Helmut Mehrer

Diffusion in metallic glasses and supercooled melts

Amorphous metallic alloys, also called metallic glasses, are of considerable technological importance.The metastability of these systems, which gives rise to various rearrangement processes at elevatedtemperatures, calls for an understanding of their diffusional behavior. From the fundamental point ofview, these metallic glasses are the paradigm of dense random packing. Since the recent discovery ofbulk metallic glasses it has become possible to measure atomic diffusion in the supercooled liquid stateand to study the dynamics of the liquid-to-glass transition in metallic systems. In the present article theauthors review experimental results and computer simulations on diffusion in metallic glasses andsupercooled melts. They consider in detail the experimental techniques, the temperature dependenceof diffusion, effects of structural relaxation, the atom-size dependence, the pressure dependence, theisotope effect, diffusion under irradiation, and molecular-dynamics simulations. It is shown thatdiffusion in metallic glasses is significantly different from diffusion in crystalline metals and involvesthermally activated, highly collective atomic processes. These processes appear to be closely related tolow-frequency excitations. Similar thermally activated collective processes were also found to mediatediffusion in the supercooled liquid state well above the caloric glass transition temperature. Thisstrongly supports the mode-coupling scenario of the glass transition, which predicts an arrest ofliquidlike flow already at a critical temperature well above the caloric glass transition temperature.

Anomalous self-diffusion in a single crystal of α-zirconium

Abstract Self-diffusion in an α-zirconium single crystal was investigated over the temperature range 779 to 1128 K. The measurements were made by simultaneous diffusion of 95Zr and its radioactive daughter 95Nb and by subsequent ion-beam-sputter sectioning (IBS). The activity of 95Zr in each section was determined from the 724 keV γ peak using a Ge-Li spectrometer. Gaussian penetration curves were observed. The diffusivities vary in the range between 3.28 × 10 −23 m 2 s −1 and 1.04 × 10 −18 m 2 s −1 . The present results are compared with previous studies of self-diffusion in α- and β-Zr. The Arrhenius plot of self-diffusion coefficients in α-Zr is strongly curved downward. This means that an anomalous behaviour of self-diffusion is observed not only in the β- but also in the α-phase of Zr. Some results on the diffusion of 95Nb in α-Zr are reported in an Appendix.

Diffusion of gold in dislocation-free or highly dislocated silicon measured by the spreading-resistance technique

The diffusion of Au in dislocation-free or plastically deformed Si (1011 to 1013 dislocations/m2) was measured with the aid of the spreading-resistance technique. The Au profiles produced indislocation-free Si slices by in-diffusion from both surfaces possess nonerfc-type U shapes as predicted by the so-called kick-out diffusion model. This model is used to calculate the contribution of self-interstitials to the (uncorrelated) Si self-diffusion coefficient,DISD=0.064×exp(−4.80 eV/kT)m2 s−1, from the present and previous data on the diffusivity and solubility of Au in Si in the temperature range 1073–1473 K. Inhighly dislocated Si the diffusion of Au is considerably faster than in dislocation-free Si. From the erfc-type penetration profiles found in this case, effective Au diffusion coefficients were deduced and combined with data on the solubility of Au in Si. ThusCieqDi=0.0064 ×exp(−3.93 eV/kT)m2 s−1 was obtained in the temperature range 1180–1427 K, whereCieq andDi are the solubility and diffusivity of interstitial Au in Si.

Diffusion in intermetallic phases of the Fe–Al and Fe–Si systems

Abstract Self-diffusion of Fe and impurity diffusion of In in Fe–aluminides of 26.5, 34 and 50 at.% aluminium have been investigated over wide temperature ranges. For Fe diffusion in Fe 3 Al an influence of A2–B2 and B2–D0 3 transitions has been observed. The activation enthalpy increases with increasing order. Diffusion in alloys with higher Al content shows linear Arrhenius behaviour. Impurity diffusion of In is faster than Fe diffusion in Fe 66 Al 34 and Fe 50 Al 50 by about a factor of two. In Fe 3 Al the ratio between the diffusion coefficients of In and Fe varies between two and ten. Indium is homologous to Al and considered as substitute of Al, for which an affordable radiotracer is not available. Self-diffusion of Fe (and Si) and impurity diffusion of Ge in D0 3 -type Fe–Si alloys (24, 21 and 18 at.% Si) published in detail elsewhere are summarized. Diffusion of the majority component Fe is very fast. It occurs via nearest neighbour jumps into vacant sites on the Fe sublattice, which are available in high thermal concentrations. Fe diffusion is fastest for the stoichiometric alloy (highest Si content) and decreases with increasing Fe content. Ge (and Si) diffusion is slower than Fe diffusion by orders of magnitude. Some preliminary results on Fe diffusion in the B20 structured compound FeSi are also reported. Diffusion is by orders of magnitude slower than in Fe 3 Si indicating a strong influence of structure and/or decreasing metallicity on diffusion in this silicide. The results will also be discussed in connection with available studies of Mosbauer spectroscopy, positron annihilation experiments and ab-initio electron theory calculations of defect properties.

