Short-range Order In Alloys Research Articles

Atomistic simulations reveal strength reductions due to short-range order in alloys

A theory for strengthening for multicomponent non-dilute alloys possessing short-range order (SRO) has recently been developed. The theory predicts that, in addition to a well-known athermal strengthening, there is a notable effect of SRO on the solute–dislocation interactions that can decrease or increase the strength relative to a random alloy. Here, carefully designed atomistic simulations in a model binary NbW alloy are used to demonstrate that alloy strength due to solute–dislocation interactions can be increased or decreased, depending on the SRO and consistent with theoretical predictions. Specifically, SRO is introduced using fictitious solute–solute interactions in an alloy system with very small true solute–solute interactions, and the Nudged Elastic Band (NEB) method is then used to compute the energy barriers for edge dislocation motion for various levels of SRO. Energy barriers, and hence alloy strengths, can be decreased when the Warren-Cowley SRO parameters are negative (attraction of unlike solutes). The theoretical predictions for the same system are in reasonable quantitative agreement with the simulation results. These findings demonstrate the unexpected possibility of reduced strength due to SRO and also further validate the analytical theory as a tool to guide alloy design.

COMPUTER SIMULATION OF NANO-DIMENSIONAL EDUCATION STRUCTURES ON THE SURFACE OF A MONOCRYSTAL AT THE SLIDE ION BOMBING

This work deals with the computer simulation of low- and medium energy (E0=0.5÷10 keV) N+, Ne+, Ar+, Kr+, Be+ и Se+ions sliding collisions on the surface of a Cu(100), Ag(110), Si(001), SiC(001) and GaAs(001) solids, and of the accompanying effects, namely, scattering, sputtering and surface implantation. It has been shown that under these conditions the inelastic energy losses become predominant over the elastic ones. The anomalous energy losses observed experimentally at the grazing ion scattering by the single crystal surface were explained. It has been shown that from the correlation of the experimental and calculated energy distributions of the scattered particles, one may determine a spatial extension of the isolated atomic steps on the single crystal surface damaged by the ion bombardment. Results obtained can be also used to study short-range order in alloys undergoing ordering. Dissociative and non-dissociative desorption of adsorbed molecules were simulated. It was shown that at grazing ion bombardment the intensive nondissociative desorption of adsorbed molecules is possible. A preferential emission of Cu atoms in the case of Cu3Au (001) surface sputtering is observed. It was shown that in the case of grazing ion bombardment the layer-by-layer sputtering is possible and its optimum are observed within the small angle range of the glancing angles near the threshold sputtering angle. The obtained results allow to select the optimum conditions for obtaining implanted depth distributions with demanded shape in narrow near-surface region (5–10 atomic layers) of crystals. The highly sensitive layer-by-layer analysis method was proposed on the basis of layer-by-layer sputtering mechanism.

Analysis of short-range order in Cu3Au using X-ray pair distribution functions

Cu3Au is often cited as a case example of a metallic system exhibiting both short-range order in the solid solution phase and a long-range order-disorder transition. In this work, X-ray total scattering data obtained from the in situ heating of a gas-atomised powder sample of Cu3Au are used to demonstrate the suitability of total scattering, in conjunction with large-box modelling, for the analysis of short-range order in alloys. The existence of an ordering transition at c. 400° is confirmed, and the development of short-range order reminiscent of the L12 long-range ordered structure is observed prior to this transition. Furthermore, it is found that a degree of short-range order is present even in quenched samples (usually assumed to be completely random) which throws into question the identification of short-range order in previous ex situ studies. It is demonstrated that total scattering can be used successfully to identify the type and degree of ordering, differences in the bond length distributions in the first coordination shell and to suggest a likely mechanism for the formation of order in the system.

Influence of correlation effects on radiation damage in solid solutions

The influence of correlation effects due to thermodynamic interaction of alloy components on segregation processes upon radiation treatment has been analyzed. The analysis has been performed for 53 metallic solid solutions. It has been shown that the short-range order in alloys causes a redistribution of flows of radiation defects and changes the mechanism of their annihilation, which in a certain temperature range is responsible for the high resistance of alloys to radiation swelling. The presence of two maxima in the curve of the temperature dependence of swelling for austenitic nickel–chromium alloys is associated with the existence therein of different types of short-range order at different temperatures.

