Crystallographic Correlations Research Articles

Inference and uncertainty propagation of GB structure-property models: H diffusivity in [100] tilt GBs in Ni

In this work we present a non-parametric Bayesian approach for developing structure-property models for grain boundaries (GBs) with built-in uncertainty quantification (UQ). Using this method we infer a structure-property model for H diffusivity in [100] tilt GBs in Ni at 700 K based on molecular dynamics (MD) data. Once a GB structure-property model is developed, it can be used as an input to mesoscale simulations of the effective properties of polycrystals, microstructure evolution, etc. A significant advantage of the Bayesian approach presented here is that it facilitates propagation of uncertainties from the underlying structure-property model to the output predictions from mesoscale modeling. Leveraging this capability, we perform mesoscale simulations of the effective diffusivity of polycrystals to investigate the interaction between structure-property model uncertainties and GB network structure. We observe a fundamental interaction between crystallographic correlations and spatial correlations in GB networks that causes certain types of microstructures (those with large populations of J2- and J3-type triple junctions) to exhibit intrinsically larger uncertainty in their effective properties. Data and code are provided in supplementary materials.

Neutron-diffraction study of the cubic-tetragonal phase structural transition in the single crystals of the solid solutions of zirconium and yttrium oxides

Objectives. The determination of the phase relations, crystallographic characteristics, microstructure features, and atomic crystal structure of zirconium oxide crystals that are partially and completely stabilized by yttrium oxide additives, and the identification of the crystallographic and crystal-chemical correlations with the physicochemical properties of single crystals.Methods. The neutron structure of the crystals was studied using the neutron time-of-flight and constant wavelength methods using a high-resolution Fourier diffractometer on the IBR-2 pulsed fast reactor and a four-circle neutron diffractometer “Syntex.” Single crystals were grown by directed crystallization from the melts of mixtures (1 − х)ZrO2 ∙хY2O3 , х = 0.03 and х = 0.12 with different growth rates (10 and 40 mm/h).Results. It was observed that when growing single crystals with x = 0.03–0.05, the crystal was stratified into cubic and tetragonal phases, and the ratio between the phases depended on the growth rate. At a growth rate of 40 mm/h, the content of the cubic phase was insignificant. In the crystals of partially stabilized zirconium dioxide (ZrO2) with the additions of 3 mol % Y2O3, the coherent coexistence of cubic and tetragonal phases was established, and the twin law for a tetragonal component (rotation of unit cell axis by 90° around the a (b) axis) that was observed during the phase transition from high-temperature cubic phase to tetragonal phase was determined. For the fully stabilized zirconium oxide of the cubic symmetry (with 12 mol % Y2O3), the 0.3 Å displacements of oxygen atoms from their partial structural positions in the directions [100] and [111] were determined. These displacements correlated with the directions of the ion transport.Conclusions. Previous studies have shown that the ratio between the cubic and tetragonal phases of the single crystals of the ZrO2 –Y2O3 system depends on the growth rate of the single crystals. The content of Y2O3 in the cubic and tetragonal phases of a single crystal was determined using the non-destructive neutronography method on the same volume sample of a solid solution of this system. Moreover, the displacements of oxygen atoms from the main position of the crystal were determined.

Modeling the role of local crystallographic correlations in microstructures of Ti-6Al-4V using a correlated structure visco-plastic self-consistent polycrystal plasticity formulation

This paper presents a multi-level crystal plasticity-based simulation framework for modeling mechanical response and microstructure evolution of Ti-6Al-4V with α-lath/lamellar microstructures. The model is a correlated structure visco-plastic self-consistent (CS-VPSC) formulation linking three scales: a single crystals micro-scale, a lath/lamellar colony meso-scale, and a lath/lamellar aggregate macro-scale. A selected hardening law for the evolution of critical resolved shear stress per slip system used in CS-VPSC is phenomenological. However, it adjusts the resistances of basal and prismatic slip systems based on the geometry of slip transfer between adjacent lamellae. Consistent with experimental evidences, the resolved shear stress on the pyramidal slip planes is dependent not only on the stress in the direction of slip but also on the two orthogonal shear stress components and the three normal stress components (non-Schmid effects). Electron backscatter diffraction (EBSD) data in conjunction with a procedure relying on α→β phase transformation is used to construct paired variants of α-laths/lamellae satisfying their local crystallographic correlations. The procedure fits volume fractions of individual laths/lamellae with the experimental EBSD data and selects a distribution of habit planes between adjacent variants with respect to the loading direction. The simulation framework is applied to interpret the deformation behavior in tension and compression along two sample directions of Ti-6Al-4V fabricated via laser powder bed fusion. Moreover, the model is used to simulate texture evolution during rolling of the material to large strains. It is demonstrated that the model is capable of predicting plastic anisotropy/asymmetry and the concomitant texture evolution. While the model reveals a significant effect of habit plane inclination with respect to the loading direction on yield stress, the comparison of the data and model predictions shows that a random distribution of habit planes fits the flow response. It is further inferred that the tension-compression asymmetry arises from the non-Schmid effects.

