Misfit Strain Energy Research Articles

Investigations on the effect of arsenic and phosphorus atomic exchange on the origin of crystal potential fluctuations in InAsP/InP epilayers

The study investigates the anion exchange mechanism between the ad-atoms of arsenic and phosphorus followed by their inter-diffusion processes, in InAsP/InP hetero-structures grown by metal organic vapor phase epitaxy technique. The energetics and kinetics of the ad-atoms like arsenic and phosphorus are governed by the growth conditions. It has been found that the percolation of arsenic and phosphorus in the epilayer depends on various factors, such as gas-phase diffusion coefficients, surface reaction rates, misfit strain energy, bond energy, segregations, and the presence of defects and dislocations. Effects of anion exchange mechanisms on generating local crystal potential states that originated due to the local crystal bonding environment are further investigated. The magnitude of these local potential states strongly depends on the strain states associated with the layer thickness. If the difference between the potential minima is small (< 25 meV), it leads to distinct “S” shaped temperature-dependent luminescence/absorption spectra. In contrast, a large difference gives rise to two distinctive luminescence/absorption peaks. Thus, by controlling the strain states associated with the energetics and kinetics of ad-atoms like arsenic/phosphorus and layer thickness, such “S” shaped behavior can be controlled.

Seed-crystal-induced directional solidification toward Al2O3/(Y0.2Er0.2Yb0.2Ho0.2Lu0.2)3Al5O12/ZrO2 ternary eutectic ceramics

The present work successfully prepared a novel Al2O3/(Y0.2Er0.2Yb0.2Ho0.2Lu0.2)3Al5O12/ZrO2 (or Al2O3/(5RE0.2)AG/ZrO2 in short) ternary eutectic ceramic with the seed-crystal-induced technique by directional solidification. ZrO2 was a cubic structure and was stabilized by all oxides of Y2O3, Er2O3, Yb2O3, Ho2O3, and Lu2O3. The three phases interpenetrated each other and ZrO2 was highly dispersed. Al2O3 inherited well the direction of the c-sapphire seed. The orientation relationship among the three was determined to be [0001]Al2O3 || [100](5RE0.2)AG || [110]ZrO2, (11–20)Al2O3 || (004)(5RE0.2)AG || (002)ZrO2. The three interfaces were all semi-coherent and showed higher interfacial misfit strain energy due to the solid solution effect of (5RE0.2)AG. The novel Al2O3/(5RE0.2)AG/ZrO2 ternary eutectic ceramic showed improved mechanical properties compared to other Al2O3-based eutectic ceramics. The solid solution effect was the main reason for its enhanced hardness and elastic modulus. Several toughening mechanisms including crack bridging, bifurcation, deflection, and screening can be found in the Al2O3/(5RE0.2)AG/ZrO2 ternary eutectic ceramic. The micro-scale suture-like deflection was newly found in the microstructure, which contributed to its fracture toughness.

The Mechanism of Dendrite Formation in a Solid-State Transformation of High Aluminum Fe-Al Alloys.

The mechanism of solid-state dendrite formation in high-aluminum Fe-Al alloys is not clear. Applying an in-situ observation technique, the real-time formation and growth of FeAl solid-state dendrites during the eutectoid decomposition of the high-temperature phase Fe5Al8 is visualized. In-situ experiments by HT-CSLM reveal that proeutectoid FeAl usually does not preferentially nucleate at grain boundaries regardless of rapid or slow cooling conditions. The critical radii for generating morphological instability are 1.2 μm and 0.9 μm for slow and rapid cooling, respectively. The morphology after both slow and rapid cooling exhibits dendrites, while there are differences in the size and critical instability radius Rc, which are attributed to the different supersaturation S and the number of protrusions l. The combination of crystallographic and thermodynamic analysis indicates that solid-state dendrites only exist on the hypoeutectoid side in high-aluminum Fe-Al alloys. A large number of lattice defects in the parent phase provides an additional driving force for nucleation, leading to coherent nucleation from the interior of the parent phase grains based on the orientation relationship {3¯30}Fe5Al8//{1¯10}FeAl, <111¯>Fe5Al8//<111¯>FeAl. The maximum release of misfit strain energy leads to the preferential growth of the primary arm of the nucleus along <111¯> {1¯10}. During the rapid cooling process, a large supersaturation is induced in the matrix, driving the Al atoms to undergo unstable uphill diffusion and causing variations in the concentration gradient as well as generating constitutional undercooling, ultimately leading to morphological instability and the growth of secondary arms.

