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Two-step nucleation, in which a metastable intermediate phase acts as a precursor for nucleating a thermodynamically stable phase, has been widely observed in many materials systems and solid-state reactions. Among the advantages of two-step nucleation is that the stable phase may nucleate heterogeneously at the hetero-phase interface between the original and the precursory phases. Although heterogeneous nucleation (HN) theories for homo-phase grain boundaries and inert surfaces are well established, our understanding of HN at reactive hetero-phase interfaces remains incomplete. This deficiency stems from the discontinuity of the chemical potential driving force across the hetero-phase interface, which profoundly affects the fundamental properties of the nucleus in a way that is not properly accounted for in existing models. Herein, we incorporate these effects to extend the classical nucleation theory to HN at hetero-phase interfaces. Our extended model demonstrates that the nucleus shape along the minimum energy path is strongly size-dependent, and this additional degree of freedom can result in the reduction of the critical nucleus volume and associated activation energy barrier by orders of magnitude relative to conventional predictions. The simulation results are used to construct a sensitivity map in the parameter space of interfacial energy and bulk driving force ratios, which quantifies the difference in nucleation barriers predicted by different models.

Recent experiments suggest that Suzuki segregation may play an important role during deformation in Ni-base superalloys at intermediate temperatures. In this study, a segregation isotherm model incorporating segregation enthalpy from ab initio calculations is proposed to predict quantitatively solute enrichment at superlattice intrinsic stacking faults (SISF) within the γ’ precipitates in Ni-base superalloys. A sublattice model is employed to describe the γ’ phase. A strong correlation between segregation enthalpy and solute enrichment is found. Even though the segregation enthalpy is relatively small, the predicted solute enrichment is consistent with experimental observations. The simulation predictions also suggest a strong cross-correlation among different alloying elements. For example, it is found that segregation of Co on the Ni sublattice at the fault draws segregation of Cr that has a positive segregation enthalpy at the fault without the presence of Co. Such quantitative predictions of equilibrium segregation of solutes at stacking faults in γ’ precipitates and its effect on the stacking fault energy could aid the investigation of deformation mechanisms and help the design of superalloys.

Understanding the phase transformation pathways (PTPs) and microstructural evolution in multi-phase HEAs will aid alloy and process designs to tailor the microstructures for specific engineering applications. In this work, we study microstructural evolution in two-phase HEAs where a disordered parent phase separates into a mixture of two phases: an ordered phase ($\beta'$) + a disordered phase ($\beta$) upon cooling following two different PTPs: (i) congruent ordering followed by spinodal decomposition in the ordered phase and then disordering of one of the ordered phases, i.e., $\beta \rightarrow \beta' \rightarrow \beta_1' + \beta_2' \rightarrow \beta + \beta_2'$ and (ii) spinodal decomposition in the disordered phase followed by ordering of one of the disordered phases, i.e., $\beta \rightarrow \beta_1 + \beta_2 \rightarrow \beta_1+\beta'$. We systematically investigate the effects of equilibrium volume fractions of individual phases, free energy landscapes (in particular, the location of the critical point of the miscibility gap relative to the compositions of the final two equilibrium phases), and elastic modulus mismatch between the two equilibrium phases on the microstructural evolution of these HEAs. We focus on the following morphological characteristics: bi-continuous microstructures vs. precipitates + matrix microstructures, ordered matrix + disordered precipitates vs. disordered matrix + ordered precipitates, and the discreteness of the precipitate phase. This parametric study may aid in multi-phase HEA design for desired microstructures., Comment: Submitted to Acta Materialia

In addition to conventional dislocation plasticity, mechanical twinning and structural phase transformations are another two important plasticity carriers. Although both are symmetry-breaking processes and theories to treat each of them individually have been well-established, the intrinsic coupling between the two has not been investigated. Here we employ a phase transition graph approach to analyze systematically deformation modes arising from the interplay between mechanical twinning and phase transformations. Using metastable β Ti-alloys as an example, we show that mechanical twinning and phase transformations are intrinsically coupled in the symmetry-breaking processes, which results in multiple interconnected transformation and non-transformation deformation pathways and characteristic twinning modes. This work not only reveals the physical origin of unique twinning modes (e.g., {332}, {5 8 11} and {3 9 10} twins) and extended core structures of twin boundaries (e.g., nested twins) observed in experiments, but also provides a new insight into the enhanced plasticity of metastable β Ti-alloys through coupled twinning and transformation pathway engineering.

Materials with certain heterogeneous microstructures have been shown to hold a synergistic combination of strength and ductility. In this study, we demonstrate novel transformation pathways for creating such heterogeneous microstructure in Ti-alloys by integrating thermodynamic databases with phase field simulations. The results show that the concentration modulations at different length scales produced by (a) precursory spinodal decomposition in the parent phase and (b) interdiffusion in multi-layers having different alloy compositions can generate effectively hierarchical and gradient α + β two-phase microstructures, with a mixture of fine α precipitate regions and α precipitate-free-zones or coarse α precipitate regions. The novel microstructures produced include “inverted globular α” bi-modal microstructures and gradient microstructures with controlled spatial gradients in particle size and number density of α precipitates. This study may shed light on how to design novel hierarchical and gradient two-phase microstructures with tunable size and density of precipitates as well as the length scale of their spatial heterogeneity for desired properties.

