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The face-centered cubic structure (fcc) and its deformation behaviors, as well as the distinctive role of fcc-Ti in nanocrystallization in TC17 subjected to high energy shot peening (HESP), were investigated by using comprehensive high-resolution transmission electron microscopy (HRTEM). The results showed that there was a stress-induced fcc-Ti in TC17 with a lattice constant of 0.420-0.433 nm and the B-type orientation relationship between the hcp-Ti and the fcc-Ti as [20]hcp//[10]fcc and (0001)hcp//(111)fcc, which was accomplished by the gliding of Shockley partial dislocations with Burgers vector of 1/3[010] on the basal plane. The deformation twinning dominated the subsequent deformation of fcc-Ti, producing two types of {111} twins with different characteristics. Among them, the I-type twin with complete structure was generated by successive gliding of Shockley partial dislocations with the same Burgers vector of 1/6[11]. In contrast, the cooperative slip of three Shockley partials, whose sum of Burgers vectors was equal to zero, produced the II-type twin with zero net macroscopic strain. And then, the emission of Shockley partial with the Burgers vector of 1/6[11] on every three (111)fcc planes resulted in the formation of a 9R structure. Due to the dissociation effect of lamellar fcc-Ti and the superior deformation ability of fcc structure, the occurrence of fcc-Ti effectively promoted surface nanocrystallization of TC17.

An intermediate state of basal-type (B-type) face-centered cubic (FCC) zirconium phase is firstly reported in as-solidified pure zirconium by means of transmission electron microscopy (TEM) technique. The B-type hexagonal close-packed (HCP) to FCC phase transformation can be realized by following path: HCP→Intermediate state→FCC and each stage contained Shockley partial dislocations with Burgers vector of 1 / 6 [ 0 1 ¯ 10 ] . The observed intermediate state is direct evidence of the B-type FCC zirconium phase via partial dislocation.

In this study, we report atomistic calculations of the core structure of screw dislocations with [001] Burgers vector in Mg2SiO4 olivine. Computations based on the THB1 empirical potential set for olivine show that the stable core configurations of the screw dislocations correspond to a dissociation in {110} planes involving collinear partial dislocations. As a consequence, glide appears to be favorable in {110} planes at low temperature. This study also highlights the difference between dislocation glide mechanism in {110} versus (010) or (100) for which glide is expected to occur through a locking–unlocking mechanism.

Each 2D material has a distinct structure for its grain boundary and dislocation cores, which is dictated by both the crystal lattice geometry and the elements that participate in bonding. For the class of noble metal dichalcogenides, this has yet to be thoroughly investigated at the atomic scale. Here, we examine the atomic structure of the dislocations and grain boundaries (GBs) in two-dimensional PtSe2, using atomic-resolution annular dark field scanning transmission electron microscopy, combined with density functional theory and empirical force field calculations. The PtSe2 we study adopts the 1T phase in large-area polycrystalline films with numerous planar tilt GB distinct dislocations, including 5|7+Se and 4|4|8+Se polygons, in tilt-angle monolayer GBs, with features sharply distinguished from those in 2H-phase TMDs. On the basis of dislocation cores, the GB structures are investigated in terms of pathways of dislocation chain arrangement, dislocation core distributions in different misorientation angles, and 2D strain fields induced. Based on the Frank-Bilby equation, the deduced Burgers vector magnitude is close to the lattice constant of 1T-PtSe2, building the quantitative relationship of dislocation spacings and small GB angles. The 30° GBs are most frequently formed as a stitched interface between the armchair and zigzag lattices, constructed by a string of 5|7+Se dislocations asymmetrically with a small deviation angle. Another special angle GB, mirror twin 60° GB, is also mapped linearly by metal-condensed asymmetric or Se-rich symmetric dislocations. This report gives atomic-level insights into the GBs and dislocations in 1T-phase noble metal TMD PtSe2, which is a promising material to underpin extending properties of 2D materials by local structure engineering.

A triangular single Shockley stacking fault (1SSF) in 4H-SiC, expanding from the surface to the substrate/epilayer interface, was investigated. The triangular 1SSF was observed during electroluminescence examination of PIN diodes that had line-and-space anodes with open windows. The threshold current density of the 1SSF expansion was comparatively intermediate, and differed from that of a 1SSF that expanded from a basal plane dislocation (BPD) that had penetrated from the substrate into the epilayer, and from that of a 1SSF that expanded from a BPD that had converted into threading edge dislocations (TEDs) at the substrate/epilayer interface. No BPDs or surface damage such as cracks were observed by photoluminescence imaging, synchrotron x-ray topography imaging, or scanning electron microscope imaging near the origin of the expansion region. High-resolution observation using cross-sectional transmission electron microscopy showed that a partial dislocation (PD) was present on the basal plane and two inclined TEDs were present on both sides of the PD. A g·b analysis showed that this dislocation had a Burgers vector of ± (1/3) [11 $$\overline{2}$$ 0], and it was estimated to be a combination of a TED-BPD-TED structure with a short BPD before expansion. Therefore, the triangular 1SSF from the surface side can be explained to have expanded from this BPD. Furthermore, considering the possibility of the BPD-TED conversion at the epitaxial growth process, the TED-BPD-TED dislocation was speculated to have formed after epitaxial growth. The perfect control of the forward voltage degradation of 4H-SiC device is thought to be realized by focusing on this type of BPD.

The deformation of crystalline materials by dislocation motion takes place in discrete amounts determined by the Burgers vector. Dislocations may move individually or in bundles, potentially giving rise to intermittent slip. This confers plastic deformation with a certain degree of variability that can be interpreted as being caused by stochastic fluctuations in dislocation behavior. However, crystal plasticity (CP) models are almost always formulated in a continuum sense, assuming that fluctuations average out over large material volumes and/or cancel out due to multi-slip contributions. Nevertheless, plastic fluctuations are known to be important in confined volumes at or below the micron scale, at high temperatures, and under low strain rate/stress deformation conditions. Here, we develop a stochastic solver for CP models based on the residence-time algorithm that naturally captures plastic fluctuations by sampling among the set of active slip systems in the crystal. The method solves the evolution equations of explicit CP formulations, which are recast as stochastic ordinary differential equations and integrated discretely in time. The stochastic CP model is numerically stable by design and naturally breaks the symmetry of plastic slip by sampling among the active plastic shear rates with the correct probability. This can lead to phenomena such as intermittent slip or plastic localization without adding external symmetry-breaking operations to the model. The method is applied to body-centered cubic tungsten single crystals under a variety of temperatures, loading orientations, and imposed strain rates.

