Binary Solid Solutions Research Articles

Mössbauer studies of interactions between titanium atoms dissolved in iron

The room temperature 57Fe Mossbauer spectra for binary iron-based solid solutions Fe1 − x Ti x , with x in the range 0.010 ≤ x ≤ 0.045, were analysed in terms of binding energy E b between two Ti atoms in the Fe-Ti system. The extrapolated values of E b for x = 0 were used for computation of enthalpy of solution of titanium in iron. The results were compared with that resulting from the Miedema’s model of alloys as well as those derived from the heat of formation of the system, obtained with both calorimetric measurements and theoretical calculations. The comparison shows that our Mossbauer spectroscopy findings are in a quite good agreement with all the other results mentioned above.

Thermodynamics of dilute binary solid solutions using the cluster variation method

AbstractA transformation of correlation functions used in the cluster variation method is introduced, such that the transformed correlation functions represent departures of the untransformed correlation functions from their values corresponding to ideal solutions. Analytical solutions for the transformed correlation functions and their derivatives with respect to composition in the infinite dilution limit are obtained for the first time for disordered binary bcc (under irregular tetrahedron approximation), fcc, and cph (both under tetrahedron-octahedron approximation) phases using the framework of the cluster variation method. These results are utilized to obtain the configurational contribution to self-interaction coefficients which occur in the expansion of the logarithm of the activity coefficient.

Magnetic properties of Ni and Ni–Cu nanoparticles

AbstractNanoparticles of pure Ni and Ni–Cu solid solution were synthesized by the sol–gel method at 400–600 °C. The particle sizes and values of specific surface of powders were dependent on the synthesis temperature. The magnetization of the obtained powders was studied using a high‐temperature magnetic balance. The Curie temperature for particles of pure nickel did not depend on their size but the specific magnetization at 300 K decreased linearly with increasing specific surface area of particles. For particles of the Ni–Cu binary solid solutions, the Curie temperature and values of magnetization increased with decreasing particle size for particles with diameters up to values less than 100 nm. The amount of adsorbed copper on the particles surface, the change of nickel concentration in the volume of the particles and the Curie temperatures, depending on the Cu (Ni) concentration in a volume of particles, were calculated using the Gibbs equation. The calculations made in the framework of a perfect solution showed qualitative agreement between experimental and calculated values of the Curie temperature for the system Ni–Cu.

Temperature dependence of nucleation rate in a binary solid solution

The influence of regression (partial dissolution) effects on the temperature dependence of nucleation rate in a binary solid solution has been studied theoretically. The results of the analysis are compared with the predictions of the simplest Volmer–Weber theory. Regression effects are shown to have a strong influence on the shape of the curve of nucleation rate versus temperature. The temperature TM at which the maximum rate of nucleation occurs is found to be lowered, particularly for low interfacial energy (coherent precipitation) and high-mobility species (e.g. interstitial atoms).

Alloy solid solution strengthening of Mg alloys: Valence effect

AbstractAb initio density functional theory (DFT) calculations were carried out to investigate alloy solid solution strengthening of hexagonal close packed (HCP) Mg. The binary solid solution Mg–X base alloys (X = Gd, Nd, Ce, Bi, In, and Sn) were examined to identify a possible valence effect on the solution strengthening in terms of electronic density of states (DOS) and electron localized function (ELF). An addition of rare earth (RE) elements Gd, Nd, and Ce in Mg results in a hybridization between the localized f electrons of RE elements and the p electrons of Mg. The hybridization is primarily responsible for the formation of covalent bonds between RE elements and Mg. This electronic structure was then validated by the calculated ELF, illustrating a distribution of localized electrons between Mg and RE atoms. This peculiar chemical bonding characteristic successfully explains the experimentally observed solid solution strengthening induced by Gd, Nd, and Ce additions. An addition of sp‐elements of Bi, In, and Sn in Mg, however, leads to the formation of typical ionic bonds, which are not capable of inducing solid solution strengthening in Mg alloys. A discussion was made on a possible relationship between the chemical bonds and solid solution strengthening in Mg alloys.

Combined Major and Trace Element LA-ICP-MS Analysis of Compositional Variations in Simple Solid Solutions through Cross Correlation with an EPMA-Characterized Working Standard

Determining correlated major and trace element zoning profiles is an important goal in modern microanalysis and is critical to some geospeedometric applications. We show that a precise determination of relative variations in major element compositions of simple solid solutions is possible by LA-ICPMS, and that low accuracy (analytical bias) can be corrected for through cross correlation with electron problem microanalyzer (EPMA)-characterized working standards. Further, the relative uncertainties on binary or quasibinary solid solution endmember proportions are always lower than the relative uncertainties on the ratio of the principle substituting elements by at least a factor of 2. In calcic plagioclase, for example, the relative uncertainty on X(An) is a factor of (1-X(An)) smaller than the relative uncertainty on Ca/Na. Using a well-characterized, concentrically zoned bytownite crystal as an example, we compare reproducibilities of FE-EPMA and W-EPMA analyses with 2 μm beam diameter and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) with 16 μm beam diameter. While the accuracy of LA-ICP-MS analyses is low (analytical bias), the precision of LA-ICP-MS analyses is slightly higher than that of FE-EPMA data and comparable to that of the W-EPMA data. EPMA-corrected LA-ICP-MS data can thus be used to characterize major oxide compositional variations and potential covariations with trace elements within individual crystals.