Deformation twinning in crystals is one of the major strain carrier during plastic deformation, which plays a critical role in determining the mechanical properties of metals and alloys. One of the key issues to understand deformation twinning mechanisms is the determination of deformation path, which is critical for the calculations of twinning strain and critical shear stress. This work provides a new perspective on deformation twinning by systematically investigating the relationship between symmetry breaking and deformation path, with the purpose of establishing a theoretical foundation to identify the broken symmetries associated with twinning and predicting the twinning modes using group theory and graph theory. From a physical point of view, deformation twins can be regarded as one type of the so-called topological defects that are induced by symmetry-breaking. Taking BCC crystals as an example, we demonstrate how the presence of intermediate high symmetry states in the deformation strain space (strain calculated through lattice distortion) along the twinning path, such as FCC, HCP or orthorhombic state, can lead to different characteristic twinning modes. Our predictions not only agree well with classical theoretical analyses and experimental observations in BCC metals and alloys, but also reveal the origin of recently observed high-index twinning modes (such as {5 8 11} and {3 9 10} twins). This work may open a new avenue for analyzing deformation twinning through the symmetry breaking along twinning pathways.

As a new ferroelastic state, strain glass, has attracted a lot of recent attentions and, most importantly, strain glass transitions (SGTs) could underpin many phenomena that have puzzled the physics community for decades, including the quasi-linear superelasticity and Invar and Elinvar anomalies. However, there has been a lack of fundamental understanding at the atomistic level beyond the phenomenological Landau theory. In this paper, we propose a way to obtain quantitatively the continuous strain/stress fields distribution caused by doped point defects through molecular statics calculations by incorporating a Gaussian probability distribution function. By using the quantitative strain/stress fields distribution to inform phase field simulations, we reproduce quantitatively the experimentally observed critical defect concentrations separating the normal martensitic phase transition from strain glass transition at different temperatures and critical temperatures for spontaneous strain glass to martensitic transition at different defect concentrations. Based on percolation theory, we demonstrate how the strain network created by point defects with a critical concentration regulates nucleation and growth of martensitic domains, suppresses autocatalysis by strain frustration, and changes the sharp first-order martensitic transformation into a continuous SGT. A general temperature- and defect-concentration-dependent percolation criterion is formulated for accurate prediction of SGT, which could enable high throughput computations for systematic search of new strain glass systems using simply molecular static calculations.

Implementing the phase-field model at finite strains is usually considered unattainable through the spectral method, largely because of the nonlinearity in the transformation-induced microelasticity. Here we present a phase-field microelasticity (PFM) theory at finite strains with a representation in the reference configuration, allowing the spectral method to be readily incorporated. Following the spirit of Khachaturyan’s PFM theory at small strains, the elastic energy is formulated as a functional of microstructure (order parameters) solely, which should automatically satisfy the mechanical equilibrium. Thermodynamic consistency of the current theory under multiplicative decomposition of the total deformation gradient (into elastic and inelastic parts) and in conjunction with hyperelasticity and the time-dependent Ginzburg-Landau equation is shown rigorously. The new theory is first applied to the classical Eshelby’s inclusion problem, where shear-dilation coupling due to geometric nonlinearity is shown and a convergence study between small strain and finite strain theories is also carried out. The effects of geometric nonlinearity on the co-evolution of micromechanics and microstructure is further studied through modeling the growth of { 1 0 1 ¯ 2 } 〈 1 ¯ 0 1 1 〉 deformation twins in magnesium. The simulation results suggest significant differences in terms of the shape of and the stress field around the deformation twin. In particular, the current finite strain PFM theory predicts a deviation of the twin boundary plane from the theoretical K1 plane, which is not captured in the small strain theory nor in the crystallographic theory. A parametric study further reveals that the observed deviation is caused by the tip effect of the finite-sized twin plate when the aspect ratio is relatively small. The symmetry of the stress field distribution around the twin tip is also found to be drastically different between the small strain and finite strain based phase-field modeling. The sharp twin tip observed in experiments is also shown to be likely related to the anisotropy in twin/matrix interface mobility.

The mechanical properties of two-phase γ-TiAl alloys depend strongly on the scale of their lamellar microstructures. In this study, we investigate the effect of alloy composition on lamellar thickness in Ti100-xAlx by simulating microstructural evolution during the α2′ → α2 + γ phase transformation using the phase field method. From both existing experimental data and our simulation results we find that the average thickness of γ lamellae first decreases and then increases with increasing Al content. Further analyses reveal that this unique composition-dependence of the lamellar thickness could be associated with non-conventional pseudospinodal decomposition and congruent structural transformation mechanisms that generate ultra-high densities of nuclei at the initial stage, which impacts the later growth processes. The interplay between the number density of nuclei and the number of coalescence events during growth results in the non-monotonic dependence of the lamellar thickness on the alloy composition. These findings may offer new insights on the design of ultrafine lamellar microstructures for γ-TiAl alloys.

