Kinetics of electron trapping reactions in amorphous solids; a non-Gaussian diffusion model

Hamill, William H.; Funabashi, Koichi

doi:10.1103/physrevb.16.5523

Cited by 101 publications

(23 citation statements)

References 12 publications

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“…Eq. 9 is the basic equation of Hamill and Funabashi (13). From the paper of Montroll and Weiss (9) on continuoustime random walks, it can be shown that the Laplace transform of l(t) is A(u) = I I Fn(s) [I(*(u)]ln s#O n=O [11] where F,(s) is the probability that a walker originally at s arrives at the origin for the first time at the nth step and 4i*(u) is the Laplace transform of the pausing-time distribution qi(t) J ( 41* (U) = 4i(t) e-uldt.…”

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confidence: 99%

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On the Williams—Watts function of dielectric relaxation

Shlesinger

Montroll

1984

Proc. Natl. Acad. Sci. U.S.A.

373

145

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It has been observed over the past 15 years that experimental frequency-dependent dielectric constants of broad classes of materials including polymeric systems and glasses may be interpreted in terms of the Williams-Watts polarization decay function 4a(t) = exp[-(t/T) ¶, 0 < a < 1.The exponent a and the time constant T depend on the material and fixed external conditions such as temperature and pressure. We derive this form of 4.(t) from the following randomwalk model. Suppose that an electric field has been applied for some time to a medium containing many polar molecules (or polar groups in complex molecules) and the direction of their dipole moments remains frozen as the field is removed. Furthermore, suppose that the medium contains mobile defects that on reaching the site of a frozen dipole relax the medium to the degree that the dipole may reorient itself. If the diffusion of defects toward dipoles is executed as a continuous-time random walk composed of an alternation of steps and pauses and the pausing-time distribution function has a long tail of the form qi(t) a: t-"-, then the relaxation function has the above fractional exponential form.In the theory of dielectric relaxation, one writes the frequency-dependent dielectric constant, E(4,)), asEs -Exo°w here EX is the high-frequency limit of the dielectric constant and Es, the static dielectric constant. The function 4(t) describes the decay of polarization of a dielectric sample with time after sudden removal of a steady polarizing electric field. One generally writesEs -Eoc where En(w) and E'"(w) are, respectively, the real and imagi- [4] The En(w) data of Ishida and Yamafugi (3) on polyvinylacetate at 62.5°C was identified with 4a(t) with a = 0.56 over five frequency decades. The Williams and Watts group, Moynihan and his collaborators (4, 5), Ngai and White (6), and other investigators have found the Williams-Watts function 4 to represent a "universal" model for a wide class of materials, especially polymeric substances and glasses. The remarkable empirical success of the Williams-Watts relaxation function motivates one to seek a physical model to give some intuitive understanding of it. The purpose of this paper is to discuss such a model. Suppose that we have applied an electric field for some time to a medium containing many polar molecules (or polar groups in complex molecules such as polymers) and that the medium has relaxed around the polar groups so that the dipole moments freeze in direction after the field has been removed. Furthermore, suppose that the medium contains defects that, through thermal excitation, become mobile, some reaching frozen dipoles and on doing so relax the medium in the neighborhood of the dipoles so that they may reorient themselves as required in an approach to equilibrium. In polymeric materials, the defects may be local conformational abnormalities induced by interaction of a polymer chain with itself or with neighbors, thus introducing local strains into a system. In glassy systems, often with small a va...

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confidence: 99%

“…The theory of such diffusion-controlled reactions for a continuous-time random walk has been given by Helman and Funabashi (12) and Hamill and Funabashi (13) who used it as a model for electron scavenging in low-temperature glasses. In our analysis, we follow Tachiya's (14,15) derivation of the basic kinetic equation used by Hamill and Funabashi.…”

mentioning

confidence: 99%

On the Williams—Watts function of dielectric relaxation

Shlesinger

Montroll

1984

Proc. Natl. Acad. Sci. U.S.A.

