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Modified lattice-statics approach to dislocation calculations. II - Application

The atomic structure of a screw dislocation core of the 110 line type in aluminum is calculated by the modified lattice-statics method developed in the preceding paper. The method includes anharmonic as well as harmonic forces and permits relaxation of the atoms in all three dimensions. All forces used in the present calculations were derived from a first-principles interatomic pair potential obtained via pseudopotential theory. Several significant differences from the ordinary lattice statics results are noted, including the displacement field, Peierl's energy barrier, and the equilibrium core-center location.

Esterling, D. M.

Structure and migration of heavily irradiated grain boundaries and dislocations in Ni in the athermal limit

The microstructural evolution at and near preexisting grain boundaries (GBs) and dislocations in materials under high radiation doses is still poorly understood. In this work, we use the creation relaxation algorithm (CRA) developed for atomistic modeling of high-dose irradiation in bulk materials to probe the athermal limit of saturation of GB and dislocation core regions under irradiation in fcc Ni. We find that, upon continuously subjecting a single dislocation or GB to Frenkel pair creation in the athermal limit, a local steady-state disordered defect structure is reached with excess properties that fluctuate around constant values. Case studies are given for a straight screw dislocation which elongates into a helix under irradiation and several types of low- and high-angle GBs, which exhibit coupled responses such as absorption of extrinsic dislocations, roughening, and migration. A positive correlation is found between the initial GB energy and the local steady-state GB energy under irradiation across a wide variety of GB types. Metastable GB structures with similar density in the defect core region but different initial configurations are found to converge to the same limiting structure under CRA. The mechanical responses of pristine and irradiated dislocations and GB structures are compared under an applied shear stress. Irradiated screw and edge dislocations are found to exhibit a hardening response, migrating at larger flow stresses than their pristine counterparts. Mobile GBs are found to exhibit softening or hardening responses depending on GB character. Although some GBs recover their initial pristine structures upon migration outside of the radiation zone, many GBs sustain different flow stresses corresponding to altered mobile core structures.

36 MATERIALS SCIENCE

Dislocation dissociation in some f.c.c. metals

The dissociation of a perfect screw dislocation into a stacking fault in an f.c.c. lattice is modeled by the modified lattice statics. The interatomic potentials are obtained from the work of Esterling and Swaroop and differ substantially from those empirical potentials usually employed in defect simulations. The calculated stacking fault widths for aluminum, copper, and silver are in good agreement with weak beam microscopy results.

Esterling, D. M.

Modified lattice-statics approach to dislocation calculations. I - Formalism

A modified lattice-statics method to calculate the atomic displacements associated with a screw dislocation is outlined. The model incorporates an anharmonic region wherein the forces are derived from a pair potential. Appropriate energy and force expressions are derived. The modifications necessary for the implementation of the conjugate-gradient function minimization method are also derived.

Esterling, D. M.

Modeling the contributions to acoustic nonlinearity from complex dislocation networks using 3D dislocation dynamics

Nonlinear ultrasonic parameters are highly sensitive to microstructural features that affect macroscale material behavior, providing a nondestructive means to characterize their evolution. Although dislocations are known to be a strong source of acoustic nonlinearity, establishing quantitative links between the acoustic nonlinearity parameter (β), measured via Second Harmonic Generation, and dislocation morphology—such as dislocation length and density—remains an open challenge. This work advances the numerical modeling of dislocation–β relationships using 3D dislocation dynamics (DD) simulations in two approaches: a “static” method computing strain and stress fields from dislocation configurations in the absence of external loading, and a “quasi-static” method to estimate β from the curvature of dislocation lines under applied load. First, the static method is combined with finite element analysis to investigate a recent assertion that heterogeneous initial strain fields can induce higher harmonic generation in a linear elastic medium; the present results do not corroborate this outcome. Then, the quasi-static method is applied to multiple-dislocation scenarios through parametric studies, revealing behaviors not predicted by analytical models, such as the competing interactions of edge and screw dislocations and the significant influence of applied stress on β. Finally, the simulations are used to model SHG experimental results and validate the hypothesis that β can decrease during plastic deformation, despite increasing dislocation density. As the DD code used here is open-source, it provides a practical platform for future investigation into microstructure–β relationships important to the interpretation of SHG results.

