Burgers Vector Research Articles

Transmission electron microscopic study on rutile-type GeO2 film on TiO2 (001) substrate

Rutile-type GeO2 (r-GeO2) with an ultrawide bandgap of ∼4.7 eV has emerged as a promising material for next-generation power-electronic and optoelectronic devices. We performed transmission electron microscopy (TEM) observation to analyze the structural properties of r-GeO2 film on r-TiO2 (001) substrate at an atomic level. The r-GeO2 film exhibits a threading dislocation density of 3.6 × 109 cm−2 and there exist edge-, screw-, and mixed-type dislocations in the film as demonstrated by two-beam TEM. The edge-type dislocations have Burgers vectors of [100] and/or [110]. The bandgap of the r-GeO2 film is 4.74 ± 0.01 eV as determined by electron energy loss spectroscopy.

Deformation anisotropy and lamellar α re-orientation of TC17 alloy under the different slip modes of HCP structure

Deformation anisotropy and re-orientation for α phase during isothermal compression of TC17 alloy with basketweave microstructure were investigated systematically by quantitative analysis the influence of tilt angle between compression axis and c-axis on LABs density, rotate factor and ratio of activated slip system. The test results revealed that the tilt angle between compression axis and c-axis affects the deformability of α grain by affecting the rotation tendency and the number of activated slip systems. It results in the different prone of lamellar α with different orientation to globularization. Therein, the variation of the rotation factor with tilt angle conforms to the quadratic function, reaching a maximum value around 45°. When the rotation factor is small, the ratio of (01–11) [1–210] slip system with small Burgers vector at the phase boundary is large, the rotation tendency is poor, and the intragranular dislocation slip replaces the grain rotation as the strain accommodation mechanism, the lamella is more prone to globularization. And when the tilt angles are between 0°–13°, 13°–35°, 35°–78° and 78°–90°, the most easily activated slip systems are pyramidal <a+c> slip, basal <a> slip, pyramidal <a> slip and prismatic <a> slip, respectively. The more slip systems may be activated, the lamella is more prone to globularization. In addition, isothermal compression destroys the initial preferred orientations of the α grains and causes the lamellar α to rotate towards the direction that forms (0 0 0 1) plane texture, which is formed due to the activation of the prismatic <a> slip. Then, the (0 0 0 1) plane texture will be weakened due to a large number of randomly oriented grains generated by recrystallization under larger height reduction.

Effects of grain size and stacking fault energy on twinning stresses of single-phase CrxMn20Fe20Co20Ni40-x high-entropy alloys

Deformation twinning was investigated in single-phase face-centered-cubic (FCC) high-entropy alloys of the CrxMn20Fe20Co20Ni40-x system (14 ≤ x ≤ 26 at.%). The intrinsic stacking fault energies (γisf) of these alloys varied systematically across this composition range, but other physical properties that have the potential of affecting deformation twinning remained constant allowing us to isolate the effects of γisf on twinning. Tensile tests were performed at 293 and 77 K, and the tests interrupted at several different strains to evaluate deformation-induced changes in microstructure by transmission electron microscopy. The critical stress above which deformation twinning occurs was thus determined. We also evaluated how grain size (19 ≤ d ≤ 237 µm) affects the yield stress (σy) and the uniaxial critical twinning stress (σtw), which allowed us to subtract the corresponding Hall-Petch contributions and compare our polycrystalline results with experimental and theoretical data reported for single crystals. Taking into account the critical resolved shear stresses for deformation twinning in our alloys (τtw) along with those of FCC pure metals and binary alloys reported in the literature, we derived the following relationship that rationalizes most of the experimental data: τtw = 10-3G + γisf/(3·bp), where G is the shear modulus and bp is the magnitude of the Burgers vector of a Shockley partial dislocation. This expression, involving only measurable material properties, can serve as a basis for the design and optimization of new HEAs with tunable twinning stresses and, in turn, exceptional strength-ductility combinations.

