R. Kirchheim

Grain coarsening inhibited by solute segregation

It will be shown that grain boundaries are in a metastable thermodynamic equilibrium in the presence of solute atoms and, therefore, grain coarsening is stopped as there is no driving force. This is in contradiction to a generally accepted interpretation, where solute drag, i.e. zero mobility of the boundaries, stops grain coarsening. Based on the empirical relation between terminal solubility of a solute and its grain boundary segregation it can be shown that a two-phase mixture with solute atoms agglomerating in a precipitated phase will be the stable thermodynamic equilibrium state. However, if precipitation is kinetically hindered, the metastable equilibrium with a certain grain boundary area and a zero grain boundary energy is attained. Changes in this grain boundary area or grain size respectively are calculated as a function of temperature and compared with experimental findings.

SOLUBILITY, DIFFUSIVITY AND TRAPPING OF HYDROGEN IN DILUTE ALLOYS, DEFORMED AND AMORPHOUS METALS—II

Abstract The chemical potential and diffusivity of interstitial solute atoms was calculated for disordered materials in a general way. Disorder may be of chemical nature as in alloys or caused by a strain field as around dislocations and a crack tip or disorder may be as total as in an amorphous alloy. For these examples of disordered systems relations were derived from a general expression and compared with corresponding special theoretical results which are mostly related to attractive interaction (trapping) and repulsive interaction (antitrapping) between interstitially and substitutionally dissolved impurity atoms. A comparison with experimental results is namely made for the solubility and diffusivity of hydrogen in dilute alloys, deformed Fe and Pd and amorphous Pd77.5Si16.5Cu6 and Ni64Zr36.

Hydrogen in amorphous metals—I

The solubility and diffusivity of hydrogen in amorphous Pd77.5Cu6Si16.5 and Ni49.9Pd31.8P18.3 have been measured using an electrochemical method. The pressure-concentration isotherms show remarkable deviations from Sieverts Law while the amount of hydrogen dissolved lies in between the solubility of the components of the alloy. The diffusivity of hydrogen is rather high (about 10−8 cm2/s) and it depends on temperature and also on concentration even at very low hydrogen levels contrary to crystalline metals. A consistent interpretation of the results is given within the framework of a Fermi-Dirac statistics, developed and used recently for the interaction of hydrogen with defects in solids. Equivalent to electrons in metals, hydrogen is distributed among sites of different energy caused by the disorder in an amorphous metal. The density of sites of a definite energy is assumed to be a Gaussian function. An equation is derived which relates the width of this function to the width of the radial distribution function which describes the structure of an amorphous alloy. Changes in this structure are believed to take place during annealing and were revealed by changes of hydrogen solubility.

The passivity of iron-chromium alloys

Abstract The composition of the passive film formed in 1 N H 2 SO 4 at 25°C on several iron-chromium alloys (0.6, 1.0, 2.3, 6, 10, 13, 15 and 18 at.%) has been determined using XPS. The total enrichment of chromium in the film can be explained quantitatively for the stationary state by a very strong chromium enrichment in the outermost cation layer of the film due to preferential dissolution of iron ions into the electrolyte and a chromium enrichment in the following layers of the film due to a lower mobility of chromium cations compared to iron cations. This model of a compositional change within the passive film is a direct consequence of the equation of continuity and it is supported by various experimental observations. For example, the removal of a small fraction of the film by sputtering results in a pronounced decrease of the average chromium concentration. The model is able to explain quantitatively the marked decrease of the stationary current density by small chromium additions and the changes of the passivation potential in Fe/Cr alloys. Conclusions of the model concerning other alloying additions to iron such as molybdenum and nickel will be presented.

Stress and electromigration in Al-lines of integrated circuits

Abstract The generation of tensile and compressive stress by the annihilation and production of vacancies which are subject to driving forces due to electromigration and due to the developing stress gradient is calculated. The rate of the stress changes is related to the deviation of the vacancy concentration from its equilibrium concentration. Depending on the magnitude of the rate constant different mechanisms of annihilation and production of vacancies (i.e. in the grain boundary itself, in adjacent grain boundaries or at dislocations) are covered. The resulting differential equations are solved numerically and analytically for some limiting cases. A quasi steady state concentration profile is established witin a short initial period of time, which is determined by one of the three processes diffusion, electromigration or rate of vacancy annihilation. During the quasi steady state the stresses increase linearly with time. When stresses are large enough to change the equilibrium vacancy concentration deviation from the linear increase occur and a rather long period follows where the true steady state is approached. If the time to failure, tf, of an Al-line is defined as the time necessary to reach a critical stress, tf is proportional to j−n where the current exponent changes from 1 at low critical stresses to 2 at higher stresses. The theoretical results are in excellent agreement with recent measurements of compressive stresses both with respect to the dependence on time and position.