A new approach to the analysis of short-range order in alloys using total scattering

In spite of its influence on a number of physical properties, short-range order in crystalline alloys has received little recent attention, largely due to the complexity of the experimental methods involved. In this work, a novel approach that could be used for the analysis of ordering transitions and short-range order in crystalline alloys using total scattering and reverse Monte Carlo (RMC) refinements is presented. Calculated pair distribution functions representative of different types of short-range order are used to illustrate the level of information contained within these experimentally accessible functions and the insight into ordering which may be obtained using this new method. Key considerations in the acquisition of data of sufficient quality for successful analysis are also discussed. It is shown that the atomistic models obtained from RMC refinements may be analysed to identify directly the Clapp configurations that are present. It is further shown how these configurations can be enhanced compared with a random structure, and how their degradation pathways and the distribution of Warren-Cowley parameters, can then be used to obtain a detailed, quantitative structural description of the short-range order occurring in crystalline alloys.

Cluster coherent potential approximation for the electronic structure of disorderedalloys

We extend the single-site coherent potential approximation (CPA) to include the effects ofnon-local disorder correlations (alloy short-range order) on the electronic structure ofrandom alloy systems. This is achieved by mapping the original Anderson disorder problemto that of a self-consistently embedded cluster. This cluster problem is then solvedusing the equations of motion technique. The CPA is recovered for cluster sizeNc = 1. Various new features, compared to those observed in CPA, and related to repeatedscattering on pairs of sites, reflecting the effect of short-range order are clearlyvisible in the density of states. It is explicitly shown that the cluster-CPA methodalways yields a positive-definite density of states. Anderson localization effectshave been investigated within this approach. In general, we find that Andersonlocalization sets in before band splitting occurs, and that increasing partial orderdrives a continuous transition from an Anderson insulator to an incoherent metal.

Investigation of the dynamics of changes of the Cu 3 Au [formula omitted] surface in the course of ordering by low energy ion scattering

In the present work Cu 3 Au(1 0 0) alloy surface has been investigated with low energy ion scattering at temperatures below and above the bulk order–disorder transition temperature. The trajectories of Ar + low energy ions scattered from atomic chains on the surface of Cu 3 Au(1 0 0) along 〈1 0 0〉 and 〈1 1 0〉 directions were computer simulated. The dependencies of the energy of scattered ions E on the scattering angle θ and corresponding angular distributions were calculated. It has been shown that a comparison of the angular and energy distributions of ions scattered from the surface of an alloy in the process of ordering with similar distributions for pure targets made up of the alloy components permits a conclusion that two or more neighboring atoms in an alternating sequence are of the same species. The results obtained can be used to study short-range order in alloys undergoing ordering.

Order–disorder reaction in Alloy 600

Abstract Differential scanning calorimetric tests were carried out in Alloy 600 from room temperature to 800°C on various specimens, in order to investigate the origin of the exothermic and endothermic reactions that occur during thermal analyses. Since it is reasonable that there is a Ni 2 Cr short-range order in Alloy 600, which is a Cr-rich Ni-base alloy, the differential scanning calorimetry (DSC) results are interpreted on the existence of order–disorder reaction relevantly. The exothermic reactions were observed at lower temperatures in the cold worked specimen, compared to the quenched one. However, the endothermic reactions were observed at 490–580°C in all specimens. Especially, a convex endothermic reaction was observed at about 500–600°C for a specimen aged at 474°C for 1100 and 10 000 h. The extent of energy released by the exothermic reaction occurring at 430–520°C in a specimen quenched after a 874°C–1-h treatment was 8.4 J g −1 , which is nearly the same as the energy of ordering for the Ni–25%Cr alloy. In addition, the activation energy for an exothermic reaction in a specimen quenched after a 1095°C–1/2-h treatment was Q =190 kJ mol −1 (2 eV atom −1 ), which suggests that this exothermic reaction is related to a substitutional diffusion process. It was concluded that the exothermic and endothermic reactions in quenched Alloy 600 are due to the ordering and disordering reactions, respectively. It seems that the existence of ordering in Alloy 600 should be considered in the physical metallurgy of Alloy 600.

Analytical description of the short-range order in alloys with many-body atomic interactions. II

The recently elaborated approach (Chepulskii R V and Bugaev V N 1998 J. Phys.: Condens. Matter 10 7309-26, 7327-48) based on the joint application of the thermodynamic fluctuation method and perturbation theory is generalized to the case of the presence of not only pair but also nonpair atomic interactions of arbitrary orders in an alloy. Within such an approach, a number of new analytical approximations are derived for calculation of the grand thermodynamic potential as well as of the short-range order parameters and their Fourier transform in disordered binary alloys of arbitrary compositions and with Bravais crystal lattices. The effective radius of atomic interactions is not limited a priori. The inverse effective number of atoms interacting with one fixed atom as well as the inverse temperature are successively used as a small parameter of expansion. The developed approach may be also followed in studies of magnetics in the framework of the Ising model and of fluids and amorphous materials within the lattice gas model as well as in investigations of low-dimensional lattice systems.

