Shape Evolution and Splitting of a Single Coherent Particle

1997 ◽  
Vol 481 ◽  
Author(s):  
J. D. Zhang ◽  
D. Y. Li ◽  
L. Q. Chen

ABSTRACTThe morphology and its evolution of a single coherent precipitate was investigated using the Cahn-Hilliard equation and Khachaturyan's continuum elasticity theory for solid solutions. A cubic solid solution with negative elastic anisotropy and isotropic interfacial energy was considered. The lattice mismatch between the precipitate and the matrix was assumed to be purely dilatational and its compositional dependence obeys the Vegard's law. Both two- and three-dimensional systems were studied. The Cahn-Hilliard equation was numerically solved using a semi-implicit Fourier-spectral method. It was demonstrated that, with increasing elastic energy contribution, the equilibrium shape of a coherent particle gradually changes from a circle to a square in two dimensions, and from a sphere to a cube in three dimensions, and the composition profile becomes increasingly inhomogeneous within the precipitate with the minimum at the center of the particle, consistent with previous theoretical studies and experimental observations. It was also shown that, with sufficiently large elastic strain energy contribution, a coherent particle may split to four particles from a square, or eight particles from a sphere, during its evolution to equilibrium. For both two and three dimensions, the splitting starts by nucleating the matrix phase at the center of the particle.

1988 ◽  
Vol 60 (22) ◽  
pp. 2311-2314 ◽  
Author(s):  
Raúl Toral ◽  
Amitabha Chakrabarti ◽  
James D. Gunton

Author(s):  
Thomas Blesgen ◽  
Isaac Vikram Chenchiah

We consider a generalization of the Cahn–Hilliard equation that incorporates an elastic energy density which, being quasi-convex, incorporates micro-structure formation on smaller length scales. We explore the global existence of weak solutions in two and three dimensions. We compare theoretical predictions with experimental observations of coarsening in superalloys.


1995 ◽  
Vol 398 ◽  
Author(s):  
Jong K. Lee ◽  
Jun H. Choy

ABSTRACTMorphological evolution of coherent precipitates with arbitrary transformation strain is studied via a discrete atom method. With a purely dilatational misfit strain, a soft precipitate tends to have a plate-like equilibrium shape, whereas a hard precipitate takes up a shape of high symmetry such as a circle. If the stiffness is comparable between the matrix and precipitate, however, the equilibrium shape depends on the degree of anisotropy, misfit strain, size, and interfacial energy. Shape bifurcation phenomena from circular to rectangular shapes are also revealed during clustering. With either a tetragonal misfit strain of mixed signs or a pure shear misfit strain, a precipitate takes up a plate-like shape whose major axis lies along the direction containing an invariant line in accordance with the continuum elasticity prediction. Both elastic anisotropy and elastic inhomo-geneity exert little influence on the preferred orientation relationship. With a misfit strain of combined shear and dilatation, a precipitate follows an orientation and shape dictated by both components of the misfit strain.


2010 ◽  
Vol 1258 ◽  
Author(s):  
Paulo Sergio Branicio ◽  
David J Srolovitz

AbstractWhen materials are very thin in one or more dimensions, their equilibrium shapes are often curved/bent. Such shapes commonly represent a compromise between elastic strain energy and other thermodynamic forces (e.g. related to surface stresses, electrostatic interactions, or adsorption). Examples include ZnO and SnO2 nanobelts, silica/carbonate helicoids, and graphene sheets and nanoribbons. Here, we demonstrate that when the equilibrium shape of a nanomaterial is not flat/straight, important fundamental material properties may be orders of magnitude different from their bulk counterparts. We focus here primarily on the graphene edges. Graphene in three dimensions is a codimension c = 1 material; the codimension is c = D – d = 3 – 2 = 1, where D is the dimensionality of the space in which the material is embedded and d is the dimensionality of the object. By contrast, a flat graphene sheet has c = 2 – 2 = 0. We use the REBO-II interatomic potential to calculate the edge orientation dependence of the edge energy and edge stresses of graphene with c = 0 and c = 1. The edge stress for all edge orientations is compressive with c = 0. Both edge energy and stresses are in reasonable agreement with DFT calculations. The compressive edge stresses in c = 0 lead to edge buckling (out-of-the-plane of the graphene sheet) for all edge orientations (c = 1). The edge buckling in c = 1 reduces all edge energies and dramatically reduces all edge stresses to near zero (more than an order of magnitude drop). We also report the effect of codimension on the free energy and entropy of a graphene sheet and the elastic properties of ZnO nanohelices.


