Annihilation Of Free Volume Research Articles

Elastic moduli, density, and structural relaxation in bulk amorphous Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5 alloy

The thermal expansion and elastic properties of bulk amorphous Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5 alloy are reported. The thermal expansion was measured between 80 K and 773 K, which includes the glass transition and crystallization temperatures. The elastic moduli were measured at room temperature using a novel resonant ultrasonic spectroscopy technique in samples annealed at increasing temperatures between 300 K to 773 K. The thermal expansion data were used to deduce the Debye temperature Θ D, and the Grüneisen parameter, γ. The changes in elastic properties are discussed in terms of the annihilation and redistribution of free volume in the bulk amorphous state.

Combined measurements of modulus and length and their correlation for different amorphous alloys

Combined measurements of length and modulus change on the same specimen of Ni 78Si 8B 14, Cu 64Ti 36 and Co 66Fe 4(MoSiB) 30 are presented. These properties are sensitive to different aspects of structural changes during relaxation in the amorphous state. The change of length is mainly sensitive to the topological long range relaxation. The change of the eigenfrequency is mainly sensitive to atomic rearrangements changing the chemical short range order. The results of the correlation between the effect of relaxation of frequency versus that of length can be described as follows: The observed structural relaxation in the amorphous states of each material can be divided up into two regimes. The first regime (I) with a prevailing change of eigenfrequency is attributed to short range rearrangements of the chemically different atomic species in the material; the second regime (II) with a larger amount of length change is interpreted as a long range topological relaxation with enhanced loss of “free volume”. This interpretation is supported by a comparison of the diffusion coefficients at the characteristic transition temperature T C between the regimes I and II. It shows that the average diffusion path lengths of the possible diffusors below the characteristic temperature are in the order of 2 to 5 next neighbour distances, i.e. diffusion is only possible in a short range changing the species of neighbouring atoms. Above T C , the average diffusion path lengths are in the order of 5 to 50 next neighbour distances suggesting long range relaxation rearrangements by a diffusion process preferentially connected with the annihilation of free volume.

Diffusion Enhancement in Glassy Metals Under Non-Equilibrium Conditions

AbstractThe diffusion properties of a Ni-Zr metallic glass formed at the interface of a bulk diffusion couple have been studied in conditions far from a fully relaxed state. The growth kinetics of the interface film have been enhanced by both plastic deformation and high energy electron irradiation. Different results have been obtained in the two cases, since in the first case the film grows exponentially with time, while in the second case the usual square root dependence on time is observed. This behaviour has been interpreted as a consequence of the annihilation kinetics of the excess free volume introduced in the glass by the above methods. Two different mechanisms of free volume annihilation , namely exchange with a crystal vacancy at the glass-crystal interface and structural relaxation in the bulk glassy phase have been considered to be operative so that the nature of the growth kinetics has been found to depend on the mechanism predominant in each experimental condition.

Atomic diffusion and structure relaxation in compositionally modulated amorphous 3d transition metal-Zr alloy films

Atomic interdiffusion in compositionally modulated amorphous TM-Zr (TM = Fe, Co, Ni or Cu) alloy films were studied by mean of in-situ X-ray diffraction measurements during successive isothermal annealing. The results were analyzed as free volume-dependent atomic diffusion with activation energy of atomic diffusion, Q D (8−10×10 4 J/ mol) and that of the free volume annihilation, Q A (4−6×10 4 J/ mol).

Model for stress and volume changes of a thin film on a substrate upon annealing: Application to amorphous Mo/Si multilayers.

A model is given for the stress change in a thin film on a thick substrate during annealing. It takes into account temperature changes, volume changes, viscous flow, and anelastic relaxation occurring in the film. The stress change in amorphous Mo/Si multilayer films deposited on Si single-crystal substrates was obtained from in situ wafer-curvature measurements during annealing at temperatures below the glass temperature. The thickness change and the interdiffusion coefficient were obtained from the position and the intensity of the first-order multilayer x-ray reflection. The unconstrained volume change was derived from the measured stress and thickness changes. The free-volume model for amorphous solids has been used to interpret the interdiffusion in and the volume change of the amorphous Mo/Si multilayers. The stress change as it occurred during isothermal annealing was explained by free-volume annihilation, viscous flow, and anelastic relaxation. If anisotropy of the volume change is accepted, the stress change could also be described with free-volume annihilation and viscous flow alone. The product of the experimentally observed viscosity and diffusion coefficient for amorphous Mo/Si multilayers was compared to the value expected from the free-volume-model-based equivalent of the Stokes-Einstein relation.

