Neutron Irradiated Copper Single Crystals Research Articles

On slip band growth in neutron-irradiated copper single crystals

AbstractA transmission electron microscopy (TEM) study of the dislocation structure in slip bands at the Lüders band front in neutron-irradiated copper (Cu) single crystals reveals bands in various stages of development. This permits to specify the dislocation processes in particular for termination of slip band growth in the yield region. The important processes occurring during slip band growth are obstacle destruction by moving dislocations, formation of dynamic pile-ups, frequency of microscopic cross-slip and climb processes, formation of multipoles and of clusters of heavily jogged edge dipoles, which ultimately stop the local deformation in the cleared slip band channel. The formation of a dislocation group in the stress gradient within the Lüders band region is considered and it is shown that the group behaves like a single dislocation placed in the “center of gravity” of the quasi-stationary distribution which is the same as in the static case.

Slip-Band Formation and Dislocation Kinetics in the Stage I Deformation of Neutron-Irradiated Copper Single Crystals

The velocity of edge and screw dislocations moving in primary slip bands and the formation rate of primary slip bands were measured in stage I deformation of neutron-irradiated copper single crystals at different strain rates at room temperature using micro-cinematography and optical micrography. The average velocity of edge dislocations was larger at least by one order than that of screw ones, and that of screw dislocations did not depend so strongly on strain rate. The formation rate of primary slip bands was proportional to strain rate. From these results, it is concluded that (1) jogs produced on moving dislocations by cutting dislocation loops result in the difference in velocity between edge and screw dislocations and (2) the change in the density of mobile dislocations as well as velocity of dislocations is responsible for the change of plastic strain rate of a crystal.

The inhomogeneity of stress and plastic deformation in neutron-irradiated copper single crystals

The plastic deformation in stage I of neutron-irradiated copper single crystals in a uniaxial tensile test is studied at 77 K and room temperature from the view point of stress-inhomogeneity due to the constraint of grips. Primary slip bands appearing in clusters are examined on the two surfaces where the slip step height of a slip band is the maximum by using optical microscopy. Main results are as follows: 1. (i) in the specimen deformed at 77 K, the morphology of primary slip bands and the width of individual clusters of them on one surface are not the same as those on the opposite surface except around the middle part of the specimen; 2. (ii) in the specimen deformed at room temeprature, the difference mentioned in (i) is not found; 3. (iii) in both specimens, the growth of the clusters in width in the upper half of the specimen is larger in the direction of the upper grip than in the direction of the lower grip. This situation is reversed in the lower half. It is concluded that the heterogeneous plastic deformation of neutron-irradiated copper single crystals in a uniaxial tensile test is related with the stress-inhomogeneity caused not only by the constraint of the grips but also by the clustering of primary slip bands.

Velocities of Dislocation Groups in Very Thin Neutron-Irradiated Copper Single Crystals Measured by Slip Line Cinematography

Slip line development on very thin flat single crystals of neutron-irradiated Cu (thickness down to only 15 to 20 μm, orientation for single glide, yield region, room temperature) is recorded by high-speed cinematography during tensile deformation. In such very thin crystals glide dislocations on the slip plane must be arranged in a rather simple way. Drops in tensile load occuring during initiation of single slip lines at the Luders band front indicate that in the beginning of a slip line development dislocation groups traverse the whole glide plane in very short times. Evaluating the data measured for the slip line growth vs ≧ 10 cm/s is found for screw dislocations and ve ≧ vs for edge dislocations. For later stages on thin crystals and for all stages on thick crystals (≧ several 100 μm) slip line development is much slower and slip lines show many cross slip events which then appear to control the mean velocity of the dislocations. Die Gleitlinienentwicklung auf sehr dunnen, flachen Einkristallen aus neutronenbestrahltem Cu (Dicke bis hinab zu nur 15 bis 20 μm, Orientierung fur Einfachgleitung, Fliesbereich, Zimmertemperatur) wird wahrend der Zugverformung mit Hochfrequenz-Kinematographie aufgezeichnet. Gleitversetzungen mussen in derart dunnen Kristallen recht ubersichtlich auf der Gleitebene angeordnet sein. Einbruche im Lastschrieb, die bei der Entstehung einzelner Gleitlinien an der Ludersband-Front auftreten, deuten darauf hin, das die Versetzungsgruppen zu Beginn einer Gleitlinienentwicklung in sehr kurzen Zeiten die ganze Gleitebene uberstreichen. Durch Auswertung des gemessenen Gleitlinienwachstums wird vs ≧ 10 cm/s fur Schraubenversetzungen und ve ≧ vs fur Stufenversetzungen gefunden. In spateren Stadien auf dunnen Kristallen und in allen Stadien auf dicken Kristallen (≧ einige 100 μm) ist das Gleitlinienwachstum erheblich langsamer und die Gleitlinien weisen viele Quergleitstellen auf, welche dann die mittlere Versetzungsgeschwindigkeit bestimmen.

