Mixed Dumbbell Research Articles

An atomic resolution study of radiation-induced precipitation and solute segregation effects in a neutron-irradiated W-25 at.% Re alloy

The phenomena of radiation-induced precipitation and solute segregation effects in a W-25 at.% Re alloy have been investigated using the atom-probe field-ion microscope. This alloy is supersaturated with respect to the solvus line of the primary β-solid solution. The specimens had been irradiated in the Experimental Breeder Reactor (EBR-II) to a fast neutron fluence of ~4 × 10 22 neutrons cm −2 ( E > 0.1 MeV) at 575, 625 and 675°C. This fluence corresponds to 8.6 dpa and an average displacement rate, for the 2 year irradiation time, of 1.4 × 10 −7 dpa s −1. The results of the present work show significant alteration of the microstructure of this alloy as a result of neutron irradiation. Coherent, semicoherent and incoherent precipitates with the composition ~Wre 3 were detected; the precipitate's number density is ~ 10 17 cm −3 with a mean diameter of ~40Å. The coherent WRe 3, precipitates were not associated with either line or planar defects or with any impurity atoms. Therefore, a true homogeneous radiation-induced precipitation occurs in this alloy. The semicoherent and incoherent WRe 3 precipitates were associated with 4He atoms; i.e. these precipitates may have been heterogeneously nucleated. Voids at a number density of ~10 17cm −3 and a mean diameter of ~90Å were detected. Neither a significant enrichment or enhancement of Re was found at these voids. A two-dimensional WRe 3, phase has been observed at a grain boundary. A physical argument is presented for the nucleation of WRe 3 precipitates in the vicinity of displacement cascades. It is suggested that the first step in the nucleation of WRe 3 precipitates is the formation of tightly-bound mobile mixed dumbbells which react to form an immobile di-rhenium cluster. A possible sequence of point-defect reactions is detailed which can lead to a WRe 3 cluster. The growth of this cluster into a precipitate is most likely driven by the irreversible vacancy: self-interstitial atom (SIA) annihilation reaction, as suggested recently by Cauvin and Martin. Point defect mechanisms for all the other observations are also discussed.

An atomic resolution study of homogeneous radiation-induced precipitation in a neutron irradiated W-10at.% Re alloy

The phenomenon of radiation-induced precipitation has been investigated in a W-10at.% Re alloy using the atom-probe field-ion microscope. This alloy is subsaturated with respect to the solvus line of the primary solid solution (β phase). The specimens had been irradiated in the Experimental Breeder Reactor II (EBR-II) to a fast-neutron fluencc of ~4 × 10 22 neutrons cm −2 ( E > 0.1 MeV) at 575, 625 and 675°C. This corresponds to 8.6 dpa and an average displacement rate, for the 2 year irradiation time, of 1.4 × 10 −7 dpa s −1 The results of the present work show a significant alteration of the microstructure of this alloy as a result of the fast-neutron irradiation. Precipitates with the composition ~WRe were detected at a density of 10 16cm −3. Coherent, semicoherent and possibly incoherent precipitates of the σ phase have been observed. They were not associated with either linear or planar defects, or with any impurity atoms; i.e. a true homogeneous radiation-induced precipitation occurs in this alloy. A physical argument is presented for the nucleation of the WRe precipitates in the vicinity of displacement cascades produced by primary knock-on atoms. It is suggested that the nucleation of WRe is due to the formation of tightly-bound mobile mixed dumbbells which react to form an immobile rhenium cluster. A possible sequence of point-defect reactions is detailed which can lead to a WRe cluster. The growth of this cluster into a precipitate is most likely driven by the irreversible vacancy: self-interstitial atom (SIA) annihilation reaction, as suggested recently by Cauvin and Martin. A mechanism for the suppression of voids, in this alloy, is presented which is self-consistent with the homogeneous radiation-induced precipitation mechanism.

Oxygen gettering by hafnium implanted in beryllium: A 〈0001〉 Hf-O dumbbell?