The unprecedented properties of multi-functional metastable β-Ti alloys, including superelasticity over a wide temperature range, ultra-low modulus, and Invar and Elinvar anomalies, have attracted a great deal of attention. Persistent research efforts have been made towards the understanding of the origins of these unique properties. In this article we report a novel shuffle-nanodomain regulated strain glass transition in a metastable β-Ti alloy, Ti-24Nb-4Zr-8Sn (wt.%, Ti2448), which could be the dominant transformation pathway that offers these unique properties. Using the ex-situ aberration-corrected scanning transmission electron microscopy and in-situ cooling transmission electron microscopy, we find that randomly distributed {011} 〈 0 1 ¯ 1 〉 β O′ phase (orthorhombic, shuffle only) nanodomains embedded in the β phase (BCC) matrix at room temperature transform to α″ phase (orthorhombic) with a continuous increase in the amount of {2 1 ¯ 1 } 〈 1 ¯ 1 ¯ 1 〉 β shear upon cooling or loading. Crystallographic analysis shows that the shuffle of the O′ phase will restrain the twelve possible shears that transform a BCC lattice to α″ martensite to only two. Thus, the randomly distributed O′ nanodomains prevent the formation of long-range-ordered, self-accommodating transformation-strain domain patterns seen in normal martensitic transformations and suppress completely the sharp first-order, auto-catalytic and avalanche-like martensitic transformation into a high-order-like (continuous) strain glass transition. Such a continuous β → O′ → α″ strain glass transition has been confirmed by dynamic mechanical analysis, resistivity and differential scanning calorimetric measurement. This unique transition pathway allows us to offer new insights into the unique properties found in this alloy.

Thanks to its small hysteresis, large electrostrictive strain in relaxor ferroelectrics is superior than piezoelectric strain for applications in precision microactuators. Although relaxor ferroelectrics exhibit the largest electrostrictive strain in ceramics, the magnitude of the strain is limited to ∼0.20% at room temperature due to the large amount of non-ferroelectric defects existing in relaxors. In this work, we develop a relaxor with a morphotropic phase boundary (MPB) by doping a rhombohedral (R3m) ferroelectric BaZr0.2Ti0.8O3 into a tetragonal (P4 mm) ferroelectric 0.89Bi0.5Na0.5TiO3-0.11BaTiO3. A high electrostrictive strain of 0.27% is achieved at room temperature in the relaxor sample. Experimental results illustrate that the composition is near the MPB and exhibits the existence of nanodomains, favoring the achievement of high electrostrictive strain. Moreover, phase field simulations show that the high electrostrictive strain obtained at this composition originates from the low defect fields needed to induce relaxor as a result of small polarization anisotropy at the phase boundary as compared to conventional relaxors away from phase boundaries. Our work provides a new design strategy for the next generation of high-performance ferroelectric relaxors.

Nanoscale concentration modulation (CM) is a novel and effective approach of manipulating martensitic transformations (MTs) for developing next-generation high-performance shape memory alloys (SMAs). Spinodal decomposition is one of the most economic methods to obtain bulk compositionally modulated materials for practical applications. The wavelength, amplitude, and statistical distribution of CM generated by spinodal decomposition are tunable via adjusting the aging temperature, or the aging time. However, how these features influence the effect of CM on MTs still remains largely unexplored. In this study, theoretical analyses and computer simulations are combined to dissect the influence of these features on the kinetic process of MTs and mechanical properties of SMAs. The findings of this study provide insights and guidance on the design of SMAs for desired mechanical properties via CM engineering. Moreover, the findings are applicable to not only SMAs but also other materials that have MTs, e.g. steels and high-entropy alloys.

Traditional viewpoints state that defects, such as pores or cracks, that generally exist in plasma sprayed thermal barrier coatings (TBCs) can provide fast infiltration channels for molten calcia-magnesia-alumino-silicate (CMAS). In contrast with this viewpoint, results from this study suggest that the effect of defects on the CMAS infiltration of the yttria stabilized zirconia (YSZ) coating is limited, even though the dense YSZ bulk material still cannot inhibit the infiltration of CMAS. However, a few additions of Sc2O3 can significantly improve the CMAS resistance of the YSZ coating owing to the lower solubility of Sc3+ in the CMAS. Our findings provide key insights for the development of CMAS-resistant TBCs.