373

145

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“…Therefore, one initial state, one final state. It has already been shown that nearly equal slopes have been obtained for decay at 550 nm and 77 K for the same matrix doped with electron acceptors (6). The value of cz does not depend upon the impurity or its concentration, although the rate of decay increases with increased concentration.…”

Section: Experimental Evidencementioning

confidence: 58%

“…We present here a more detailed derivation for the electron scavenging rate expression according to the CTRW model from that obtained previously (6). The system of interest consists of trapped electrons and acceptor sites, e.g.…”

Section: Rate Constatzt For Electron Sca~'engingmentioning

confidence: 99%

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The role of electron–phonon interaction and non-Gaussian transport in spectral changes of trapped electrons in glasses

Funabashi¹,

Hamill²

1979

Can. J. Chem.

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The continuous-time-random-walk (CTRW) model which was developed for electron scavenging reactions in polar glasses is extended to the phenomenon of spectral relaxation of electrons in shallow traps e , in a wider range of systems. The central role of electron-phonon coupling in understanding the initial electron localization, the "pre-existing trap", and electron transfer processes are emphasized. The reactivity of e , with scavengers, including protons, is discussed in terms of the theory of multi-phonon non-radiative transitions. KOICHI F L~A B A S H I et W I L L I A~I H . H A~I I L S .Can. J. Chem. 57. 197 (1979) On a etendu le modele de la marche aleatoire en temps continu (CTRW) qui avait ete developpe pour les reactions de piegeage d'electrons dans des verres polaires au phenomene de relaxation spectrale des electrons dans des pieges superficiels, e,-, dans un do~naine plus large de systemes On met en relief le r61e central ~L I couplage electron-phonon pour la comprehension de la localisation initiale de l'electron, "le piege pre-existant", et les processus de transfert d'electrons. On discute de la riactivite des e,-avec les pieges, y compris les photons, en termes de la theorie des transitions non-radiatives multi-phonons.[Traduit par le journal]

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Stretched exponential relaxation of viscous remanence and magnetic dating of erratic boulders

et al. 2016

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Viscous remanence continuously increases with the duration of reorientation of rocks, and the remanence gets partially overprinted in rocks parallel to the Earth's magnetic field. This overprinted viscous remanence is unblocked at a certain temperature that enables the estimation of the time required for the rock to acquire the magnetism, by assuming the exponential law of Néel's single‐domain theory. However, previous results of dating the rocks by the exponential law have shown older ages than radiometric or cosmogenic exposure ages. Néel's exponential decay law is applicable to a system whose magnetic grains have an identical relaxation time. However, in real systems, the expected behavior is not usually observed because relaxation times vary for individual grains. Moreover, the variation of viscous remanence with the logarithmic law for a distribution of relaxation times is predicted to be concave downward. Here we found that the stretched exponential law, exp{−(t/τ)1 − n} with 0 ≤ n < 1, explains previously published data on viscous decay. The observed stretched exponential relaxation can be interpreted in terms of the global relaxation of a system containing many relaxing species, each of which decays exponentially in time with a specific fixed relaxation rate. Using this law, we derived an extended time‐temperature relationship of magnetite involving the Néel's exponential decay law with n = 0 and a system containing many relaxing times with variable n. The extended time‐temperature relationship shows that the age of a coral tsunami boulder with high anomalous unblocking temperatures can be fitted with an assigned radiometric age.

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Kinetics of electron trapping reactions in amorphous solids; a non-Gaussian diffusion model

Cited by 101 publications

References 12 publications

On the Williams—Watts function of dielectric relaxation

On the Williams—Watts function of dielectric relaxation

The role of electron–phonon interaction and non-Gaussian transport in spectral changes of trapped electrons in glasses

Stretched exponential relaxation of viscous remanence and magnetic dating of erratic boulders

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