The interaction of hafnium implanted into beryllium single crystals with diffusing oxygen was studied using hyperfine interaction and Rutherford backscattering channeling techniques. It was observed that oxygen is trapped at hafnium in a well defined lattice position. The formation of a 〈0001〉 Hf-O mixed dumbbell in the tetrahedral interstitial cage of the beryllium lattice is suggested to explain the experimental results.

An interpretation of defect production and annealing throughout stage II in dilute Ag(Cu) alloys

The experimental results presented in the previous paper (see ibid., vol.14, p.1379, 1984) are analysed with a simple chemical rate model for the damage production above stage I. It is assumed that the trapping of a second interstitial (i), an impurity-interstitial complex (ti), is a shallow trapping for which the resistivities are additive. Several assumptions are tried for the specific resistivity retained per trapped single interstitial, rho Ft(i). The one which leads to the best consistency yields rho Ft(i)=(160+or-10) mu Omega cm if one takes the Frenkel pair specific resistivity, rho F=200 mu Omega cm. The fact that rho Ft(i) is found to be smaller than rho F is an indication of deep trapping: a mixed dumbbell is formed, as expected. A corresponding value of the trapping radius, relative to the capture radius by a vacancy is found: Rt=rt/rv=0.2-0.3, which depends little on the temperature. The recovery spectra show that the mixed dumbbell Ag-Cu becomes mobile at about 120K. During its long-range migration it may either annihilate with a vacancy or combine with a second copper atom. The decrease in the resistivity which is found to correspond to this latter possibility leads us to assume that a dumbbell Cu-Cu can be formed, which is stable up to higher temperature.

Proton induced X-ray excitation applied to lattice location studies in molybdenum (cobalt) by channeling

Proton induced X-ray excitation (PIXE) and ion channeling have been applied to study the location of Co atoms with respect to the host lattice in a dilute Mo(Co) alloy single crystal. The yields of proton induced K X rays from the cobalt impurity, of K and L X rays and of backscattered protons from the molybdenum host were measured simultaneously as a function of the crystal orientation with respect to the analysing 600 keV proton beam. The experimental yields around the 〈111〉, 〈110〉 and 〈100〉 axes were compared with theoretical yields calculated on the basis of Monte Carlo computer simulations. Experimental scans for the Mo matrix are in good agreement with calculated scans for a perfect crystal, provided that the X-ray absorption in the target, the energy and impact parameter dependence of the X-ray production cross section are taken into account in the calculations. For the Co foreign atoms it is shown that more than 95% are initially substitutional. After irradiation with 600 keV protons at 50 K a considerable fraction of Co atoms is displaced from substitutional to interstitial lattice sites. The measurements are compatible with a displacement by 0.105 nm into the 〈110〉 direction which is the dominant configuration. In addition a small fraction of Co atoms, displaced by 0.14 nm into the 〈100〉 direction, can be identified at higher irradiation fluences. The fluence dependence of the displaced fractions is in good agreement with the unsaturable trap model, when the 〈110〉 displacement is attributed to the trapping of a single Mo interstitial atom to form a “ 〈110〉 mixed dumbbell” with the Co, and when the 〈100〉 displacement is assigned to the trapping of two Mo interstitials at the Co impurity.

Computer simulation of the atomic structure of defects in metals

The basic methods used in the computer simulation of the atomic structure and structural changes of defects in metals?molecular dynamics, variational procedures, and the lattice statics method?are briefly reviewed. There is a discussion of some new interatomic potentials, in particular, potentials which incorporate the partially filled d shells of transition metals. Some typical results of the calculations of the atomic structure of defects and their formation and migration energies are reported. These results refer to mixed dumbbells, complexes consisting of a vacancy and an impurity atom, clusters of vacancies and interstitial atoms, and dislocation cores in bcc and hcp metals, including transition metals, and in alloys with a long-range order; special grain boundaries; defects in void superlattices in irradiated metals; and point defects in amorphous metals. The future outlook for simulation is discussed.