Slip transmission across α / β interfaces is of great significance in understanding the strength of Ti-alloys, but currently a detailed mechanistic understanding of the process is still lacking. Here we develop a microscopic phase-field framework that incorporates the generalized stacking fault energy and the interface crystallography, which are, respectively, calculated by atomistic methods and revealed by crystallographic theories of phase transformations and experimental characterization. The model is then applied to studying the transmission of a constant flux of discrete dislocations across multiple α / β interfaces at micron-scale. The simulations predict interesting slip transmission mechanisms that have not been reported before, wherein Shockley partials play a critical role in assisting the dislocation transfer across the interfaces. The dislocation configurations generated by these mechanisms seem to agree well with experimental characterizations. Spatial cross-over between full dislocations in α is also seen from the simulations, which is again attributed to a reaction mechanism involving Shockley partials. A parametric study further reveals that stacking fault energy can influence the slip transmission in terms of transmitted dislocation types, transmission rate, and the residual dislocation content, suggesting a new strengthening strategy at the α / β interface level. This work offers new understanding of the complex slip transmission process in Ti-alloys and demonstrates a new computational tool complementary to advanced electron microscopy analysis of plastic deformation.

Strain glass, a glassy state of lattice strain, has been found in Ti50-xNi50+x alloys and later in many metallic ferroelastic/martensitic systems, where shear or shuffle serves as a primary order parameter (POP). Another class of non-metallic ferroelastic ceramics are also known to widely exist and commonly possess a polyhedral tilt as the POP. So far, it is unclear whether a “tilt” strain glass exists. Here, we report a finding of a tilt strain glass in La1-xSrxAl0.95Nb0.05O3-δ ceramics. With increasing Sr2+ dopants, the ferroelastic transition from cubic to rhombohedral phases is gradually suppressed. At a critical concentration (xc ∼10%), a strain glass transition emerges, characterized by five sets of evidence: (I) an invariance of average structure; (II) frequency dependence of elastic moduli at a strain glass transition temperature Tg; (III) non-ergodicity; (IV) formation of rhombohedral nanodomains; (V) a gradual increase of tilt angle upon cooling. Surprisingly, the established phase diagram shows an increase of Tg with increasing dopants (a positive correlation), which is different from previous strain glass phase diagrams. The positive and negative correlations can be explained as a balance between two factors of strain glass transition: a global transition factor producing a negative contribution competes with a local field one producing a positive contribution. Our discovery of strain glass in ceramics may also bring novel properties as in metals.

A correct description of interfacial dislocations is critical to the understanding of physical and mechanical properties of the interfaces and their impact on phase transformation and deformation mechanisms. The O-lattice theory provides a general theoretical framework for determining interfacial dislocation structures. However, for systems having an invariant line (IL) or an invariant plane, the O-elements do not always exist in the three-dimensional (3D) space, which impedes the capability of the O-lattice theory to the interfaces in these systems. To determine the dislocation structures in interfaces for which the O-elements do not extend in the 3D space, we introduce a generalized O-element approach by employing the Moore-Penrose pseudoinverse. The generalized O-elements, as the least square solutions to the O-lattice, play a parallel role as that of the ideal O-elements and extend the candidate locations for the coherent regions between dislocations. Worked examples for dislocation structures in both homo-phase and hetero-phase systems are presented. The predicted interface structures are in good agreement with experimental observations and molecular statics (MS)/molecular dynamics (MD) simulations.

We predict structure and energy of low-angle ( 1 1 ¯ 0 ) pure twist grain boundaries (GBs) in five BCC transition metals ( β -titanium, molybdenum, niobium, tungsten, and tantalum) using a combination of atomistic and microscopic phase-field (MPF) modeling. The MPF model takes as inputs solely the generalized stacking fault energy surfaces (i.e., the γ -surface) and elastic constants obtained from the atomistic simulations. Being an energy-based method, the MPF model lifts the degeneracy of the geometric models in predicting GB structures. For example, the multiple indefinite solutions offered by the Frank-Bilby equation are shown to converge to exactly the same equilibrium structure. It predicts a transition of the equilibrium GB structure from a pure screw hexagonal network (Mo and W) to mixed hexagonal networks (Nb and Ta) to a rhombus network (β-Ti) of dislocations. Parametric simulation studies and detailed analyses of the underlying dislocation reactions that are responsible for the formation of the rhombus and hexagonal structures reveal a close correlation between material properties (including the elastic anisotropic ratio and the local curvature on the γ -surface) and the GB structure and energy in BCC metals. This integrated approach allows one to explore, through high throughput calculations, the potential to tailor the structure and energy of special GBs in BCC metals by alloying.

We show in this paper how strain engineering alters the fundamental characteristic of a martensitic transformation (MT) and gives it a new set of properties including large quasi-linear elastic strain response with nearly vanishing hysteresis and low elastic modulus. The work is motivated and inspired by a recent experimental study on elastic and inelastic (transformation) strain matching in a pre-strained nano-composite with Nb nanowires embedded in a NiTi shape memory alloy matrix. In particular, we demonstrate by computer simulation that dislocations at Nb/NiTi interfaces produced by the pre-straining are responsible for the unprecedented properties. Microstructural evolution captured in the simulations reveals that local stress fields associated with the dislocations regulate the nucleation and growth of martensite, turning the otherwise sharp, strong first-order transition into a continuous, high-order like transition. The simulations predict that the stress-strain hysteresis and modulus of the composite decrease with increasing amount of pre-strain, which agrees well with the experimental measurement. This study suggests a design strategy by introducing non-uniform stress fields for enhanced properties of shape memory alloys.

