Void Superlattice Research Articles

A review of void and gas bubble superlattices self-organization under irradiation

Irradiation by high-energy particles has been well known as a destructive force that “damages” crystalline materials by creating lattice defects. One surprising outcome from irradiation is the self-organization of void superlattices and gas bubble superlattices in various materials under irradiation. While these superlattices exhibit crystal structures that mimic atomic lattices, their self-organization takes place in far-from-equilibrium environment. A thermodynamic driving force that entails ordering is either absent or yet to be identified. In the past few decades, extensive research efforts have been made to generate such superlattices and to discern their formation mechanisms. While a consensus is yet to reach, these studies have substantially enriched our understanding on defect evolution and self-organization under irradiation. Appending previous reviews that are mostly done two decades ago, this article presents a comprehensive review of new experimental, theoretical, and simulational studies of void and gas bubble superlattices in the past two decades. An in-depth discussion on the formation mechanisms and their implications on superlattice properties is provided for the purpose of encouraging future studies.

Three-dimensional strain imaging of irradiated chromium using multi-reflection Bragg coherent diffraction

Radiation-induced materials degradation is a key concern in limiting the performance of nuclear materials. The formation of nanoscale void and gas bubble superlattices in metals and alloys under radiation environments can effectively mitigate radiation-induced damage, such as swelling and aid the development of next generation radiation tolerant materials. To effectively manage radiation-induced damage via superlattice formation, it is critical to understand the microstructural changes and strain induced by such superlattices. We utilize multi-reflection Bragg coherent diffraction imaging to quantify the full strain tensor induced by void superlattices in iron irradiated chromium substrate. Our approach provides a quantitative estimation of radiation-induced three-dimensional (3D) strain generated at the microscopic level and predicts the number density of defects with a high degree of sensitivity. Such quantitative evaluation of 3D strain in nuclear materials can have a major impact on predicting materials behavior in radiation environments and can revolutionize design of radiation tolerant materials.

A phase-field model for void and gas bubble superlattice formation in irradiated solids

A phase-field model to simulate the formation of both void and gas bubble superlattices is derived from a grand potential functional, assuming 1D diffusion of self-interstitial atoms. The model is capable of accounting for superlattice formation by either a nucleation and growth or spinodal decomposition mechanism; in this work, we focus on the nucleation and growth mechanism, using a discrete nucleation approach in the phase-field model. In simulations of void formation, short aligned rows of voids were initially formed, followed by growth in the size of the aligned rows, and finally leading to superlattice formation, consistent with experimental observations. Void superlattice spacing as a function of model parameters was quantified. Increased nucleation rates led to smaller superlattice spacing, while increased vacancy diffusivity led to larger superlattice spacing. In simulations of gas bubble superlattice formation, superlattice spacing decreased with increasing gas atom flux, consistent with experimental observations. Simulations with increasing ratio of gas atom flux to vacancy–interstitial pair production led to increased superlattice spacing, which is inconsistent with experimental observations at high gas atom flux rates; this discrepancy is attributed to the fact that the model does not account for bound gas atom–vacancy pairs that may dominate at high gas flux rates.

Unveiling the interaction of nanopatterned void superlattices with irradiation cascades

Nanopatterned microstructures in materials can have a profound impact on materials’ physical and chemical properties. While voids are typically considered as detrimental defects in irradiated materials, the patterning of nanoscale voids causes the formation of void superlattices and provides a highly efficient mechanism for gas storage. Despite the important applications of nanopatterned defect superlattices, how they degrade under irradiation remains unclear. Here we provide direct observation of the evolution of void superlattices under irradiation and elucidate the interaction of void superlattices with irradiation cascades. We reveal that the instability of void superlattices under irradiation is caused by heterogenous void shrinkage and demonstrate the imperative role of mixed 1D/3D diffusion of self-interstitial atoms and injected inert gas atoms on void shrinkage and void superlattice instability. Understanding the degradation mechanisms of nanopatterned microstructures is essential to designing damage-tolerant materials and broadening their applications in extreme environments.

The effects of temperature and dose rate on the properties of irradiation induced void superlattices

Void and gas bubble superlattices have been known to form in materials under irradiation for decades, while the exact formation mechanism remains debated in the literature. It has been indicated by recent theories and experiments that such void self-organization is due to an instability in the vacancy concentration field combined with the anisotropic self-interstitial-atom diffusion. The superlattice constant was found to critically depend on the irradiation conditions such as temperature and dose rate. Following the theoretical framework laid out in the literature, the present study provides a deeper insight on the temperature and dose rate dependence of several superlattice properties, including superlattice constant, ordering, and critical dose of formation. The latter two properties have rarely been studied in the literature. The results suggest that temperature and dose rate are strongly correlated, with an equivalency between logarithmic dose rate and inverse temperature. Such a correlation can be used to guide experiments for optimal superlattice ordering and a tailored lattice constant.