Accurate prediction of threshold stress for hydride reorientation in Zircaloy-4 with directly measured interface orientation relationship

Hydride reorientation is a major degradation mechanism of zirconium-based alloys used for nuclear fuel cladding tubes. A previous commonly used thermodynamic model has limited accuracy in predicting the threshold stress for hydride reorientation owing to assumptions that all basal pole of α-Zr is oriented along the radial direction on cross-section of cladding tube and all hydrides precipitate at the prismatic plane of α-Zr. We analyzed fractions of each zirconium-hydride interface orientation relationship by EBSD (Electron Backscatter Diffraction) and found that the typical macroscopic radial hydrides are primarily formed upon aggregation of {101¯1}α-Zr // {111}δ-ZrH1.66 and {0001}α-Zr // {111}δ-ZrH1.66 orientation relationships in mesoscale. The former is statistically favored due to the large number of available sites, and the latter is energetically favored due to the low strain energy. Using the fraction-weighted average misfit strain and strain energy and the texture information, we demonstrated that the accuracy of the thermodynamic model can significantly improve. This work consummates the present thermodynamic model for hydride reorientation in zirconium-based alloys.

Phase-field crystal study on the influence of nanoscale intergranular structures on grain boundary segregation

Grain boundary (GB) segregation can substantially affect the performance of materials by greatly changing the chemical compositions of GB. It is well known that GB segregation is essentially attributed to the structural differences between the bulk of grain and GB. Nevertheless, we still lack a clear understanding about the correlation between nanoscale intergranular structures and solute segregation. In this work, by using the phase-field crystal model, we performed atomic scale simulations to investigate the segregation of Li atoms to symmetric ⟨110⟩ tilt GBs in binary Al–Li alloys. It was found that the amount of segregated solute increases proportionally to GB misorientation angle in the case of low-angle tilt GBs, and converges at high-angle tilt GBs, except some special GBs with coincidence-site lattice. This is analogous to the dependences of GB energy and density on the misorientation angle. The correlations among GB structure, misfit strain around GBs and solute segregation are quantified at atomic scale. In low-angle tilt GBs, Li atoms are segregated to the compress zone around the core of intergranular dislocations to release the misfit strain energy. In the general high-angle tilt GBs, since the GB structure and misfit strain energy is uniform, the segregated atoms distribute homogeneously along GB. Particularly, the regular arrangement of structural units in some low Σ GBs lead to very low misfit strain energy, and accordingly to a periodically distributed and very low amount of solute segregation.

Mechanism for H-shaped precipitate formation in 1.25Cr-0.5Mo steel

Needle-like M2C precipitates with a hexagonal close-packed (HCP) structure, which are referred to as Mo2C, are well known to be responsible for the precipitation strengthening of low Cr heat-resistant steel. This paper reports H-shaped precipitation of M2C on CrN in a 1.25Cr-0.5Mo ferritic steel aged at 550 °C for 5000 h and explains the precipitation mechanism. Mo diffuses into CrN from the ferrite matrix during the aging. Chemical elemental mapping in transmission electron microscopy (TEM) shows that Mo-enriched regions in CrN act as nucleation sites of M2C. Furthermore, the thermodynamic calculation indicates that the solubility of Mo in CrN is higher than that in the matrix at 550 °C. The precipitation of M2C on CrN seems to reduce the misfit strain energy between the ferrite matrix and CrN during long-term aging. High resolution transmission electron microscopy (HRTEM) reveals that M2C has a specific orientation relationship with the ferrite matrix as well as CrN. Only M2C precipitates meeting the orientation relationship with the matrix tend to grow dominantly in one direction, which seems to be responsible for the H-shaped precipitation.

