Dilute Fe-Cu Alloys Research Articles

Identification and evolution of ultrafine precipitates in Fe-Cu alloys by first-principles modeling of positron annihilation

Understanding the formation and evolution of Cu precipitates in Fe-based alloys is crucial as they are key factors responsible for hardening and embrittlement. Dilute FeCu alloys are model materials for structural components in various application areas, including that of reactor pressure vessel steels for light water nuclear reactors. Positron annihilation spectroscopy (PAS) is a powerful tool to study the nucleation stage of both homogeneous and heterogeneous Cu precipitation, which are beyond the reach of most other experimental techniques. In this work, we present a first-principles study of positron annihilation in Fe-Cu systems. The positron annihilation characteristics (positron lifetimes, Doppler broadening spectra) are calculated for both homogeneous vacancy-free Cu clusters and heterogeneous vacancy-Cu complexes using two-component density functional theory. The theoretical results excellently agree with the available reference PAS experimental results. Our calculations show that the types of Cu precipitates can be clearly distinguished by positron annihilation, and the sizes of Cu precipitates can also be reasonably well estimated with our calculations. Moreover, we also successfully analyze the evolution of the experimental signals during isochronal annealing where the small Cu clusters change character. This work improves the understanding of the early-stage Cu precipitation in Fe matrix.

Simulation of Cu precipitation in Fe-Cu dilute alloys with cluster mobility

Cu-rich precipitates formation is associated with the precipitation hardening of Fe-Cu based steels and the embrittlement of reactor pressure vessel steels under neutron irradiation. The accurate modeling of the time evolution of Cu-rich precipitates is therefore of fundamental importance for the design of Fe-Cu based steels and the prediction of the irradiation induced shift of the ductile to brittle transition temperature of reactor pressure vessels. This work applies cluster dynamics with mobile Cu monomers and clusters to model Cu precipitation in dilute Fe-Cu alloys at several temperatures. Optimized model parameters can be used to simulate the mean radius, number density, volume fraction, and matrix composition evolution during isothermal annealing with reasonable accuracy. The possible reduction of the mobility of Cu-rich clusters due to additional alloying elements in Fe-Cu based steels is discussed.

First-principles model study of the phase stabilities of dilute Fe-Cu alloys: Role of vibrational free energy

The aim of our first-principles study is to model dilute Fe-Cu alloys by including vibrational properties for the determination of phase boundaries. Single-atom and pairwise defects of Cu in bcc Fe and Fe in fcc Cu are considered in terms of structurally relaxed supercells, for which the corresponding total energies are calculated by a density-functional theory (DFT) approach. Based on DFT total energy differences strongly nonbonding substitutional formation energies for all defects are derived. For determining the entropy of mixing, a mechanical statistical model is designed, which is also able to include pairwise and larger defects. By the same DFT approach and within the harmonic model vibrational properties and, in particular, the temperature-dependent vibrational free energies are calculated. Based on these results a vibrational free energy for each defect species is obtained, which in combination with the corresponding DFT formation energies and the entropy of mixing is added up to a grand canonical potential. Minimizing this potential as a function of defect concentrations yields the desired free energies as a function of concentration and temperature, from which the phase boundaries are derived. Analyzing our results we find that the vibrational entropies are determining the temperature dependency of the vibrational free energies. We find, that including the vibrational free energy via the vibrational entropy is very important for explaining the rather wide miscibility range of mixing Cu to bcc Fe as observed experimentally. On the Cu-rich side of the Fe-Cu system including the vibrational entropy narrows the miscibility range.

Magnetization andCu63NMR studies on granular FeCu alloys

Nanostructured FeCu granular alloys (Fe $\ensuremath{\sim}1%--20%$) have been prepared by borohydride reduction and characterized by energy dispersive spectroscopy, x-ray, and transmission electron microscopy studies. Study of zero-field-cooling--field-cooling magnetization yields blocking temperature distribution of magnetic fine particles system in all samples. At low Fe concentration, the magnetizations of the samples combine superparamagnetism and paramagnetism near room temperature and small hystereses at $5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. High Fe content alloys are almost entirely ferromagnetic even at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. However, in all these samples, the observation of the $^{63}\mathrm{Cu}$ nuclear magnetic resonance signal at all temperatures $4--300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ confirms the existence of a paramagnetic component having $\ensuremath{\sim}0.02--0.04\phantom{\rule{0.3em}{0ex}}\mathrm{at.}\phantom{\rule{0.2em}{0ex}}%$ Fe in Cu. The temperature dependence behavior of Fe contribution to $^{63}\mathrm{Cu}$ NMR linewidth and the Knight shift indicate that the paramagnetic component might exhibit a Kondo temperature of $\ensuremath{\sim}24\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ that is significantly higher than that obtained in bulk dilute FeCu alloys.

