Activation Energy Spectrum Research Articles

A sensitive method to detect very low levels of long chain branching from the molar mass distribution and linear viscoelastic response

We have developed a sensitive method to detect very low levels of long chain branching in sparsely branched polymers and applied it to high-density polyethylene samples with broad molar mass distribution obtained by Ziegler-Natta, Phillips, and metallocene catalysis. We compare experimental dynamic moduli with predicted values. The predicted moduli, which are only valid for truly linear chains, are computed from a known molar mass distribution by the application of a modified time-dependent diffusion reptation model described in [van Ruymbeke et al., Macromolecules 35, 2689 (2002)]. Discrepancies between experimental and predicted moduli are observed at branching levels below the usual detection limit Of C-13 nuclear magnetic resonance (about I branch per 10000 carbon atoms). Our method is easier to implement and the results more clearcut than those obtained by the zero-shear viscosity method. The sensitivity is comparable with the activation energy spectrum method described in [Wood-Adams et al., Macromolecules 33, 7489 (2000)]. The use of our method is however not restricted to thermorheologically complex polymers. The interest of polymer fractionation is also demonstrated for the detection of extremely low levels of long chain branching. (c) 2005 The Society of Rheology.

Stress relaxation of bulk and ribbon glassy PdCuNiP

Abstract Detailed measurements of linear heating and isothermal stress relaxation of bulk and ribbon glassy Pd 40 Cu 30 Ni 10 P 20 below the glass transition temperature have been performed. Using the activation energy spectrum reconstructed from these measurements, the temperature dependence of the shear viscosity has been calculated. It has been found that this dependence agrees with that derived directly from the creep measurements. This provides strong support for understanding the stress relaxation as a result of the stress-oriented irreversible structural relaxation with distributed activation energies.

Fluctuations of impurity composition and their role in dislocation cross slip in crystals

The influence of impurities on the kinetics of split-dislocation cross slip caused by a change in the stacking-fault energy is studied theoretically. It is shown that the fluctuations in the impurity composition of a crystal make a considerable contribution to the kinetics of dislocation cross slip. The activation-energy spectrum and the average frequency of the processes of dislocation cross slip are calculated for a model of random impurity distribution in a crystal. The calculation shows that the fluctuations in impurity concentration, reducing the stacking-fault energy, play an important role in the low-temperature region.

Time and Amplitude Dependences of the Damping Decrement and Shear Modulus upon Irreversible Structural Relaxation in a Zr–Cu–Ni–Al–Ti Bulk Metallic Glass

The time dependences of the irreversible relaxation of the damping decrement and the shear modulus of a Zr52.5Ti5Cu17.9Ni14.6Al10 bulk metallic glass are investigated using an inverse torsion pendulum in the range from room temperature to ∼650 K. The spectrum of activation energies of irreversible structural relaxation is evaluated from the results obtained. Analysis of the amplitude dependences of the damping decrement and the shear modulus allows the conclusion that the relaxation centers responsible for the amplitude dependence differ from those associated with the irreversible structural relaxation at temperatures below and in the vicinity of the glass transition point.

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

A procedure is shown to quantitatively analyze the morphology of the internal friction peak resulting from grain-boundary sliding. A Si3N4 polycrystal containing chlorine-doped SiO2 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 SiO2-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.

Evidence of B- and Si-type magnetic relaxations in Co-based amorphous alloys

The kinetics of the structural magnetic relaxations (MRs) in the Co-based amorphous alloys has been investigated by magnetic after-effect spectroscopy. The experimental evidence and characterization of two types of MRs in the amorphous ${\mathrm{Co}}_{75}{\mathrm{B}}_{25}$ and ${\mathrm{Co}}_{75}{\mathrm{Si}}_{15}{\mathrm{B}}_{10}$ alloys are rendered in this work. The binary CoB alloy shows only the B-type MR with the most probable energy of the activation energy spectrum $Q*=1.35\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and the preexponential factor ${\ensuremath{\tau}}_{0}=2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. In the ternary CoSiB amorphous alloy, the additional Si-type MR with $Q*=1.96\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and ${\ensuremath{\tau}}_{0}=6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$ occurs. Low-temperature annealing shifts either of the relaxation parameters of both alloys to higher values. Roles of the free volumes, the dimension, and affinity of the B and Si atoms for Co in the MR are discussed.