Author(s):  
Yazhen Liang ◽  
Xiaogang Chen ◽  
Constantinos Soutis

AbstractDespite of the fact that more and more accessory devices are integrated to functionalize a ballistic helmet system, its core ballistic protective function needs to be improved with weight reduction was and still is the main course in engineering design. The two major generic classes of synthetic fibres for ballistic composites are Ultra High Molecular Weight Polyethylene (UHMWPE) fibre (0.97 g/cm3) and aramid fibre (1.44 g/cm3). In the area of military helmets, these fibres are constructed into different topologies, draping/forming into double-curvature geometric shape in multiple plies, serving as reinforcement for composite shell. The preforming ways influence the subsequent impregnation / solidification and curing step in manufacture, in terms of the fibre orientation and fibre volume fraction. The inherent structural heterogeneity thus leads to scatter in permeability and composite thickness, and have further impact in generating process-induced defects. During the processing, the fibre continuity without wrinkles, together with voids-free are determinative factors to a quality final part. The aim of this paper is to review the manufacturing technologies characterised by thermo-mechanical forming and Liquid Composite Moulding (LCM), relating their processing parameters respectively to the properties of reinforcements in one dimension (1D), two dimensions (2D) and three dimensions (3D), along with that of the matrix in dry or wet phase, interdependency of them are sought.


Author(s):  
R. A. Ricks ◽  
Angus J. Porter

During a recent investigation concerning the growth of γ' precipitates in nickel-base superalloys it was observed that the sign of the lattice mismatch between the coherent particles and the matrix (γ) was important in determining the ease with which matrix dislocations could be incorporated into the interface to relieve coherency strains. Thus alloys with a negative misfit (ie. the γ' lattice parameter was smaller than the matrix) could lose coherency easily and γ/γ' interfaces would exhibit regularly spaced networks of dislocations, as shown in figure 1 for the case of Nimonic 115 (misfit = -0.15%). In contrast, γ' particles in alloys with a positive misfit could grow to a large size and not show any such dislocation arrangements in the interface, thus indicating that coherency had not been lost. Figure 2 depicts a large γ' precipitate in Nimonic 80A (misfit = +0.32%) showing few interfacial dislocations.


Data ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 27
Author(s):  
Domingo Villavicencio-Aguilar ◽  
Edgardo René Chacón-Andrade ◽  
Maria Fernanda Durón-Ramos

Happiness-oriented people are vital in every society; this is a construct formed by three different types of happiness: pleasure, meaning, and engagement, and it is considered as an indicator of mental health. This study aims to provide data on the levels of orientation to happiness in higher-education teachers and students. The present paper contains data about the perception of this positive aspect in two Latin American countries, Mexico and El Salvador. Structure instruments to measure the orientation to happiness were administrated to 397 teachers and 260 students. This data descriptor presents descriptive statistics (mean, standard deviation), internal consistency (Cronbach’s alpha), and differences (Student’s t-test) presented by country, population (teacher/student), and gender of their orientation to happiness and its three dimensions: meaning, pleasure, and engagement. Stepwise-multiple-regression-analysis results are also presented. Results indicated that participants from both countries reported medium–high levels of meaning and engagement happiness; teachers reported higher levels than those of students in these two dimensions. Happiness resulting from pleasure activities was the least reported in general. Males and females presented very similar levels of orientation to happiness. Only the population (teacher/student) showed a predictive relationship with orientation to happiness; however, the model explained a small portion of variance in this variable, which indicated that other factors are more critical when promoting orientation to happiness in higher-education institutions.


Sign in / Sign up

Export Citation Format

Share Document