Precipitation of the γ ' ' phase on { 100 } facets of preceding γ ' precipitates is found to prevent the latter from overaging upon slow cooling from solution treatment in Ni-base superalloys based on the composition of alloy 718. By computer simulation using a multi-phase-field model, we find that the growth of a coprecipitate involves several concurrent and closely coupled processes, including thickening and lengthening of γ ' ' shells, growth of the γ ' core along the " open=" 001 γ ' , " open=" 011 γ ' and " open=" 111 γ ' directions, hard impingement between γ ' and γ ' ' precipitates, and soft impingement among γ ' ' precipitates of different variants. These processes at different stages of growth are analyzed systematically as a function of coprecipitate size and configuration, and the results show that the growth kinetics of the γ ' core in a coprecipitate is controlled by the interplay among: (1) partial removal of supersaturated γ matrix surrounding the γ ' core by coprecipitation of γ ' ' shells, (2) cooperative growth of γ ' and γ ' ' in the coprecipitates and (3) atomic mobility of γ ' -formers in the γ ' ' phase. To maximize the effect of coprecipitation on preventing γ ' from overaging upon slow cooling, the alloy composition and heat treatment schedule should be optimized to minimize the size of γ ' cores at which coprecipitation of γ ' ' shells occurs and to reduce diffusion of γ ' -formers through γ ' ' .

We report the first direct quantification of the structural heterogeneity in metallic glasses using intensity variance and angular correlation analyses of the 4-dimensional (4-D) scanning transmission electron microscopy (STEM) data. We demonstrate that the real-space reconstruction and analyses of the 4-D nanodiffraction data acquired using a pixelated fast STEM detector enables quantitative determination of the details of local structural heterogeneity, including the type, size, volume fraction and spatial distribution of local ordering at the nano- to meso-scale, beyond the limits of the previous measurements using conventional detectors. We show that different types of local ordering are present in Zr55Co25Al20 glass, leading to a high degree of structural heterogeneity, with the total volume of locally ordered regions making up to ∼14% of the entire volume. These findings are significant, as the structure-property relationship in metallic glasses and other amorphous materials has been difficult to establish because of the lack of detailed structural information from experiments.

The Ni-base superalloy 718 is the most widely used material for turbomachinery in the aerospace industry and land-based turbines. Although the relationship between processing and the resulting properties is well known, an understanding of the specific deformation mechanisms activated across its application temperature range is required to create more mechanistically accurate property models. Direct atomic-scale imaging observations with high angle annular dark-field scanning transmission electron microscopy, complemented by phase-field modeling informed by generalized stacking fault surface calculations using density functional theory, were employed to understand the shear process of ${\gamma}''$ and ${\gamma}'/{\gamma}''$ co-precipitates after 1 \% macroscopic strain at lower temperature (ambient and $427 {\deg}C$). Experimentally, intrinsic stacking faults were observed in the ${\gamma}''$, whereas the ${\gamma}'$ was found to exhibit anti-phase boundaries or superlattice intrinsic stacking faults. Additionally, the atomically flat ${\gamma}'/{\gamma}''$ interfaces in the co-precipitates were found to exhibit offsets after shearing, which can be used as tracers for the deformation events. Phase-field modeling shows that the developing fault-structure is dependent on the direction of the Burgers vector of the $a/2 \langle110\rangle$ matrix dislocation (or dislocation group) due to the lower crystal symmetry of the ${\gamma''}$ phase. The interplay between ${\gamma}'$ and ${\gamma}''$ phases results in unique deformation pathways of the co-precipitate and increases the shear resistance. Consistent with the experimental observations, the simulation results indicate that complex shearing mechanisms are active in the low-temperature deformation regime and that multiple $a/2 \langle110\rangle$ dislocations of non-parallel Burgers vectors may be active on the same slip plane., Comment: 32 pages, 17+6 figures, submitted to Acta Materiallia

Precipitate microstructure in the B2 parent phase is known to have profound impacts on the properties of NiTi-based high temperature shape memory alloys (HTSMAs), including the martensitic transformation (MT) start temperature M s , temperature- and stress-hysteresis, work output, dimensional stability and functional fatigue resistance. In order to understand the underlying mechanisms and hence to optimize aging heat treatments to achieve desired properties, we systematically investigate both the mechanical and chemical effects associated with nanoscale coherent precipitates on the behavior of MT. Using NiTi-Hf HTSMA as an example, we first study the equilibrium shape and stress and strain fields of an H-phase precipitate as a function of its size. We then determine quantitatively the elastic interaction energy between a precipitate and a nucleating martensitic particle consisting of either a single variant or multiple self-accommodating variants. In the meantime, we calculate the variation of concentration field around an H-phase precipitate during its growth. Finally, we quantify and compare the effects of the spatially inhomogeneous stress and concentration fields around an H-phase precipitate on M s . The results indicate that the former is the dominant factor for long aging times while latter is the dominant factor for short aging times. Since the model predicts M s as a function of aging temperature and time, it can aid the design of aging heat treatment schedule to achieve desired M s .

