Elastic After-Effect Due to Oxygen Relaxation in Yba2Cu3O7−δAbove Tc

1990 ◽  
Vol 209 ◽  
Author(s):  
J. R. Cost ◽  
P. E. Armstrong ◽  
R. B. Poeppel ◽  
J. T. Stanley
Keyword(s):  
Activation Energy ◽  
Relaxation Time ◽  
Internal Friction ◽  
Relaxation Times ◽  
Tracer Diffusion ◽  
Induced Motion ◽  
Arrhenius Temperature Dependence ◽  
After Effect ◽  
Friction Measurements ◽  
Arrhenius Temperature

ABSTRACTIsothermal elastic after-effect measurements to obtain relaxation times for the stress-induced motion of oxygen in YBa2Cu3O7−δ have been made from 50°C to 110°C. These results extend our previous internal friction measurements of the same oxygen relaxation to lower temperatures. The combined results, which cover nine orders of magnitude in relaxation time, show a classical Arrhenius temperature dependence, activation energy Q−1.13±0.01 eV and attempt frequency τ0−1.6×10−13 s (log τ0−.12.79±0.13). The mechanism of the relaxation is considered to be stress-induced ordering of oxygen atoms on theCuO basal plane. Diffusivities obtained from these results are compared with those from tracer diffusion of oxygen.

scholarly journals Unentangled Vitrimer Melts: Interplay between Chain Relaxation and Cross-link Exchange Controls Linear Rheology

2020 ◽  
Author(s):  
RALM RICARTE ◽  
Sachin Shanbhag
Keyword(s):  
Activation Energy ◽  
A Priori ◽  
Relaxation Times ◽  
Cross Link ◽  
Time Dynamics ◽  
Temperature Dependences ◽  
Long Time ◽  
Arrhenius Temperature Dependence ◽  
Short Time ◽  
Arrhenius Temperature

<div>Using this theoretical approach, we explore the influence of molecular structure and temperature on vitrimer linear</div><div>viscoelasticity. We observe that vitrimers with uniform and random cross-link distributions exhibit larger viscosities</div><div>and relaxation times than gradient and blocky types. Polydimethylsiloxane vitrimer (which has a flexible backbone) shows an Arrhenius temperature dependence for viscosity, while polystyrene vitrimers (which has rigid backbones) are only Arrhenius at high temperatures. During stress relaxation, the short time dynamics represent monomer friction, while the long time dynamics encompass a combination of network strand relaxation and cross-link exchange. Because of the different temperature dependences of the processes, time-temperature superposition fails. We also show that the effective rheological activation energy can be estimated a priori using only the cross-link exchange activation energy and the backbone Williams-Landel-Ferry parameters.</div><div><br></div><div>(Submitted to Macromolecules)</div>

scholarly journals Unentangled Vitrimer Melts: Interplay between Chain Relaxation and Cross-link Exchange Controls Linear Rheology

2021 ◽  
Author(s):  
RALM RICARTE ◽  
Sachin Shanbhag
Keyword(s):  
Activation Energy ◽  
A Priori ◽  
Relaxation Times ◽  
Cross Link ◽  
Time Dynamics ◽  
Temperature Dependences ◽  
Long Time ◽  
Arrhenius Temperature Dependence ◽  
Short Time ◽  
Arrhenius Temperature

<div>Using this theoretical approach, we explore the influence of molecular structure and temperature on vitrimer linear viscoelasticity. We observe that vitrimers with uniform and random cross-link distributions exhibit larger viscosities and relaxation times than gradient and blocky types. Polydimethylsiloxane vitrimer (which has a flexible backbone) shows an Arrhenius temperature dependence for viscosity, while polystyrene vitrimers (which has rigid backbones) are only Arrhenius at high temperatures. During stress relaxation, the short time dynamics represent monomer friction, while the long time dynamics encompass a combination of network strand relaxation and cross-link exchange. Because of the different temperature dependences of the processes, time-temperature superposition fails. We also show that the effective rheological activation energy can be estimated a priori using only the cross-link exchange activation energy and the backbone Williams-Landel-Ferry parameters.</div><div><br></div><div>(Submitted to Macromolecules)</div>

scholarly journals Unentangled Vitrimer Melts: Interplay between Chain Relaxation and Cross-link Exchange Controls Linear Rheology

2020 ◽  
Author(s):  
RALM RICARTE ◽  
Sachin Shanbhag
Keyword(s):  
Activation Energy ◽  
A Priori ◽  
Relaxation Times ◽  
Cross Link ◽  
Time Dynamics ◽  
Temperature Dependences ◽  
Long Time ◽  
Arrhenius Temperature Dependence ◽  
Short Time ◽  
Arrhenius Temperature