Materials science

The revised elastic field of an edge dislocation

We modify the traditional linear-elastic field of an edge dislocation. The modifications stem from symmetry and energy requirements imposed in terms of embedded (deformed) coordinates. These requirements are satisfied if a line force is added to the dislocation field. The modification to the stress field is expressed by coefficients that are a function only of Poisson’s ratio. Qualitatively, the field of the dislocation is increased in the glide direction and decreased in the climb direction. There are small changes to the field of a screw dislocation that do not entail the addition of a line force. Effects of nonlinearity, anisotropic elasticity, and image forces are briefly considered.

Hirth, J. P.

Inversion of dislocation-impurity interactions in α -Fe under magnetic state changes

Here, in this work, we investigate the dislocation-impurity interaction energies and their profiles for various 3d elements —V, Cr, Mn, Cu, Ni, and Co —in and around 1/2 $\langle111\rangle$ screw dislocations in α -Fe using ab initio methods. We consider the ferromagnetic and paramagnetic states, with the latter being modeled through both the disordered local moment model and a spin-wave approach. Our findings reveal that (1) magnetic effects are large compared to size misfit effects of substitutional impurities, and (2) dislocation-impurity interactions are dependent on the magnetic state of the matrix and thermal lattice expansion. In particular, Cu changes from core-attractive in the ferromagnetic state to repulsive in the paramagnetic state.

36 MATERIALS SCIENCE

Tensile Creep of Polycrystalline Near-Stoichiometric NiAl

Long term tensile creep studies were conducted on binary NiAl in the temperature range 700-1200 K with the objectives of characterizing and understanding the creep mechanisms. Inverse and normal primary creep curves were observed depending on stress and temperature. It was concluded that the creep of NiAl is limited by dislocation mobility. The stress exponent for creep, n, increased from 5.5 at 1200 K to 13.9 at 700 K. The true activation energy for creep, Qc, was constant and equal to about 400 kJ per mole between 20 and 50 MPa but decreased to a constant value of 250 kJ per mole between 50 and 110 MPa. The activation energy was observed to be stress dependent above 110 MPa. The tensile creep results reported in this investigation were compared with compression creep data reported in the literature. A detailed discussion of the probable dislocation creep mechanisms governing compressive and tensile creep of NiAl is presented. It is concluded that the non-conservative motion of jogs on screw dislocations influenced the nature of the primary creep curves, where the climb of these jogs involves either the next nearest neighbor or the six-jump cycle vacancy diffusion mechanism. The probable nature of the atom vacancy exchange that occur within the core of an edge dislocation undergoing climb in NiAl are schematically examined.

Raj, Sai V.

Compression and Tensile Creep of Binary NiAl

Compression creep and long term tensile creep studies were conducted on cast and extruded binary NiAl in the temperature range 700-1200 K with the objectives of characterizing and understanding the creep mechanisms. Inverse and normal primary creep curves were observed in both compression and tension creep depending on stress and temperature although an asymmetrical response was observed under these two stress states. It was concluded that the primary creep of NiAl is limited by dislocation mobility. The stress exponents, n, for compression and tensile creep were similar varying between about 5 and 14. However, there were significant differences in the stress dependence of the activation energies for compression and tensile creep. The true activation energy for tensile creep, Q(sub c), was constant and equal to about 400 kJ/mol between 20 and 50 MPa but decreased to a constant value of 250 kJ/mol between 50 and 110 MPa. The activation energy was observed to be inversely stress dependent above 110 MPa. In contrast, Q(sub c) = 300 kJ/mol for compression creep was constant between 25 and 70 MPa and inversely dependent on the true stress above 70 MPa. A detailed discussion of the probable dislocation creep mechanisms governing compressive and tensile creep of NiAl is presented. It is concluded that the non-conservative motion of jogs on screw dislocations influenced the nature of the primary creep curves, where the climb of these jogs involves either the next nearest neighbor or the six-jump cycle vacancy diffusion mechanism. The probable natures of the atom-vacancy exchange that occur within the core of an edge dislocation undergoing climb in NiAl are schematically examined.