Ab initio calculations of self-interstitial interaction and migration with solute atoms in bcc Fe

The embrittlement of pressure vessel steels under radiation has been long ago correlated with the presence of solute Cu. Indeed the atom probe and the small angle neutron scattering, principally, have revealed the formation of Cu clusters under neutron flux in reactor pressure vessel (RPV) steels and dilute FeCu alloys. Other solutes such as Ni, Mn and Si which are also found within the clusters, are now suspected to contribute to the embrittlement. The interactions of these solutes with radiation induced point defects need thus to be characterized properly in order to understand the elementary mechanisms behind the formation of these clusters. We have investigated by ab initio calculations based on the density functional theory the interactions of self-interstitials with solute atoms in dilute FeX alloys (X = Cu, Mn, Ni or Si). Different possible configurations of solute–dumbbell complexes have been studied. Their binding energies are discussed, as well as their relative stability. The migration of dumbbells with a solute atom in their vicinity was also investigated. All these results are compared to some experimental ones obtained on dilute FeX model alloys. Our results indicate that for Mn solute atoms, diffusion via an interstitial mechanism is very likely.

Solute interaction with point defects in α Fe during thermal ageing: A combined ab initio and atomic kinetic Monte Carlo approach

Solute Cu plays a major role in the embrittlement of reactor pressure vessel (RPV) steels under radiation. In RPV steels and dilute FeCu alloys, characterization techniques such as the tomographic atom probe (TAP), or the small angle neutron scattering (SANS) have revealed the formation of solute rich clusters (with Cu, Ni, Mn and Si) under neutron flux. It is thus very important to characterize the interactions of these solutes with radiation-induced point defects in order to understand the elementary mechanisms behind the formation of these clusters. Ab initio calculations based on the density functional theory have been made in order to build a database used to parameterise an atomic kinetic Monte Carlo model. The interactions of point defects and solute atoms in dilute FeX alloys (X = Cu, Mn, Ni or Si) have been evaluated for different configurations of small solute clusters and solute–vacancy complexes. First results obtained with the kinetic Monte Carlo model will be presented and compared to some experimental observations.

Ab initio calculations of vacancy interactions with solute atoms in bcc Fe

Solute Cu plays a major role in the embrittlement of reactor pressure vessel (RPV) steels under radiation. In RPV steels and dilute FeCu alloys, the tomographic atom probe has revealed the formation of Cu atmospheres under neutron flux. More recently the role of other solutes such as Ni, Mn and Si which are also within the atmospheres has been put forward. It is thus very important to characterise the interactions of these solutes with radiation-induced point defects in order to understand the elementary mechanisms behind the formation of these atmospheres. We have investigated by ab initio calculations based on the density functional theory the interactions of point defects in dilute FeX alloys (X=Cu, Mn, Ni or Si). The structure of X-vacancy complexes has been determined, as well as their binding energies. Their relative stability is discussed and compared to experimental results obtained with model alloys.

Ab initio contribution to the study of complexes formed during dilute FeCu alloys radiation

Cu plays an important role in the embrittlement of pressure vessel steels under radiation and entities containing both Cu atoms and vacancies seem to appear as a consequence of displacement cascades. The characterisation of the stability as well as the migration of small Cu–vacancy complexes is thus necessary to understand and simulate the formation of these entities. For instance, cascade ageing studied by kinetic Monte Carlo or by rate theory models requires a good characterisation of such complexes which are parameters for these methods. We have investigated, by ab initio calculations based on the density functional theory, point defects and small defects in dilute FeCu alloys. The structure of small Cu clusters and Cu–vacancy complexes has been determined, as well as their formation and binding energies. Their relative stability is discussed. Vacancy migration energies in the presence of Cu atoms have been calculated and analysed. All the results are compared to the figures obtained with empirical interatomic potentials.

Ab initiocalculations of defects in Fe and dilute Fe-Cu alloys

Point defects in Fe and dilute FeCu alloys are investigated hy ab initio calculations based on density functional theory. The relaxed vacancy and interstitial and substitutional Cu atom formation energies are determined as well as some migration energies. The binding energies of various Cu containing defects believed to play an important role in the embrittlement of pressure vessel steels under radiation are calculated and discussed. The results are consistent with a Cu transport via a vacancy mechanism. The introduction of a Cu atom decreases the energy difference between the dumbbell and the dumbbell configurations, and should make the dumbbell rotation motion easier. The ab initio results are compared to the figures obtained with empirical interatomic potentials. The convergence of the results with the simulated system size is examined.

