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NASA NTRS2004

Subsurface Stress Fields in FCC Single Crystal Anisotropic Contacts

Single crystal superalloy turbine blades used in high pressure turbomachinery are subject to conditions of high temperature, triaxial steady and alternating stresses, fretting stresses in the blade attachment and damper contact locations, and exposure to high-pressure hydrogen. The blades are also subjected to extreme variations in temperature during start-up and shutdown transients. The most prevalent high cycle fatigue (HCF) failure modes observed in these blades during operation include crystallographic crack initiation/propagation on octahedral planes, and non-crystallographic initiation with crystallographic growth. Numerous cases of crack initiation and crack propagation at the blade leading edge tip, blade attachment regions, and damper contact locations have been documented. Understanding crack initiation/propagation under mixed-mode loading conditions is critical for establishing a systematic procedure for evaluating HCF life of single crystal turbine blades. This paper presents analytical and numerical techniques for evaluating two and three dimensional subsurface stress fields in anisotropic contacts. The subsurface stress results are required for evaluating contact fatigue life at damper contacts and dovetail attachment regions in single crystal nickel-base superalloy turbine blades. An analytical procedure is presented for evaluating the subsurface stresses in the elastic half-space, based on the adaptation of a stress function method outlined by Lekhnitskii. Numerical results are presented for cylindrical and spherical anisotropic contacts, using finite element analysis (FEA). Effects of crystal orientation on stress response and fatigue life are examined. Obtaining accurate subsurface stress results for anisotropic single crystal contact problems require extremely refined three-dimensional (3-D) finite element grids, especially in the edge of contact region. Obtaining resolved shear stresses (RSS) on the principal slip planes also involves considerable post-processing work. For these reasons it is very advantageous to develop analytical solution schemes for subsurface stresses, whenever possible.

Arakere, Nagaraj K.↗

DOE OSTI2012

Universal relationships for the phonon spectra in BCC, FCC, and HCP crystals with a short-range interatomic interaction

The frequencies of the phonon branches that correspond to the vibrations of the close-packed atomic planes in bcc, fcc, and hcp crystals with short-range interatomic interaction are shown to be described by a universal relationship, which only contains two parameters for each branch, for any polarization {lambda}. These phonon branches correspond to the ({xi}, {xi}, 0) direction in bcc crystals, the ({xi}, {xi}, {xi}) direction in fcc crystals, and the (0, 0, {xi}) direction in hcp crystals. This universal relationship can only be violated by long-range interactions, namely, the interactions outside the sixth coordination shell in a bcc crystal, the fifth coordination shell in an fcc crystal, and the eleventh or tenth coordination shell in an hcp crystal. The effect of these long-range interactions for each phonon branch can be quantitatively characterized by certain parameters {Delta}{sub n{lambda}}, which are simply expressed in terms of the frequencies of three phonons of the branch. The values of these parameters are presented for all bcc, fcc, and hcp metals whose phonon spectra are measured. In most cases, the proposed relationships for the frequencies are found to be fulfilled accurate to several percent. In the cases where the {Delta}{sub n{lambda}} parameters are not small, they can give substantial information on the type and scale of long-range interaction effects in various metals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Origin of Interfacial Magnetic Anisotropy in Ta/CoFeB/MgO and Pt/CoFeB/MgO Multilayer Thin Film Stacks

Interfacial perpendicular magnetic anisotropy (PMA) in Pt/Co{sub 40}Fe{sub 40}B{sub 20}/MgO and Ta/Co{sub 40}Fe{sub 40}B{sub 20}/MgO multilayer structures has been researched at various CoFeB layer thicknesses. Magneto-optical Kerr effect (MOKE) and vibrating sample magnetometer (VSM) measurements show that while strong PMA is achieved in Ta/Co{sub 40}Fe{sub 40}B{sub 20}/MgO structure for the thickness of Co{sub 40}Fe{sub 40}B{sub 20} range from 0.5 to 1.0 nm, a very weak PMA is observed in Pt/Co{sub 40}Fe{sub 40}B{sub 20}/MgO film stack for the same Co{sub 40}Fe{sub 40}B{sub 20} thicknesses. Based on the experimental results, the interfacial anisotropy energy in Ta/Co{sub 40}Fe{sub 40}B{sub 20}/MgO (1.17 erg/cm{sup 2}) was found to be almost 2.5× larger than that in Pt/Co{sub 40}Fe{sub 40}B{sub 20}/MgO (0.43 erg/cm{sup 2}). It is accepted that the PMA comes from the seed/ferromagnetic and ferromagnetic/oxide layer interfaces. Thus, the origin of interfacial magnetic anisotropy can be hybridization and/or crystallinity properties at the interfaces in Ta- and Pt-seeded stacks. While the PMA is strong in Pt/Co/MgO structure, it becomes in-plane in Fe-rich Pt/CoFeB/MgO structure. It is deduced that hybridization between 3d-5d (Co-Pt) orbitals is more dominant in Pt/CoFeB interface than 2p-3d (O-Fe) hybridization at CoFeB/MgO interface in Pt-seeded stacks. In addition, the crystallinity was studied by performing high-resolution x-ray diffraction (HR-XRD) technique. The crystal orientations of Ta and Pt are found as (002) and (111), respectively. The ferromagnetic layer might be induced out-of-plane orientation in Ta-seeded stack due to observing highly crystallized MgO (001). Thus, another reason for in-plane magnetic anisotropy in Pt/Co{sub 40}Fe{sub 40}B{sub 20}/MgO might be the absence of MgO crystallization because Pt is crystallized fcc (111) orientation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

