Grain Boundaries In Polycrystals Research Articles

Calorimetric and Volumetric Studies of Dislocations During Martensitic Transformations in Shape Memory TiNi Alloy

Based on the use of appropriate approaches, methods and results of the analysis of a number of topical problems of physical materials science, an in-depth analysis has been done of calorimetric and volumetric data for direct, reverse and deformation martensitic transformations in a nanostructured Ti49.3Ni50.7 shape memory alloy obtained by cold rolling with simultaneous action of pulsed high-density current. For the first time, by applying a new technique for processing calorimetric spectra (peaks), the staging and “kinetics” of changes in heat content, as well as thermal effects (enthalpies of individual stages) during direct and reverse martensitic transformations during cooling or heating of samples at a constant rate (3 × K/ min) in the range 170–370 K has been done. It is shown, by processing volumetric data, using theoretical values of the dislocation density and elements of the classical theory of dislocations, that in the Ti49.3Ni50.7 shape memory alloy subjected to cold deformation accompanied by the action of a pulsed current, a deformation martensitic transformation occurs, leading to a positive volume effect (∆V/V) ≈ 3 × 10–3), which can be largely due to dislocations. It is shown, by applying the theoretical values of the dislocation density and elements of the classical theory of dislocations, that the possible contributions of dislocations to the enthalpies of direct and reverse martensitic transformations (in the Ti49.3Ni50.7 alloy) can and should be significantly lower in absolute value, but opposite in sign to the observed enthalpies of direct and reverse martensitic transformation in a given alloy. It is shown that the physics of the processes under consideration is contained to a certain extent in scientific discoveries No. 239 “The phenomenon of thermoelastic equilibrium during phase transformations of the martensitic type – the Kurdyumov effect” and No. 339 “The phenomenon of the formation of non-equilibrium grain boundaries in polycrystals when they absorb lattice dislocations”.

Reversible-to-irreversible transition of colloidal polycrystals under cyclic athermal quasistatic deformation.

Cyclic loading on granular packings and amorphous media exhibits a transition from reversible elastic behavior to irreversible plasticity. The present study compares the irreversibility transition and microscopic details of colloidal polycrystals under oscillatory tensile-compressive and shear strain. Under both modes, the systems exhibit a reversible to irreversible transition. However, the strain amplitude at which the transition is observed is larger in the shear strain than in the tensile-compressive mode. The threshold strain amplitude is confirmed by analyzing the dynamical properties, such as mobility and atomic strain (von Mises shear strain and the volumetric strain). The structural changes are quantified using a hexatic order parameter. Under both modes of deformation, dislocations and grain boundaries in polycrystals disappear, and monocrystals are formed. We also recognize the dislocation motion through grains. The key difference is that strain accumulates diagonally in oscillatory tensile-compressive deformation, whereas in shear deformation, strain accumulation is along the x or y axis.

Analysis of grain-boundary segregation of hydrogen in bcc-Fe polycrystals via a nano-polycrystalline grain-boundary model

Hydrogen embrittlement caused by hydrogen segregation at grain boundaries (GBs) is the most serious issue in the development of high-strength steels, but the mechanisms behind this process are still not well understood. The GB segregation behavior of hydrogen in body-centered cubic (bcc)-Fe polycrystals was comprehensively analyzed based on the interatomic potentials derived from first-principles calculations. Considering that the atomic structure of GBs is almost independent of the grain size, the GBs in polycrystals were modeled as nano-polycrystalline GBs with random orientations. The segregation energies of hydrogen for ∼17 million interstitial sites in this GB model were calculated. From these segregation energies, the effective segregation energy for the polycrystalline GB at thermal equilibrium under various temperature and hydrogen content conditions were determined, and the validity of the calculation method was verified by comparing the results with experimental data. The relationship between the segregation energy of hydrogen at each segregation site and the surrounding local atomic environment was used to identify the major hydrogen segregation sites at the atomic level, and the changes in the crystal structure near the GB that dominated segregation were clarified. The effective segregation energies at the polycrystalline GBs were in the range of −0.48 to −0.42 eV, which are in good agreement with the experimentally reported binding energy of hydrogen at GBs of bcc-Fe polycrystals (−0.52 eV). The major hydrogen segregation sites were octahedral sites with Voronoi volumes larger than 7.0 Å3, and the segregation energy was mainly due to the uniaxially distorted crystal structure in the short-axis direction of octahedral sites. Our findings and the developed calculation method contribute to the understanding of the hydrogen segregation behavior and hydrogen embrittlement mechanism in polycrystalline metallic materials.

