Die Berechnung optischer und elektrostatischer Gitterpotentiale;

Die Berechnung optischer und elektrostatischer Gitterpotentiale;

| von P. P. Ewald
This chapter discusses the calculation of optical and electrostatic lattice potentials, as outlined by P. P. Ewald. It begins with an introduction to electrostatic and electrodynamical potentials, emphasizing the need to determine their numerical values at any point within a lattice. The electrostatic potential of an ionic lattice is defined, and the total energy of the lattice is derived. The chapter then delves into the calculation of lattice potentials for simple and composite lattices, including the concept of excited potentials and the structure factor. It also covers the transition to electrostatic potentials and provides examples for lattice energies of zincblende and fluorspar. The second part focuses on the transformation formula for theta functions, which is crucial for the numerical calculation of lattice potentials. The third part discusses the calculation of optical potentials and their derivatives, while the fourth part explores the transition to electrostatic potentials and the use of dimensionless quantities. The chapter concludes with a discussion on the numerical methods for calculating lattice potentials, highlighting the importance of the structure factor and the choice of a suitable transition point for convergence.This chapter discusses the calculation of optical and electrostatic lattice potentials, as outlined by P. P. Ewald. It begins with an introduction to electrostatic and electrodynamical potentials, emphasizing the need to determine their numerical values at any point within a lattice. The electrostatic potential of an ionic lattice is defined, and the total energy of the lattice is derived. The chapter then delves into the calculation of lattice potentials for simple and composite lattices, including the concept of excited potentials and the structure factor. It also covers the transition to electrostatic potentials and provides examples for lattice energies of zincblende and fluorspar. The second part focuses on the transformation formula for theta functions, which is crucial for the numerical calculation of lattice potentials. The third part discusses the calculation of optical potentials and their derivatives, while the fourth part explores the transition to electrostatic potentials and the use of dimensionless quantities. The chapter concludes with a discussion on the numerical methods for calculating lattice potentials, highlighting the importance of the structure factor and the choice of a suitable transition point for convergence.
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Understanding Die Berechnung optischer und elektrostatischer Gitterpotentiale