Energy minimization mechanisms of semi-coherent interfaces

In this article, we discussed energy minimization mechanisms of semi-coherent interfaces based on atomistic simulations and dislocation theory. For example, of (111) interfaces between two face centered cubic (FCC) crystals, interface comprises of two stable structures (normal FCC stacking structure and intrinsic stacking fault structure), misfit dislocations, and misfit dislocation intersections or nodes (corresponding to the high energy stacking fault (HESF) structure). According to atomistic simulations of four interfaces, we found that (1) greater spacing between misfit dislocations and/or larger slopes of generalized stacking fault energy at the stable interface structures leads to a narrower dislocation core and a higher state of coherency in the stable interfaces; (2) the HESF region is relaxed by the relative rotation and dilation/compression of the two crystals at the node. The crystal rotation is responsible for the spiral feature at the vicinity of a node and the dilation/compression is responsible for the creation of the free volume at a node; (3) the spiral feature is gradually frail and the free volume decreases with decreasing misfit dislocation spacing, which corresponds to an increase in lattice mismatch and/or a decrease in lattice rotation. Finally, the analysis method and energy minimization mechanisms explored in FCC (111) semi-coherent interfaces are also applicable for other semi-coherent interfaces.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2013

The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high-entropy alloy

An equiatomic CoCrFeMnNi high-entropy alloy, which crystallizes in the face-centered cubic (FCC) crystal structure, was produced by arc melting and drop casting. The drop-cast ingots were homogenized, cold rolled, and recrystallized to obtain single-phase microstructures with three different grain sizes in the range 4~160 m. Quasi-static tensile tests were then performed at temperatures between 77 and 1073 K. Yield strength, ultimate tensile strength and ductility all increased with decreasing temperature. During the initial stages of plasticity (up to ~2% strain), deformation occurs by planar dislocation glide on the normal FCC slip system {111} 110 at all temperatures and grain sizes investigated. Undissociated 1/2 110 dislocations were observed, as were numerous stacking faults, which imply the dissociation of several of these dislocations into 1/6 112 Shockley partials. At later stages ( 20% strain), nanoscale deformation twins were observed after interrupted tests at 77 K, but not in specimens tested at room temperature where plasticity occurred exclusively by dislocations which organized into cells. Deformation twinning, by continually decreasing the mean free path of dislocations during tensile testing, produces a high degree of work hardening and a significant increase in the ultimate tensile strength. This increased work hardening prevents the early onset of necking instability and is a reason for the enhanced ductility observed at 77 K. A second way in which twinning can contribute to ductility is by providing an additional deformation mode to accommodate plasticity. However, it cannot explain the increase in yield strength with decreasing temperature in our high-entropy alloy since twinning was not observed in the early stages of plastic deformation. Since strong temperature dependencies of yield strength are also seen in binary FCC solid solution alloys, it may be an inherent solute effect, which needs further study.