Raj, Sai V.

Anomalous thermal transport in Eshelby twisted van der Waals nanowires

Dislocations in van der Waals (vdW) layered nanomaterials induce strain and structural changes that substantially impact thermal transport. Understanding these effects could enable the manipulation of dislocations for improved thermoelectric and optoelectronic applications, but experimental insights remain limited. Here, in this study, we use synthetic Eshelby twisted vdW GeS nanowires (NWs) with single screw dislocations as a model system to explore the interplay between dislocation-induced structural modifications and lattice thermal conductivity. Our measurements reveal a monoclinic structure stabilized by the dislocation, leading to a substantial drop in thermal conductivity for larger-diameter NWs (70% at room temperature), supported by first-principles calculations. Interestingly, we also find an anomalous enhancement of thermal conductivity with decreasing diameter in twisted NWs, contrary to typical trends in non-twisted GeS NWs. This is attributed to increased conductivity near the NW cores due to compressive strain around the central dislocations, and aligns with a density-functional-theory-informed core–shell model. Our results highlight the critical role of dislocations in thermal conduction, providing fundamental insights for defect and strain engineering in advanced thermal applications.

36 MATERIALS SCIENCE

Apparent activation volume for creep of copper and alpha brass at intermediate temperatures

Experimental measurements of the apparent activation volume for creep, V-asterisk, of Cu and Cu-30 pct Zn conducted at intermediate temperatures showed two types of strain dependencies. At the lower temperatures and higher stresses, V-asterisk decreased with increasing creep strain, while at higher temperatures and lower stresses, V-asterisk was essentially independent of strain. The low temperature-high stress behavior for Cu and Cu-30 pct Zn was found to be consistent with the dominance of a dislocation intersection mechanism. The high temperature-low stress data for the pure metals suggest that the rate-controlling process involves the nonconservative motion of jogs on screw dislocations. For the latter conditions, an additional contribution from solute drag-limited dislocation glide also appears to be important in governing the creep behavior of the alloy.

Raj, S. V.

EBIC/TEM investigations of defects in solar silicon ribbon materials

Transmission electron microscopy was used to investigate the defect structure of edge defined film growth (EFG) material, web dentritic ribbons (WEB), and ribbon to ribbon recrystallized material (RTR). The most common defects in all these materials are coherent first order twin boundaries. These coherent twins can be very thin, a few atomic layers. Bundles of the twins which contain odd numbers of twins will in optical images appear as a seemingly single first twin boundary. First-order coherent twin boundaries are not electrically active, except at locations where they contain intrinsic (grain boundary) dislocations. These dislocations take up small deviations from the ideal twin relation and play the same role in twin boundaries as conventional and play the some role in twin boundaries as conventional edge and screw dislocations in small angle tilt and twist boundaries.

Ast, D. G.

Phase field dislocation dynamics formulation coupled with Fourier based micromechanics solver and its application to grain boundary–dislocation interactions

A new phase field dislocation dynamics (PFDD) formulation for homogeneous and heterogeneous materials is presented, which couples micromechanical solvers and the time-dependent Ginzburg–Landau equation. The strain fields are obtained from the micromechanical solver by solving the Lippmann–Schwinger equation and then used to define energy terms to model the evolution of the dislocations. Grain boundary (GB)–dislocation interactions are studied using the coupled PFDD formulation and by describing GBs as inclusions. GB energy and stiffness tensors are computed from molecular statics simulations, and a newly proposed lattice energy term that is dependent on the GB energy is considered in the calculations. Interaction of a screw dislocation with minimum energy and metastable states of low and high angle ⟨110⟩ symmetric tilt grain boundaries are studied. We show good agreement between predictions from our PFDD formulation and molecular dynamics simulations of grain boundary–dislocation interactions.