Solvent Mediated Nanoscale Quasi-Periodic Chirality Reversal in Self-Assembled Molecular Networks Featuring Mirror Twin Boundaries.

Grain boundaries in polycrystals have a prominent impact on the properties of a material, therefore stimulating the research on grain boundary engineering. Structure determination of grain boundaries of molecule-based polycrystals with submolecular resolution remains elusive. Reducing the complexity to monolayers has the potential to simplify grain boundary engineering and may offer real-space imaging with submolecular resolution using scanning tunneling microscopy (STM). Herein, the authors report the observation of quasi-periodic nanoscale chirality switching in self-assembled molecular networks, in combination with twinning, as revealed by STM at the liquid/solid interface. The width of the chiral domain structure peaks at 12-19nm. Adjacent domains having opposite chirality are connected continuously through interdigitated alkoxy chains forming a 1D defect-free domain border, reflecting a mirror twin boundary. Solvent co-adsorption and the inherent conformational adaptability of the alkoxy chains turn out to be crucial factors in shaping grain boundaries. Moreover, the epitaxial interaction with the substrate plays a role in the nanoscale chirality reversal as well.

A fully coupled chemo-mechanical cohesive zone model for oxygen embrittlement of nickel-based superalloys

For nickel-based superalloys subjected to high temperatures and oxygen-rich environments, mechanical loading in combination with oxygen diffusion along grain boundaries leads to an acceleration of crack propagation. To account for these phenomena, a fully coupled thermodynamically consistent chemo-mechanical modeling framework for stress-assisted oxygen embrittlement of grain boundaries in polycrystals is proposed. We formulate an extended cohesive zone model where the grain boundary strength is reduced by the presence of oxygen and the oxygen diffusion is enhanced by tensile mechanical loading. We show that the model can qualitatively predict experimental results such as: reduction of ultimate tensile strength and accelerated crack growth due to dwell time combined with mechanical loading and saturation of crack growth rates for increasing environmental oxygen pressure levels. In addition, numerical simulation results of intergranular crack growth are shown for a 2D polycrystalline structure. An emphasis is put on the difference in cracking behavior after dwelling with or without mechanical loading.

Investigation of Grain Boundary Content on Crack Propagation Behavior of Nanocrystalline Al by Molecular Dynamics Simulation

The nanocrystalline metal material has been an investigation hotspot due to its excellent mechanical property. The high content of grain boundaries (GBs) in microstructure is the key factor affecting its fracture behavior during service. Therefore, it is essential to investigate the effect mechanism of nanoscale GB on crack propagation. In this study, four molecular dynamics (MD) models of nanocrystalline aluminum (Al) with different GB contents are established. The results show that the high‐content GBs in polycrystals can increase the toughness and absorb energy, reducing the risk of brittle crack propagation. The presence of GB can reduce the stress concentration of the crack, and the dislocation emission from the crack tip can be absorbed by the front GB. The microstructure with high‐content GBs can actuate more plastic deformation mechanisms such as multiple slips, GB slip, and migration. The region with more GBs can induce a more even deformation of the whole microstructure by means of dislocation emission and GB migration to the region with fewer GBs. The purpose of this study is to provide a rational mechanism reference for the failure of nanocrystalline metal material.

Tracking the sliding of grain boundaries at the atomic scale.

Grain boundaries (GBs) play an important role in the mechanical behavior of polycrystalline materials. Despite decades of investigation, the atomic-scale dynamic processes of GB deformation remain elusive, particularly for the GBs in polycrystals, which are commonly of the asymmetric and general type. We conducted an in situ atomic-resolution study to reveal how sliding-dominant deformation is accomplished at general tilt GBs in platinum bicrystals. We observed either direct atomic-scale sliding along the GB or sliding with atom transfer across the boundary plane. The latter sliding process was mediated by movements of disconnections that enabled the transport of GB atoms, leading to a previously unrecognized mode of coupled GB sliding and atomic plane transfer. These results enable an atomic-scale understanding of how general GBs slide in polycrystalline materials.

