Robert Englman

Quantitative theory of luminescent centres in a configurational diagram model: I. Description of the method

Abstract A description is given of a method which yields numerical estimates for line or band intensities of emissions in localized centres in solids. In this method the eigenstates of the “system” characterized by two or three intersecting parabolae (each belonging to a different electronic state), are obtained by numerical matrix diagonalization. Rate equations involving both radiative and non-radiative processes are derived and solved numerically. The non-radiative processes arise from the coupling of the “system” with the phonons of the lattice, which acts as a thermal bath. Two types of tunnelling (called horizontal and vertical) between potentials are distinguished and their relative importance determined. Numerical results are presented in the sequel paper.

Quantitative theory of luminescent centres in a configurational diagram model: II. Results and their interpretation

Abstract Theoretical values are presented for the fluorescence and phosphorescence of localized centres in solids with special reference to Cr 3+ in oxides as functions of time, temperature and other physical parameters. The phosphorescence quantum yield exhibits a maximum at a temperature equal to about half the vibrational quantum, provided the crossing point of the potential wells is near the first excited level of the upper well. There is an oscillatory dependence of the phosphorescence quantum yield varying sharply with the height of the minimum of the upper well above the lower, however this behaviour ceases at large values of the height and the phosphorescence intensity then decreases as the height increases. Two or three decay rates corresponding to different physical processes were found on examining the time dependence of the fluorescence.

COVALENCY EFFECTS IN TRIGONAL DISTORTION.

The trigonal field experienced by a paramagnetic ion owing to its surroundings is studied theoretically, account being taken of covalency effects. In addition to the parameter v, due to the trigonal field of the second‐order harmonic acting at the metal ion, there is also the splitting parameter V acting on the corresponding molecular orbitals formed from the ligand orbitals. Covalency mixing then results in an effective splitting parameter that is (in general) different for each configuration in the t and e subshells and which replaces the one‐electron splitting parameter used in the absence of covalency. The effect may be particularly marked when V is of opposite sign and larger than v. Under these conditions the Jahn—Teller‐type trigonal distortion may also switch over because of covalency.

Operator for Spin‐Forbidden Transitions

It is shown that the use of the dipole‐moment operator to calculate probabilities of transitions with change of spin gives results in many cases correct to within 1% to 1/100%. The matrix element of the operator is between the large components of spinors.

Zero-phonon lines in diamond and localized modes☆

Abstract The vibrational structures for emission and absorption of the 415 mmicro system in diamond indicate that genuinely localized vibrations are brought into play. These vibrations affect the intensity of the zero-phonon line; however, the decrease with temperature of the intensity arises not from these but from the phonon-continuum. The observed temperature change in the line-width is apparently due to the discrete modes, while the temperature variation of the shift may be traced to either the discrete or the continuous modes, with the weight of experimental evidence favouring the latter.

Vibrational Frequency Sum Rules for Distorted Complexes

The calculation of thermodynamic quantities that involve the change of frequencies due to distortion of octahedral complexes can be effectively simplified by calculating the mean frequency change within a vibrational type, rather than the change in each component individually. On the average each stretching mode frequency changes by the same amount, each bending mode frequency changes by the same amount, while the mixed mode frequencies change by amounts that depend on the percentages of stretching and bending motions in the mode.

Intermittency from maximum entropy distribution

A maximum entropy distribution has been formulated in which the imposed constraint contains a stochastic (rather than a deterministic) variable. The distribution depends on the observational bin size through the smoothing of population by intrabin averaging. Moments of fluctuations calculated with this distribution give bin-size dependences (intermittency exponents) that agree reasonably with those obtained from the size dependence in nuclear multifragmentation. The exponents depend on the spread of the stochastic mechanism (supposed to be a cascading, multiplicative process) and on the magnitude of the constraint imposed. An information-theoretic interpretation is provided for the relation between statistical and mechanism-induced (dynamic) fluctuations.

Vibrations in interaction with impurities

A review is presented of the effects of interaction between electronic states on an impurity ion or molecule and the vibrations of the host. Primarily, interactions linear in the vibrational amplitude are treated for their static and time-dependent effects, while mass or force-constant defects are considered only to the extent of bringing out the analogies and distinctions between them and linear interactions. Some emphasis is placed on degenerate impurity states and on the phase-correlation in the electronic and vibrational motions. We describe in some detail experimental and theoretical works which throw light on the character of the vibrational motion that is in interaction with impurity electrons. We conclude that this can vary with circumstances, between extremely localised, molecular type and extended, phonon-like behaviours, where large energy exchange (as e.g. optical) phenomena belong to the former and small energy exchange or scattering experiments to the latter.