Atomic jump processes in self-diffusion

Abstract The atomic jump processes involved in the vacancy mechanisms of self-diffusion in metals are reviewed with particular attention to disvacancies. The most important measurements which are helpful to separate mono- and divacancy contributions — temperature, mass, and pressure dependence of the diffusion coefficient and correlation effects — are discussed. The recent experimental progress will be considered also. The extension of direct tracer studies to much lower temperatures has greatly increased the reliability with which monovacancy properties may be deduced. Amongst the indirect techniques like nuclear-magnetic-relaxation, Mossbauer effect and quasi-elastic neutron-scattering, especially nuclear magnetic relaxation may be considered nowadays as a quantitative tool. In a discussion of individual metals the above mentioned topics will be illustrated by examples, with emphasis on those metals where a considerable deepening of our understanding of atomic jump processes has been achieved.

Effect of hydrostatic pressure and temperature on the self-diffusion rate in single crystals of silver and gold

Abstract The pressure dependence of the rate of self-diffusion has been measured up to about 6 kbar by a radiotracer sputter-sectioning technique in Ag at 594, 683, 766, 885 and 994 K and in Au at 692 K. In the case of Aga gradual increase of the activation volume from 0.66ω (ω=atomic volume) to 0.84ω was observed. This observation may be considered as a further ‘weak’ anomaly of self-diffusion in addition to the already known curvature of the Arrhenius plot at ambient pressure and the decrease of the isotope effect with increasing temperature. In the case of Au the activation volume of 0.73ω from the present work, together with literature values near the melting temperature, indicates that the activation volume is almost temperature independent. This observation fits into the overall picture that for Au the other two anomalies are also very weak. It is concluded that a consistent analysis of the available data is possible in terms of the monovacancy-divacancy model. It appears that an interpretation of s...

A universal ion-beam-sputtering device for diffusion studies

An apparatus for ion-beam-sputtering is described which offers for the first time the possibility of measuring radiotracer diffusion profiles with mean diffusion length (D is the tracer diffusion coefficient and t is the diffusion time) in the nano- as well as in the micrometre range. It is also possible to use the device for ion milling, especially for the deposition of thin layers of radiotracer onto diffusion samples. Investigations of diffusion in pure metals, in a metallic glass, in a compound semiconductor and in intermetallic compounds are presented as examples.

Self-diffusion in intrinsic germanium and effects of doping on self-diffusion in germanium

Self-diffusion in intrinsic germanium single crystals has been investigated over the temperature range 822-1163K using 71Ge as radioisotope and a sputtering technique for serial sectioning. The data can be described by a preexponential factor of (2.48+or-0.6)*10-3 m2 s-1 and an activation enthalpy of (3.14+or-0.92) eV. The present data are discussed together with literature data obtained with conventional sectioning techniques at higher temperatures. The self-diffusion coefficients at 870 and 894K were also measured for Ga-doped (1.7*1018 atoms cm-3) and Sb-doped (1.8*1018 atoms cm-3) samples. The diffusivity is higher in n-type and lower in p-type germanium than in intrinsic material. Since it is known that a vacancy in germanium acts as an acceptor the observed direction and order of magnitude of the doping dependence can be understood in terms of the shift of the Fermi level in doped crystals. This supports the view that self-diffusion in germanium proceeds by a vacancy mechanism.

Solubility, diffusion and thermodynamic properties of silver in silicon

Concentration-depth profiles of Ag in Si have been measured with the aid of neutron activation analysis combined with serial removal of sections. The Ag diffusion appears to be very fast. In the bulk of dislocation-free Si wafers saturation is achieved after short periods of annealing. From this the authors conclude that interstitial Agi is the predominant configuration in Si without dislocations. Equilibrium concentrations of Agi are determined for temperatures between 1287 and 1598 K. The results are thermodynamically analysed, taking into account Ag-Si liquidus data. In dislocated Si much higher Ag concentrations are observed, which vary irregularly with the penetration depth. A comparison of the diffusion and solubility of Ag and Au in Si suggests that in Si with dislocations substitutional Ags may arise from Agi-Ags transitions. Finally an estimate of the Agi diffusivity is obtained.

Self-diffusion in the amorphous and supercooled liquid state of the bulk metallic glass Zr46.75Ti8.25Cu7.5Ni10Be27.5

Nickel and zirkonium self-diffusion in the amorphous and the supercooled liquid state of the bulk metallic glass Zr46.75Ti8.25Cu7.5Ni10Be27.5 has been investigated using the radiotracer method. Encompassing four orders of magnitude in the diffusivity self-diffusion of 63Ni cannot be fitted to a single Arrhenius function. The deviation from an Arrhenius function is attributed to differences between the supercooled liquid and glassy state. This explanation is supported by recent diffusion studies reported by other authors. Self-diffusion of the major component studied with the isotope 95Zr is much slower compared to the above-mentioned measurements. We also performed high pressure experiments in the supercooled liquid state from which activation volumes for 63Ni diffusion of about one mean atomic volume were deduced. This suggests that diffusion in the supercooled liquid state proceeds by a hopping process involving vacancy-like defects.