Stacking Fault Tetrahedra Research Articles

Compositional stability in medium and high-entropy alloys of CoCrFeMnNi system under ion irradiation

The equiatomic high-entropy alloy (HEA) CoCrFeMnNi not only has excellent mechanical properties but also good irradiation resistance. However, the mechanical properties of some equiatomic medium-entropy alloys (MEAs) are superior to those of CoCrFeMnNi HEA. In this study, the irradiation resistance and changes in composition due to irradiation in CoCrNi and CoCrFeNi MEAs and CoCrFeMnNi HEA are investigated. Thin film samples of the MEAs and HEA and Ni used for comparison were irradiated with up to 1.7 × 1019 ions/m2 of 2.4 MeV Cu ions at 673 and 873 K. The average damage in the observed area was 1 displacement per atom (dpa). No voids were observed in any of the MEA and HEA samples even after irradiation at 873 K; however, large voids were formed in Ni irradiated at 873 K. This indicates that the irradiation resistance of CoCrNi and CoCrFeNi MEAs and CoCrFeMnNi HEA was better than that of Ni. In addition, the formation of stacking fault tetrahedra (SFTs), a type of vacancy cluster, at 873 K was much more pronounced in CoCrNi and CoCrFeNi MEAs than in CoCrFeMnNi HEA. Therefore, the irradiation resistance of CoCrNi and CoCrFeNi MEAs is lower than that of CoCrFeMnNi HEA. Moreover, significant Cr segregation occurred in the CoCrNi and CoCrFeNi MEA samples irradiated at 873 K. In contrast, no segregation occurred in CoCrFeMnNi HEA. First-principles calculation results show that the formation rate of Cr-dumbbells is higher in CoCrNi and CoCrFeNi MEAs than in CoCrFeMnNi HEA, and that Cr interstitials are more stable in the MEAs. Therefore, Cr segregation is more likely to occur in the MEAs. Element segregation may affect the irradiation resistance of the alloys.

Direct transformation of equilateral hexagonal Frank vacancy loops to stacking fault tetrahedra under thermal fluctuation

Stacking fault tetrahedra (SFTs) are highly interesting three-dimensional vacancy defects in quenched, plastically deformed or irradiated face-centered-cubic metals and have a significant impact on the properties and subsequent microstructural evolution of the materials. Their formation mechanism and stability relative to two-dimensional vacancy loops are still debated. Equilateral hexagonal Frank vacancy loops (faulted, sessile) observed in microscopy have been considered unable to directly transform to SFTs due to separation of Shockley partial dislocations as well as embryonic stacking faults. Here using sufficiently long (up to tens of nanoseconds) molecular dynamic simulations, we demonstrate that such a transformation can in fact take place spontaneously at elevated temperatures under thermal fluctuation, reducing potential energy of defected atoms by <0.05 eV/atom. The transformation becomes easier with increasing temperature or decreasing loop size.

Molecular dynamics study of interactions between edge dislocation and irradiation-induced defects in Fe–10Ni–20Cr alloy

Irradiation-induced defects frequently impede the slip of dislocations, resulting in a sharp decline in the performance of nuclear reactor structural materials, particularly core structural materials. In the present work, molecular dynamics method is used to investigate the interactions between edge dislocations and three typical irradiation-induced defects (void, Frank loop, and stacking fault tetrahedron) with the sizes of 3 nm, 5 nm, and 7 nm at different temperatures in Fe–10Ni–20Cr alloy. The critical resolved shear stresses (CRSSs) are compared among different defect types after interacting with edge dislocations. The results show that the CRSS decreases with temperature increasing and defect size decreasing for each defect type during the interaction with edge dislocations, except for the case of 3-nm Frank loops at 900 K. According to a comparison, the CRSS in Frank loop is significantly higher than that of others of the same size, which is due to the occurrence of unfaulting and formation of superjog or stacking-fault complex during the interaction. The atomic evolution of irradiation-induced defects after interacting with dislocations can provide a novel insight into the design of new structural materials.

