A dislocation model for the plastic relaxation of the transformation strain energy of a misfitting spherical particle

Residual stress and crystalline defects in silicon wafers can affect solar cell reliability and performance. Infrared photoelastic measurements are performed for stress mapping in monocrystalline silicon photovoltaic (PV) wafers and compared to photoluminescence (PL) measurements. The wafer stresses are then quantified using a discrete dislocation-based numerical modeling approach, which leads to simulated photoelastic images. The model accounts for wafer stress relaxation due to dislocation structures. The wafer strain energy is then analyzed with respect to the orientation of the dislocation structures. The simulation shows that particular locations on the wafer have only limited slip systems that reduce the wafer strain energy. Experimentally observed dislocation structures are consistent with these observations from the analysis, forming the basis for a more quantitative infrared photoelasticity-based inspection method.

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Diffusion Induced Stress and Strain Energy in a Phase-Transforming Spherical Particle

ECS Meeting Abstracts ◽

10.1149/ma2011-02/15/731 ◽

2011 ◽

Keyword(s):

Spherical Particle ◽

Strain Energy ◽

Stress And Strain ◽

Induced Stress ◽

Diffusion Induced Stress

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Strain and interface energy of ellipsoidal inclusions subjected to volumetric eigenstrains: shape factors

Archive of Applied Mechanics ◽

10.1007/s00419-021-02066-1 ◽

2022 ◽

Author(s):

H. J. Böhm ◽

G. A. Zickler ◽

F. D. Fischer ◽

J. Svoboda

Keyword(s):

Elastic Strain ◽

Strain Energy ◽

Materials Science ◽

Elastic Strain Energy ◽

Transformation Strain ◽

Interface Energy ◽

Shape Factors ◽

Computational Materials Science ◽

The Matrix ◽

Computational Materials

AbstractThermodynamic modeling of the development of non-spherical inclusions as precipitates in alloys is an important topic in computational materials science. The precipitates may have markedly different properties compared to the matrix. Both the elastic contrast and the misfit eigenstrain may yield a remarkable generation of elastic strain energy which immediately influences the kinetics of the developing precipitates. The relevant thermodynamic framework has been mostly based on spherical precipitates. However, the shapes of actual particles are often not spherical. The energetics of such precipitates can be met by adapting the spherical energy terms with shape factors. The well-established Eshelby framework is used to evaluate the elastic strain energy of inclusions with ellipsoidal shapes (described by the axes a, b, and c) that are subjected to a volumetric transformation strain. The outcome of the study is two shape factors, one for the elastic strain energy and the other for the interface energy. Both quantities are provided in the form of easy-to-use diagrams. Furthermore, threshold elastic contrasts yielding strain energy shape factors with the value 1.0 for any ellipsoidal shape are studied.

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Plastic yielding from sharp notches

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1964.0085 ◽

1964 ◽

Vol 279 (1376) ◽

pp. 1-9 ◽

Cited By ~ 75

Keyword(s):

High Strain ◽

Finite Thickness ◽

Numerical Calculations ◽

Plastic Relaxation ◽

Dislocation Model ◽

Plastic Yielding ◽

Similar Model ◽

Uniform Stress ◽

Macroscopic Theory ◽

Plastic Displacement

In a previous paper a model of a relaxed crack has been treated in which the plastic relaxation round an isolated crack is represented by an array of dislocations collinear with the crack itself. A similar model is used here to consider the behaviour of an infinite row of relaxed cracks subject to a uniform stress at infinity. The model is used to represent a plastic notch in a plate of finite thickness and the results compared with numerical calculations for the same problem using the macroscopic theory of plasticity. Compared with the dislocation model of the isolated crack, the relaxation spreads further in the presence of other cracks and the length of the relaxed zone required to accommodate a given plastic displacement at a tip is increased by about 10 %. Some applications of the results to the theory of notch brittleness and to high-strain fatigue are briefly discussed.

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The wustite-spinel interface

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100126226 ◽

1987 ◽

Vol 45 ◽

pp. 268-269

Author(s):

S.R. Summerfelt ◽

C.B. Carter

Keyword(s):

Solid State ◽

Solid State Reaction ◽

Strain Energy ◽

Matrix Material ◽

Lattice Misfit ◽

Solid State Reactions ◽

Oxygen Sublattice ◽

Large Particles ◽

Small Lattice ◽

Coherent Interfaces

The wustite-spinel interface can be viewed as a model interface because the wustite and spinel can share a common f.c.c. oxygen sublattice such that only the cations distribution changes on crossing the interface. In this study, the interface has been formed by a solid state reaction involving either external or internal oxidation. In systems with very small lattice misfit, very large particles (>lμm) with coherent interfaces have been observed. Previously, the wustite-spinel interface had been observed to facet on {111} planes for MgFe2C4 and along {100} planes for MgAl2C4 and MgCr2O4, the spinel then grows preferentially in the <001> direction. Reasons for these experimental observations have been discussed by Henriksen and Kingery by considering the strain energy. The point-defect chemistry of such solid state reactions has been examined by Schmalzried. Although MgO has been the principal matrix material examined, others such as NiO have also been studied.

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