Astm stp 870 1985

EFFECTS OF RADIATION ON MATERIALS: TWELFTH INTERNATIONAL SYMPOSIUM Volume I A symposium sponsored by ASTM Committee E-10 on Nuclear Technology and Applications Williamsburg, VA, 18-20 June 1984 ASTM SPECIAL TECHNICAL PUBLICATION 870 F A Garner, Westinghouse Hanford Co and J S Perrin, Office of Nuclear Waste Isolation, editors ASTM Publication Code Number (PCN) 04-870000-35 1916 Race Street, Philadelphia, PA 19103 Library of Congress Cataloging-in-Pub!ication Data Effects of radiation on materials (ASTM STP; 870) Papers presented at the Twelfth International Symposium on the Effects of Radiation on Materials "ASTM publication code number (PCN) 04-870000-35." Includes bibliographies and index Materials—Effect of radiation on—Congresses I Garner, F A II Perrin, J S III ASTM Committee E-10 on Nuclear Technology and Applications IV International Symposium on Effects of Radiation on Materials (12th; 1984: Williamsburg, Va.) V Series: ASTM special technical publication; 870 TA418.6.E333 1985 620.1'1228 85-11257 ISBN 0-8031-0450-2 Copyright © by AMERICAN SOCIETY FOR T E S T I N G AND MATERIALS 1985 Library of Congress Catalog Card Number; 85-11257 NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication Printed in Baltimore, MD November 1985 Foreword The symposium on Effects of Radiation on Materials: Twelfth International Symposium contains papers presented at the Twelfth International Symposium on the Effects of Radiation on Materials The symposium was sponsored by ASTM Committee E-10 on Nuclear Technology and Applications J S Perrin, Office of Nuclear Waste Isolation, presided as chairman with F A Garner, Westinghouse Hanford Company, and J J Koziol, Combustion Engineering, Inc., as cochairmen J S Perrin and F A Garner are editors of this publication Related ASTM Publications Effects of Radiation on Materials (11th Conference), STP 782 (1982), 04-782000-35 Effects of Radiation on Materials (10th Conference), STP 725 (1981), 04-725000-35 Effects of Radiation on Structural Materials (9th Conference), STP 683 (1979), 04-683000-35 Effects of Radiation on Structure and Mechanical Properties of Metal, STP 529 (1973), 04-529000-35 A Note of Appreciation to Reviewers The quality of the papers that appear in this publication reflects not only the obvious efforts of the authors but also the unheralded, though essential, work of the reviewers On behalf of ASTM we acknowledge with appreciation their dedication to high professional standards and their sacrifice of time and effort ASTM Committee on Publications ASTM Editorial Staff Helen M Hoersch Janet R Schroeder Kathleen A Greene Bill Benzing Contents Overview IRRADIATION CREEP OF STRUCTURAL METALS In-Reactor Creep of Selected Ferritic Alloys—RAYMOND J PUIGH Evaluation of Ferritic Alloy Fe-lViCr-lMo After Neutron Irradiation: Irradiation Creep and Swelling—DAVID S GELLES AND RAYMOND J PUIGH 19 Influence of a Temperature Change on In-Reactor Creep— BRYAN A CHIN AND E ROBERT GILBERT 38 Non-Isothermal In-Reactor Creep of Nickel Alloys Inconel 706 and P E - — E ROBERT GILBERT AND BRYAN A CHIN 52 In-Pile Creep Strain and Failure of Cold-Worked Type 316 Titanium Pressurized Tubes—JEAN-LOUIS BOUTARD, ARLETTE MAILLARD, YVETTE CARTERET, VIVIANE LEVY, AND JEAN-MARIE BOYER Discussion 61 74 Critical Assessment of Low-Fluence Irradiation Creep Mechanisms— CHARLES H HENAGER, JR., AND EDWARD P SIMONEN 75 Irradiation-Creep-Induced Anisotropy in a/1 (110) Dislocation Populations—DAVID S GELLES 98 MiCROSTRUCTURAL DEVELOPMENT Effect of Irradiation Temperature on the Precipitation in Cold-Worked Titanium-Stabilized Type 316 Stainless Steel—DIDIER GILBON, LUCIEN LE NAOUR, CHRISTIAN RIVERA, AND HENRI LORANT 115 Microstructure of Irradiated Inconel 706 Fuel Pin Cladding— WALTER J S YANG AND BRUCE J MAKENAS 127 Microsegregation Observed in Fe-35.5Ni-7.5Cr Irradiated in EBR-II—HOWARD R BRAGER AND FRANK A GARNER 139 Transmission Electron Microscope Studies and Microhardness Testing of Irradiated Ferritic Steels—DEBORAH K H U L E T T A N D WILLIAM A JESSER 151 Phase Stability in Irradiated Alloys by Constrained Equilibrium Thermodynamics—JAMES PAUL HOLLOWAY AND J A M E S F STUBBINS 167 NEUTRON-INDUCED SWELLING Swelling of Austenitic Iron-Nickel-Chromium Ternary Alloys During Fast Neutron Irradiation—FRANK A GARNER A N D HOWARD R BRAGER 187 Swelling of 20% Cold-Worked Type 316 Stainless Steel Fuel Pin Cladding and D u c t s — B R U C E J MAKENAS 202 Swelling of AISI Type 304L Stainless Steel in Response to Simultaneous Variations in Stress and Displacement Rate— DOUGLAS L PORTER AND FRANK A, GARNER 212 Some Observations on the Effect of Stress on Irradiation-Induced Swelling in AISI Type 316 Stainless Steel—THOR LAURITZEN, WALTER L BELL, JERRY M ROSA, AND SAM VAIDYANATHAN 221 Swelling of Microstructure of Neutron-Irradiated Titanium-Modified Type 316 Stainless S t e e l — J E A N LOUIS SERAN, LUCIEN LE NAOUR, PIERRE GROSJEAN, MARIE PIERRE HUGON, YVETTE CARTERET, AND ARLETTE MAILLARD 233 Role of Dislocations, Dislocation Walls, and Grain Boundaries in Void Formation During Early Stages of Fast Neutron Irradiation— ANDY