Isothermal Relaxation Research Articles

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.

Isothermal relaxation of field-biased barium stannate titanate

The isothermal time dependences of the dielectric constant and the discharging current of barium stannate titanate ceramics after application or removal of a step field were investigated in both ferroelectric and paraelectric temperature regions. The experimental results exhibited a substantial difference for these two phases. For the ferroelectric phase, the relaxation of the dielectric constant is weak and the discharging current obeys Hammon’s model. While for the paraelectric phase, the relaxation is relatively strong and the discharging current obeys the complex exponential decay model. The relaxation of the field-induced piezoelectric resonance indicated the first relaxation observed in a paraelectric phase sample corresponding to homocharges. The authors proposed that the transportation of homocharges is the microscopic origin of the strong relaxation observed in the paraelectric phase.

Creep-resistant aluminum alloys for use in MEMS

Creep is expected to be a reliability issue in MEMS where high temperatures and stresses are present in the moving part. In this paper, we describe a method of measuring the creep parameters, ΔF and τ, in metal thin films. Substrate curvature measurements were used to study different Al alloys—Al98.3Cu1.7, Al99.7V0.2Pd0.1, Al93.5Cu4.4Mg1.5Mn0.6 and Al99.6Cu0.4 films—during isothermal tensile stress relaxation. We show that there is a direct relation between the measured creep parameters and the coherency, size and spacing of precipitates observed by TEM and SEM in the alloys. Furthermore, we confirm that the plastic deformation is controlled by the motion of dislocations inside grains in the Al alloy films. A strengthening process called precipitation hardening was used to create stronger precipitates within the grains in Al99.6Cu0.4 to hinder the movement of dislocations more effectively and thus to make the alloy more creep resistant.

The effect of Pd on the isothermal relaxation of short-range order in Au(Ag)-based ternary alloys

The effect of Pd on the isothermal relaxation of short-range order (SRO) was studied in Au x Ag x Pd 100−2 x ( x = 25 , 40 at%) alloys, using the residual resistometry at 77 K. The short-range ordering resulted in an increase of electrical resistivity. The equilibrium values of this property characterizing the SRO-equilibrium states exhibit a linear dependence on the reciprocal of temperature. The analysis of the resistivity data using the fundamental laws of SRO-kinetics shows that the resistivity behavior can be satisfactorily explained by the two-exponentials law and leads to the determination of characteristic time constants and the activation enthalpies for the two processes. Further, it is found that both the equilibrium and kinetic behavior of these alloys are highly dependent on the concentration of Pd. The presence of Pd reduces the atomic mobility which results from a decrease in the vacancy mobility linked to the positive size effect of Pd in these alloys.

Isothermal stress relaxation in electroplated Cu films. II. Kinetic modeling

In Part I we reported experimental results obtained from isothermal stress relaxation tests of electroplated Cu thin films with and without a passivation layer and deduced grain-boundary and interface diffusivities based on a kinetic model. Here in Part II we describe the detail of the model, which is based on coupling of grain-boundary diffusion with surface diffusion for unpassivated films and with interface diffusion for passivated films. Numerical solutions are obtained for the coupled diffusion problems and analytical solutions are obtained for several limiting cases. The effects of surface diffusivity and interface diffusivity on stress relaxation of polycrystalline thin films are analyzed and compared with experiments. The model predicts a transient behavior of stress relaxation and provides a quantitative correlation between stress relaxation and the kinetics of mass transport. In particular, the models can be used together with isothermal stress relaxation tests to characterize interface diffusion and to evaluate selected cap layers for improving electromigration reliability of Cu interconnects.