The Misfit Strain Energy Collapse during Precipitation in Solid Transformations

The misfit strain energy collapse (MSEC) which results in the dendritic or split γ’ precipitating particles during solid transformations in Ni-base alloys is discovered. Three parameters of the MSEC function, the MSEC delay, the MSEC rate, and the initial value of the MSEC function, are correlated to the persistence of the isothermal cooling, the rate during the continuous cooling, and the initial misfit strain during nucleation respectively. The MSEC point is the intersection of the two crystal lattice parameters \U0001d44e\U0001d6fe’(T) and \U0001d44e\U0001d6fe(T) of the two different phases.

Stress-Controlled Three-Dimensional Phase Evolution in Lithium Iron Phosphate

Many battery compounds undergo first-order phase transformations induced by ion (de)intercalation during battery operation, and their rate capability is often controlled by the kinetics of two-phase boundary movement. LiFePO4, a commercial cathode materials for Li-ion batteries, is a model system for studying the unique aspects of phase transitions in battery intercalation compounds. In a recent in-situ scanning transmission X-ray microscopy (STXM) study [Ohmer et al. Nature Communication 6, 6045 (2015)], Li deintercalation and phase evolution in microsized LiFePO4 single crystal upon delithiation are found to be highly non-uniform. FePO4 phase was observed to form [010]-aligned filaments growing into the LiFePO4 crystal, which is postulated to be dominated by elastic effects. In this work, we performed three-dimensional phase-field simulation to examine in the details phase evolution in LiFePO4 and the effect of misfit strain energy arising from the lattice match between FePO4 and LiFePO4. Our simulation reproduces the filamentary growth morphology of FePO4 phase (Figure 1) as observed in experiment, and confirms the dominating role of misfit stress in causing such behavior. We show that phase evolution in LiFePO4 goes through two steps during delithiation. In the first step, phase separation occurs in LiFePO4 via surface-mode coherent spinodal decomposition and results in the formation of individual FePO4 domains on particle surface. Next, FePO4 grows into the LiFePO4 matrix as wedge shaped domains that coarsen at the same time. The filamentary morphology of FP phase within (001) plane is mainly a result of the anisotropic misfit strain between LiFePO4 and FePO4, which favors the elongation of FP domains along the [010] axis to reduce elastic strain energy. Simulation reveals that Li diffusion anisotropy also significantly influences the phase growth morphology. The existence of three-dimensional Li diffusion in LiFePO4, which results from the presence of antisite defects, is found to be essential for the development of filamentary FePO4. The excellent agreement between the phase-field simulation and in-situ STXM experiment suggests that misfit stress plays an important role in triggering non-uniform Li (de)intercalation especially in large electrode particles, which is detrimental to battery performance and life and deserves close attention. Figure 1

Variant selection of intragranular Ni2(Mo,Cr) precipitates (γ′) in the Ni-Mo-Cr-W alloy

Variant selection of Ni2(Mo,Cr) precipitates (γ′) in a low coefficient of thermal expansion Ni-Mo-Cr-W alloy has been investigated as a function of precipitate size and applied stress. The lenticular-shaped, coherent γ′ precipitates form with a {110}M/(010)p habit plane. During conventional aging, all 6 variants of the Ni2(Mo,Cr) precipitates form and coarsen with aging time. With the application of external loading below the yield stress during aging, variants with {110}M habit planes that experience the largest dilations resulting from the externally applied stress are favored. Phase field modeling, coupled with elasticity theory, has been employed to simulate the development of variant selection of γ′ precipitates with and without applied external loading. Similar to the experimental results, the γ′ precipitates tend to form parallel to each other during coarsening and display variant selection when external stress is applied during aging. The mechanism is believed to be the reduction of elastic strain energy caused by the precipitate/matrix lattice mismatch. Thus, the nature of the selection indicates that the sign of the misfit is positive along [010]p. Because the misfit strain energy increases with increasing precipitate size, variant selection occurs during coarsening.