Structural magnetic relaxation of amorphous Co75B25 alloy

The structural magnetic relaxation of the amorphous Co75B25 alloy in the as-cast and annealed states has been investigated by means of the magnetic after-effect (MAE) spectroscopy. The relaxation process is realised by reorientations of atom pairs minimizing a free energy of the ferromagnetic system. The pre-exponential factor τ0=2×10−17 s and the most probable activation energy Q*=1.34 eV have been obtained from numerical analyses of MAE spectra and isotherms of the amorphous alloy in the as-cast state. A peak of the 180 s isochrone occurs at the temperature 383 K. Annealing at 653 K for 1800 s reduces relaxation intensity Δr/r from 38% to 9% and shifts the peak temperature to 473 K. Activation parameters of the magnetic relaxation of the annealed Co75B25 alloy were changed to τ0=9×10−16 s and Q**=1.53 eV. These effects are connected with reduction of the free volumes near to active atom pairs. Numeric analyses of the MAE isochrones and long time isotherms give very similar activation energy spectra.

Some new results on amorphous Curie-temperature relaxation

Two reversible relaxation processes of similar activation energies can be separated in Cr-doped FeNiSiB metallic glasses by combined Curie-point and enthalpy-relaxation measurements. While one of the processes has a positive contribution to the activation-energy spectrum of the Curie-point, the other gives a negative contribution to it. The positive effect is associated with the ordering of Fe and Ni atoms in the FeNiSiB matrix while the negative effect is attributed to the Cr atoms.

Viscosity of bulk and ribbon Zr-based glasses well below and in the vicinity ofTg:A comparative study

Tensile creep tests of bulk and ribbon samples of ${\mathrm{Zr}}_{52.5}{\mathrm{Ti}}_{5}{\mathrm{Cu}}_{17.9}{\mathrm{Ni}}_{14.6}{\mathrm{Al}}_{10}$ metallic glass have been performed over a wide range of heating rates. It has been found that a change of the quenching rate at least by three orders of magnitude exerts little influence on the shear viscosity below the glass transition temperature ${T}_{g}.$ In all cases, the viscosity is strongly dependent on the heating rate, which can be explained as a result of irreversible structural relaxation with distributed activation energies. It is argued that the volume spectral density of relaxation centers in the high-energy part of the activation energy spectrum (AES) of irreversible structural relaxation is higher for ribbon samples than that for bulk specimens by about 30%, whereas the low-energy part of the AES remains unchanged. Above ${T}_{g},$ the viscosity of bulk samples is always lower than that of ribbons, which may be interpreted in terms of the phase decomposition.

Isothermal creep of bulk glassy Zr52.5Ti5Cu17.9Ni14.6Al10 below T g

The results of an isothermal creep investigation of Zr52.5Ti5Cu17.9Ni14.6Al10 bulk metallic glass at temperatures below the glass transition temperature are presented. The long-time (t > (2–4) × 103 s) creep regularities were found to be the same as those known for ribbon metallic glasses, in spite of the pronounced difference in the production quenching rates. It is argued that creep behaviour of bulk metallic glass is determined by the rate of irreversible structural relaxation. The apparent activation energy spectrum reconstructed from isothermal creep measurements agrees well with that determined from linear heating creep data.

Silicon thin films deposited at very low substrate temperatures

A series of investigations were performed to study the influence of the substrate temperature on the structure and properties of silicon thin films. Substrate temperature was varied in the wide range of 35–200 °C. It has been shown that the films grown below 60 °C exhibit an unusual structural behavior. A sharp TO phonon peak at 520 cm −1 was detected in Raman spectra, which is associated with the crystalline structure. In contrast to these results, the same samples do not show any crystallite-related peak by X-ray diffraction and their optoelectronic properties (dark conductivity, activation energy and subgap absorption spectra) show amorphous features. A similar discrepancy was observed for a hydrogen dilution ratio ( r H=([SiH 4]+[H 2])/[SiH 4]) series of samples deposited at 60 °C. Hydrogen dilution ratio was varied from 25 to 170. It seems that at low substrate temperature a parameter window exists where the silicon thin films can be grown with the properties combining both crystalline and amorphous behavior.