HORSEWELL AND BACHU N SINGH Discussion 248 260 C H A R G E D PARTICLE IRRADIATION Influence of Applied Stress on Swelling Behavior in Type 304 Stainless Steel —NAOHIRO IGATA, YUTAKA KOHNO, HIDEO TSUNAKAWA, AND TATSUHIKO FUJIHIRA 265 Evolution of Cavity Microstructure in Ion-Irradiated Type 316 Stainless Steel and Fe-20Ni-15Cr Alloy—AKIRA KOHYAMA, BEN A LOOMIS, GUY AYRAULT, AND NAOHIRO IGATA Discussion 277 296 Experimental Investigation of the Effect of Injected Interstitials on Void Formation—BUCKY B A D G E R , JR., D O N A L D L PLUMTON, STEVEN J ZINKLE, ROBERT L SINDELAR, GERALD L KULCINSKI, RICHARD A DODD, AND WILHELM G WOLFER 297 Influence of Helium on Swelling of Steels—VIVIANE LEVY, DIDIER GILBON, AND CHRISTIAN RIVERA 317 Comparison of Depth-Dependent Microstructures of Ion-Irradiated Type 316 Stainless Steels—ROBERT L SINDELAR, R ARTHUR DODD, AND GERALD L KULCINSKI 330 Experimental Determination of the Critical Cavity Radius in Fe-lOCr for Ion Irradiation—LINDA L H O R T O N A N D LOUIS K MANSUR Discussion 344 357 Comparison of Thermal and Irradiated Behavior of High-Strength, High-Conductivity Copper Alloys—STEVEN J ZINKLE, R ARTHUR DODD, AND GERALD L KULCINSKI 363 Ion Bombardment Damage in a Modified Fe-9Cr-lMo Steel— KENNETH FARRELL AND EAL H LEE 383 Helium and Displacement Damage Produced by 600 MeV Proton Beams in High Purity Aluminum—DIDIER GAVILLET, ROLF G O T T H A R D T , JEAN-LUC MARTIN, SHERRON L GREEN, WALTER V GREEN, AND MAXIMO VICTORIA 394 Direct Observation of Cascade Defect Formation at Low Temperatures in Ion-Irradiated Metals—TAKEO M U R O G A , K O I C H I HIROOKA, AND SHIORI ISHINO Solute Segregation and Void Formation on Grain Boundaries in Electron-Irradiated Type 316 Stainless Steel—SOMEi OHNUKi, HEISHICHIRO TAKAHASHI, AND TARO TAKEYAMA 407 419 520 EFFECTS OF RADIATION ON MATERIALS variable that determines the height of the nucleation barrier is the segregation parameter As shown in Fig 3, the nucleation barrier falls rapidly with an increasing segregation parameter Since nucleation is appreciable only when the barrier falls below 50 kT, it is obvious that without over-segregation, voids will not nucleate The previous results on void nucleation that reported appreciable nucleation rates [8-101 are undoubtedly due to their choice of an unjustifiably low surface energy for essentially pure elements (For ferrous and nickel alloys the "standard" choice has been J/m^ that is approximately a factor of lower than the generally accepted measured values of a clean, flat surface.) We have suggested previously that, contrary to intuition, voids with a higher bias for interstitials are more susceptible to void nucleation [7] The basis for the prediction was the nodal line analysis that shows a smaller critical size for a higher ratio of Z°/Zv°, with other materials parameters being equal [7] This prediction is confirmed in the fluctuation analysis by the nucleation barrier shown in Fig The physical origin of such unexpected results lies in the fact that in dilute alloys the interstitials are primarily responsible for nonequilibrium segregation Inasmuch as nonequilibrium segregation is the cause of enhanced nucleation, a higher bias for interstitials should facilitate such a mechanism and, hence, nucleation as well For bare voids, theoretical considerations indeed predict a stronger bias for interstitials [7(5] Thus, copious nucleation can be rationalized with a modest value of the segregation parameter without invoking an unreasonably low surface energy at all [5-70] Both results of the stabihty analysis [7] and fluctuation analysis demon- = Tm T = 0.25 S, = I0« p=:::~l—_^ _^ \r"^\~~~"^"\ 00 OD \ ,(SP) c *L_ kT \ \ \\ \ 7° \ z!" \ \Z°—=\' \ Z° - ^ = 1.0 VZ° 10 1 1.2 1.3 \ 1.4 \ 1 1.6 1.7 1.5 X Segregation Parameter FIG 3—Nucleation barrier for different values of segregation parameter and bias ratio CHEN AND TAIWO ON NUCLEATION OF VOIDS 521 strated that spontaneous nucleation operates at sufficiently strong segregation The nodal lines in Fig become tangent to each other at X = 1.73, while the nucleation barrier in Fig vanishes at the corresponding value Three regimes can be delineated, as shown in Fig 4, that are designated as (a) spontaneous nucleation, (b) homogeneous nucleation, and (c) no nucleation The range of X over which the three regimes are encompassed is relatively narrow [7] [ l - (e - 1) {j~- ~ l); ij = ^min < X < X„ (•-'/ ^ ) '} is the smaller of X and y For reasonable values of the interaction parameter, r, both the maximum above which spontaneous nucleation operates and the minimum below which nucleation is suppressed are of the order of unity Thus, the segregation parameter must be regarded as the most sensitive materials parameter that influences void nucleation under irradiation The physical origin of the segregation effect was pointed out previously [i] Essentially, nonequilibrium solute segregation, which is entirely kinetic in origin, forces small embryos to acquire solute atoms and to exceed equilib- 0.7 r FIG 4—Three regimes of void nucleation 522 EFFECTS OF RADIATION ON MATERIALS rium segregation