Deformation twinning↗

DOE OSTI2017

Sensitivity of polycrystal plasticity to slip system kinematic hardening laws for Al 7075-T6

The prediction of formation and early growth of microstructurally small fatigue cracks requires use of constitutive models that accurately estimate local states of stress, strain, and cyclic plastic strain. However, few research efforts have attempted to systematically consider the sensitivity of overall cyclic stress-strain hysteresis and higher order mean stress relaxation and plastic strain ratcheting responses introduced by the slip system back-stress formulation in crystal plasticity, even for face centered cubic (FCC) crystal systems. This paper explores the performance of two slip system level kinematic hardening models using a finite element crystal plasticity implementation as a User Material Subroutine (UMAT) within ABAQUS, with fully implicit numerical integration. The two kinematic hardening formulations aim to reproduce the cyclic deformation of polycrystalline Al 7075-T6 in terms of both macroscopic cyclic stress-strain hysteresis loop shape, as well as ratcheting and mean stress relaxation under strain- or stress-controlled loading with mean strain or stress, respectively. The first formulation is an Armstrong-Frederick type hardening-dynamic recovery law for evolution of the back stress. This approach is capable of reproducing observed deformation under completely reversed uniaxial loading conditions, but overpredicts the rate of cyclic ratcheting and associated mean stress relaxation. The second formulation corresponds to a multiple back stress Ohno-Wang type hardening law with nonlinear dynamic recovery. The adoption of this back stress evolution law greatly improves the capability to model experimental results for polycrystalline specimens subjected to cycling with mean stress or strain. As a result, the relation of such nonlinear dynamic recovery effects are related to slip system interactions with dislocation substructures.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Random Close Packing as a Dynamical Phase Transition

Sphere packing is an ancient problem. The densest packing is known to be a face-centered cubic (FCC) crystal, with space-filling fraction Φ FCC = π / √ 18 ≈ 0.74 . The densest “random packing,” random close packing (RCP), is yet ill defined, although many experiments and simulations agree on a value Φ RCP ≈ 0.64 . We introduce a simple absorbing-state model, biased random organization (BRO), which exhibits a Manna class dynamical phase transition between absorbing and active states that has as its densest critical point Φ cmax ≈ 0.64 ≈ Φ RCP and, like other Manna class models, is hyperuniform at criticality. The configurations we obtain from BRO appear to be structurally identical to RCP configurations from other protocols. This leads us to conjecture that the highest-density absorbing state for an isotropic biased random organization model produces an ensemble of configurations that characterizes the state conventionally known as RCP.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Nucleation and structural growth of cluster crystals

We study the nucleation of crystalline cluster phases in the generalized exponential model with exponent n = 4. Due to the finite value of this pair potential for zero separation, at high densities the system forms cluster crystals with multiply occupied lattice sites. Here, we investigate the microscopic mechanisms that lead to the formation of cluster crystals from a supercooled liquid in the low-temperature region of the phase diagram. Using molecular dynamics and umbrella sampling, we calculate the free energy as a function of the size of the largest crystalline nucleus in the system, and compare our results with predictions from classical nucleation theory. Employing bond-order parameters based on a Voronoi tessellation to distinguish different crystal structures, we analyze the average composition of crystalline nuclei. We find that even for conditions where a multiply occupied fcc crystal is the thermodynamically stable phase, the nucleation into bcc cluster crystals is strongly preferred. Furthermore, we study the particle mobility in the supercooled liquid and in the cluster crystal. In the cluster crystal, the motion of individual particles is captured by a simple reaction-diffusion model introduced previously to model the kinetics of hydrogen bonds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRSDate not supplied

Energy landscape in Ni-Co-Cr and related alloys

Among multi-principal element alloys, the NiCoCr middle-entropy alloy has an outstanding combination of strength and ductility at both low and elevated temperatures. Equiatomic NiCoCr is a single-phase alloy with the face centered cubic (fcc) crystal structure. A low stacking fault energy in the fcc matrix is a cause of a relatively low creep in this alloy. The hexagonal close-packed (hcp) structure differs from the fcc by a stacking of atomic layers. The energy difference between the hcp and fcc structures is known to correlate with the stacking fault energy in the fcc phase. We compute formation and relative structural energies versus composition in the Ni-Co-Cr ternary and related quaternary systems, discuss possibilities of compositional adjustments, and compare theoretical predictions with experiment. We acknowledge funding by NASA’s Aeronautics Research Mission Directorate (ARMD) via Transformational Tools and Technologies (TTT) Project.

