Coherency Stresses Research Articles

Synthesis and phase separation of (Ti,Zr)C

Synthesis and phase separation of (Ti,Zr)C were investigated in the present work. The (Ti,Zr)C phase was synthesized at 2200°C and subsequently aged at 1300°C for different times. The microstructure was investigated using X-ray diffraction and electron microscopy, and supplemented by first-principles calculations. The (Ti,Zr)C phase separates into a lamellar nanostructure with alternating Ti- and Zr-rich face-centered cubic domains as well as non-stoichiometric TiC and ZrC. The lamellar structure is a consequence of phase separation within the miscibility gap that is directionally constrained by high coherency stresses, as indicated by the first-principles calculations. Moreover, the increased hardness due to the phase separation suggests that the mixed carbide could be used as a strengthening constituent in, for example, cemented carbides.

Strategies to Avert Electrochemical Shock and Their Demonstration in Spinels

We demonstrate that extensive electrochemical shock–electrochemical cycling induced fracture–occurs due to coherency stresses arising from first order cubic-to-cubic phase transformations in the spinels LiMn2O4 and LiMn1.5Ni0.5O4. Electrochemical shock occurs despite the isotropy of the shape changes in these materials. This electrochemical shock mechanism is strongly sensitive to particle size; for LiMn2O4 and LiMn1.5Ni0.5O4, fracture can be averted with particle sizes smaller than ∼1 μm. As a further critical test of the proposed mechanism, iron-doping was used to induce continuous solid solubility of lithium in LiMn1.5Ni0.5O4, and shown to virtually avert electrochemical shock, while having minimal impact on the electrode potential and capacity.

Chemically induced fracturing in alkali feldspar

Fracturing in alkali feldspar during Na+–K+ cation exchange with a NaCl–KCl salt melt was studied experimentally. Due to a marked composition dependence of the lattice parameters of alkali feldspar, any composition gradient arising from cation exchange causes coherency stress. If this stress exceeds a critical level fracturing occurs. Experiments were performed on potassium-rich gem-quality alkali feldspars with polished (010) and (001) surfaces. When the feldspar was shifted toward more sodium-rich compositions over more than about 10 mole %, a system of parallel cracks with regular crack spacing formed. The cracks have a general (h0l) orientation and do not correspond to any of the feldspar cleavages. The cracks are rather oriented (sub)-perpendicular to the direction of maximum tensile stress. The critical stress needed to initiate fracturing is about 325 MPa. The critical stress intensity factor for the propagation of mode I cracks, K Ic, is estimated as 2.30–2.72 MPa m1/2 (73–86 MPa mm1/2) from a systematic relation between characteristic crack spacing and coherency stress. An orientation mismatch of 18° between the crack normal and the direction of maximum tensile stress is ascribed to the anisotropy of the longitudinal elastic stiffness which has pronounced maxima in the crack plane and a minimum in the direction of the crack normal.

Surface directed spinodal decomposition at TiAlN/TiN interfaces

In contrast to the monolithic c-Ti1−xAlxN, the isostructural spinodal decomposition to c-AlN and c-TiN in c-Ti1−xAlxN/TiN multilayers has almost the same onset temperature for the compositions x = 0.50 and 0.66. Differential scanning calorimetry also shows that the decomposition initiates at a lower temperature compared to the monoliths with the same Al-content. Z-contrast scanning transmission electron microscopy imaging reveals a decomposed structure of the multilayers at temperatures where the monoliths remain in solid solution. In the multilayers, the decomposition is initiated at the internal interfaces. The formation of an AlN-rich layer followed by a TiN-rich area parallel to the interface in the decomposed Ti0.34Al0.66N/TiN coating, as observed in atom probe tomography, is consistent with surface directed spinodal decomposition. Phase field simulations predict this behavior both in terms of microstructure evolution and kinetics. Here, we note that surface directed spinodal decomposition is affected by the as-deposited elemental fluctuations, coherency stresses, and alloy composition.