Mechanical spectroscopy methods for the quantitative analysis of intergranular glass viscosity in polycrystalline ceramics

Mechanical spectroscopy methods for the analysis of viscous behavior of grain boundaries are described and applied to glass-bonded polycrystalline ceramics. Emphasis is placed on the analysis of a high-temperature peak, which originates from grain-boundary sliding relaxation, with respect to: (i) peak shift with damping frequency change; (ii) peak intensity for a given testing geometry and amount of glassy phase; and, (iii) peak morphology characteristics. According to analyses (i) and (ii), an activation energy for intergranular viscous flow and the magnitude of glass-phase viscosity are quantitatively determined. The morphology of the peak depends on the activation energy for intergranular viscous flow, but it is also affected by the volume fraction of intergranular glass and by the presence of chemical gradients at grain boundaries. In addition microstructural inhomogeneities, such as grain size distribution and grain texture, can affect the peak morphology. Chemical and microstructural inhomogeneities generate spectra of activation energies and relaxation times, respectively. With inherently different characteristics, they both contribute to peak broadening. Internal friction experiments as a function of glass volume fraction and chemical composition experimentally confirmed that the above features are actually represented in the internal friction curve of a ceramic polycrystal as a function of temperature.

Temperature Dependences of the Low-Frequency Internal Friction and Shear Modulus in a Bulk Amorphous Alloy

The logarithmic decrement and shear modulus of a bulk amorphous Zr52.5Ti5Cu17.9Ni14.6Al10 alloy were studied with an inverse torsion pendulum in the range from room temperature to the crystallization temperature and in the frequency range 5–40 Hz. The activation energy spectra of reversible and irreversible structural relaxation were estimated. The results obtained are discussed in the context of a two-energy-level model.

Dislocation motion in a random solid solution

Abstract The thermally activated motion of a dislocation through an array of randomly distributed solute atoms is studied. The influence of fluctuations in the solute density on the activation energy for dislocation motion is investigated, and the stress dependences of the effective activation energy and the activation volume are determined. It is shown that, in creep deformation, fluctuations in the activation energies may lead to a creep strain which increases with time according to a power law, with an exponent that increases linearly with increasing temperature. Implications of the calculated activation energy spectrum for low-frequency internal friction are discussed.

Dislocation motion in a random solid solution

Abstract The thermally activated motion of a dislocation through an array of randomly distributed solute atoms is studied. The influence of fluctuations in the solute density on the activation energy for dislocation motion is investigated, and the stress dependences of the effective activation energy and the activation volume are determined. It is shown that, in creep deformation, fluctuations in the activation energies may lead to a creep strain which increases with time according to a power law, with an exponent that increases linearly with increasing temperature. Implications of the calculated activation energy spectrum for low-frequency internal friction are discussed.

Temperature dependence of structural and magnetic relaxation in amorphous and nanocrystalline Co-based alloys

Structural and magnetic relaxations in amorphous alloys containing a nanostructured phase are compared with those of the amorphous precursors Metglas 2714A and Vitrovac 6025, in the temperature range 20 K to the Curie temperature. The analysis is performed by considering the magnetic after-effect (MAE) of the reluctivity which is represented by its relative change Δ r/ r between two fixed times after demagnetization. The nanostructured samples, obtained by suitable thermal treatments of the amorphous alloys, have superior soft magnetic properties (much higher initial permeability and lower coercive field) but are characterized by a lower structural and magnetic stability in wide ranges of temperature. The characteristics of the MAE in nanostructured alloys seem to be connected with the mean radius of the grains. The activation energy spectra are evaluated on the basis of the logarithmic kinetics observed for MAE. It results that the formation of nanocrystallites makes more uniform the distribution of these energies without modifing significantly the range of their values.