Application of Grain Boundary Segregation Prediction Using a Nano-Polycrystalline Grain Boundary Model to Transition Metal Solute Elements: Prediction of Grain Boundary Segregation of Mn and Cr in bcc-Fe Polycrystals

A prediction method for grain boundary segregation using a nano-polycrystalline grain boundary model is applied to the grain boundary segregation of Cr and Mn in bcc-Fe polycrystals for which experimental results exist, and the validity of the prediction method is verified. In this prediction method, focusing on the fact that the atomic structure of grain boundaries is almost independent of grain size, grain boundaries of polycrystals with grain sizes of the order of micrometers are modeled as grain boundaries of nano-polycrystals, for which structural relaxation calculations by molecular dynamics calculations are possible. For this grain boundary model, the grain boundary segregation energy of each site is calculated exhaustively using the interatomic potential. In addition, the average amount of grain boundary segregation in the polycrystal is calculated from the obtained grain boundary segregation energy. With this prediction method, the average amounts of grain boundary segregation and segregation energies of Cr and Mn in bcc-Fe polycrystals can be calculated and compared with the experimental results. Calculated results for both elements reproduced the experimental results well, suggesting that this prediction method is also effective in predicting the grain boundary segregation of other solute elements.

Models of activated recrystallization on isolated grain boundaries in polycrystals

New phenomenological models of recrystallization of a polycrystalline material in two regimes are proposed taking into account the finite width of grain boundaries. The solutions are obtained in an analytical form for the initial-boundary value problems formulated. They describe the distributions of the concentration of impurities diffusing from the surface coating, both in the grain boundary and in the grain itself in the recrystallized region. The speed of the recrystallization front movement is indicated, which agrees with the types of the corresponding kinetic dependences observed in experiments.

Application of Grain Boundary Segregation Prediction Using a Nano-Polycrystalline Grain Boundary Model to Transition Metal Solute Elements: Prediction of Grain Boundary Segregation of Mn and Cr in bcc-Fe Polycrystals

A prediction method for grain boundary segregation using a nano-polycrystalline grain boundary model is applied to the grain boundary segregation of Cr and Mn in bcc-Fe polycrystals for which experimental results exist, and the validity of the prediction method is verified. In this prediction method, focusing on the fact that the atomic structure of grain boundaries is almost independent of grain size, grain boundaries of polycrystals with grain sizes of the order of micrometers are modeled as grain boundaries of nano-polycrystals, for which structural relaxation calculations by molecular dynamics calculations are possible. For this grain boundary model, the grain boundary segregation energy of each site is calculated exhaustively using the interatomic potential. In addition, the average amount of grain boundary segregation in the polycrystal is calculated from the obtained grain boundary segregation energy. With this prediction method, the average amounts of grain boundary segregation and segregation energies of Cr and Mn in bcc-Fe polycrystals can be calculated and compared with the experimental results. Calculated results for both elements reproduced the experimental results well, suggesting that this prediction method is also effective in predicting the grain boundary segregation of other solute elements.

A new approach to understand the deformation behavior and strengthening mechanism of molybdenum alloy: From single crystal to polycrystal

The deformation behavior and strengthening mechanism for Mo-3Nb single crystal with 〈111〉 orientation and polycrystal have been investigated and disclosed comprehensively in a wide temperature range by quasi-static compression with 7% plastic strain. The slip traces of single crystal and polycrystal at room temperature show different features, which long continuous slip traces appear on the surface of deformed Mo-3Nb single crystals while some branch-off slip lines can only be observed in large grains for polycrystals. The conjugate slip planes of single crystals are activated at the elevated temperature, while the slip lines of polycrystals are difficult to be observed because of the grain boundary sliding effect. The compressive stress of single crystals and polycrystals shows different results at different deformation temperatures, suggesting that grain boundaries in polycrystals play an important role in the strengthening mechanism. TEM analysis shows that dislocation entanglement is the main strengthening mechanism both in single crystal and polycrystal during the room temperature deformation. With the increase of temperature, the strengthening mechanism caused by dislocation entanglement becomes ineffective, while grain boundaries continue to hinder the dislocation movement and the strengthening effect greatly weakened due to the dynamic recovery.