36 MATERIALS SCIENCE

Electronic descriptors for dislocation deformation behavior and intrinsic ductility in bcc high-entropy alloys

Controlling the balance between strength and damage tolerance in high-entropy alloys (HEAs) is central to their application as structural materials. Materials discovery efforts for HEAs are therefore impeded by an incomplete understanding of the chemical factors governing this balance. Through first-principles calculations, this study explores factors governing intrinsic ductility of a crucial subset of HEAs—those with a body-centered cubic (bcc) crystal structure. Analyses of three sets of bcc HEAs comprising nine different compositions reveal that alloy chemistry profoundly influences screw dislocation core structure, dislocation vibrational properties, and intrinsic ductility parameters derived from unstable stacking fault and surface energies. Key features in the electronic structure are identified that correlate with these properties: the fraction of occupied bonding states and bimodality of the d-orbital density of states. The findings enhance the fundamental understanding of the origins of intrinsic ductility and establish an electronic structure–based framework for computationally accelerated materials discovery and design.

36 MATERIALS SCIENCE

Temperature and dose rate effects on dislocation loop formation and decoration in self-ion irradiated high-purity Fe-Cr model alloys

Body-centered cubic (BCC) Fe-based alloys are promising candidate materials for advanced nuclear reactors. A widespread perception is that the addition of Cr favors the formation of ½ <111> dislocation loops. However, the Cr effects on dislocation loop formation/evolution remain unclear due to the limited experimental studies. In this study, we irradiate ultra-high purity bulk BCC Fe-xCr (x = 3, 5, and 8 wt%) with 6.7-8 MeV Fe ions over a wide range of temperatures (Tirr = 250-500 °C) and dose rates (10⁻⁵ to 10⁻³ dpa/s) to two midrange doses (0.35 and 3.5 dpa). The major irradiation-induced microstructures are loop decoration along non-screw dislocation lines at low temperatures and high dose rates as well as self-assembled loops at elevated temperatures. Post-irradiation Burgers vector analysis via g•b method on loops and electron tomography reveals that <001> preponderance is observable in all irradiated Fe-Cr samples at elevated temperature, resulting from stronger elastic energy originating from <001> edge.

Li, Yao [University of Tennessee (UT)]

Quantification Of 4H- To 3C-Polymorphism In Silicon Carbide (SiC) Epilayers And An Investigation Of Recombination-Enhanced Dislocation Motion In SiC By Optical Emission Microscopy (Oem) Techniques

Environments that impose operational constraints on conventional silicon-(Si) based semiconductor devices frequently appear in military- and space-grade applications. These constraints include high temperature, high power, and high radiation environments. Silicon carbide (SiC), an alternative type of semiconductor material, has received abundant research attention in the past few years, owing to its radiation-hardened properties as well as its capability to withstand high temperatures and power levels. However, the growth and manufacture of SiC devices is still comparatively immature, and there are severe limitations in present crystal growth and device fabrication processes. Among these limitations is a variety of crystal imperfections known as defects. These imperfections can be point defects (e.g., vacancies and interstitials), line defects (e.g., edge and screw dislocations), or planar defects (e.g., stacking faults and double-positioning boundaries). All of these defects have been experimentally shown to be detrimental to the performance of electron devices made from SiC. As such, it is imperative that these defects are significantly reduced in order for SiC devices to become a viable entity in the electronics world. The NASA Glenn High Temperature Integrated Electronics & Sensors Team (HTIES) is working to identify and eliminate these defects in SiC by implementing improved epitaxial crystal growth procedures. HTIES takes two-inch SiC wafers and etches patterns, producing thousands of mesas into each wafer. Crystal growth is then carried out on top of these mesas in an effort to produce films of improved quality-resulting in electron devices that demonstrate superior performance-as well as fabrication processes that are cost-effective, reliable, and reproducible. In this work, further steps are taken to automate HTIES' SiC wafer inspection system. National Instruments LabVIEW image processing and pattern recognition routines are developed that are capable of quantifying and mapping defects on both the substrate and mesa surfaces, and of quantifying polymorphic changes in the grown materials. In addition, an optical emission microscopy (OEM) system is developed that will facilitate comprehensive study of recombination-enhanced dislocation motion (REDM).

