Evaluation of grain boundary energy, structure and stiffness from phase field crystal simulations

2021 ◽  
Vol 30 (1) ◽  
pp. 014002
Author(s):  
Kevin Hult Blixt ◽  
Håkan Hallberg
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Phase Field ◽  
Boundary Energy ◽  
Md Simulations ◽  
Alternative Methods ◽  
Energy Structure ◽  
Grain Boundary Energy ◽  
Equilibrium Configurations ◽  
Phase Field Crystal

Abstract A two-mode phase field crystal (PFC) model is employed to investigate the equilibrium configurations of a range of grain boundaries in fcc-structured materials. A total of 80 different symmetrical tilt grain boundaries are evaluated by PFC simulations in 3D and the results are shown to agree well with data taken from the literature, both regarding the variation of grain boundary energy and also in terms of the resulting grain boundary structures. This verification complements existing PFC studies which are almost exclusively focused either on grain boundaries found in 2D systems or in bcc lattices in 3D. The present work facilitates application of PFC in the analysis of grain boundary mechanics in an extended range of materials, in particular such mechanics that take place at extended time scales not tractable for molecular dynamics (MD) simulations. In addition to the verification of predicted grain boundary energies and structures, wavelet transforms of the density field are used in the present work to obtain phase fields from which it is possible to identify grain boundary fluctuations that provide the means to evaluate grain boundary stiffness based on the capillarity fluctuation method. It is discussed how PFC provides benefits compared to alternative methods, such as MD simulations, for this type of investigations.

Fractional phase-field crystal modelling: analysis, approximation and pattern formation

2020 ◽  
Vol 85 (2) ◽  
pp. 231-262
Author(s):  
Mark Ainsworth ◽  
Zhiping Mao
Keyword(s):  
Pattern Formation ◽  
Grain Boundary ◽  
Fractional Order ◽  
Phase Field ◽  
Boundary Energy ◽  
Classical Case ◽  
Experimental Measurements ◽  
Grain Boundary Energy ◽  
Material Interface ◽  
Phase Field Crystal

Abstract We consider a fractional phase-field crystal (FPFC) model in which the classical Swift–Hohenberg equation (SHE) is replaced by a fractional order Swift–Hohenberg equation (FSHE) that reduces to the classical case when the fractional order $\beta =1$. It is found that choosing the value of $\beta $ appropriately leads to FSHE giving a markedly superior fit to experimental measurements of the structure factor than obtained using the SHE ($\beta =1$) for a number of crystalline materials. The improved fit to the data provided by the fractional partial differential equation prompts our investigation of a FPFC model based on the fractional free energy functional. It is shown that the FSHE is well-posed and exhibits the same type of pattern formation behaviour as the SHE, which is crucial for the success of the PFC model, independently of the fractional exponent $\beta $. This means that the FPFC model inherits the early successes of the FPC model such as physically realistic predictions of the phase diagram etc. and, therefore, provides a viable alternative to the classical PFC model. While the salient features of PFC and FPFC are identical, we expect more subtle features to differ. The prediction of grain boundary energy arising from a mismatch in orientation across a material interface is another notable success of the PFC model. The grain boundary energy can be evaluated numerically from the PFC model and compared with experimental measurements. The grain boundary energy is a derived quantity and is more sensitive to the nuances of the model. We compare the predictions obtained using the PFC and FPFC models with experimental observations of the grain boundary energy for several materials. It is observed that the FPFC model gives superior agreement with the experimental observation than those obtained using the classical PFC model, especially when the mismatch in orientation becomes larger.

Survey of Grain Boundary Energies in Four Elemental Metals

2012 ◽  
Vol 715-716 ◽  
pp. 179-179
Author(s):  
David L. Olmsted ◽  
Elizabeth A. Holm ◽  
Stephen M. Foiles
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Energy Minimization ◽  
Boundary Energy ◽  
Atomic Scale ◽  
Energy Structure ◽  
Grain Boundary Energy ◽  
Fcc Metals ◽  
Composition And Structure ◽  
Boundary Properties

Grain boundary properties depend on both composition and structure. To test the relative contributions of composition and structure to the grain boundary energy, we calculated the energy of 388 grain boundaries in four elemental, fcc metals: Ni, Al, Au and Cu. We constructed atomic-scale bicrystals of each boundary and subjected them to a rigorous energy minimization process to determine the lowest energy structure. Typically, several thousand boundary configurations were examined for each boundary in each element.