Thus, the surface term of the void formation energy is unduly higher than the minimal value at equilibrium segregation Such embryos are nevertheless stabilized against shrinkage that would reduce the surface area and thus aggravate the over-segregation Instead, the voids prefer to grow to increase the surface area and to alleviate over-segregation In this way, segregation facilitates nucleation Spontaneous nucleation results when ;S„ > fi^^, even the smallest embryos will then accumulate solute and grow by absorbing vacancies Accordingly, the substitutional impurities most potent in causing void nucleation are ones that not segregate thermally but segregate nonequilibriumly under irradiation Their levels of segregation on void surfaces usually exceed the equilibrium values by many times, and such over-segregation is condusive to spontaneous nucleation It should be noted that in spontaneous nucleation, only the nucleation barrier, but not the time required for defect clustering, vanishes In the case of impurity-catalyzed spontaneous nucleation, clustering needs to proceed along FA = 0, in Fig 1, to acquire enough solute atoms before unbounded growth in the «A direction can take place Therefore, additional steady-state and transient analysis of the type undertaken by Russell [75] and Parker et al [22} for helium-assisted void nucleation is still required, and a strong impurity concentration dependence thus introduced is expected Previous studies on segregation effects emphasized their importance in reducing the surface energy and the bias for interstitials [70,75] Although such studies probably are adequate for void growth, the treatment on this subject in literature, which computes the reduction of the surface energy and the sink bias assuming a priori a certain segregation level during the entire course of void formation, cannot be regarded as a rigorous one for void nucleation In dilute alloys, embryo fluctuations traverse a range of composition prior to nucleation Thus, the surface energy and the bias must be computed along the nucleation path Indeed, they must affect the path taken during nucleation and cannot be fixed a priori Although our picture of surface energetics and sink bias is admittedly a simplistic one, the formalism presented here offers for the first time a correct analysis of the segregation effects on void nucleation It was shown elsewhere [7] that the condition for spontaneous nucleation coincides with /3,^ = fi^^ Thus, an embryo of very small size becomes stable when it receives excess solute atoms by irradiation-induced segregation This condition is primarily determined by the segregation parameter and is less sensitive to the surface properties To this extent, we may regard the present mechanism of void nucleation as a kinetic one that is more closely related to the inherent kinetic properties of defect diffusion and less connected to the interfacial properties of the void This observation provides some justification, a posteriori, to our simplistic modeling of surface structures and energetics CHEN AND TAIWO ON NUCLEATION OF VOIDS 523 Closure It is appropriate to make an analogy between the solute segregation effect and the inert gas effect, drawing the parallel between over-pressure by inert gas atoms trapped in the voids and the over-segregation by solute atoms pumped to the voids The chemical effect due to solute impurities catalizes void nucleation in much the same way that the internal pressure of inert gas impurities catalizes void nucleation Beyond such analogy, we nevertheless regard the solute segregation effect as an even more genuine irradiation effect in the kinetic sense than the inert gas effect, since nonequilibrium segregation owes its origin entirely to irradiation-induced defect fluxes It is one example of the possible coupling mechanisms operational under irradiation that, in the end, recover some of the enormous inflow of energy during irradiation for the manifestation of novel nonequilibrium effects As one of the nonequilibrium dissipative phenomena, it is not surprising that use of equilibrium thermodynamics and kinetics is found largely irrelevant in the present problem and generally in this realm of materials science Indeed materials scientists should be thankful that some powerful tools developed in nonequilibrium statistical physics are already at their disposal, as we have demonstrated here The present study of impurity effects supports the contention that nonequilibrium segregation is crucial to our understanding of void nucleation Even in its simplest form, the new mechanism proposed here can rationahze void nucleation under irradiation without invoking unreasonable assumptions such as a very low surface energy It is found, however, that quantitative estimates of physical quantities of interest here, especially that of nucleation barrier, are sensitive to the properties of small solute-vacancy clusters It is this regime where the simple relationships governing the segregation level and the formation energy as employed in our analysis are found inadequate Further research on the energetics