Interstitialcy diffusion in B. C. C. metals and dilute alloys

Abstract The fundamental processes whose knowledge is necessary to the understanding of interstitialcy diffusion in bcc—as compared to fee—lattices are discussed. A major difference is that there is no possible cage effect for mixed dumbbells in bee lattices, whatever the jump mechanism (with or without rotation) may be. Besides, jumps without rotation are favoured in bee's as compared to fee's. For these two reasons, long range diffusion of solute atoms apt to form mixed interstitials, by an interstitialcy mechanism, that is at low temperature, should be greatly favoured in bcc lattices.

A channelling study of defect-impurity complexes in proton irradiated molybdenum (cobalt)

Channelling experiments have been performed to determine the configuration of impurity-defect configurations in MoCo after irradiation with 600 keV protons at 50 K. Proton Induced X-ray Excitation (PIXE) was used to identify the Co impurities. It is shown that the Co atoms can be displaced from substitutional lattice sites by the trapping of interstitial atoms that are mobile at the irradiation temperature. Experimental angular scans were compared with detailed Monte-Carlo calculations. The fluence dependence was investigated for two samples with mean impurity concentrations of 2×10 −3 and 5×10 −3 . The experiments are compatible with the concept that the trapping of a single interstitial leads to the formation of 〈110〉-mixed dumbbells and the trapping of a second interstitial leads to a displacement of the Co impurity into the 〈100〉-direction.

Ion beam analysis of defect trapping

Channeling measurements using medium energy ions (e.g. 1 MeV He +) have been used to determine the positions of solute atoms which are displaced from lattice sites by the trapping of vacancies and self-interstitial atoms. In this way, some simple defect trapping configurations have been identified in fcc metals. One of these is the mixed dumbbell (created when a self-interstitial is trapped by a small solute atom), consisting of a host atom and solute atom stradding a normal lattice site. Another is the tetravacancy-solute atom complex, consisting of four nearest neighbour vacancies surrounding a solute atom displaced into the tetrahedral interstitial site. In addition, from detailed analyses of displacements into different crystallographic channels as a function of irradiation fluence and annealing temperature, the evolution of a variety of defect complexes containing self-interstitials or vacancies has been studied in Al, Cu, Ni, Fe, and Mg crystals. Information from channeling analyses will be compared with data obtained from measurements of electrical resistivity, Mössbauer effect, perturbed angular correlation, extended X-ray absorption fine structure, muon precession, positron annihilation and internal friction. The advantages of the different methods will be discussed.

Observation of a 〈100〉 mixed dumbbell at181HF in tungsten

TDPAC measurements were carried out in Tungsten foils and single crystals using implanted181Hf as a probe nucleus. After proton irradiation at 25 K the trapping of a defect at the Hf probe was observed, which lead to a quadrupole interaction frequency of νQ=354(5) MHz. The defect could be identified as a W self interstitial forming a 〈100〉 mixed dumbbell with a Hf impurity atom.

Investigation of radiation induced defect impurity complexes in aluminium alloys by channeling A critical analysis by computer simulation

The flux distributions of channeled He + ions in Al and their development with penetration depth are calculated for the major axial and planar directions using Monte Carlo simulations. A strong depth oscillation of the flux in the channel center is observed in the near surface region indicating the statistical nonequilibrium of the flux. The Monte Carlo program is applied to evaluate published yields measured in different directions (〈100〉, 〈110〉, 〈111〉, {100}, {111}) of He + irradiated Al alloys. It is shown that the solute atoms Mn, Cu, Zn, Ge, and Ag which react with irradiation induced self-intersitials are displaced from their lattice site into the 〈100〉 or 〈111〉 direction. The distance of the displaced atoms to the octahedral interstitial site is found to be less than 0.1 nm. The displacement of the solute atom in the 〈100〉 direction agrees quite well with published analytically determined values. A decision which kind of the 〈100〉 or 〈111〉 mixed dumbbell configuration does exist is not possible. It requires the knowledge of the correct mixed dumbbell concentration.

