Coherency Stresses Research Articles

Spinodal decomposition in the A IIIxB III1− xC VyD V1− y quaternary alloys

Spinodal decomposition of the A x IIIB 1− x IIIC y VD 1− y V quaternary alloys as the result of the internal stresses, coherency stress and transformations of the chemical bonds is presented. The alloys are described in the strictly regular approximation. Ranges of spinodal decomposition of the In x Ga 1− x As y P 1− y , In x Ga 1− x Sb y As 1− y and Al x Ga 1− x Sb y As 1− y quaternary alloys lattice-matched to their conventional substrates are estimated. It is shown that the temperatures of spinodal decomposition of the In x Ga 1− x As y P 1− y , In x Ga 1− x Sb y As 1− y and Al x Ga 1− x Sb y As 1− y should be smaller than their growth temperatures.

Mantle flow beneath a continental strike-slip fault: postseismic deformation after the 1999 Hector Mine earthquake.

Two recent large earthquakes in the Mojave Desert, California-the magnitude 7.3 1992 Landers and magnitude 7.1 1999 Hector Mine earthquakes-have each been followed by elevated crustal strain rates over periods of months and years. Geodetic data collected after the Hector Mine earthquake exhibit a temporally decaying horizontal velocity field and a quadrant uplift pattern opposite to that expected for localized shear beneath the earthquake rupture. We interpret the origin of this accelerated crustal deformation to be vigorous flow in the upper mantle in response to the stress changes generated by the earthquake. Our results suggest that transient flow in the upper mantle is a fundamental component of the earthquake cycle and that the lower crust is a coherent stress guide coupling the upper crust with the upper mantle.

Growth, microstructure, and microhardness of W/Mo nanostructured multilayers

Artificially modulated W/Mo multilayers on polished stainless-steel substrates with modulation wavelength Λ ranging from 4.0 to 60.0 nm and total film thickness of 2.0 μm were prepared by magnetron sputtering. X-ray diffraction (XRD) and cross-sectional transmission electron microscopy showed that though the polycrystalline films exhibited coherent interfaces, the interfaces have a wave-like appearance due to the different orientations of individual crystals. The interplanar spacings of the W and Mo layers determined by the XRD method in W/Mo multilayers varied with the modulation wavelength. The mechanical properties of these films were investigated by a low-load microhardness indentation technique. The maximum hardness enhancement is about 51% higher than the value calculated from the role of mixtures at wavelength Λ=10.0 nm. The Koehler’s modulus difference model and Cahn’s coherent stress model have been used to estimate the hardness enhancement of W/Mo multilayers. From the comparison of theoretical calculation results with experimental dates, it is obvious that the combination of the two models can explain the hardness enhancement in W/Mo multilayers.

The Influence of Coherent and Semi-Coherent TiCu Precipitates on the Martensitic Transformation of Melt-Spun Ti<SUB>50</SUB>Ni<SUB>25</SUB>Cu<SUB>25</SUB> Shape Memory Ribbons

Thin coherent as well as thicker semi-coherent plate-like precipitates of the same type, i.e. TiCu, were generated by different heat treatments of melt-spun Ti 50 Ni 25 Cu 25 ribbons. Their influence on the martensitic transformation behavior was investigated by means of differential scanning calorimetry (DSC) and transmission electron microscopy (TEM). It was found that thin coherent plate-like precipitates lower the temperatures of both martensitic and its reverse transformation and broaden the peak form of the DSC signal. On the other hand, thicker semi-coherent plates act to raise both transformation temperatures. The role of coherency stresses, arrangements of misfit dislocations, and compositional aspects are discussed.