of small solute-vacancy clusters is therefore needed Assuming impurities and irradiation conditions that qualify for spontaneous nucleation exist in most cases, we expect impurity-assisted heterogeneous nucleation to be of general importance Embryos containing some impurity atoms may first form barrierlessly along FA = by solute-vacancy clustering and later overcome a significantly reduced nucleation barrier by absorbing only vacancies and moving in the MA direction This is similar to the gasassisted heterogeneous nucleation mechanism that was recently studied in detail by Parker and Russell [22] Additional numerical computation to elucidate the latter aspect is currently in progress References [-/] Chen, I-W., "Void Nucleation Under Nonequilibrium Segregation—I A Stability Analysis," to be published [2] Stratonovich, R L., Topics in the Theory of Random Noise, Vols and 2, Gordon and Breach, New York, 1967 524 EFFECTS OF RADIATION ON MATERIALS [3] Onsager, L and Machlup, S., Physical Review, Vol 91, 1953, p 1505, [4] Onsager, L and Machlup, S., Physical Review, Vol 91, 1953, p 1512 [J] Graham, R in Fluctuations, Instabilities, and Phase Transitions, T Riste, Ed., Plenum, New York, 1975, p 215 [6] Graham, R., Physical Review Letters, Vol 38, 1977, p 51 [7] Stratonovich, R L in Selected Translations in Mathematical Statistics and Probability, American Mathematical Society, Providence, Vol 10, 1971, p 273 [S] Russell, K C , Acta Metallurgica, Vol 19, 1971, p 753 [9] Katz, J L and Wiedersich, H., Journal of Chemical Physics, Vol 55, 1971, p 1414 [10] Wolfer, W, G., Mansur, L K., and Sprague, J A., in Radiation Effects in Breeder Reactor Stuctural Materials, M L Bleiberg and J W Bennett, Eds., American Institute of Mining, Metallurgical, and Petroleum Engineers, New York, 1977, p 841 [/7] Feder, J„ Russell, K, C , Lothe, J., and Pound, G M., Advances in Physics, Vol 15, 1966, p 111 [12] Chen, I-W and Yoo, M H., Acta Metallurgica, Vol 32, 1984, p 1499 [13] Wiedersich, H., Okamoto, P R., and Lam, N A., Journal of Nuclear Materials, Vol 83, 1979, p 98 [14] Chen, l-"^., Journal of Nuclear Materials, Vol 116, 1983, p 249 [15] Russell, K C , Acta Metallurgica, Vol 26, 1978, p 1615 [16] Wolfer, W G and Mansur, L K., Physica Status Solidi, Vol A37, 1976, p 211 [17] Mansur, L K., Nuclear Technology, Vol 40, 1978, p [18] Graham, R., Zeitschrift fur Physik B, Vol 26, 1977, p 281 [19] Graham, R., Zeitschrift fur Physik B, Vol 26, 1977, p 397 [20] Graham, R., Zeitschrift fur Physik B, Vol 40, 1980, p 149 [21] Powell, R W and Russell, K C , Radiation Effects, Vol 12, 1972, p 127 [22] Parker, C and Russell, K C , Journal of Nuclear Materials, Vol 119, 1983, p 82 John H Evans^ A Mechanism of Void Lattice Formation Based on Two-Dimensional Self-Interstitial Diffusion REFERENCE: Evans, J H., "A Mechanism of Void Lattice Formation Based on TwoDimensional Self-Interstitial Diffusion," Effects of Radiation on Materials: Twelfth International Symposium, ASTM STP 870, F A Garner and J S Perrin, Eds., American Society for Testing and Materials, Philadelphia, 1985, pp 525-533 ABSTRACT: Experimental work by Jacques and Robrock has suggested that the selfinterstitial atoms (SIA) in molybdenum migrate two-dimensionally on {011} planes The present author has recently explored the spatial effects that could result if this mode of diffusion were extended up to void formation temperatures for molybdenum and other body centered cubic (bcc) metals, and concluded that void lattice formation is a plausible outcome This paper will summarize both the qualitative and rate theory arguments and the available evidence to support the two-dimensional diffusion of SIA at high temperatures in molybdenum and niobium Although it was argued previously that the effect of planar void alignment on all six sets of {01 Ij planes should lead to a bcc void lattice, it was not possible to demonstrate this via the rate theory approach This weakness has now been rectified in a computer study that followed the growth and position of individual voids placed in a block of material and subjected to twodimensional SIA migration on the {Oil) planes Results from this work will be presented showing that under these conditions there is little doubt that the void positions can indeed evolve, as predicted, into a bcc void lattice There is no difficulty in extending the present model to include bubble and vacancy loop lattices, while extrapolation to the face centered cubic (fee) and hexagonal close packed (hep) metals is also possible if the requirement of two-dimensional SIA diffusion on the close packed planes can be met KEY WORDS: radiation effects, molybdenum, voids, void lattices, bubble lattices, interstitial diffusion, radiation Since the first unexpected observations of a void lattice in irradiated molybdenum [/,2], more than a decade ago, a steady flow of literature has been produced on the topic of void (and bubble) lattice formation in metals Both the experimental and theoretical studies in this area have been covered in the extensive review of Krishan [5], while the analogous lattices in the alkaline