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We provide an overview of interatomic potentials, explaining their components and significance. Moving from simple to complex formalisms, we discover pair-wise potentials and multi-body potentials, demonstrating their importance in modelling atomic interactions. We then focus on interatomic potentials for metals, exploring their specific characteristics and applications. Additionally, we discuss force fields and machine learning approaches, highlighting their role in enhancing accuracy and efficiency. Finally, we outline the essential requirements for developing high-quality interatomic potentials.
We begin by explaining the notion of pressure and stress tensors as energy derivatives with respect to volume. Then, we discuss equations of state, elasticity, and the rheology of crystals, providing a comprehensive understanding of crystal mechanics.
This chapter lays the groundwork for ab initio calculations. Beginning with an introduction to density functional theory (DFT) and the Kohn–Sham equations, we explore the exchange-correlation term and essential techniques like planewaves, k-Points, and pseudopotential construction. Expanding further, we investigate the Projector Augmented-Wave Method (PAW) and conclude with insights into the Quantum Monte Carlo (QMC) technique. This concise chapter serves as a comprehensive guide, enabling researchers to explore and understand ab initio methods for accurate and efficient computation of mineral properties.
The first part of the phonon analysis is focused on the Gamma point. This leads to defining the infrared and Raman spectroscopies. The dispersion of the acoustic modes around Gamma defines the Brillouin spectroscopy. We introduce third-order derivatives of the energy to obtain the Raman tensors.
We explore the behaviour of the crystalline lattice under the action of external electric fields. We treat polarization as an energy derivative and define the atomic charges in terms of charge exchange; we define the dielectric tensors and visit the higher-order dielectric response of the lattice.
Chapter 1 sets out the foundations of the book, beginning with a basic discussion of what is climate change and the global climate crisis. The chapter then moves on to the important Global North-Global South colonial context and the fundamental issues of environmental justice, climate justice and carbon colonialism. From there, the discussion ventures into an overview of who bears the brunt of climate change, concluding in a final section on the calls for a gender-based approach to solving the global climate crisis and the rationale for the book.