Misfit Parameter Research Articles

A New Elastic Theory of Nanocomposites With Incoherent Interface Effect Based on Interface Energy Density

Abstract A continuum theory of elasticity based on the concept of interface free energy density is proposed to account for the effect of incoherent interfaces in nano-phase reinforced composites. With the help of the lattice model, the corresponding interface energy density is formulated in terms of the surface free energy densities of two bulk materials forming interfaces, the lattice relaxation parameters due to the spontaneous surface relaxation and lattice misfit parameters yielded by interface incoherency, while the stress jump at interfaces is formulated with an interface-induced traction as a function of interface free energy density. Compared with existing theories, the interface elastic constants difficult to determine are no longer introduced, and all the parameters involved in the present theory have definite physical meanings and can be easily determined. The coupling effects of characteristic size and interface structure in nanoparticle-reinforced composites are further analyzed with the present theory. It is found that both the decrease of nanoparticle size and the increase of interface incoherence will lead to the decrease of interface fracture toughness and increase of effective bulk and shear moduli of nanocomposites. All these results predicted by the present theory are consistent well with those obtained by previous experiments and computations, which further indicate that the present theory can effectively predict the mechanical properties of nanomaterials with complex interfaces, such as nano-phase reinforced composites and nano-scale metal multilayer composites.

Impact of Shale Anisotropy on Seismic Wavefield

During unconventional resources exploration, ignoring shale anisotropy may lead to wrong seismic interpretations, thus affecting the accuracy and credibility of sweet spots prediction and reservoir characterization. In order to investigate the impact of shale anisotropy on the seismic wavefield, we propose a quantitative evaluation method by calculating the waveforms’ amplitude and phase deviations. Based on the 3D elastic wave equation and the staggered-grid finite-difference method, the forward modeling theory with the consideration of shale anisotropy is established. Then, we use the envelope misfit (EM) and phase misfit (PM) parameters to illustrate the differences in waveforms’ amplitude and phase morphology, which are caused by anisotropy. Lastly, by comparing the waveforms of the models with/without anisotropy and calculating their EM and PM values, a practical and quantitative evaluation method is constructed. We used synthetic models of different complexity and oilfield models to validate the proposed method. Through the research, we also gained some new insights about the anisotropy’s effects. For a certain medium model, the impact of shale anisotropy on seismic wavefield is complicated and needs specific analysis. The proposed method provides a useful and quantitative tool for the evaluation of shale anisotropy’s impact.

Influence of high stacking-fault energy on the dissociation mechanisms of misfit dislocations at semi-coherent interfaces

By introducing constituent phases with high stacking fault energy (SFE), we have investigated the dissociation mechanisms of misfit dislocations existing in several semi-coherent interfaces using atomistic simulations and interface dislocation theory. Under large misfit dislocation spacing induced by huge lattice mismatch, misfit dislocation will dissociate independently with little influence of SFE. Meanwhile, the formation of a twin structure via dislocation climbing and the generation of Kink structure is found. When the dislocation spacing is sufficiently small, the supposed dissociated defect structure based on the geometric analysis becomes energetically unfavorable due to the high SFE, and distinct dissociation processes of the misfit dislocations occur: the dissociation of the dislocations at certain nucleate sites is hindered; the misfit dislocation decomposes towards bilateral phases rather than to only one of the constitute phase; the dissociation direction is reversed. Our work presents a novel understanding on the plastic-deformation mechanisms of semi-coherent interfaces and provides several feasible solutions to tune defect structures for material strengthening by introducing constitute phases with high SFE, controlling misfit parameters and applying different loading schemes.

Effects of Zn and Cr additions on precipitation and creep behavior of a dilute Al–Zr–Er–Si alloy