Mean velocity of edge and screw dislocation groups in neutron-irradiated copper single crystals

During deformation of n-irradiated Cu single crystals (n-dose 2.6 × 1018 cm−2) in the yield region at room temperature the development of slip bands on several surfaces around the crystal is recorded by high-speed cinematography. From microphotometric evaluation of the films (rate of growth of slip bands in length and in height) the mean velocity of dislocation groups, the distances of dislocations in the moving groups, and their average angle to the crystal surface is obtained. Velocities of screw (v⊙) and edge (v⊥) dislocation groups at different surfaces indicate an effect of the surface (“image forces”). An increase of deformation rate by a factor of 21 causes an increase of v⊙ and v⊥ by only a factor of six. Without surface effects v⊙/v⊥ ≈ 4. Wahrend der Verformung von n-bestrahlten Cu-Einkristallen (n-Dosis 2,6 × 1018 cm−2) im Fliesbereich bei Raumtemperatur wird die Entwicklung von Gleitbandern auf mehreren Flachen rund um den Kristall mit Hochfrequenz-Kinematographie registriert. Die mikrophotometrische Auswertung der Filme (Wachstumsgeschwindigkeit der Gleitbander in die Lange und Hohe) ergibt die mittlere Geschwindigkeit der Versetzungsgruppen, die Versetzungsabstande in bewegten Gruppen und ihren mittleren Winkel gegen die Kristalloberflache. Die Geschwindigkeiten von Schrauben- und Stufenversetzungsgruppen (v⊙ bzw. v⊥) lassen einen Einflus der Oberflache („Bildkrafte”) erkennen. Eine Zunahme der Dehngeschwindigkeit um den Faktor 21 hat eine Zunahme von v⊙ und v⊥ nur um den Faktor sechs zur Folge. Ohne Oberflacheneffekt ist v⊙/v⊥ ≈ 4.

Study of slip band development on neutron-irradiated copper single crystals by high speed cinematography

Microcinematography using a high speed film camera was applied in studying slip band development on n-irradiated Cu crystals during deformation in the yield region at room temperature. Particulars of taking the films and evaluating them photometrically are reported and limits of resloution are discussed. Measured quantities taken from the films ara the formation times of slip band clusters in the Lüders band, of single slip bands within clusters, and of slip lamellae within slip bands, further the characteristic times for “microscopic” and macroscopic cross slip, as well as the growth rate in length of slip bands. The measured data suggest that in addition to dislocation cutting through irradiation produced obstacles and cross slip processes the local constraints and work hardening play an important part in initiation, development, and termination of slip in the bands. Conclusions concerning the active crystal length and the thermal activation analysis are discussed.

Study of slip band development on neutron-irradiated copper single crystals by high speed cinematography

Study of slip band development on neutron-irradiated copper single crystals by high speed cinematography

Ultrasonic Measurement of the Nonlinearity Parameters of Copper Single Crystals

The nonlinearity parameters, which are combinations of third-order elastic constants, of neutron-irradiated copper single crystals were determined at room temperature by measuring quantitatively the harmonic distortion of pulsed MHz ultrasonic waves propagating in three crystallographic directions. For this purpose, a capacitive detector was used with which ultrasonic displacement amplitudes of the order of ${10}^{\ensuremath{-}10}$ cm can be detected and measured absolutely. Using the nonlinearity parameters in combination with other data, a complete set of third-order elastic constants for copper is calculated. The experiments represent a new technique for determining third-order elastic constants which is of special interest for measurements on easily deformed metal crystals.

The strengthening mechanism in neutron irradiated copper single crystals after mild annealing

The thermally activated rate controlling mechanism for slip in neutron irradiated copper single crystals given post-irradiation annealing at 306°C has been investigated. Measurements are made of the temperature dependence of the flow stress at constant strain rate, and the strain rate dependence of the flow stress at constant temperature. The activation enthalpy for slip is determined as a function of effective stress, and the results indicate that H 0, the enthalpy at zero effective stress, is independent of the annealing at 306°C. The stress dependence of both the activation enthalpy and the activation volume in the post-irradiation annealed crystals is in agreement with Fleischer's theory for strengthening by tetragonal distortions. A low temperature athermal deformation process is observed in these crystals, and this observation helps to explain some of the previous conclusions regarding the deformation mechanism in post-irradiation annealed crystals. It is concluded that the post-irradiation annealing at 306°C does not change the thermally activated rate controlling slip mechanism. In addition, the effective obstacle size remains constant, independent of the annealing.