Effect of applied stress on γ’-rafting behavior in a Ni-based single-crystal superalloy: experiments and finite element analysis

The effect of applied tensile stress on the γ′-rafting behavior for a Ni-based single-crystal superalloy with more negative misfit was investigated. By conducting interrupted creep tests at high temperature, it indicated that the increase in the applied stress accelerates the γ′-rafting (directional coarsening of γ′ phase). In the early stage of rafting, the γ′-cubes start interconnecting at the ends of the parallel-to-applied-stress γ′-channel. The distributions of misfit stress, coherent strain and strain energy density of the γ/γ′ phases are then calculated by finite element analysis. The calculation results show that the rafting acceleration is mainly ascribed to the reduced strain energy density in the parallel-to-applied-stress γ-channel that is driven from the couple interaction of external load and misfit stress. Interface dislocation network formation, resulting from the misfit-induced increase in resolved shear stress, also contributes to the γ′-rafting.

Lattice-Mismatch-Induced Oscillatory Feature Size and Its Impact on the Physical Limitation of Grain Size

Size control of nanocrystals is becoming more crucial in growing, for example, granular ferromagnetic thin films for heat-assisted magnetic recording, or self-assembled quantum dots for quantum computing. This study identifies granular patterns with surprisingly ``quantized'' feature sizes in Fe-Pt thin film grown on lattice-mismatched MgO. This arises from the periodic nature of the misfit-strain energy in such a system; island lengths that are integer multiples of the misfit dislocation period are energetically favored. These results point to synthesizing nanostructured materials with well-controlled grain size by tuning the interlayer lattice mismatch.

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.

Misfit-driven β′′′ precipitate composition and morphology in Mg-Nd alloys

We report on a combined computational and experimental examination of coherent precipitation in a Mg-Nd alloy, a prototypical Mg-rare earth alloy. Three-dimensional phase field simulations are conducted to predict the composition and morphology of β′′′ precipitates, a unique family of hierarchically ordered phases that are metastable in a wide Nd concentration range. Predictions are compared to experimental high-angle annular dark-field scanning transmission electron microscopy observations. The phase field model thermodynamic description is parameterized entirely from first-principles calculations. The simulations predict an elevated Nd composition in β′′′ that is above the stress-free equilibrium value. The elevated Nd concentration in β′′′ is in very good agreement with experimental observations and arises from a large misfit strain energy penalty and the low curvature of the β′′′ free energy well. The phase field simulations predict that isolated precipitates are lenticular with a (100) habit plane, and are approximately equiaxial when viewed along the [100] direction. The predicted habit plane and precipitate dimensions are shown to be generally consistent with experimental observations, within the uncertainty introduced by density functional theory calculations of the stress-free transformation (misfit) strain and by precipitate interactions not accounted for in the simulations. Contrary to the predictions for isolated precipitates, some experimentally observed precipitates are elongated along the [001] direction relative to the [010] direction. This elongation is frequently correlated with a particular arrangement of two orientation variants of β′′′. A phase field simulation of two precipitates in this arrangement is shown to exhibit similar [001] elongation.

