Non-adiabatic Hopping Research Articles

Nonadiabatic polaron hopping in undoped and Pb-doped Bi2Sr2Ca2Cu3O10- delta glasses.

Electrical conductivity of undoped and Pb-doped ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ glasses is reported in the temperature range 150\char21{}450 K. The temperature dependence of the conductivity can be interpreted consistently in terms of nonadiabatic polaron hopping theories proposed for amorphous semiconductors.

D.c. conductivity and hopping mechanism in Bi2O3-B2O3 glasses

The physical and transport properties of semiconducting glasses are highly interesting, providing useful information regarding the structure and conduction mechanism, respectively. The physical and transport properties such as density, number of ions per unit volume, hopping distance, polaron radius, d,c. conductivity and activation energy are reported. Similarly the hopping conduction mechanism is examined. The physical property (density) is used to determine the probable structure of the glass sample. The small polaron hopping model is applied to the glass system. The methods of examining the hopping conduction mechanism are discussed in the light of the small polaron model. The methods suggested by Holstein and by Sayer and Mansingh are applied to the determination of adiabatic or non-adiabatic hopping conduction. It was observed that in this system adiabatic hopping conduction is present.

Phonon-assisted diffusion and electromigration of light interstitials in metals.

We present a microscopic description of phonon-assisted diffusion of light interstitial impurities in metals including migration in the presence of an electron current (electromigration). The approach is self-consistent without separation into two parts (atom diffusion and electron scattering) and is appropriate for the regime of incoherent nonadiabatic atom hopping between polaron-type states at adjacent interstices. A general expression is obtained in the linear-response approximation for both the diffusion and the electron conduction contributions to atomic current. The atom current is shown to be related to an effective driving force through a Nernst-Einstein expression, and this driving force is shown to be the sum of a direct force and a wind force from the electron flow. The wind force in the general case is not determined by the Fiks-Huntington ballistic-model expression but decreases rapidly with the quantity ${\mathit{k}}_{\mathit{F}}$d, where ${\mathit{k}}_{\mathit{F}}$ is the electron Fermi momentum and d is the hopping distance. This decrease is due to strong recoil effects associated with momentum transfer to the lattice. Our results do not require the validity of the Condon approximation of small-polaron theory.

H/D isotope effect in the predissociation of C2HD

Resonance-enhanced multiphoton ionization (2+1 REMPI) spectroscopy near 243 nm was used to detect H and D photofragments of the 193 nm photolysis of C2HD. Measurements were performed in a molecular beam, laser photolysis apparatus, equipped with a time-of-flight mass spectrometer. The measured H/D ratio of 2.85±0.3 may indicate nonadiabatic surface hopping occurs between 2 3 A′ and 1 3 A′ and/or 2 1 A′and 1 1 A′surfaces in exit channels leading to ground state C2H(X̃ 2 Σ+ )+H(2 S) fragments in the predissociation of C2H2.

Adiabatic and non-adiabatic small polaron hopping in molecularly doped polymers

New hole drift mobility measurements for the molecularly doped polymer DEH ( p-diethylaminobenzaldehyde-diphenyl hydrazone) in polycarbonate and literature data for TPD (N,N′-diphenyl-N,N′-bis (3-methylphenyl)-[1,1′-biphenyl]-4,4′-diamine) in polycarbonate are analyzed by a new procedure which separates the functional dependence of the mobility on temperature and molecular spacing ϱ. Our analysis indicates that the dependence of the mobility on ϱ arises from different sources. In DEH: polycarbonate it is due to an overlap integral, as normally expected. In TPD: polycarbonate it is due entirely to the dependence of the activation energy on p, a significant clue to the underlying microscopic hole hopping mechanism. These data are consistent with the small polaron hopping theory in two regimes, non-adiabatic hopping in DEH:polycarbonate and adiabatic hopping in TPD: polycarbonate.

A vibrational state-selected study of the reaction H+2(v′0)+H2(v′′0=0)→H+3+H using the tandem photoionization mass spectrometry and radio frequency ion guide methods

A new ion–molecule rection apparatus, which consists of a photoionization source, a tandem mass spectrometer, and a radio frequency octopole reaction cell is described. Using a quadrupole mass filter to reject H+3 background ions formed at the photoionization source, absolute total cross sections for the reaction H+2 (v′0) +H2 (v′0 =0)→H+3 +H, have been measured as a function of the vibrational state of reactant H+2, where v′0 =0–4, over the center-of-mass collision energy (Ec.m.) range of 0.04–15 eV. The experimental results are compared with phenomenological cross sections obtained in previous single gas cell studies, the quasiclassical trajectory calculations of Stine and Muckerman, and the recent similar calculations of Eaker and Schatz. The absolute total cross sections measured for v0 =0 and 3 at Ec.m. =0.5, 1, 3, and 5 eV are found to be in agreement with ‘‘trajectory surface hopping’’ calculations which include nonadiabatic surface hopping throughout the reaction.