High dielectric constant observed in (1 − x)Ba(Zr0.07Ti0.93)O3–xBa(Fe0.5Nb0.5)O3 binary solid-solution

Binary solid-solutions of the (1−x)Ba(Zr0.07Ti0.93)O3–xBa(Fe0.5Nb0.5O3) system, with 0.1≤x≤0.9,were fabricated via a solid-state processing technique. X-ray diffraction analysis revealed that all samples exhibited a single perovskite phase. The BaFe0.5Nb0.5O3 also promoted densification and grain growth of the system. Dielectric measurements showed that all samples displayed a relaxor like behavior. The x=0.1 sample presented a dielectric-frequency and temperature with low loss tangent (<0.07 at 10kHz). For x>0.2 samples, the dielectric data showed a broad dielectric constant–temperature curve with a giant dielectric characteristic. In addition, a high dielectric constant>50,000 (at 10kHz and temperature>150°C) was observed for the x=0.9 sample.

A mean field approach of nucleation

The nucleation pathway in binary solid solution was investigated using mean field theory coupled to the string method. The string method has been used to locate the minimum free energy pathway for thermally activated nucleation, i.e. the most probable path for the phase transition. The overall behaviour of the system and the properties of the nucleus, composition and size were found to be in good agreement with other non-classical nucleation theories. It was found that the size of the critical nucleus diverges near the spinodal line.

Diffusion-induced stress in inhomogeneous materials: concentration-dependent elastic modulus

By incorporating the contribution of solute atoms to the Helmholtz free energy of solid solution, a linear relation is derived between Young’s modulus and the concentration of solute atoms. The solute atoms can either increase or decrease Young’s modulus of solid solution, depending on the first-order derivative of the Helmholtz free energy with respect to the concentration of solute atoms. Using this relation, a closed-form solution of the chemical stress in an elastic plate is obtained when the diffusion behavior in the plate can be described by the classical Fick’s second law with convection boundary condition on one surface and zero flux on the other surface. The plate experiences tensile stress after short diffusion time due to asymmetrical diffusion, which will likely cause surface microcracking. The results show that the effect of the concentration dependence of Young’s modulus on the evolution of chemical stress in elastic plates is negligible if the change of Young’s modulus due to the diffusive motion of solute atomsis is not compatible in magnitude with Young’s modulus of the pure material. Also, a new diffusion equation is developed for strictly regular binary solid solution. The effective diffusivity is a nonlinear function of the concentration of solute atoms.

Threshold stress for superplasticity in solid solution magnesium alloys

The effect of alloying elements on the threshold stress for superplasticity was investigated using two binary solid solutions, namely, Mg–Al and Mg–Y alloys. Both alloys exhibited superplasticity, and in spite of the absence of fine particles showed threshold-stress-like behavior. Different origins were suggested for the threshold-stress-like behavior after considering grain growth during deformation. The threshold-stress-like behavior in Mg–Al alloys originates from the effects of microstructural instability (grain-growth hardening). On the other hand, analysis of grain-boundary segregation suggested that the threshold-stress-like behavior in Mg–Y alloy originates from the segregation of yttrium in grain boundaries and its interaction with grain-boundary dislocations.

Work Function Controlled Zn:Cu Electrode for All-Printed Polymer Diode

We have developed a pressure annealing technique for fabricating low-work-function metal patterns on plastic substrates. The pressure annealing technique can destroy the metal oxide layer and can form a conductive layer on printed metal patterns. Furthermore, we have confirmed that a binary solid solution is easily formed on metal patterns including two kinds of metal particles by using the pressure annealing technique. Changing the composition ratio of the binary metal paste led to the work function control of the pressure-annealed metal patterns. The formation of the binary solid solution was confirmed by X-ray diffraction (XRD) analysis, and work function was measured by photoelectron emission spectroscopy. In the case of the binary metal paste of Cu and Zn, we have succeeded in controlling work function from 3.8 to 5.0 eV. Since the Cu–Zn paste is composed of relatively cheap metals, this would be applicable to large-scale flexible electronic devices.