Gradient structured Al alloy with a synergistic improvement of strength-ductility obtained by friction stir processing

One Al 6061 with gradient microstructure is prepared by friction stir processing (FSP). Microscopic characterization indicates that the regulation of grain size gradient could be achieved by adjusting the process parameters of FSP. The mechanical property test indicates that one gradient Al 6061 combines an ultimate tensile strength of 266 MPa with a uniform elongation of 27 %, and the other comes 258 MPa with 29 %, which provides an excellent combination of strength and ductility. Moreover, the molecular dynamics (MD) method is employed to reconstruct and simulate the mechanical behavior of the gradient region and the dynamic evolution of the microstructure. When the stacking faults (SFs) with antisymbolic Burgers vector meet and detwinning occurs, grain refinement will induce localized strengthening. When the Shockley partials occur cross-slip, numerous sessile dislocations obstruct the dislocation motion more facilitate strain hardening. Meanwhile, a unique interaction mechanism between shear bands (SBs) and intergranular cracks in Al 6061 is discovered in plastic deformation. The coarse net-like SBs in the small-grain region are highly susceptible to catastrophic fracture of the material, and the large cracks formed within the severely band-like SBs in the large-grain region weaken the strength substantially. However, the formation of sessile dislocations in the gradient region effectively mitigates strain localization and inhibits the nucleation of large cracks. The results interpret the dynamic evolution process of gradient microstructure prepared by FSP and the mechanism of strengthening and toughening and provide process and theoretical references for the research and development of new engineering materials.

The Green's functions of two-dimensional piezoelectric quasicrystal semi-infinite crack and finite crack

This paper investigates the interactions of a semi-infinite crack / finite crack with multiple loadings in a two-dimensional piezoelectric quasicrystal under different boundary conditions. Utilizing the Stroh formalism and conformal mapping, Green's functions of generalized displacements and stresses are obtained for two general cases: a semi-infinite crack and a finite crack subject to free-free or fixed-fixed boundary conditions. The stress and electric displacement intensity factors at the crack tip and the image forces on how dislocations are affected by the crack surfaces are given explicitly. The results are analyzed and compared with special cases documented in the scholarly literature. At the same time, the effects of the Burgers vector components on the generalized stresses and image forces numerically illustrate as well as the impacts of line forces on generalized stress intensity factors.

Characterization of irradiation-induced dislocation loops in Vanadium at 25-500 °C

Vanadium-based alloys have emerged as promising candidates for structural materials in fusion applications. However, as its base metal, the response of V to irradiation has received limited attention in prior studies. To gain a fundamental understanding of the irradiation damage in V, its microstructure evolution under 6 MeV Ti ion irradiation at 25–500 °C is investigated in the present study, with the focus on the detailed and comprehensive characterization of the behavior of the irradiation-introduced dislocation loops. Under room temperature irradiation, the “black dot” dislocation loops agglomerate linearly into rafts, during which their Burgers vectors are well aligned. With the temperature increases to 300 °C, the size of rafts increases and the density decreases, while the size of small loops maintains similar to the room temperature irradiation condition. As the irradiation temperature reaches 500 °C, the defects become highly mobile, resulting in the formation of extended dislocation loops or lines with hundreds of nanometers in size, with the rafts vanishing. All the observable loops under this irradiation temperature range exhibit the Burgers vectors of a/2 < 111>. All the loops observed in the displacement region are identified to be interstitial-type, while a small portion of loops observed in the diffusion region under elevated temperatures are vacancy-type.

Structures and migrations of interfaces between β precipitates and α′ matrix in a Ti-2.6 wt% Mo alloy

While the precipitation of α (hcp) from β (bcc) in various Ti alloys has been investigated in great detail, less is known about the precipitation of β from α. This study conducts a systematic investigation of structures and migrations of interfaces between β precipitates and α′ matrix in a Ti-2.6 wt% Mo alloy. Utilizing conventional and high-resolution transmission electron microscopy (TEM), assisted with molecular dynamics and generalized O-element analysis approaches, we unveil the dislocation and atomic structures of three typical portions of the interface surrounding a β precipitate, i.e., the habit plane, the side facet, and the end face. The habit plane of β precipitates contains two sets of dislocations with Burgers vectors b1=[21¯1¯3]α/6|[11¯1]β/2 and b4=[21¯1¯3¯]α/6|[111¯]β/2, in contrast to the single set of b1 dislocations previously found on the habit plane of α laths precipitated from β matrix in various Ti alloys. Interface migrations during shrinkage of β precipitates are characterized via in-situ TEM, showing that both the habit plane and side facet migrate through the lateral motion of nanometer-high growth ledges. The dislocation structures of various growth ledges were obtained through generalized O-element calculations, suggesting a potential non-conservative dislocation trajectory as semicoherent growth ledges sweep across the interface.

Fatigue Life Prediction of a SAE Keyhole Specimen as a Subcase of Certification by Analysis.