The results of structural studies of GaN nanowires containing screw dislocations are presented. It is found that the length of the Burgers vector of dislocations may reach 5 nm, i.e., exceed many times the c parameter of the gallium nitride unit cell. The formation of such dislocations leads in some cases to the occurrence of an ordered sequence of basal stacking faults with a period of 1.3–3.9 nm.

The second-order elastic constants, third-order elastic constants, and the generalized-stacking-fault energy for semiconductor GaAs are investigated using the first-principles calculations. The predictions of elastic constants are obtained from the coefficients of the fitted polynomials of the energy-strain functions. It is found that the nonlinear elastic effects must be considered when the applied deformations are larger than approximately 1.5%. With the Lagrangian strains up to 6.4%, the terms included up to third order in energy expansion functions are sufficient. The elastic constants given in this work agree well with the previous results and experimental data except for C144. C144 given by the present paper is a positive value, and the estimated 3 GPa agrees well with the experimental result of 2 GPa. The research results can provide a reference for understanding the elasticity of GaAs. The generalized-stacking-fault energy has been calculated without and with structural relaxation, respectively. The unstable stacking fault energy with structural relaxation is about two-thirds of that without relaxation. The dislocation width and Peierls stress for 30° partial in GaAs have been investigated based on the improved P-N theory. The dislocation width is very narrow (only about one-fifth of Burgers vector b), which is reasonable for covalent materials. The Peierls stress is about 4 GPa, in good agreement with the experimental result of 2∼3 GPa.

Silicon carbide (SiC) is an important semiconductor material for a variety of electronic and optoelectronic applications owing to the unique combination of its superior electronic and physical properties. In order to continuously improve the crystal quality and improve device performance, obtaining a clear understanding of the defect types and their distribution and potential influence on device operation is of great importance. In this study, 6H-SiC crystals grown by physical vapor transport (PVT) have been characterized by synchrotron monochromatic beam x-ray topography (SMBXT). By recording six different $$11{\bar{2}},12$$ grazing incidence reflections and analyzing the contrast patterns of threading screw dislocations (TSDs), threading edge dislocations (TEDs), threading mixed dislocations (TMDs), and basal plane dislocations (BPDs) observed in conjunction with ray-tracing simulation, the Burgers vectors of these dislocations have been determined. This successfully demonstrated a direct Burgers vector determination approach for each type of dislocation. Understanding these dislocation types and their distributions in 6H-SiC wafers can provide crucial feedback for pursuing crystal quality enhancement during growth process. High-resolution x-ray diffraction (HRXRD) has been performed on the wafer to carry out the rocking curve analysis of areas with different degrees of lattice distortion.

X-ray topography is a useful and nondestructive method for direct observation of crystal defects in nearly perfect single crystals. The grown-in dislocations from the cross-linked seed crystal in tetragonal hen egg-white lysozyme crystals were successfully characterized by digital X-ray topography. Digital X-ray topographs with various reflections were easily obtained by reconstruction of sequential rocking-curve images. The Burgers vector of the dislocation is different from those reported previously. Interestingly, one of the dislocations had a bent shape. The preferred direction of the dislocation line was analysed by the estimated dislocation energy based on the dislocation theory. The dislocation energy can be estimated by the dislocation theory even in protein crystals composed of macromolecules.

An equiatomic CuFeMnNi high-entropy alloy (HEA) was synthesized and homogenized at 1000 °C to achieve a microstructure of single face centered cubic phase based on CALPHAD (CALculation of PHAse Diagrams) prediction. The strength and ductility of this Co-free (low cost) HEA can be tuned through thermomechanical processing (cold rolling and annealing at temperatures ranging from 650 °C to 950 °C). Electron backscattered diffraction, transmission electron microscopy and scanning transmission electron microscopy techniques were used to characterize the deformation microstructure of this new HEA. The results show that plastic deformation was achieved through the slip of full dislocations with Burgers vector of a/2 . No dissociated dislocations and deformation twins were observed, indicating that this alloy poses high stacking-fault energy, which is supported by first principle calculations. The research suggests that further improvement on the mechanical properties of this alloy can be achieved by reducing stacking-fault energy via alloying, providing a promising low-cost alternative to CoCrFeMnNi HEAs for engineering applications.

A problem related to the development of instability of a homogeneous state in an ensemble of screw dislocations under plastic deformation of metals is considered . The study of the development of instability and structure formation in the dislocation ensemble is carried out on the basis of the method developed for charged particles in plasma and associated with the correlation interaction of electrons and positively charged ions. Accordingly, the screw dislocation ensemble is represented as a system of dislocations with an opposite Burgers vector, i.e., as a plasma-like medium with opposite dislocation charges. The total dislocation charge of the dislocation ensemble is equal to zero due to the law of conservation of the Burgers vector. In this situation, the elastic field of dislocations is “cut off”. The stress field of a single dislocation is shielded by a uniformly distributed dislocation “background” and is characterized by a certain effective potential. It is found that at long distances it decreases exponentially. Therefore, the value in the argument of the falling potential can be considered as the radius of screening of the elastic field of dislocations. It is shown that the screening radius is equal to the correlation radius, which makes it possible to construct a two-particle correlation function and find the energy of the correlation interaction of dislocations. A system of kinetic equations for a dislocation ensemble is formulated, taking into account the elastic and correlation interaction of dislocations, as well as the processes of their generation and annihilation. The criterion of instability of the homogeneous distribution of dislocations for the formulated system of equations is established. The instability criterion is met under the condition that the dislocation density exceeds a certain critical value that depends on the square of the flow stress and material constants (such as the Burgers vector modulus and shear modulus, as well as indirectly, the packing defect energy). In the framework of linear analysis, it is shown that when one system of sliding screw dislocations is taken into account, a one – dimensional periodic dislocation dissipative structure is formed at the moment of instability occurrence, and when multiple sliding is taken into account, solutions appear in the form of various variants of polyhedral lattices (cellular structures). It is established that the characteristic size of the cellular structure coincides with the experimental dependence both qualitatively and quantitatively ( the cell size is proportional to the square root of the dislocation density, and the proportionality coefficient is about ten). It is shown that the origin of spatially inhomogeneous dislocation structures, based on correlation instability, depends mainly on the features of the elastic interaction of dislocations and is not critical to the choice of the mechanisms of their kinetics (i.e., the mechanisms of generation, annihilation, and runoff of dislocations).

