Nano systems
  • Phase diagram
  • Phase rule
  • Quaternary point
  • Thallium

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Chemistry(all)
  • Materials Science(all)
  • Bioengineering
  • Biomedical Engineering

Cite this

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abstract = "The phase rule of Gibbs has been extended to nano-systems in this paper. For that, first the total number of atoms or stable molecules (N) in the system is selected as a new independent thermodynamic variable to characterize the size of nano-systems. N is preferred to r (the radius of the system) as the volume and radius are functions of other independent variables (p, T, composition) and therefore r is not an independent variable. As follows from the extended phase rule, the maximum number of phases and the degree of freedom at a given number of phases is increased by 1 for nano-systems compared to macro-systems, due to the new independent thermodynamic parameter N. The extended phase rule can serve as the basis to work out topological details of nano phase diagrams. As an example, an existence of a quaternary point is predicted in one component nano phase diagram of thallium (in contrast to usual one component phase diagrams with triple points at most). At given values of p = 7.2E-12 bar, T = 544 K, and N = 1.2E5, HCP (hexagonal closely packed solid), BCC (body centered cubic solid), liquid and vapour phases of pure Tl are predicted to be in equilibrium.",
keywords = "Nano systems, Phase diagram, Phase rule, Quaternary point, Thallium",
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