earth halides are discussed in the recent paper by Johnson and Chadderton 'Principal scientific officer Materials Development Division, AERE Harwell, Oxon, OX 11 ORA, UK 525 Copyright® 1985 b y A S l M International www.astm.org 526 EFFECTS OF RADIATION ON MATERIALS [4] In discussing the theoretical models of lattice formation in metals, Krishan concluded that this was still an open question This led the present author to consider [5] a new model based on the Jacques-Robrock [6] suggestion that a self-interstitial atom (SIA) in molybdenum might have twodimensional diffusion properties This was not the first model to be based on possible SIA behavior: Foreman, in an internal but widely quoted report [7], suggested that the alignment of voids might arise from the one-dimensional motion of interstitials via a simple shadowing effect Although the model was presented without any formal mathematical input, the simple explanation of the void lattice crystallography was considered by many to be rather attractive The fundamental disadvantage, as pointed out by Foreman, was the absence of evidence for such SIA behavior in metals and, consequently, the model was not developed further The new two-dimensional SIA model for the void lattice formation follows the one-dimensional model in the use of the diffusional properties of the self-interstitial atom but the mode of operation is somewhat different Clearly, if the SIA migrates in two dimensions then no direct shadowing of voids is possible; instead, the model uses the property that pure two-dimensional SIA motion would cause every plane in the material to be isolated as far as the interstitial behavior was concerned The consequences of this property was developed previously [5] in some detail and demonstrated that planar ordering of voids into sheets on the plane of the SIA motion would not be unexpected In this paper, the essential details of the previous presentation are summarized before describing a new computer-aided approach to the evolution of the void lattice Summary of the Two-Dimensional SIA Model Jacques-Robrock Model for SIA Diffusion in Molybdenum The accepted configuration for the SIA in molybdenum and similar body centered cubic (bcc) metals is the dumbbell or split interstitial It had been expected that this defect should migrate as shown in Fig la, rotat- < , ^ = ^ FIG I—(a) The interstitial Jump-step involving the rotation of the dumbbell configuration; (b) the jump-step proposed in Refd; the absence of any rotation means that the SIA will diffuse twodimensionally on the plane in which it lies EVANS ON VOID LATTICE FORMATION 527 ing itself by 60° on each jump However, in a study of the elastic after-effect in molybdenum after electron irradiation at K, Jacques and Robrock [6] found no evidence that such a rotation took place; it was thus necessary to suggest a jump-step where such a rotation was absent The result of this was the jump configuration shown in Fig 1Z>, a close examination of which immediately indicates that the SIA diffusion will be two-dimensional with any SI A confining itself to the particular {011} plane on which it was created Naturally, the three-dimensional jump-step cannot be excluded, but the evidence implies that its activation energy is higher than that for the twodimensional step Consequences of Two-Dimensional SIA Diffusion In rate theory, the concentrations of vacancies and interstitials are normally assumed to be uniform over the volume of the crystal if local variations due to the proximity of defect sinks are ignored If we now postulate that all the SIA's diffuse two-dimensionally with the jump-step already described (for the moment ignoring the possibility of three-dimensional jumps) then each individual (Oil) plane becomes isolated from its neighbors as far as the SIA's are concerned This dramatically changes the usual rate theory position for the interstitials; instead of three-dimensional migration ensuring that the SIA concentration is uniform everywhere, each (011) plane will have its own particular SIA concentration This can be calculated on a plane-byplane basis and, in its simplest form, will be inversely proportional to the sink strength on each plane For the case where we only consider voids, this has interesting consequences since planes that cut a large number of voids will have a lower SIA concentration than a plane cutting a smaller number, and it is immediately seen that voids in the former plane will acquire interstitials at a slower rate than in the latter case Meanwhile, the vacancies are unaffected by any planar effects and, for voids of equal size, will be trapped with equal probability everywhere; thus, the net result is of greater void growth on planes that are more heavily populated with voids than others This demonstrates the main effect of two-dimensional SIA motion, that is, that spatial variations of swelling rate can occur from void to void with the variations being such as to favor voids which share a common SIA-carrying plane with other voids This is the heart of the argument for the planar alignment of voids since the favored