The effects of 5 MeV Fe2+ ion irradiation at 300°C on the microstructure evolution and deformation behavior of a FeCrAl C26M alloy are presented. It has been found that dislocation loop density increases an order of magnitude from 1 dpa to 16 dpa irradiations, whereas, the dislocation loop size saturates with increasing damage. Micropillars, 600 nm in diameter and 1.3 µm in height, were fabricated and compressed inside grains with , and crystallographic orientations, respectively. {112} has been identified as the primary slip system in both unirradiated and irradiated alloys. The increase in yield stress after irradiation is observed with measurable variation along and vs. along . By applying the Orowan dispersed barrier model, the increase of yield stress is found mainly due to the slip resistance of radiation generated defect loops. Detailed transmission electron microscopy (TEM) studies were performed to quantify the Burgers vector and the distribution of irradiation induced dislocations at elevated strains. It is revealed that localized shear instability is caused by avalanche slip events of ½ dislocations gliding out of tested pillars. Simultaneously, a large number of sessile/immobile dislocations formed in the vicinity of slip band, leading to the hardening at elevated strains.

A pseudodifferential operator is constructed that describes the stress field in an anisotropic medium caused by a dislocation with a variable Burgers vector. Under the assumption $${\mathbf{b}} \in {{H}_{{1/2}}}(\Pi ,{{R}^{3}})$$ , analytical expressions for the energy of circular dislocations with a variable Burgers vector in an elastic medium with general anisotropy are obtained for the first time. It was found that in an isotropic medium the energy of formation of an edge dislocation and a slip dislocation is determined only by the uniform norm of the Burgers vector.

The dislocation structure of single-crystalline germanium crystals grown by the Czochralski method in [2 1 1] and [1 1 0] directions has been examined by white beam X-ray topography. The dislocation densities in different parts of the crystals ranged from around 40 to 4000 cm−2. It was demonstrated that utilizing a well-executed Dash necking procedure with high growth speeds in growth directions parallel to a dislocation glide plane leads to the selection of dislocation line and type. Dislocations in the [2 1 1] crystal were mainly oriented in the [1 0 1] and [1 1 0] directions and hence confined within the ( 1 1) glide plane. A comprehensive Burgers vector analysis revealed that they were predominantly screw dislocations. The dislocation lines in the [1 1 0] crystal were mostly aligned to the [0 1 ], [1 0 ], and [1 0 1] orientations, within the ( 1 1) and (11) glide planes and predominantly 60° dislocations.

Slip systems in triclinic hen egg-white lysozyme (Tri-HEWL) crystals, which are typical protein crystals, were identified by an indentation method. Eleven kinds of slip systems are clearly observed. These slip systems are determined by surface energy estimation using phenomenological macro-bond methods. Based on the analysis of the slip systems, it can be suggested that the active slip systems are controlled by not the Burgers vector but the slip plane with lower surface energy for crystals with complex macromolecules and lower crystallographic symmetry such as Tri-HEWL crystals. This mechanism to decide active slip systems is unique compared with the conventional crystals such as FCC metals and covalent materials. It is expected to establish a more comprehensive dislocation theory including macromolecular crystals.

Plastic deformation of polycrystalline solids is accompanied by the appearance of linear rotational-type mesodefects at grain boundary ledges and triple junction of grains, such as starin induced junction disclinations. Junction disclinations generate long-range spatially inhomogeneous fields of elastic stresses, which significantly influence on the structure formation, strain hardening and fracture of materials. In present work a comparative analysis of the contributions of junction disclinations of different sign and strength to the plastic flow stress of a polycrystal is performed. The results of calculationsshow, that when a pile-up of lattice dislocations passes through the elastic field of disclinations, general regularities are observed.Regardless of the sign of disclination, it has a retarding effect on the plastic shear. The equilibrium distributions of the linear density and the density of the Burgers vector of dislocations pile-upretarded by the elastic field of disclination are calculated.It is shown that the largest number of dislocations is concentrated not in the pile-up head, as in classical dislocation pile-upsstoped near impenetrable barriers, but in its central part. The dependences of the critical stress of the passage of the head dislocation of the pile-up through the force barrier of disclination are calculated depending on the strength and sign of disclination, the number of dislocations in the pile-up, and the distance between the disclination and the slip plane of lattice dislocations.It is shown that the change in the sign of disclination significantly influences on the form of the equilibrium distribution of dislocations along the length of the pile-up, but practically does not affect the value of the critical shear stress. It is shown that for a fixed number of dislocations in the pile-up, the critical shear stress increases with the distance between the slip plane and disclination. Thus, when plastic deformation is localized, the greatest strengthening effect from the elastic field of junction disclination is achieved not near the boundary, but far from it.

In-situ TEM observation and molecular dynamics simulation were used to investigate the evolution of irradiation-induced dislocation loops and their interactions with the pre-existing dislocation lines in molybdenum irradiated by 30 keV He+ at 673 K. The nucleation, annihilation, merging, size change, and types of dislocation loops were investigated in detail, and the hardening effect from dislocation loops was analyzed. With the increase of helium fluence, the volume number density of dislocation loops increased rapidly and then decreased slowly to a saturation value, while the average size of dislocation loops increased continuously until it reached an upper limit. Both 1/2 and loops were formed, with a proportion of 60.2% to 39.8% at 3.95 × 1015 He+.cm−2 (0.07 dpa). The pre-existing dislocation lines would suppress the nucleation and growth of the dislocation loops, while the irradiation-induced dislocation loops had a strong pinning effect on the dislocation lines and impeded their motion. Molecular dynamics simulations were used to clarify the atomistic mechanisms of some major features of the line-loop interactions observed in the in-situ experiment, which showed in a good agreement. The different interaction processes depended on the Burgers vector and plane of the dislocation loop, the motion and reaction kinetics of dislocation segments, and the external loading.