Mechanisms of Dopant‐Induced Changes in Intergranular SiO2 Viscosity in Polycrystalline Silicon Nitride

Mechanical spectroscopic methods and first‐principles density functional calculations were applied to attempt a quantitative analysis of both atomic structure and viscous behavior of Si3N4 grain boundaries. In particular, the effect on the intergranular structure/viscosity of small fractions of selected anion/cation dopants was examined in comparison with the undoped polycrystal. From the point of view of mechanical spectroscopy, emphasis was placed on the morphologic analysis, as a function of frequency of oscillation, of a relaxation peak that originates from grain‐boundary sliding. The morphologic characteristics of the grain‐boundary peak clearly revealed the presence of significant chemical gradients among different grain boundaries for particular dopants (e.g., Cl and Ba). On dopant addition, a reduction in activation energy for viscous intergranular flow was observed which broadened the grain‐boundary peak. Chemical inhomogeneities also broadened the peak shape by generating a spectrum of activation energies. First‐principles density functional calculations were conducted for cluster fragment models representative of the amorphous SiO2 intergranular film. The results explicitly showed the mechanism by which the respective dopants break bonds in the host, an action that directly reduces the viscosity of the SiO2 film. These complementary theoretical studies assist understanding and atomic‐scale rationalization of the differences in segregation behavior of different dopants incorporated into the SiO2 film.

Phase and structural transformations in a molecular dynamics model of iron under ultrafast heating and cooling

It is shown that a system of classical particles considered in a molecular dynamics model with Pak-Doyama pairwise interatomic potential adequately describes not only the various structural states of iron (melt, bcc crystal, metal glass) but also the complex self-organization processes occurring in first-and second-order phase transitions (crystallization and vitrification, respectively). When the temperature is varied at a constant rate of 6.6×1011 K/s, crystallization sets in from both the amorphous and the liquid state; at a rate of 1.9×1012 K/s, crystallization is observed only in the amorphous state; and when heated at a rate of 4.4×1012 K/s, the model amorphous iron transfers to the liquid state without crystallization. The energy of homogeneous formation of a crystal nucleus in the bulk of the amorphous phase of iron is calculated to be ∼0.71 eV under the assumption that there is a spectrum of activation energies.

Activation Energy Spectrum of Irreversible Structural Relaxation of Finemet Glassy Alloy

The apparent activation energy spectrum (AES) of irreversible structural relaxation of Finemet Fe73.5Cu1Nb3Si13.5B9 metallic glass is reconstructed using the analysis of (i) linear heating and (ii) isothermal creep tests within the framework of the Directional Structural Relaxation (DSR) model. It is shown that the two independent ways of AES reconstruction used give consistent results indicating the validity of the corresponding DSR model flow equations. The AES determined, in accordance with previous findings, takes the form of a monotonously increasing function indicating that the potential profile for irreversible atomic rearrangements during irreversible structural relaxation might have more than two local minima.

Enthalpy recovery during structural relaxation of Se 96In 4 chalcogenide glass

Structural relaxation of isothermally and isochronally heat-treated Se 96In 4 chalcogenide glass in the glass transition region has been studied using a differential scanning calorimeter (DSC). The recovery of excess enthalpy Δ H excess has been calculated from the knowledge of excess apparent specific heat Δ C p,a ( T) and plotted as a function of annealing time t a. Δ H excess has been found to vary with t a; this variation follows a power-law behaviour and an expression of the form Δ H excess=Δ H o[ t a] y has been proposed to describe such variation . Following the Kissinger formalism the activation energy of structural relaxation E t, both for annealed and un-annealed samples, has been obtained. The so obtained values of structural relaxation activation energies are indicative of the fact that some kind of bond interchange has taken place which in turn accounts for the relaxation process in Se 96In 4 glass. From the knowledge of Δ H excess( T a, t a) and the corresponding activation energy, the activation energy spectra have also been drawn and discussed.