<div>Using this theoretical approach, we explore the influence of molecular structure and temperature on vitrimer linear</div><div>viscoelasticity. We observe that vitrimers with uniform and random cross-link distributions exhibit larger viscosities</div><div>and relaxation times than gradient and blocky types. Polydimethylsiloxane vitrimer (which has a flexible backbone) shows an Arrhenius temperature dependence for viscosity, while polystyrene vitrimers (which has rigid backbones) are only Arrhenius at high temperatures. During stress relaxation, the short time dynamics represent monomer friction, while the long time dynamics encompass a combination of network strand relaxation and cross-link exchange. Because of the different temperature dependences of the processes, time-temperature superposition fails. We also show that the effective rheological activation energy can be estimated a priori using only the cross-link exchange activation energy and the backbone Williams-Landel-Ferry parameters.</div><div><br></div><div>(Submitted to Macromolecules)</div>

Internal friction due to oxygen relaxation in superconducting YBa2Cu3O7−δ above Tc

1991 ◽  
Vol 6 (2) ◽  
pp. 232-243 ◽  
Author(s):  
J.R. Cost ◽  
J.T. Stanley
Keyword(s):  
Activation Energy ◽  
Internal Friction ◽  
Relaxation Process ◽  
Detailed Analysis ◽  
Peak Height ◽  
Tracer Diffusion ◽  
Internal Friction Peak ◽  
Exponential Factor ◽  
Half Height ◽  
Induced Motion

YBa2Cu3O7−δ has an internal friction peak near 210 °C measured at 1.18 Hz. The shift in the temperature of this peak with frequency as measured with different internal friction techniques indicates that the relaxation process has an average activation energy of 1.14 ± 0.05 eV and a pre-exponential factor, τ0 = 1.5 × 10−13s (log τ0 = −12.82 ± 0.23). The peak height decreases during annealing at above 375 °C in helium and increases when annealed in oxygen. The mechanism for the relaxation is believed to be the stress-induced motion of oxygen atoms in the Cu–O plane. Detailed analysis shows that the internal friction peak is determined by a spectrum of activation energies; this spectrum is a symmetrical single peak 0.12 eV wide at half-height. Models for the relaxation are considered and the resulting diffusivities are compared to tracer diffusion results.

Self-diffusion of Ag+ and Na+ in molten Ca(NO3)2-KNO3

1972 ◽  
Vol 25 (8) ◽  
pp. 1613 ◽  
Author(s):  
BJ Welch ◽  
CA Angell
Keyword(s):  
Electrical Conductance ◽  
Ionic Species ◽  
Tracer Diffusion ◽  
Dilute Solution ◽  
Self Diffusion ◽  
Capillary Method ◽  
Arrhenius Temperature Dependence ◽  
Radio Tracer ◽  
Tracer Diffusion Coefficients ◽  
Arrhenius Temperature

In order to explore the behaviour of diffusing ionic species in a molten salt in which non-Arrhenius behaviour of other transport properties is established, the diffusivities in dilute solution of Ag+ and Na+ in 38.1 mol% Ca(NO3)2+ 61.9 mol% KNO3 have been measured. For both ions limited radio-tracer diffusion coefficients, determined using a diffusion-out-of-capillary method, are reported. D(Ag+) has also been measured by chronopotentiometry, by which means the range and reliability of the measurements were considerably extended. Chronopotentiometric and tracer data agree within expected errors of measurement. Both ionic diffusivities show a non-Arrhenius temperature dependence which is indistinguishable in magnitude from that of the electrical conductance of the solvent melt.

Activation Energy Measurement in Thin Gold Film by MEMS-Based Tensile Testing Device

Materials ◽  
2004 ◽  
Author(s):  
Jong H. Han ◽  
Taher M. Saif
Keyword(s):  
Activation Energy ◽  
Relaxation Time ◽  
Stress Relaxation ◽  
Analytical Model ◽  
Tensile Testing ◽  
Relaxation Times ◽  
Tensile Specimen ◽  
Testing Device ◽  
Free Standing ◽  
Tensile Tester

In this paper, we report a methodology to measure activation energy for time-dependent stress-relaxation in a thin free-standing tensile specimen by utilizing a MEMS-based tensile testing device. An analytical model is developed to investigate its stress-relaxation behavior. Along with this analytical model of the MEMS tensile tester, Arrhenius relation is applied to estimate relaxation times for different temperatures of a free-standing sample beam. From the relation between relaxation time and temperature, the activation energy for the stress-relaxation is obtained. For a 200-nm Au film, we obtained the relaxation time of 250, 67, and 40 seconds for the corresponding temperatures of 295, 312, and 323 K, respectively. The activation energy for stress-relaxation was 0.544 eV. The experimental data is fitted with the analytical model to find the relaxation time. The thin film on the MEMS tensile tester is prepared by sputter-deposition. By optical lithography and ICP DRIE Si etching, the MEMS tensile tester with a free standing beam is fabricated.