The effects of adding 0.08 at.% Cr or 1 at.% Zn to a dilute Al-0.11Zr-0.005Er-0.02Si at.% alloy are studied in terms of the precipitation behavior of Al3Zr (L12-structure) nanoprecipitates and the resulting alloy's creep resistance. Although Cr and Zn additions do not affect measurably the precipitation kinetics or coarsening resistance, the modified alloys exhibit changes in dislocation creep resistance at 300 °C: the creep threshold stress is decreased by 17% (2 MPa) in the Zn-modified alloy and increased by 25% (3 MPa) in the Cr-modified alloy. This is attributed to a modification of the lattice parameter of Al3Zr(L12), which affects the ease with which matrix dislocations climb over the nanoprecipitates. The Zn-modified alloy exhibits Al3Zr(L12) nanoprecipitates containing 6–7 at.% Zn, as determined by atom-probe tomography, which reduces the lattice parameter by 0.17% as a result of Zn substituting for Al on its sublattice, as calculated utilizing density functional theory. The Al3Zr(L12) nanoprecipitates in the Cr-modified alloy contain 0.10–0.20 at.% Cr (1.2–2.5 times more than the matrix) and 0.28–0.51 at.% Er (a 60- to 100-fold enrichment). Erbium, which increases the lattice parameter misfit of Al3Zr(L12) with the Al matrix, is confirmed to be particularly potent in increasing the creep resistance of aluminum alloys containing L12 nanoprecipitates. An alloy design methodology for creep resistance is also validated, whereby precipitate compositions measured by APT are input to DFT calculations to determine their effects on lattice parameter misfit.

Effect of Re on microstructure and mechanical properties of γ/γʹ Co-Ti-based superalloys

Three compositions of Re containing Co-Ti-based alloys with γ/γ′ two-phase microstructure were obtained based on the determined phase relationship in the Co-rich corner at 800 °C. The effect of Re on microstructure, elemental partition behavior, thermodynamic properties, lattice parameter misfits, mechanical properties and γ′ coarsening behavior of the Co-Ti-Re alloys were investigated. The γ/γ′ lattice parameter misfit of the alloys decreases from 0.72% to 0.50%, and the γ′ coarsening rate constant K of alloys decreases from 0.30 × 10−27 m3 s−1 to 0.073 × 10−27 m3 s−1 as Re content increasing form 1 at. % to 5 at. %. Additionally, the volume fraction of γ′ phase (Vγ′) increases from 42.15% to 53.19% and the γ′ solvus temperature increases from 1059 °C to 1085 °C (Tsolvus-γ′) with increasing Re content. Moreover, the 0.2% flow stresses and the 0.2% specific flow stresses of all three alloys exhibit negative temperature dependence at the temperatures ranging from room temperature to 900 °C. And both the 0.2% flow stresses and the 0.2% specific flow stresses increase with the Re content.

Sliding paths for series of Frenkel-Kontorova models – a contribution to the concept of 1D-superlubricity

Newton trajectories are used to calculate low energy pathways for a series of Frenkel-Kontorova models with 6 and up to 69 particles thus up to a medium chain, and an expedition to 101 particles. The model is a finite chain with free-end boundary conditions. It has two competing potentials and an additional, external force. We optimize stationary structures and calculate the low energy paths between global minimums for a movement of the chain over its on-site potential, if an external tilting by a push- and/or pull direction is applied. We propose to understand a low energy path for a possibility of a superlubricity of the chain. We compare different misfit parameters. The result is that the minimums differ only little, however, the critical length of the chain, Ncr, depends on the misfit parameter. Ncr describes the end of a ‘good’ calculability of the Newton trajectory which follows the low energy pathway of the chain through the potential energy surface, for a movement of the chain along the axis. We discuss reasons for the boundary of an Ncr. However, we assume that the low energy paths exist beyond their calculability by NTs.

A Method to Robustify Exact Linearization Against Parameter Uncertainty

This paper addresses the issue of uncertain parameters in the case of the control of nonlinear systems which are exact linearizable by state feedback. It is shown that the linearizing feedback may be complemented by an additional robustifying compensator, designed to ensure robust stability and performance against the uncertainty of some model parameters. This allows to bridge two state-of-the-art design methodologies such as exact linearization and robust control synthesis. Exact linearization allows the transformation of nonlinear dynamics into linear ones by an eventually dynamic state feedback and by a change of coordinates. However, due to the uncertain nature of some model parameters, their nominal values used in the transformation may be different from their real values. This parameter misfit implies that the resulting transformed dynamics may still include non-linearities or may be a linear system, but different from the one that results for the nominal parameter values. The paper proposes a procedure to cover the uncertainties remaining after exact linearization and to design an additional linear compensator, denoted by K(s), to ensure robust performance and stability. The design of the compensator K(s) involves standard $$\mathcal{H}_\infty$$ techniques, based on an output multiplicative uncertainty structure. The weighting matrices of the output multiplicative structure are obtained such that they cover a model set obtained by linearizing the transformed nonlinear system over a sufficiently fine grid above the uncertain parameter range. The suggested approach is illustrated by multiple (SISO and MIMO) examples, including a two-degrees-of-freedom robotic arm. It is shown by simulation that the additional robustifying compensator may stabilize the system for parameter values that would result in unstable behavior without its application and may also result in a better tracking performance.

