### 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 language | English |
---|---|

Pages (from-to) | 8164-8170 |

Number of pages | 7 |

Journal | Journal of Nanoscience and Nanotechnology |

Volume | 10 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 2010 |

### Fingerprint

### 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

**The extension of the phase rule to nano-systems and on the quaternary point in one-component nano phase diagrams.** / Kaptay, G.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - The extension of the phase rule to nano-systems and on the quaternary point in one-component nano phase diagrams

AU - Kaptay, G.

PY - 2010/12

Y1 - 2010/12

N2 - 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.

AB - 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.

KW - Nano systems

KW - Phase diagram

KW - Phase rule

KW - Quaternary point

KW - Thallium

UR - http://www.scopus.com/inward/record.url?scp=79955543377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955543377&partnerID=8YFLogxK

U2 - 10.1166/jnn.2010.3047

DO - 10.1166/jnn.2010.3047

M3 - Article

C2 - 21121311

AN - SCOPUS:79955543377

VL - 10

SP - 8164

EP - 8170

JO - Journal of Nanoscience and Nanotechnology

JF - Journal of Nanoscience and Nanotechnology

SN - 1533-4880

IS - 12

ER -