Sm2Co17-type permanent magnets have important application value due to their advanced magnetic properties, which can be ascribed to their unique cellular structure and element segregation in various phases developed after isothermal aging treatment. In this study, the evolution of the microstructure combined with the microchemistry of Sm2Co17-type magnets from solid solution precursor to the cellular structure is investigated, and a new insight into the formation of the cellular structure is provided. We report for the first time that a large number of strip-like nanoscale short-range ordered micro-domains are distributed in the disordered matrix of the solution precursor, which serve as the nucleation centers in the formation of the embryos of the cellular structure. Based on atomic scale structural analyses, a new mechanism concerning the ordering transformation from short-range 2:17R microtwins to long-range 2:17R phase is proposed, involving collective glide of three partial dislocations on successive basal planes with the net Burgers vector to be zero. Furthermore, microchemistry analysis reveals that the segregation of Cu and Fe in the early stage of isothermal aging is accelerated substantially during the ordering transformation, indicating that the ordering transformation can act as a new driving force for element segregation in Sm2Co17-type magnets. These findings provide new considerations for the development of high performance Sm2Co17-type magnets.

Even though it is widely accepted that the Laves phase is a promising strengthener for chromium-containing stainless steels, there is little information available on its microstructural evolution and growth. Therefore, in this study, we analysed the behaviour of Laves (C14) precipitates in high-Cr ferritic stainless steel, Fe-20Cr-2Mo-0.5Nb (at%), annealed at 1073 K for different time periods. A high density of (Fe,Cr)2(Mo,Nb) precipitates was formed in the α matrix during annealing. Morphological evolution in the Laves phase followed the sequence of spheroidal → faceted ellipsoidal → faceted needle-like → faceted plate-like. The Laves phase is related to the α matrix by two sets of orientation relationships, viz. OR-1: [ 1 ¯ 1 ¯ 2 ] α / [ 1 2 ¯ 10 ] L , [ 111 ] α / [ 0 1 ¯ 10 ] L , and ( 1 ¯ 10 ) α / ( 000 1 ¯ ) L and OR-2: [ 1 1 ¯ 0 ] α / [ 0001 ] L , [ 113 ] α / [ 1 ¯ 1 ¯ 20 ] L , and ( 3 ¯ 3 ¯ 2 ) α / ( 1 1 ¯ 00 ) L . The habit plane of the Laves phase was found to deviate slightly from the ( 3 ¯ 3 ¯ 2 ) α / ( 1 1 ¯ 00 ) L plane. Interfacial defects, namely disconnections (bD, h) and super disconnections (mbD, mh), observed experimentally along the habit plane, were consistent with theoretical results based on OR-2 as the reference coordinate frame. The Burgers vector bD exhibited an edge component b y D (0.1539 nm) parallel to Y / [ 113 ] α / [ 1 ¯ 1 ¯ 20 ] L and a small normal component b z D (0.0747 nm) perpendicular to the terraces; meanwhile, the overlap step height h = d ( 1 1 ¯ 00 ) L . The morphological evolution of Laves precipitates was described based on the lateral motion of disconnections and super disconnections on { 3 ¯ 3 ¯ 2 } α / { 1 1 ¯ 00 } L terraces in the 〈 113 〉 α / 〈 1 ¯ 1 ¯ 20 〉 direction. Arrays of the disconnections (bD, h) were found to be capable of accommodating the misfit strain on { 3 ¯ 3 ¯ 2 } α / { 1 1 ¯ 00 } L terraces.

A model describing the formation of a strain-induced facet at a high-angle boundary during its interaction with a dislocation pile-up is proposed in this work. The model of continuous dislocation distribution in a pile-up has been used to analyze the conditions under which a facet appears and to calculate its length as a function of the total Burgers vector of the dislocation pile-up and the boundary misorientation angle. The formation of a facet at a grain boundary is possible only if the total Burgers vector exceeds a certain critical value that depends on the external stress and boundary misorientation. The facet length as a function of the initial distance between a dislocation source and a grain boundary at various external stresses and misorientation angles has been calculated in the case of a pile-up replenished by a dislocation source. It is found that the material grain structure refinement and a shift of grain boundaries misorientation spectra into the region of large angles suppress strain induced grain boundary faceting. The facet formation has been shown to be accompanied by the formation of a shear band in the body of the adjacent grain.

Atomic-resolution scanning transmission electron microscopy is used to study stacking faults and their configurations formed in cold deformed samples of a face-centered cubic (FCC) Fe42Mn38Co10Cr10 (at.%) high-entropy alloy (HEA). It is found that the deformed microstructures contain at least four types of intrinsic stacking faults and two types of extrinsic stacking faults that are bounded by different partial dislocations, including Shockley, Frank and unusual 1/6 partials. Additionally, seventeen types of stacking fault configurations are also found, including the well-known Lomer-Cottrell lock, Hirth lock and faulted dipole, the rarely reported intrinsic-extrinsic fault bend, and thirteen hitherto unreported configurations containing different stacking faults and partial dislocations. Among these seventeen configurations, fifteen of them are constructed by conjugate stacking faults connecting at their edges, with a stair-rod partial belonging to 1/6 , 1/3 or 1/3 lying at every joint point of the stacking faults; and the rest two configurations have two intersecting stacking faults but contain different stair-rod dipoles at the intersection. Fourteen of these configurations are all comprised exclusively of intrinsic stacking faults, while three of them consist of a mixture of intrinsic and extrinsic stacking faults. Moreover, three out of the seventeen configurations contain surprisingly a Frank partial at one edge, in contrast to previously reported configurations that are all bounded exclusively by Shockley partials. Based on Burgers vector analysis, the formation mechanisms of the six types of stacking faults and the seventeen types of configurations are proposed and discussed.

Plasticity in hexagonal close-packed zirconium is mainly controlled by the glide of dislocations with 1/3 Burgers vectors. As these dislocations cannot accommodate deformation in the [0001] direction , twinning or glide of dislocations, i.e. dislocations with 1/3 Burgers vector, have to be activated. We have performed in situ straining experiments in a transmission electron microscope to study the glide of dislocations in two different zirconium samples, pure zirconium and Zircaloy-4, at room temperature. These experiments show that dislocations exclusively glide in first-order pyramidal planes with cross-slip being activated. A much stronger lattice friction is opposing the glide of dislocations when their orientation corresponds to the direction defined by the intersection of their glide plane with the basal plane. This results in long dislocations straightened along which glide either viscously or jerkily. This direction governs the motion of segments with other orientations, whose shape is merely driven by the minimization of the line tension. The friction due to solute atoms is also discussed.