Influence of annealing on the character of structural-phase mismatch in single crystals of heat-resistant nickel alloys

The lattice parameter mismatch between the γ and γ′ phases (γ/γ′ misfit) in single crystals of heat-resistant nickel alloys (HRNAs) ZhS32 and VZhM4 after annealing of varying duration at 900 to 1100°C was studied by X-ray diffraction. It was established that relaxation of coherent stresses in single crystals of HRNAs is accompanied by removal of tetragonal splitting of the matrix (004) γ reflection, and the relaxation dynamics depends on the heat resistance of the single crystal and is determined by the level and duration of temperature exposure. A qualitative change in the profile of the matrix X-ray reflection from the VZhM4 single crystal after long-term annealing at a temperature of 1100°C was revealed.

Suppression of relaxation in (202¯1) InGaN/GaN laser diodes using limited area epitaxy

Confinement factor (Γ) of semipolar (202¯1) green laser diodes (LDs) is limited by relaxation of coherency stresses in the waveguiding heterostructure. In this paper, we demonstrate the suppression of relaxation by blocking glide of pre-existing threading dislocations using limited area epitaxy (LAE). With LAE, we show a factor of three increase in thickness before the observation of significant misfit dislocation formation for (202¯1) oriented In0.08Ga0.92N/GaN heterostructures. We then apply this technique to fabricate coherent AlGaN-cladding-free LDs with 73% enhanced Γ relative to planar devices without LAE, having an emission wavelength of 495 nm and threshold current density of 10.7 kA/cm2. This technique is readily applicable to AlGaN or AlInGaN cladding in addition to InGaN waveguiding layers to improve Γ of semipolar LDs.

Finite Substrate Effects on Critical Thickness in Epitaxial Systems

During the growth of an epitaxial overlayer on a thick substrate (GeSi on Si), an interfacial misfit dislocation becomes energetically favourable on exceeding the critical thickness. In substrates of finite thickness, the value of critical thickness is altered with respect to thick substrates. Thin substrates can bend and partially relax the coherency stresses, thus contributing to the altered value of the critical thickness. The current work aims at simulating the stress state of a growing finite epitaxial overlayer on a substrate of finite thickness, using finite element method. The numerical model is used to calculate the critical thickness for substrates with finite thickness. Eigenstrains will be imposed in selected regions in the domain towards this end. Size of the substrate for which it is not energetically favourable to accommodate a misfit dislocation is determined from the simulations (i.e. the system remains coherent for substrates below this thickness). Important effects arising in the transition regime of substrate thicknesses are also investigated.

Decomposition and phase transformation in TiCrAlN thin coatings

Metastable solid solutions of cubic (c)-(TixCryAlz)N coatings were grown by a reactive arc evaporation technique to investigate the phase transformations and mechanisms that yield enhanced high-temperature mechanical properties. Metal composition ranges of y < 17 at. % and 45 < z < 62 at. % were studied and compared with the parent TiAlN material system. The coatings exhibited age hardening up to 1000 °C, higher than the temperature observed for TiAlN. In addition, the coatings showed a less pronounced decrease in hardness when hexagonal (h)-AlN was formed compared to TiAlN. The improved thermal stability is attributed to lowered coherency stress and lowered enthalpy of mixing due to the addition of Cr, which results in improved functionality in the temperature range of 850–1000 °C. Upon annealing up to 1400 °C, the coatings decompose into c-TiN, bcc-Cr, and h-AlN. The decomposition takes place via several intermediate phases: c-CrAlN, c-TiCrN, and hexagonal (β)-Cr2N. The evolution in microstructure observed across different stages of spinodal decomposition and phase transformation can be correlated to the thermal response and mechanical hardness of the coatings.

Compositionally graded relaxed AlGaN buffers on semipolar GaN for mid-ultraviolet emission

In this Letter, we report on the growth and properties of relaxed, compositionally graded AlxGa1 − xN buffer layers on freestanding semipolar (202¯1) GaN substrates. Continuous and step compositional grades with Al concentrations up to x = 0.61 have been achieved, with emission wavelengths in the mid-ultraviolet region as low as 265 nm. Coherency stresses were relaxed progressively throughout the grades by misfit dislocation generation via primary (basal) slip and secondary (non-basal) slip systems. Threading dislocation densities in the final layers of the grades were less than 106/cm2 as confirmed by plan-view transmission electron microscopy and cathodoluminescence studies.

