Wolfgang Schüle

Radiation enhanced diffusion in F.C.C. metals

Abstract Near surface and bulk radiation enhanced self-diffusion of Ni0.3 in nickel was measured after irradiations with 2 MeV electrons. In the temperature range between 550 and 800°K the bulk diffusion coefficient is DRad = 1.347 × 10−12 exp (-0.41/kT cm2/s) for a flux of 20 μA/cm2. The measured diffusion coefficients are at least two orders of magnitude larger than those predicted by theories based either on the one- or the two- interstitial model. This discrepancy between experiment and theory is resolved for the two-interstitial model by considering the interactions between sell-interstitials and vacancies during their life times. These interactions led to an effective migration energy of self-interstitials of EM eff , = 0.82 eV. which is smaller than EM = 1.0 eV. The experimental data can be described by DRad α2 n f(Kvell 1)1 2. Radiation enhanced diffusion data obtained in other laboratories for gold in gold. silver in silver, for copper and for gold in aluminium arc analysed and results analogous ...

The dependence of radiation enhanced diffusion on the high energy particle flux

Abstract Radiation enhanced ordering in copper-zinc alloys was measured in the temperature region between 50 and 160°C by means of electrical resistivity techniques using 2 MeV electrons from a Van de Graaff generator. It could be confirmed that the ordering rate during irradiation is determined by an interstitialcy diffusion mechanism. It was found that the activation migration energy of interstitials increases from 0.60 to 0.70 eV for electron fluxes decreasing from about 3.5 to 0.035 μA cm−2 due to an interaction between the irradiating particles and the lattice atoms, in agreement with results of measurements of radiation enhanced self-diffusion in pure metals.

Radiation-enhanced diffusion in nickel-10.6% chromium alloys

Results of investigations of the diffusion rate of nickel-10.6% chromium alloys after plastic deformation, after quenching from 700°C and from 1030°C, and during irradiation with 18 MeV protons and 1.85 MeV electrons are reported. The diffusion rate is measured by means of the electrical resistivity which increases with increasing degree of short range order. It was found that the characteristic temperature below which short range order develops is T t = 550°C. Below about 400°C the atomic mobilities of the component atoms of the alloy are so small that no further increase in the degree of short range order is found in due laboratory times. The activation energy for self-diffusion was determined after quenching from 700°C to Q SD = 2.88 eV. For the migration activation energy of vacancies a value of E 1V M = 1.18 eV was obtained after quenching from 1030°C. For the migration activation energies of interstitials and vacancies values of E 1I M = 1.04 eV and E IV M = 1.16 eV are derived from results of measurements of radiation enhanced diffusion, respectively. These values decrease with increasing high energy particle flux. It was further found that a vacancy diffusion mechanism is rate-determining during irradiation for the increase of the degree of short range order. Interstitials have to jump about 150 times more often than vacancies for the degree of short range order to increase by the same amount. The characteristic temperature for interstitial cluster formation is T t = 300°C. Above this temperature radiation-induced interstitials and vacancies annihilate mainly by pair recombination. Below this temperature interstitials also annihilate at sinks which are formed during irradiation so that the concentration of vacancies increases with irradiation time. Their migration activation energy is approximately obtained in a straight-forward way from the experimental data. Above about 380°C the radiation enhanced diffusion rate is surprisingly much smaller than the thermal diffusion rate. The quasi-dynamic vacancy concentration built up during irradiation is much smaller than the thermal vacancy concentration.

Radiation-enhanced diffusion due to interstitials and dynamic crowdions

Abstract It is shown from measurements of the radiation damage rate in copper and in gold that dynamic crowdions cause spontaneous annihilation of radiation-produced vacancies and interstitials during irradiation so that the initial production rate of interstitials and vacancies is decreased by orders of magnitude with respect to the initial damage rate. The number of replacement collision sequences is N = 40 000 in pure materials decreasing to N = 15 if under- or over-sized atoms are added. It is shown that dynamic crowdions cause tracer-diffusion and inter-diffusion, e.g. of silver in nickel and of nickel in silver, and that they are able to destroy order very effectively. Three-dimensionally migrating radiation-produced point defects cause micro-structural changes above the temperature range above which they are sufficiently mobile, e.g. above 125°C in nickel and above − 16°C in copper. There is no three-dimensionally migrating defect below these respective temperatures in nickel and copper contributing to diffusion.

On the validity of the one- and two-interstitial model

Abstract Experimental results are discussed, which are not in agreement with the predictions of the one-and of the simple two-interstital-model. From the experimental data a large recombination volume between vacancies and self-interstitials of the order of α = 105 is derived. With this feature the predictions of the extended TIM are in agreement with the experimental findings including also such ones, which have been claimed so far to be only in favour of the OIM.

