Investigation of the Lindemann criterion and the melting point in complex alloys

Ryan Warren

doi:10.59973/emjsr.102

Authors

Ryan Warren School of Mathematics and Physics, University of Portsmouth, Portsmouth PO1 3HF, UK https://orcid.org/0009-0000-6771-9499

DOI:

https://doi.org/10.59973/emjsr.102

Keywords:

Lindemann coefficient, Melting Point, Melting of alloys

Abstract

Despite various theories, the understanding of melting points remains incomplete. This project extends the Lindemann melting criterion to A_1-x B_x alloys in an attempt to predict the melting temperatures of complex alloys. Frederick Lindemann developed a theory to predict melting temperatures over 100 years ago, with the assumption that melting occurs when a critical fraction of root-mean-square displacement of a crystal and interatomic spacing, known as the Lindemann coefficient, η, is exceeded. 100 years
later, Melvin Vopson developed a relationship between element groups and this coefficient, assigning a different value of this coefficient to 12 element groups on the periodic table. Presented here is an extension of this generalised Lindemann melting
criterion to extend to binary alloys, finding fair agreement with experimental data by applying effective parameters for atomic mass, Lindemann coefficient, interatomic spacing and Debye temperature, assuming these parameters take weighted averages and
applying a correction to the resulting plot.

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