Model of Melting and Heat Transfer in Metals

E S Filippov

doi:10.5539/apr.v9n2p1

Abstract

Volumetric relationships under the thermal expansion of metals are analyzed. It is shown that the metals with the bcc structure possess a two-step structural change at the melting point: first, the transformation of the bcc structure to a fcc one takes place and then, liquid phase clusters with K = 12 are formed. The hexagonally packed (6 + 6) layered Cd and Zn change their structure from K=6 to K = 8 before melting. For the polymorphic transformations fcc (hcp) -- bcc, the value of thermal expansion was sufficient to change K = 12 for K = 8 long before the melting point. It is assumed that at high temperatures, thermal energy transfer is associated with the exchange fluctuations: higher electron density +K lambda and low electron density –K lambda over the coordinate of interatomic distances, wher lambda = h/mc and K is the number of nearest neighbors.

Highlights

Introduction and Statement of the ProblemTwo points essentially define the initial premises for the model - theoretical studies at high temperatures: blurring of band structure and a pseudo-potential approximation of the electronion interaction
This makes it possible to admit the electron density fluctuations in the coordinate space ra - ri, the occurrence of which we connect with the distance from the nucleus and the formation of a self-closing orbital, that is, with the formation of a standing wave from the side of ri that, can be attributed to the maximum electron density fluctuation
We have a basic assumption – the volume of thermal expansion (∆Vт) from 0K to Tmelt and the derivative of it - a linear increment (∆Vт)1/3 - we refer to the value of the anharmonicity

Summary

Introduction

Searching for this limit led to a quantity directly related to the pseudo-potential approximation of the electron-ion interaction: (∆Vт)1/3 + ri = ra Equation (7) is valid within ± 3,5% for 14 metals. The adiabatic assumption allows to consider it as a condition for the occurrence of the density fluctuation: (∆Vт)1/3 + ri = ra, the size of which corresponds to the atomic size (ra), that is, to the fluctuation K + 1, and to the experimentally determined increase in the number of vacancies at the melting point ( up to 10 atomic % ≈ 100 [(K + 1) – K] / K).

Results

Conclusion