https://iopscience.iop.org/article/10.1088/0034-4885/18/1/301/pdf

The Displacement of Atoms in Solids by Radiation

Publisher Summary This chapter discusses statistical exchange-correlation in the self-consistent field. There are two sides to a self-consistent field calculation: the determination of the potential and the solution of Schrodinger's equation for the one-electron problem. The solution of Schrodinger's equation has fortunately advanced far enough through the application of the electronic digital computer so that it can be regarded for most purposes as being a standardized technique. The main point of the method of Gaspar, Kohn, and Sham is that they derive the approximate exchange correction from an approximate Hamiltonian for the system by varying the spin-orbitals to minimize the average value of this Hamiltonian for the ground state. The approximate Hamiltonian has many important and valuable features that are described in the chapter.

Statistical Exchange-Correlation in the Self-Consistent Field

The distinction between adiabatic and nonadiabatic reaction mechanisms at an electrode/solution interface is emphasized; in general, only adiabatic or near‐adiabatic paths are important in thermally activated reactions. The role of the dielectric in determining the course of such reactions is discussed. A general interpretation of the transfer coefficient and an account of the activation process in simple systems are given in terms of the distribution of electron charge density in the transition state; these are shown to be in good accord with experiment. The conventional approach to these problems, in which an approximate potential‐energy path for the reaction is calculated from intersecting potential‐energy curves for the initial and final states of the system, is criticized, and an alternative representation in terms of charge variation is proposed.

Adiabatic Rate Processes at Electrodes. I. Energy-Charge Relationships

Publisher Summary This chapter discusses that the subject of exchange in magnetic materials is divided into two parts, referring to insulators and to metals. This distinction is useful from the magnetic point of view because in insulators the spins and magnetic moments whose alignments lead to magnetic effects are certainly localizable so that phenomenologically is described by a spin Hamiltonian that contains spin operators and exchange terms of Heisenberg type. It discusses that there is relationship among the mechanisms important in metals, such as conduction electron polarization, and those in insulators. The chapter provides historical discussion of the subjects of antiferromagnetism and of exchange in insulators. It focuses on the Heisenberg Hamiltonian, with a brief derivation and a discussion of some of the statistical theories of magnetism based upon it, primarily molecular field theory, which is by far the most generally useful in the experimental measurement of exchange. The chapter also describes older theories and presents ideas about super-exchange, and gives a discussion and a diagrammatic classification of all the possible higher-order processes.

Theory of Magnetic Exchange Interactions:Exchange in Insulators and Semiconductors

It is shown that the dynamical Jahn-Teller effect in a complex having orbital degeneracy may partially quench spin-orbit interaction, the orbital parts of the Zeeman and hyperfine interactions, and other orbital operators governing response to perturbations such as strain or applied electric fields. Such dynamical quenching thus decreases the value of orbital reduction factors usually attributed in paramagnetic resonance studies to covalent bonding, without necessarily causing anisotropy in the spectrum of an individual complex. The dynamical Jahn-Teller effect may also substantially enhance various second-order effects. Such dynamic effects thus may make important changes in the parameters of the spin Hamiltonian without changing its symmetry. It is shown that the dynamical Jahn-Teller effect accounts qualitatively for unusual features in the spectra of interstitial transition-metal ions ${\mathrm{Cr}}^{0}$, ${\mathrm{Mn}}^{+}$, ${\mathrm{Mn}}^{0}$, and ${\mathrm{Fe}}^{+}$ in silicon and that it is probably of importance equal to or greater than that of covalent bonding in the interpretation of the spectrum of ${\mathrm{Fe}}^{2+}$ in MgO and CaO. A mathematical analysis of the dynamical effects is given for an orbital triplet state in interaction with a doublet or triplet vibrational mode, and some results are given also when the coupling is with the phonon continuum.

Dynamical Jahn-Teller Effect in Paramagnetic Resonance Spectra: Orbital Reduction Factors and Partial Quenching of Spin-Orbit Interaction

The typical colours of paramagnetic salts containing [M(H$\_{2}$O)$\_{6}$], M = 3d$^{n}$, complexes, are generally assumed to arise from optical transitions between the orbital energy levels of the 3d ion which are split by the crystalline electric field due to the surrounding water dipoles. The available optical absorption data are analyzed using this ionic model and the associated crystal field theory, and it is shown that while experiment and theory agree fairly well, there are systematic discrepancies. In addition, the orbital level separations given by the optical spectrum are found to be smaller than those predicted from magnetic data. It is shown how these discrepancies can be accounted for by introducing weak covalent bonds into the [M(H$\_{2}$O)$\_{6}$] complex, so that there is charge transfer between the paramagnetic ion and the attached water molecules.