NiCoCr↗

NASA NTRSDate not supplied

Energy landscape in Ni-Co-Cr and related alloys

Multiscale↗

DOE OSTI2013

Report on the Implementation of Homogeneous Nucleation Scheme in MARMOT-based Phase Field Simulation

In this report, we summarized our effort in developing mesoscale phase field models for predicting precipitation kinetics in alloys during thermal aging and/or under irradiation in nuclear reactors. The first part focused on developing a method to predict the thermodynamic properties of critical nuclei such as the sizes and concentration profiles of critical nuclei, and nucleation barrier. These properties are crucial for quantitative simulations of precipitate evolution kinetics with phase field models. Fe-Cr alloy was chosen as a model alloy because it has valid thermodynamic and kinetic data as well as it is an important structural material in nuclear reactors. A constrained shrinking dimer dynamics (CSDD) method was developed to search for the energy minimum path during nucleation. With the method we are able to predict the concentration profiles of the critical nuclei of Cr-rich precipitates and nucleation energy barriers. Simulations showed that Cr concentration distribution in the critical nucleus strongly depends on the overall Cr concentration as well as temperature. The Cr concentration inside the critical nucleus is much smaller than the equilibrium concentration calculated by the equilibrium phase diagram. This implies that a non-classical nucleation theory should be used to deal with the nucleation of Cr precipitates in Fe-Cr alloys. The growth kinetics of both classical and non-classical nuclei was investigated by the phase field approach. A number of interesting phenomena were observed from the simulations: 1) a critical classical nucleus first shrinks toward its non-classical nucleus and then grows; 2) a non-classical nucleus has much slower growth kinetics at its earlier growth stage compared to the diffusion-controlled growth kinetics. 3) a critical classical nucleus grows faster at the earlier growth stage than the non-classical nucleus. All of these results demonstrated that it is critical to introduce the correct critical nuclei into phase field modeling in order to correctly capture the kinetics of precipitation. In most alloys the matrix phase and precipitate phase have different concentrations as well as different crystal structures. For example, Cu precipitates in FeCu alloys have fcc crystal structure while the matrix Fe-Cu solid solution has bcc structure at low temperature. The WBM model and KimS model, where both concentrations and order parameters are chosen to describe the microstructures, are commonly used to model precipitations in such alloys. The WBM and KimS models have not been implemented into Marmot yet. In the second part of this report, we focused on implementing the WBM and KimS models into Marmot. The Fe-Cu alloys, which are important structure materials in nuclear reactors, was taken as the model alloys to test the models.

Fe Alloys↗

NASA NTRS1989

Effects of crystal-melt interfacial energy anisotropy on dendritic morphology and growth kinetics

Morphological and kinetic studies of succinonitrile, a BCC crystal with a low (0.5 percent) anisotropy and pivalic acid, and FCC crystal with relatively large (5 percent) anisotropy in solid-liquid interfacial energy, show clearly that anisotropy in the solid-liquid interfacial energy does not affect the tip radius-velocity relationship, but has a profound influence on the tip region and the rate of amplification of branching waves. Anisotropy of the solid-liquid interfacial energy may be one of the key factors by which the microstructural characteristics of cast structures reflect individual material behavior, especially crystal symmetry.

Glicksman, M. E.↗

DOE OSTI2014

Smooth cubic commensurate oxides on gallium nitride

Smooth, commensurate alloys of 〈111〉-oriented Mg{sub 0.52}Ca{sub 0.48}O (MCO) thin films are demonstrated on Ga-polar, c+ [0001]-oriented GaN by surfactant-assisted molecular beam epitaxy and pulsed laser deposition. These are unique examples of coherent cubic oxide|nitride interfaces with structural and morphological perfection. Metal-insulator-semiconductor capacitor structures were fabricated on n-type GaN. A comparison of leakage current density for conventional and surfactant-assisted growth reveals a nearly 100× reduction in leakage current density for the surfactant-assisted samples. HAADF-STEM images of the MCO|GaN interface show commensurate alignment of atomic planes with minimal defects due to lattice mismatch. STEM and DFT calculations show that GaN c/2 steps create incoherent boundaries in MCO over layers which manifest as two in-plane rotations and determine consequently the density of structural defects in otherwise coherent MCO. This new understanding of interfacial steps between HCP and FCC crystals identifies the steps needed to create globally defect-free heterostructures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