Deformation of neutron-irradiated copper single crystals

Abstract The deformation of neutron-irradiated copper single crystals has been studied by transmission electron microscopy techniques. The width of the defect-free channels formed by the passage of dislocations has been measured as a function of temperature, dose and strain, in sections cut normal to the primary glide plane. The width and spacing of the channels have also been compared with surface replicas. Sections parallel to the primary glide plane have also been examined to provide details of the dislocation structure within a channel. The formation and development of the channels are discussed and the destruction of loops by dislocations is examined. The deformed state of neutron-irradiated crystals is compared with that of unirradiated crystals.

Stress relaxation in neutron irradiated copper single crystals

The thermally activated slip mechanism in neutron irradiated copper single crystals has been investigated with stress relaxation measurements from 77 to 420°K. The stress dependence of the strain rate at constant temperature and the temperature dependence of the flow stress at constant strain rate have been established. Using these two quantities, the activation enthalpy and activation volume are calculated as a function of effective stress. The experimental observations of these activation parameters are in good agreement with the theoretical stress dependencies predicted by the Fleischer theory for strengthening by tetragonal distortions. An experimental force-distance curve for the dislocation-defect interaction responsible for neutron irradiation strengthening is also in excellent agreement with Fleischer's theory. The results indicate that the thermally activated, rate controlling mechanism for slip in these crystals can be expressed entirely through the relationship, γ ̇ = γ ̇ 0 exp − H 0 kT [1 − ( τ ∗ τ 0 ∗ ) 1 2 ] 2 , where γ is the strain rate, γ ̇ 0 a constant, H 0 (= 3.0 eV) the activation enthalpy at zero effective stress, τ ∗ the effective stress, γ ̇ 0 the effective stress at 0°K, and kT has the usual meaning.

The correlation between the critical shear stress of neutron irradiated copper single crystals and the density of defect clusters

Abstract An attempt has been made to determine experimentally the relationship between the density of defect clusters, as observed by transmission electron microscopy, and the critical shear stress of single crystals during the annealing of neutron irradiated copper. Single crystals and foil specimens of the same purity (99·999%) were irradiated together for the same dose (2·5 × 1018 f.n.cm−2) and examined after annealing for various times at 275°, 306° and 336°c. It was found that a single linear relationship existed between the critical shear stress at 4·2°k and the square root of the density of clusters less than 50 Å in diameter after anneals at all of the three temperatures. For the larger clusters, which are thought to be interstitial loops, linear relationships were not obtained and the results for the three annealing temperatures did not coincide. This work suggests that irradiation hardening is almost entirely due to the small vacancy clusters and that the average value of the resistance F max of each cluster is not less than 1·25 × 10−4 dynes. It is also concluded that although clusters of different size are present they all have approximately the same F max.

Some Notes on the Strengthening Mechanism in Neutron Irradiated Copper Single Crystals

AbstractDiscussions are presented in some of the controversial areas regarding the interpretation of the strengthening mechanism in neutron irradiated copper single crystals. The specific topics that are discussed include the following: the correlation of cross‐head speed changes to strain rate changes, the strain rate dependence of the flow stress, the temperature dependence of the pre‐exponential factor, the free energy and the enthalpy of a activation, the defect and obstacle size spectrum, and the nature of the force‐distance behavior for the interaction of mobile dislocations with irradiation produced obstacles. It is shown that many of the recent arguments made against our previously published explanation of the strengthening mechanism can be readily explained without changing our interpretation.

On the Strengthening Mechanism in Neutron Irradiated Copper Single Crystals. II. Analysis of the Thermally Activated Processes Critical Comments on the Preceding Paper of T. J. Koppenaal and R. J. Arsenault

AbstractKoppenaal's and Arsenault's analysis of the thermally activated glide processes in neutron irradiated copper is discussed and compared with a similar investigation of the present authors. It is shown that Koppenaal and Arsenault use a number of very restrictive and not very realistic assumptions, e.g. regarding the behaviour of the dislocations and the nature of the dislocation obstacles, which are not necessary in our investigations. Koppenaal's and Arsenault's arguments against our analysis can easily be refuted.