Extended x-ray-absorption fine structure of Ag impurity atoms in electron-irradiated aluminum

Extended x-ray-absorption fine-structure measurements were used to study radiation-induced defects for 400-ppm Ag impurity atoms in Al samples after irradiation with 2.8-MeV electrons at 95 K and after subsequent thermal-annealing treatment. During irradiation, Al interstitials are mobile and annihilate with vacancies or are trapped by the Ag impurity atoms. After irradiation about $\frac{1}{3}$ of the Ag atoms have captured an Al interstitial atom. A very pronounced new Ag-Al distance $R=2.35$ \AA{} is then observed which can be attributed to the Ag-Al distance in a mixed dumbbell that is formed. The observed distances suggest a $〈111〉$ orientation of the mixed dumbbell. During thermal annealing this new structure disappears at about 165 K, and another structure grows at 165 K and disappears at 185 K.

Defect complexes in ion-irradiated aluminum

Channeling measurements of solute atom positions were used to compare the concentrations of specific defect structures produced by ∼1 MeV He + and Kr + bombardment of Al. For both ion bombardments, the same major defect complexes were observed: in Al-0.1 at.% Ag crystals, AlAg 〈100〉 mixed dumbbells were created by the trapping of Al interstitials from 35–70 K; in Al-0.04 at.% Sn crystals, trivacancy-, tetravacancy-, and hexavacancy-Sn atom clusters were created by the trapping of vacancies from 180–220 K. From the rate of creation of AlAg mixed dumbbells during bombardment at 70 K (extrapolated to zero fluence), the production rate of free self-interstitials was determined directly, and was compared with the deposited nuclear energy distribution for the different ion bombardments. Similarly, the creation rates of the vacancy-Sn atom complexes were measured. The thermal stability and annihilation of the mixed dumbbells and vacancy complexes were also studied for the different ion bombardments.

Channeling studies of defects

Since channeled ions are scattered by any atoms which are displaced from lattice sites, channeling measurements can be used to study a variety of lattice defects. Three areas of investigation will be described: (1) dechanneling caused by multiple scattering from point defects, dislocations, thermal displacements, and disordered regions; (2) direct backscattering from amorphous zones; and (3) direct backscattering from displaced solute atoms. In topic (3) the following point defect-solute atom configurations have been identified: (a) 〈100〉 mixed dumbbells in fcc metals, in which a small solute atom and a host atom straddle a lattice site; and (b) vacancy complexes in fcc metals, in which 3, 4 or 6 vacancies surround a large solute atom which is at a position ( 1 6 , 1 6 , 1 6 )a 0, ( 1 4 , 1 4 , 1 4 )a 0 or ( 1 2 , 1 2 , 1 2 )a 0 , respectively.

Point defects-impurity interactions in copper

The effective charge on impurities is calculated considering the bound state, size effect and ionic configuration of the copper host matrix. It is found that both the impurity-interstitial capture radii and the vacancy-impurity binding energy are proportional to the magnitude of the effective charge on the impurities. The occurrence of mixed dumbbells is predicted on the grounds of the attractive interaction of each atom of the pair with the pseudo-vacancy left in between.

TUNNELING OF MIXED DUMBBELLS IN Al-Zn

Evidence for the caged mixed dumbbell configuration for the interstitial impurity complex is obtained from the polarization and annealing dependence of the ultrasonic diaelastic and paraelastic response in irradiated aluminum with zinc impurities. From the temperature dependence of the relaxation time, it can be deduced that the complex tunnels between equivalent configurations.