The effect of elastic anisotropy on the symmetry selection of irradiation-induced void superlattices in cubic metals

Self-organized microstructures and patterns have been widely observed in non-equilibrium physical systems. In particular, irradiation in metals creates far-from-equilibrium environments, in which the competing dynamics of defect production and annihilation can lead to unique self-organized superlattice structures, e.g., void and gas bubble superlattices. From a physical point of view, the superlattice structures are dictated by the intrinsic symmetry breaking in the metals, i.e., anisotropy caused by the breaking of continuous rotational symmetry. In the literature, two distinctive anisotropies, elastic anisotropy and diffusion anisotropy of interstitials, have been proposed to be the origins of superlattice formation. However, it is still unclear which anisotropy dominates the symmetry selection of superlattice structures. In this paper, we study elastic anisotropy and its effect on the symmetry of void superlattices. By using theoretical analyses and phase field simulations, we show that elastic anisotropy in cubic metals can lead to either face-centered cubic or simple cubic superlattices depending on the Zener anisotropy ratio. The superlattices formed under this elastic anisotropy mechanism must form under the influence of spinodal decomposition, as the mechanism requires perturbations in the vacancy concentration field to develop into spatially-static concentration waves. We compare to existing work on symmetry selection in superlattices via diffusion anisotropy and to experimental observations, and we suggest that concentration wave development under the influence of elastic anisotropy is not the mechanism for symmetry selection during the formation of irradiation-induced void superlattices, but that diffusion anisotropy could be the dominant mechanism.

A short review of defect superlattice formation in metals and alloys under irradiation

Irradiation damage drives complex and coupled phenomena in materials at far-from-equilibrium conditions. The self-organization of nanoscale defects in materials under irradiation shows great potential to tailor the physical properties of materials by controlling nanopatterned microstructures. Irradiation-induced gas bubble and void superlattices are two important ordered nanostructures of great scientific interest. Although both types of superlattices have been investigated extensively, a consensus has yet to be reached on their formation mechanisms. In this review article, the current research status of gas bubble and void superlattices in metals and alloys and their characterization, structural stability, and mechanistic modeling are summarized. The fundamental research goals to advance the mechanistic understanding of gas bubble and void superlattices are outlined.

The Effects of Temperature and Dose Rate on the Properties of Irradiation Induced Void Superlattices

The Effects of Temperature and Dose Rate on the Properties of Irradiation Induced Void Superlattices

Symmetry breaking during defect self-organization under irradiation

One of the most intriguing phenomena under radiation is the self-organization of defects, such as the void superlattices, which have been observed in a list of bcc and fcc metals and alloys when the irradiation conditions fall into certain windows defined by temperature and dose rate. A superlattice features a lattice parameter and a crystal structure. Previously, it has been shown that the superlattice parameter is given by the wavelength of vacancy concentration waves that develop when the uniform concentration field becomes unstable. This instability is driven thermodynamically by vacancy concentration supersaturation and affected by the irradiation condition. However, a theory that predicts the superlattice symmetry, i.e., the selection of superlattice structure, has remained missing decades after the first report of superlattices. By analyzing the nonlinear recombination between vacancies and self-interstitial-atoms (SIAs) in the discrete lattice space, this work establishes the physical connection between symmetry breaking and anisotropic SIA diffusion, allowing for predictions of void ordering during defect self-organization. The results suggest that while the instability is driven thermodynamically by vacancy supersaturation, the symmetry development is kinetically rather than thermodynamically driven. The significance of SIA diffusion anisotropy in affecting superlattice formation under irradiation is also indicated. Various superlattice structures can be predicted based on different SIA diffusion modes, and the predictions are in good agreement with atomistic simulations and previous experimental observations.

Turing Instability in the Solid State: Void Lattices in Irradiated Metals.

Turing (or double-diffusive) instabilities describe pattern formation in reaction-diffusion systems, and were proposed in 1952 as a potential mechanism behind pattern formation in nature, such as leopard spots and zebra stripes. Because the mechanism requires the reacting species to have significantly different diffusion rates, only a few liquid phase chemical reaction systems exhibiting the phenomenon have been discovered. In solids the situation is markedly different, since species such as impurities or other defects typically have mobilities ∝exp(-E/k_{B}T), where E is the migration barrier and T is the temperature. This often leads to mobilities differing by several orders of magnitude. Here, we use a simple, minimal model to show that an important class of emergent patterns in solids, namely void superlattices in irradiated metals, could also be explained by the Turing mechanism. Analytical results are confirmed by phase field simulations. The model (Cahn-Hilliard equations for interstitial and vacancy concentrations, coupled by generation and annihilation terms) is generic, and the mechanism could also be responsible for the patterns and structure observed in many solid state systems.