Dislocation impediment by the grain boundaries in polycrystals

Thermodynamic dislocation theory incorporating dislocation impediment by the grain boundaries is developed to analyze the shear test of polycrystals. With a small set of physics-based material parameters, we are able to simulate the stress–strain curves for the load and its reversal, which are consistent with the experimental curves of Thuillier and Manach (Int J Plast 25:733–751, 2009). Representative distributions of plastic slip under load and its reversal are presented, and their evolution explains the extended length of the transition stage during load reversal.

Equation of motion for grain boundaries in polycrystals

Grain boundary (GB) dynamics are largely controlled by the formation and motion of disconnections (with step and dislocation characters) along with the GB. The dislocation character gives rise to shear coupling; i.e. the relative tangential motion of two grains meeting at the GB during GB migration. In a polycrystal, the shear coupling is constrained by the presence of other grains and GB junctions, which prevents large-scale sliding of one grain relative to the other. We present continuum equations of motion for GBs that is based upon the underlying disconnection dynamics and accounts for this mechanical constraint in polycrystals. This leads to a reduced-order (zero-shear constrained) model for GB motion that is easily implemented in a computationally efficient framework, appropriate for the large-scale simulation of the evolution of polycrystalline microstructures. We validated the proposed reduced-order model with direct comparisons to full multi-disconnection mode simulations.

Revisiting the Application of Field Dislocation and Disclination Mechanics to Grain Boundaries

We review the mechanical theory of dislocation and disclination density fields and its application to grain boundary modeling. The theory accounts for the incompatibility of the elastic strain and curvature tensors due to the presence of dislocations and disclinations. The free energy density is assumed to be quadratic in elastic strain and curvature and has nonlocal character. The balance of loads in the body is described by higher-order equations using the work-conjugates of the strain and curvature tensors, i.e., the stress and couple-stress tensors. Conservation statements for the translational and rotational discontinuities provide a dynamic framework for dislocation and disclination motion in terms of transport relationships. Plasticity of the body is therefore viewed as being mediated by both dislocation and disclination motion. The driving forces for these motions are identified from the mechanical dissipation, which provides guidelines for the admissible constitutive relations. On this basis, the theory is expressed as a set of partial differential equations where the unknowns are the material displacement and the dislocation and disclination density fields. The theory is applied in cases where rotational defects matter in the structure and deformation of the body, such as grain boundaries in polycrystals and grain boundary-mediated plasticity. Characteristic examples are provided for the grain boundary structure in terms of periodic arrays of disclination dipoles and for grain boundary migration under applied shear.

Equilibrium and kinetic shapes of grains in polycrystals

The equilibrium crystal shape is a convex shape bound by the lowest energy interfaces. In many polycrystalline microstructures created by grain growth, the observed distribution of grain boundary planes appears to be dominated at low driving forces (after long grain growth times) by the planes present in the equilibrium crystal shape. However, at earlier stages of grain growth, it is expected that kinetic effects will play an important role in grain boundary motion and morphology. Analogous to the equilibrium crystal shape, the kinetic crystal shape of seed crystals growing from a liquid at higher supersaturations is bound by the slowest growing orientations. This study presents an equivalent construction for grain boundaries in polycrystals and uses it to determine the kinetic crystal shape for strontium titanate as a function of temperature. Relative grain boundary mobilities for strontium titanate for the low energy crystallographic orientations from seeded polycrystal experiments are used to calculate the kinetic crystal shapes as a function of temperature and annealing atmosphere. The kinetic crystal shapes are then compared to the morphologies and orientations of the interfaces of the growing seed crystals, and to the equilibrium crystal shapes, as well.The conclusions are that (1) the kinetic crystal shape is extremely anisotropic and displays significant transitions as a function of temperature that do not mirror changes in equilibrium crystal shape, (2) the kinetic shapes observed in the microstructures are dominated by the growing side of the interface (single crystal) and not by the dissolving side (polycrystalline matrix), and (3) faster growing orientations break up into macroscopic facets composed of slower growing orientations. The implications for grain growth underscore the applicability of crystal growth models to grain growth in polycrystals. In particular, in strontium titanate, the anisotropy of the grain boundary mobility as represented in the kinetic crystal shape is expected to be reduced from five macroscopic parameters to two (interface normal) allowing for incorporation of growth rate anisotropy in simulations of microstructure evolution at the earliest stages of grain growth, i.e. at the highest driving forces.