Optimizing The Metalloid Content in Bulk Metallic Glasses

AbstractWe have studied the effect of phosphorus content on the formation and properties of bulk Pd-Cu-P and Pd-Ni-P metallic glasses. It was found that the molar volumes of the Pd-Ni-P bulk glasses plotted as a function of P content follow a straight line whereas those for the Pd-Cu-P glasses follow two straight lines of different slopes, intersecting at a critical P concentration. The transition in molar volume behavior is attributed to a change in the alloy's short-range order with increasing P content. The origin of this structural change is discussed based on x-ray photoelectron spectroscopy (XPS) measurements.

Analytical methods for calculation of interatomic potentials through the data on the short-range order in alloys

Within the framework of the high-accuracy ring approximation elaborated by the authors (Chepulskii R V and Bugaev V N 1998a, b 10 7309-26, 7327-48) in the context of the modified thermodynamic perturbation theory as applied to the lattice gas model, two methods are developed for calculation of the atomic interaction parameters in binary disordered alloys with Bravais crystal lattices through the data on the atomic short-range order (SRO) - the iteration method resulting in explicit analytical relationships and the variational method. Within both methods, the Fourier components of SRO parameters are used as initial data, thus, the most complete information on SRO in the alloy is taken into account. Both the iteration and variational methods permit us to calculate the atomic interaction parameters for an arbitrary number of the coordination shells as well as the Fourier components of the atomic interaction potentials. It is demonstrated that both methods have wide temperature-concentration intervals of applicability. The methods can be used under investigation not only of alloys, but also of other lattice systems (including low-dimensional ones, semiconductors and magnetics).

Analytical methods for calculation of the short-range order in alloys: I. General theory

In the context of a modified thermodynamic perturbation theory within the grand canonical ensemble, by the use of the thermodynamic fluctuation method, a number of new analytical approximations for calculations of the grand thermodynamic potential as well as of the short-range order parameters and their Fourier transform in disordered binary alloys with a Bravais crystal lattice are elaborated. An alloy of an arbitrary composition is considered in the framework of the lattice gas model with pair atomic interactions of arbitrary effective radius of action. The inverse effective number of atoms interacting with one fixed atom and inverse temperature as well as the concentration of the impurity component are used as small parameters of expansion. The developed approach may be also followed in studies of magnetics within the framework of the Ising model, and of fluids and amorphous materials within the lattice gas model as well as in investigations of low-dimensional lattice systems.

Anaytical methods for calculation of the short-range order in alloys: II. Numerical accuracy study

The numerical accuracy of the analytical approximations elaborated in part I and of a variety of other approximations advanced to date is examined, accepting the data on the short-range order parameters obtained by the Monte Carlo method as a standard. The approximations exhibiting the most promise for description of actual alloys and other lattice systems (for instance, interstitial alloys, semiconductors and magnetics) including those with a long-range character of atomic interactions are revealed. It is stated that, in the framework of the lattice gas model within a modified thermodynamic perturbation theory, the choice of the inverse effective number of atoms interacting with one fixed atom as a small parameter of the cumulant expansion along with taking account of the contributions from only linked irreducible diagrams ensures the fastest convergence of expansion. It is demonstrated that the use of the grand canonical ensemble yields the highest numerical accuracy in the statistical-thermodynamic description within the framework of all approximations elaborated in part I.

Analytical method for calculation of the short-range order in alloys

A new simple analytical approximation for calculations of the shortrange order parameters and their Fourier transform in disordered binary alloys with a Bravais crystal lattice and with atomic interactions of arbitrary effective radius of action is proposed. On the basis of the comparison with the Monte Carlo simulation data, the high numerical accuracy of approximation is demonstrated and it is shown that this accuracy turns higher with the increase of the effective radius of atomic interactions. The developed approach may be also followed in studies of magnetics within the framework of the Izing model, of fluids and amorphous materials within the lattice gas model as well as in investigations of the low-dimension lattice systems.

Analytical description of the short-range order in alloys with many-body atomic interactions

Three simple analytical approximations are elaborated for calculation of the short-range order parameters and their Fourier transform in disordered binary alloys with many-body atomic interactions of arbitrary order and effective radius of action. Within all the approximations the account of non-pair atomic interactions is reduced to the replacement of the pair mixing potential by the effective concentration-dependent potential. From the form of such an effective potential it is concluded that the temperature-concentration phase diagram of an alloy with non-pair atomic interactions is asymmetrical with respect to the equiatomic composition and that the effect on the structural properties of the alloy of such interactions decreases with concentration decrease. These conclusions are justified by simulation within the Monte Carlo method. On the basis of the comparison with the simulation data, an approximation which demonstrates high numerical accuracy of results in a wide temperature-concentration interval is determined and it is shown that its accuracy increases with the increase of the effective radius of atomic interactions. We prove the general invariance of the statistical-thermodynamic properties of binary alloys with respect to a number of transformations which results in symmetry of the phase diagrams of alloys with respect to equiatomic composition in a particular case of the presence of nothing but concentration-independent pair atomic interactions.

