The exact solution of the diffusion trapping model of defect profiling with variable energy positrons

We report an exact analytical solution of so-called positron diffusion trapping model. This model have been widely used for the treatment of the experimental data for defect profiling of the adjoin surface layer using the variable energy positron (VEP) beam technique. However, up to now this model could be treated only numerically with so-called VEPFIT program. The explicit form of the solutions is obtained for the realistic cases when defect profile is described by a discreet step-like function and continuous exponential-like function. Our solutions allow to derive the analytical expressions for typical positron annihilation characteristics including the positron lifetime spectrum. Latter quantity could be measured using the pulsed, slow positron beam. Our analytical results are in good coincidence with both the VEPFIT numerics and experimental data. The presented solutions are easily generalizable for defect profiles of other shapes and can be well used for much more precise treatment of above experimental data.     

Hamiltonian formulation for the positron trapping model

Summary A Hamiltonian formulation is used to build up an adequate Hamiltonian for the positron trapping model. The number of positrons annihilated in the free state,n _f, or the trapped one,n _v, are considered canonical conjugate variables; this point of view provides a route to propose a Hamiltonian which leads to the previously proposed phenomenological master equations.

---

Riassunto Si usa una formulazione hamiltoniana per elaborare un'hamiltoniana adeguata per il modello a trappola dei positroni. Il numero di positroni annichilati nello stato libero,n _f, o in quello intrappolato,n _v, è considerato come variabili coniugate canoniche; in questo senso si fornisce una via per proporre un'hamiltoniana che porti alle equazioni principali fenomenologiche proposte precedentemente.

---

Резюме Гамильтонова формулировка используется для конструирования адекватного Гамильтониана для модели захвата позитрона. Число аннигилированных позитронов в свободном состоянии,n _f, или число захваченных позитронов,n _v, рассматриваются как канонически сопряженные переменные. Этот подход приводит к Гамильтониану. Который дает ранее предположенные феноменологические ?управляющие? уравнения.

     

The annealing behavior of implanted nitrogen in fcc stainless steel

Post-implantation annealing of N-implanted 304 stainless steel at 400 °C has been investigated by conversion electron Mössbauer spectroscopy, X-ray diffraction and Auger electron spectroscopy. After a 1 h anneal, the near complete dissolution of the as-implanted Fe₂N-like nitride phase results in a 9 at.% N fcc solid-solution phase. After the final anneal (64 h), N has diffused to a depth of about 2 m and remains in solid solution with an average content of 4 at.%. An average N diffusion coefficient at 400 °C is estimated to be 10^-12-10^-14 cm²/s, depending on anneal time, too small to explain the deep penetration observed in high-flux, high-dose N-implanted stainless steel. The present results provide additional evidence for beam controlled N migration where Cr plays an important role.     

Magnetically induced immiscibility in the Ising model of FeCr stainless steel

The iron-chromium alloy system has an unexplained anomaly: although there is a broad miscibility gap it appears to be favorable for chromium to dissolve in iron. This is consistent with ab initio calculation, but no simpler physically intuitive picture has been presented. Here it is shown that the Ising model, based on the bcc lattice with antiferromagnetic and ferromagnetic species, has the potential to exhibit similar behavior, with a skew miscibility gap arising from the solubility of antiferromagnetic species on nonadjacent sites. Essential characteristics of stainless steel (high Cr solubility and surface segregation) are correctly reproduced. Under some conditions, magnetization increases with temperature. The equilibrium miscibility gap due to mixed magnetism and segregation-driven positive dM/dT are fundamental features of the bcc Ising model itself, not just FeCr.     

Temperature characteristics of positron trapping at defects in electron-irradiated silicon

Positron-annihilation lifetime and Doppler-broadening measurements are used to investigate defects in silicon irradiated at 373 K with 6 MeV electrons to a dose of 1×l0¹⁹e/cm². In the unirradiated silicon sample (p type) a temperature-independent behaviour of the bulk-lifetime is observed in the temperature interval 110–500 K with a constant value of 220±1 ps. The slight effect observed on the S-parameter evolution is explained taking into account the thermal expansion of the lattice. The lifetime results obtained at 80 K and at 300 K after isochronal annealing as well as the behaviour of the intensity of the second lifetime componentI ₂ during lifetime measurements below the irradiation temperature in the irradiated silicon sample (n type), clearly indicate the temperature dependent characteristics of the positron trapping cross section _t(T) T ⁿ withn= –1.905±0.016. From isochronal annealing results, an annealing stage is observed in which di-vacancies agglomerate into quadri-vacancies. The mean positron lifetime in those quadri-vacancies is 350 ps.A.B.O.S., on leave from University of Kinshasa, Zaïre     