Fe-B-Si系アモルファス合金の不可逆的構造緩和過程

Irreversible structural relaxation processes have been investigated for Fe75B10Si15, Fe78B7Si15 and Fe79B10Si11 amorphous alloys by electrical resistivity measurements and Mössbauer spectroscopy.The electrical resistivity of as-quenched alloys decreased irreversibly with isothermal annealing. Such resistivity changes are mainly associated with decrease of free volume introduced by quenching from the melt. The irreversible decrease of resistivity was reproduced well using the free-volume-Ziman model which was based on the Ziman theory of resistivity and the free-wolume model for viscous flow. The activation energy for annihilation of free volume was evaluated to be 222 kJ/mol (Fe75B10Si15) and 154 kJ/mol (Fe78B7Si15, Fe79B10Si11) from resistivity changes. On the other hand, a significant difference in the annealing behavior of the average isomer shift and internal magnetic field with time between Fe75B10Si15 and Fe78B7Si15 amorphous alloys was observed. This indicates that the local structural change in relaxation process differs much in both amorphous alloys. Such compositional dependence of activation energy and Mössbauer parameters was explained well by the structural model proposed by Dubois et al.

Hyperfine field relaxations in the Fe−Co−B amorphous alloys

A systematic increase of the average hyperfine magnetic induction at57Fe measured at room temperature during interrupted isothermal annealing was found to be inherent to the irreversible relaxation processes in the Fe−B based soft magnetic alloys at moderately elevated temperatures. Assuming superimposed asymptotic exponential field vs. time dependences. several processes can be distinguished, their relaxation times determined and from the Arrhenius-like log τ vs. 1/T plots average activation enthalpies estimated. Results on the Fe70Co10B20 and Fe85−x Co x B15 (x=17, 19 and 21 at. % Co) amorphous ribbons between 100 and 200°C are compared and discussed in terms of possible stress relief, free volume annihilation and short range ordering mechanisms.

On the nature of the glass transition in metallic glasses

Abstract The glass transition, observed in glasses during differential scanning calorimetry 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 in free volume towards equilibrium near T g. This can be calculated by making use of the well known kinetics of free-volume annihilation and production in some metallic glasses. Calculations performed on this basis are in good agreement with available experimental data on the glass transition.

Relaxation and embrittlement of Fe40Ni40Si8B12 glass

Structural relaxation and embrittlement of Fe40Ni40Si8B12 glass was studied by a combination of calorimetric and bending tests. The homogeneous deformation mode decreased as a result of free volume annihilation and embrittlement resulted from the development of chemical short range order. A wide, reversible endothermic peak, similar to a glass transition was observed and described by changes in the cluster concentration in the glassy phase.

Isothermal changes of volume and Young's modulus of amorphous CoP

The isothermal shrinkage and the isothermal increase of Young's modulus E of electrodeposited CoP samples were studied in the amorphous state and during crystallization. The lower limit of the activation spectrum of the elementary processes responsible for these changes is shifted from 0.8 to 1.6 eV by annealing at temperatures ascending from 100°C to 220°C. From the Arrhenius equation a frequency constant of 10 9.5±2.5 was derived. On account of the different behavior of the two properties we conclude that the changes of E in connection with the relaxation of the amorphous structure is mainly a consequence of the homogenization of the material and the shrinkage is mainly a consequence of the annihilation of free volume. Based on the observations a model is proposed concerning the nature of the elementary processes involved in the different steps of structural relaxation. During crystallization the correlation between the increases in Young's modulus and in density is totally removed. These results show that the observation of temporal and thermal changes of only one physical property does not yield full information about the kinetics of structural relaxation and crystallization.