An Approach to Calculate the Elastic Interaction Energy of Inhomogeneous Precipitates: Application to γ′-Ni3Ti in A-286 Steel

The elastic interaction energy between several precipitates is of interest since it may induce ordering of precipitates in many metallurgical systems. Most of the works on this subject assumed homogeneous systems, namely, the elastic constants of the matrix and the precipitates are identical. In this study, the elastic fields, and self and interaction energies of inhomogeneous anisotropic precipitates have been solved and assessed, based on a new iterative approach using the quasi-analytic Fourier transform method. This approach allows good approximation for problems of several inhomogeneous precipitates in solid matrix. We illustrate the calculation approach on γ′-Ni3Ti precipitates in A-286 steel and demonstrate that the influence of elastic inhomogeneity is in some incidences only quantitative, while in others it has essential effect. Assuming homogeneous system, disk shape precipitate is associated with minimum elastic energy. Only by taking into account different elastic constants of the precipitate, the minimum self-energy is found to be associated with spherical shape, and indeed, this is the observed shape of the precipitates in A-286 steel. The elastic interaction energy between two precipitates was calculated for several configurations. Significant differences between the interactions in homogeneous and inhomogeneous were found for disk shape morphologies. Only quantitative differences (9% higher interaction between inhomogeneous precipitates) were found between two spherical precipitates, which are the actual shape.

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Perovskite Ti3AlC Carbide Splitting in High Nb Containing TiAl Alloys

MRS Proceedings ◽

10.1557/opl.2014.950 ◽

2014 ◽

Vol 1760 ◽

Cited By ~ 1

Author(s):

Li Wang ◽

Heike Gabrisch ◽

Uwe Lorenz ◽

Frank-Peter Schimansky ◽

Andreas Stark ◽

...

Keyword(s):

Electron Microscopy ◽

Transmission Electron Microscopy ◽

Interaction Energy ◽

Elastic Interaction ◽

Morphological Development ◽

Tial Alloys ◽

Transmission Electron ◽

The Matrix

ABSTRACTTransmission electron microscopy has been used to investigate the morphological development of the perovskite (P-) Ti3AlC carbides in the γ matrix of a Ti-45Al-5Nb-0.75C alloy during annealing. P-Ti3AlC carbides in the γ matrix initially have a needle-like shape but during annealing at 800 °C they change to a plate-like shape. In the needle-like shape the carbides are orientated parallel to the [001] direction of the matrix. They extend along the [100]γ or [010]γ direction into plates later and subsequently split into sub particles after extended annealing. It is proposed that the elastic interaction energy between the split sub domains may be the reason that this decomposition into sub-particles is energetically favorable.

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Spectral analysis of M/G/1 and G/M/1 type Markov chains

Advances in Applied Probability ◽

10.1017/s0001867800027300 ◽

1996 ◽

Vol 28 (01) ◽

pp. 114-165 ◽

Cited By ~ 16

Author(s):

H. R. Gail ◽

S. L. Hantler ◽

B. A. Taylor

Keyword(s):

Markov Chains ◽

Generating Functions ◽

Complex Analysis ◽

Linear Equations ◽

Sufficient Conditions ◽

Equilibrium Analysis ◽

Transform Method ◽

Technical Problems ◽

The Matrix ◽

Transient Case

When analyzing the equilibrium behavior of M/G/1 type Markov chains by transform methods, restrictive hypotheses are often made to avoid technical problems that arise in applying results from complex analysis and linear algebra. It is shown that such restrictive assumptions are unnecessary, and an analysis of these chains using generating functions is given under only the natural hypotheses that first moments (or second moments in the null recurrent case) exist. The key to the analysis is the identification of an important subspace of the space of bounded solutions of the system of homogeneous vector-valued Wiener–Hopf equations associated with the chain. In particular, the linear equations in the boundary probabilities obtained from the transform method are shown to correspond to a spectral basis of the shift operator on this subspace. Necessary and sufficient conditions under which the chain is ergodic, null recurrent or transient are derived in terms of properties of the matrix-valued generating functions determined by transitions of the Markov chain. In the transient case, the Martin exit boundary is identified and shown to be associated with certain eigenvalues and vectors of one of these generating functions. An equilibrium analysis of the class of G/M/1 type Markov chains by similar methods is also presented.

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Elastic Interaction of Defects on Crystal Surfaces

Journal of Engineering Materials and Technology ◽

10.1115/1.2812357 ◽

1999 ◽

Vol 121 (2) ◽

pp. 129-135 ◽

Cited By ~ 8

Author(s):

Demitris Kouris ◽

Alonso Peralta ◽

Karl Sieradzki

Keyword(s):

Interaction Energy ◽

Surface Defects ◽

Film Growth ◽

Crystal Surface ◽

Elastic Field ◽

Elastic Interaction ◽

Flow Mode ◽

Elastic Model ◽

Far Field ◽

Embedded Atom

Surface defects corresponding to adatoms, vacancies and steps interact, affecting and often dominating kinetic processes associated with thin-film growth. A discrete harmonic model for the evaluation of the interaction energy between surface defects is presented. It is based on the concept of eigenstrains and allows for the accurate evaluation of the elastic field, both at the immediate vicinity of the defects, as well as in the far field. Results for the interaction energy suggest conditions for which a body-centered-cubic crystal surface will grow in a stable, two-dimensional, step-flow mode. In order to verify the accuracy of the discrete elastic model, we present results of atomic simulations that incorporate Embedded Atom Method (EAM) potentials. The discrete elastic model results compare favorably with results from our atomic EAM simulations and agree with the far-field predictions of continuum elastic theory.