On the relative contributions of point defect clusters to macroscopic swelling of metals

Swelling of metals under irradiation is commonly assessed by calculating the volume fraction of voids, which appear at temperatures where vacancies are mobile. However, other clusters are formed, which may also have an impact on swelling. In particular, interstitial loops have recently been considered to give a significant contribution to swelling owing to their large relaxation volume. In this work, we perform calculations in nickel, based on interatomic potentials, to estimate the contributions of the various point defect clusters. We show that voids produce much more swelling than loops and stacking fault tetrahedra, whose contribution is essentially due to the dislocation core field, inducing a dilatation per unit length of around 1b2, where b is the Burgers vector. Evaluation of swelling should indeed be done by summing formation volumes, not relaxation volumes, the latter being related to lattice parameter change as measured by x-ray diffraction. We also discuss the case of “lattice swelling” occurring when vacancies are immobile. When self-interstitial atoms cluster as dislocation loops, this swelling mode turns out to be nothing but “void” swelling in a regime where vacancy mobility is so low that vacancies do not cluster appreciably, leaving only interstitial loops visible in transmission electron microscopy.

Volume of a dislocation network

We derive a simple analytical line integral expression for the relaxation volume tensor of an arbitrary interconnected dislocation network. This quantity determines the magnitude of dislocation contribution to the dimensional changes and volumetric swelling of a material, and highlights the fundamental dual role of dislocations as sources of internal strain as well as carriers of plastic deformation. To illustrate applications of the method, we compute the relaxation volume of a stacking fault tetrahedron, a defect commonly occurring in fcc metals; the volume of an unusual tetrahedral configuration formed by the (a/2) and a dislocations in a bcc metal; and estimate the relative contribution of extended dislocations to the volume relaxation of heavily irradiated tungsten.

Dynamic interactions between low-angle grain boundary and stacking fault tetrahedron in Ni-Fe solid solution alloys

A stacking fault tetrahedron (SFT) is a very common kind of defects in face-centered cubic (FCC) metals under irradiation environment. The migrating GB can heal the SFT through dislocation reactions. To explore the healing mechanisms and conditions required, the low-angle GB interactions with an SFT in pure Ni and Ni-Fe bicrystals were investigated using molecular dynamics (MD) simulations. Ni-Fe bicrystals have higher healing efficiency on SFT than pure Ni due to their more diverse dislocation reactions. The addition of Fe atom can reduce the stacking fault energy (SFE), so that most of stair-rod dislocations (SRDs) of SFT in Ni-Fe bicrystals can be transformed into Shockley partial dislocations (SPDs) through the energetically unfavorable reactions. As a result, the vacancies of SFT are redistributed and some of them are carried away by migrating GBs. In pure Ni, however, only a small part of SRDs can undergo the energetically unfavorable reactions, and the SPDs generated would spontaneously be transformed back to SRDs after the GB-SFT interaction. The healing efficiency on SFT can be gradually enhanced with the increasing Fe atom concentration and elevated temperature. • Dislocation reactions of low-angle GB and SFT in Ni-Fe are more diverse than in Ni. • Stair-rod dislocations of SFT can be converted into Shockley partial dislocations. • The vacancies of SFT are redistributed and carried away by migrating GB in Ni-Fe. • The SFT absorbed by low-angle GB is regenerated after GB-SFT interaction in Ni. • The healing efficiency on SFT can be enhanced with increasing Fe atom concentration.