To advance the technology of Certification by Analysis (CbA), as called for by the aerospace industry, the fatigue problems of SAE keyhole specimens are analyzed to demonstrate a subcase of CbA. First, phenomena identification and ranking table (PIRT) analysis is performed. Second, modeling of the key phenomena is conducted, and finally, verification and validation with the experimental results are achieved. In particular, the elastic/elastoplastic stress distributions in the keyhole specimens are obtained using the finite element method (FEM). Plasticity correction for stress/strain at the notch root is made using the modified Neuber's rule along with the Ramberg-Osgood equation. The low cycle fatigue (LCF) crack nucleation life is analytically predicted using the modified Tanaka-Mura model, a.k.a. the TMW model, given the material's elastic modulus, Poisson's ratio, Burgers vector, and surface energy, without the need for coupon fatigue data regression. The Tomkins equation is used to simulate plastic crack growth within the notch plastic zone. The above analytical life predictions are validated against the SAE keyhole specimen tests, becoming the first successful case of fatigue CbA at a sub-element level.

Generalized grain boundary constitutive description implemented in a strain-gradient large-strain FFT-based formulation: Application to nano-metallic laminates

This paper presents a general treatment of grain boundary constitutive behavior in the context of strain-gradient (SG) plasticity, and its numerical implementation in a large-strain (LS) elasto-viscoplastic (EVP) fast Fourier transform (FFT)-based micromechanical model. Two novel grain boundary constitutive equations are proposed, allowing for more accurate description of the Burgers vector flow at the grain boundary. The capabilities of the generalized SG-LS-EVPFFT formulation are illustrated for the case of kink-band formation during layer-parallel compression of nano-metallic laminates (NMLs), requiring consideration of the interaction between dislocations and interfaces.

Relative molecular orientation can impact the onset of plasticity in molecular crystals

Abstract Creating or moving dislocations is the first step to dissipating mechanical energy via plastic deformation under contact loading. In molecular crystals there is both a lattice that defines crystal orientation and a relative orientation of the basis of the molecules. We define a normalization parameter which relates strain at yield, the hardness of the bulk crystal, and a distance parameter analogous to a Burgers vector that nominally predicts the relative ease of initiating plasticity in this broad class of materials. Analyzing the yield behavior of 10 different molecular crystals of varying space groups shows the inter-molecular orientation predicts the experimentally observed applied stress needed to nucleate dislocations. When molecules are oriented ‘parallel’ relative to one another the normalized maximum shear stress at the onset of plasticity is on the order of 3–5 times lower than when molecules within the crystal are ‘anti-parallel’, and molecules with a more equiaxed shape fall in between these bounds. This provides an initial indication of a structural feature which predicts the relative ease of initiating plasticity during contact loading in molecular crystals.

Disconnection units of twinning in body-centered-cubic metals

Twin boundary (TB) migration, facilitated by the motion of disconnections, plays a pivotal role in the deformation of body-centered cubic (BCC) crystals. Comprehending the migration rules of twinning disconnections (TDs) under shear stress is significant in elucidating the role of twin migration in BCC plasticity. Nevertheless, our understanding of the atomic structure and migration mechanics of TDs remains incomplete. In this study, we employ the theory of interfacial defects and molecular dynamics (MD) simulations to thoroughly investigate potential {112}[111] TDs in BCC tantalum (Ta). These TDs are characterized by their Burgers vectors, which were predicted through related dichromatic pattern analysis. We reveal that single-layer and double-layer TDs represent the fundamental building blocks (units) of multi-layer TDs. Their migration directions are entirely opposite under the same shear loading, and they cannot annihilate each other when they migrate “face to face”. Furthermore, these migration rules governing single-layer and double-layer TDs offer a comprehensive explanation for the complex composition and decomposition patterns observed among various multi-layer TDs. What's more, we demonstrated that TDs with zero Burgers vector can only be driven as a whole under coupled loading conditions. These findings significantly enhance our understanding of TB migrations in BCC metals.

Dissociation of [formula omitted] misfit dislocation at the interface of α-Ga2O3 thin film deposited on m-plane sapphire

In this study, α-Ga2O3 films of thickness about 1 μm were epitaxially deposited on m-plane sapphire substrate by halide vapor phase epitaxy. The lattice mismatch between α-Ga2O3 and sapphire substrate is about 3.5 % along c-axis and 4.8 % along a-axis, resulting in the formation of misfit dislocations. High-angle annular dark-field scanning transmission electron microscopy was employed to study the misfit dislocations at the α-Ga2O3/sapphire interface. The study was carried out along the [112‾0] zone axis and focused on the dislocations responsible for a misfit strain relaxation along c-axis. The resulting magnitude of the projected Burgers vector onto (112‾0) plane has been compared with the estimated values for 13<1‾101> and 13<2‾021> dislocations. It has been revealed, that misfit dislocations tend to dissociate into partial dislocations at the interface.