Interactive effects of cyclic oxidation and structural evolution for Ti-6Al-4V/(TiC+TiB) alloy composites at elevated temperatures

A kind of Ti-6Al-4V alloy matrix composite with coupled (TiC+TiB) networks as reinforcements was conceived and actually prepared by reaction hot pressing technique. Its internal microstructures transferred from Widmanstätten lamellae into equiaxed α-Ti grains during in-situ synthesizing reactions, which were characterized by HRTEM analyses to reveal the crystallographic correlations. With an effort to enhance its high-temperature oxidation resistance, the cyclic oxidation kinetics and concomitant structural evolution were experimentally investigated and thermodynamically elucidated in the 873–1073 K temperature range. The specially designed network configuration of hybrid reinforcers was found to improve the oxidation resistance to a remarkable extent. The cyclic oxidation kinetics followed the classic parabolic relation at the relatively lower temperature of 873 K, but this was replaced by a linear trend once temperature rose up to 1073 K. It was revealed that the thermal-stress induced spallation of oxide scales was the dominant factor to modulate the interaction of oxidation kinetics and structural evolution. A phenomenological model of oxide scale growth was proposed accordingly to depict the kinetics transition of cyclic oxidation process.

New insights into crystallographic correlations between ferrite and cementite in lamellar eutectoid structures, obtained by SEM–FEG/EBSD and an indirect two-trace method

Four different ferrite/cementite orientation relationships (ORs) in near-eutectoid steel are derived using SEM–FEG/EBSD (scanning electron microscopy–field emission gun/electron back-scatter diffraction) and an indirect two-trace method. They show a common feature of close-packed plane parallelism between ferrite and cementite. Their crystallographic compatibility with habit planes shows a variety of possible habit planes and excludes the existence of the exact conventional Bagaryatsky and Pitsch–Petch ORs. Each of these new ferrite/cementite ORs is correlated with a different edge-to-edge matching condition between austenite and pearlitic ferrite, and between austenite and pearlitic cementite, and possesses specific morphological features. The present results may give deep insight into the crystallography of pearlitic transformation and provide useful information for materials design through interface tailoring in steels.

Quantitative misorientation characteristics of interphase boundaries in composites

Specific crystallographic correlations between neighbouring grains in composites were established by the use of selected area electron diffraction in the transmission electron microscope. However, it was the development of orientation mapping techniques that made it possible to obtain a quantitative description of the distribution of boundaries between the grains of both the same phase and different phases. This study shows that orientation topography measurements made by electron backscatter diffraction in the scanning electron microscope allowed determination of the crystallographic relationships between grains of different phases. An alumina-based composite with a content of 10 vol% tungsten carbide was chosen for investigations. Misorientation distribution functions were calculated to describe the distribution density of misorientations with respect to the nearest neighbouring measured point located in the grain of the second phase. The analysis of misorientation distribution functions permitted the evaluation of preferences for some special crystallographic correlations between the grains of composite matrix and inclusions as well as shares of interphase boundaries characterized by those correlations.

Diffusion on grain boundary networks: Percolation theory and effective medium approximations

Grain boundary networks in polycrystalline materials are heterogeneous and comprise a spectrum of local boundary diffusivities. Although it is desirable to ascribe a single “effective” grain boundary diffusivity to a polycrystal, this quantity is a complex average over the grain boundary character distribution, in view of the network topology and connectivity among boundaries of different character. Here we evaluate the macroscopic diffusivity of grain boundary networks with both randomly distributed and crystallographically correlated grain boundary character. In high-contrast networks, where the local diffusivity varies by more than four orders of magnitude between grain boundaries of different character, the macroscopic diffusivity is governed by the development of a percolating path of high-diffusivity boundaries. In low-contrast systems, the effective network diffusivity is less sensitive to topology and can be described by composite averaging schemes. We quantitatively delineate high- and low-contrast regimes, and discuss a generalized effective medium approximation that quantitatively links the network structure to effective macroscopic transport properties at all levels of contrast. We also illustrate how effective medium theory can be adapted to capture crystallographic correlations among boundary types, and expanded to include a broader spectrum of boundary character.

