Marek Danielewski

Time-dependent phenomena in the potential response of ion-selective electrodes treated by the Nernst-Planck-Poisson model. Part 2: Transmembrane processes and detection limit.

The detection limit of ion-selective electrodes (ISEs) is of great interest because of the many possible practical applications of ISEs in trace analysis. Existing theoretical interpretations of the detection limit of ISEs are restricted by severe assumptions such as steady-state and electroneutrality, which hamper theorizing on this problem. For this reason, the Nernst-Planck-Poisson (NPP) equations are used to predict and visualize the detection limit variability under nonequilibrium conditions. For the first time, the NPP model is applied to the so-called inverse problem: finding the optimal measurement time and inner solution concentration for lowering the detection limit.

The sulphidation and oxidation behaviour of sputter-deposited amorphous AlMo alloys at high temperatures

Abstract The sulphidation behaviour of sputter-deposited amorphous AlMo alloys has been studied as a function of temperature (973–1273 K) and alloy composition (34–46 at%Mo) in pure sulphur vapour at 10 3 Pa pressure. It has been shown that under these conditions the sulphidation process follows parabolic kinetics, being diffusion controlled. No influence of the alloy composition on the reaction rate has been observed. The scales were heterogeneous and composed of two layers. The outer scale layer was built of aluminium sulphide, while the inner layer was heterogeneous and composed of a mixture of Al 0.5 Mo 2 S 4 , Al 2 S 3 and MoS 2 phases, the latter being the major component. It is believed that the slowest step, determining the overall reaction rate, is the inward diffusion of sulphur through the inner barrier layer of the scale. Over the whole temperature range studied the alloys showed excellent resistance to sulphide corrosion, their sulphidation rates being comparable with, or even lower than the oxidation rates of chromia forming materials. The better protective properties of the sulphide scale on AlMo alloys in comparison with those of the MoS 2 scale on pure molybdenum result probably from lower defect concentration in aluminium-doped MoS 2 phase, constituting the major part of the inner barrier layer. Preliminary results indicate that the alloys under investigation show satisfactory oxidation resistance in the temperature range not exceeding about 1123 K. Under these conditions a protective oxide scale is formed composed virtually only of Al 2 O 3 and the oxidation rates are lower than those of chromia formers. At higher temperatures aluminium activity in the alloy is too low to suppress the formation and evaporation of molybdenum oxides.