voids must be those aligned along the planes of SIA motion, that is, the {011} planes AMth six sets of such planes, the real situation is clearly complex but it can be argued that the only spatial position for all the voids to be favored is when they are in perfect alignment with their neighbors on all six sets of {011} planes; this condition is only met when the voids make a bcc void lattice The preceding description is a short summary of the argument presented in a previous paper [J] that included a formal rate theory approach to the sit- 528 EFFECTS OF RADIATION ON MATERIALS uation of SIA's diffusing two-dimensionally along one set of planes Although it was necessary to represent an individual void as a disk on a plane, it was easy to show more quantitatively the advantage accruing to voids on a plane with a high density of voids It was argued that in any random distribution of voids a distribution of planar void densities would have to occur; those with the highest void density would grow fastest so that out of an initial random distribution, planar ordering would emerge The rate theory approach was useful in showing the effect of dislocation density in damping the variations of void growth rates and the similar effect of introducing a probability for occasional three-dimensional SIA jump-steps A number of other features coming out of the rate theory approach can be listed: (1) the requirement of a high void sink strength relative to the dislocation sink strength (The large effect of oxygen content on void lattice formation in niobium [8] and tantalum [9] was argued [5] to operate via this requirement.); (2) the correct order of magnitude for the ratio of void lattice parameter to void radius was found, including the far lower value characteristic of bubble lattices Taking both void and bubble lattices together, the factor of three spread in this ratio (from up to 15 [ i ] ) might tend to rule out mechanisms that predict a constant value It is worth discussing some of the less strong points in the mechanism The first is the slight unease that might be felt in taking the SIA jump-step suggested for molybdenum at low temperatures and extrapolating to the void formation temperature regime As already stated, the two-dimensional jump-step appears to have a lower activation energy than the three-dimensional step, and it is therefore true that the probability, P, of two-dimensional jumps relative to those involving rotation will decrease with temperature (It will be proportional to exp(A£'/^7'), where A is is the activation energy difference for the two processes.) However, the crucial point is that at higher temperatures, the value of P begins to be dominated by the ratio of the pre-exponentials for the two different jump-steps Once it is accepted that the pre-exponentials can differ, then the situation concerning the dominance of one jump-step relative to the other becomes much more flexible and allows one to accept more easily the possibility of two-dimensional SIA motion at high temperatures, both in molybdenum and equally in the other bcc metals (niobium, tantalum, and tungsten) in which void lattices have been found The author has suggested [10] that some unusual void behavior in niobium [11] and molybdenum [12] is evidence for high temperature twodimensional SlA diffusion In niobium, the behavior in question was that reported by Loomis and Gerber [77] on the effects of temperature changes during ion irradiations Voids formed at 1230 K were shown to shrink when subsequently irradiated at 1050 K, a phenomena not seemingly explicable on conventional rate theory However, two-dimensional SIA motion provides an explanation through the different sink strengths that the voids will have EVANS ON VOID LATTICE FORMATION 529 for interstitials and vacancies This has been shown to lead to a void swelling saturation condition where the maximum void radius is inversely proportional to the void concentration [5] If the void concentration increases, as found in niobium when the irradiation temperature was lowered, then the maximum value of void radius has to decrease The calculated decrease [10] in void size was in close agreement with the niobium results The same approach also explained the results of void shrinkage during isothermal irradiations of molybdenum [12]; it can thus be argued that evidence for high temperature SIA diffusion exists for both these metals A second point of difficulty with the proposed void lattice mechanism is its extrapolation to face centered cubic (fee) metals where an fee defect lattice (for example, as found for void and vacancy loop lattices in nickel) would require two-dimensional SIA motion along the {111} planes This is not possible with the accepted dumbbell configuration found at low temperatures for the fee SIA Instead, it is necessary that the SIA configuration changes with temperature to one allowing two-dimensional-SIA diffusion on the {111} planes, a requirement that geometrically could be satisfied by the < 1 > dumbbell Although this suggestion is somewhat novel, it must be noted that if the same two-dimensional