Effect of Grain Boundary Energy Anisotropy on Faceting and Migration of Low Angle Grain Boundaries

2014 ◽  
Vol 783-786 ◽  
pp. 1634-1639
Author(s):  
Dmitri A. Molodov ◽  
Jann Erik Brandenburg ◽  
Luis Antonio Barrales-Mora ◽  
Günter Gottstein
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Elevated Temperatures ◽  
Boundary Energy ◽  
Migration Behavior ◽  
Grain Boundary Energy ◽  
Contrast Imaging ◽  
Orientation Contrast ◽  
And Migration ◽  
Twist Boundaries

The faceting and migration behavior of low angle <100> grain boundaries in high purity aluminum bicrystals was investigated. In-situ technique based on orientation contrast imaging was applied. In contrast to the pure tilt boundaries, which remained straight/flat and immobile during annealing at elevated temperatures, mixed tilt-twist boundaries readily assumed a curved shape and steadily moved under the capillary force. Computational analysis revealed that this behavior is due to the inclinational anisotropy of grain boundary energy, which in turn depends on boundary geometry – the energy of pure tilt low angle <100> boundaries is anisotropic, whereas that of mixed tilt-twist boundaries isotropic with respect to boundary inclination.

Grain-Boundary Energy and Grain-Boundary Groove Angles in Ice

1972 ◽  
Vol 11 (62) ◽  
pp. 265-277 ◽  
Author(s):  
Shigenao Suzuki ◽  
Daisuke Kuroiwa
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Boundary Energy ◽  
Grain Boundary Energy ◽  
Boundary Groove ◽  
Grain Boundary Grooves

Abstract Relative grain-boundary energies in ice were measured as a function of mismatch angles made by the c-axes or a-axes in grains, using ice specimens having triple grain boundaries. It was found that the Read–Shockley equation for grain-boundary energy was valid for grain boundaries tilted between 0° and 15°. Angles of the solid–vapour grain-boundary groove in ice were measured by the use of micro-interferometry at grain-boundary grooves covered with extremely thin metalic foil. The data were compared with those measured by a silvered replica of grain-boundary grooves.

Phase Field Model of Grain Growth Using Quaternions

2012 ◽  
Vol 715-716 ◽  
pp. 776-781
Author(s):  
Santidan Biswas ◽  
Indradev Samajdar ◽  
Arunansu Haldar ◽  
Anirban Sain
Keyword(s):  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Boundary Energy ◽  
Scaling Law ◽  
Phase Field Model ◽  
Polycrystalline Sample ◽  
Mechanical Processing ◽  
Grain Boundary Energy ◽  
Grain Orientations

The microstructure of a material determines its mechanical properties. Since microstructure can be tailored by thermo-mechanical processing of the metal, it is important to understand how the microstructure evolves under thermo-mechanical processing. We have constructed a phase field formalism to study recrystallization and grain growth in polycrystalline material. A unique feature of our model is that the Euler Angles (φ1,φ,φ2), obtained from Electron Back Scattered Diffraction (EBSD) data of a polycrystalline sample can be taken as an input to our model. In our model, the grain orientations at discrete grid points are represented by a non-conserved vector field, namely a quaternion. The free energy used for the evolution of the local orientations contains bulk energy for various preferred grain types and grain boundary energy. The grain orientations evolve in time following a Langevin dynamics. So far we have established that the rate of grain growth follows the usual L ~ t1/2scaling law when the grain boundary energy is independent of the misorientation angle between neighboring grains. Work on other aspects of this model is in progress.

Development of multi-phase-field crack model for crack propagation in polycrystal

2014 ◽  
Vol 03 (02) ◽  
pp. 1450009 ◽  
Author(s):  
Kento Oshima ◽  
Tomohiro Takaki ◽  
Mayu Muramatsu
Keyword(s):  
Grain Boundary ◽  
Crack Propagation ◽  
Phase Field ◽  
Crack Surface ◽  
Crack Path ◽  
Boundary Energy ◽  
Crack Model ◽  
Grain Boundary Energy ◽  
Basic Characteristics ◽  
Multi Phase

It is vitally important to ensure the safety of brittle materials. Therefore, it is essential to deeply understand the interaction of the material's microstructure and crack propagation. In this study, we constructed a multi-phase-field crack model which can express crack propagation in polycrystal. To evaluate the basic characteristics of the developed model, we performed two-dimensional crack propagation simulations in a bicrystal where a crack enters an inclined grain boundary by changing the ratio of the grain boundary energy to the crack surface energy. As a result, it is confirmed that the model can reasonably determine the crack path, depending on those conditions. Furthermore, by performing crack propagation simulations in a polycrystal, it is concluded that the model can properly express transgranular and intergranular cracks.

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