Papers by Author: Dezső L. Beke

Abstract: Two interesting features of formation and growth of intermetallic phases in nanoscale solid state reactions will be discussed:Linear-parabolic “normal” growth: it will be summarized that at the very early stages of the growth of an already existing new phase (i.e. when nucleation problems can be neglected) the linear kinetics can be observed due to the so-called diffusion asymmetry. Indeed, it was shown that if the ratio of the diffusion coefficients differ by orders of magnitude in the parent materials (and so also in the new phase), during the growth of a phase bordered by parallel interfaces from the parent phases (normal growth geometry), the shift of the individual interfaces can be linear at the beginning and a transition to the parabolic regime can take place even after a shift of several tens of nanometres. In addition, an AB compound in contact with the pure A and B phases can be dissolved if the diffusion in B is much faster than in either A and AB. This means that the thickness of this phase should decrease, or even can be fully dissolved, at the beginning and only after some time—when the composition in B will be high enough allowing the re-nucleation of this AB phase—will the AB phase grow further.The common problem of two stages of solid state reactions will be revisited: usually the growth can be divided into two stages: a) the formation (nucleation) and lateral growth of the new phases and b) the “normal” growth of the already continuous phase. It was concluded in different previous reviews that in stage b) in the majority of cases the parabolic growth was observed in accordance with the above i) point: the linear-parabolic transition length was typically below 1 μm, which was the lower limit of detection in many previous investigations. On the other hand recently the application of the linear-parabolic growth law for the analysis of experimental data obtained in nanoscale reactions became very popular, not making a clear distinction between a) and b) stages. It will be emphasized here that care should be taken in all cases when the experimental methods applied provide information only about the increase of the amount of the reaction product and there is no information where and how the new phase (s) grow. We have illustrated in a series of low temperature experiments - where the bulk diffusion processes are frozen - that even in this case a full homogeneous phase can be formed by cold homogenization called Grain Boundary Diffusion Induced Solid State Reaction (GBDIREAC). In this case first the reaction starts by grain-boundary (GB) diffusion and nucleation of the new phase at GBs or their triple junctions, then the growth of the new phase happens by the shift of the new interfaces perpendicular to the original GB. This is a process similar to the diffusion induced grain-boundary motion (DIGM) or diffusion induced recrystallization (DIR) phenomena and in this case the interface shift, at least in the first stage of the reaction until the parent phases have been consumed, can be considered constant. This means that the amount of the phase increases linearly with time, giving a plausible explanation for the linear kinetics frequently observed in stage a).

Abstract: Abstract. Thermoelasic martensitic transformations are controlled by the local equilibrium of chemical and non-chemical free energy contributions (D and E being the dissipative and elastic energies, respectively). The derivatives of non-chemical free energies ( ) as a function of the transformed martensite fraction (ξ) can be expressed from the experimental data obtained from the temperature-elongation, temperature-resistance, etc hysteresis loops. This method, developed in our laboratory, was used for the investigation of non complete, partial thermoelastic transformation cycles. In the first set of experiments the subsequent cycles were started below the Mf temperature and the maximum temperature was decreased gradually from a value above Af (series U). In the second (L) set the cycles were started above the Af and the minimum temperature was gradually increased from a value below Mf. In the third (UL) set the minor loops were positioned into the centre of the two phase region (i.e. the cycling was made with an increasing T temperature interval with T0.5 and <0.5, respectively. On the other hand the d() functions show a maximum at about the central point of the sub-cycles, and deviate considerably from the d() function obtained from the full cycles. This is also reflected in the  dependence of the integral value of the dissipative energy, D(): its value for the partial loops is lower than the dissipative energy calculated from the full cycle for the same transformed fraction interval. An opposite tendency (i.e. higher values for the partial loops) was obtained for the integral value of the elastic energy, E. The relative values of the dissipated energies, D, (calculated from the areas of the minor loops and normalized to the area of the major loop) are not very sensitive to the details of the cycling process, i.e. they are very similar for all sets.