Microstructural evolution and high-temperature strength of a γ(f.c.c.)/γ’(L12) Co–Al–W–Ti–B superalloy

We characterized the microstructural features and mechanical performance of a model Co-5.6Al-5.8W-6.6Ti-0.12B (at.%) alloy consisting of γ(L12)-precipitates in a γ(f.c.c.)-matrix. Scanning electron microscopy (SEM) was used to follow the isothermal aging of the microstructure at 900 and 1000 °C for 256 h, and 950 °C for 1000 h. The compositions of the γ'(L12)-precipitates and γ(f.c.c.)-matrix were evaluated by atom-probe tomography (APT) for solution-treated and air-cooled conditions, as well as in specimens aged at 950 °C for 16 and 100 h. Boron was shown to partition preferentially to the γ'(L12)-precipitates, and profiles taken across the γ(f.c.c.)-matrix channels in both aged specimens revealed confined segregation of Al at one of the two γ(f.c.c.)/γ′(L12) heterophase interfaces. After aging at 950 °C for 16 h, Co-5.6Al-5.8W-6.6Ti-0.12B (at.%) exhibited anomalous flow-strength behavior in the range 625–900 °C with a peak yield stress of 822 MPa between 800 and 825 °C. Compressive creep tests performed at 850 °C demonstrated a creep strength comparable to archival literature results for Co–9Al–9W-0.12B (at.%), despite a smaller γ′(L12)-volume fraction and lack of strengthening borides along the grain boundaries (GBs). The activation energy for creep in the temperature range 800–900 °C was 606 kJ mol−1. The post-creep microstructure consists of rafted γ′(L12)-precipitates perpendicular to the compression axis, consistent with the positive γ(f.c.c.)/γ'(L12) lattice parameter misfit character of this class of alloys. Creep failure could occur due to GB embrittlement caused by deleterious Ti-rich (L21 or B2) and D019 phases formed at the GBs during creep.

Parabolic pulse regeneration in normal dispersion-decreasing fibers and its equivalent substitutes in presence of third-order dispersion

The present work deals with the compensation of third-order dispersion (TOD) in view of parabolic pulse (PP) generation in standard normal dispersion-decreasing fiber (NDDF) links by using phase modulator (PM) at certain position within the link. Since the inherent TOD in the fiber leads to an asymmetric pulse shape and thus degrades the PP formation, there is a strong requirement to minimize the TOD within the fiber link. It is seen that insertion of PM at the estimated critical length reduces misfit parameter satisfactorily at the output end and an equivalent PP is regenerated. A three-stage cascaded system comprising the first section of NDDF, dispersion-shifted fiber (DSF) and a normal dispersion fiber (NDF) may also be useful to mitigate TOD by showing the equivalent performance as that obtained by employing PM in the previous case.

Correlation of microdistortions with misfit volumes in High Entropy Alloys

The yield strengths of High Entropy Alloys have recently been correlated with measured or computed picometer-scale atomic distortions. Here, the root mean square microdistortion in a multicomponent alloy is shown to be nearly proportional to the misfit-volume parameter that enters into a predictive model of solute strengthening. Analysis of two model ternary alloy families, face-centered cubic Cr-Fe-Ni and body-centered cubic Nb-Mo-V, demonstrates the correlation over a wide composition space. The reported correlation of yield strength with microdistortion is thus a consequence of the correlation between microdistortion and misfit parameter and the derived dependence of yield strength on the misfit parameter.