Carbon Effect on Thermal Ageing Simulations in Ferrite Steels

ABSTRACTTwo major causes of hardening and subsequent embrittlement in ferrite steels are the spinodal decomposition of the binary Fe-Cr solid solution and the carbide formation due to the presence of carbon as foreign interstitial atoms. In the present work, simulations of the microstructure evolution due to thermal ageing are performed by means of a kinetic Monte Carlo code and using a state-of-the-art interatomic potential based on density functional theory (DFT) predictions and experimental data. The main issues concern the possibility to perform thermal ageing simulations in an acceptable computational time frame and to reproduce a realistic behavior of carbon kinetics and carbide formation. The simulations on the binary system show the microstructural evolution during thermal ageing and allowed to find an exponential trend related to the acceleration as a function of temperature. With the insertion of carbon in the model, the chromium precipitation tends to accelerate. The carbon clustering, analyzed separately, is faster with higher C concentrations and in lattices with segregated chromium.

Estimation of component activities in some oxide solid solutions by the molecular interaction vacancy model

The molecular interaction vacancy model (MIVM) is used to estimate simultaneously activities of all components in a range of entire composition of six binary oxide solid solutions and the MnO-FeO-CaO ternary solid solution by their binary inflnite dilute activity coe‐cients. The average errors are the 0.03%{5.0% for the binaries and the 4.11%{25.2% for the ternary which is less than that (4.84%{41.2%) of the sub-regular solution model (SRSM). This shows that MIVM is more efiective and reliable than SRSM for the ternary and does not depend on a polynomial approximation with some

THE ROLE OF COMPOSITIONAL STRAIN IN THE INSTABILITY OF SOLID-FLUID THIN FILM INTERFACES

Consider a binary substitutional solid solution not in equilibrium with a fluid rich in either solid component. At the interface, depending on the chemical energy, the solid may selectively lose or gain atoms from the fluid. Any atom exchange upsets the nominal composition; thereby stresses are generated in the solid by simultaneous action of lattice dilation and interdiffusion. As stresses build up, the local changing volume tends to split up into islands in an effort to escape from stresses, while curvature tends to amalgamate the islands in an effort to minimize surface energy. This competition could lead to substantial corrugations of the solid-fluid interface. These corrugations and the thresholds for noticeable competition between stresses and curvatures had an old tradition in chemo-mechanical models of sharp interfaces beginning with Srolovitz (1989). However, stresses were generally considered as a mere cause of external loads, so a pure solid was tacitly asserted. This paper couples elasticity with a conserved-phase field model to mainly investigate the effect of compositional strain on the interface instability process between a binary solid selectively interacting with a fluid. The chemical energy barrier is considered, however, uncoupled from stress, and the mobility quadratically dependent on the gradient of composition. Under initial enforced sinusoidal perturbations, results of simulations showed that the compositional strain parameter can dramatically alter the effect of the chemical energy barrier on the critical wavelength of perturbations that trigger interface instability.

Hydration thermodynamics of the SWy-1 montmorillonite saturated with alkali and alkaline-earth cations: A predictive model

The aim of the present work was to study the thermodynamic equilibria between water and a homo-ionic montmorillonite SWy-1 saturated by different cations. The choice of this smectite is justified by the large set of experimental data available from the literature for eight different interlayer cations: Na +, K +, Rb +, Cs +, Mg 2+, Ca 2+, Sr 2+, and Ba 2+. In particular, studies by Cases et al. (1992, 1997) and Bérend et al. (1995) are providing heat of adsorption data, pairs of desorption–adsorption isotherms, and information about the partition of adsorption–desorption water molecules between external surfaces and internal spaces. By calculating the effective amount of hydration water as the difference between the so-called gravimetric water and the surface covering water, a thermodynamic model was then developed, based on the concept of Ransom and Helgeson (1994) considering an asymmetric subregular binary solid solution between a fully hydrated and a anhydrous smectite. A set of six thermodynamic parameters ( Δ H ∘ hyd , S ∘ hyd and four Margules parameters) was extracted by a least square method from measurements of enthalpies of adsorption and paired adsorption–desorption isotherms for each interlayer cation. These six initial parameters were then used to determine a complete set of standard thermodynamic hydration parameters ( Δ H ∘ hyd , Δ G ∘ hyd , Δ S ∘ hyd , heat capacity, molar volume, and number of interlayer H 2O) and quantify, for each cation, the number of moles of hydration water molecules as a function of relative humidity and temperature. The validation of the standard state thermodynamic properties of hydration for each end member was carried out using three approaches: (1) a comparison with experimental isotherms obtained on hetero-ionic and homo-ionic SWy-1 smectite at different temperatures; (2) a comparison with the experimental integral enthalpy and entropy of hydration of the SWy-1 smectite; and (3) a comparison with experimental isotherms acquired on various smectites (Upton, MX80, Arizona) with different layer charges. Eventually, the present work demonstrates that, from a limited number of measurements, it is possible to provide the hydration thermodynamic parameters for hydrated smectites with different compositions and under different conditions of temperature and relative humidity, using the newly developed predictive model.