Carrier transport properties of nanocrystalline Er{sub 3}N@C{sub 80}

Electrical transport properties of the nanocrystalline Er{sub 3}N@C{sub 80} with fcc crystal structure were characterized by measuring both temperature-dependent d.c. conductance and a.c. impedance. The results showed that the Er{sub 3}N@C{sub 80} sample has characteristics of n-type semiconductor and an electron affinity larger than work function of gold metal. The Er{sub 3}N@C{sub 80}/Au interface has an ohmic contact behavior and the contact resistance was very small as compared with bulk resistance of the Er{sub 3}N@C{sub 80} sample. The charge carriers in the sample were thermally excited from various trapped levels and both acoustic phonon and ionic scatterings become a dominant process in different temperature regions, respectively. At temperatures below 250 K, the activation energy of the trapped carrier was estimated to be 35.5 meV, and the ionic scattering was a dominant mechanism. On the other hand, at temperatures above 350 K, the activation energy was reduced to 15.9 meV, and the acoustic phonon scattering was a dominant mechanism. In addition, a polarization effect from the charge carrier was observed at low frequencies below 2.0 MHz, and the relative intrinsic permittivity of the Er{sub 3}N@C{sub 80} nanocrystalline lattice was estimated to be 4.6 at frequency of 5.0 MHz.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

A continuum dislocation-based model of wedge microindentation of single crystals

Recent Electron Backscatter Diffraction (EBSD) experiments have revealed the emergence of heterogeneous dislocation microstructures forming under a wedge indenter in fcc crystals, where micro-meter dislocation patterns challenge the predictions of traditional models of plasticity. In order to explain the formation of these features and develop a relationship between the force-displacement curve and the dislocation substructure, here we present a model of wedge indentation based on the continuum theory of dislocations. The model accounts for large deformation kinematics through the multiplicative split of the deformation gradient tensor, where the incompatible plastic component of deformation results from the flux of dislocations on different and interacting slips systems. Constitutive equations for dislocation fluxes are determined from a dissipative variational principle. As a result, each dislocation density satisfies an initial-boundary value problem with convective-diffusive character, which is coupled to the macroscopic stress and displacement fields governing the deformation process. Solution to the self-consistent continuum formulation is found using the finite element method. Computer simulations mimic the experimental conditions of wedge micro-indentation experiments into Ni single-crystals used by Kysar et al. (2010a). A comparison of overall dislocation density distribution and macroscopic mechanical response shows good overall agreement with the experimental results in terms of the detailed features of dislocation patterns and lattice rotations as well as the macroscopic force-displacement response.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms

Here, we present the numerical implementation of a non-local polycrystal plasticity theory using the FFT-based formulation of Suquet and co-workers. Gurtin (2002) non-local formulation, with geometry changes neglected, has been incorporated in the EVP-FFT algorithm of Lebensohn et al. (2012). Numerical procedures for the accurate estimation of higher order derivatives of micromechanical fields, required for feedback into single crystal constitutive relations, are identified and applied. A simple case of a periodic laminate made of two fcc crystals with different plastic properties is first used to assess the soundness and numerical stability of the proposed algorithm and to study the influence of different model parameters on the predictions of the non-local model. Different behaviors at grain boundaries are explored, and the one consistent with the micro-clamped condition gives the most pronounced size effect. The formulation is applied next to 3-D fcc polycrystals, illustrating the possibilities offered by the proposed numerical scheme to analyze the mechanical response of polycrystalline aggregates in three dimensions accounting for size dependence arising from plastic strain gradients with reasonable computing times.

36 MATERIALS SCIENCE↗

DOE OSTI2014

Nucleation of fcc Ta when heating thin films

Thin tantalum films have been studied during in-situ heating in a transmission electron microscope. Diffraction patterns from the as-deposited films were typical of amorphous materials. Crystalline grains were observed to form when the specimen was annealed in-situ at 450°C. Particular attention was addressed to the formation and growth of grains with the face-centered cubic (fcc) crystal structure. As a result, these observations are discussed in relation to prior work on the formation of fcc Ta by deformation and during thin film deposition.

36 MATERIALS SCIENCE↗

DOE OSTI2011

Long-Range Topological Order in Metallic Glass

Glass lacks the long-range periodic order that characterizes a crystal. In the Ce{sub 75}Al{sub 25} metallic glass (MG), however, we discovered a long-range topological order corresponding to a single crystal of indefinite length. Structural examinations confirm that the MG is truly amorphous, isotropic, and unstrained, yet under 25 gigapascals hydrostatic pressures, every segment of a centimeter-length MG ribbon devitrifies independently into a face-centered cubic (fcc) crystal with the identical orientation. By using molecular dynamics simulations and synchrotron x-ray techniques, we elucidate that the mismatch between the large Ce and small Al atoms frustrates the crystallization and causes amorphization, but a long-range fcc topological order still exists. Pressure induces electronic transition in Ce, which eliminates the mismatch and manifests the topological order by the formation of a single crystal.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