Isomorphs in Metals: from equilibrium crystal dynamics to melting curve determination

This thesis uses computer simulations as the main tool to explore the phase diagram of metals in the liquid and solid part of the phase diagram in the context of isomorph theory.

This work has two main goals. The first is to test the validity of isomorph theory and its predicted invariance along isomorphs throughout the solid and/or liquid part of the phase diagram of the candidate metals. The second key prediction from isomorph theory that this work focuses on pertains to the melting and freezing curve. Isomorphs that started from a point at coexistence are predicted to be closely related to the nearby freezing and melting curve and a method was devised that enables the prediction of the freezing and melting curve from data of the neighbouring isomorphs on the solid and the liquid side. The second goal of this thesis is therefore to combine predictions from isomorph theory with results from DFT to predict the freezing and melting curve over a significant range of the phase diagram from simulations at one state point only, making the most out of the costly DFT simulations.

The work is structured as follows: Some background information with focus on metals and isomorph theory will be given in the first chapter followed by a detailed review of isomorph theory and its predictions in the subsequent chapter. Chapter 3 provides an introduction to computer simulation in general. A review of the two methods employed in the simulations used for this work, density functional theory (DFT) and the effective medium theory (EMT) is given in chapter 4.
The results can be found in chapter 5 and 6 with each chapter corresponding to one of the two main focus points of this work. The first presents an investigation of the invariances predicted by isomorph theory in different candidate metals. The study includes (a) mono-atomic crystals (Ni, Cu, Pd, Ag, Pt, Au) and (b) liquid CuZr simulated using the EMT potential as well as (c) two metals (Mg, Al) simulated using DFT in the solid and liquid state. The second part of the results (Ch.~6) is dedicated to a method predicting the melting curve from nearby isomorphs that is applied to one EMT metal (Cu) and three DFT metals (Al, Mg, Na). The chapter also includes the review of and comparison to other state of the art methods to predict (points on) the freezing and melting curves.
This work establishes good isomorph invariance in all candidate metals with the exception of DFT-Mg investigated in the first part of the study. The second part demonstrates good agreement between the freezing and melting curves predicted by our method when compared to the literature. The agreement is best with other methods using DFT-based simulations while state points taken from experiments show more significant (though still small) deviations.