An improved model based on thermally activated dislocation glide is proposed to describe the dislocation detachment-controlled creep of extruded and annealed GlidCop Al-15 and extruded GlidCop Al-60 at 973 K as well as the threshold behavior observed at lower stresses. Unlike the customary analysis using the Rosler-Arzt approach, both steady-state and strain-transient stress reduction creep tests were performed to obtain the activation energies and the obstacle strengths for creep. In contrast to pure copper, the constant-structure creep rates of GlidCop were greater than the subsequent steady-state creep rates in all tests. This result supports the concept that dislocation detachment from particles, rather than dislocation-dislocation interactions, is rate-controlling. In addition, the constant-structure creep rates at the same reduced stresses were found to be greater at higher initial stresses. This observation is interpreted as evidence that a forward internal stress arising from inter-dislocation interactions near the particles acts on the ready-to-detach dislocations and scales with the initial stress. This forward stress and an explicit treatment of the stress dependence of mobile dislocation density were incorporated in the improved model. Furthermore, the operational activation area for dislocation glide was determined at constant temperature and structure, and the values are consistent with the interparticle distances multiplied by the Burgers vector, which further supports the interpretation of detachment controlled glide. Finally, the true threshold stress for creep is modeled as originating from thermodynamic back jumps of just-detached dislocations due to the attractive nature of the particle/matrix interface.

The present article focuses on interpreting mechanical interface energies/parameters which have been introduced within gradient plasticity and can capture the ability of grain boundaries to deform plastically. Molecular dynamics simulation compression tests were performed on body-centered cubic Fe bicrystals with tilt and twist grain boundaries of different misorientations. The simulations allowed for the formation of dislocation pile-ups, which give rise to gradients in the plastic strain, and therefore it was possible to employ interfacial gradient plasticity to interpret the stress-strain curves and obtain values for the mechanical interface parameter. The simulations showed that the atomic structure at the grain boundary changed during dislocation absorption, illustrating that the initial grain boundary static energy cannot characterize boundaries after the onset of plastic deformation. It was found that the value of the mechanical interface parameter (i) depended on the GB type and GB-dislocation interactions that led to slip transmission across the GB, and (ii) was positively related to the magnitude of residual Burgers vector, indicating that as the mechanical interface parameter increased the GB strength increased. Repeating the simulations by adding hydrogen atoms at the grain boundaries, showed that segregation increased the mechanical interface energy. Changing the sample size indicated that such mechanical energy terms are size-dependent, however their ratio with the internal length was size independent and depended only on the GB type. A detailed understanding of these mechanical grain boundary energies may pave a new way to engineering materials in the sub-micron scales.

The effect of length scale on mechanical strength is a significant consideration for semiconductor materials. In III-V semiconductors, such as InSb, a transition from partial to perfect dislocations occurs at the brittle-to-ductile transition temperature (~150 °C for InSb). High temperature micro-compression reveals InSb to show a small size effect below the transition, similar to ceramics, while in the ductile regime it shows a size effect consistent with fcc metals. The source truncation model is found to agree with the observed trends in strength with size once the change in Burgers vector and bulk strength are taken into account.

A carrot defect with a shallow pit has been detected in a 4H-SiC epitaxial wafer using mirror projection electron microscopy inspection. The origin of the carrot defect and the microstructure of the conversion point at the interface between the epitaxial layer and the substrate were investigated using transmission electron microscopy and high-resolution scanning transmission electron microscopy. We found that two types of threading edge dislocations (TEDs) in the substrate, with $$ {\varvec b} = 1/3\left[ {\bar{2}110} \right] $$ and $$ {\varvec b} = 1/3\left[ {\bar{1}\bar{1}20} \right] $$ , generated the carrot defect with a shallow pit in the epitaxial layer. The two TEDs converted to basal plane dislocations (BPDs) at the conversion point. Furthermore, one of the two BPDs led to the pair generation of a threading dislocation running to the epi surface and four partial dislocations propagating on each basal plane. The other BPD joined one of the four partial dislocations at the conversion point; this merged dislocation was assumed to cause a prismatic stacking fault.

In this paper, we examine the transient response of two bonded dissimilar functionally graded magneto-electro-elastic (MEE) layers with multiple interfacial cracks under magneto-electro-mechanical impacts. Material properties of the MEE layers are assumed to vary exponentially in the thickness direction of the layers. However, the rate of material properties gradation are different. First, the analytical solution is developed by considering a dynamic magneto-electro-elastic dislocation with time-dependent Burgers vector be situated at the interface of bonded layers by means of the Fourier and Laplace transform. The solutions are used to derive singular integral equations for the MEE layers containing interfacial cracks. Then, the integral equations are solved numerically for the density of dislocations on a crack surface. The dislocation densities are employed to determine the field intensity factors and the dynamic energy release rate. The effects of crack spacing and FGM exponent as well as crack interaction are studied.

The structure of partial dislocations (PDs), which surround triangular single Shockley stacking faults (1SSFs) expanded during electroluminescence observation in a 4H-SiC PiN diode, is investigated by photoluminescence (PL) imaging, PL spectroscopy, plan-view transmission electron microscopy (TEM) imaging, g·b analysis, cross-sectional bright-field scanning TEM (BF-STEM) imaging, and high-resolution high-angle annular dark-field (HAADF)-STEM imaging. The zigzag configuration is found on the upstanding side of the triangular 1SSF by plan-view TEM imaging, while it is observed as a single line by PL imaging. Using g·b analysis, the zigzag line is confirmed to be constructed by 30° and 90° PDs. Cross-sectional BF-STEM observation proved that the expanding 1SSF penetrates through the p–n interface whose position was estimated from secondary-ion mass spectrometry (SIMS) depth profile measurements of the aluminum and nitrogen concentrations. This provides experimental evidence that the 1SSF loses its driving force for recombination-enhanced dislocation glide when it stops somewhere in the p-layer where sufficient electrons no longer exist. Using cross-sectional HAADF-STEM observation, core species of the PDs were analyzed and the Burgers vector for the dislocation loop uniquely determined. Also, the first experimental observation of a 90° silicon-core PD, reported so far, is confirmed. According to these PD analyses, the possible atomic arrangement around the 1SSF is examined and the way tetrahedrons face across each PD is summarized, based on HAADF-STEM analysis of the 1SSF line.