Using ab initio calculations, we investigate the elastic properties of paramagnetic AlxCrMnFeCoNi (0

A phase-field model is developed to study the formation and autocatalytic nucleation of { 10 1 ¯ 2 } twins in polycrystalline Mg. The twins are found to nucleate most favourably in grains with the most negative interaction energy. Within such grains, the energetically most favoured nucleation site is determined by stresses concentrated near the grain boundaries that are related to the elastic anisotropy of the material. Furthermore, in a structure consisting of three lamellar grains with an incoming twin in the central grain, the simulation results show that before autocatalytic nucleation, the incoming twin often has a lenticular shape. The stress field around the tip of the incoming twin plays the major role in the autocatalytic nucleation. After a twin has nucleated in the neighbouring grain, the incoming and the outgoing twins evolve simultaneously, and the shape of the incoming twin gradually changes from lenticular to parallel-sided plate. Under the condition that the crystallographic orientation of the central grain and the applied strain remains unchanged, the driving force for twin nucleation decreases with increasing misorientation (up to 90°) across the grain boundary. It is further derived that the interaction energy values between the pre-existing stress field of the polycrystalline structure and the eigenstrain of the to-be-nucleated twin is mathematically related to the resolved shear stress of twins.

Developing ultra-high strength in rare-earth-free Mg alloys using conventional extrusion process is a great challenge. What is even more difficult is to achieve such a goal at a lower processing cost. In this work, we report a novel low-alloyed Mg-2Sn-2Ca alloy (in wt. %) that exhibits tunable ultra-high tensile yield strength (360–440 MPa) depending on extrusion parameters. More importantly, there is little drop in mechanical properties of this alloy even when it is extruded at a speed several times higher than those used in the reported high strength Mg alloys. Examination of as-extruded microstructures of this Ca-containing Mg alloy reveals that the ultra-high strength is mainly associated with the presence of surprisingly submicron matrix grains (down to ∼0.32 μm). The results suggest that the Ca addition promotes accumulations of the pyramidal dislocations, which eventually transform into the low angular grain boundaries (LAGBs). The high number density of LAGBs separate the α-Mg matrix via either discontinuous dynamic recrystallization (DDRX) mechanism in the early stage or the continuous dynamic recrystallization (CDRX) mechanism in the later stage of extrusion, which effectively enhances the nucleation rates of the DRXed grains. More importantly, large amount of Ca segregation along LAGBs, accompanied with dynamically precipitated Mg2Ca nano-phases, are detected in the present non-severely deformed samples. It is the combination of solute segregations and numerous Mg2Ca nano-precipitates that contributes to the formation of the ultra-fine grains via pinning mechanism. The ultrafine grains size, Ca enrichment in most LAGBs, and residual Mg2Ca nano-precipitates would in turn contribute significantly to the enhancement of the yield strength of the as-extruded Mg-2Sn-2Ca (wt.%) alloy. The low content of alloying elements and the fast one-step extrusion process render the present alloys low-cost and thus have great potential in large-scale industry applications.

2,6-bis(trimethylstannane)-4,8-bis(2-octyldecyloxy)benzo[1,2-b:4,5-b′]dithiophene coupled with 2,5-didecyloxy-1,4-dibromobenzene and 4,7-dibromo-5,6-dioctyloxy-2,1,3-benzothiadiazole using Stille-coupling polymerization to afford the non D-A type polymer P1 and D-A type polymer P2, respectively. Two polymers displayed excellent solubility in normal organic solvents, so series of chemical instrumental analysis, such as NMR, GPC and elemental analysis, were carried out to confirm the inner structure and composition of the polymers. Different structure types exerted great influence on polymer's optical, electrochemical and electrochromic properties. Compared with P1 film, the introduction of the strong electron-withdrawing group benzothiadiazole improved conjugate effect along the polymer backbone of P2, which caused the redshift of ultraviolet–visible absorption spectrum and significant reduction in energy band gap. In addition, electrochromic performance test results showed that the P1 polymer film can switch between the orange-yellow and gray, while P2 film changed from blue in the neutral state to light yellow in the oxidation state. Moreover, the optical contrasts and response times of the polymer films also showed great differences due to the different molecular structure types. Higher transmittance changes and less sensitivity to the step interval on optical contrast indicated the fast switching speed and the superior cycle stability of P2 film.