Isothermal stress relaxation in electroplated Cu films. I. Mass transport measurements

Recent studies on Cu interconnects have shown that interface diffusion between Cu and the cap layer dominates mass transport for electromigration. The kinetics of mass transport by interface diffusion strongly depends on the material and processing of the cap layer. In this series of two papers, we report in Part I the interface and grain-boundary mass transport measured from isothermal stress relaxation in electroplated Cu thin films with and without a passivation layer and in Part II a kinetic model developed to analyze the stress relaxation based on the coupling of grain boundary and interface diffusion. We show that a set of isothermal stress relaxation experiments together with appropriate modeling analysis can be used to evaluate the kinetics of interface and grain-boundary diffusion that correlate to electromigration reliability of Cu interconnects. Thermal stresses in electroplated Cu films with and without passivation, subjected to thermal cycling and isothermal annealing at selected temperatures, were measured using a bending-beam technique. Thermal cycling experiments showed the effect of passivation and provided information to select the initial stresses and temperatures for isothermal stress measurements. Isothermal experiments at moderate temperatures showed a significant transient behavior of stress relaxation. Based on the kinetic model developed in Part II, grain boundary and interface diffusivities were deduced. While the deduced grain boundary diffusivity reasonably agrees with other studies, the diffusivity at the Cu∕SiN cap layer interface was found to be generally lower than the grain-boundary diffusivity at the temperature range of the present study.

Nanoparticles of Fe in SiO2: A superparamagnet with a collective state?

We present a detailed experimental characterization of the irreversible response of a thin film of nanodimensional Fe particles embedded in SiO2, which includes measurements of the field and temperature dependence of the field-cooled moment, the zero-field-cooled moment, the thermoremanent moment, and the isothermal remanent moment, as well as measurements of the relaxation of the moment with time following various field application and removal protocols. The data are analyzed within the framework of a Preisach ensemble of temperature-dependent, thermally activated, asymmetric double-well subsystems. The analysis allows us to estimate the thermal fluctuation field, and to reconstruct the Preisach spectrum of double-well dissipation fields and bias fields, and its evolution with temperature. Relaxation isotherms exhibit an age dependence which suggests that the free-energy landscape of the thermally blocked state may possess an organization similar to that which characterizes the collectively frozen state of spin glasses.

Z-DNA's Conformer Substates Revealed by FT-IR Difference Spectroscopy of Nonoriented Left-Handed Double Helical Poly(dG-dC)

Nonoriented hydrated films of double helical poly(dG-dC) in the Z-form were studied by Fourier transform infrared (FT-IR) spectroscopy either as equilibrated slow-cooled samples between 290 and 220 K or, after quenching into the glassy state, as nonequilibrated film isothermally at 200, 220, and 240 K. IR spectral changes on isothermal relaxation at 200 and 220 K toward equilibrium, caused by interconversion of two conformer substates (CS) called Z1 and Z2, are revealed by IR difference spectra. Pronounced spectral changes on Z1-to-Z2 interconversion occur between ≈750–1250 cm−1 and these are attributed to structural changes of the phosphodiester-sugar backbone caused by changes of torsion angles, and to decreasing hydrogen-bonding of the ionic phosphate group with water molecules. These spectral changes on Z1-to-Z2 transition can be related to structural differences between ZI and ZII CS observed in single crystals. ZI/ZII CS occurs only at (dGpdC) base steps, and similar behavior is assumed for Z1/Z2. The Z1/Z2 population ratio was determined via curve resolution of marker bands for Z1 and Z2 centered at 785 and 779 cm−1. This ratio is 0.64 at 290 K, corresponding to 39% of the phosphates of the (dGpdC) base steps in Z1 and 61% in Z2, and it increases to 1.24 on cooling to 220 K. For the Z2⇔Z1 equilibrium, an enthalpy change of −4.9 ± 0.2 kJ mol(dGpdC)−1 is obtained from the temperature dependence of the equilibrium constant. Z1 interconverts into Z2 at isothermal relaxation at 200 and 220 K, whereas on slow cooling from ambient temperature, Z2 interconverts into Z1. This unexpected reversal of CS interconversion is attributed to slow restructuring of hydration shells of the CS on quenching, in the same manner reported by Pichler et al. for the BI and BII CS of B-DNA (J. Phys. Chem. B 106, 3263–3274 (2002)). IR difference curves demonstrate two time scales on isothermal relaxation of Z1→Z2 interconversion, a fast one for structural relaxation of the sugar-phosphate backbone, and a slow one for relaxation of the hydration shells. This slowing down of restructuring of CS hydration shells at ≈220–240 K could be the cause for the suppression of biological functions at low temperatures.

