Permissions for Reuse

The solidification of a liquid by nucleation is an important first order phase transition process. It is known that in order for elemental liquids to solidify homogeneously, it is necessary to supercool the liquid to a characteristic temperature (T_UC) below the thermodynamic melting point (T_MP). Approximately 60 years ago Turnbull [J. Appl. Phys. 21, 1022 (1950)] established the empirical rule that T^*=|T_UC−T_MP| is approximately given by 0.18  T_MP for several elemental metallic liquids. We show here that the magnitude of T^* and T_UC for the metals can be accurately predicted from classical nucleation theory (CNT) provided the excess volume resulting from the density difference between liquid and solid be accounted for. Specifically, the density change accompanying the formation of a microscopic nucleus of the solid from the liquid results in a volume change in the surrounding liquid. When this is included in the free energy calculations within CNT, the resulting predictions for T^* and T_UC for several metals with T_MP ranging from ~200 to 2900 K are in very good agreement with experimental measurements. This theory also shows that there is a universal character in the minimum nucleation barrier energy and the critical radius. The minimum barrier energy occurs at temperature T_N~0.27  T_MP for all the elemental liquids investigated, while the temperature dependencies of the barrier energy and the critical radius appear identical when expressed as a function of the scaled temperature T_UC/T_MP. ©2008 American Institute of Physics

Contents

• INTRODUCTION
• THEORY
  • A.Modified CNT
• RESULTS
  • A.Characteristic undercooling in bulk liquids
  • B.Critical activation barrier energy and radius for solidification
• DISCUSSION AND CONCLUSION
• § 5
• REFERENCES
• FIGURES
• TABLES
• FOOTNOTES