Transcending Lindemann's predictions for the melting temperatures of metals and for the long-wavelength limit of their liquid structure factors

Abstract

Lindemann's melting criterion remains useful. However, one prediction it makes for liquid metals (our focus here) is that the long-wavelength limit of the structure factor S(q) at freezing, S _{T m} (0), where T _m is the melting temperature, is a universal constant. For 34 metals we have calculated S _{T m} (0) from input data, which is essentially the measured T _m and the surface thickness L, defined near freezing as the product of isothermal compressibility and surface tension. To complete the characterization of S _{T m} (0) we fit to one metal, chosen as Rb, for which S _{T m} (0) is well established experimentally. For a wide variety of metals considered, S _{T m} (0) is then found to vary by a factor of 10.

Keywords:

• melting temperature
• liquid metals
• Lindemann criterion

Acknowledgements

This work was supported by MEC of Spain (Grant MAT2005-60544-C03-01) and Junta de Castilla y Leon (Grants VA017A08 and GR23). J.A. Alonso acknowledges an Ikerbasque fellowship from the Basque Foundation for Science. N.H. March wishes to acknowledge the hospitality of Departamento de Física Teórica, Atómica y Optica, University of Valladolid. He also thanks Professors D. Van Dyck and D. Lamoen for making possible his continuing affiliation with the University of Antwerp (UA). Partial financial support from the UA is acknowledged through the BOF–NOI.