Do intermediate‐ and deep‐focus earthquakes occur on preexisting weak zones? An examination of the Tonga subduction zone

It has been proposed that intermediate‐ and deep‐focus earthquakes occur on preexisting planes of weakness that were created at shallow depth. The purpose of this study is to test this hypothesis. We examined fault plane solutions for 360 events that occurred in the Tonga subduction zone from January 1976 to February 1999. For events in the slab, each fault plane solution is rotated by the slab dip angle so that the slab is in its original horizontal position. We then compare fault plane solutions for events in the slab with those for events at the outer rise. We find that an asymmetric fault system, corresponding to that found for outer rise events, persists down to about 450 km depth. This suggests that earthquakes down to this depth are caused by the reactivation of preexisting faults created in the oceanic plate before subduction. A similar pattern, though less well constrained, is found in the Kurile subduction zone down to 200 km depth. For earthquakes deeper than 450 km the fault plane solutions are much more scattered. In some places the fault plane pattern suggests the creation of new fault planes along orientations of maximum shear with zero internal friction. The pattern of fault plane solutions in particular localized volumes cannot be easily explained by the creation of new faults in the direction of maximum shear under a coherent regional tectonic stress field. Thus, either a highly heterogeneous stress field exists or preexisting planes of weakness also account for some deep earthquakes.

Atomistic simulations of dislocation-interface interactions in the Cu-Ni multilayer system

Abstract Experimental results show that a nanolayered composite structure made of two kinds of metals strengthens dramatically as the layer thickness is reduced. In epitaxial systems, this strengthening has been attributed to the modulus, lattice parameter, gamma surface and slip-plane mismatches between adjacent layers. The modulus mismatch (the Koehler barrier) introduces a force between a dislocation and its image in the interface. The lattice parameter mismatch generates oscillating coherency stresses and van der Merwe misfit dislocations at or near the interfaces, which interact with mobile dislocations. The gamma surface (chemical) mismatch introduces a localized force on gliding dislocations due to core energy changes at or near the interfaces. Slip-plane misorientations across the interfaces require mobile screw dislocations to cross-slip for slip transmission and other dislocations to leave a difference dislocation at the interface. In this paper, atomistic simulations using the embedded-atom method are used to study the four components of dislocation–interface interactions in epitaxial Cu–Ni multilayers in a systematic fashion. The interaction of misfit dislocations with mobile dislocations is modelled using continuum theory. In thick Cu–Ni bilayers, the Koehler barrier is almost independent of interface orientation and dislocation character and is equal to 0.01μ–0.015μ but, when the layer thickness is comparable with the core width of a dislocation, the Koehler barrier falls rapidly (from 0.01μ at a wavelength of 10nm to 0.004μ at 1.75 nm). This behaviour is in accordance with available experimental observations in the literature on the yield of epitaxial Cu–Ni multilayered systems. The gamma surface mismatch or chemical strengthening component of the blocking strength of Cu–Ni interfaces to (a/2)(110) screw dislocations is 0.003μ, a factor of three lower than the Koehler stress. Coherency stresses, apart from exerting direct forces on dislocations, alter the barrier strengths by three mechanisms: firstly, they reduce the density of van der Merwe misfit dislocations, secondly, they enhance the Koehler barrier by altering the elastic constants of both Cu and Ni and, thirdly, non-glide stress components change the core structure of gliding dislocations, thereby altering the Koehler barrier. Overall, the barrier strength of (111) interfaces is independent of the wavelength of the multilayer and about 0.02μ up to the wavelength of Λc, the coherence wavelength limit. At Cu(001)–Ni(001) interfaces the total barrier strength decreases from a value of 0.02μ at long wavelengths (Λ ≈ ∞) to about 0.01μ at Λ = Λc, as considered by Rao et al. in 1995 in their yield stress model for Cu–Ni multilayered structures. Slip-plane misorientations provide powerful barriers to slip transmission. Even at a (111) twinned interface in a coherent Cu–Ni multilayer, screw dislocations cross-slip on to the interface rather than into Ni because the stacking-fault energy at the interface is lower than in Ni. The blocking strength of the same interface to 60° dislocations (which must leave a step and a residual dislocation in the boundary) is very large, 0.03–0.04μ.

Atomistic simulations of dislocation–interface interactions in the Cu-Ni multilayer system

Abstract Experimental results show that a nanolayered composite structure made of two kinds of metals strengthens dramatically as the layer thickness is reduced. In epitaxial systems, this strengthening has been attributed to the modulus, lattice parameter, gamma surface and slip-plane mismatches between adjacent layers. The modulus mismatch (the Koehler barrier) introduces a force between a dislocation and its image in the interface. The lattice parameter mismatch generates oscillating coherency stresses and van der Merwe misfit dislocations at or near the interfaces, which interact with mobile dislocations. The gamma surface (chemical) mismatch introduces a localized force on gliding dislocations due to core energy changes at or near the interfaces. Slip-plane misorientations across the interfaces require mobile screw dislocations to cross-slip for slip transmission and other dislocations to leave a difference dislocation at the interface. In this paper, atomistic simulations using the embedded-atom met...