X-ray Compton Scattering from Aluminium and Silicon Crystals at Low Scattering Angles

A correction is shown for the Compton scattering intensity that is calculated theoretically for free atoms, if the loosely bound outer electrons of the atoms construct the conduction or valence band in crystals, typically in the case of aluminium and silicon. The correction originates from the Pauli exclusion principle forbidding the electron in the band to make a transition to a filled state inside the band. The corrected figures satisfactorily explain the observed intensity at low scattering angles. The correction should be taken into account in analyses of diffuse scattering such as that caused by thermal vibration of crystals or by short-range order in alloys, particularly in the range of low scattering angles.

Investigation of short-range order in magnesium-terbium alloy

Using the model potential method with Ashcroft form factors, we predict the existence of short-range order in the alloy Mg−2.9 at. % Tb, which is experimentally confirmed by diffuse x-ray scattering. We use the diffuse x-ray scattering method to determine the characteristic temperature of the alloy: θ D = 325 K.

Commensurate and incommensurate ordering tendencies in the ternary fcc Cu-Ni-Zn system.

We show that Fermi-surface (FS) nesting drives both the incommensurate and commensurate ordering tendencies of the fcc ternary Cu-Ni-Zn system. Surprisingly, commensurate order persists over a wide range of composition, despite its origins. For ${\mathrm{Cu}}_{2}$NiZn, we discuss how FS nesting and the other effects of alloying lead to ordering tendencies consistent with the experimentally observed order-disorder transformations. All calculations are based on a first-principles theory of the atomic short-range order in alloys with an arbitrary number of components.

Compositional short-range ordering in metallic alloys: Band-filling, charge-transfer, and size effects from a first-principles all-electron Landau-type theory.

Using a mean-field statistical description, we derive a general formalism to investigate atomic short-range order in alloys based on a density-functional description of the finite-temperature, grand potential of the random alloy. This ``first-principles,'' Landau-type approach attempts to treat several contributions (electronic structure, Fermi surface, electrostatics, magnetism, etc.) to the electronic energy on an equal footing. An important ingredient for the statistical averaging is the replacement of the molecular mean fields (Weiss fields) with Onsager cavity fields, which forces the diagonal part of the fluctuation-dissipation theorem to be obeyed. To show its general applicability and usefulness, we apply the theory to three fcc alloy systems. In ${\mathrm{Cu}}_{0.75}$${\mathrm{Pd}}_{0.25}$, the incommensurate atomic short-range order is driven by a Fermi-surface effect, in agreement with earlier work. In contrast, ${\mathrm{Pd}}_{0.5}$${\mathrm{Rh}}_{0.5}$ exhibits clustering tendencies, with both band-filling and charge-rearrangement effects being important in setting the spinodal temperature at 1150 K, in good agreement with experiment. In the final examples of three nickel-rich NiCr alloys, previously ignored electrostatic effects are found to play a significant role in determining the atomic short-range order.

Recent studies of short-range order in alloys: the Cowley theory revisited

We present comparisons of various statistical theories for effective pair interactions (EPI) in alloys. We then evaluate these EPIs using the Cowley theory, the Krivoglaz-Clapp-Moss (KCM) approximation, the γ-expansion method (GEM) of Tokar, Masanskii and co-workers, and the exact inverse Monte Carlo (IMC) method, introduced by Gerold and Kern. Via a series of model calculations on a hypothetical bcc alloy with a single nearest-neighbor interaction we show that the Cowley theory is successful in evaluating the EPIs in more dilute alloys but tends to overestimate the magnitude of the nearest-neighbor energy at higher concentrations, whereas the KCM expression becomes increasingly inaccurate at lower concentrations. In general, however, the approximate mean-field theories are most accurate at higher concentrations and higher temperatures. Recent studies of short-range order in single crystals are discussed in which these EPIs have been evaluated using the IMC, KCM, GEM and Cowley theories. Examples include the bcc alloy Fe 0.53Cr 0.47 and the fcc alloys Cu 3Au, Cu 0.69Zn 0.31 and Ni 0.89Cr 0.11. In all cases the approximate expressions do quite well, especially the GEM.