Complex three-dimensional microstructural patterns arise during deposition of immiscible alloys and their morphologies depend sensitively on alloy composition, deposition rates and substrate temperatures. Using phase field simulations, we construct a microstructure morphology map in a multi-dimensional space of material properties and processing parameters. We consider simultaneous effects from temperature-dependent surface and bulk diffusivities and thermodynamic driving force for phase separation, temperature- and composition-dependent interphase boundary and surface energies, as well as alloy composition, substrate temperature and deposition rate. The microstructural patterns and morphological transition sequences in as-deposited films revealed by the microstructure map are validated using experimental data from sputtered Cu-Mo alloy films as well as from other systems. Such a microstructural map can guide synthesis of three-dimensional compositionally modulated nanostructures via self-organization during deposition of immiscible alloy films.

The local compositional changes associated with stacking fault and microtwin formation during creep at intermediate temperatures in a commercial Ni-base disk superalloy are explored. In order to investigate microtwin formation, an [001] single crystal of ME3 was tested in compression at 760 °C under a stress of 414 MPa – a stress-temperature regime found to promote microtwinning. Atomic resolution scanning transmission electron microscopy combined with state-of-the-art energy dispersive X-ray (EDX) spectroscopy analysis reveals the presence of Co and Cr rich Cottrell atmospheres around leading dislocations responsible for the creation of SISFs, SESFs, and microtwins. This analysis also highlights the role that tertiary γ particles inside γ′ precipitates have on γ′ shearing deformation mechanisms. Through the use of CALPHAD calculations, combined with new experimental observations, new insights into the rate-controlling processes during creep deformation are discussed.

Using ab initio alloy theory, we investigate the lattice stability of paramagnetic AlxCrMnFeCoNi (0 ≤ x ≤ 5) high-entropy alloys considering the competing body-centered cubic (bcc) and face-centered cubic (fcc) crystal structures. The theoretical lattice constants increase with increasing x, in good agreement with experimental data. Upon Al addition, the crystal structure changes from fcc to bcc with a broad two-phase field region, in line with observations. The magnetic transition temperature for the bcc structure strongly decreases with x, whereas that for the fcc structure shows weak composition dependence. Within their own stability fields, both structures are predicted to be paramagnetic at ambient conditions. Bain path calculations support that within the duplex region both phases are dynamically stable. As compared to AlxCrFeCoNi, equiatomic Mn addition is found to shrink the stability range of the fcc phase and delay the appearance of the bcc phase in terms of Al content, thus favoring the duplex region in 3d-metals based high-entropy alloys.

Precipitation of Ni4Ti3 is effective in tuning martensitic transformations (MTs) in NiTi shape memory alloys (SMAs). However, several fundamental issues concerning the influence of Ni4Ti3 on MTs remain unclear. In this study, the microstructure evolution process during precipitation and its influence on B2→R MT are investigated using computer simulations based on the phase field method. In particular, the roles played by Ni concentration gradient in the B2 matrix and internal coherency stress fields associated with different precipitate microstructures are analyzed in detail. It is found that Ni concentration gradient in the B2 matrix created by Ni4Ti3 precipitates alters significantly local martensitic start temperature and the overall MT behavior, while the internal coherency stress field associated with the Ni4Ti3 precipitates dictates the structure of martensitic domains via variant selection. The latter effect makes it promising to develop Invar alloys via stress-ageing to tailor the precipitate microstructure. These findings provide fundamental insights into the mechanism controlling the MT behavior in precipitate-bearing SMAs and provide guidance for the design of thermomechanical treatment for desired precipitate microstructures and the corresponding MT behavior.

Structural heterogeneity at the nanoscale such as medium-range order (MRO) in metallic glasses (MGs) has been suggested by theories and simulations for many years and recently been observed by experiments. However, its correlation with plastic deformation is still poorly understood and investigation into this correlation has just begun. In this study, we first propose a correlation between the properties of shear transformation zone (STZ) and the local structural information at the MRO length scale. As revealed by experiments, the MRO exhibits different types of atomic order and symmetry in MGs depending strongly on the processing history and service condition. We then carry out STZ dynamics simulations to document effects of volume fraction and symmetry of dissimilar STZs (derived from experimental characterization of the MRO) on shear banding dynamics and stress-strain behavior. In particular, a “precipitation-hardening” effect is observed and “strain frustration” is introduced to explain and better understand the influence of nanoscale structural heterogeneity on mechanical behavior of MGs. Our approach intends to provide new fundamental insights into the relationship between the mechanical properties of MGs and their MRO-level structural heterogeneities.

With the fast development of modern science and technology, two or three-dimensional surface profile measurement techniques with high resolution and large dynamic range are urgently required. Among them, the techniques based on optical interferometry have been widely used for their good properties of non-contact, high resolution, large dynamic measurement range and well-defined traceability route to the definition of meter. A review focused on surface profile measurement techniques of optical interferometry is introduced in this paper with a detailed classification sorted by operating principles. Examples in each category are discussed and analyzed for better understanding.