Crystallography and morphology of D0 23-Al 11Ti 5 precipitation in Ag-modified L1 2-Al 3Ti

A detailed transmission electron microscopy (TEM) study has been made of the crystallographic characteristics of precipitation of D0 23-Al 11Ti 5 in Ag-modified Al 3Ti with an L1 2-ordered structure. TEM observations revealed that plate-like D0 23-Al 11Ti 5 precipitates form multi-domain structures which can be considered as a twin related structures with the tetragonal axis of twin I parallel to [100] direction and that of twin II parallel to [010] direction of the matrix. The particular habit plane, orientation relationship and twin plane variants were carefully determined. A quantitative X-ray microanalysis for determining the chemical compositions of the precipitate and matrix has been done by using an analytical electron microscope. It is found that these crystallographic and morphological features can be explained excellently by adopting the linear elastic theory developed primarily by Khachaturyan. The coherency stresses across the precipitate/matrix interface is considered to be the main factor controlling the precipitate morphology.

Character of dislocations at the γ/ γ′ interfaces and internal stresses in nickel-base superalloys

It is experimentally observed in Ni-based superalloys that the dislocation substructure after deformation at elevated temperatures is different on horizontal and vertical γ/ γ′ interfaces. Edge dislocation networks are predominantly observed at horizontal interfaces while screw dislocation segments are seen mostly on the vertical interfaces. A crystallographic model of the critical shear stress for dipole expansion for screw and 60° dislocation segments in the γ/ γ′ interfaces is used to explain the observations in high γ′ volume fraction (∼70%) alloys. However, the same model is found to be inadequate in explaining the substructure observations in those alloys with lower γ′ volume fraction (∼40%) which have wider matrix ( γ) channels ( ≈180 nm ). It is shown by superimposition of the dislocation's stress field, the internal coherency stresses and the externally applied stress that between 60° and screw dislocation segments the former increase the internal stresses in vertical interfaces more than the latter.

A model study on internally generated variability in subtropical mode water formation

Internally generated variability in the subtropical gyre is studied as a possible mechanism for the observed interannual to decadal variability in subtropical mode water formation. An isopycnic ocean model with idealized geometry and forcing which mimics the North Atlantic subtropical gyre is used for this purpose. The horizontal resolution is sufficiently high and the friction and diffusion sufficiently low for the flow to become barotropically and baroclinically unstable. Two modes of low‐frequency variability are found. Both modes consist of westward propagating thickness anomalies. The anomalies have a first baroclinic modal structure with a maximum amplitude at the thermocline. One mode has a timescale of 8 years and a basin wide spatial scale; the other has a timescale of 4.5 years and a smaller spatial scale. The modes appear to be damped when the diffusion is high. In that case, the 8‐year mode can be excited by a spatially coherent stochastic wind stress. The evolution of the modes is determined by an interaction between the mean flow and the low‐frequency variability itself. The modes are instabilities of the mean flow determined by the basic stratification. It appears that coupling to the atmosphere and a parameterization of surface mixing are necessary for the low‐frequency variability to appear in the mixed layer. The coupling and surface mixing do not play a role in generating the modes. It is concluded that these internally generated modes may play a role in the observed variability in mode water formation.

The Mechanism of Braze Metal Penetration by Migration of Liquid Films in Aluminium

Samples of braze-clad AA3003 alloy, have been examined in various conditions after heat treatments simulating stages of the brazing process. Sheet material was produced in the annealed temper using both homogenised and unhomogenised ingots and was subsequently strained to different degrees before brazing. A critical degree of deformation leads to unfavourable penetration of braze metal into the core alloy. This process involves the dragging of liquid films under the action of the stored energy of deformation, analogous to the grain boundary tension effect reported previously, and is different from the phenomenon of liquid film migration driven by alloying and associated coherency stresses.