Phase-field modeling of domain evolution in ferroelectric materials in the presence of defects

The properties of ferroelectric devices are strongly influenced, besides crystallographic features, by defects in the material. To study this effect, a fully coupled electromechanical phase-field model for 2D ferroelectric volume elements has been developed and implemented in a Finite Element code. Different kinds of defects were considered: holes, point charges and polarization pinning in single crystals, as well as grain boundaries in polycrystals, without and with additional dielectric interphase. The impact of the various types of defects on the domain configuration and the overall coercive field strength is discussed in detail. It can be seen that defects lead to nucleation of new domains. Compared to the energy barrier for switching in an ideal single crystal, the overall coercive field strength is significantly reduced towards realistic values as they are found in ferroelectric devices. Also the simulated hysteresis loops show a more realistic shape in the presence of defects.

Evolution of spherical nanovoids within copper polycrystals during plastic straining: Atomistic investigation

The evolution, growth and coalescence, of nanovoids play a significant role in the plasticity of nanocrystalline metallic materials. Previous atomistic studies of void growth in face centered copper, and other metallic materials, have considered voids in single crystals, and those located at grain boundaries in polycrystals. The evolution of a spherical nanovoid in copper polycrystals under uniaxial tension is the focus of this atomistic investigation. In this paper, a critical stress based criterion is proposed for emission of dislocations from spherical void surfaces. The preference of dislocation source, GBs or spherical void surfaces, is determined by the relative magnitude of the critical stresses to emit dislocations from GBs or spherical void surfaces. The criterion reveals that there exists a grain size dependent critical void diameter at which the dislocation emission transits from GBs to spherical void surfaces as the spherical void grows. Simulation results show that, in intragranular voided models, the critical void diameter is 13 nm for simulation models with a 16.32 nm grain size and is 5.5 nm for simulation models with a 6.92 nm grain size. The critical void diameters revealed by simulations are in agreement with that obtained by the criterion. In addition, the simulation results indicate that the Gurson's model may be extended to predict the global yield conditions for simulation models with intragranular spherical voids. In the simulation models with intergranular voids, the spherical void continuously grows due to the initial dislocation emission from the intersections of GBs and spherical void surfaces.

Topological changes in coarsening networks

Curvature driven grain growth proceeds by the motion of curved grain boundaries in polycrystals leading to a decrease in the total interfacial free energy. However, grain growth cannot occur without the so-called topological transitions. Indeed, it is a mathematical impossibility that a decrease in the number of grains per unit volume may take place without the topological transition that corresponds to the grain disappearance. Nonetheless, despite their importance, no previous work has studied the topological transitions in detail that take place during the transient as well as the self-similar state of coarsening. In the present work, the three classical topological changes are tracked during 2-d grain growth simulated by a Monte Carlo method. It is shown and discussed how topological transitions reach a self-similar state together with the grain size and the number of edges (faces) per grain distribution.

Fabricating large two-dimensional single colloidal crystals by doping with active particles.

Using simulations we explore the behaviour of two-dimensional colloidal (poly)crystals doped with active particles. We show that these active dopants can provide an elegant new route to removing grain boundaries in polycrystals. Specifically, we show that active dopants both generate and are attracted to defects, such as vacancies and interstitials, which leads to clustering of dopants at grain boundaries. The active particles both broaden and enhance the mobility of the grain boundaries, causing rapid coarsening of the crystal domains. The remaining defects recrystallize upon turning off the activity of the dopants, resulting in a large-scale single-domain crystal.

Macroscopic modeling of material interfaces based on atomistic descriptions

AbstractThe effective macroscopic properties of a broad variety of different materials are defined by the properties of the involved material interfaces. Grain boundaries in polycrystals represent a well‐known example. However, in contrast to classical bulk materials, the mechanical properties of material interfaces can oftentimes not be identified in a straightforward manner. In this paper, a multiscale framework is presented which allows to compute macroscopic properties of material interfaces based on molecular dynamics. The key idea of the elaborated multiscale framework is the coupling of an RVE associated with the atomistic scale to an RVE based on a continuum mechanics description by means of the principle of energy equivalence. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)