Stability criteria for homogeneously stressed materials and the calculation of elastic constants

Zhou, Zicong; Joós, Béla

doi:10.1103/physrevb.54.3841

Cited by 95 publications

(94 citation statements)

References 24 publications

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“…We have shown that Born's results are valid only when the solid is under no load, by invoking the formulation of a Gibbs integral [6]. Further discussions were given by Zhou and Joos [7] and by Morris and Krenn [8], the latter emphasizing the thermodynamic basis of the concept of theoretical strength by showing the generalized stability criteria [6] are consistent with the internal conditions for elastic stability formulated by Gibbs in 1876. A consequence of these investigations is that theoretical strength should be considered a property which can be affected by the symmetry and magnitude of the applied load, rather than an intrinsic property of the material.…”

Section: Theoretical Strength: the Elastic Limitmentioning

confidence: 95%

Elastic criterion for dislocation nucleation

Zhu

Yip

et al. 2004

Materials Science and Engineering: A

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The notion of theoretical strength, the critical stress at which a perfect crystal under uniform loading becomes structurally unstable, is extended to non-uniform loading. A position-dependent defect nucleation criterion has been derived and applied in molecular dynamics (MD) and finite-element simulations of dislocation emission in single-crystal nanoindentation. The resulting measure has the physical meaning of a local stiffness; it provides a rigorous basis for modeling the incipient plasticity in a thin-film material. Furthermore, a close connection has been shown to exist between the initial unstable elastic wave and the final atomistic defect.

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Section: Theoretical Strength: the Elastic Limitmentioning

confidence: 95%

Elastic criterion for dislocation nucleation

Zhu

Yip

et al. 2004

Materials Science and Engineering: A

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“…The stability criteria of material under pressure are similar to those under zero pressure, just replacing C ij withC ij (i = j = 1, 2, 3, 4, 5, 6) [35]. As for Fe 2 B in the tetragonal structure, there are six independent elastic constants, C 11 , C 12 , C 13 , C 33 , C 44 , C 66 , because C 22 = C 11 , C 23 = C 13 , C 44 = C 55 as a result of the crystal symmetry.…”

Section: Elastic Properties Under Pressurementioning

confidence: 99%

Anisotropic elastic properties of FexB (x = 1, 2, 3) under pressure. First-principles study

Gueddouh

Bentria

Bourourou³

et al. 2016

Materials Science-Poland

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Spin-polarization (SP) and pressure effects have been used to better clarify and understand anisotropic elastic properties of Fe-B intermetallic compounds using the first-principles calculation with generalized gradient approximation (GGA) within the plane-wave pseudopotential density functional theory. Elastic properties, including bulk, shear and Young's moduli as well as Poisson ratio were obtained by Voigt-Reuss-Hill approximation. All studied Fe-B compounds were mechanically stable. The brittle and ductile properties were discussed using bulk to shear moduli ratio (B/G) of the studied structures in the pressure range of 0 GPa to 90 GPa in order to predict the critical pressure of phase transition from ferromagnetic (FM) to nonmagnetic (NM) state. Mechanical anisotropy in both cases was discussed by calculating different anisotropic indexes and factors. We have plotted three-dimensional (3D) surfaces and planar contours of the bulk and Young's moduli of Fe x B (x = 1, 2, 3) compounds for some crystallographic planes, (1 0 0), (0 1 0) and (0 0 1), to reveal their elastic anisotropy. On the basis of anisotropic elastic properties the easy and hard axes of magnetization for the three studied compounds were predicted.

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“…These rather simple criteria have been helpful in elucidating simulation results on structural phase stability [28,54]. Further discussions of the stability criteria may be found in the literature [40,54,55,59]. In the following we confine our attention to intrinsic or ideal behavior of homogeneous deformation of a defect-free the crystal, conditions achievable only in simulation.…”

Section: Theoretical Strength Of Materialsmentioning

confidence: 99%

Multiscale Materials Modelling: Case Studies at the Atomistic and Electronic Structure Levels

Silva¹,

Först²,

et al. 2007

ESAIM: M2AN

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Abstract.Although the intellectual merits of computational modelling across various length and time scales are generally well accepted, good illustrative examples are often lacking. One way to begin appreciating the benefits of the multiscale approach is to first gain experience in probing complex physical phenomena at one scale at a time. Here we discuss materials modelling at two characteristic scales separately, the atomistic level where interactions are specified through classical potentials and the electronic level where interactions are treated quantum mechanically. The former is generally sufficient for dealing with mechanical deformation at large strain, whereas the latter is necessary for treating chemical reactions or electronic transport. We will discuss simulations of defect nucleation using molecular dynamics, the study of water-silica reactions using a tight-binding approach, the design of a semiconductor-oxide interface using density functional theory, and the analysis of conjugated polymer in molecular actuation using Hartree-Fock calculations. The diversity of the problems discussed notwithstanding, our intent is to lay the groundwork for future problems in materials research, a few will be mentioned, where modelling at the electronic and atomistic scales are needed in an integrated fashion. It is in these problems that the full potential of multiscale modelling can be realized.Mathematics Subject Classification. 74A25, 74A45, 74F25, 74M05, 81V55.

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Stability criteria for homogeneously stressed materials and the calculation of elastic constants

Cited by 95 publications

References 24 publications

Elastic criterion for dislocation nucleation

Elastic criterion for dislocation nucleation

Anisotropic elastic properties of FexB (x = 1, 2, 3) under pressure. First-principles study

Multiscale Materials Modelling: Case Studies at the Atomistic and Electronic Structure Levels

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