Morphology of L1 0-TiAl(Ag) precipitation in Ag-modified L1 2–Al 3Ti

Transmission electron microscopy (TEM) examinations of Ag-modified Al 3Ti with an L1 2-ordered structure have revealed the precipitation of L1 0–TiAl upon aging after quenching from higher temperatures. TEM observations revealed that plate-like L1 0–TiAl precipitates lie on {001} planes of (Al,Ag) 3Ti matrix in the short aging period and the habit plane changed from {001} to {hhl} after a long period aging or higher temperature aging and finally to {225} of the matrix lattice. A quantitative X-ray microanalysis for determining the chemical compositions of precipitate and matrix has been done by using an analytical electron microscope. The L1 2 phase field in the Ti–Al–Ag system is severely skewed with respect to the temperature axis and is restricted into a much smaller field at lower temperatures. The coherency stresses across the precipitate/matrix interface is considered to be the main factor controlling the precipitate morphology.

Transmisson electron microscopy of phase composition and lattice misfit in the Re-containing nickel-base superalloy CMSX-10

Phase compositions of matrix and γ′ phase in the third-generation superalloy CMSX-10 containing 6 wt.% Re were measured locally by energy dispersive X-ray spectroscopy in a transmission electron microscope. The corresponding lattice misfits between matrix and γ′ phase were determined by convergent beam electron diffraction. All measurements were performed in dendrites and interdendritic regions. Comparing the as-cast condition to the standard heat treated condition, remarkable enrichments of Re in the γ′ phase of dendrites and segregation of W and Ta in the matrix are detected. After standard heat treatment, an enrichment of Re remains in the matrix of dendrites. This results in differences in amount and sign of lattice misfit. Coherency stresses were calculated using the Finite Elements Method.

Simple model for interface stresses with application to misfit dislocation generation in epitaxial thin films

A simple model for the interfacial free energy of a semicoherent interface is used to develop expressions for interface stresses, which are surface thermodynamic quantities associated with solid–solid interfaces. An analysis of the thermodynamics of thin film epitaxy is presented that incorporates the effects of free surface and interface stresses, and an expression for the critical thickness for thin film epitaxy is obtained. Based on this analysis, the concept of effective pressures exerted by the thin film free surface and film–substrate interface is introduced. If it is assumed that misfit dislocations are generated at the film–substrate interface as a result of glide of threading dislocations, the thermodynamics and kinetics of stress relaxation can be discussed in terms of a balance of Peach–Koehler forces acting on the threading dislocations owing to the surface and interface pressures as well as to the coherency stress. An example is given that shows that, if the film has a relatively large surface pressure that opposes lattice matching, the dependence of the coherency strain on film thickness can be very different from that obtained from conventional analyses which ignore the effect of the free surface; specifically, the largest equilibrium coherency strain of the same sign as the misfit can be much smaller than the total misfit, and an “anomalous” coherency strain of sign opposite that of the misfit can be thermodynamically favorable at small film thicknesses. The analysis used to obtain the critical thickness for thin film epitaxy is extended to give an expression for the critical thickness for misfit dislocation generation at the interface between a substrate and a superlattice thin film. It is shown that this critical thickness depends on a superlattice pressure associated with the interlayer interface stress in addition to the free surface and film–substrate interface pressures.

Kinetics of diffusion-induced grain-boundary migration in dispersion-hardened Pb−Sb alloy

A complex DIGM and discontinuous phase- dissolution reaction is revealed for the first time. The volume diffusion at the front of the complex reaction and the driving force due to coherent concentration-induced stresses are studied in aPb−Sb alloy. The activation energy for the reaction is determined.

Atomistic Simulations of Steps in Bimetallic Interfaces as Barriers to Interface Slip Transmission

ABSTRACTAtomistic models of coherent interfaces in the CuNi system with and without (111)-steps were used to study slip transmission across interfaces in CuNi metallic bilayers. The lattice mismatch of the CuNi system results in large coherency stresses at the interface. The (111)-steps afford a larger barrier to slip than the flat, coherent interface. The coherent flat interface dislocation barrier is largely due to the large compressive stresses in the Cu layer that must be overcome by applied tensile stresses. Additional Koehler forces are present as the dislocation in the elastically softer Cu approaches the stiffer Ni layer. The step, however, possesses a small residual edge dislocation with a Burgers vector equal to the difference of bCu and bNi times the height of the (111)-step in (111)-layers. We find that these steps are potent slip barriers, which suggests that homogeneous slip is preferred in such systems.