Abstract: Using our local equilibrium model of the martensitic transformation [ the elastic energy contributions, as the function of martensite volume fraction, ξ, in the phase transformation of single crystalline Cu-11.5wt%Al-5.0wt%Ni shape memory alloy were calculated from our measurements published earlier [. The derivative of the elastic energy δE/δξ=e (E is the total elastic energy stored/released during the austenite to martensite (AM) as well as MA transformation) could be calculated only irrespectively of the ST₀ term (T₀ is the equilibrium transformation temperature and S is the entropy change of phase transformation). But, since ST₀ is independent of ξ, the functions obtained reflect the ξ dependence of e as well as E quantities. From the DSC curves measured at zero uniaxial stress (σ = 0) [, the ξ-T hysteric loop was constructed. Then the e (ξ) curves at fix σ as well as fix T were calculated. The E values obtained from the integral of e (ξ), fit well to the E(σ) as well as E(T) curves calculated from the strain-temperature and stress-temperature curves measured in [.

Abstract: Interdiffusion in Zn/InSb system has been investigated under high (0.59×10⁶ G) and low (1 G) gravity conditions at 673, 593 and 573K, respectively. Samples annealed at 0.59×10⁶ G, 673K for 60 hours, indicated the formation of a periodic reaction layer structure. Since such structures can be formed in solid state reactions of ternary systems [, the effect of high gravitational field and high hydrostatic pressure (approximately 3kbar) in the formation of periodic patterns was investigated. Systematic investigations at ambient pressure and low gravitational field were carried out at 593 and 573 K in sandwich geometry. SEM and EDX analysis had shown that there are different phases between the initial components. Starting from the Zn side of the specimen there is a very thin single-phase with high (about 90%) In content. Next to it is a thin two-phase layer, containing mainly 50-50% InSb and some elongated Zn particles and then there is a thick phase with the composition of Zn₅In₂Sb₄ which is followed by a similar two-phase mixture (InSb+Zn) similar to the Zn side of the sample. Although the diffusion zone is not a well developed periodic structure, but every layer (clearly distinguishable form the others and was either a single-or multiphase layer) grows with the time.

Abstract: It was shown more recently in our Laboratory [1,2,3] that having a substrate/diffusant/thin-film/cap-layer structure (the thin film was typically several 10 nm thick, with the same order of magnitude of grain size; the refractory metal cap layer was used just to avoid the oxidation), first the diffusant atoms migrated very fast across the thin film and segregated at the film/cap-layer interface. The accumulated atoms at the film/cap layer interface form a secondary diffusion reservoir and atoms diffuse back to the layer. Later on, the thin film was gradually filled up with the diffusing atoms and composition depth profiles, determined by Secondary Neutral Mass Spectroscopy (SNMS), showed a maximum at the cap layer-thin film interface. The accumulated atoms at this interface formed a secondary diffusion reservoir and atoms diffused back to the layer. These observations can be interpreted supposing a bimodal grain boundary structure with different (fast and low) diffusivities. The observed grain boundary diffusion phenomena can be classified as C-type diffusion. The appearance of the peak observed at the cap layer interface can be used as a tool to determine the grain boundary diffusivity along the fast boundaries. Because the fast boundaries were saturated in the first stage of the process, this back-diffusion took place along the low-diffusivity boundaries only. Thus the SNMS depth-profiling is a good method to determine grain boundary diffusivities in a bimodal structure. In addition, from the overall impurity content inside the film the segregation can also be estimated, if the bulk solubility is low and the GB density is known. Numerical simulations of C-type GB diffusion in thin films with a bimodal structure confirmed that the interpretation of the result depicted above is reasonable [4]. In order to estimate roughly the GB diffusion data we determined the fast diffusivity using the first appearance method. The lower diffusivity was determined from the time evolution of the broadening of the diffusant/thin film interface. In addition both (slow and fast) diffusivities were also estimated from fitting numerical solutions obtained in [4] too.