diffusion of SIA on {111} planes, were transferred to the hexagonal close packed (hep) system, one would immediately predict planar ordering of voids parallel to the basal plane Since this is exactly what is seen in magnesium, the possibility of such two-dimensional SIA diffusion on these close-packed planes cannot easily be ignored A third point brought out in the previous report was the difficulty in demonstrating (at least in any analytical way) that even if planar ordering along {011} planes did occur in a bcc metal, the voids would evolve to a perfect bcc lattice when all six sets of {011} planes were considered It is hoped that the following section will show that this question has now been resolved Computer Simulation of Void Alignment Effects The rate theory approach just mentioned has now been complemented by a computer study in which a number of voids are placed randomly in a block of material and their growth followed under conditions of two-dimensional SIA migration This approach has the advantage, relative to the rate theory, of treating each void individually, realistically allowing all the planes cutting a void to be taken into account while also allowing void movement The capture of vacancies at any void followed the simplest form of rate theory with the vacancy flow, F(/), per unit dose to Void / of Radius r, being given by the expression V(i) = 47rr,/[247rr, + p] For the interstitials, rate theory was again applied but, as outlined earlier, the isolation induced by the two-dimensional SIA motion made it necessary 530 EFFECTS OF RADIATION ON MATERIALS to treat each plane individually The sink strength of a void with respect to a given plane was taken as being proportional to Iwr, where r here was the radius of the circle formed by the bisection of the void by the plane Taking into account that any single plane can cut several voids and a dislocation component p, and that a single void is cut by several planes, it is easy to show that with n voids in the system and P parallel planes, the general equation for SIA acquisition for Void / is E [ r r , „ / ( E 27rr,;, + p)] where rij is the radius of the circle formed by Void i on Plane y The computing effort was reduced considerably by the fact that a large number of rij values are zero A significant part of the model was to allow void movement in the direction perpendicular to the plane of SIA diffusion, the driving force being the imbalance of SIA collected on one side of the void relative to the other The importance of this was that it always tended to move a void into a region of low interstitial flux; since such regions will be those with more (or larger) voids, it is easy to see that the overall effect will be to align the voids in sheets parallel to the plane of SIA migration SIA Diffusion in One Set of Planes The first use of the preceding model was to examine the same situation as that previously treated with rate theory in which the SIA's in a block of material were allowed to diffuse only in one set of planes Using Cartesian coordinates, the set in question was chosen to be perpendicular to the x axis in a cube of material, 25 nm edge length The x and y coordinates of 100 voids were then randomly chosen and their growth and position followed as the vacancies and interstitials were distributed following the description just • • •^• • * »• FIG 2—Computer results showing the effect of SIA diffusion on one set of planes; as the dose increases (left to right), the initially random void positions change to create the planar alignment of voids parallel to the plane of SIA motion EVANS ON VOID LATTICE FORMATION 531 given Using this approach, it was easy to repeat the general findings of the previous rate theory approach, namely, that where voids were more densely packed (in a planar sense) they grew quicker, while voids less well placed were found to shrink However, it was also of interest to see how the void positions changed with displacement dose; Fig plots the evolution of void coordinates, demonstrating the planar ordering of voids parallel to the plane of SIA diffusion The void aUgnment into rows is clear, although as predicted previously [5], the row spacing is irregular It is felt that this unidimensional lattice is particularly relevant to the situation in hep magnesium referred to in an earlier section The preceding approach, where each void is treated individually, clearly complements the previous rate theory work and bears out its predictions However, it was not possible to extend the model to include the probabihty of occasional three-dimensional jump-steps SIA Diffusion on Six Sets of [Oil] Planes The planar alignment of voids just demonstrated is not proof that in the real case the formation of a void lattice would take place; clearly with six sets of {011} planes on which the SIA's are proposed to migrate, any single void will be receiving complicated information via the SIA fluxes on every plane bisecting the void However, it was found that the preceding computer approach could be extended to treat the real situation simply by transferring the SIA motion