Modeling Cascade Aging in Dilute Fe-Cu Alloys

ABSTRACTThe continued safe operation of nuclear reactors and their potential for lifetime extension depends on ensuring reactor pressure vessel integrity. Reactor pressure vessels and structural materials used in nuclear energy applications are exposed to intense neutron fields that create highly non-equilibrium defect concentrations, consisting of a shell of self-interstitial atom and clusters surrounding a vacancy-rich core, over picosecond time scales. This spatially correlated defect production initiates a long chain of events responsible for microstructure evolution and hence irradiation embrittlement. In this paper, we describe the combined use of molecular dynamics (MD) and kinetic lattice Monte Carlo (KMC) to simulate the long-term rearrangement (aging) of displacement cascades in dilute Fe-Cu alloys. The simulations reveal the formation of a continuous distribution of three dimensional cascade vacancy-Cu cluster complexes and demonstrate the critical importance of spatial, as well as short and long-time correlated processes that mediate the effective production of primary defects. Finally, this approach can generate production cross-sections for vacancy-Cu clusters that can then be used in rate theory type models of long term global micro and microstructural evolution.

Micromechanical Modeling of the Banded Structure of Martensite in Small Inclusions

The stability of austenite against strain induced martensitic transformation (SIMT) strongly depends on the grain size of the austenite. This is observed in austenitic steels with grain sizes from several μm up to several hundred μm and for much smaller austenitic grains (three orders of magnitude) that are embedded in a non austenitic matrix. fcc Fe-precipitates may be formed in dilute Cu-Fe alloys by a certain heat treatment. These Fe-particles transform only by plastic deformation of the alloy. The SIMT leads to a banded structure with parallel layers of martensite. We investigate the influence of the external stress state on the microstructure (number of twin bands, relative thickness of the bands) with the help of a micromechanical model. The grain size effect on the austenite's stability against SIMT and on the microstructure may be explained by a thermodynamic transformation criterion and the local mechanical driving force.

Kinetic Lattice Monte Carlo Simulations of Diffusion and Decomposition Kinetics In Fe-Cu Alloys: Embedded Atom and Nearest Neighbor Potentials

ABSTRACTIn principle, Kinetic Lattice Monte Carlo (KLMC) methods can accurately simulate the precipitation of coherent phases by tracking the motion of a vacancy and the corresponding diffusion and clustering of solutes. The fidelity of the KLMC simulations depends primarily on the validity of the assumed interatomic potentials. These potentials must provide accurate solute-solute-solvent-vacancy energetics over the length scales relevant to the physical decomposition paths. Of course, simulating long range strain energy interactions is the biggest challenge, but the significance of this contribution is less in systems manifesting primarily dilational strains. Simple nearest neighbor (NN) potentials, used in previous KLMC of decomposition kinetics of dilute Fe-Cu alloys are generally not able to reproduce alloy property combinations like vacancy formation energies, dilute heats of solution and the coherent interface energies. Further, solute diffusion in bcc alloys requires jumps between first and second nearest neighbors, and is governed by, at minimum, at least three independent jump frequencies. The jump frequencies are controlled by the binding energies of atoms out to at least second nearest neighbor positions (which are only about 15% further away from the solute than the first nearest neighbor) and are also influenced by solute-modified saddle point activation energies. Thus longer range multiatom embedded-atom-method (EAM) type potentials can, in principle, provide a more realistic simulation of diffusion and solute clustering compared to NN based models. However, this refinement comes at a much higher computational cost. While they cannot be directly compared, this study presents KLMC results for both a simplified EAM versus a NN potential, and describes important new mechanistic insight provided by these atomistic simulations.

Phase-separation kinetics of dilute Cu-Fe alloys studied by anomalous small-angle x-ray scattering and Mössbauer spectroscopy.

