A. van den Beukel

The glass transition as a free volume related kinetic phenomenon

Abstract The glass transition, observed in glasses during DSC experiments at a constant heating rate, is described as a kinetic phenomenon caused by the continuous approach of free volume towards equilibrium during the warming up. At a certain temperature below the glass temperature T g , the amount of free volume becomes smaller than the equilibrium value at that temperature. The glass transition is caused by a rather sudden increase of free volume towards equilibrium near T g . This can be calculated by making use of the well known kinetics of free volume annilation and production in some metallic glasses. Calculations performed on this basis are in good agreement with available experimental data, both on structural relaxation and the glass transition.

Structural disordering in amorphous Pd40Ni40P20 induced by high temperature deformation

The influence of plastic deformation on the structural state of amorphous Pd40Ni40P20 is investigated by means of tensile test measurements as a function of temperature, strain rate and pre-annealing time. The structural state of the material after the deformation is investigated by means of differential scanning calorimetry (DSC). It is found that amorphous Pd40Ni40P20, when pre-annealed into its metastable equilibrium state, shows a large strain softening effect when deformed at temperatures close to the glass transition temperature. The strain softening effect is less pronounced or even absent in samples that are only briefly pre-annealed. The DSC traces show that the structural state of the material disorders during the deformation and that the material reaches a strain rate and temperature dependent equilibrium state, which differs from the thermal equilibrium state. It is shown that the strain softening effect is caused by the creation of additional free volume during the deformation.

On the kinetics of structural relaxation in metallic glasses

Abstract A model is proposed to describe the simultaneous changes in topological (TSRO) and chemical (CSRO) short range order during structural relaxation of metallic glasses. Changes in free volume and order parameter during isothermal and isochronal annealing were calculated. Corresponding changes in internal energy and Curie temperature are—at least qualitatively—in good agreement with experimental observations. The amount of free volume and short range order frozen in during the quench from the liquid state were also calculated and found to be of the correct order of magnitude.

The strain dependence of static and dynamic strain-aging

Abstract A model is proposed that combines possible aging effects on the friction stress and on forest hardening. The dependence of both static and dynamic strain-aging on strain is predicted and compared with available experimental information. In body-centered cubic interstitial alloys, the friction component should dominate, and the strain dependence be minimal, in agreement with observation on a mild steel. In face-centered cubic interstitial alloys, a friction theory would also demand an independence of static aging on strain, whereas the forest theory predicts a linear relation between stress increment and flow stress: this is a critical test that has not yet been performed. Static strain-aging of substitutional alloys can discriminate between the mechanisms if its dependence on the flow stress is nonlinear, as it was observed in the case of gold-copper alloys: this cannot be explained on the basis of a forest mechanism alone. A linear relation, as it was observed in a nickel alloy and aluminum-magnesium, can be explained equally well by both mechanisms provided that, for the friction theory, the volume diffusivity depends essentially linearly on the flow stress. Dynamic strain-aging observations can, in addition, be influenced by any strain dependence of the mobile dislocation density. This effect can be assessed by a comparison of static and dynamic strain-aging: it was shown to be significant in one case, but negligible in another.

On the mechanism of serrated yielding and dynamic strain ageing

Abstract Theoretical models of dynamic strain ageing in general and the onset of serrated yielding in particular are based on the interaction between moving dislocations and diffusing solute atoms. In substitutional solid solutions the solute diffusion is assumed to be caused by the vacancies produced by deformation. Although in general the experimental data on the onset of serrated yielding and the effect of dynamic strain ageing on the strain rate sensitivity are well described by the ‘vacancy models’, in the recent literature a number of apparent exceptions have been reported. In this paper this data is critically examined. The conclusion is that the objections raised do not cast a serious doubt on the validity of the vacancy models.