Fick’s Laws

2020 ◽  
pp. 141-161
Author(s):  
Brian Cantor
Keyword(s):  
Solid Material ◽  
Kirkendall Effect ◽  
Tracer Diffusion ◽  
Wide Range ◽  
German Science ◽  
Arrhenius Temperature Dependence ◽  
The Difference ◽  
Tracer Diffusion Coefficients ◽  
Medicine And Culture ◽  
Arrhenius Temperature

Atoms and molecules are not completely immobile within a solid material. They move by jumping into vacancies or interstitial sites in the crystal lattice. The laws describing their motion were discovered by Adolf Fick in the mid-19th century, modelled on analogous laws for the flow of heat (Fourier’s law) and electricity (Ohm’s law). According to Fick’s first law, the rate at which atoms move is proportional to the concentration gradient, with the diffusion coefficient defined as the constant of proportionality. Fick’s second law generalises the first law to a wide range of situations and is called the diffusion equation. This chapter examines a number of characteristic diffusion profiles; the difference between self, intrinsic, inter- and tracer diffusion coefficients; the Kirkendall effect and porosity formation when different components move at different speeds; and the Arrhenius temperature dependence of diffusion. Fick was a physiologist and derived his laws initially to describe the flow of blood through the heart. He made advances in anatomy, physiology and medicine, developing methods of monitoring blood pressure, muscular power, corneal pressure and glaucoma. He lived at the time of Bismarck’s post-Napoléonic unification of Germany and the associated flowering of German science, engineering, medicine and culture.

The effect of interfacial stabilizing films on the elastic and viscous properties of emulsions

1955 ◽  
Vol 232 (1191) ◽  
pp. 567-577 ◽  
Keyword(s):  
Relaxation Time ◽  
Internal Friction ◽  
Steady Flow ◽  
Viscous Liquid ◽  
Elastic Moduli ◽  
Relaxation Times ◽  
Solid Particles ◽  
Retardation Time ◽  
Interfacial Film ◽  
Viscous Behaviour

The investigation in a previous paper (Oldroyd 1953) of the elastic and viscous properties of a dilute emulsion of one incompressible viscous liquid in another, when subjected to small variable rates of strain, is extended to include the possibility of an interfacial film being present everywhere between the two components, which resists deformation as a result of internal friction or of elasticity. When the film is purely viscous its presence has no effect on the type of elastico-viscous behaviour of the emulsion, although the values of the viscosity, relaxation time and retardation time of the system are altered. When the film is ideally elastic, the viscosity in slow steady flow is the same as that of a suspension of solid particles, and two relaxation times and two retardation times are required to describe the elastico-viscous behaviour of the emulsion completely. When the interfacial film shows more complicated elastic and viscous properties combined, these can be described by means of two operators (expressible in terms of d/d t ) taking the place of elastic moduli. A viscosity operator describing the macroscopic elastic and viscous properties of the emulsion is calculated in terms of the elasticity operators of the film in the general case.

scholarly journals Measurements of the Electrical Properties of Ice Ih Single Crystals by Admittance and Thermally Stimulated Depolarization Techniques

1978 ◽  
Vol 21 (85) ◽  
pp. 219-230 ◽  
Author(s):  
Arturo Loria ◽  
Ezio Mazzega ◽  
Umberto del Pennino ◽  
Giovanni Andreotti
Keyword(s):  
Activation Energy ◽  
Relaxation Time ◽  
Electrical Properties ◽  
Single Crystals ◽  
Relaxation Spectrum ◽  
Relaxation Times ◽  
Dielectric Strength ◽  
Inert Gas ◽  
Complex Admittance ◽  
Thermally Stimulated Depolarization

Abstract Ice Ih single crystals were investigated by complex admittance and thermally stimulated depolarization (TSD) techniques, in the relaxation-time ranges 10–5–10 s and 10–104 s respectively. The relaxation spectrum was resolved and three components of it were studied. Second-order kinetics had to be assumed for two of the TSD spectra to obtain Arrhenius-type relaxation times. The “Debye spectrum” had an activation energy for the relaxation time of 0.64 eV at the high temperatures and its dielectric strength revealed a possible defect cross-over at T c = 190 K. Far below this temperature the activation energy was 0.38 eV, that is about half of that necessary for a pair of ion defects to form. In comparison with the results of other authors, a lower concentration of ionic defects, or possibly of Bjerrum–ion aggregates, was deduced to occur in our crystals. Inert-gas host molecules were proposed as a possible origin of the two other spectra, having relaxation times shorter than the “Debye spectrum” and energies of 0.33 eV and 0.37 eV. Moreover the 0.33 eV spectrum, whose dielectric strength appears at a temperature below T c, might alternatively be related to the cross-over of the “Debye spectrum”.

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