Lognormal Distribution Function for Describing Anelastic and Other Relaxation Processes II. Data Analysis and Applications

Nowick, A. S.; Berry, B. S.

doi:10.1147/rd.54.0312

Cited by 70 publications

(42 citation statements)

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“…We conclude that the increase in f m,JG with time is concomitant with the decrease in the distribution of times or narrowing of the spectra and decrease in ⌬ JG . ͑Calculations were done also for a lognormal distribution of a Gaussian type, 53 which yielded similar results, but for simplicity of illustration here, we have shown only the results of the box distribution.͒ Since the earlier studies of the JG relaxation had been performed without regard to the structural relaxation effect, differences in the f m values as a result of this effect may lead to different activation energies. Only in the equilibrium liquid state would these values be free from time-dependent effects.…”

Section: -5mentioning

confidence: 85%

Kinetics of spontaneous change in the localized motions of D-sorbitol glass

Power

Vij

Johari

2006

The Journal of Chemical Physics

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The dielectric relaxation spectra of D-sorbitol glass have been studied in real time during annealing at 221.1 K, which is 47 K below its T g of 268 K. As the glass structurally relaxes during annealing, features of the Johari-Goldstein ͑JG͒ relaxation change with time: ͑i͒ the relaxation strength decreases, ͑ii͒ the relaxation peak at 48 Hz shifts to a higher frequency, and ͑iii͒ the relaxation spectra become narrower. All seem to follow the relation p ϰ exp͓−͑kt͒ n ͔, where p is the magnitude of a property, k the rate constant, and t the time. The parameter n may well be less than 1, but this could not be ascertained. It is proposed that shift of the relaxation peak to a higher frequency and narrowing of the relaxation spectra occur when local, loosely packed regions of molecules in the glass structure collapse nonuniformly and the relaxation time of some of the molecules in the collapsed state becomes too long to contribute to the JG-relaxation spectra. Consequently, the half width of the spectra decreases, and the relaxation peak shifts to a higher frequency. Molecules whose diffusion becomes too slow after the local regions' collapse would contribute to the ␣-relaxation spectra and thus the net relaxation strength would increase on structural relaxation. It is argued that these findings conflict with the NMR-based conclusions that motion of all molecules in the glass and supercooled liquid contributes to the faster relaxation process.

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Section: -5mentioning

confidence: 85%

Kinetics of spontaneous change in the localized motions of D-sorbitol glass

Power

Vij

Johari

2006

The Journal of Chemical Physics

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“…This analysis, based on microstructural parameters, is considered to represent an improvement with respect to peakwidth analysis based on merely the choice of mathematical functions, selected to fit a posteriori the experimental peaks. 18,19 Fig . 4.…”

Section: (3) Peak Broadening By Microstructural Inhomogeneitymentioning

confidence: 99%

Low‐Frequency Measurements on the Grain‐Boundary Internal Friction Peak in Chlorine‐Doped Silicon Nitride

Pezzotti

2001

Journal of the American Ceramic Society

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A procedure is shown to quantitatively analyze the morphology of the internal friction peak resulting from grainboundary sliding. A Si 3 N 4 polycrystal containing chlorinedoped SiO 2 at grain boundaries is selected as a model system for discussing chemical (e.g., anion) gradients at glassy grain boundaries. In this model material, grain boundaries lodging Cl ؊ anions show nonuniform thickness characteristics, which suggests a non-negligible dependence of the intergranular SiO 2 -network structure upon grain misorientation. Both chemical and microstructural inhomogeneities existing in a polycrystalline ceramic body can result in peak broadening.The key for separating broadening contributions of chemical gradients from grain-size/morphology distributions resides in analyzing the peak-width change upon damping frequency. Groups of grain boundaries with different chemical characteristics may produce broadening because different peak components are generated that obey a spectrum of activation energies. On the other hand, microstructural inhomogeneities obey a single activation energy, but they generate a distribution of relaxation times. As a result, when a chemical gradient is present at grain boundaries, the peak may shift upon changing damping frequency with obeying a true activation energy, but its width increases with decreasing damping frequency. When peak broadening results only from microstructural inhomogeneities, the peak width is independent of damping frequency.

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“…The log-normal distribution represented by (3) has been the subject of earlier papers devoted mainly to the numerical computation of quasi-static response functions as a function of time, and of dynamic response functions as a function of frequency [3]. Often, however, the experimental investigation of thermally-activated relaxation phenomena is feasible only through the observation of dynamic loss peaks as a function of temperature, rather than frequency.…”

Section: Kt'mentioning

confidence: 99%

Computer Modeling of Relaxation Peaks Involving a Gaussian Distribution of Activation Energies

Berry

Pritchet

1987

Physica Status Solidi (b)

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To extend previous work in the frequency domain, as a function of temperature, the forms of anelastic or dielectric loss peaks are computed directly involving a Gaussian distribution of activation energies. The calculations provide the height, width, asymmetry, and frequency-shift behavior of the loss peak as a function of a dimensionless parameter defining the width of the distribution. The calculations are used to determine how well the input distribution cap be recovered or deconvoluted from a set of peaks, obtained for several different frequencies, by a simple empirical procedure termed a cross-cut analysis. The procedure is found to work well for peaks whose width is more than twice the Debye width.I n Fortsetzung friiherer Analysen im Frequenzbereich wird die Form anelastischer oder dielektrischer Relaxationsmaxima als Funktion der Temperatur numerisch fur den Fall, daB eine Gaussverteilung von Aktivierungsenergien vorliegt, berechnet. Die Rechnungen ergeben die Hohe, Breite, Asymmetrie und Frequenzverschiebung des Verlustmaximums als Funktion eines dimensionslosen Parameters, der die Breite der Gaussverteilung charakterisiert. Es wird untersucht, wie gut eine vorgegebene Verteilung aus einem simulierten Satz von Relaxationsmaxima bei verschiedenen Frequenzen durch ein spezielles Schnittverfahren wiedergewonnen werden kann. Das Verfahren erweist sich als brauchbar, wenn die Breite eines Maximums grol3er als die doppelte Debye-Breite ist.

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Lognormal Distribution Function for Describing Anelastic and Other Relaxation Processes II. Data Analysis and Applications

Cited by 70 publications

References 1 publication

Kinetics of spontaneous change in the localized motions of D-sorbitol glass

Kinetics of spontaneous change in the localized motions of D-sorbitol glass

Low‐Frequency Measurements on the Grain‐Boundary Internal Friction Peak in Chlorine‐Doped Silicon Nitride

Computer Modeling of Relaxation Peaks Involving a Gaussian Distribution of Activation Energies

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