On the correlation between Ta/W ratio and γ′-Ni3(Al,Ta) lattice ordering

Evolution of lattice characteristics in ordered γ′ and γ phases affected by Ta/W ratio was investigated in experimental Ni-base superalloys. Experimental analysis using Energy Dispersive Spectroscopy (EDS) and X-Ray Diffraction (XRD) and theoretical calculations illustrated that the ordering degree can be enhanced by the substitution of Ta for Al sites in the γ′-Ni3(Al,Ta) lattice. A gradual increase in Ta/W ratio led to a noticeable increase in atomic ordering degree of γ′-Ni3(Al,Ta) precipitates and the intensity values of the γ′ superlattice peaks normalized to that of the γ+γ′ fundamental peaks in XRD patterns. EDS elemental analyses indicated that this phenomenon was associated with Ta atoms occupying Al sites in Ni3(Alx,Ta1-x) superlattice and raise its ordering tendency. Deconvolution of overlapped γ+γ′ XRD peaks indicated that γ′ lattice constant varies with the concentrations of Ta and Al. Furthermore, increasing Ta/W content up to 0.5 leads to substitution of Al and Ta for W atoms in the ordered γ′ lattice. Also, by increasing Ta/W ratio far from 0.5, Ta atoms substitute for Al and W atoms. Meanwhile, γ/γ′ lattice misfit and lattice parameters of ordered γ′ varied systematically with Ta, W and Al contents of γ′ superlattice.

Analysis of temperature distribution in shell mould during thin-wall superalloy casting and its effect on the resultant microstructure

This work focuses on the influence of temperature distribution in a shell mould during investment casting of thin wall parts on macrostructure, chemical composition of microstructural constituents and γ/γ′ misfit parameter. A reduction of production costs is associated with the optimization of precision casting technology of aircraft engine critical parts, including control of the solidification front in thin-walled castings of nickel superalloys.Appropriate lost-wax casting parameters lead to the creation of coarse grained structure, desired for high-temperature service applications. As a result of non-equilibrium solidification, substantially large chemical inhomogeneities in the dendrite core and interdendritic spaces are formed. Interdendritic spaces are occupied by constituents formed as a consequence of segregation of alloying elements, namely eutectic islands γ/γ′, borides, carbides, and an intermetallic compound of Ni and Zr. Dendrite cores consist of cubic-shaped γ′ precipitates surrounded by Ni-rich γ channels. Low lattice misfit influences cubic morphology of γ′ precipitates, which is favourable for jet engine application because it can guarantee good creep resistance.

Microstructure and mechanical properties of mechanically alloyed ODS copper alloy for fusion material application

Advanced oxide dispersion strengthened copper alloys are promising structural materials for application in divertor system of future fusion reactors due to high irradiation resistance, high thermal conductivity, and good mechanical properties. In this study, a new ODS copper including 0.42wt%Y2O3 nanosized oxide particles was developed successfully by mechanical alloying method using addition of 1 wt% Stearic acid in Ar atmosphere. Mechanical alloying resulted in decrease of crystallite size to 28 nm in concurrent with increment of dislocation density and hardness to the saturated level of 1.7×1015m−2 and 226HV0.1 after 48 h milling, respectively. Consolidated ODS copper by SPS and then hot roll-annealing at 900 °C/60 min showed an average grain size of 1.1 µm with a near random texture. Furthermore, TEM observations demonstrated fine semicoherent Y2O3 oxide particles distributed with a misfit parameter (δ) of 0.17 in copper matrix with an average size of 10.8 nm and interparticle spacing of 152 nm. Finally, tensile test evaluation determined comparable mechanical properties of the annealed ODS copper (Cu-0.42wt%Y2O3) with Glidcop-Al25 including a yield strength of 272 MPa and total elongation of 12%, by two mechanisms of grain boundary strengthening and oxide particle strengthening.

Prospective use of a normally dispersive step-index chalcogenide fiber in nonlinear pulse reshaping.

In this work, several normally dispersive highly nonlinear chalcogenide optical fibers (NDHNCFs) with a step-index profile have been designed and optimized in view of efficient parabolic pulse (PP) generation. A typical NDHNCF is selected such that the group velocity dispersion is highest among them and the corresponding nonlinearity is also very high. The input pulse parameters are optimized to find the lowest possible optimum length (Lopt) of the fiber where the linearly chirped PP is obtained. Further, it is found that for a shorter input pulse width, PP can be generated at a sufficiently smaller length of the NDHNCF with a slight compromise for its misfit parameter. A detailed analysis of the effect of pre-chirping helps to identify the suitable amount of initial chirp for different chalcogenide fibers with a choice of input pulse parameters. Although no improvement in PP generation is found for normal and initially chirped hyperbolic secant pulses, a highly efficient triangular pulse is achieved for a particular value of input pulse energy and the initial chirp parameter. Finally, the comparative study substantiates that our optimized NDHNCF is capable enough to generate quality PP at a length almost 70% shorter than a standard silica-based fiber.