to the diagonal planes of a cube and then successively rotating the cube to all three cube projections In this way, all six sets of {011} planes could be allowed to contribute to the growth and movement of each void The results of this work are demonstrated in Fig where a projection of the void positions down , , and directions at successively higher doses is drawn The result of the final frames need particular emphasis since it is clear that the random void positions at the start have evolved into a near perfect lattice with bcc symmetry and axes parallel to that of the host lattice, exactly as found in practice The only obvious difference is that in the computer this process takes a dose of about two displacements per atom (dpa) compared to the 10 to 50 dpa found experimentally The mechanism is therefore extremely strong and clearly has adequate potential to cope with any moderating effects of three-dimensional jump-steps during SIA diffusion It is worth noting that when these three-dimensional jump-steps are considered, the void density can immediately be seen to be an important parameter; for low void densities, and therefore large diffusion distances, the probability of an interstitial reaching a void before a three-dimensional jump must clearly decrease and reduce the tendency for planar ordering For this reason, a high void density is very hkely to be a crucial factor in the lattice formation process 532 EFFECTS OF RADIATION ON MATERIALS 1.16 dpa 2.12 dpa FIG 3—The application of the model in text to SIA diffusion on all six sets of (Oil) planes: 125 voids of radius 0.7 nm have been placed randomly in a cube of edge length 31.4 nm, and their positions followed with increasing dose By examining the projections along the , , and directions, it is clear that the initial void positions have evolved into a bcc lattice with axes parallel to the host matrix Conclusions It is felt that enough evidence has been put forward for the two-dimensional SIA diffusion model to be given serious consideration Evidence for high temperature two-dimensional SIA motion comes from its ability to ex- EVANS ON VOID LATTICE FORMATION 533 plain the puzzling results of void shrinkage in both niobium and molybdenum, while the computer study given here definitely shows that pure twodimensional SIA diffusion on the {011} planes can cause the void positions to move into a bcc lattice The only necessary extra assumption in the mechanism appears to be introduction of void movement due to the imbalance of SIA fluxes to opposite sides of a void This does not seem too unreasonable One interesting question is still outstanding, namely, the effect of increasing the probability of three-dimensional SIA jumps and the consequent suppression of lattice formation; this was discussed in the rate theory approach [5] but so far has not been treated in the computer work The extension of the model to helium bubble lattice formation in bcc metals was discussed in Ref J; the only difference between the void and bubble cases was considered to be the change from bias-driven to gas pressure-driven in the mode of vacancy acquisition Since the SIA's are unaffected by this, the lattice formation mechanism must be the same The same mechanism should apply to any vacancy cluster and can thus explain the rarer phenomena of vacancy loop lattices in metals Finally, there is no difficulty, in the theoretical sense, in extending the two-dimensional SIA model to both fee and hep metals As already outlined, any two-dimensional diffusion of the SIA on the closepacked {111} planes will lead in the respective cases to the fee and planar ordering of voids found in practice The computer model in this paper has been recently adapted to demonstrate fee void lattice formation [13], but clearly some independent evidence to support such a diffusion mode would be welcome References [1] Evans, J H., Nature, Vol 229, 1971, p 403; also Radiation Effects, Vol 10, 1971, p 55 [2] Wiffen, F W., Radiation Induced Voids in Metals, Albany, 1971, J W Corbett and L C lanniello, Eds., U.S Atomic Energy Commission, 1982, p 386 [3] Krishan, K., Radiation Effects, Vol 66, 1983, p 121 [4] Johnson, E and Chadderton, L T., Radiation Effects, Vol 79, 1983, p 183 [5] Evans, J H., Journal of Nuclear Materials, Vol 119, 1983, p 180 [6] Jacques, H and Robrock, K-H., Proceedings, Yamada Conference on Point Defects in Metals, Kyoto, Japan, 1981, J Takamura, M Doyama, and M Kiritani, Eds., University of Tokyo Press, 1982, p 159 [7] Foreman, A J E., AERE Harwell Report R-7135, 1972 [«] Loomis, B A., Gerber, S B., and Busch, D E., Journal of Nuclear Materials, Vol 73, 1978, p 58 [9] Loomis, B A and Gerber, S B., Journal of Nuclear Materials, Vol 71, 1978, p 377 [10] Evans, J H., Journal of Nuclear Materials, Vol 20, 1984, p 349, [11] Loomis, B A and Gerber, S B., Journal of Nuclear Materials, Vol 102, 1981, p 154 [12] Bentley, J., Eyre, B L., and Loretto, N H., Proceedings, Conference on Fundamental Aspects of Radiation Damage in Metals, Gatlinburg, 1975, US-ERDA Conf-7510006,p 925 [13] Evans, J H., Journal of Nuclear Materials, Vol 132, 1985