A semi-quantitative description of the kinetics of structural relaxation in amorphous Fe40Ni40B20

Abstract Measurements are presented of the change of length and Youngs modulus during structural relaxation of amorphous Fe 40 Ni 40 B 20 . The results have been analysed in terms of a model which ascribes the effects to a combination of chemical and topological structural relaxation (CSRO reap. TSRO). It was possible to separate both contributions. TSRO is the slower process and starts when CSRO is nearly completed. CSRO is a process containing a spectrum of activation energies between 150 and 250 kJ/mol. The TSRO contribution can be well described by the free volume model with a single activation energy of 250 kJ/mol, which corresponds to the value found from viscosity measurements.

Defect production and annihilation near equilibrium in amorphous Pd40Ni40P20 investigated from viscosity data

Abstract The viscosity of amorphous Pd40Ni40P20 has been measured at temperatures near the glass transition temperature. The results of these measurements were analyzed in terms of the free volume model to find equations for defect production and annihilation during structural relaxation. It was shown that it is not possible to find these equations from viscosity data alone. A description of the viscosity data together with the thermal effects observed in a DSC was, however, more successful in determining the defect relaxation equation. The viscosity data were used to accurately determine the parameters of the kinetic process and the equilibrium defect concentration. The DSC data were used to discriminate between different relaxation equations.

Change of viscosity during structural relaxation of amorphous Fe40Ni40B20

Abstract Measurements of viscosity as a function of time and temperature have been carried out on amorphous Fe40Ni40B20 in a temperature range where structural relaxation occurs (450–600 K). Analysis of the data shows different behaviour in two temperature ranges: 1. (1) Range I (520–600 K). In this range the observed changes of viscosity can be described consistently in terms of the annealing out of flow defects (TSRO). The activation energy for motion and annihilation of the flow defects is Q = 250 kJ/mol. The isoconfigurational viscosity is temperature dependent according to η ~ exp( Q η RT ) with Qη = 304 kJ/mol. A possible explanation for the difference between Q and Qη is proposed. 2. (2) Range II ( Here the isoconfigurational In η vs T−1 plots yield an activation energy of about 250 kJ/mol, close to the value found for the annihilation of flow defects. The increase of viscosity observed in this range is ascribed to an increase of chemical order (CSRO). In a narrow temperature range between I and II, the contributions of TSRO and CSRO to the increase of the viscosity can be clearly distinguished.

Structural relaxation in amorphous Pd40Ni40P20

Abstract Measurements are presented on the change of Youngs modulus during structural relaxation of amorphous Pd 40 Ni 40 P 20 . The data are analysed in terms of the mixed model, considering that structural relaxation involves two sub-processes: Chemical Short Range Ordering (CSRO) and Topological Short Range Ordering (TSRO). To describe the kinetics of CSRO and TSRO the Activation Energy Spectrum (AES) model and free volume model are used, respectively. Pd 40 Ni 40 P 20 is stable enough to bring it to the equilibrium state for both CSRO and TSRO. Therefore reversible relaxation can be shown by performing temperature cycling experiments. Since no theoretical description for the kinetics of TSRO near equilibrium is available, three possible equations are proposed, which were fitted to the Youngs modulus data. The obtained parameters were used to describe the glass transition as observed during a DSC experiment. On the basis of the experimental data a choice for one of the three proposed equations could be made. The kinetics of CSRO is rather well described by the AES model.

The calorimetric glass transition of amorphous Pd40 Ni40 P20

The calorimetric glass transition in amorphous Pd40Ni40P20 was measured in a series of Differential Scanning Calorimetry (DSC) experiments. Especially the exact shape and position of the glass-transition peak were examined after different pre-annealing treatments of the sample and at different heating rates. The experimental results are in good agreement with a kinetic model of the glass transition. In particular, we found strong support for the existence of an equilibrium state when amorphous Pd40 Ni40 P20 is heated above its glass transition, and derived that the shape and position of glass-transition peak of amorphous Pd40 Ni40P20 at a given heating rate depends on a single structure parameter, in this paper designated as the average amount of free volume. The kinetics of free-volume changes are fully in agreement with results from viscosity measurements and speed-of-sound measurements. In order to obtain a good agreement between the model calculations and the experimental DSC curves, heat effects from chemical ordering were included in the calculations and the thermal delay of the measurement device was modelled with a simple RC-model.