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Application of Fluorine Containing Bioactive Glass Nanoparticles in Dentin Hypersensitivity Treatment

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.696.103 ◽

2016 ◽

Vol 696 ◽

pp. 103-107 ◽

Cited By ~ 4

Author(s):

Carolina Emmanuelle Camargos Lins ◽

Sandhra Maria de Carvalho ◽

Agda Aline Rocha de Oliveira ◽

Marivalda de Magalhães Pereira

Keyword(s):

Heat Treatment ◽

Bioactive Glass ◽

Glass Structure ◽

Spherical Shape ◽

Dentin Hypersensitivity ◽

Dentinal Tubules ◽

Mineralized Tissues ◽

The Matrix ◽

New System

The effect of Bioactive Glass on remineralization of dentin is the focus of the present study due to its excellent regenerative properties in mineralized tissues. It is known that the effect of Bioactive Glass can be enhanced at the nanoscale. In addition, the incorporation of Fluorine in the glass structure makes possible the formation of Fluorapatite (FAP). The aim of this study was to synthesize and characterize a new system of Fluorine containing Bioactive Glass Nanoparticles (FBGNP), and evaluate the potential for in vitro dentin remineralization by occlusion of dentinal tubules. The FBGNPs produced were uniform, with spherical shape and nanoscale size. Agglomeration or partial sinterization of the particulate system probably occurred after heat treatment. The results suggest the formation of FAP crystals embedded within the matrix of the Bioactive Glass. The gel containing FBGNP produced was effective in obliterating the dentinal tubules in vitro, showing that FBGNP is a potential material to be used for treatment of dentin hypersensitivity.

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The effect of elastic interaction energy on the morphology of γ′precipitates in nickel-based alloys

Materials Science and Engineering ◽

10.1016/0025-5416(84)90056-9 ◽

1984 ◽

Vol 67 (2) ◽

pp. 247-253 ◽

Cited By ~ 125

Author(s):

Minoru Doi ◽

Toru Miyazaki ◽

Teruyuki Wakatsuki

Keyword(s):

Interaction Energy ◽

Elastic Interaction

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Implementation of Finite Deformation Triphasic Modeling in the Finite Element Code FEBio

ASME 2012 Summer Bioengineering Conference, Parts A and B ◽

10.1115/sbc2012-80148 ◽

2012 ◽

Author(s):

Gerard A. Ateshian ◽

Steve Maas ◽

Jeffrey A. Weiss

Keyword(s):

Soft Tissues ◽

Mixture Theory ◽

Solid Matrix ◽

Osmotic Swelling ◽

Solute Content ◽

Counter Ions ◽

The Matrix ◽

Triphasic Theory ◽

Ion Species ◽

And Diffusion

Many biological soft tissues exhibit a charged solid matrix, most often due to the presence of proteoglycans enmeshed within the matrix. The predominant solute content of the interstitial fluid of these tissues consists of the monovalent counter-ions Na+ and Cl−. The electrical interactions between the mobile ion species and fixed charge density of the solid matrix produces an array of mechano-electrochemical effects, including Donnan osmotic swelling, and streaming and diffusion potentials and currents. These phenomena have been successfully modeled by the triphasic theory of Lai et al. [1], which is based on the framework of mixture theory [2]. Other similar frameworks have also been proposed [3, 4]. The equations of triphasic theory are nonlinear, even in the range of infinitesimal strains. Therefore, numerical schemes are generally needed to solve all but the simplest problems using this framework.

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Effect of Aluminum, Iron and Chromium Alloying on the Structure and Mechanical Properties of (Ti-Ni)-(Cu-Zr) Crystalline/Amorphous Composite Materials

Metals ◽

10.3390/met10070874 ◽

2020 ◽

Vol 10 (7) ◽

pp. 874

Author(s):

Andrey A. Tsarkov ◽

Vladislav Yu. Zadorozhnyy ◽

Alexey N. Solonin ◽

Dmitri V. Louzguine-Luzgin

Keyword(s):

Mechanical Properties ◽

Testing Machine ◽

High Strength ◽

Alloying Elements ◽

Solid Matrix ◽

Complete Suppression ◽

Structural Investigations ◽

X Ray ◽

Composites Materials ◽

The Matrix

High-strength crystalline/amorphous composites materials based on (Ti-Ni)-(Cu-Zr) system were developed. The optimal concentrations of additional alloying elements Al, Fe, and Cr were obtained. Structural investigations were carried out using X-ray diffraction equipment (XRD) and scanning electron microscope (SEM) with an energy-dispersive X-ray module (EDX). It was found that additives of aluminum and chromium up to 5 at% dissolve well into the solid matrix solution of the NiTi phase. At a concentration of 5 at%, the precipitation of the unfavorable NiTi2 phase occurs, which, as a result, leads to a dramatic decrease in ductility. Iron dissolves very well in the solid solution of the matrix phase due to chemical affinity with nickel. The addition of iron does not cause the precipitation of the NiTi2 phase in the concentration range of 0–8 at%, but with an increase in concentration, this leads to a decrease in the mechanical properties of the alloy. The mechanical behavior of alloys was studied in compression test conditions on a universal testing machine. The developed alloys have a good combination of strength and ductility due to their dual-phase structure. It was shown that additional alloying elements lead to a complete suppression of the martensitic transformation in the alloys.

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