Correlation effects on the small-polaron hopping conductivity

On the basis of a spinless fermion model, which takes into account the intersite Coulomb interaction and the formation of small polarons (SP) due to the interaction with phonons, the correlation effects (due to the SP-SP interaction) on the electrical SP hopping conductivity are investigated. The particle transfer is treated in lowest nonvanishing order of perturbation theory, and the case of non-adiabatic SP hopping is considered. The polaronic short-range order (SRO) results in an additional activation of the dc conductivity due to hopping processes without and with changes of the Coulombic configurational energy. For sufficiently low SRO the dc conductivity is enhanced relative to its magnitude in the case of non-interacting SP. The SRO leads to an additional optical absorption and a positive shift of the absorption spectrum. The theory maybe relevant for the description of inhomogeneous mixed-valence compounds and superionic conductors.

Electron delocalization in ilvaite, a reinterpretation of its 57Fe M�ssbauer spectrum

The Mossbauer spectra of ilvaite CaFe 2 2+ Fe3+[Si2O7/O/OH] and their temperature dependence between 298 K and 455 K can be satisfactorily least-squares fitted by a superposition of the resonances for Fe2+(8d), Fe3+(8d) and Fe2+(4c). The relative areas under the three resonances are nearly equal and vary only weakly with temperature. No additional resonances or line broadenings have to be introduced, if we assume that the hyperfine interactions of Fe2+(8d) and Fe3+(8d) fluctuate between their values due to electron hopping between the iron ions at the 8d sites. Hopping can be assumed to occur homogeneously among nearly equivalent sites. The fluctuation rate is described by an Arrhenius law with a pre-exponent of about 9 × 108 s−1 and an activation energy of 0.11 eV indicating non-adiabatic hopping. In addition to the intersite hopping process, the strong decrease of the quadrupole splitting and the isomer shift of Fe2+(8d) between 298 K and 360 K suggests the occurrence of intrinsic charge delocalization from Fe2+(8d) which does not involve the neighbouring Fe3+(8d) ions.

The application of small polaron theory to transition metal oxide glasses

A review of the experimental data on a range of transition metal oxide glasses shows a strong relationship between activation energy and site spacing for glasses based on V 2O 5. The behaviour confirms that transport in amorphous V 2O 5 and vanadate glasses is by adiabatic hopping with an appreciable polaron bandwidth, while non-adiabatic hopping between isolated centres is apropriate for glasses based on most other transition metal oxides. The behaviour of vanadium is linked to the retention of a well-defined VO 5− structural unit in the glass network and to optimisation of the packing of this unit within the glass.

Electrical conduction in biotite micas

The direct current electrical conductivity tensor of biotitic phyllosilicates (mica) has been measured as a function of temperature, of electric field, and of chemical composition. It is found that conductivity depends exponentially upon iron impurity content, and upon electric field at high fields. The dependence upon temperature is more complicated. These results are best interpreted by a model in which mica is an isotropic Fermi glass in which electrical conduction takes places by nonadiabatic hopping of small polarons between iron sites in the crystal.

Adiabatic polaron theory of electron hopping in crystals: A reaction-rate approach

The paper presents an application of reaction-rate theory to nonradiative electron transitions in polar crystals based on a "two-site" model. For this purpose localized electronic states are described by using the adiabatic approximation. Both "large" polarons in ionic crystals and "small" polarons in molecular crystals are considered from a unified point of view. By assuming a single frequency of the lattice vibrations (Einstein model) one can calculate the transition probability for both the limits of adiabatic and nonadiabatic electron transfer as well as for the whole intermediate range. The relevant expressions, earlier derived in treating electron transfer in solution, are reviewed and discussed in order to give a justification of their application to polaron hopping in crystals. In a similar way, a review is made of the reaction-rate approach to electron transfer to obtain the appropriate rate equations for the low- and high-temperature limits and the intermediate temperature range as well. New expressions for the polaron-hopping rate are also derived. The conditions of its validity are discussed. This paper provides an essentially new approach to nonradiative electron transfer in polar crystals. It permits one to overcome the limitations of the usual methods, such as the multiphonon approach, entirely based on time-dependent perturbation theory and/or the Franck-Condon approximation which restrict their applicability only to nonadiabatic polaron hopping. The reaction-rate treatment exactly reproduces the results of the more rigorous multiphonon theory of nonadiabatic transitions. Moreover, it yields correct rate expressions for adiabatic transitions, in particular, in the high-temperature range, in which the classical occurrence-probability approach greatly overestimates the activation energy. Some problems concerning the Einstein one-frequency oscillator model assumed and the irreversibility of the electron transfer are discussed with some details from standpoint of both reaction-rate theory and multiphonon theory. The advantages of the reaction-rate approach are emphasized.