Formation and self-organization of void superlattices under irradiation: A phase field study

Self-organized patterns, realized in non-equilibrium processes, have been widely observed in physics and chemistry. As a powerful tool to create far-from-equilibrium environments, irradiation produces a variety of types of defects, which can self-organize through physical interactions and chemical reactions. Such a process becomes complicated especially when both thermodynamics and kinetics play critical roles in pattern formation. In this paper, we investigate the formation and self-organization mechanism of void superlattices in metals and alloys under irradiation through phase field modeling and simulations. For the first time, three different formation mechanisms of void superlattices are clearly distinguished according to their thermodynamic origin and reaction kinetics. It is found that the characteristic length and symmetry of an emerging superlattice is determined by the interplay of the thermodynamic driving force and the kinetic anisotropy of the system. Through parametric study, the effects of kinetic coefficients, such as atomic mobility and irradiation dose rate, on the nucleation, growth, coarsening, coalescence, and ordering of voids are systematically investigated. The theoretical model developed in this work may provide guidelines for designing desired self-organized microstructures under irradiation.

Method for determining the electron and positron work function from a metal containing vacancies

A method is proposed that combines self-consistent solutions for a monovacancy in metal without regard to the outer surface and the solution in the stable jelly model for metal with homogeneous volume and flat surface, but a lowered vacancy density due to the presence of a superlattice of vacancy voids with relative concentration c v . When using c v as a small parameter, all energy characteristics are expanded in a functional series. Zero expansion terms relate to defect-free metal, and linear in c v corrections are expressed in terms of its characteristics. Exact formulas allowing the consideration of the effect of vacancies on the electron and positron work function are derived. Characteristics are calculated at various temperatures for Al and Na by the Kohn–Sham method. The method application to spherical clusters is briefly discussed.

Current status and future developments in preparation and application of colloidal crystals

Colloidal crystals (CCs) are ordered arrays of monodisperse colloidal particles. Because of the presence of a periodic superlattice of colloids and voids, CCs bear many unique structures and fascinating properties which are distinctly different from those of standard crystals with atoms, ions or molecules as repeating subunits. The research on CCs has surprisingly blossomed during recent decades, and many practical materials based on CCs with potential applications in photonic devices, material science and biomedical engineering have been generated. In this review, we give a systematic, balanced and comprehensive summary of the main aspects of CCs related to their preparation and application, and propose perspectives for the future developments of CCs.

Void superlattice formation in electron irradiated CaF 2: Theoretical analysis

CaF 2 is widely adopted as deep-UV window material and thin film optical coating. The void superlattice was observed experimentally under electron irradiation at room temperature. We performed kinetic Monte Carlo (kMC) simulations of the initial stages of the process when short- and intermediate-range order of defects in small Ca colloids and larger interstitial aggregates (F 2 gas voids) is created. The kMC model includes fluorine interstitial–vacancy pair creation, defect diffusion, similar defect attraction and dissimilar defect recombination. Special attention is paid to the statistical analysis of the defect aggregate distribution functions under different conditions (dose rate, defect migration and recombination rates). These simulations demonstrate that under certain conditions the dissimilar aggregate recombination is strongly suppressed which stimulates growth of mobile interstitial aggregates that is a precondition for further void ordering into a superlattice.

Computer simulation study of defect formation and migration energy in calcium fluoride

A theoretical study of the defect formation (vacancy, interstitial and Frenkel defects) energy, and vacancy migration energy in calcium fluoride is presented in this paper. Calculations were conducted using the ab initio method with the plane-wave pseudopotential and molecular-dynamics simulation to determine the energetic and defect properties of the CaF2 crystal. For cation and anion vacancies, the relaxed vacancy formation energies were calculated to be 13.75 and 8.34eV, respectively. It was also found that only the octahedral positions are stable sites for Ca and F interstitial atoms. For cation the second nearest neighbor Frenkel defects were found to be stable within the simulation time (5ps) and the defect formation energy was estimated to be 9.3eV, while the third nearest neighbor Frenkel defects for anion were stable and the formation energy was only 2.49eV. The results are in agreement with Ure’s experimental results. The migration energy of cation vacancy in the direction of 〈110〉 is lower than that of 〈100〉 (3.93eV versus 4.62eV), suggesting 〈110〉 is the most likely path for Ca vacancies to migrate, while most anion vacancies may diffuse in the 〈100〉 directions due to a very low (0.33eV) anion migration energy in the direction. The data are useful for better understanding the formation of nano-scale void superlattice in calcium fluoride under electron beam irradiation.