Theoretical and Experimental Evidences of Sequential Phase Formation during Sub-Nanometric-Thick Film Reactive Diffusion

Silicide sequential phase formation during tens-of-nanometer-thick metallic film reaction on Si substrate has been extensively studied. Nevertheless, the reasons of sequential phase formation are still under debate, and have been poorly studied at the atomic scale. Using atomistic kinetic Monte Carlo simulations, we show that considering a binary fcc non-regular solid solution, without diffusion asymmetries, the diffusive reaction of a sub-nanometer-thick film (~5 atomic monolayers) on a semi-infinite substrate leads to the sequential formation of all the phases present in the binary phase diagram, starting with the film atom richest phase. These predictions are supported by experimental observations: the dissolution of a 4 monolayer-thick Si film on a Ni(111) substrate, during in-situ ultra high vacuum Auger electron spectroscopy, shows delays and kinetic changes in the dissolution process that may correspond to the sequential formation of the Ni-Si compounds, i.e. NiSi2, NiSi, Ni3Si2, Ni2Si, Ni31Si12 and Ni3Si.

Thermodynamic stability of binary nanocrystalline alloys: analysis of solute and excess vacancy

Regarding that the excess volume in grain boundaries (GBs) is released as the vacancies which are accommodated by the crystal bulk during grain growth, a free-energy function for binary nanocrystalline solid solution is proposed, based on the pairwise nearest-neighbor interactions. The model, for the given composition and temperature, predicts an equilibrium grain size, subjected to a mixed effect due to solute segregation and due to excess vacancies. Furthermore, excess-vacancy-inhibited grain coarsening can be attained, which plays a minor role in holding the thermal stability of nanocrystalline alloys, as compared to the effect of solute segregation.

A mean-field model for amorphization in crystalline solid solutions

Based on our understanding of the atomic mechanisms of melting in binary crystalline solid solutions, we propose a unified two-order-parameter mean-field model to describe solid-state amorphization under polymorphic constraints. In this framework, we treat both thermal melting and amorphization on equal footing as a topological-order-to-disorder transition. The primary order parameter is defined such that it represents the loss of the long-range order. The elastic strain field induced by composition disorder that plays an important role at low temperature is described by a bilinear coupling with the primary order parameter. We show that solid-state amorphization can be considered as an extension of a melting transition at low temperature under polymorphic constraints. This theory can also address endothermic melting as well as exothermic melting at low temperature. We present phase diagrams and the corresponding thermodynamic quantities for a model binary crystalline solution system at and near the transitions.

Growth dynamics of Ge1−x Si x single crystals obtained by directional constitutional supercooling of the melt

The problem of growth dynamics for crystals of binary solid solutions, obtained by the constitutional supercooling of the melt with a silicon feeding rod, has been solved within the Pfann approximation. The dependences of the change in the axial growth rate of Ge1−xSix crystals (0 ≤ x ≤ 0.3) are calculated. It is shown that the Ge1−xSix crystallization rate significantly changes during growth. The results make it possible to determine the optimal conditions and technological parameters for growing Ge1−xSix single crystals (0 ≤ x ≤ 0.3) with a specified concentration gradient along the crystallization axis.

A first principles study of coupled substitution in galena

Coupled substitution is an important mechanism responsible for Ag enrichment in galena. Studies show that the concentration of Ag in galena tends to equal the sum of the concentrations of Sb and Bi ( Foord et al., 1988). The thermodynamic mixing properties of the binary solid solution: Pb 2S 2–AgSbS 2(gal), Pb 2S 2–AgBiS 2(gal), and Pb 2S 2–AgAsS 2(gal) have been investigated using quantum-mechanical and Monte-Carlo simulations (where gal. indicates phases constrained to the galena structure). Quantum-mechanical methods were used to account for electron transfer between the substituting species. Total energies for different substitution configurations were used in Monte-Carlo calculations to derive the excess enthalpy of mixing (ΔH mix), entropy of mixing (ΔS mix), and free energy of mixing (ΔG mix) at temperatures ranging from 200 °C to 1300 °C. ΔG mix was used to calculate phase diagrams that can be compared with experimental results. Electron transfer between Ag and either Sb, Bi, or As is shown to affect cation ordering in these systems. Quantum-mechanical simulations allow for the visualization of specific orbitals that are predominantly responsible for this electron transfer. Intermediates of the Pb 2S 2–AgBiS 2 solid solution tend to order into alternating Ag-rich and Pb/Bi-rich layers parallel to [111]. Phase diagrams were determined for each solid solution series and an Ag solubility limit of 6.0 mol% of AgSbS 2 (at 350 °C) was determined to be in reasonable agreement with experiments showing a value of ~ 5.5 mol% AgSbS 2.