Morphological and compositional evolution of omega (ω) precipitates in a model Titanium-20 wt%Vanadium (or 19 at.%V) alloy has been systematically investigated by coupling transmission electron microscopy and atom probe tomography with atomistic ab initio and continuum microelasticity computations. The initial water quenched microstructure comprised of a fine scale distribution of athermal ω precipitates, which form congruently from the β phase via a complete displacive collapse of {222} β planes, that has been rationalized based on DFT computations. Subsequent annealing at 300 °C, over progressively increasing time periods, resulted in isothermal evolution of the ω precipitates, whose morphology changes from ellipsoidal to cuboidal, accompanied with V rejection. The highly V-enriched β matrix consisted of short V V bond lengths, further distorting the bcc lattice, and increasing the β/ω misfit. This facilitates the change in the morphology of omega precipitates from ellipsoidal to cuboidal resulting in a {001} β habit plane for these precipitates. The coupled experimental and computational approach permits rationalizing the evolution of ω precipitate morphology and composition in such high β−ω misfit β-Ti alloys.

Martensitic transformation (MT) is typically a strongly first-order transition with autocatalysis in nucleation followed by rapid growth. It usually takes place within a narrow temperature or stress range, making its utilization in a controllable manner difficult. We show by computer simulations how MTs can be tailored by concentration modulation at the nanoscale in the parent phase, which induces spatial variations of both the stability of martensite and the transformation strain and tunes the overall MT kinetics from a typical first-order transition into a high-order like continuous transition. Such a unique MT characteristic reduces or even eliminates the transformation hysteresis and produces quasi-linear elasticity with ultra-low apparent elastic modulus.

The symmetry of a crystal has profound effects on its physical properties and so does symmetry-breaking on the characteristics of a phase transition from one crystal structure to another. For an important class of smart materials, the ferroics, their functionality and performance are associated with cycles of transitions from multiple structural states of one phase to those of the other . Using group and graph theories, we construct phase transition graph (PTG) and show that both the functionality and performance of ferroics are dictated by the topology of their PTGs . In particular, we demonstrate how the giant piezoelectricity in ferroelectrics and the functional fatigue in shape memory alloys (SMAs) are related to their unique PTG topological features. Using PTG topology as a guide, we evaluate systematically new systems potentially having giant piezoelectricities and giant electro- and magneto-strictions and discuss the design strategies for high performance SMAs with much improved functional fatigue resistance.

Migration of phase boundaries in crystalline solids eliminates one set of lattice sites and establishes another. Using a combination of phase field crystal modeling and crystallographic analysis, we present here a complete atomistic description of the migration mechanism of a high-index planar interface during a diffusional hexagon to square phase transformation. In particular we show that a terrace-step interface advances macroscopically in the form of growth ledges, while microscopically its migration occurs by opposite shearing on the terraces and a one-to-two splitting of lattice sites, giving a new class of lattice site correspondence and superabundant vacancies. In addition, a new approach capable of finding a critical nucleus with atomic resolution is developed by combining the phase field crystal energetics with the free-end nudged elastic band algorithm.

We report a giant strain (0.72%) with a low degree of hysteresis (ca. 36.2%) and a giant Smax/Emax ratio (916 pm V−1, Smax and Emax denote the maximum strain and the corresponding electric field, respectively) for lead-free (1−x)(0.8Bi0.5Na0.5TiO3-0.2Bi0.5K0.5TiO3)-xSr0.8Bi0.1□0.1Ti0.8Zr0.2O2.95 piezoceramics with x = 0.06. The giant strain originates from a reversible transition between the ergodic relaxor and ferroelectric states under applied electric fields. A-site vacancies (VA) and oxygen vacancies (VO), deliberately introduced to the system, induce a randomly distributed local polarization field. The local field induces embryonic polarization domains that have a broad distribution of maturity and thus smears the transition between the ferroelectric and relaxor states. This leads to a narrow hysteresis loop. The poling field required for the relaxor-to-ferroelectric transition is reduced significantly, due to the remanent ferroelectric phase at zero field acting as the seed, and the point defects synergistically facilitating the nucleation and growth of the ferroelectric phase. Our work provides a novel route for designing piezoelectric materials with both a giant strain and a narrow hysteresis for practical actuator applications.

Functional fatigue (FF) during thermal and mechanical cycling, which leads to the generation of macroscopic irrecoverable strain and the loss of dimensional stability, is a critical issue that limits the service life of shape memory alloys (SMAs). Although it has been demonstrated experimentally that such a phenomenon is related to microstructural changes, a fundamental understanding of the physical origin of FF is still lacking, especially from a crystallographic point of view. In this study, we show that in addition to the normal martensitic phase transformation pathway (PTP), there is a symmetry-dictated non-phase-transformation pathway (SDNPTP) during phase transformation cycling, whose activation could play a key role in leading to FF. By investigating crystal symmetry changes along both the PTPs and SDNPTPs, the characteristic types of defects (e.g., dislocations and grain boundaries) generated during transformation cycling can be predicted systematically, and agree well with those observed experimentally in NiTi. By analyzing key materials parameters that could suppress the SDNPTPs, strategies to develop high performance SMAs with much improved FF resistance through crystallographic design and transformation pathway engineering are suggested.