Strain Effect on the γ′ Dissolution at High Temperatures of a Nickel-Based Single Crystal Superalloy

The kinetics of the γ′ phase dissolution have been studied at 1473 K and 1523 K (1200 °C and 1250 °C) for CMSX-4® alloy. Interrupted creep tests at 1323 K (1050 °C) and pure thermal aging at 1373 K (1100 °C) have been used to vary the initial γ′ morphology. Subsequent dissolution studies were conducted with or without an applied load. Differences in γ′ dissolution kinetics were observed between the dendrite cores and the interdendritic regions, resulting from the chemical microsegregations remaining after the standard heat treatments. It is shown that the initial γ′ morphology, the relaxation of the coherency stresses and the accumulated plastic strain are critical parameters controlling the dissolution kinetics. An increase of the accumulated plastic strain leads to an increase of the dissolution kinetics, whatever the location in the dendritic structure. In addition, once a given accumulated creep strain is reached prior to the dissolution tests (i.e., a given dislocations density), the dissolution kinetics are the same at 1473 K and 1523 K (1200 °C and 1250 °C). A modified equation of the recently developed Polystar model is proposed to incorporate the role of the accumulated plastic strain on the γ′ dissolution kinetics and to achieve a better predictability of the creep deformation under non-isothermal loading paths.

Superfunctionalities in Nanodispersive Precipitation-Hardened Alloys

Although nanodispersive precipitation-hardened alloys have been intensively studied over decades as important structural materials, the possibility that these alloys may have superfunctional properties has been completely overlooked. As shown in this Letter, they may have giant low-hysteretic strain responses to external stimuli if the nanosized single-domain precipitates can switch their orientation variants under applied fields. We demonstrate that the misfit-generated coherency stress can significantly reduce the variant switching barriers and may drastically decrease or even eliminate the hysteresis of the strain super responses to external stress and/or magnetic fields. These alloys can thus be functionalized as shape memory, superelastic, and/or supermagnetostrictive materials. The conditions of such functionalization are established by the interpretation-transparent analytical calculations, and confirmed by computer prototyping. In particular, the obtained results pave the way for the engineering of rare-earth free alloys with excellent magnetomechanical and good mechanical properties.

Phase-field simulation of twin boundary fractions in fully lamellar TiAl alloys

The phenomenon of high twin boundary fractions found experimentally for neighboring γ lamellae in fully lamellar TiAl alloys was investigated by phase-field simulations. The nucleation and growth processes during α2′→α2+γ transformation that leads to the lamellar structure were simulated. In particular, the effects of coherency stress and the interfacial energy difference among different types of interfaces and undercooling on the nucleation mechanism were analyzed. It is found that the twin boundary fraction increases with increasing coherency elastic strain energy and increasing interfacial energy difference among different types of interfaces, and with decreasing undercooling. Depending on the relative contributions of these factors, the nucleation events simulated by the Langevin noises could be collective, correlated or independent. These findings could shed light on the control of twin boundary fraction within lamellar structures by adjusting alloy composition and cooling route.

Effect of high pressure and high temperature on the microstructural evolution of a single crystal Ni-based superalloy

The application of high nearly hydrostatic pressures at elevated temperatures on the LEK94 single crystal (SX) nickel-based superalloy directly affects its microstructure. This is due to a combination of the effect of pressure on the Gibbs free energy, on the diffusion coefficients of the alloying elements, on the internal coherent stresses, and on the porosity distribution. The last effect depends at least on the first three. Therefore, based on the theoretical influences of the pressure, the main objective of this work is to understand, by means of an experimental work, the effect of high pressure at elevated temperature during annealing on the evolution of the phases morphology, and porosity of the high-temperature material LEK94. Specifically, pressures up to 4 GPa, temperatures up to 1180 °C, and holding times up to 100 h were investigated. The main findings are that, porosity can be considerably reduced without affecting significantly the γ/γ′ microstructure by high pressure annealing and the verification that increasing the external pressure stabilizes the γ′-phase.