Interaction of Si, Ge, and Be solutes with vacancies and interstitials in Ni

The solute-vacancy and the solute-interstitial binding energies for Si, Ge, and Be solutes in Ni matrix have been calculated, using the results of an augmented-plane-wave calculation of the electronic structure of the solute and the solvent atoms. The electronic wave function of the solute is expressed in terms of the wave functions of the unperturbed host lattice. This allows the partial densities of states (DOS) of different angular momentum type at the solute site to be written in terms of those at the solvent atom site and their energy-dependent phase shifts. It is found that the $d$ electron DOS which is large and dominant at the Ni site is rather small at the solute site for all the solutes studied here. At the Si and Ge sites the $p$ DOS is dominant while at the Be site both $s$ and $p$ components are important. The excess charge density displaced by the solute and the potential associated with it show the oscillatory behavior. The $3s$ and $4s$ electrons of Si and Ge, respectively, form bound states below the bottom of the Ni conduction band. These states influence in a profound manner the interaction of these solutes with both vacancies and interstitials. No bound state is formed in the case of Be, where the scattering states in the conduction band are the sole contributors to the interaction energy. We have found that Ge, even though oversized, has a positive binding energy of 0.28 eV with the interstitial in the mixed dumbbell configuration. The undersized Si and Be form mixed dumbbells with binding energies of 0.90 and 0.58 eV, respectively. Contrary to usual expectations the vacancy-solute binding is calculated to be rather strong, 0.73 and 0.55 eV, respectively, for Si and Ge in the nearest-neighbor vacancy-solute configuration. The corresponding interaction with Be is found to be repulsive with a binding energy of -0.32 eV.

Molecular dynamics study of interstitial-solute interactions in irradiated alloys. I. Configuration, binding and induced migration of mixed dumbbells in Al-Zn alloys

The molecular dynamics technique has been used, in conjunction with the interionic potentials of Dagens et al. (1975), to study the stability, configuration, binding, and induced migration of mixed dumbbells in an irradiated Al-Zn alloy. For the purpose of comparisons, self-interstitials in pure Al were also investigated. The Al-Al and Al-Zn interactions were described by pair potentials which extended to ninth-neighbour distances. Both the self-interstitial dumbbell and the mixed dumbbell were found to be stable in the (100) configuration. The formation energy of the self-interstitial is 2.89 eV and the mixed-dumbbell binding energy is 0.38 eV. As a result of this strong binding, the threshold energy required to induce the migration of the mixed dumbbell is about 1.2 eV, which is significantly larger than the minimum energy of about 0.15 eV transferred to a self-interstitial to induce its jumps in pure Al. Caging motions of the mixed dumbbell were observed. The present computer-simulation results are compared with experimental measurements.

Channeling measurements of interstitial trapping in Al – 0.07 at% Cr crystals

The channneling method has been used to study the trapping of Al self-interstitials by Cr atoms in an Al – 0.07 at% Cr crystal. Al–Cr [Formula: see text] mixed dumbbell interstitials were created by this trapping during irradiation with 1 MeV He+ ions at 50 or 70 K. The mixed dumbbell configuration was stable up to 200 K. No evidence could be obtained for a change in this trapping configuration between 50 and 70 K.

Trapping of irradiation-induced defects by tin atoms in an Al-0.03 at.% Sn crystal

The backscattering-channeling method was used to investigate the trapping of irradiation-induced defects by Sn atoms in an Al-0.03 at.% Sn crystal. Since Sn atoms were not displaced appreciably from lattice sites by irradiation of the crystal at 35 or 70 K, or by subsequent annealing up to 160 K, it was concluded that mixed dumbbells were not formed by interstitial trapping in that temperature range. Further annealing up to 220 K produced a considerable displacement of Sn atoms from lattice sites. Channeling measurements along the $〈110〉$, $〈100〉$, and $〈111〉$ axes indicated that the displaced Sn atoms were located in tetrahedral and octahedral interstitial sites. These displacements were attributed to multiple vacancy trapping at Sn atoms, because further irradiation at 70 K reduced the apparent displaced fraction of Sn atoms more than did irradiation at 35 K. Annealing at temperatures above 240 K caused a change in the Sn atom positions, indicating an alteration of the configuration of vacancy clusters.