Atomistic study of coreshell and functionally graded nanospheres under compressive loading

Functionally grading and coreshell are two interesting engineering modifications to nanomaterials structure for tailored applications in electronics, energy conversion devices and so on. Understanding the mechanical response of these nanostructures are of particular importance to ensure the reliability of these devices under service conditions. In this paper, functionally graded and coreshell Silver–Gold (Ag–Au) nanospheres are studied under compression load using molecular dynamics simulation. The fracture and deformation mechanism along with the incipient plasticity through dislocation nucleation and propagation has been studied for both functionally graded and coreshell structure for different percentages of Ag and Au of the nanosphere. Our results indicate that plastic deformation is dictated by the partial dislocation nucleation and propagation from the contact surface which varies as the alloying percentages of the coreshell and functionally graded nanosphere. An inverse size effect is observed for the mechanical properties which also affects the deformation mechanism of the nanosphere by forming stacking fault tetrahedra for both the nanostructures. For a range of Ag percentages in Au, the coreshell nanospheres showed higher compressive strength compared to functionally graded nanospheres. As coreshell and functionally grading are two promising nanoscale materials design, current work will inspire developing new metal nanospheres to harness the materials potential for different engineering applications.

Healing stacking fault tetrahedron in NiFe solid solution alloys through grain boundary migration

A stacking fault tetrahedron (SFT) is a very common kind of defects in face-centered cubic metals under irradiation environment. The grain boundary (GB) migration can effectively heal the SFT through the GB-SFT interaction to improve the irradiation resistance of materials. In this study, the GB-SFT interactions in pure Ni and NiFe bicrystals subjected to shear loading were investigated by the molecular dynamics simulations. After the GB-SFT interaction, the GB in pure Ni is pinned, and a void appears as it migrates further, but the GB in NiFe solid solution alloys still remains flat. The migrating GB in the alloys has a higher efficiency to heal the SFT than that in pure Ni. The GB roughening caused by the alloying element brings more transitional structural units into the GB to accommodate more vacancies. As a result, similar to elevated temperature, increasing Fe atom concentration could improve the capacity of GB to heal the SFT.

Conversion of stacking fault tetrahedra to bubbles in dual (Kr, He)-beam irradiated copper

Stacking fault tetrahedrons (SFTs) are commonly observed in irradiated face-centered-cubic metals with low-to-medium stacking fault energies. Several mechanisms were previously proposed for the removal of SFTs in irradiated solids, including high temperature annealing, interactions with interstitial atoms, dislocations, and twin boundaries, and transformation to dislocation loop under compressive stress. We propose a previously unreported mechanism for the removal of SFT in irradiated copper, supported by experiments and atomistic simulations. In situ experiments showed that helium bubble density increased at the expense of SFT density following the initial phase of dual 1 MeV Kr/12 keV He ion irradiation, suggesting a possible conversion of SFTs to helium bubbles. Atomistic simulations of the interactions of helium atoms with SFTs confirmed this possibility and revealed the collective effects of helium-induced shear stress that deformed the atomic planes of Cu leading to the destruction of the SFT and leaving behind helium atoms in vacancy clusters (bubbles).

Effects of Fe atoms on hardening of a nickel matrix: Nanoindentation experiments and atom-scale numerical modeling

Significant hardening effect due to Fe concentrations in Ni-based alloys with face-centered-cubic structure has been studied by using a combined experimental and atomistic-based computational approach via nanoindentation tests. The obtained experimental load–displacement data for the [001] crystal orientation reached a qualitative good agreement with molecular dynamics simulations results, leading to strong evidence that the main strengthening factors are associated to sluggish dislocation diffusion, reduced defect sizes and the nucleation of tetrahedral stacking faults. Here, interstitial type prismatic dislocation loops mainly formed by ⅙〈112〉 Shockley dislocations are nucleated during the loading process, where their interaction leads to the formation of pyramidal shaped stacking fault which are mainly created by ⅓〈100〉 Hirth dislocations lines. Observing both types of defects coexisting in the same plastic deformation zone by both approaches. Reported mechanical data, measured experimentally and interpreted numerically, are also in accordance with microstructural SEM and TEM investigations.

