Irradiation-Induced Recrystallization of Cellular Dislocation Networks in Uranium-Molybdenum Alloys
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Irradiation-Induced Recrystallization of Cellular Dislocation Networks in Uranium-Molybdenum Alloys* J. Rest and G. L. Hofman Argonne National Laboratory, Argonne, IL Abstract We developed a rate-theory-based model to investigate the nucleation and growth of interstitial loops and cavities during low-temperature in-reactor irradiation of uranium-molybdenum alloys. Consolidation of the dislocation structure takes into account the generation of forest dislocations and capture of interstitial dislocation loops. The theoretical description includes stress-induced glide of dislocation loops and accumulation of dislocations on cell walls. The loops accumulate and ultimately evolve into a low-energy cellular dislocation structure. Calculations indicate that nanometer-size bubbles are associated with the walls of the cellular dislocation structure. The accumulation of interstitial loops within the cells and of dislocations on the cell walls leads to increasing values for the rotation (misfit) of the cell wall into a subgrain boundary and a change in the lattice parameter as a function of dose. Subsequently, increasing values for the stored energy in the material are shown to be sufficient for the material to undergo recrystallization. Results of the calculations are compared with SEM photomicrographs of irradiated U10Mo, as well as with data from irradiated UO2.
Theory and Experimental Confirmation The model [1] consists of a set of coupled equations for the time rate of change of the vacancy ( c v ) and interstitial ( c i ) concentrations, the interstitial loop diameter ( d l ) and density ( n l ), the density of forest dislocations ( f d ), the cavity radius ( rc ) and density ( c c ), the average number of gas atoms in each cavity ( N g ), and the concentration of gas atoms in solution in the fuel matrix ( c g ). These equations are dc v (t ) = K − α r c v (t )ci (t ) − k v ( ρl ) D v c v (t ) − 2Ω1/ 3b v D v c v (t )n l (t ) / π d l (t ) , (1) dt dci (t ) = K − α r c v (t )ci (t ) − k i ( ρl ) Di ci (t ) − 2Di ci (t )ci (t )/Ω 2/3 (2) dt 1/ 3 + 2Ω b v D v c v (t )n l (t ) / π d l (t ),
dn l (t ) 2 Di ci (t )ci (t )/Ω5/ 3 − 4vl ( t ) n l (t )/dl (t ) = dt 2 − 2Ω−2 / 3 b v D v c v (t)n l (t ) / π d l (t )- vg b 2v n l (t )/(dl2 (t ) Lc (t )),
(3)
n l’ ( t ) ddl (t ) = g ( t ) vl ( t ) − d l ( t ) − d 0 , dt n l ( t )
(4)
df d (t ) = π vl (t)n l (t)+π v g bv2 nl (t ) /(d l (t ) Lc (t )) − bv vl (t)f d2 (t ) , dt
(5)
*
Work supported by U.S. Department of Energy, Office of Arms Control and Nonproliferation under Contract W-31-109-Eng-38.
R1.7.1
drc (t ) = k v ( ρl ) D v c v (t ) − c 0v (t ) − k i ( ρl ) Di ci (t ) , dt dcg (t ) = β K − 16π f n rg D g c g (t )cg (t ) − 4π D g rc (t )cc (t )cg (t ) + bN g (t )cc (t ) , dt dcc (t ) = 16π f n rg Dg cg (t )cg (t )/N g (t ) − 16π Dc cc (t )cc (t ) , dt dN g (t ) = 4prc D g c g (t ) - bN g (t ) + 16pDc N g (t ) rc (t )c c (t ) , dt − Pg − 2γ /rc ( t ) −σ / ΩkT c0v (t ) = cTv e , 2 vl ( t ) = z i Di ci ( t ) − z v D v c v ( t )
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