Phosphorus segregation in nanocrystalline Ni–3.6 at.% P alloy investigated with the tomographic atom probe (TAP)

Abstract The microstructures of electroless plated and thermally aged nanocrystalline nickel–3.6 at.% phosphorus layers were investigated on an atomic scale with a tomographic atom probe (TAP). After heat treatments at 250 and 400°C, a continuous P-segregation in the grain boundaries of the nanocrystalline structure was directly proved for the first time. This segregation effect explains the comparatively high thermal stability of the material. Assuming the existence of a metastable equilibrium, a simple mass balance calculation, which uses experimentally determined data exclusively, makes it possible to predict grain sizes of other NiP alloys within the thermal stability region.

Hydrogen in amorphous and nanocrystalline metals

Abstract Experimental results on hydrogen solubility, diffusivity and phase changes are presented for nanocrystalline palladium and compared with those for amorphous PdSi and amorphous NiTi alloys. The solubility of the amorphous alloys can be explained by assuming a gaussian distribution for the site energies. For the nanocrystalline palladium a gaussian function for the grain boundary regions and a Dirac δ function for the interior of the grains have been used successfully. In contrast to the amorphous alloys, attractive HH interaction plays an important role within the grain boundaries. The concentration dependence of the diffusivity can be explained by the same distribution function for the palladium-containing materials. Deviations from this behaviour occur for NiTi, which will be explained by a correlation between site and saddle point energies. Although the width of the gaussian distributions for the grain boundaries is between that of two amorphous PdSi alloys (formed by melt spinning and sputtering), the average activation energy for diffusion is much less, indicating a more open structure within the boundaries.

Growth kinetics of passive films

A new model of growth of passive films is presented which includes both the transport through the film in the presence of a strong and varying electric field and the transport through the film—electrolyte interface by a reaction with a varying potential drop at the interface. By neglecting the second mechanism the Cabrera-Mott and Vetter model is obtained as a special case of the general model. Galvanostatic and potentiostatic results for passive iron in acid and neutral solutions are explained qualitatively and quantitatively. Only this new model is in overall agreement with experimental findings for different pH values. The thickness of the passive layer is calculated to be 2.7 ± 0.5 nm in 1 N H2SO4 at 1.08 VH which is in excellent agreement with experimental values.

Atomistic and computer modeling of metallization failure of integrated circuits by electromigration

Nonstationary and stationary concentration profiles of vacancies in a grain boundary are calculated for the case of electromigration and various conditions of vacancy formation and annihilation. If supersaturation of vacancies is assumed for void formation, current densities necessary for voiding have to be larger than a critical value jcrit, which is related to the length l of the grain boundary by the relation ljcrit=const. An estimation of the value of the constant in the last equation is in agreement with experimental values. An approximate equation for the median time to failure (MTF) is derived from the model for grain boundaries conducting the flux of matter parallel or in series. The results explain many features of experimental studies. First values of MTF for a network of grain boundaries obtained by computer simulations are presented as well, and the effect of resistance heating and nonstationarity on the current exponent is discussed in some detail.

Electrochemical Methods for Measuring Diffusivities of Hydrogen in Palladium and Palladium Alloys

A palladium bielectrode has been used in a viscous electrolyte consisting of glycerin and phosphoric acid. The transport of molecular hydrogen from and to the electrode is remarkably diminished in this electrolyte in comparison with aqueous electrolytes. Therefore, changes of the electrode potential are unambiguously related to concentration changes caused by diffusion within the electrode. A single current pulse and a potentiostatic technique were applied to determine the diffusion coefficients of H in Pd over a wide range of concentration and at different temperatures. New evaluation methods for current‐time and potential‐time curves also yield values of the initial concentration, which are in excellent agreement with the values calculated from previous coulometric titrations. A special arrangement of two bielectrodes also allows the measurement of small differences in the diffusivities of hydrogen in the two electrodes. Results for hydrogen diffusion in pure palladium are in excellent agreement with Gorsky effect measurements.