Ageing behaviour of Pd40Cu30Ni10P20 bulk metallic glass during long-time isothermal annealing

In this paper, positron annihilation spectroscopy and differential scanning calorimetry were applied to study the structural relaxation of Pd40Cu30Ni10P20 bulk metallic glass during long-time annealing at 523 K. It was found that the relaxation of the alloy follows a two-stage process. In the initial stage, with increasing annealing time, the height of the glass transition peak (namely Δcp) increased, while the average positron lifetime decreased. The isothermal relaxation kinetics obeys a Kohlrausch law with exponent of β = 0.5± 0.03. However, when the annealing time is beyond 32 h, the height of the glass transition peak (Δcp) decreased, and the average positron lifetime increased. This is possibly due to the enhancement of the topological short-range ordering, which results in the generation of new defects on the interfaces between the solid-like regions and the liquid-like regions in amorphous phase. The experimental results were tentatively discussed in terms of free-volume theory and percolation theory.

Contact residual stress relaxation in soda-lime glass: Part I. Measurement using nanoindentation

The contact residual stress field created by a Vickers indentation is a micro-size region of high and varying stresses. Stress relaxation studies in such a micro-region may not be accessible to the conventional methods of investigation. In this paper the elastic response during nanoindentation has been used to study the isothermal stress relaxation of a Vickers residual stress field in soda-lime glass at 540 and 630 °C. At each temperature, the stress relaxation profile varied from one location of the stress field to the other suggesting non-linear response to stress. Also, the relaxation profiles at identical positions were different for the two temperatures suggesting that the Vickers residual stress field is not a thermorheologically simple region of material.

Evolution of Microstructures in a Low Carbon Bainitic Steel during Reheating

Cooled in water after isothermal relaxation of deformed austenite for different time, a Nb-bearing microalloyed steel always exhibited synthetic microstructures of bainitic ferrite, granular bainite and acicular ferrite. When these samples were reheated to and held at 650°C or 700 °C, the non-equilibrious microstructures tended to evolve into equilibrious ones, accompanied by obvious change of hardness. The rate of microstructures evolution was closely related to relaxation time of deformed austenite. The sample relaxed for 60s displayed the highest thermal stability, while microstructure evolution was quickest in the sample relaxed for 1000s even though it was softest before reheating. By hardness measurement, it was found that softening was not only process occurring during reheating, in which hardness fluctuated with time. There were two peaks in hardness-time curve of each sample having undergone relaxation, while single peak occurred in the curve of the sample not being relaxed. These results indicate that thermal stability of microstructures is determined by their history of formation.

Modeling the large-strain constitutive behavior of polycarbonate under isothermal and anisothermal conditions

The tensile behavior of polycarbonate was studied at large strains below the glass-transition temperature. Experiments were carried out at a series of constant temperatures and also under conditions of falling temperatures. The specimens necked with a natural draw ratio of approximately 2, and the study was mainly focused on the necked material. Isothermal experiments revealed an elastic mechanism that initiated beyond the natural draw ratio. A model consisting of an Eyring process and two Gaussian elastic mechanisms was found to be applicable to both the isothermal and anisothermal stress-relaxation and stress–strain results. The same model also produced reasonable estimates of the stresses generated during the necking process. In addition, a simple relationship between the isothermal and anisothermal stress relaxation was demonstrated. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 2105–2116, 2005

Metastable magnetic response across the antiferromagnetic to ferromagnetic transition inGd5Ge4

Results of isothermal magnetization and magnetic relaxation measurements are presented probing the nature of the magnetic-field-induced magnetostructural transition in the intermetallic compound ${\mathrm{Gd}}_{5}{\mathrm{Ge}}_{4}$. This transition shows the characteristics of a disorder-influenced first order transition including distinct metastable behavior. Below approximately $21\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the transition from the magnetic-field-induced ferromagnetic state back to the antiferromagnetic state shows additional interesting features. Similarities with other classes of magnetic systems exhibiting magnetostructural transitions are pointed out.

