Absence of diagonal force constants in cubic Coulomb crystals

The quasi-harmonic model proposes that a crystal can be modelled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss’s law shows that the ion–ion potential for a cubic Coulomb system can have no diagonal harmonic contribution and so cannot necessarily be modelled by springs. We investigate the repercussions of this observation by examining three illustrative regimes: the bare ionic, density tight-binding and density nearly-free electron models. For the bare ionic model, we demonstrate the zero elements in the force constants matrix and explain this phenomenon as a natural consequence of Poisson’s law. In the density tight-binding model, we confirm that the inclusion of localized electrons stabilizes all major crystal structures at harmonic order and we construct a phase diagram of preferred structures with respect to core and valence electron radii. In the density nearly-free electron model, we verify that the inclusion of delocalized electrons, in the form of a background jellium, is enough to counterbalance the diagonal force constants matrix from the ion–ion potential in all cases and we show that a first-order perturbation to the jellium does not have a destabilizing effect. We discuss our results in connection to Wigner crystals in condensed matter, Yukawa crystals in plasma physics, as well as the elemental solids.

Electrical Properties of Materials

A classic text in the field providing a readable and accessible guide for students of electrical and electronic engineering. Fundamentals of electric properties of materials are illustrated and put into context with contemporary applications in engineering. Mathematical content is kept to a minimum allowing the reader to focus on the subject. The starting point is the behaviour of the electron, which is explored both in the classical and in the quantum-mechanical context. Then comes the study of bonds, the free electron model, band structure, and the theory of semiconductors, followed by a chapter on semiconductor devices. Further chapters are concerned with the fundamentals of dielectrics, magnetic materials, lasers, optoelectronics, and superconductivity. The last chapter is on metamaterials, which has been a quite popular subject in the past decade. The book includes problems, the worked solutions are available in a separate publication: Solutions manual for electrical properties of materials. There is an appendix giving a list of Nobel Prize winners whose work was crucial for describing the electric properties of materials, and there are further appendices giving descriptions of phenomena which did not fit easily within the main text. In particular there is a quite detailed appendix that summarizes the properties of memory elements. The book is ideal for undergraduates, and is also an invaluable reference for graduate students and others wishing to explore this rapidly changing field.

Inelastic O+H collisions and the O I 777 nm solar centre-to-limb variation

The O I 777 nm triplet is a key diagnostic of oxygen abundances in the atmospheres of FGK-type stars; however, it is sensitive to departures from local thermodynamic equilibrium (LTE). The accuracy of non-LTE line formation calculations has hitherto been limited by errors in the inelastic O+H collisional rate coefficients; several recent studies have used the Drawin recipe, albeit with a correction factor SH that is calibrated to the solar centre-to-limb variation of the triplet. We present a new model oxygen atom that incorporates inelastic O+H collisional rate coefficients using an asymptotic two-electron model based on linear combinations of atomic orbitals, combined with a free electron model based on the impulse approximation. Using a 3D hydrodynamic STAGGER model solar atmosphere and 3D non-LTE line formation calculations, we demonstrate that this physically motivated approach is able to reproduce the solar centre-to-limb variation of the triplet to 0.02 dex, without any calibration of the inelastic collisional rate coefficients or other free parameters. We infer log ϵO = 8.69 ± 0.03 from the triplet alone, strengthening the case for a low solar oxygen abundance.

On the Concentration and Phase-relation Dependence of Seebeck Coefficient and the Contact Angle in Metallic Solutions

The focus of this paper is the deeper understanding of the effect of the change in the electronic structure on the wetting angle and transport properties. For this purpose, using the alloys from the earlier study, the thermopower has been measured and the Seebeck coefficient has also been determined in room temperature (solidified state). During the experiments in both case the modification of the electronic structure were performed by alloying on a way, that the investigated systems are terminal (α) solutions in solid state. The concentration dependence of property changes are interpreted on the bases of free electron model elaborated earlier for this alloy types. This prediction fits well also to the concentration dependence of heat of formation in these alloys. Similar concentration dependence has been also found between the Seebeck coefficient, the resistivity and the heat of mixing in α-phase Fe-Ni alloys. The shift of thermopower were also monitored in order to detect the crystallization (first oreder transformation) starting form amorphous Fe-B alloys.

Conductivity and dissociation in liquid metallic hydrogen and implications for planetary interiors

Liquid metallic hydrogen (LMH) is the most abundant form of condensed matter in our solar planetary structure. The electronic and thermal transport properties of this metallic fluid are of fundamental interest to understanding hydrogen’s mechanism of conduction, atomic or pairing structure, as well as the key input for the magnetic dynamo action and thermal models of gas giants. Here, we report spectrally resolved measurements of the optical reflectance of LMH in the pressure region of 1.4–1.7 Mbar. We analyze the data, as well as previously reported measurements, using the free-electron model. Fitting the energy dependence of the reflectance data yields a dissociation fraction of 65 ± 15%, supporting theoretical models that LMH is an atomic metallic liquid. We determine the optical conductivity of LMH and find metallic hydrogen’s static electrical conductivity to be 11,000–15,000 S/cm, substantially higher than the only earlier reported experimental values. The higher electrical conductivity implies that the Jovian and Saturnian dynamo are likely to operate out to shallower depths than previously assumed, while the inferred thermal conductivity should provide a crucial experimental constraint to heat transport models.

Self-organizing atom chains

This article examines the intriguing physical properties of nanowires, with particular emphasis on self-organizing atom chains. It begins with an overview of the one-dimensional free electron model and some interesting phenomena of one-dimensional electron systems. It derives an expression for the 1D density of states, which exhibits a singularity at the bottom of the band and extends the free-electron model, taking into consideration a weak periodic potential that is induced by the lattice. It also describes the electrostatic interactions between the electrons and goes on to discuss two interesting features of 1D systems: the quantization of conductance and Peierls instability. Finally, the article presents the experimental results of a nearly ideal one-dimensional system, namely self-organizing platinum atom chains on a Ge(001) surface, focusing on their formation, quantum confinement between the Pt chains and the occurrence of a Peierls transition within the chains.