On ordering kinetics in electron irradiated alloys: a reply

Abstract Abromeit and Poerschke measured radiation enhanced diffusion rates in alpha-brass which were much larger than those we obtained previously under similar irradiation conditions. They state that these discrepancies are due to the large impurity levels of our materials and that, consequently, the interpretation of our data can also be disregarded. They did not notice that i) the materials used in both laboratories were of similar purity and that, ii) the additional enhancement of radiation enhanced diffusion they were reporting is caused by dislocations introduced during mounting in well annealed specimens. This additional enhancement of diffusion is a kind of intrinsic phenomenon and has been carefully studied on alpha copper-aluminium alloys recently.

On the recovery stages in fcc materials

Abstract It is shown that the migration activation energy of vacancies in copper resulting from experiments performed in thermal equilibrium is E M IV = 1.06 eV. The same value was also obtained for recovery stage IV after quenching from high temperatures or after irradiation with high energy particles forty years ago. The activation energy obtained for the recovery stage III is the migration activation energy of interstitials E M II = 0.71 eV. Radiation-enhanced 63 Ni-diffusion in copper is above the stage III temperature region determined only by interstitials and below the stage III temperature region determined only by dynamic crowdions. Dynamic crowdions jump in pure materials about N = 40 000 times during their life time. In recovery stages I and II correlated interstitial—vacancy pairs annihilate. The activation energy for the annihilation of these pairs increases with increasing distance between correlated interstitials and vacancies. Correlated crowdion—vacancy pairs and crowdions annihilate in the recovery stages I D and I E , respectively, in materials in which crowdions are stable.

Dynamic crowdions, interstitials and vacancies in copper

Abstract We determined the increase of the electrical resistivity in copper, Be doped copper, and in gold during irradiation with 1.85 MeV electrons below the temperature corresponding to the stage III recovery region. From the analysis of these data by means of rate equations we are able to determine the variations of the concentrations of interstitials, vacancies and agglomerates of interstitials as a function of the irradiation time and of the irradiation temperature. The number of replacement collision sequences of dynamic crowdions is about N = 4.104 before they convert into stable interstitials in well annealed pure copper, in commercial copper, and in pure gold. This number decreases with beryllium additions and is about N = 15 in copper doped with 763 ppm beryllium. The rate of spontaneous annihilation of vacancies with dynamic crowdions during irradiation depends on the number of replacement collisions sequences. Thus the production rate of vacancies and interstitials decreases in pure materials ...

On the Fundamentals of Radiation Damage in FCC Materials, A Review

A short historical report is given on the formation of the one-interstitial model (OIM) which was introduced by F. Seitz and H. B. Huntington in the late fifties. In the early sixties J. F. Brinkman and A. Seeger suggested the two-interstitial model (TIM) after many new experimental and theoretical results became available and raised a continous discussion on the validity of the two models. A few of the many experimental results obtained on radiation damage in fcc metals and alloys over the last thirty-five years are discussed and it is shown that all these results only support the TIM. It could further be shown that the migration activation energies of point defects decrease with increasing high energy particle flux, that dynamic crowdions can change lattice sites 50,000 times before their energy is dissipated to the lattice, that the recombination volume a between self-interstitials and vacancies is one order of magnitude larger than assumed so far etc.. These and many other features of point defects are discussed and the extended version of the TIM, namely the modified two interstitial model (MTIM), is presented. It is further shown that the rate equations to calculate point defect concentrations built up during irradiation with high energy particles are powerful ways to understand and explain radiation damage. However, the advocates of the OIM in the past used only the steady state solutions of the rate equations which are only mathematical solutions and do not reflect physical reality. Correlated self-interstitial-vacancy pairs annihilate in recovery stages I and II and correlated crowdion-vacancy pairs annihilate in the broad recovery sub-stage I D in such materials in which crowdions are stable. Crowdions migrate in the tiny sub-recovery stage I E , self-interstitials in recovery stage III, and vacancies in recovery stage IV. The implications and importance of the application of the MTIM for the development of radiation resistant materials are outlined.

Vacancy Properties During Irradiation with High Energy Particles

Results of investigations of radiation enhanced diffusion on copper-15at% aluminum alloys are reported where the electron flux, the irradiation temperature, and the thickness d of the specimens are varied. The activation energy of ordering or of diffusion is Q i r r = 0.355 eV for an electron current density of 4.25 μA cm - 2 almost independent of d. Q i r r increases slightly with decreasing flux, and Q i r r = 0.377 eV is found for 0.04 μA cm - 2 and 0.1-mm-thick specimens. This behavior is in agreement with the assumptions that (1) the migration energy of vacancies E M 1 V decreases with increasing flux and (2) interstitials have to jump about 30 times more often than vacancies in order to change the degree of order by the same amount. It is further found that small sink concentrations cause an acceleration of the ordering rate rather than a decrease of this quantity through an increase of the mobility of the defects. In copper-aluminum alloys almost no sinks for point defects are formed during irradiation; thus defects annihilate mainly by pair recombination even at low irradiation temperatures in contrast to results obtained for many other alloys.