Coherency stresses and deuterium diffusion in NbD0.33

Concentration fluctuations of impurity atoms in solids, such as hydrogen in metals, are accompanied by coherency stresses if the impurity atoms expand or contract the lattice. The coherency stresses raise the elastic energy which accelerates the diffusive decay of the fluctuations and increases, therefore, the value of a diffusion coefficient defined according to Fick’s law. We studied the influence of coherency stresses on deuterium diffusion in NbD 0.33 by neutron spectroscopy, separating coherent and incoherent scattering by neutron spin analysis. The diffusion coefficient D bulk of the deuterium interstitials, obtained from the coherent scattering intensity, was found up to 30 times larger than the diffusion coefficient D chem reported from Gorsky effect measurements [H.C. Bauer, J. Völkl, T. Tretkowski, G. Alefeld, Z. Physik B29 (1978) 17] on the same system, in spite of the fact that both diffusion coefficients describe deuterium diffusion according to Fick’s law. We demonstrate that the large differences between D bulk and D chem reflect a dissimilar influence of coherency stresses on these two quantities, and that the differences can quantitatively be described within the elasticity-theoretical concept of Wagner and Horner.

Simulation of an edge source in the Cu-Ni multilayer system

Metallic multilayered structures are known to possess unusual physical and mechanical properties. At small layer wavelengths ({approximately}10--50nm), multilayered structures are reported to have significant enhancements in their yield and fracture strengths. Yield strength enhancements in metallic multilayered structures have been observed in a large number of systems. Theoretical models predicting the yield strength of multilayered systems can be classified into two categories: (1) Models based on the Orowan strengthening mechanism and (2) Hall-Petch strengthening type of models. The purpose of this paper is to test the Matthews and Blakslee theory in a very thin layer by simulating a dislocation source in Ni atomistically. In this manuscript, 3-dimensional (3-D) atomistic simulations incorporating Green's function boundary conditions (GFBC's) are used to calculate the bowing of a short edge segment (Burgers' vector = 1/2[110], line direction = [1 {bar 1}2]) of length 8 nm under an applied shear stress in FCC Ni. Atomistic simulation results on the bowing of the source is shown to be in excellent agreement with anisotropic elasticity predictions even at these short segment lengths. Elasticity calculations are then used to show that for all wavelengths and volume fracture of Ni in the Cu-Ni multilayered system, coherency stresses present inmore » Ni are almost identical to the stresses required for activating a source. These results are equally applicable for activation of sources in the softer Cu layer. This indicates that the Orowan mechanism of yielding occurs at almost no applied stress and the yield strengthening observed in the Cu-Ni multilayered system is a result of either the interface barrier to dislocation motion or the effect of the coherency stress in the disfavored layer.« less

Coherency stresses and interface-related deformation phenomena in two-phase titanium aluminides

Phase equilibria and transformations in near-equiatomic titanium aluminides lead to the formation of a lamellar structure comprising of the intermetallic phases α 2(Ti 3Al) and γ(TiAl). Due to differences in lattice parameters and crystal structure, coherency stresses and mismatch structures occur at various types of semicoherent interfaces present in the material. The present paper reports an electron microscope study of the atomic structure of the interfaces. The residual coherency stresses present at the interfaces were determined by analysing the curvature of dislocation loops which were emitted from the network of interfacial dislocations. The implication of these stresses on the deformation behaviour of the material will be discussed.

Coherent and incoherent flow structures behind a normal flat plate

By means of triple-decomposition, characteristics of coherent and incoherent contributions in the wake of a flat plate were examined in a domain x/D=2–8 at a Reynolds number of 3.3 × 104. Significant lateral momentum transfer to a growing vortex was obtained 13 period after a vortex was shed. Coherent and incoherent energy production was initiated at the edges of the flat plate with subsequent diffusion laterally and then in free-stream direction. Coherent shear stress 〈ũṽ〉 alternates twice per cycle due to ṽ lagging behind ũ by 14 of a cycle; time mean coherent stress is zero. Although normal incoherent stresses are around 10% of U∞2, peak values for 〈u′v′〉 are at most 3% or lower.