Rafting of γ′ precipitates in a Co-9Al-9W superalloy during compressive creep

The rafting of γ′ precipitates was investigated in a single crystal of Co-9Al-9W(at%) superalloy after compression creep tests at 850 °C. Scanning electron micrographs show that the γ′ precipitates raft perpendicular to the compressive stress axis, due to their positive lattice parameter misfit. The rafting of γ′ precipitates occurred after the minimum strain rate was reached. The dislocation structure and stacking faults were investigated by transmission electron microscopy. Dislocations preferentially moved in the horizontal γ matrix channels where they can relieve the coherency stress at horizontal γ/γ′ interfaces. After extended periods of creep, rafting of the γ′ precipitates perpendicular to the external compressive stress axis occurred. The merging of γ′ precipitates during rafting initiated at the precipitates corners, leaving pockets of matrix phase in the vertical γ channels between adjacent γ′ precipitates. The necessary diffusion of alloying elements during the rafting process between the two orientations of matrix channels should be decelerated as diffusion is slower in the ordered L12 γ′ phase than in the disordered γ phase.

Multicomponent γ’-strengthened Co-based superalloys with increased solvus temperatures and reduced mass densities

Several Co-Al-(W)-based γ-(FCC)/γ’-(L12) alloys are investigated to combine recent results indicating significant increases in the γ′-solvus temperature with additions of Ni, Ta, and Ti, and reduced mass density with the substitution of Mo and Nb for W. A maximum solvus temperature of 1167 ± 6 °C is achieved for an alloy with the composition Co-30Ni-7Al-4Ti-7W-1Ta (mole fraction × 100); while the composition Co-30Ni-7Al-4Ti-3Mo-2W-1Nb-1Ta (L19) exhibits a promising combination of high γ′ volume fraction and solvus temperature, low mass density, and excellent two-phase γ-γ′microstructural stability. Atom probe tomographic measurement of L19 aged for 4 h at 900 °C indicates that Ni, Al, Ti, W, Nb, and Ta partition preferentially to the γ′-precipitates while Co partitions strongly to the γ-matrix. Molybdenum segregates at the γ/γ′ interface, resulting in a reduction in the interfacial free energy of 1.63 ± 0.85 mJ m−2. Decreasing the mole fraction of Ni from 30% to 10% decreases the partitioning of Al and Ti to the γ′-phase and increases partitioning of Co, Mo, W, Nb, and Ta to the γ′-phase. From an analysis of coarsening kinetics (Ostwald ripening) at 900 °C in Co-xNi-7Al-4Ti-3Mo-2W-1Nb-1Ta (x = 10 and 30) interfacial free energies of 35.0 ± 18.6 mJ m−2 and 29.2 ± 15.5 mJ m−2 are calculated for mole fractions of Ni of 10% and 30%, respectively. This decrease in interfacial free energy with increasing Ni-concentration is attributed partially to both Mo-segregation at the γ-γ′ interface and a decrease in the lattice parameter misfit between the γ′-precipitate and γ-matrix, and concomitantly the misfit strain energy.

Interplay between a crystal's shape and spatiotemporal dynamics in a spin transition material.

We investigated by means of optical microscopy (OM) the spatiotemporal features of the thermo-induced spin transition of [Fe(2-pytrz)2{Pd(CN)4}]·3H2O (1) (2-pytrz = 4-(2-pyridyl)-1,2,4,4H-triazole) single crystals having two different shapes (triangle and rectangle). While magnetic and calorimetric measurements, performed on a polycrystalline material, showed the respective average heating and cooling transition temperatures of (Tdown1/2 ∼ 152 K, Tup1/2 ∼ 154 K) and (Tdown1/2 ∼ 160.0 K, Tup1/2 ∼ 163.5 K), OM studies performed on a unique single crystal revealed significantly different switching temperatures (Tdown1/2 ∼ 152 K and Tup1/2 ∼ 162 K). OM investigations showed an interface spreading over all crystals during the spin transition. Thanks to the color contrast between the low-spin (LS) and the high-spin (HS) states, we have been able to follow the real time dynamics of the spin transition between these two spin states, as well as access the thermal hysteresis loop of each single crystal. After image processing, the HS-LS interface's velocity was carefully estimated in the ranges [4.4-8.5] μm s-1 and [2.5-5.5] μm s-1 on cooling and heating, respectively. In addition, we found that the velocity of the interface is shape-dependent, and accelerates nearby the crystal's borders. Interestingly, we observed that during the propagation process, the interface optimizes its shape so as to minimize the excess of elastic energy arising from the lattice parameter misfit between the LS and HS phases. All of these original experimental results are well reproduced using a spatiotemporal model based on the description of the spin-crossover problem as a reaction diffusion phenomenon.