Abstract: General description of the interplay between the Kirkendall shift (as a special way of relaxation) and diffusion induced driving forces in diffusion intermixing of binary systems is given. It is shown that, if the Kirkendall shift is negligible, a steady state Nernts-Planck regime is established with diffusion coefficient close to the slower diffusivity, independently of the type of the diffusion induced field and also independently whether this is a single field or a combination of different fields (e.g. stress field and extra chemical potential of non-equilibrium vacancies). Deviations from parabolic kinetics are expected only before or after this steady state stage. Using the results of our previous paper, on development and relaxation of diffusion induced stresses, it is illustrated that the setting of time of the Nernst-Planck regime is very short: intermixing on the scale of few tenths of nanometer is enough to reach it. It is also illustrated that this stage is realized even in the case of asymmetric interdiffusion (in one side of the diffusion zone the diffusion is orders of magnitude higher than in the other), when the stress distribution has a more complex form (having a sharp peak at the interface). Surprisingly the steady state is longer than it would be expected from the relaxation time of Newtonian flow: This is so because the composition profile is not static but changes fast in the timescale of the stress relaxation, and thus the stress re-develops continuously.

Abstract: General form of the well known-relation between the critical stress, necessary to start/finish martensite/austenite formation, and the test temperature is simply and plausibly obtained from our local equilibrium model of phase transformation [1], and compared to the classical forms of the Clausius-Clapeyron relation. Although in general, first of all because of the stress and temperature dependence of the transformation strain, εtr, the above relations are not inevitably linear, in most of the cases linear functions were observed. Using the results of our experiments carried out on single crystalline Cu-11.5wt%Al-5.0wt%Ni samples for the strain stress hysteretic loops at constant temperatures [2], the slopes of these functions are analyzed on the basis of the relations obtained and it is shown that these are different due to different stress dependence of the elastic energy contributions.

Abstract: There are a number of well-known empirical relations for diffusion in solids. For example the proportionality between the self-diffusion activation energy and melting point or between the entropy of the diffusion and the ratio of activation energy and the melting point (Zener rule) are perhaps the best known ‘rules of thumb’. We have shown earlier in our Laboratory, that these relations are direct consequences of the similarity of interatomic potentials seen by ions in solids. On the basis of this, similar relations were extended for impurity and self diffusion in binary solid alloys. In this paper, results for binary liquid mixtures will be reviewed. First a minimum derivation of the temperature dependence of the self-diffusion coefficient, D, is presented (minimum derivation in the sense that it states only that the reduced (dimensionless) D should be a universal function of the reduced temperature), using the similarity of interatomic potentials and dimensional analysis. Then the extension of this relation for determination of the pressure and composition dependence of the self-diffusion coefficients is described using pressure and composition dependent scaling parameters (melting point, atomic volume and mass). The obtained universal form (valid for binary liquid alloys) is very useful for the estimation of the temperature, composition and pressure dependence of the self-diffusion coefficients. Finally, the relation for the ratio of the impurity and self-diffusion coefficients is derived.

Abstract: In this paper, examples of some of the most challenging features of GB diffusion are considered covering selected problems, strongly related to the research activity at our Laboratories and to the scientific interest of Boris Bokstein too. The following problems (and still open questions related to them) are addressed: i) Diffusion in a random network of grain boundaries with different structures and diffusion coefficients in polycrystalline materials; ii) Segregation effects; iii) Stress effects and iv) Effect of the presence of moving and/or non-equilibrium grain boundaries.

Abstract: The influence of hydrogen on the structural stability of multilayers made of ultrathin (3 nm) Si and Ge amorphous layers submitted to annealing to activate Si and Ge intermixing has been studied by TEM and AFM. By energy dispersive microanalysis the interdiffusion of Si and Ge has been observed. The Si/Ge multilayers, however, underwent remarkable structural degradation because of the formation of hydrogen bubbles which give rise to surface bumps and eventually craters when the bubbles blow up because of too high internal pressure in samples with high H content and annealed at high temperatures. The hydrogen forming the bubbles comes from the rupture of the Si-H and Ge-H bonds activated by the thermal energy of the annealing and by the energy released by the recombination of thermally generated electron hole pairs.