Self- and Interdiffusion in Ternary Cu-Fe-Ni Alloys

Diffusion of Cu, Fe, and Ni radiotracers has been measured in Cu–Fe–Ni alloys of different compositions at 1271 K. The measured penetration profiles reveal grain boundary-induced part along with the volume diffusion one. Correction on grain boundary diffusion was taken into account when determining the volume diffusivities of the components. When the Cu content in the alloys increases, the diffusivities increase by order of magnitude. This behaviour correlates well with decreasing of the melting temperature of corresponding alloys, as the Cu content increases. Modelling of interdiffusion in the Cu–Fe–Ni system based on Danielewski-Holly model of interdiffusion is presented. In this model (extended Darken method for multi-component systems) a postulate that the total mass flow is a sum of the diffusion and the drift flows was applied for the description of interdiffusion in the closed system. Nernst-Planck’s flux formula assuming a chemical potential gradient as a driving force for the mass transport was used for computing the diffusion flux in non-ideal multi-component systems. In computations of the diffusion profiles the measured tracer diffusion coefficients of Cu, Fe and Ni as well as the literature data on thermodynamic activities for the Cu–Fe–Ni system were used. The calculated interdiffusion concentration profiles (diffusion paths) reveal satisfactory agreement with the experimental results. Introduction Advanced materials are very often multi-component and have complex structure (gradient materials, coatings, etc.) and from thermodynamic point of view are non-ideal. Interdiffusion and interfacial reactions play important role during processing of many functional materials and limit their long term exploitation. Understanding of these processes has fundamental practical importance. There are different approaches to reach this goal. These are Onsager phenomenology [1] and Darken method [2], they differ in form of the constitutive flux formula. Up to now they were not unified and the fundamental question is whether the computed diffusivities or interdiffusion coefficients represent real material constants [3]. Situation is even more difficult because the proof of the uniqueness of the inverse Darken problem does not exist [4]. We selected relatively simple Cu-Fe-Ni system to study the interdiffusion in non-ideal alloys showing limited solubility. This system has advantage because its thermodynamic and kinetic data are fairly well known. This paper has two goals: first to measure the tracer diffusivities of all components as a function of the ternary alloy composition, second the theoretical examination of the extended Darken method (Danielewski-Holly model) for a ternary system. Experimental measurements Sample preparation and radiotracer measurements Copper, iron and nickel (99.99 pct purity) were used as starting materials. The ternary alloys (Table 1) were melted in induction furnace in argon atmosphere. Such obtained ingots were homogenized at 1273 K for 250 hour in argon ( 2 6 10 O p atm − < ). Subsequently, the alloys of different composition were reannealed at the temperature 50 C below their melting temperature for 4 hours for recrystalization. The grain size of polycrystalline alloys was measured to vary from 30 (Cu-richest alloy) to about 300 μm. Alloys in the form of the cylindrical ingots of 8 mm in diameter were cut into slices of 3 mm thick by spark erosion. One face of the specimen was polished to optical quality by standard metallographical procedure. The samples were encapsulated into Cu–Fe–Ni containers (made of nearly the same alloy which was under study), wrapped in Ta foil, and sealed in silica tubes under purified Ar atmosphere. The use of the containers guarantees that the chemical composition of the specimen was not changed during thermal treatment. The samples were subsequently annealed at 1373 K for 24 h in order to remove the mechanical stresses, which could be built up during cutting and polishing procedures and which could affect the diffusion behaviour. After the pre-annealing the blanc surface was slightly chemically polished with Syton colloidal silica slurry to remove the effects of thermal etching. Table 1. Alloy compositions in wt. % Alloy Fe Ni Cu #1 12 68 20 #2 25 50 25 #3 10 45 45 #4 28 37 35 #5 45 40 15 #6 6 24 70 #7 75 20 5 #8 10 80 10 Penetration profile measurements The radiotracer Cu (half-life 12.7 hours) was produced by neutron irradiation of a cupper chip at the research reactor in Geesthacht, Germany. The nuclear reaction was used. Its initial specific activity was about 500 MBq/mg. Due to short life-time of the isotope it was delivered to the lab in Munster in few hours after irradiation. The activated chip was dissolved in nitric acid and then diluted with double-distilled water. 63 64 29 29 Cu(n, ) Cu γ The radiotracer Fe (half-life 45 days) was also produced by neutron irradiation of iron powder at the research reactor in Geesthacht according to the nuclear reaction . The activated isotope material was dissolved in 30% HCl and then further diluted with double-distilled water. 58 59 26 26 Fe(n, ) Fe γ The radiotracer Ni (half-life 100 years) was purchased in form of a HCl solution and dissolved with double-distilled water. Each radiotracer (Cu, Fe, or Ni) was dropped as a dilute acid solution on the polished face of the samples. The samples were again encapsulated into containers, which were then wrapped into Ta foil, to avoid any undesirable contamination. The specimens were sealed in silica tubes under purified Ar atmosphere and subjected to the diffusion anneals at T = 1271 K. The temperatures were measured and controlled with Ni–NiCr thermocouples with an accuracy of about ±1 K. After the diffusion anneal the samples were reduced in diameter (at least 1 to 2 mm) by grinding on a lathe to remove the effect of lateral and surface diffusion. The penetration profiles were determined by the precision grinding sectioning technique using special abrasive mylar foils. The radioactivity of each section was determined with high efficiency using a Packard TRI CARB 2500 TR liquid scintillation counter. The penetration profiles present the plots of the normalized activity of each sections (the activity divided by the weight of the section) against the penetration depth x. The latter was calculated from the weight loss of the sample with known geometry after each sectioning step. The uncertainties of individual points on the penetration profiles, stemming from the counting procedure and the errors of the depth determination, were estimated to be typically less than 10 %. 0 5 10 15 20 25 Ni Fe Cu42.8Fe10.8Ni46.4

Diagnostic of functionality of polymer membrane – based ion selective electrodes by impedance spectroscopy

Electrochemical impedance spectroscopy (EIS) is a powerful tool for the analysis of various electrochemical systems because it allows the separation and characterization of individual kinetic processes. In this paper we investigate whether changes in the EIS characteristics can be used to distinguish between solid-state ISE membrane that have been subjected to physical damage, biofouling or leaching of active components. We conclude that with these relatively simple electronic measurements, we can effectively evaluate the functionality of the ISE membrane; i.e. we can predict whether the sensors are fully functional, in need for calibration or are completely non-functional. We believe this could form the basis of a simple but effective diagnostic tool for probing the condition of remotely deployed ISEs in widely distributed chemo-sensor networks (e.g. for environmental monitoring) and for enhancing the reliability of these devices. Our ultimate goal is to implement such tools in place of conventional approaches to ISE testing like calibration with standard solutions, which require the integration of complex and costly fluidics.