Unraveling the apparent magnitude threshold of remote earthquake triggering using full wavefield surface wave simulation

Empirical studies with earthquake catalogs suggest that large events (M > 5) are rarely triggered in significant numbers by passing surface waves at remote distances from main shocks. Triggered, small (M < 5) earthquakes are routinely associated with the passage of surface waves from large (M > 7) main shocks. Since large earthquakes involve larger rupture areas, we study the spatial and temporal characteristics of dynamic stress change for clues. Using a 3D finite element method, we model the complete wavefield from the 2002 M= 7.9 Denali earthquake recorded near the Wasatch Front in Utah, where details about triggered seismicity are known. In particular, we load our model with a displacement seismogram to acquire a time series of the stress change tensor and model failure of a representative normal fault based on these stress changes. We note that the stress‐change regime varies rapidly between favoring strike‐slip, thrust, and normal faulting, with durations lasting ∼1–4 s. We find that these stress regimes usually affect only some fraction of a fault surface at any given time. Stress amplitudes also vary, meaning that ideal conditions for triggering are short‐lived and spatially limited. Stress conditions can also rapidly reverse to regimes that inhibit slip. Given these stressing conditions, we conclude that it may be difficult for a larger rupture area to experience the temporally and spatially coherent stress change necessary to develop into a large magnitude earthquake.

384 nm laser diode grown on a (202¯1) semipolar relaxed AlGaN buffer layer

We demonstrate an electrically injected semipolar (202¯1) laser diode grown on a partially relaxed AlGaN buffer layer. The coherency stresses are relaxed by misfit dislocations at the GaN/AlGaN heterointerface which form by glide of preexisting threading dislocations along the (0001) basal plane. The defects are confined to the heterointerface which allows the growth of high aluminum composition films with threading dislocation densities of less than 108 cm−2. The lasing wavelength was 384 nm with a threshold current density of 15.7 kA/cm−2. UV lasers grown on semipolar relaxed AlGaN buffers provide an alternative to devices grown on AlN or sapphire.

Experimental Na/K exchange between alkali feldspar and an NaCl–KCl salt melt: chemically induced fracturing and element partitioning

The exchange of Na+ and K+ between alkali feldspar and a NaCl–KCl salt melt has been investigated experimentally. Run conditions were at ambient pressure and 850 °C as well as 1,000 °C. Cation exchange occurred by interdiffusion of Na+ and K+ on the feldspar sub-lattice, while the Si–Al framework remained unaffected. Due to the compositional dependence of the lattice parameters compositional heterogeneities resulting from Na+/K+ interdiffusion induced coherency stress and associated fracturing. Depending on the sense of chemical shift, different crack patterns developed. For the geometrically most regular case that developed when potassic alkali feldspar was shifted toward more sodium-rich compositions, a prominent set of cracks corresponding to tension cracks opened perpendicular to the direction of maximum tensile stress and did not follow any of the feldspar cleavage planes. The critical stress needed to initiate fracturing in a general direction of the feldspar lattice was estimated at ≤0.35 GPa. Fracturing provided fast pathways for penetration of salt melt or vapor into grain interiors enhancing overall cation exchange. The Na/K partitioning between feldspar and the salt melt attained equilibrium values in the exchanged portions of the grains allowing for extraction of the alkali feldspar mixing properties.

A formation mechanism for ultra-thin nanotwins in highly textured Cu/Ni multilayers

High density nanotwins with average twin thickness varying from 3 to 6 nm are formed in sputtered highly (111) textured Cu/Ni multilayers, when individual layer thickness is 25 nm or less. Twin interfaces are normal to growth direction. Both maximum twin thickness and volume fraction of twins vary with the individual layer thickness. Coherency stress plays an important role in tailoring the formation of nanotwins. Nanotwins compete with misfit dislocations in accommodating elastic strain energy in epitaxial Cu/Ni multilayers.

Effects of coherency stress and vacancy sources/sinks on interdiffusion across coherent multilayer interfaces – Part II: Interface sharpening and intermixing rate