A combination of anomalous small-angle x-ray scattering and Mossbauer spectroscopy was used to study the very early stages of decomposition in the model system Cu-Fe. Applying these two kinds of measurements to the same samples, it was possible to observe a gradual transition from short-range clustering to the first precipitates. The decomposition proceeds by a classical nucleation process where the nucleation barrier is lowered, however, by the presence of small aggregates appearing as fluctuations in the (meta)stable solid solution

NMR spin lattice relaxation in dilute CuFe alloys with impurity interactions

Previous measurements by Wilkening and Hesse have shown, that the excess relaxation rate Δ T -1 1 of the matrix nuclei in CuF e dilute alloys can be explained in terms of the LD-model with rapid spin diffusion. Measurements reported in this paper confirm the existence of an electric quadrupole diffusion barrier. It could be shown that the influence of the quadrupole barrier is coupled to large clusters within the alloy. The electron spin lattice relaxation time τ 1 behaves temperature independent in the range 30 K ⩽ T ⩽ 300 K. This can be understood if an effective correlation time τ is introduced, which results from a distrubution of temperature dependent times τ cl( T) belonging to clusters of different size.

Influence of charge and spin density oscillations on the CW63Cu NMR in CuFe

Results of cw63Cu NMR measurements in dilute CuFe alloys containing from 0.01 up to 0.2 at.-% Fe are presented. The temperature was well above the Kondo temperature of this specimen. The broadening of the NMR line width is caused by the localized magnetic moment of the Fe impurities. The decreasing signal amplitude with increasing iron content is due to the quadrupolar interactions appearing simultaneously. The line broadening correspond strongly to that of the impurity susceptibility behaviour in CuFe. The quadrupolar disturbances are temperature independent. The influence of the simultaneously appearing magnetic and electric interactions on the spin lattice nuclear relaxation time is discussed.

Atomic short range order in CuFe alloys

The clustering of iron atoms in a copper matrix, as determined by earlier Mossbauer effect studies on alloys containing up to 3.1 at.% Fe, has been analysed in terms of the atomic short range order parameter alpha 1. Good agreement is found between the experimental and calculated values of the clustering in groups of two and three nearest neighbour iron atoms and the results are consistent with previous magnetization studies of impurity interaction effects in dilute CuFe alloys. The variation of alpha 1 with concentration can be considered to reflect the mobility of the iron atoms in copper at different compositions and indicates that the diffusion rate of iron atoms is greater in dilute alloys than in more concentrated alloys.

Evidence of spin compensation in copper-iron alloys obtained from thermal conductivity measurements

The formation of a spin-compensated state in extremely dilute Cu-Fe alloys in the liquid helium range has been recently discussed by us on the basis of our electrical resistivity measurements. Based upon our thermal conductivity measurements in the liquid helium range, the electronic Lorenz number for the same alloys containing 115 and 380 at. ppm iron are reported in this paper in their unannealed and annealed states. For the well-annealed alloys, where the effective iron concentrations are estimated to be 10 to 20 at. ppm, the electronic Lorenz number is found to be equal to the Sommerfeld value of 2.45×10−8 V 2 /K 2 , which is consistent with the concept of the spin-compensated state of these alloys.

The magnetic susceptibility of dilute CuFe alloys in the temperature range 1.7–300 K

The paramagnetic susceptibility ofCuFe alloys (100–300 ppm Fe) has been measured in the temperature range 1.7 to 300 K. The susceptibility is very well represented by the expression $$\chi = \chi _0 + \frac{{C_1 }}{{T - \theta _1 }} + \frac{{C_2 }}{{T - \theta _2 }}$$ the first and second Curie Weiss terms being associated with single and paired iron atoms respectively. A Cu0-9 Au0-1 Fe alloy was also studied.

Toward simple powers of T in the Kondo effect: I. Low-temperature electrical resistivity of dilute Cu—Fe alloys

The electrical resistivity of some dilute Cu-Fe alloys (30 ppm to 1000 ppm Fe) has been measured very precisely (1 : 50 000) down to 0.05 K and in magnetic fields of 0, 1000 and 2000 Oe. Analysis of the data reveals a contribution due to isolated Fe atoms, varying as T 2 for T ≦̸ T K , and a contribution due to Fe pairs, proportional to In T. The magnitude of the pair term is used to estimate a pair concentration, which is in good agreement with data obtained from magnetic susceptibility and specific heat. An empirical transport relaxation time is developed which can be used to compute the temperature-dependent Lorenz number from resistivity and thermopower data. Another empirical relaxation time provides a unified description of electrical resistivity, thermal conductivity and thermopower for T ≦̸ T K . The Kondo temperature is determined from the (- T 2) term in the electrical resistivity and appears to decrease with increasing Fe concentration.

Lorenz-number and the Kondo-effect in copper-iron

The Lorenz number ( L) for electron-impurity scattering in dilute Cu-Fe alloys has been determined below 9 K. All information necessary to account for the observed temperature dependence of L appears to be contained in the electrical resistivity and the thermoelectric power.