Muon diffusion and trapping by defects in electron-irradiated Nb and Ta

The transverse spin relaxation of positive muons ( ⁺) has been measured on Nb and Ta after irradiation with 3 MeV electrons. In high-purity Nb the ⁺ diffusivity derived from the trapping at irradiation-induced defects above 100 K is explained in terms of adiabatic hopping. At lower temperatures there is evidence for the dominating processes to be fewphonon incoherent tunnelling and coherent hopping. Annealing results in the formation of new defects capable of trapping the ⁺. In Ta at least two types of irradiation-induced defects capable of trapping ⁺ survive up to annealing temperatures of 400 K.     

The influence of implanted yttrium on the cyclic oxidation behaviour of 304 stainless steel

High-temperature alloys are frequently used in power plants, gasification systems, petrochemical industry, combustion processes and in aerospace applications. Depending on the application, materials are subjected to corrosive atmospheres and thermal cycling. In the present work, thermal cycling was carried out in order to study the influence of implanted yttrium on the oxide scale adherence on 304 steel specimens oxidised in air at 1273 K. In situ X-ray diffraction indicates that the oxides formed at 1273 K are different on blank specimens compared to implanted specimens. Glancing angle XRD allows to analyse the oxide scale composition after cooling to room temperature.Experimental results show that yttrium implantation at a nominal dose of 10¹⁷ ions cm⁻² does not improve significantly the cyclic oxidation behaviour of the austenitic AISI 304 steel. However, it appears that yttrium implantation remarkably enhance the oxidation resistance during isothermal oxidation. It reduces the transient oxidation stage and the parabolic oxidation rate constant by one order of magnitude.     

A positron trapping study of non-equilibrium defects created by the hcp ∌ fcc phase change in cobalt

Measurements of annihilation lineshape parameter S show that the hcp ? fcc phase change in cobalt creates a non-equilibrium defect population capable of trapping positrons. These defects can be removed by annealing above 870 K. This effect explains the discontinuous behaviour of S(T) at 690 K, which had been attributed to a lattice-structure dependence of free positron annihilation.     

Behavior of structure defects and hydrogen in neutron-irradiated stainless steels studied by positron annihilation method

Measurements of angular distributions of annihilation photons are applied to investigating structural defects and hydrogen behavior in annealed, plastically deformed, and irradiated stainless steels. It is determined that the whole cycle of investigations performed by positron diagnostics helped in tracing the formation and evolution of the defect structure and hydrogen behavior in different kinds of steels being subjected to complex physical–mechanical influences such as plastic deformation, hydrogenation and irradiation by fission neutrons. The high sensitivity of the electron–positron annihilation method allowed understanding even of details of the changes of the crystalline structure of multi-component materials.     

Microstructure change in deuterium implanted CLAM steel induced by electron irradiation

As Reduced Activation Ferritic/Martensitic (RAFM) steel is considered the primary candidate for use as a structural material in fusion power reactors,many countries are developing different kinds of RAFM.China is developing new CLAM (China Low Activation Martensitic) steel.The study investigates microstructural changes in CLAM steel implanted with deuterium ions induced by 1250 keV electron irradiation from R.T.to 873 K,and observes both the growth and shrinkage of the defect clusters produced by deuterium ...     

He离子注入ZnO中缺陷形成的慢正电子束研究

在ZnO单晶样品中注入了能量为20—100keV、总剂量为4.4×10¹⁵cm^-2的He离子.利用基于慢正电子束的多普勒展宽测量研究了离子注入产生的缺陷.结果表明，He离子注入ZnO产生了双空位或更大的空位团.在400℃以下退火后，He开始填充到这些空位团里面，造成空位团的有效体积减少.经过400℃以上升温退火后，这些空位团的尺寸开始增大，但由于有少量的He仍然占据在空位团内，因此直到800℃这些空位团仍保持稳定.高于800℃退火后，由于He的脱附，留下的空位团 关键词： 慢正电子束 ZnO 离子注入 缺陷     

Influence of escape from traps on parameters in the positron trapping model

Positron detrapping may explain weak trapping in some metals, and it can affect deduced vacancy formation energies. However, it appears that the recently observed additional temperature dependence of the positron capture rate cannot be attributed to escape from traps.     