Uncovering all possible dislocation locks in face-centered cubic materials

Dislocation reactions and locks play an important role in the plastic deformation and mechanical behavior of crystalline materials. Various types of dislocation locks in face-centered cubic (FCC) materials have been reported in the literature pertaining to material-specific molecular-dynamic simulations and high-resolution transmission electron microscopy observations. However, it is unknown how many dislocation locks are possible, and how immobile all the dislocation locks are, with respect to each other. Here we present a discrete mathematics-based approach to reveal all possible dislocation locks in the FCC crystal structure. Totally eight types of dislocation locks are uncovered, resulting from all possible reactions of mobile/glissile (namely, perfect and Shockley partial) dislocations with (a) non-coplanar Burgers vectors which reside on two slip planes intersecting at both obtuse and acute angles and (b) coplanar Burgers vectors. We redefine the degree of dislocation lock immobility based on misorientations between non-close-packed lock planes and close-packed {111} slip planes. The subsequently derived sequences for the dislocation lock immobility and formation tendency are rationalized by the reported experimental and dislocation-dynamics simulation results.

Resolving localized geometrically necessary dislocation densities in Al-Mg polycrystal via in situ EBSD

The distribution of geometrically necessary dislocation (GND) densities is critical to understanding the heterogeneous plastic deformation at intragranular scales in polycrystals. In this work, we performed an in situ electron backscatter diffraction (EBSD) measurement during the tensile test on a polycrystalline Al-Mg alloy. The EBSD patterns were processed through the integrated digital image correlation algorithm to enhance angular resolution. Based on the Nye dislocation density tensor, GND densities of 18 dislocation types in fcc crystals were resolved and mapped at macroscopic strains ranging from 5% to 16%. The evolution of GND distribution showed that GNDs were generated near grain boundaries at small strains and later localized at grain interiors along subgrain boundaries and slip bands at large strains. The inhomogeneous increase in GND densities of different dislocation types, representing dislocation substructures, along the subgrain boundaries was disclosed. Meanwhile, high GND densities were observed along the slip bands when a double noncoplanar slip system was activated inside the grains. The obstructed movement of dislocations by Lomer junctions explained the GND storage in different {111} slip planes. The existence of Lomer junctions was proven by Burgers circuit analysis with high-resolution transmission electron microscopy, which explained the increase in [101] screw dislocation density according to the dislocation reaction.

Characterization of extended defects in 2D materials using aperture-based dark-field STEM in SEM

Quantitative diffraction contrast analysis with defined diffraction vectors is a well-established method in TEM for studying defects in crystalline materials. A comparable transmission technique is however not available in the more widely used SEM platforms. In this work, we transfer the aperture-based dark-field imaging method from the TEM to the SEM, thus enabling quantitative diffraction contrast studies at lower voltages in SEM. This is achieved in STEM mode by inserting a custom-made aperture between the sample and the STEM detector and centering the hole on a desired reflection. To select individual reflections for dark-field imaging, we use our Low Energy Nanodiffraction (LEND) setup [Schweizer et al., Ultramicroscopy 213, 112956 (2020)], which captures transmission diffraction patterns from a fluorescent screen positioned below the sample. The aperture-based dark-field STEM method is particularly useful for studying extended defects in 2D materials, where (i) stronger diffraction at the lower voltages used in SEM is advantageous, but (ii) two-beam conditions cannot be established, making quantitative diffraction contrast analysis with standard bright-field and annular dark-field detectors impossible. We demonstrate the method by studying basal plane dislocations in bilayer graphene, which have attracted considerable research interest due to their exceptional structural and electronic properties. Direct comparison of results obtained on identical dislocations by the established TEM method and by the new aperture-based dark-field STEM method in SEM shows that a reliable Burgers vector analysis is possible by applying the well-known g·b=0 invisibility criterion. We further use the LEND setup to acquire 4D-STEM data and show that the virtual dark-field images match well with those in aperture-based dark-field STEM images for reliable Burgers vector analysis.

Effect of vacuum diffusion bonding on the mechanical and conductive properties of bonded bulk copper single crystals

Recrystallization-free atomic-level (AL) bonding between bulk copper single crystals was achieved by combining chemical mechanical polishing (CMP) and vacuum diffusion bonding. Under various bonding conditions, the bonded copper specimens can be classified into three categories: AL-bonded, HH-bonded, and L-bonded specimens. AL-bonded copper single crystals were obtained by performing bonding under 20 MPa at 600 °C for 60 min, achieving the mechanical and electrical properties that are closest to those of the parent copper single crystal. The AL-bonded interface is characterized by an asymmetrically tilted sub-grain boundary with a 2° misorientation and consists of two sets of edge dislocations with mutually perpendicular Burgers vectors. The formation of the AL-bonded interface depends on two critical factors: the creation of ultra-flat bonded surfaces and performing diffusion bonding within the elastic deformation range. Achieving an ultra-flat surface that eliminates residual stress allows for bonding under relatively low pressure. With a moderate bonding temperature and holding time, it is possible to simultaneously avoid the formation of voids and recrystallizations at the bonding interface, thereby achieving a high-quality AL-bonded interface between bulk copper single crystals.