DC conduvtivity of V 2O 5TeO 2 glasses

The dc conductivity of semiconducting vanadium tellurite glasses of compositions in the range 50 to 80 mol% V 2O 5 has been measured in the temperature region 77 to 400 K. Measurements have been made on annealed samples at different annealing temperatures. Annealing the samples at temperature of about 250°C causes the appearance of a complex crystalline phase resulting in an increase of conductivity. Results are reported for amorphous samples of different compositions. The conductivity of tellurite glasses is slightly higher than the corresponding composition of phosphate glasses, but the general trend of the increase of conductivity and decrease of high temperature activation energy with increasing V 2O 5 content is similar in the two systems. The data have been analysed in the light of existing models of polaronic hopping conduction. A definite conclusion about the mechanics of conduction (adiabatic or nonadiabatic) is difficult in the absence of a precise knowledge of the characteristic phonon frequency v 0. Adiabatic hopping is indicated for v 0∼10 11 Hz, however this value leads to unreasonably low value for the Debye temperature θ D, and higher values for v 0∼10 13 hz satifiies the conditions for nonadiabatic hopping which appears to be the likely mechanism of conduction in V 2O 5TeO 2 glasses. The low temperature data (< 100 K) can be fitted to Mott's variable range hopping, which when combined with ac conductivity data gives reasonable values of α, but a high value for the disorder energy.

Dipole reorientation from bound-polaron hopping in single crystal NiO

Abstract We report observation of a first order thermal depolarization peak at 190 K in NiO single crystals which we attribute to the reorientation of Ni 3+ Ni V 2+ dipoles. Analysis of the data in terms of these bound polarons, using a non-adiabatic hopping model, yields values of activation energy, E = 0.31eV and the polaron band width, J = 8.6 × 10 −6 eV.

Phonon-assisted transition rates I. Optical-phonon-assisted hopping in solids

Abstract An extensive calculation of the optical-phonon-assisted transition rates for non-adiabatic electronic hopping motion in a solid is presented. Holstein's Molecular Crystal Model is used as a basis for study and the computation involves no restrictions on either the magnitude of the electron-lattice coupling strength, the temperature, or the difference between the electronic energies of the initial and final sites. In the strong-coupling small-polaron regime, the jump rates, associated d.c. conductivity, a.c. conductivity, and electric-field dependence of the d.c. conductivity, for a crystal are all calculated. These transport properties manifest qualitatively distinct behaviours corresponding to whether the temperature is above or well below the optical-phonon temperature. In the low-temperature regime the energy-conserving processes which involve the absorption of the minimum amount of vibrational energy provide the dominant contribution to the thermally activated jump rates. At sufficiently high...

Dielectric properties of NiO and NiO(Li)

The dielectric constant of NiO produced by the oxidation of Ni has been studied as a function of frequency up to 10 8 Hz and of temperature from 300° to 550°K. The effect of Li doping on the dielectric constant has also been investigated. In addition, the behavior of the a.c. conductivity σ(ω) as a function of frequency ω has been determined up to 10 8Hz and the loss tangent tan δ has been calculated. The results are interpreted on the basis of a non-adiabatic hopping mechanism at lower frequencies and an adiabatic hopping mechanism at higher frequencies. The dielectric breakdown field as a function of Li concentration has also been determined and is found to decrease exponentially with increasing Li concentration. In the NiNiONi structure, the capacitance is independent of the applied field up to fields of 10 5 V cm , and the resistivity is high up to fields of 10 5 V cm .

Transport and dielectric properties of thin polycrystalline CoO films

Transport and dielectric properties of polycrystalline CoO films were studied as functions of the applied field, frequency and temperature. TheI–V plots showed that the Poole-Frenkel field emission mechanism is responsible for conduction at fields>105 V/cm. The ac conductivity σ(ω), the imaginary part of the dielectric constante2, and tan δ plots as functions of frequency revealed three dispersion regions. The σ(ω) ande2 frequency dependence indicates a non-adiabatic hopping of charge carriers at low frequencies and adiabatic hopping at high frequencies. The activation energy of a dielectric oscillator is 0.15 eV.

Hole transport in solid xenon

The hole mobility μ η in solid Xe has been investigated by drift mobility techniques in the temperature range from 110K to 160K. μ η = 1.8 × 10 −2 cm 2 Sec −1 V −1 at 160K and has a temperature dependence of the form μ η ∞ T −1.6. It is concluded that a non-adiabatic hopping transport with a small polaron binding energy and small intermolecular overlap is the most likely transport mechanism.