Vacancy-mediated interdiffusion in coherent Mo/V and Cu/Ni multilayers is simulated to evaluate the effects of coherency stress and vacancy sources/sinks on interface sharpening and the intermixing rate, using the phase field model developed in a previous paper for two limiting cases: ideal vacancy sources/sinks densely distributed or not present at all. Interface sharpening stems from a large diffusion coefficient asymmetry across the interface, which in turn originates from the large difference in vacancy formation and migration energies between the two constituent layers. Remarkable sharpening is found in Mo/V multilayers either with dense or without vacancy sources/sinks, but only in Cu/Ni with a high density of sources/sinks. Sharpening is suppressed by coherency stress in Cu/Ni regardless of the existence of vacancy sources/sinks, but only promoted in Mo/V with a high density of sources/sinks. The intermixing rate is suppressed in Mo/V by the introduction of a high density of vacancy sources/sinks that are parallel or perpendicular to the interfaces, or uniformly distributed in all orientations, but only promoted in Cu/Ni by the introduction of vacancy sources/sinks that are parallel to the interfaces. The intermixing rate is promoted in Mo/V by coherency stress regardless of the existence of vacancy sources/sinks, but promoted in Cu/Ni by coherency stress only when the vacancy sources/sinks are parallel to the interface or not present at all. The effects of that part of coherency stress induced by the mismatch in atomic volumes on interface sharpening and the intermixing rate are opposite to, but dominant over, those of the stress induced by lattice creation/annihilation in vacancy sources/sinks.

Effects of coherency stress and vacancy sources/sinks on interdiffusion across coherent multilayer interfaces – Part I: Theory

A phase field model corresponding to vacancy-mediated interdiffusion in coherent multilayers with completely miscible constituents is developed to explore the effects of several factors on interdiffusion across coherent multilayer interfaces, such as: (1) the dependence of diffusion potentials and mobilities on coherency stress; (2) the dependence of diffusion potentials and mobilities on composition; (3) the elastic constant inhomogeneity resulting from a inhomogeneous composition distribution; and (4) the properties of vacancy sources/sinks. The Gibbs free energy of the system consists of chemical and elastic energies. The gradient energy is neglected as the multilayers under consideration can be chemically well approximated by an ideal substitutional solution model. Elastic energy is a function of the stress-free strain and inhomogeneous elastic moduli distributions, while the stress is solved by anisotropic phase field microelasticity theory. The diffusion potentials are obtained straightforwardly as functional derivatives of the free energy with respect to composition and are in keeping with previous derivations that involved many mathematical manipulations or quite advanced theories. The diffusion mobilities are affected by the stress through modification of the vacancy formation and migration energies. Two limiting cases of vacancy sources/sinks are taken into account: ideal vacancy sources/sinks are uniformly and densely distributed, or not present at all, so the vacancy concentration is in equilibrium all the times, as determined by the local stress and composition in the former case, but deviates from the equilibrium concentration in the latter. The model can be conveniently extended to consider the non-ideal activity of vacancy sources/sinks by introducing a general kinetic relation for the vacancy creation rate.

Interfacial coherency stress distribution in TiN/AlN bilayer and multilayer films studied by FEM analysis

The development of interfacial coherency stresses in TiN/AlN bilayer and multilayer films was investigated by finite element method (ABAQUS) using the four-node bilinear quadrilateral axisymmetric element CAX4R. The TiN and AlN layers are always in compression and tension at the interface, respectively, as may be expected from the fact TiN has larger lattice parameter than AlN. Both, the bi-layer and the multilayer stacks bend due to the coherency stresses. For the TiN/AlN bilayer system, the curvature of the bending is largest for the TiN/AlN thickness ratios ∼0.5 and ∼2 (at which one of the two layers is fully in compression or tension), while it is smaller for the layers with the same thickness (at which both layers posses regions with compressive as well as tensile stresses). This stress distribution over the bi-layer thickness is shown to be strongly influenced by the presence and the properties of a substrate.Furthermore, the coherency stress profile and specimen curvature of a TiN/AlN multilayer system was studied as a function of the top-most layer thickness. The curvature is maximum for equal number of TiN and AlN layers, and decreases with increasing the number of TiN/AlN periods. Within the growth of an additional TiN/AlN bilayer, the curvature first decreases to zero for a vertically symmetrical geometry over the layers when the TiN layer growth is finished (e.g. for (n+1) layers of TiN and n layers of AlN). At this stage, the coherency stresses in TiN and AlN are same in each layer type (independent on the layer position). The growth of the second half of the TiN/AlN bi-layer (i.e. the AlN) to finish the period, again bends the specimen, and generates a non-uniform stress distribution. This suggests that the top layer as well as the overall specimen geometry plays a critical role on the actual coherency stress profile.