Stress relaxation at high temperatures and the role of delayed elasticity

Closed-loop controlled isothermal ‘constant-strain’ stress relaxation tests (SRT) at different strains led to the conclusion that SRT cannot provide the anticipated viscous strain rate over a wide stress range; the stress exponent for power-law creep was found to depend on strain. The recovery phase after SRT showed that delayed elasticity, not the viscous flow, controls relaxation processes during the primary stages of stress relaxation irrespective of the level of constraint. Viscous flow controls stress relaxation only at longer times exhibiting ‘apparently’ asymptotic approach to a quasi-stable stress rate. Limitations of SRT can be explained by formulating the relaxation processes on the basis of a three-component rheological equation, derived from independent isothermal constant-stress strain relaxation and recovery tests (SRRT). Theoretical predictions were made for the time-dependent recoverable (delayed elastic) and permanent components of strain as functions of time and imposed strain. Experimental results exhibiting the short-coming of conventional experimental and analytical approaches and the strength of present formulations are illustrated by using a titanium-based, α–β, Ti–6Al–2Sn–4Zr–6Mo alloy at 600 °C (0.45 T m) as a test material.

Thickness dependence of structural relaxation in spin-cast, glassy polymer thin films

The isothermal structural relaxation of glassy, spin-cast polymer thin films has been investigated. Specifically, the thickness h of freshly cast poly(methyl methacrylate) thin films was measured over time using spectroscopic ellipsometry. The spin-cast films exhibit a gradual decrease in thickness, which is attributed to structural relaxation of the glass combined with simultaneous solvent loss. In all cases, h was found to be greater than the equilibrium thickness h(infinity) , which is obtained by cooling slowly from the melt. It is observed that both the rate of the volume relaxation and the fractional departure from h(infinity) (referred to as delta(0) ) increase with increasing film thickness. In the limit of very thin films, the initial h is close to h(infinity) , and delta(0) is small, whereas in thick films (>500 nm) , a plateau value of delta(0) of 0.16 is observed, which is close to the volume fraction of the solvent at the vitrification point. This dependence of delta(0) on thickness is observed regardless of the substrate, polymer molecular weight, or angular velocity during spin casting. Enhanced mobility near film surfaces could be leading to greater relaxation in thinner films prior to, and immediately after, the vitrification of the polymer during the deposition process.

Roles of cyclic units in copolyethylene crystallization: a molecular dynamics simulation

Molecular dynamics (MD) simulations of several polyethylene copolymer chains containing 1,2-, 1,3- or 1,4-disubstituted cyclopentane or hexamethylene structures in the main chain (with 500 CH 2) are performed to investigate the influence of cyclic units on the crystallization properties of polyethylene (PE). From the isothermal relaxation process it is found that they generally collapse to a globule via a local collapse process. The copolymer chains containing 1,2-disubstituted cycloparaffin structures form more kinks and take shorter time to totally collapse into a single globule than the others. Moreover, from the morphology of the crystal structures after annealing it is found that the copolymer chains containing 1,2-disubstituted cycloparaffin structures can yield more ordered structures with cyclic units rejected to the fold surface. For the copolymer chains containing 1,3- or 1,4-disubstituted cycloparaffin, the lamellar structures are not perfect and some cyclic units are always incorporated in the crystalline phase.

Characterization of Adsorbed Athabasca Asphaltene Films at Solvent−Water Interfaces Using a Langmuir Interfacial Trough

Characteristics of adsorbed monolayers of fractionated high molecular weight, low molecular weight, and unfractionated whole asphaltenes at a heptol (a mixture of heptane and toluene)−water interface have been studied with a Langmuir interfacial trough. The deposited monolayer Langmuir−Blodgett (LB) asphaltene films were characterized with atomic force microscopy (AFM), contact angle measurements, and Fourier transform infrared spectroscopy (FTIR). Monolayers of the three asphaltene samples behave similarly at a heptol−water interface, as characterized by close resemblance of the corresponding pressure−area, hysteresis, and relaxation isotherms. For pressure−area isotherms, a monolayer of the low molecular weight asphaltene is the most expanded, while a monolayer of the high molecular weight asphaltene is the most condensed. In terms of relaxation characteristics, a monolayer of the high molecular weight asphaltene relaxes most quickly. Similarity among the three asphaltene samples is further evidenced by close resemblance of topographies of AFM images, contact angle values, and FTIR spectra of the deposited LB asphaltene films. In general, an asphaltene monolayer is more flexible at a heptol−water interface than at an air−water interface.

