### Abstract

An empirical relation for the "surface free enthalpy excess" (γ) of metals is αΔH′ where ΔH′ is the internal enthalpy (heat) of atomization and α is nearly constant (0 <α <1) with values generally between 0.2 and 0.3. It has been found that the value of a is proportional to the average number of neighbors of an atom in the surface phase. In a previous report a statistical mechanical treatment of the surface led to a temperature dependence of α that was proportional to ln m where m is the number of layers in the surface. This expression does not depend on the crystal structure, crystal face, or coordination number, and a proof of this is given here. Comparisons to the experimental results for ∂α/∂T indicate that the m = 4-10 upper layers constitute the surface, which is in good agreement with other experiments. With ΔH′ independent of temperature the temperature dependence of α also determines the temperature dependence of γ. Experimentally it is found that α decreases with temperature by about ∂α/∂T ≈ -10^{-5} K^{-1} for all metals in the periodic table. The sign of the above value is interpreted here as the average number of neighbors of an atom in the surface phase increasing with increasing temperature. The number of surface layers (m) has been calculated for solid chemical elements from their surface free enthalpy excess (γ^{0}), and the number of surface layers (m′) in their liquid phase is also suggested. The correspondence of this result to the known Eotvos semiempirical rule is discussed. A 5-20% increase in the average number of neighbors of an atom in the surface phase between 0 K and the melting temperature T_{m} is also found for different metals. This statistical mechanical treatment also leads to expressions for other thermodynamic quantities such as heat capacities and entropy. Applications to various types of shortages are also presented.

Original language | English |
---|---|

Pages (from-to) | 921-932 |

Number of pages | 12 |

Journal | Journal of Physical Chemistry |

Volume | 95 |

Issue number | 2 |

Publication status | Published - 1991 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Journal of Physical Chemistry*,

*95*(2), 921-932.

**Statistical mechanical treatment of the surface free enthalpy excess of solid chemical elements. 1. Temperature dependence.** / Kristyán, S.; Olson, John A.

Research output: Contribution to journal › Article

*Journal of Physical Chemistry*, vol. 95, no. 2, pp. 921-932.

}

TY - JOUR

T1 - Statistical mechanical treatment of the surface free enthalpy excess of solid chemical elements. 1. Temperature dependence

AU - Kristyán, S.

AU - Olson, John A.

PY - 1991

Y1 - 1991

N2 - An empirical relation for the "surface free enthalpy excess" (γ) of metals is αΔH′ where ΔH′ is the internal enthalpy (heat) of atomization and α is nearly constant (0 <α <1) with values generally between 0.2 and 0.3. It has been found that the value of a is proportional to the average number of neighbors of an atom in the surface phase. In a previous report a statistical mechanical treatment of the surface led to a temperature dependence of α that was proportional to ln m where m is the number of layers in the surface. This expression does not depend on the crystal structure, crystal face, or coordination number, and a proof of this is given here. Comparisons to the experimental results for ∂α/∂T indicate that the m = 4-10 upper layers constitute the surface, which is in good agreement with other experiments. With ΔH′ independent of temperature the temperature dependence of α also determines the temperature dependence of γ. Experimentally it is found that α decreases with temperature by about ∂α/∂T ≈ -10-5 K-1 for all metals in the periodic table. The sign of the above value is interpreted here as the average number of neighbors of an atom in the surface phase increasing with increasing temperature. The number of surface layers (m) has been calculated for solid chemical elements from their surface free enthalpy excess (γ0), and the number of surface layers (m′) in their liquid phase is also suggested. The correspondence of this result to the known Eotvos semiempirical rule is discussed. A 5-20% increase in the average number of neighbors of an atom in the surface phase between 0 K and the melting temperature Tm is also found for different metals. This statistical mechanical treatment also leads to expressions for other thermodynamic quantities such as heat capacities and entropy. Applications to various types of shortages are also presented.

AB - An empirical relation for the "surface free enthalpy excess" (γ) of metals is αΔH′ where ΔH′ is the internal enthalpy (heat) of atomization and α is nearly constant (0 <α <1) with values generally between 0.2 and 0.3. It has been found that the value of a is proportional to the average number of neighbors of an atom in the surface phase. In a previous report a statistical mechanical treatment of the surface led to a temperature dependence of α that was proportional to ln m where m is the number of layers in the surface. This expression does not depend on the crystal structure, crystal face, or coordination number, and a proof of this is given here. Comparisons to the experimental results for ∂α/∂T indicate that the m = 4-10 upper layers constitute the surface, which is in good agreement with other experiments. With ΔH′ independent of temperature the temperature dependence of α also determines the temperature dependence of γ. Experimentally it is found that α decreases with temperature by about ∂α/∂T ≈ -10-5 K-1 for all metals in the periodic table. The sign of the above value is interpreted here as the average number of neighbors of an atom in the surface phase increasing with increasing temperature. The number of surface layers (m) has been calculated for solid chemical elements from their surface free enthalpy excess (γ0), and the number of surface layers (m′) in their liquid phase is also suggested. The correspondence of this result to the known Eotvos semiempirical rule is discussed. A 5-20% increase in the average number of neighbors of an atom in the surface phase between 0 K and the melting temperature Tm is also found for different metals. This statistical mechanical treatment also leads to expressions for other thermodynamic quantities such as heat capacities and entropy. Applications to various types of shortages are also presented.

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UR - http://www.scopus.com/inward/citedby.url?scp=33646284912&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33646284912

VL - 95

SP - 921

EP - 932

JO - Journal of Physical Chemistry

JF - Journal of Physical Chemistry

SN - 0022-3654

IS - 2

ER -