Percolation in the classical blockmodel

Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation transition in the classical blockmodel has not been examined so far, although the phenomenon has been studied in a variety of much more complicated models of interconnected and multiplex networks. In this paper we derive the self-consistent equation for the size the global percolation cluster in the classical blockmodel. We also find the condition for percolation threshold which characterizes the emergence of the giant component. We show that the discussed percolation phenomenon may cause unexpected problems in a simple optimization process of the multilevel network construction. Numerical simulations confirm the correctness of our theoretical derivations.Comment: 7 pages, 6 figure

Frank loop unfaulting mechanism in fcc metals during neutron irradiation

The unfaulting mechanism whereby sessile Frank dislocation loops evolve into a complex tangle of glissile dislocations during irradiation of face centered cubic metals is not well understood. It is presumed that such loops grow by absorption of point defects until interactions develop which provide sufficient impetus for nucleation of an unfaulting event. The loops then become glissile, interact and form a dislocation network. An alternate mechanism which has been observed to occur in an austenitic precipitation-strengthened commercial alloy irradiated in the EBR-II fast reactor. The mechanism requires an interaction between the sessile a/3 <111> Frank loop and a moving glissile a/2 <110> perfect dislocation. An unfaulting a/6 <112> dislocation is created which, as it moves, eliminates the Frank loop and leaves only a perfect dislocation with the original a/2 <110> Burgers vector. This process is demonstrated. This alternate mechanism can have significant impact on the development of the dislocation microstructure in a metal undergoing irradiation creep. This impact will be discussed in relation to relevant irradiation creep models

Post-irradiation deformation in a Fe-9%Cr alloy

The deformed microstructures of both irradiated and unirradiated Fe-9%Cr (Fe-9Cr) uniaxial tensile specimens have been examined to identify controlling mechanisms. Deformation following irradiation is found to occur in poorly defined channels about 100 nm wide, causing formation of discrete steps at surfaces and, interestingly, designated by nonuniformly distributed highly elongated voids. Deformation is by motion of a(0)/2 dislocations, which interact with and decompose irradiation-induced a(0) loops. The structure formed after extensive deformation consists of highly complex cell walls and moderate densities of individual slip dislocations. It appears that the deformation mechanism is channeling. (C) 2001 Elsevier Science B.V. All rights reserved

Frank loop formation in irradiated metals in response to applied and internal stresses

The Frank loop and dislocation microstructures developed in three face-centered cubic alloys during fast reactor irradiation have been examined to determine the influence of applied and internally-generated stress on loop evolution. It is shown that anisotropic stresses generate a corresponding anisotropy of Frank loop populations on the four close-packed planes. The loop populations thus represent a microstructural record of the irradiation creep processes in action. The ease of interpreting this record depends on the relative magnitudes of external and internal stresses. Metals with low irradiation creep rates which also undergo concurrent and substantial phase changes during irradiation are subject to large and indeterminate levels of internally-generated stress which render the microstructural record uninterpretable with respect to the applied stress state. When the internally-generated stresses are small in comparison to the externally-applied stresses, a clear record of the SIPA (Stress-Induced-Preferential-Absorption) growth mechanism of irradiation creep is imprinted at low neutron fluences in the density and sizes of loops present on each set of close-packed planes. This record fades at higher fluences when the continued anisotropic formation, growth and unfaulting of Frank loops generates a corresponding anisotropy in the resultant free dislocation network, a process which alters the competition of sinks for point defects

HVEM in-situ deformation of neutron irradiated Fe-0. 3a/oCu

In an effort to better understand the nature of irradiation embrittlement of low alloy steels, in-situ HVEM deformation tests have been performed on pure iron and iron-0.3% copper ribbon tensile specimens in both the unirradiated and irradiated (2.5 x 10/sup 19/ n/cm/sup 2/, E > 1 MeV at 290/sup 0/C) conditions. Microstructural response is described principally in terms of the matrix in which cracks were observed to propagate across the different specimens. Major differences between the irradiation iron-copper alloy and the other material conditions were (1) the plastic zone which developed ahead to propagating cracks was smaller, and (2) dislocations were found to develop a crenulated structure uncharacteristic of the other conditions studied. It is inferred that the crenulations result from the presence of obstacles to dislocation motion and thereby demonstrate the matrix strengthening effect of small, radiation-induced, presumably copper-rich precipitates. However, the obstacles which are most effective in retarding dislocation motion are found to be distributed on a much coarser scale than that of the radiation-induced loops