Development of Grain Boundary Precipitate-Free Zones in a Ni-Mo-Cr-W Alloy

In this study, the morphology and development of precipitate-free zones (PFZs) near grain boundaries (GBs) in low coefficient of thermal expansion (CTE) Ni-Mo-Cr-W alloys (based on Haynes 244) have been investigated as a function of thermal history and composition using electron microscopy techniques. It is shown that the formation of wide, continuous PFZs adjacent to GBs can be largely attributed to a vacancy depletion mechanism. It is proposed that variations in the vacancy distributions that develop after solution heat treatment (SHT) and subsequent quenching and aging greatly influence the development of the γ′-Ni2(Mo,Cr) precipitates during the aging process and result in the development of PFZs of varying sizes. The relatively large (5 to 10 μm) PFZs are distinct from the smaller, more common PFZs that result from solute depletion due to GB precipitation that are typically observed after prolonged aging. During the course of this investigation, heat treatment parameters, such as aging time, SHT temperature, cooling rate after SHT, and heating rate to the aging temperature—all of which change vacancy concentration and distribution adjacent to GBs—were investigated and observed to have significant influence on both the size and morphology of the observed PFZs. In contrast to results from other Ni-based alloys studied previously, PFZ development in the current alloys was observed across a broad range of aging temperatures. This appears to be due to the high misfit strain energy of the γ′ precipitates, resulting in a nucleation process that is sensitive to vacancy concentration. It is also shown that a slightly modified alloy with higher Mo concentrations develops smaller, more typical PFZs; this is presumably due to an increased driving force for γ′ precipitation which overshadows the influence of misfit strain energy, thereby decreasing the sensitivity of precipitation on vacancy concentration.

The split of dendritic precipitates with interfacial anisotropy in solid transformations in alloys

The dendritic precipitates may be obtained during isothermal treatment at the MSC temperature for a long time in solid transformations in the modeled alloy. The split of dendrite may occur while the temperature declines successively from the MSC point during quenching. The dendritic morphology is determined by the intensity of the interfacial anisotropy, and the split is related to the competition between the interfacial energy and the misfit strain energy. The doublet and octocube are possible while the dendritic particle is small, but if dendritic particle is large, the octodendrite may be obtained. The split of dendritic particles during aging is induced by the MSC effect which may be expressed by the MSC function which is determined by three parameters, the MSC rate β, the MSC delay t0 and the initial value of the MSC function α. The phase transformations during isothermal treatment at MSC point are spontaneous and equilibrium processes, however, phase transformations from MSC to the lower temperature during quenching are the spontaneous but non-equilibrium processes.

Hydride formation on deformation twin in zirconium alloy

Hydrides deteriorate the mechanical properties of zirconium (Zr) alloys used in nuclear reactors. Intergranular hydrides that form along grain boundaries have been extensively studied due to their detrimental effects on cracking. However, it has been little concerns on formation of Zr hydrides correlated with deformation twins which is distinctive heterogeneous nucleation site in hexagonal close-packed metals. In this paper, the heterogeneous precipitation of Zr hydrides at the twin boundaries was visualized using transmission electron microscopy. It demonstrates that intragranular hydrides in the twinned region precipitates on the rotated habit plane by the twinning and intergranular hydrides precipitate along the coherent low energy twin boundaries independent of the conventional habit planes. Interestingly, dislocations around the twin boundaries play a substantial role in the nucleation of Zr hydrides by reducing the misfit strain energy.

Three-dimensional nanostructures on Ge/Si(100) wetting layers: Hillocks and pre-quantum dots

The annealing of sub-critical Ge wetting layers (WL &amp;lt; 3.5 ML) initiates the formation of 3D nanostructures, whose shape and orientation is determined by the WL thickness and thus directly related to the strain energy. The emergence of these nanostructures, hillocks and pre-quantum dots, is studied by scanning tunneling microscopy. A wetting layer deposited at 350 °C is initially rough on the nanometer length-scale and undergoes a progressive transformation and smoothening during annealing at T &amp;lt; 460 °C when vacancy lines and the 2xn reconstruction are observed. The metastable Ge WL then collapses to form 3D nanostructures whose morphology is controlled by the WL thickness: first, the hillocks, with a wedding cake-type structure where the step edges run parallel to the ⟨110⟩ direction, are formed from thin wetting layers, while {105}-faceted structures, called pre-quantum dots (p-QDs), are formed from thicker layers. The wetting layer thickness and thus the misfit strain energy controls the type of structure. The crossover thickness between the hillock and p-QDs regime is between 1.6 and 2.1 ML. The hillocks have larger lateral dimensions and volumes than p-QDs, and the p-QDs are exceptionally small quantum dots with a lower limit of 10 nm in width. Our work opens a new pathway to the control of nanostructure morphology and size in the elastically strained Ge/Si system.