Speer, Kevin M.

Cross slip of extended dislocations in face-centered cubic metals through phase-field modeling

Cross slip is a dislocation mechanism that significantly impacts the mechanical behavior of engineering alloys. Here, in this work, we advance a 3D phase-field dislocation dynamics (PFDD) mesoscale technique to simulate cross slip across a broad range of face-centered cubic (FCC) metals. The formulation incorporates elastic anisotropy, an FCC numerical grid, and a high-fidelity representation of the entire γ -surface from density functional theory for eight FCC metals and no adjustable parameters or rules. The relaxed core structures under zero stress for all metals are predicted to extend in plane. The analytical model for stacking fault width agrees well with the PFDD result under the assumption of elastic isotropy but overestimates it under elastic anisotropy, when the degree of anisotropy is large. The dynamic simulations are designed to elucidate the material parameters that influence the propensity for cross slip. Whether cross slip occurs under a non-Schmid stress or to bypass a hard obstacle, the critical stress to cross slip scales strongly with the anisotropic energy coefficient for a screw dislocation.

36 MATERIALS SCIENCE

Growth from Solutions: Kink dynamics, Stoichiometry, Face Kinetics and stability in turbulent flow

1. Kink dynamics. The first segment of a polygomized dislocation spiral step measured by AFM demonstrates up to 60% scattering in the critical length l*- the length when the segment starts to propagate. On orthorhombic lysozyme, this length is shorter than that the observed interkink distance. Step energy from the critical segment length based on the Gibbs-Thomson law (GTL), l* = 20(omega)alpha/(Delta)mu is several times larger than the energy from 2D nucleation rate. Here o is tine building block specific voiume, a is the step riser specific free energy, Delta(mu) is the crystallization driving force. These new data support our earlier assumption that the classical Frenkel, Burton -Cabrera-Frank concept of the abundant kink supply by fluctuations is not applicable for strongly polygonized steps. Step rate measurements on brushite confirms that statement. This is the1D nucleation of kinks that control step propagation. The GTL is valid only if l* <Dk/vk, the diffusion path of a kink that has diffusivity Dk and average growth velocity vk. This is equivalent to supersaturations sigma less than approx. alpha/2l*, where alpha is the building block size. For lysozyme, sigma much less than (1%). Conventionally used interstep distance generated by screw dislocation, 19(omega)alpha/Delta(mu) should be replaced by the very different real one, approx.4l*. 2. Stoichiometry. Kink, and thus step and face rates of a non-Kossel complex molecular monocomponent or any binary, AB, lattice was found theoretically to be proportional to 1/(zeta(sup 1/2) + zeta(sup - 1/2)), where zeta = [B]/[A] is the stoichiometry ratio in solution. The velocities reach maxima at zeta = 1. AFM studies of step rates on CaOxalate monohydrate (kidney stones) from aqueous solution was found to obey the law mentioned above. Generalization for more complex lattice will be discussed. 3. Turbulence. In agreement with theory, high precision in-situ laser interferometry of the (101) KDP crystal face shows step bunching if solution flows parallel to the step flow. The bunch height increases with the distance the bunch travels, i.e. with the face size. However, when the flow rate, u, increases, at u greater than approx. 1 m / s , the average step bunch height decreases as 1/u. The pheonomenon is attributed to the turbulent rather than laminar viscous boundary layer where diffusivity Dt = 0.5u(sub tau),y, i.e. increases linearly with the distance y from the solid face. Friction velocity, u(sub tau) approx. u(sup 7/8). Dramatically larger rate of the mass/heat transport within the turbulent, as compared to the laminar, viscous layer will be discussed.

Chernov, A. A.