A micro-electromechanical system (MEMS) based technique is demonstrated for in situ transmission electron microscopy (TEM) measurements of stress relaxation with simultaneous observation of the underlying plastic deformation processes. True activation volumes are determined from repeated stress relaxation transients and thus provide a signature parameter of the governing mechanisms of plastic deformation. The technique is demonstrated with 100 nm-thick ultrafine-grained gold microspecimens under uniaxial tension. True activation volumes of approximately 3-5b3 (where b is the Burgers vector length) are obtained for tensile stresses ranging from 200-450 MPa. Grain boundary-dislocation interactions are observed via in situ TEM during stress relaxation measurements. The miniaturization of stress relaxation tests inside the TEM provides unique opportunities to characterize the plastic kinetics and underlying mechanisms in ultrafine-grained and nanocrystalline materials.

Transmission electron microscopy was used to study the interaction of a + c and a dislocations in a thick (14 μm) semipolar GaN layer grown by hydride vapor phase epitaxy on a 3C-SiC/Si(001) template. It is shown that the propagation of a dislocation half-loop with a Burgers vector b = $$\frac{1}{3}\left\langle {1\bar {2}10} \right\rangle $$ during cooling can be blocked due to its reaction with a threading dislocation with a Burgers vector b = $$\frac{1}{3}\left\langle {\bar {1}2\bar {1}3} \right\rangle $$ with the formation of a dislocation segment with a Burgers vector b = 〈0001〉. The gain in energy of the system as a result of such reaction is theoretically estimated. Within the approximation of dislocation linear tension, this gain is ~7.6 eV/A, which gives ~45.6 keV for new dislocation segment with a length of ~600 nm. The contribution of the energy of the dislocation core is estimated as ~19.1 keV.

In this study, the structures of threading dislocations (TDs) in a 4H-SiC epilayer were directly characterised using large-angle convergent beam electron diffraction (LACBED) via transmissi...

The γ-surfaces in planes (110), (120), (210), (130), and (310) containing Burgers vector [001] of a perfect dislocation in cementite were studied using the molecular dynamics method. Slip vectors corresponding to stable stacking faults (SFs) were identified, and the energy of these SFs was determined. The energy of unstable stacking faults characterizing the tendency towards plastic relaxation was estimated. It was found that local minima with low energies of both stable and unstable stacking faults are present in plane (210) of cementite. This implies the possibility of the formation of extended SFs. The possibility of splitting of a perfect dislocation with Burgers vector [001] into two partial dislocations was demonstrated.

Irradiation induced dislocation loops in Fe-based alloys can cause material hardening by impeding the mobility of dislocation. Using molecular dynamics (MD), the interaction between 1 / 2 1 1 1 > { 1 1 ¯ 0 } edge dislocation (ED) and 1/2 interstitial dislocation loops with Burgers vector (BV) along different directions in BCC (body centered cubic)-Fe were investigated, and the influence of interaction geometry (means the relative position between dislocation glide plane (GP) and loop equator plane) on the CRSS (critical resolved shear stress) for dislocation to move again induced by loops was analyzed. It was found that the pinning strength of 1/2 loop was estimated to be 0.2–0.8, varying with the BVs direction of loops and the interaction geometries. The present study clearly showed that when parameterizing the dislocation dynamics, more interaction geometries should be considered in order to get a more quantitative pinning strength.

10 1 ¯ 1 compression twins with high density stacking faults were studied at atomic scale using Cs-correction transmission electron microscopy. On one side of the 10 1 ¯ 1 twin boundary, there were many steps arranged alternately with the coherent twin boundaries. Most of the steps were linked with stacking faults inside twins. Burgers vector of twinning dislocations and the mismatch strain at steps were characterized. Due to the compressive mismatch strain at steps, the high density stacking faults inside twins were formed at twin tips during twinning process. The localized strain at the steps would be related to the crack nucleation in magnesium alloys.

In the present study, the Fe-9Cr model alloy was irradiated with 240 keV He2+ at 550°C with a dose of 0.5 dpa at the peak damage region. The depth distribution of bubbles in Fe-9Cr alloy was investigated by transmission electron microscopy (TEM). The experimental results revealed that the spatial distribution of bubbles along the depth is different. In the region with higher helium concentration and irradiation dose, the bubbles inclined to be situated inside the plane of loops, forming a structure of “bubble-loop complex.” However, in regions where the helium concentration and irradiation dose are relatively low, the number of “bubble-loop complexes” significantly decreased. In addition, the Burgers vector of “bubble-loop complexes” was identified as type. Radiation-induced enrichment of Cr atoms at the “bubble-loop complexes” was also quantitatively estimated by energy-dispersive X-ray spectroscopy (EDS) in the scanning TEM mode.

A phase-field model is developed to simulate the hardening effect of sessile loops (vacancy and interstitial discs) resulted from neutron irradiation in tungsten. According to experimental observations, the gliding dislocations on the {1 1 0} prism planes and the Burgers vector is 1/2 〈1 1 1〉, while the sessile damage loops are perpendicular to the slip plane and the Burgers vector is same with gliding dislocation. It is found that the size and spatial distribution of the damage loops as well as their amount have strong impact on their hindrance to dislocation glide. The increases in the number density and radius of damage loops enhance the hardening effect. As the edge dislocation glides through the top and bottom of the damage loop, the hardening effect is more pronounced than that in other cross section. With same stress field, the edge dislocation gliding through the bottom of damage loop requires higher critical resolved shear stress than that through the top of the damage loop, due to the sequential change in the force direction. The stress fields of two loops along 〈1 1 0〉 direction cancel out each other to some extent. Hence the hardening effect increases with increasing distance between the two loops.

In a private communication with D. M. Barnett, W. D. Nix presented a series of numerical computations in which he calculated the net interaction force between two skew dislocations separated by a distance h that are parallel to the traction-free surface of an isotropic elastic half-space. Nix drew a series of conclusions from his numerical computations including the independence of the net interaction force on the distance h. In seeking the extension of Nix’s conclusions to half-spaces of arbitrary anisotropy, Barnett called Nix’s original set of results ‘Nix’s Theorem’. In this paper, using the Stroh octet formalism, we derive new explicit and real form expressions for the net interaction force between two skew dislocations with generalized Burgers vectors, separated by a distance h, in an infinite anisotropic piezoelectric space, in a half-space and in a bimaterial. Each dislocation undergoes finite discontinuities in displacements and in electric potential across the slip plane. The net interaction force is yet again found independent of the separation distance. For an infinite space and half-space with a traction-free and charge-free surface, the net interaction force is found independent of the second component of each of the two generalized Burgers vectors and vanishes when only the second component of one generalized Burgers vector is nonzero and the remaining three components are zero.