Effect of ruthenium on the precipitation of topologically close packed phases in Ni-based superalloys of 3rd and 4th generation

The precipitation of topologically close packed (TCP) phases is detrimental for the high temperature strength of high refractory Ni-based superalloys. The beneficial influence of Ru with respect to this so called instability is nowadays well accepted. In the present paper the precipitation of topologically close packed (TCP) phases is studied quantitatively in two experimental alloys (one Ru-free and one with addition of Ru) to clarify the mechanism of the Ru effect. It is confirmed that the TCP phase precipitates undergo sequential phase transformation with the tetragonal σ-phase precipitating first. Ru retards the phase transformation and leads to decreased equilibrium volume fraction of TCP phases. The results clearly indicate that Ru decreases the driving force for TCP phase precipitation. Investigations of crystallography and chemistry of the TCP/matrix interface point to an additional effect by increase of misfit strain energy.

Determination of interfacial atomic structure, misfits and energetics of Ω phase in Al–Cu–Mg–Ag alloy

The interfacial atomic structure and misfits of Ω precipitates formed in the face-centered cubic Al in the Al–Cu–Mg–Ag alloy have been determined by combining scanning transmission electron microscopy (STEM) Z-contrast imaging with chemical analysis and ab initio density functional theory (DFT) calculations. Precipitates of several thicknesses formed after heat treatment at 250°C, starting from 0 to 2 unit cells of Ω phase, were examined by STEM in four different projections. The results show that a remarkably stable double-layered interface is formed at all observed thicknesses, which separates the Ω phase from the Al matrix. The outermost interfacial layer next to Al is composed of Ag atoms in a hexagonal structure and Mg or Cu atoms below the center of the hexagon. Structural models constructed based on the experimental data were relaxed using DFT-based molecular dynamics calculations. The results show that interfacial Mg atoms, together with Ag atoms, greatly stabilize the interface structure and consequently the Ω phase on the Al {111} habit planes. Comparison between the measured and calculated precipitate misfit along the thickness direction suggests that atomic substitutions of light atoms, Al and Mg, at the interface mediate the misfit strain and free energy, which is further supported by experimental evidence obtained from STEM. Thus, we have identified here: (i) the driving force for the Ag and Mg segregation in the formation of the Ω phase; (ii) the precipitation sequence characterized by a stable interfacial double-layer; and (iii) an interfacial substitution mechanism for misfit accommodation.

Toward single-mode active crystal fibers for next-generation high-power fiber devices.

We report what we believe to be the first demonstration of a facile approach with controlled geometry for the production of crystal-core ceramic-clad hybrid fibers for scaling fiber devices to high average powers. The process consists of dip coating a solution of polycrystalline alumina onto a high-crystallinity 40-μm-diameter Ti:sapphire single-crystalline core followed by thermal treatments. Comparison of the measured refractive index with high-resolution transmission electron microscopy reveals that a Ca/Si-rich intragranular layer is precipitated at grain boundaries by impurity segregation and liquid-phase formation due to the relief of misfit strain energy in the Al2O3 matrix, slightly perturbing the refractive index and hence the optical properties. Additionally, electron backscatter diffractions supply further evidence that the Ti:sapphire single-crystalline core provides the template for growth into a sacrificial polycrystalline cladding, bringing the core and cladding into a direct bond. The thus-prepared doped crystal core with the undoped crystal cladding was achieved through the abnormal grain-growth process. The presented results provide a general guideline both for controlling crystal growth and for the performance of hybrid materials and provides insights into how one might design single-mode high-power crystal fiber devices.