Entropy production during interdiffusion under internal stress

A theory of stress and elastic deformation during interdiffusion is presented. It is shown that it is consistent with the general Darken analysis and linear irreversible thermodynamics. Special consideration is given to local entropy production. An expression is derived for the rate of entropy production during interdiffusion and practical computations presented of the internal energy and entropy densities and the entropy production. It is shown that the entropy produced by the diffusion of mass is positive, , and it does not depend on the frame of reference. The results span the gap between the Darken method, linear irreversible thermodynamics and treatments by Larché, Cahn and Stephenson.

Chemical interdiffusion in binary systems; interface barriers and phase competition

The problem of simultaneous growth and competition of intermediate phases during reactive diffusion is formulated and solved. In this paper, we compare existing models of steady state reaction diffusion and introduce the new one basing on the bi-velocity method. We extend old problem and propose method based on material (lattice) fixed frame of reference. It allows computing the material velocity in the reacting system in which reactions at several moving interfaces occur. All reactions lead to the lattice shift due to the difference of intrinsic diffusivities and different molar volumes. The following peculiarities are taken into account: (1) the deviation from local equilibrium at all interfaces; (2) the mobilities of the components in the bulk and interphase zone; and (3) the molar volumes of the components. We show the kinetic of the reactions, the non parabolic regime, the multiphase scale growth and present the practical application of the method.

“Order–order” kinetics in Ni50.5Al49.5 single crystal

Abstract “Order–order” kinetics in a single crystal of B2-type ordered β′-Ni50.5Al49.5 was studied by means of resistometry at temperatures between 961 and 1105 K. Reversible isothermal relaxations of the electrical resistivity yielded the activation energy EA=2.3±0.1 eV, the same for ordering and disordering processes and markedly lower than the activation energy for Ni diffusion in NiAl. In view of the recently proposed mechanism for Ni-tracer diffusion in NiAl the result is discussed in terms of the formation and elimination of triple defects. The mechanism means a strict correlation between chemical ordering and vacancy formation and provides a possible explanation for the relationship between the activation energies for Ni-diffusion and ordering in β′-NiAl, as well as for the dramatic difference between the rates of ordering/disordering in β′-NiAl and the previously investigated γ′-Ni3Al.

On the growth mechanism of the sulphide scale on amorphous AlMo alloys

Abstract The growth mechanism of the sulphide scale on amorphous Al-Mo alloys has been studied using a marker technique. A very thin (5 nm) gold marker film was deposited onto the surface of the Al-46Mo alloy and after sulphidation for 5 hours at 1073 K the gold marker distribution in the scale has been determined by RBS. It has been found that the main part of the marker remained at the scale surface indicating that the double-layer sulphide scale on the discussed alloy is growing by the inward diffusion of sulphur.

Diffusion, Drift and their interrelation through Volume Density

The evolution of the understanding of the mass transport phenomena in solids and liquids allows for the unification of phenomenological models. The central Darken problem is considered from the choice of the coordinate axes for diffusion, i.e. the definition of this mode of motion and the method of diffusion displacement is defined and measured. Eulers and Liouville theorems are used extensively in the analysis. The formula is derived for volume density conservation, i.e. the volume continuity equation. This fundamental formula defines the volume-fixed frame of reference in the multicomponent solid, gas and liquid solutions. The volume-fixed frame of reference is self-consistent with the foundations of linear irreversible thermodynamics, except that is recognises the need to add volume density to the usual list of extensive physical properties undergoing transport in every continuum. Proposed modifications are self-consistent with the literature dating back to Onsager, the experiments of Kirkendall, their interpretation by Darken and recent generalized formulations. It will be shown that the method can be used in mechano-chemistry and electro-mechano-chemistry.

Three-dimensional interdiffusion under stress field in Fe-Ni-Cu alloys

We present the method of solving the mechanochemical transport problem in multicomponent solid solutions, namely, the method of quantitative description of the interdiffusion (ID) under the stress field. We postulate that the velocities appearing in the momentum balance equation should be the drift and diffusion velocity. The energy, momentum, and mass transport are diffusion controlled, and the diffusion fluxes of the components are given by the Nernst-Planck formulas. The diffusion depends on the chemical potential gradient and on the stress that can be induced solely by the diffusion as well as by the boundary conditions. The key results lie in the interpretation of the Navier-Lamé equation for the deformed regular crystal, where the concentrations are not uniform and ID occurs. The presented coupling of the Darken and CALPHAD methods with the momentum balance equation allows for quantitative analysis of the transport processes occurring on entirely different time scales. It is shown that the proposed method is effective for modeling transport processes in Fe-Ni-Cu alloys. We demonstrate the case of ID in a planar plate, and predict slower penetration and accumulation. The experimental results confirm theoretical predictions.