In situ TEM Study of Electron Beam Stimulated Organization of Three-dimensional Void Superlattice in CaF2

CaF2 is widely adopted as deep-UV window material and thin film optical coating. It has been known that ordered defect superlattices may form in electron irradiated CaF2.[1] However, the nature of the defects on the superlattice point (i.e., Ca colloids or voids) has not been certain and the self-organization mechanism has not been fully understood. In this study, single crystal CaF2 were irradiated under 200 keV electron beam at room temperature with in situ TEM observation of the dynamic process of defect ordering. The superlattice reached steady state after an electron dose of 1×1021e−/cm2 with void radius about 5 nm. Videos recorded during the in-situ observation reveal the dynamic self-organization process of the void superlattice. Coalescence was prevalent at the initial stages. Migration and preferential growth were dominant at the final stages of the superlattice formation. At a dose higher than 3×1021e−/cm2 the superlattice structure was destroyed. These critical doses of void superlattice formation and deformation seem to be independent of dose rate. The anisotropic diffusivity of the migrating “molecules” may explain the superlattice formation.

IN SITU Tem Study of Electron Beam Stimulated Organization of Three-Dimensional Void Superlattice in Caf2

ABSTRACTCaF2 is widely adopted as deep-UV window material and thin film optical coating. It has been known that ordered defect superlattices may form in electron irradiated CaF2.[1] However, the nature of the defects on the superlattice point (i.e., Ca colloids or voids) has not been certain and the self-organization mechanism has not been fully understood. In this study, single crystal CaF2 were irradiated under 200 keV electron beam at room temperature with in situ TEM observation of the dynamic process of defect ordering. The superlattice reached steady state after an electron dose of 1×1021e-/cm2 with void radius about 5 nm. Videos recorded during the in-situ observation reveal the dynamic self-organization process of the void superlattice. Coalescence was prevalent at the initial stages. Migration and preferential growth were dominant at the final stages of the superlattice formation. At a dose higher than 3×1021 e-/cm2 the superlattice structure was destroyed. These critical doses of void superlattice formation and deformation seem to be independent of dose rate. The anisotropic diffusivity of the migrating “molecules” may explain the superlattice formation.

Defect accumulation in fcc and bcc metals and alloys under cascade damage conditions – Towards a generalisation of the production bias model

In recent years, it has been shown that the problem of defect accumulation under cascade damage conditions can be properly addressed within the framework of production bias model (PBM) based on intracascade clustering of point defects, differences in the thermal stability of the resulting clusters and one-dimensional (1-D) diffusion of interstitial clusters. Within this framework, different aspects of defect accumulation such as the high swelling rate at low dislocation densities, enhanced swelling near grain boundaries, effects of grain size, irradiation dose and recoil energy on void swelling have been treated quantitatively. In the present work we have attempted to address the problem of differences in the defect accumulation behaviour between fcc and bcc metals under cascade damage conditions. In this analysis we have chosen copper and molybdenum to represent fcc and bcc metals, respectively. This choice was suggested by the fact (a) that a large amount of experimental information exists on these metals and (b) that the damage accumulation behaviour in copper can be fully accounted for in terms of the PBM. An analysis of the existing experimental observations in terms of the PBM raises the question about differences between the reaction kinetics of the one-dimensionally diffusing interstitial clusters with sinks in fcc and bcc metals. In the present paper, the impact of different frequencies of changes in the 1-D diffusion direction of such clusters on their reaction kinetics is discussed. The present considerations provide an appropriate framework for generalising the PBM in order to describe damage accumulation behaviour in metals and alloys in general, including the formation of void superlattices.

Saturation of swelling in neutron-irradiated molybdenum and its dependence on irradiation temperature and starting microstructural state

Molybdenum and its alloys are of interest for potential fusion application due to their high melting points and relatively good thermal conductivities. The development of void superlattices during neutron irradiation appears to limit void swelling in pure molybdenum to values below 4% over a wide range of irradiation temperatures. The saturation value of swelling and the void superlattice parameter each appear to be somewhat dependent on temperature, but independent of the thermomechanical starting state. Formation of technetium and ruthenium by transmutation may also play some minor role in the microstructural evolution, but do not appear to be involved in the limitation of swelling observed in this and other experiments.

Superconductors with a Superlattice of Voids

AbstractThe problem of the interaction between the vortex lattice in superconductors with the void superlattice is investigated. It is shown that the effect of the void superlattice is strong enough and under conditions that can be easily realized, changes the symmetry of the latter. Then the minimum of free energy is reached for the vortex lattice whose unit cell before deformation in the vicinity of voids has the form of a parallelogram with, in general, unequal sides.