Dislocation reaction-based formation mechanism of stacking fault tetrahedra in FCC high-entropy alloy

In conventional FCC metals and alloys, the formation mechanisms of stacking fault tetrahedron (SFT) based on the vacancy cluster and Frank loop have been widely accepted; however, the dislocation reaction-based formation mechanism of SFT without Frank loop and vacancy cluster remains controversial. In this work, we studied the formation of the SFTs in CoCrFeNiCu high-entropy alloy (HEA) bicrystals and their single-crystal counterparts subjected to shear deformation using molecular dynamics (MD) simulations. The migration and thickening of grain boundaries, and the nucleation and glide of dislocations from the grain boundaries are the predominant carriers of deformation, which are the prerequisite for the formation of SFT. We observed two types of dislocation reaction-based formation mechanisms, where there is no vacancy aggregation and Frank loop participation. The formation of SFT originates from the growth of the bottom face of the pyramid in the bicrystal HEA, while in the single-crystal HEA, SFT nucleates at its vertex, and extends towards its bottom.

Atomistic structure and thermal stability of dislocation loops, stacking fault tetrahedra, and voids in face-centered cubic Fe

Irradiation-induced hardening and changes to mechanical properties can often lead to material degradation and can limit the operation of reactor components. In addition, changes to mechanical properties can be a precursor to other material environmental degradation. Dislocation loops, stacking fault tetrahedra (SFT), and voids are major irradiation-induced lattice defects that occur in structural materials and are often observed post-irradiation. However, these defects are often considered only as obstacles to dislocation motion, with hardening assumed to be dependent on the habit plane and Burgers vector of the defect. The stability and nature of dislocation loops and SFTs with temperature are often overlooked, and this may play a crucial role in the mechanical properties of structural materials. We combine high-resolution transmission electron microscopy (HR-TEM) and atomistic simulations to determine the atomistic configurations and thermal stability of dislocation loops and SFTs. Dislocation dissociations are observed in both vacancy and interstitial-type perfect dislocation loops as well as in vacancy-type Frank loops, whereas interstitial-type Frank loops remain stable and are the least influenced by temperature. Triangle-shaped intrinsic stacking faults are formed at the edges of Frank vacancy loops, and a direct transformation from triangle-shaped Frank vacancy loops to SFTs is observed in atomistic simulations. SFTs are energetically more stable than Frank vacancy loops based on formation energy calculations in pure face-centered cubic Fe, which may explain why vacancy-type Frank loops are infrequently observed experimentally. The motivation for this study is to develop a framework for the stability and nature of irradiation defects as a function of temperature, which will be subsequently used for more complex (alloy) systems.

In-situ radiation response of additively manufactured modified Inconel 718 alloys

In this study, a novel alloy of modified Inconel 718 produced by laser powder bed fusion is studied before and after in-situ Kr irradiation up to 3 dpa at 200 and 450 °C. Before irradiation, the microstructure consists of dislocation cells having a misorientation angle less than 5° and with an average size of ~500 nm. There are also second phase particles of MC type carbides, Laves phase and oxides such as Y-O, Y-(Ti)-Al-O. While the microstructure consists of stacking fault tetrahedra, faulted and perfect loops after irradiation at 200 °C, dislocation loops are the primary defects at 450 °C. With increasing dose, the size of the defects remains similar at 200 °C while it increases at 450 °C. This has been attributed to the existence of vacancy type defects at 200 °C and the different defect transport mechanisms at different temperatures. Moreover, matrix and second phase particle compositions seem to be similar after irradiation. The sink strengths of the structures have been calculated and superior radiation resistance of this alloy has been attributed to the existence of fine cell boundaries stabilized by the second phase particles produced by additive manufacturing.