On the Strengthening Mechanism in Neutron Irradiated Copper Single Crystals. I. On Experiments Concerning Strain Rate Changes Critical Comments on the Preceding Paper of T. J. Koppenaal and R. J. Arsenault

AbstractStrain rate changes are used for analysing the flow stress of n‐irradiated copper crystals and lead to the following conclusions: a) The “active crystal length”, i. e. the number of simultaneously active slip planes, increases with the strain rate \documentclass{article}\pagestyle{empty}\begin{document}$\dot \gamma $\end{document}, resulting in \documentclass{article}\pagestyle{empty}\begin{document}$\dot \gamma $\end{document} not being proportional to ⋖ (cross‐head speed) [1]. b) The critical shear stress (css) varies with ⋖ more rapidly than is expected from theory [2]. In the preceding paper [3] arguments are advanced against both of these statements. All of these arguments will be invalidated. The proportionality \documentclass{article}\pagestyle{empty}\begin{document}$\dot \gamma $\end{document} ∼ ⋖ is shown to represent a rather special case from an atomic point of view. By far more general is a non‐proportionality \documentclass{article}\pagestyle{empty}\begin{document}$\dot \gamma $\end{document} ≁ ⋖. Taking this into accont one succeeds in describing straightforwardly the results of b). New experiments supporting our former statements are going to be reported. All conclusions drawn previously [4, 5, 6] on the strengthening mechanism in copper and based on a) and b) can be fully maintained [7].

A rate controlling mechanism for slip in neutron irradiated copper single crystals

Abstract The stress dependence of the activation energy, H, and the activation volume, ν∗, for slip in neutron irradiated (8 × 1018 nvt) copper single crystals has been determined by tensile and creep measurements using the Conrad and Wiedersich relationships. The experimental stress dependences of both H and ν∗ are in excellent agreement with that predicted by Fleischer's theory for strengthening by tetragonal distortions. A number of different correlations indicates that slip in these irradiated crystals is regulated by a single rate controlling mechanism. The activation energy for slip was found to be temperature independent. The value of this activation energy at zero effective stress is 3·0±0·5 eV. We conclude that the rate controlling mechanism for slip in these crystals is that given by Fleischer's theory. The tetragonality producing the strengthening is thought to arise from the small vacancy loops found in room temperature irradiated copper.

‘Microstrain’ in neutron irradiated copper crystals

Abstract It has been shown by a sensitive parallel plate condenser technique that no deformation (> 1 × 10−6 strain) occurs in neutron irradiated (2.5 × 1018 f. n. cm−2) copper single crystals at stresses lower than the ‘critical’ shear stress at the appropriate strain rate. When the critical stress is reached the deformation occurs entirely by the formation of prominent slip lines, there being no sign of fine slip, viz. the limited movement of dislocations on a large number of slip planes. This result supports the model of slip in neutron irradiated metals proposed by Makin and Sharp and is contrary to the large microstrain observed by Koppenaal in bend tests.

Neutron irradiation strengthening in copper single crystals

Abstract The temperature and strain rate dependence of the flow stress have been measured from 4·2°K to 373°K in neutron-irradiated copper single crystals as a function of neutron dose and solute additions. Between 77°K and 373°K solutes have very little effect on the flow stress and its temperature dependence. At 4·2°K a large amount of solute, 7–14 at. %, lowers the flow stress of pure copper crystals. From these measurements an activation energy and activation volume have been calculated. Both are solute independent and are analysed on the basis of a stress dependence, rather than a temperature dependence. It is thus shown that the results can be explained by assuming a single-valued energy for the thermally activated deformation process, rather than by assuming an obstacle size spectrum. The experimental results are shown to be in rather good agreement with Fleischer's strengthening theory based upon tetragonal distortions.

Microstrain Yield Stress in Neutron-Irradiated Copper Single Crystals

τ0, the stress necessary to produce a plastic strain of 2×10−6, has been measured with the use of electrical resistance strain gauges in neutron-irradiated copper single crystals as a function of neutron dose (∼1016 to 1020 neutrons/cm2) and testing temperature (77° and 300°K). τ0 increases from about 0.3 kg/mm2 for ∼1016 neutrons/cm2 to over 5 kg/mm2 for ∼1020 neutrons/cm2; in annealed copper crystals, τ0 is ∼0.02 kg/mm2 (previously determined by other researchers). At all neutron doses, τ0 is about 75% of the macroscopic flow stress. τ0 is observed to increase with the cube root of the neutron dose; the macroscopic flow stress shows the same dose dependence. The results are explained on the basis of dislocation generation and obstacle cutting mechanisms controlling the yielding. These mechanisms are thought to be simultaneously operative.

Slip Line Pattern and Work‐Hardening of Neutron Irradiated Copper Single Crystals

AbstractThe development of the slip line pattern during deformation of neutron irradiated copper single crystals is investigated by electron microscopy at an intermediate neutron dose (5 × 1017 n/cm2). At such a neutron dose, according to the stress‐strain curves, the work‐hardening behaviour is rather different from that at low or at high neutron doses. Using a selected area replica technique, specific areas of the crystal surface are observed up to seven times after successive deformation steps. The numerous stages and substages of the stress‐strain curve are accompained by differences in the arrangement of the slip traces as well as by changes of the characteristic properties of individual slip traces. A tentative interpretation of work‐hardening in the investigated dose range can be based on these results.