Levente Balogh

Evolution of dislocation density in a hot rolled Zr–2.5Nb alloy with plastic deformation studied by neutron diffraction and transmission electron microscopy

Abstract The evolution of dislocation density and microstructure of a hot rolled Zr–2.5Nb alloy under compressive plastic strain, at room temperature, was analysed using neutron diffraction and transmission electron microscopy (TEM). The dislocation densities of type 〈a〉, 〈c + a〉 and 〈c〉 dislocations at different plastic strains in the elastic–plastic transition regime and plastic regime have been measured by diffraction line profile analysis (DLPA). TEM microstructure characterization revealed the operation of different slip systems. It has been found that slip of type 〈a〉 dislocations contributed to most of the plastic strain at the early stage of deformation, and strong pyramidal 〈c + a〉 slip did not occur until the deformation was fully plastic. Unambiguous evidence of basal slip occurring at room temperature in Zr is provided. Loading along a plate direction with more basal poles favoured the operation of basal and pyramidal slip. Dislocation features including relative edge:screw character of 〈c + a〉 dislocations are shown to be different under tension and compression loading, providing a mechanistic driver for the previously observed asymmetry in critical resolved shear stress for 〈c + a〉 slip.

Quantitative characterization of the microstructure of heat-treated Zr-Excel by neutron line profile analysis

Neutron diffraction line profile analysis (DLPA) and transmission electron microscopy were used to characterize the components of the bimodal microstructure of Zr-Excel (Zr–3.5Sn–0.8Mo–0.8Nb), a nuclear structural material. The dual microstructure, consisting of equiaxed primary grains and martensitic domains both having hexagonal close-packed (h.c.p.) α crystal structure, forms when the as-received Zr-Excel alloy is heat treated at a high temperature and subsequently quenched, i.e. is solution treated. Because both microstructure components have the same crystal structure the reflections from the two components overlap significantly. The article presents how the multi-phase analysis capability of modern DLPA methods can be used to model the measured neutron diffraction patterns as the sum of two sub-patterns corresponding to the components of such a bimodal microstructure, which can be found in many hexagonal alloys relevant for industrial applications. The results show that the large equiaxed primary h.c.p. α grains have a highly correlated low-density dislocation structure and large sub-grains (∼300 nm), while the large martensitic domains have a randomly arranged very high density dislocation structure and sub-grains the size of ∼30 nm. The significantly different defect structures of the primary and martensitic phases manifest as large differences in the hardness and ductility of the individual components. As a result of this duality of the mechanical properties, solution-treated Zr-Excel materials can be considered as analogous to metal matrix composites where a softer ductile matrix contains a harder brittle reinforcing phase.

Contrast factors of irradiation-induced dislocation loops in hexagonal materials

Irradiation-induced defects, such as dislocation loops, significantly affect the mechanical properties of structural alloys, altering slip and influencing creep and growth. As a consequence, the quantitative characterization of irradiation-influenced defect structures as a function of dose, thermal treatments and/or cold work is essential for models which predict changes in mechanical properties due to the accumulation of irradiation defects. Whole pattern diffraction line profile analysis (DLPA) is a modern tool for microstructure characterization based on first-principles physical models, well established for dislocation density measurements in plastically deformed materials. However, the DLPA procedures that have been tailored for deformed materials account for the strain anisotropy of hexagonal crystals with theoretical contrast factors calculated specifically for dislocation types generated by plasticity which, if directly applied to irradiated materials, will inherently introduce inaccuracies. In an effort to specifically address dislocation structures consisting of irradiation defects, a method was developed to calculate theoretical contrast factors for any general elliptically shaped dislocation loop. The values of the contrast factors are calculated and compiled in tables for six common elliptical 〈a〉-type and 〈c + a〉-type loops for ten hexagonal crystals, in order to provide a database for future DLPA work on irradiated materials. The use of the dislocation loop specific contrast factors is demonstrated on neutron-irradiated Zr–2.5Nb.

On the computation of diffraction peaks from discrete defects in continuous media: comparison of displacement and strain-based methods

This study introduces a numerical tool to generate virtual diffraction peaks from known elastic displacement or strain fields arising in the presence of discrete straight or curved dislocations in continuous media. The tool allows for the generation of diffraction peaks according to three methods: the displacementbased Fourier method of Warren, the Stokes‐Wilson approximate method and a new average-strain-based Fourier method. The trade-off between the accuracy and the demand for computational power of the three methods is discussed. The work is applied to the cases of single-crystal microstructures containing (i) straight dislocations, (ii) low-angle symmetric tilt grain boundaries, (iii) a restrictedly random distribution of dislocations and (iv) complex microstructures generated by discrete dislocation dynamics, to illustrate the differences and domains of validity of the aforementioned methods. Dissimilar diffraction profiles reveal that peak broadening from dislocated crystals has additional contributions coming from strain gradients ‐ a feature that is rejected in the Stokes‐Wilson approximation. The problem of dealing with multi-valued displacement fields faced in the displacement-based Fourier method is overcome by the new average-strain-based Fourier method.

The habit plane of 〈a〉-type dislocation loops in α-zirconium: an atomistic study

Abstract We use both a model of dislocation energy and molecular dynamics (MD) simulations to explore the habit planes of 〈a〉-type dislocation loops, while cascade simulations are produced to investigate the effect of irradiation on those loops. Vacancy and interstitial loops are artificially created on perfect prism planes in MD, and they reorient to their preferred habit planes during a relaxation stage. The statistics presented in stereographic projections show that the preferred habit planes are close to the prism plane , consistent with experimental data from the literature. We also confirm that the angle between the Burgers vector and the loop’s plane is a useful parameter when identifying the stability of 〈a〉-type dislocation loops.