Continuous and intermittent stress relaxation studies on foamed polysiloxane rubber

Stress relaxation studies of foamed polysiloxane rubber samples have been conducted using a thermomechanical analyser (TMA). The data were assessed using the principle of time–temperature superposition and also by a kinetic study of the experimental results. The time–temperature superposition technique produced acceleration factors that showed good adherence to the Arrhenius relationship and showed two distinct regions where processes with different activation energies dominate. Our kinetic studies showed that the stress relaxation isotherms between 21 °C and 100 °C showed poor correlation to both first- and second-order rate equations. In comparison, the stress relaxation isotherms at elevated temperatures between 120 °C and 175 °C showed good conformity to second-order kinetics. The second-order rate constants for the isotherms at elevated temperatures showed good adherence to the Arrhenius relationship yielding an apparent activation energy of 63 ± 4 kJ/mol. These values are in close agreement to that derived using time–temperature superposition (65 ± 5 kJ/mol). The simple kinetic approach adopted here could not be used to assess the stress relaxation data below 120 °C because a suitable rate function could not be identified. Intermittent stress relaxation studies allowed compression set data to be obtained as a function of time and temperature. Comparison of intermittent and continuous stress relaxation profiles at a number of different temperatures shows that the foamed polysiloxane rubber exhibits significant physical relaxation or spring back during the recovery process. To assess the physical contribution to compression set, samples showing set were swollen in toluene for 1 day and then dried in air to constant weight. All samples with set showed significant solvent-induced recovery suggesting reversible physical relaxation processes contribute significantly to compression set in these polymers. This suggests that possible compression set damage in real-time aged foamed polysiloxane rubbers may be partially reversible using the toluene swell procedure reported here, opening up the possibility of component re-use.

An Interstitialcy Theory of Structural Relaxation and Related Viscous Flow of Glasses

A theory of isothermal structural relaxation and creep of glasses below the glass transition temperature is given. According to the interstitialcy theory, the supercooled liquid state does not exist below a Kauzmann "pseudocritical" temperature T(k), which lies above the temperature T(K), commonly called the "Kauzmann temperature." Structural relaxation is simply a reduction with time of the interstitialcy concentration to the crystalline state for T<T(k), and to the metastable supercooled liquid state for T>T(k). The predicted viscosity eta is universal, given by eta=eta(0) + eta(T)t, in agreement with experiment. eta is continuous in T, with eta discontinuous at T(k) but linear in 1/T above and below T(k). The dependence of eta on the shear modulus directly connects kinetic and thermodynamic properties of glasses and liquids.

Creep as a reliability problem in MEMS

Creep is expected to be one of the major reliability problems for certain MEMS. In particular RF-MEMS switches with metal bridges will be endangered, especially at high RF power, if the bridge material is not selected appropriately. In this paper, substrate curvature measurements are used to study creep properties of Al, Al 98.3 Cu 1.7 , Al 99.7 V 0.2 Pd 0.1 and Al 93.5 Cu 4.4 Mg 1.5 Mn 0.6 films using isothermal tensile stress relaxation. For all aluminum compositions dislocation glide describes the relaxation data very well up to 110°C. However a large difference in creep sensitivity is measured: Al 93.5 Cu 4.4 Mg 1.5 Mn 0.6 is the alloy that is most resistive to creep. We propose a very simple way of characterizing Al alloy thin films by two creep parameters: activation energy AF and athermal flow stress τ. We also show a direct relation between the parameters and the coherence, size and spacing of precipitates observed by SEM and TEM in the alloys. In addition we report that neither heating rates nor maximum temperatures (above 200°C) have an influence on stress in pure Al films.