The structures of pyramidal-II $\ensuremath{\langle}c+a\ensuremath{\rangle}$ dislocations, one of the most important defects in structural hexagonal-close-packed (HCP) metals, have not been fully characterized for many of the HCP metals in use today. Here, we employ ab initio informed phase-field dislocation dynamics to determine the minimum energy structure of pyramidal $\left\{\overline{1}\overline{1}22\right\}\ensuremath{\langle}11\overline{2}3\ensuremath{\rangle}$ dislocations in ten HCP metals, including Be, Co, Mg, Re, Ti, Zn, Cd, Hf, Y, and Zr. As input for the simulations, we calculate, using first-principles density functional theory, the $\left\{\overline{1}\overline{1}22\right\}$ generalized stacking fault energy (GSFE) curves for all ten metals. From these calculations, it is found that magnetism in Co is necessary for achieving a local minimum in the GSFE curve. We observe in simulations that edge and screw character dislocations split into two partials separated by a low-energy intrinsic stacking fault. The splitting distance is shown to scale inversely with the local minimum energy normalized by the product of its shear modulus and Burgers vector. Interestingly, some HCP metals exhibit an asymmetric structure, with either unequal partial Burgers vectors or widths, in contrast to the symmetric configuration expected from linear elastic dislocation theory. We explain these structures by properties of the local maxima in their GSFE curves. Metals with larger degrees of elastic anisotropy result in dislocations with larger splitting distances than would be expected under the commonly used assumption of elastic isotropy. These findings on the sizes and asymmetry in the structures of pyramidal-II $\ensuremath{\langle}c+a\ensuremath{\rangle}$ dislocations are fundamental to understanding how these dislocations glide and interact or react with other defects when these metals are mechanically strained.

The tensile properties of additively manufactured (AM) metals and alloys are among the most important variables that impact the potential applications of these materials. Here we examine and report on the tensile properties of AM 316L stainless steels fabricated by the laser powder-bed-fusion (L-PBF) technique, via twelve sets of optimized laser processing parameters that produce materials with density >98.8 ± 0.10%. A heterogeneous microstructure is observed in all L-PBF samples, including microscopic features such as dislocations, cellular walls, elemental segregations, local misorientations, impurities, precipitates, and a large fraction of low-angle grain boundaries (2-10°, ∼40–60%). The derived average grain size defined by high-angle grain boundaries (>10°) is ∼30–50 μm. Tensile testing reveals a yield strength ranging from 552 to 635 MPa and a tensile-elongation-to-failure (TEF) of 0.09–0.42 for directly-printed samples, whereas these values are 592–690 MPa and 0.29–0.50 for samples machined from the as-built rectangular thin plates. In all samples, we observe a variation of tensile yield strength within ∼15% but not the TEF, suggesting marginal microstructural changes despite a wide range of laser processing parameters. The large scatter of TEF in directly-printed samples originates from the sensitivity of thin gauge geometry (∼2 mm2 cross-section area) to the built-in flaws. We measured a substantially higher strain rate sensitivity (m∼0.02–0.03) of L-PBF 316L compared to the coarse-grained counterparts (∼0.006), together with a small activation volume of ∼20–30b3 (where b is the Burgers vector of 316L). These deformation kinetics parameters suggest that the tensile plasticity of L-PBF 316L is controlled by a much finer microstructural length scale than the measured grain size, consistent with the high strength and juxtaposed nano- to macro-structures seen in these materials. Strategies to optimize the tensile properties of AM materials are discussed.

Recent reports on highly mobile type II twin boundaries challenge the established understanding of deformation twinning and motivate this study. We consider the motion of twin boundaries through the nucleation and growth of disconnection loops and develop a mechanism-based model for twin boundary motion in the framework of isotropic linear elasticity. While such mechanisms are well established for type I and compound twins, we demonstrate based on the elastic properties of crystals that type II twin boundaries propagate in a similar way. Nucleation of a type I twinning disconnection loop occurs in a discrete manner. In contrast, nucleation of a type II twinning disconnection loop occurs gradually with increasing Burgers vector. The gradual nucleation of a type II disconnection loop accounts for the higher mobility of type II twin boundaries compared with type I twin boundaries. We consider the homogeneous nucleation of a disconnection loop, which is adequate for twinning in shape memory alloys with a low-symmetry crystal lattice. For the magnetic shape memory alloy Ni–Mn-Ga, the model predicts twinning stresses of 0.33 MPa for type II twinning and 4.7 MPa for type I twinning. Over a wide temperature range, the twinning stress depends on temperature only through the temperature dependence of the elastic constants, in agreement with experimental results.

The BiFeO3/YBCO heterostructures were fabricated on (001)-oriented SrTiO3 substrates by pulsed laser deposition. The superconducting transition temperature of YBCO was found to decline with increasing the c-axis parameter. The microstructure and dislocations in BiFeO3/YBCO heterostructure were detected by transmission electron microscopy (TEM) proving the epitaxial growth of BiFeO3/YBCO heterostructures on SrTiO3. The edge dislocation with a Burgers vector [100] was observed in BiFeO3, which contributed to the relaxation of BiFeO3. The results of magnetization hysteresis cycles indicated that the saturation magnetization increased from 14 emu/cm3 of BiFeO3/SrTiO3 to 42 emu/cm3 of BiFeO3/YBCO/SrTiO3. The second phase Fe2O3 on the surface of BiFeO3 was found to be α-Fe2O3 with weak magnetization at room temperature. Therefore, the increased magnetization could be accounted for by the induced ferromagnetism at the interface of BiFeO3/YBCO.

Plastic behavior of Fe–3%Si was investigated with a novel methodology at microscopic scale and higher stress resolution beyond the existing macroscopic test methods. Activation of single slip system in micropillars under compression provides perfect shear and excludes the lattice rotation. Crystallographic orientation dependency of critical resolved shear stress (CRSS) was observed. Different scenarios regarding activated slip planes are discussed to explain this orientation dependency. Schmid's law approach, which only considers the stress component parallel to the Burgers vector, fails to explain this orientation dependency of CRSS. It is shown that the non-glide stress components should be taken into account in order to precisely define the plasticity in BCC metals.