Screw dislocation dipoles in niobium: combination of STM observations and atomistic simulations

We recently developed an experimental device that allows us to observe the slip traces under stress at the atomic scale. Here, we report experimental results obtained at the latter scale on Nb single crystals making it possible to observe dislocation dipoles (DD), which are evidenced by two slip traces formed by emerging moving dislocations of opposite Burgers vectors ending very close to each other. The geometry and stability of the DD were fully characterized in the framework of linear anisotropic elasticity theory and by atomistic simulations. This allows us to calculate a local opposite stress impeding dislocation motion of the dislocations of the dipole.

Structural characterization of threading dislocation in α-Ga2O3 thin films on c- and m-plane sapphire substrates

We discuss the structure of threading dislocations in α-Ga2O3 thin films grown on c- and m-plane sapphire substrates. The thickness-dependent threading dislocation density in both films directly affects the electrical properties of the films including carrier concentration and mobility. Two distinct types of threading dislocations are identified for each of the c- and m-plane α-Ga2O3 thin films. The c-plane α-Ga2O3 thin film shows Burgers vectors of 1/3[11¯01] and 1/3[112¯0], while the m-plane α-Ga2O3 thin film displays Burgers vectors of 1/3[21¯1¯0] and 1/3[11¯01]. This paper presents a detailed structure of the threading dislocations in α-Ga2O3, which has been little disclosed thus far mainly due to the difficulty in synthesizing the metastable α-Ga2O3.

Elastic strain mapping of plastically deformed materials by TEM

A method for mapping elastic strains by TEM in plastically deformed materials is presented. A characteristic feature of plastically deformed materials, which cannot be handled by standard strain measurement method, is the presence of orientation gradients. To circumvent this issue, we couple orientation and strain maps obtained from scanning precession electron diffraction datasets. More specifically, orientation gradients are taken into account by 1) identifying the diffraction spot positions in a reference pattern, 2) measuring the disorientation between the diffraction patterns in the map and the reference pattern, 3) rotating the coordinate system following the measured disorientation at each position in the map, 4) calculating strains in the rotated coordinate system. At present, only azimuthal rotations of the crystal are handled. The method is illustrated on a Cr2AlC monocrystal micropilar deformed in near simple flexion during a nanomechanical test. After plastic deformation, the sample contains dislocations arranged in pile-ups and walls. The strain-field around each dislocation is consistent with theory, and a clear difference is observed between the strain fields around pile-ups and walls. It is further remarked that strain maps allow for the orientation of the Burgers vector to be identified. Since the loading undergone by the sample is known, this also allows for the position of the dislocation sources to be estimated. Perspectives for the study of deformed materials are finally discussed.

Effect of solid solution heat treatment duration on microstructure evolution and the high temperature and low stress creep properties of a low-cost fourth-generation single crystal superalloy

Low-cost Ni-based single crystal superalloy with high performance attracted much attention to the researchers in recent years. A Ru-free low-cost fourth-generation single crystal superalloy was designed in this study, which was rarely reported previously. This study mainly focused on the effect of solid solution heat treatment duration on the microstructure evolution and high temperature and low stress creep properties on the experimental superalloy. By the metallographic method, it was revealed that the dendritic segregation was gradually eliminated with the increasing solid solution heat treatment duration. Segregation of Al and Ta were well homogenized as well as W. Segregation of Re could still be observed after 32 h solid solution heat treatment. Quantity and fraction of pores increased, which has a significant influence on the creep properties. Compositional variation between dendritic and inter-dendritic region was the main factor that caused the qualitative difference in the size and volume fraction of the γ' phase. Gap of the γ' size and volume fraction between dendritic cores and inter-dendritic region after solid solution heat treatment became minor. Homogeneous dislocation networks formed during the creep test and the ruptured dislocation networks of the specimen subjected to 32 h solid solution heat treatment were found. In the tertiary stage of the creep test, the primary creep deformation mechanism is the super-dislocations with Burgers vector of a 〈010〉 shearing the rafted γ' phases. The specimen subjected to 16 h solid solution heat treatment has the optimal creep performance, followed by those subjected to 32 h and 8 h, respectively.