Investigation of defect structures in deuteron irradiated and deformed stainless steel 316 by positron annihilation

Abstract

Deuteron-irradiated and deformed stainless steel specimens were investigated by positron lifetime and Doppler broadening measurements. The evolution of the defect structures was studied as a function of the isochronal annealing temperature and for various degrees of deformation. A different behaviour was observed for deformed and irradiated stainless steel specimens. Evidence for vacancy clusters was found in the deuteron-irradiated steel. These clusters disappear after annealing around 900 K.     

The study of defects in crystals by positron annihilation

The study of defects in crystals through their interaction with thermalized positrons is usually based on the trapping model. The theoretical foundation of the trapping model, based on the theory of diffusion-limited reactions, is reviewed with particular emphasis on short-range interactions between positrons and trapping defects. For this case the analytical properties of the trapping model are developed in some detail, including the effects of the initial pair distribution on the trapping rate, the effects of detrapping, and the effects associated with more than one type of trap. The assumptions that are usually made in determinations of monovacancy formation enthalpies from positron annihilation experiments are critically discussed. The need for additional experiments capable of providing information on the temperature dependence of the various parameters involved is, stressed. As an illustration we treat in detail monovacancies with finite detrapping rate plus divacancies, both in thermal equilibrium. In the final section a few remarks are added on cases with long-range interactions between positrons and traps, such as electrically charged point-defects in insulators or semiconductors, and dislocations.     

Radiation defects induced by helium implantation in gold-based alloys investigated by positron annihilation spectroscopy

The formation of gas bubbles in metallic materials may result in drastic degradation of in-service properties. In order to investigate this effect in high density and medium-low melting temperature (T _M) alloys, positron annihilation spectroscopy measurements were performed on helium-implanted gold–silver solid solutions after isochronal annealing treatments. Three recovery stages are observed, attributed to the migration and elimination of defects not stabilized by helium atoms, helium bubble nucleation and bubble growth. Similarities with other metals are found for the recovery stages involving bubble nucleation and growth processes. Lifetime measurements indicate that He implantation leads to the formation of small and over-pressurized bubbles that generate internal stresses in the material. A comprehensive picture is drawn for possible mechanisms of helium bubble evolution. Two values of activation energy (0.26 and 0.53 eV) are determined below and above 0.7T _M, respectively, from the variation of the helium bubble radius during the bubble growth stage. The migration and coalescence mechanism, which accounts for these very low activation energies, controls the helium bubble growth.     

Analysis of oxide formation induced by UV laser coloration of stainless steel

Laser-induced coloration on metal surfaces has important applications in product identification, enhancing styles and aesthetics. The color generation is the result of controlled surface oxidation during laser beam interaction with the metal surfaces. In this study, we aim to obtain in-depth understanding of the oxide formation process when an UV laser beam interacts with stainless steel in air. The oxide layer is analysed by means of optical microscopy, scanning electron microscopy (SEM) and time-of-flight secondary ion mass spectrometer (TOF-SIMS). TOF-SIMS results clearly show the formation of duplex oxide structures. The duplex structure includes an inner layer of Cr oxide solution and an outer layer of Fe oxide solution. The oxide layer thickness increased as the results of Fe diffusion to surface during multiple laser scanning passes.     

The study of native defects in as-grown GaAs by positron annihilation

A mono-energetic positron beam was applied for a study of native defects in GaAs. From measurements of Doppler broadening profiles and lifetime spectra of positrons, it was found that Ga-vacancies were introduced by Si-doping. On the other hand, for p-type GaAs, interstitial clusters were found to be introduced by Zn-doping. The observed species of defects are in agreement with those expected from the Fermi level.     

不锈钢折弯板裂纹Lamb波检测技术

金属弯板广泛应用于车辆、船舶、飞机等大型装备结构件中,折弯处易形成应力集中产生裂纹,直接影响构件的使用安全和寿命.该文开展了不锈钢弯板裂纹缺陷Lamb波检测技术研究,计算了钢板的频散曲线,优选3种不同频率的S0模态:0.25 MHz、0.5 MHz、1 MHz.利用COMSOL仿真软件建立频域仿真模型,模拟了Lamb波...