Phase Transitions and Recrystallization in a Ti-46at%Al-9at%Nb Alloy as Observed by In-Situ High-Energy X-ray Diffraction

AbstractHigh-energy synchrotron X-ray diffraction is a powerful tool for bulk studies of materials. In this investigation, it is applied to the investigation of an intermetallic γ-TiAl based alloy with a composition of Ti-46Al-9Nb. The morphology of the reflections on the Debye-Scherrer rings is evaluated in order to approach grain sizes as well as crystallographic correlations. An in-situ heating cycle from room temperature to a temperature above the α-transus temperature has been conducted starting from a massively transformed sample. With increasing temperature the occurrence of strain relaxation, chemical and phase separation, domain orientations, phase transitions, recrystallization processes, and subsequent grain growth can be observed. During cooling to room temperature, crystallographic correlations between the re-appearing γ-phase and the host α-phase, known as the Blackburn correlation, are observed in the reciprocal lattice, which splits into different twinning and domain orientation relationships present in the fully lamellar microstructure.

Misorientation characteristics of interphase boundaries in particulate Al 2O 3-based composites

It is well known that the character and distribution of interphase boundaries has a significant impact on the properties of polycrystalline materials. For the quantitative characterization of interfaces between matrix and inclusions in two composite systems (Al 2O 3/WC and Al 2O 3/W), large sets of crystallographic misorientation data has been used. The misorientations were measured between the neighbouring regions of different phases. The experiment was based on orientation maps obtained by Electron BackScatter Diffraction (EBSD) in an Environmental Scanning Electron Microscope (ESEM). For the particular arrangements of crystallite symmetries, Misorientation Distribution Functions (MDF) have been developed in such a way that each physically distinct misorientation was represented only once. Preferences for the special crystallographic correlations between matrix grains and inclusions, as well as the shares of interphase boundaries characterized by those correlations, have been evaluated in both composites.

TEM and EBSD comparative studies of oxide–carbide composites

Transmission electron microscopy and electron backscatter diffraction in the scanning electron microscope have been used to investigate particulate composites with the tetragonal zirconia polycrystalline (TZP) matrix. Two carbides, mainly TaC and NbC, chemically stable in relation to zirconia, have been selected as reinforcing inclusions. Their incorporation into the TZP matrix resulted in significantly better mechanical properties of the investigated systems. The way of explaining such a phenomenon is to analyze the crystallographic correlations between the oxide and carbide phases which may influence the strength of the interphase boundary and finally lead to an increase of fracture toughness and wear resistance of the composite.

A structural and mechanistic investigation of the mono- O-phenylation of diols with BiPh 3(OAc) 2

The mono- O-phenylation of enantiomerically pure pinanediol 2 using BiPh 3(OAc) 2 1 and the biphenyl-2,2′-ylenephenylbismuth analogue 9 has been investigated. It is postulated that reductive elimination at the trigonal bipyramidal bismuth (V) centre of 1 upon exposure to ambient light affects the transfer of an apical phenyl ligand to the least sterically encumbered hydroxyl group of the diol, affording the monophenyl ether in good yield. SbPh 3(OAc) 2 fails to undergo reductive elimination, affording the stable diolate 6 instead. The X-ray crystal structure of 6 provides a reasonable model for the intermediate of the bismuth mono- O-phenylation, and suggests further studies with bismuth complexes such as 9 possessing intramolecularly tethered ligands incapable of facilitating the mono- O-phenylation reaction. The discussions are supported by X-ray crystallographic correlations, and calculations indicate that (M)-(−)- 6 adopts the lowest energy conformational diastereoisomer.

Synthesis and structure of organoantimony (V) cyclometallates: transannular interactions and the barrier to cyclisation

A variety of α-hydroxy carboxylic acid salts [AgO 2CC(OH)R 1R 2] react with SbPh 3Cl 2 1 to afford the cyclometalled complexes 4b– g. A single crystal X-ray analysis of (±)- 4g reveals the presence of conformational diastereoisomers arising from the helical chirality of the SbPh 3 propeller unit. Benzilic acid (R 1=R 2=Ph) however, reacts with 1 to afford the di-ester 3. To rationalise the steric impediment to cyclisation, the solid-state geometries of all known five coordinate dioxo cyclometallates possessing an integral XPh 3 unit are presented, along with the accessible conformations for each structural alternative. Computer modelling and crystallographic correlations identify severe 1,3-transannular interactions within the fluxional species associated with the nascent cyclometallate of benzilic acid.