Functional renormalization-group approach to the Pokrovsky-Talapov model via the modified massive Thirring fermions

We consider a possibility of the topological Kosterlitz-Thouless (KT) transition in the two-dimensional Pokrovsky-Talapov model with a finite misfit parameter and discuss its relevance to the theory of critical behavior in thin films of monoaxial chiral helimagnets. For this purpose, the initial model is reformulated in terms of the two-dimensional relativistic model of massive Thirring fermions and the Wetterich's functional renormalization-group (RG) approach is employed. In the new formalism, the misfit parameter corresponds to an effective gauge field that can be included in the RG scheme on an equal footing with the other parameters of the theory. Our main result is that the presence of the misfit parameter, which may be attributed to the Dzyaloshinskii-Moriya interaction in the magnetic system, rules out the KT transition. To support this finding, we provide an additional intuitive explanation of the KT scenario breakdown by using the mapping onto the Coulomb gas model. In the framework of the model, the misfit parameter has a meaning of an effective in-plane electric field that prevents a formation of bound vortex-antivortex pairs.

Lattice parameter misfit evolution during creep of a cobalt-based superalloy single crystal with cuboidal and rafted gamma-prime microstructures

A [h00] oriented Co-based superalloy single crystal was crept under tension at 940°C/100MPa, resulting in a P-type raft morphology with extensive particle coalescence along the [h00] loading direction. However, particle coalescence was also observed in two perpendicular directions on the (h00) plane, normal to the loading axis. Tensile creep experiments were performed with in-situ neutron diffraction at 800°C/500MPa on this initially rafted γ′ microstructure, and for comparison at (i) 900°C/260MPa, and at (ii) 750°C/875MPa, both with initially cuboidal γ′ microstructures. The alloy was shown to exhibit a positive lattice parameter misfit, and during the first hour of creep at 900°C/260MPa, the lattice parameter evolution indicated changes in phase composition associated with γ′ dissolution as the alloy achieved phase equilibrium at 900°C. For all three in-situ creep measurements, there was a significant divergence of the γ′ and γ lattice parameters as creep proceeded. The lattice parameter misfit values between the precipitates and the matrix approached their unconstrained values during creep, and were notably large compared to those of Ni-based superalloys. This is indicative of a loss of coherency at the precipitate/matrix interfaces. Such a loss of coherency at the precipitate/matrix interfaces will likely degrade certain mechanical properties such as fatigue resistance, as has been shown for the Ni-based superalloys.

Lattice strain evolution and load partitioning during creep of a Ni-based superalloy single crystal with rafted γ′ microstructure

In-situ neutron diffraction measurements were performed on monocrystalline samples of the Ni-based superalloy CMSX-4 during N-type γ′ raft formation under the tensile creep conditions of 1150 °C/100 MPa, and subsequently on a rafted sample under the low temperature/high stress creep conditions of 715 °C/825 MPa. During 1150 °C/100 MPa creep, the γ′ volume fraction decreased from ∼70% to ∼50%, the lattice parameter misfit was partly relieved, and the load was transferred from the creeping γ matrix to the γ′ precipitates. On cooling back to room temperature, a fine distribution of γ′ precipitates formed in the γ channels, and these precipitates were present in the 715 °C/825 MPa creep regime. Under low temperature/high stress creep, the alloy with rafted γ′ microstructure exhibited superior creep strength to the cuboidal γ′ microstructure produced following a standard heat-treatment. A lengthy creep incubation period was observed, believed to be associated with {111}〈110〉 dislocations hindering propagation of {111}〈112〉 dislocations. Following the creep incubation period, extensive macroscopic creep strain accumulated during primary creep as the γ phase yielded. Finally, the diffraction data suggest a loss of precipitate/matrix coherency in the (0k0) interfaces as creep strain accumulated.