Twin boundary migration and reactions with stacking fault tetrahedron in Cu and CoCrCuFeNi high-entropy alloy

FCC high-entropy alloys (HEAs) have great application potential because of their excellent mechanical properties, in which twin boundary (TB) and stacking fault tetrahedron (SFT) are two kinds of primary defects. In this work, the mechanical responses of a twinned CoCrCuFeNi HEA and twinned Cu counterpart under shear deformation were investigated using molecular dynamics simulations to explore the interactions between TB and SFT and their effects on the mechanical properties of the materials. It was found that the primary carrier of plastic deformation in both twinned CoCrCuFeNi HEA and Cu are shear coupled TB migrations assisted by the glide of partial dislocations. Increasing the size of SFT leads to lower mechanical performances. Moreover, the mechanical properties of the CoCrCuFeNi HEA, including shear modulus and critical shear stress for TB migration, were found to be dependent insignificantly on temperature (100 K–700 K). After the interaction between TB and SFT, a flip-over SFT or SFT-like structure in CoCrCuFeNi HEA, and a rhombic SFT or double-sided SF in Cu are finally formed.

Atomistic studies of the responses of composites with thermal residual stresses and defects under uniaxial loading

The thermal residual stresses and plastic deformation caused by the coefficient of thermal expansion (CTE) mismatch in the cooling process play an important role in the physical and mechanical properties of metal matrix composites (MMCs). In this study, the Cu/SiCp composites with and without cooling process are subjected to uniaxial tensile and compressive loadings through molecular dynamics (MD) simulation. We found that the cooling process leads to a decrease in strength and earlier yielding. The mechanical response depends on the temperature drop, and samples cooled from a higher temperature have a lower yield strength. The introduction of reinforcements and thermally induced defects reduce the tension/compression (C/T) asymmetry as compared with that of single crystal and defective Cu. These pre-existing defects can be the source for the initiation of plasticity in early stage of external loading, and the defect evolution shows a C/T asymmetry. For the density of two predominant dislocation types, the Shockley partial increases at the stress buildup stage, while the stair-rod dislocation decreases, regardless of tension and compression. The mechanisms for the dissociation of stair-rod dislocation and incomplete stacking fault tetrahedrons (ISFTs) at the stress buildup stage have been revealed. Our results provide an atomic-scale perspective to understand the influence of thermally residual stresses and defects on mechanical behavior of MMCs.

Formation and Anisotropic Mechanical Behavior of Stacking Fault Tetrahedron in Ni and CoCrFeNiMn High-Entropy Alloy

Stacking fault tetrahedron (SFT) is a kind of detrimental three-dimensional defect in conventional face-centered cubic (FCC) structural metals; however, its formation and anisotropic mechanical behavior in a CoCrFeNiMn high-entropy alloy (HEA) remain unclear. In this work, we first performed molecular dynamics simulations to verify the applicability of the Silcox-Hirsch mechanism in the CoCrFeNiMn HEA. The mechanical responses of the SFT to shear stress in different directions and that of the pure Ni counterpart were simulated, and the evolutions of the atomic structures of the SFTs during shear were analyzed in detail. Our results revealed that the evolution of the SFT has different patterns, including the annihilation of stacking faults, the formation and expansion of new stacking faults, and insignificant changes in stacking faults. It was found that the effects of SFT on the elastic properties of Ni and HEA are negligible. However, the introduction of SFT would reduce the critical stress, while the critical stress of the CoCrFeNiMn HEA is much less sensitive to SFT than that of Ni.

Healing of nanocracks by collision cascades in nickel

We use molecular dynamics simulations to investigate the interaction between collision cascades and pre-existing nanocracks in nickel (Ni). We find that collision cascades cause the cracks to heal whenever a cascade initiates a thermal spike whose core overlaps with the crack. Moreover, crack healing affects the distribution of radiation-induced defects generated during a collision cascade: defect clusters, such as dislocations and stacking fault tetrahedra, dominate in the presence of crack healing, while isolated point defects dominate in its absence. This work indicates that irradiation may reduce the number of pre-existing crack-like flaws in metallic components, potentially improving their mechanical resilience.