A self-consistent approach for modelling texture development of two-phase polycrystals: Application to titanium alloys

A large strain self-consistent viscoplastic model is proposed, developed and applied to a two-phase polycrystal. This model accounts for crystallographic textures and grain morphologies, as well as for the phase correlation, both in space and orientation. The basic formulation is shown and the case of lamellar (α + β) Ti alloys in rolling is studied. In these alloys, the two phases exhibit specific morphologic and crystallographic correlations. The present study shows that the model leads to better texture predictions when all these correlations are accounted for.

Polymorphic Transition in Biogenic Calcium Carbonate: Nacre/Prismatic Interface in Abalone Shell

Abstract The research in biological hard tissues offers lessons for biomimetic (structure and processing) strategies, such as for the synthesis of hierarchical architectures tailored for specific engineering applications. These biocomposites, i.e., biogenic materials in which the major phase is an inorganic component associated with macromolecules (proteins and polysaccharides), include bones, dentin, sea-urchin skeletal units, bacterial and algal particles and molluscan shells. Here, a summary is given from a recent TEM study of the interfacial region of nacreous and prismatic sections of red abalone shell to understand the morphological and crystallographic correlations across this transition region. Many mollusk species have shells made of CaCO3 in various architectures that have evolved under different ecological conditions to produce structures that best protect the organism. The shells of many species contain both aragonite (orthorhombic, Pmnc) and calcite (Rhombohedral, R3m). In red abalone (Haliotis rufescens), the outer section, prismatic (P), is composed of columnar crystallites of calcite (1-5 μm base, 5-10 μm height), and the inner section, nacre (N), is composed of pseudo-hexagonal platelets of aragonite (side 2-5 μm), stacked as 0.25 μm layers, separated by a few nm-thick organic layer (Fig. 1).

The effect of cluster size on thin film media noise

A dynamic micromagnetic model of thin film magnetic recording media with generalised structure has been used to study the effect of cluster size on thin film media noise. Clusters formed by common crystallography and by intergranular exchange coupling have been simulated, and the effects of clustering on hysteresis and noise are presented. For small clusters of a few grains, crystallographic correlations are shown to have the same effect on noise as intergranular exchange coupling, giving an increase in magnetic feature size and noise. >

Residual stresses in polycrystals as influenced by grain shape and texture

R esidual stresses in polycrystals arise because of anisotropic thermal expansion of constituent crystals. Due to the random crystal arrangement, the internal stresses also become random quantities, which have to be described by probability distributions or statistical moments. Conditional first order moments (averages) and second order moments (fluctuations) can be derived if the elastic energy stored in the residual stress field is known. By applying the Green function method, an analytical expression for this energy is obtained under some mild assumptions concerning the neglected elastic anisotropy and crystallographic correlations between the crystals. From the stored energy we calculate the average crystal stresses as depending on shape, orientation and polycrystalline texture. Furthermore we obtain a scalar second order moment of the residual stress, which also depends on grain shape and texture. The results arc evaluated for alumina ceramics and zircalloy.

置換金膜と素地銅の結晶学的関連性

Galvanically substituted Au films were deposited and developed on single-and poly-crystals by using hydrochloric auric chloride solution, and the crystallographic correlations between Au films and Cu substrates were investigated by direct observation of an electron microscope and by electron diffraction.The results obtained were as follows.(1) The correlations on the coherency between galvanically substituted Au films and Cu substrates were found to be as follows:{(001)Cu||(001)Au [100] Cu||[100] Au……(1){(011)Cu||(011)Au [100] Cu||[100] Au……(2){(111)Cu||(111)Au [011] Cu||[011] Au……(3){(111)Cu||(112)Au [101] Cu||[111] Au {(111)Cu||(112)Au [110] Cu||[111] Au {(111)Cu||(112)Au [011] Cu||[111] Au}……(4){(111)Cu||(011)Au [121] Cu||[100] Au……(5)(2) The coating rates of Au films depended on the Miller indices of the surfaces of Cu substrates. The coating rates for the substrates of high indices were higher than those for the substrates of low indices.(3) The growth rate and the shape of crystals on grain boundaries in the Au films inherited from the Cu substrates depended on the directions of grain boundaries as well as the Miller indices of the surfaces of Cu substrates.