The colours and magnetic properties of hydrated iron group salts, and evidence for covalent bonding

Paramagnetic Resonance in Neutron-Irradiated Diamond and Smoky Quartz

The paramagnetic resonance method has been applied to investigate the magnetic properties of complexes containing elements of the 4d and 5d groups. It is shown that the resonance results, and such information as is available from susceptibility measurements, can be accounted for to a good approximation by assuming that there are either covalent $\sigma $-bonds or very strong electrostatic bonds in the complex (Van Vleck 1935). In the case of d$^{5}$ complexes, however, accurate measurements of the spectroscopic splitting factors show small discrepancies with this theory. Furthermore, an anomalous hyperfine structure is observed for the complex [IrCl$_{6}$]$^{2-}$, which displays lines arising not only from the Ir nucleus, but also from the surrounding Cl nuclei. These effects are ascribed to the presence of weak $\pi $-bonds, in addition to $\sigma $-bonds, in the complex (Stevens 1953). In magnetically concentrated salts of the 5d group, it is found that there is strong exchange interaction between paramagnetic neighbours.

Paramagnetic Resonance in Palladium and Platinum Group Compounds

Measurements have been made of the magnetic susceptibilities of ammonium and potassium chloroiridates at temperatures between room temperature and 1 'K. The results obtained at high temperatures have been analysed into a susceptibility following a Curie-Weiss law together with temperature-independent terms. The values of the isotropic exchange interactions between neighbouring iridium ions deduced from the Weiss constant agree well with those calculated from paramagnetic resonance measurements. At lower temperatures the magnetic susceptibilities become almost independent of temperature over a certain range and then fall sharply at the antiferromagnetic trans-tion points (2-16 'K for the ammonium salt, 3-08 'K for the potassium salt). These results are discussed in terms of the exchanige interaction between nearest- and next-nearest-neighbour iridium ions. INTTRODIJCTION Some years ago, Griffiths & Owen (I954) reported paramagnetic resonance experiments in iridium ions present in low concentration in ammonium chloroplatinate, (NNH4)2PtCl6. These experiments showed that the isolated iridium ions behave as magnetic carriers having spin S = - and spectroscopic splitting factor g = 1-79. The paramagnetic resonance spectrum exhibited a complex hyperfine structure due not only to the iridium nuclei but also to the nuclei of the six chlorine ions surrounding

Exchange interactions in antiferromagnetic salts of iridium II. Magnetic susceptibility measurements

Paramagnetic resonance methods have been used to investigate Ir-Ir exchange interactions in K 2 IrCl 6 and (NH 4 ) 2 IrCl 6 . Measurements are described of the resonance spectrum from nearest-neighbour pairs of Ir ions in semi-dilute mixed crystals where Pt is substituted for Ir. The results show that the isotropic p art of the Ir-Ir exchange, J / k , is antiferromagnetic and of magnitude 11.5 ± 1°K and 7.5 ± 1°K for the potassium and ammonium salts, respectively. There is also found to be an anisotropic part with rhombic symmetry and with magnitude of order 1 cm -1 . No lines attributable to next-nearest-neighbour pairs were found, and it is suggested that this interaction is small. The results are com pared briefly with the magnetic susceptibility experiments of Cooke et al . (part II) who find that the concentrated salts go antiferromagnetic in the liquid-helium temperature range, and also with the theoretical analysis of the superexchange mechanism given by Judd (part III).

J. Owen

Papers

The colours and magnetic properties of hydrated iron group salts, and evidence for covalent bonding

Paramagnetic Resonance in Neutron-Irradiated Diamond and Smoky Quartz

Paramagnetic Resonance in Palladium and Platinum Group Compounds

Exchange interactions in antiferromagnetic salts of iridium II. Magnetic susceptibility measurements

Exchange Interactions in Antiferromagnetic Salts of Iridium. I. Paramagnetic Resonance Experiments