Advanced method for structure-strength-ductility assessment of dispersion-strengthened FCC metals using activation work, mean slip distance and constitutive relation analyses: Decoding the Haasen plot

The role of cross-slip activation on controlling dislocation mechanisms and deformation debris creation in a dispersion-strengthened matrix (DSM) face-centred cubic metal, GlidCop®, has been elucidated using experimental measurement of the strain rate sensitivity, S, the mean slip distance, λ, and constitutive relation analyses (CRA) from 78 to 473 K. If the stress for cross-slip activation is larger than that of DSM yield stress, geometrically necessary prismatic loops (GNPL) are generated, but the rate controlling kinetics is that of vacancy-drag for cube-textured copper wire-specimens. With increasing temperature, percolation continues to occur by Orowan looping. However, upon yielding, GNPL formation is replaced by various types of dipole loop creation due to dislocation intersections from multiple slip. Loops that convert to stacking fault tetrahedra are measurable, but opposite sign dipoles are dynamically annihilated by pipe diffusion reducing debris retention. The rate controlling mechanisms are identified in the temperature range in which S is constant and the activation energy to overcome the obstacle becomes identical to the measurable activation work. This study shows that cross-slip activation stress determined by CRA, when superposed on the yield stress versus temperature plot of DSM alloys, can identify the mechanism-change temperatures. Subsequent S versus temperature profiles, determined from a new method of Haasen plot analysis of up- and down-strain-rate change tests, can delineate the prime rate-controlling mechanisms, characterize the stored debris and determine whether non-shearing or shearing of particles had occurred. Hence, an advanced method to characterize plastic behavior of DSM alloys has been developed.

Microstructure Evolution in He-Implanted Si at 600 °C Followed by 1000 °C Annealing.

Si single crystal was implanted with 230 keV He+ ions to a fluence of 5 × 1016/cm2 at 600 °C. The structural defects in Si implanted with He at 600 °C and then annealed at 1000 °C were investigated by transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM). The microstructure of an as-implanted sample is provided for comparison. After annealing, rod-like defects were diminished, while tangled dislocations and large dislocation loops appeared. Dislocation lines trapped by cavities were directly observed. The cavities remained stable except for a transition of shape, from octahedron to tetrakaidecahedron. Stacking-fault tetrahedrons were found simultaneously. Cavity growth was independent of dislocations. The evolution of observed lattice defects is discussed.

Study on the evolution mechanism of subsurface defects in nickel-based single crystal alloy during atomic and close-to-atomic scale cutting

Nickel-based single crystal alloys are widely used in aerospace industry. From the point of view of defect evolution and energy change, the evolution mechanism of subsurface defects in the atomic and close-to-atomic scale (ACS) cutting single crystal nickel-based alloy with silicon nitride tool was studied, combining with the molecular dynamics method. The mixed potential function was used to describe the force interaction between atoms in the ACS cutting system. The process of nucleation, propagation and transformation of subsurface defects were analyzed. Based on the dislocation emission model, the relationship between dislocation slip length and change of energy was described. The variety, quantity and area of subsurface defect changes caused by the change of cutting speed, crystal orientation and cutting depth were discussed. The result shows that increasing cutting speed can effectively reduce the number and area of subsurface defects and improve the quality of machined parts. The larger the cutting speed, the larger the chip volume. With the increase of cutting depth, the number of stacking fault tetrahedrons in the subsurface area of workpiece increases. When crystal orientation 010 00 1 ¯ is used for cutting, more defects will be produced in the subsurface region. When crystal orientation are 111 10 1 ¯ and 011 01 1 ¯ , the dislocation emission angle is π /2, it is the most favorable for the emission of partial dislocations and easy to remove materials. The research content provides important references for the optimization of machining parameters and improvement of processing quality for the ultraprecision cutting of nickel-based alloy.