In-situ heavy ion (1 MeV Kr2+) irradiation was carried out to investigate the evolution of irradiation induced lattice defects at room temperature and the stability of β-Zr under irradiation at temperatures ranging from 150 to 350 °C. It was found that the irradiation induced defects started to appear at a dose between 0.5 dpa and 0.75 dpa, which is relatively high compared to the case for α-Zr. The number density of dislocation loops increased exponentially with fluence, with an exponential index ∼3.52. The statistical results show that the electron beam with which in-situ observation was carried out had an influence on the size of the dislocation loops. The g·b analysis shows that dislocation loops with Burgers vector ½ 1 ¯ 11> and are both present in the sample after irradiation to 1.5 dpa. ω phase particles precipitate out during irradiation at 250 and 350 °C, as a result of the combination of the thermal treatment and irradiation enhanced concentration of point defects.

Metals with a hexagonal close packed structure can deform by several different slip modes with different Critical Resolved Shear Stresses, which provides a great deal of complexity when considering mechanical performance of Mg, Ti and Zr alloys. Hence, an accurate but also statistically meaningful analysis of active slip systems and their contribution to plasticity is of great importance for the understanding of deformation mechanism. In the present study, a correlative scanning electron microscopy-based method of slip trace analysis has been utilised to provide statistical, accurate information of slip behaviour in a weakly textured Ti–6Al–4V alloy with a plastic strain of ∼2%. This is achieved through grain orientation mapping by Electron Backscatter Diffraction and strain mapping by High Resolution Digital Image Correlation. The initial identification of slip mode was performed by comparing the slip trace captured in the high-resolution effective shear strain map with all theoretical slip planes with an angle acceptance criterion of ±5°. Ambiguity in slip mode identification was further resolved using the Relative Displacement Ratio method, which enables the determination of the Burgers vector directly from the displacement data. The correctness of the identified slip modes has been confirmed by detailed dislocation analysis using Bright Field Scanning Transmission Electron Microscopy on thin foils extracted from specific grains employing Focused Ion Beam. This detailed investigation demonstrates the robustness of the slip trace analysis based on grain orientation and high-resolution strain mapping.

The droplet consumption step in self-catalyzed III–V semiconductor nanowires can produce material that contains a high density of line defects. Interestingly, these defects are often associated with twin boundaries and have null Burgers vector, i.e., no long-range strain field. Here, we analyze their stability by considering the forces that act on them and use in situ aberration corrected scanning transmission electron microscopy (STEM) to observe their behavior in GaAsP nanowires (NWs) using short annealing cycles. Their movement appears to be consistent with the thermally activated single- or double-kink mechanisms of dislocation glide, with velocities that do not exceed 1 nm s–1. We find that motion of individual defects depends on their size, position, and surrounding environment and set an upper limit to activation energy around 2 eV. The majority of defects (>70%) are removed by our postgrowth annealing for several seconds at temperatures in excess of 640 °C, suggesting that in situ annealing during growth at lower temperatures would significantly improve material quality. The remaining defects do not move at all and are thermodynamically stable in the nanowire.

As the Burgers vector of a secondary dislocation may not conform to the translation vectors in the periodic pattern in a high-resolution transmission electron microscope (HRTEM) image, a Burgers circuit directly constructed according to an HRTEM image may render a wrong Burgers vector. The HRTEM images of the habit plane (HP) of δ precipitate in an Inconel 718 alloy were re-examined by using different Burgers circuits, as an example. Evidence is found for predicted secondary dislocation associated with a down step. The Burgers vector of the dislocation is 1 / 6 [ 11 2 ¯ ] γ / 1 / 3 [ 00 1 ¯ ] δ , determined with the Burgers circuit built on the reference of the displacement shift completely lattice (DSCL). It is consistent with both the calculated and the measured result of the major defects in the habit plane. Different Burgers vectors due to different Burgers circuits were explained quantitatively. The present study has a general implication for the determination of the Burgers vectors of secondary interfacial dislocations in other systems.

We formulate the grain-size dependent strengthening of polycrystalline metals as a multiplicative decomposition of the coarse-grain strength σ0 and a function depending on the grain size d normalized by a characteristic coarse-grain length scale L = b(G/σ0), where G is the shear modulus, and b the magnitude of the Burgers vector. We show that this formulation leads to a collapse of all experimental data analyzed, making experimental results across different materials comparable. This suggests that the grain-size dependent strengthening of several materials can be characterized by a single function with different materials distinguished only by their coarse-grain strength.

In contrast to homoelemental graphene showing common dislocation dipole with pentagon-heptagon (5|7) core, heteroelemental MoS2 is observed to contain diverse dislocation cores that tune the chemical and physical properties. Yet, how the inevitable dislocation cores in MoS_2 affect the mechanical behaviours remains virtually unexplored. Herein, we report direct atomistic simulations of mechanical characteristics of isolated dislocation-embedded MoS_2 monolayers under tensile load. All isolated dislocation cores in MoS_2 monolayer rise polar stress-concentration, while those with larger Burgers vector are less energetically-favorable configurations but show local wrinkling behaviour. It is revealed that the intrinsic tensile strength of MoS_2 is dictated by topology and polarity of dislocation cores. There is a strong inverse correlation between the maximum residual stresses induced by the dislocation cores and the strength of MoS_2 monolayers. Mechanical failure initiates from the bond at dislocation polygon on which side there is a missing atomic chain. Armchair-oriented 4|8 dislocation exhibits sole brittle failure, however, dual brittle/ductile fractures occur in zigzag-oriented dislocations; Mo-S-Mo angle-oriented crack is brittle, while the S-Mo-S angle-oriented crack becomes ductile. Our findings shed sights on mechanical design of heteroelemental 2D materials via dislocation engineering for practical application.

s Dislocation loops are commonly observed defects in bcc-iron based alloys under radioactive environments. They are also major sources of hardening and embrittlement in such materials. In this paper, a comprehensive molecular dynamics (MD) study is conducted concerning the effects of subsequent cascades on previously formed dislocation loops, particularly changes in their Burgers vectors induced by cascades. We reveal the atomistic mechanism behind the Burgers vector transitions and then investigate the effects of temperature, initial cluster type, loop size, and cascade parameters on the transition rate and the effects of different potentials. The competing effects of loop size and cascade energy result in an overall non-monotonic effect on the transition rate to dislocation loops, which is attributed to the density of the dissolved self-interstitial atoms in the loop. We also find temperature dependence of the transition rate of loops with M07 potential function. This study provides essential information regarding the evolution of nanometric dislocation loops under irradiation.