Existence of a negative Poisson ratio in fcc crystals

Milstein, Frederick; Huang, Kan

doi:10.1103/physrevb.19.2030

Cited by 167 publications

(108 citation statements)

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“…For example, Baughman et al 7 reported that 69% of all cubic materials exhibit a negative Poisson's ratio along the [1 10]-direction when they are subjected to stretching along the [110]-direction. The origin of such single-crystal directional stretching had been previously explained by Milstein and Huang 9 . Negative Poisson's ratios were also observed in some materials near phase transitions [31][32][33][34][35] .…”

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confidence: 99%

“…W hen stretched, materials with a negative Poisson's ratio become thicker in the direction perpendicular to the original force [1][2][3][4][5][6][7][8][9][10][11] . Materials exhibiting such counterintuitive behaviour, known as auxetics, are of great interest not only because they are rare, but also because of their numerous potential applications in various fields, such as the design of fasteners 12 , prostheses 13 , pizeocomposites 14,15 , filters 16 , earphones 17 , seat cushions 18,19 and superior dampers 20 .…”

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confidence: 99%

“…Among structural networks are molecular networks 3 , hierarchical structures 4 , composites 5 and hinged structures 22,23 . Some materials exhibit auxetic properties as they are stretched or compressed in a proper direction [6][7][8][9][24][25][26][27][28][29][30] . For example, Baughman et al 7 reported that 69% of all cubic materials exhibit a negative Poisson's ratio along the [1 10]-direction when they are subjected to stretching along the [110]-direction.…”

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confidence: 99%

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Negative Poisson’s ratios in metal nanoplates

et al. 2014

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The Poisson's ratio is a fundamental measure of the elastic-deformation behaviour of materials. Although negative Poisson's ratios are theoretically possible, they were believed to be rare in nature. In particular, while some studies have focused on finding or producing materials with a negative Poisson's ratio in bulk form, there has been no such study for nanoscale materials. Here we provide numerical and theoretical evidence that negative Poisson's ratios are found in several nanoscale metal plates under finite strains. Furthermore, under the same conditions of crystal orientation and loading direction, materials with a positive Poisson's ratio in bulk form can display a negative Poisson's ratio when the material's thickness approaches the nanometer scale. We show that this behaviour originates from a unique surface effect that induces a finite compressive stress inside the nanoplates, and from a phase transformation that causes the Poisson's ratio to depend strongly on the amount of stretch.

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Negative Poisson’s ratios in metal nanoplates

et al. 2014

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“…For example, negative Poisson's ratio has been observed in cubic materials 13,14 and also crystalline SiO 2 (ref. 15).…”

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Negative poisson’s ratio in single-layer black phosphorus

2014

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The Poisson's ratio is a fundamental mechanical property that relates the resulting lateral strain to applied axial strain. Although this value can theoretically be negative, it is positive for nearly all materials, though negative values have been observed in so-called auxetic structures. However, nearly all auxetic materials are bulk materials whose microstructure has been specifically engineered to generate a negative Poisson's ratio. Here we report using first-principles calculations the existence of a negative Poisson's ratio in a single-layer, two-dimensional material, black phosphorus. In contrast to engineered bulk auxetics, this behaviour is intrinsic for single-layer black phosphorus, and originates from its puckered structure, where the pucker can be regarded as a re-entrant structure that is comprised of two coupled orthogonal hinges. As a result of this atomic structure, a negative Poisson's ratio is observed in the out-of-plane direction under uniaxial deformation in the direction parallel to the pucker.

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“…In contrast to mathematical expressions and their graphical representations for Young's modulus, Poisson's ratio and the shear modulus, as a function of crystal orientation for cubic crystals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], expressions in the literature for the orientation dependence of the biaxial modulus of cubic materials subjected to an equi-biaxial elastic strain are limited to circumstances where this strain is in a {001}, {111} or {011} plane [17][18][19][20][21][22][23]. In almost all studies in which biaxial moduli are of interest, the material can reasonably be assumed to be isotropic, e.g., if the material is a glass or a fully annealed polycrystalline metal or ceramic.…”

Section: Introductionmentioning

confidence: 99%

The Biaxial Moduli of Cubic Materials Subjected to an Equi-biaxial Elastic Strain

Knowles

2015

J Elast

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Formulae for the biaxial moduli along the directions of principal stress for (hkl) interfaces of cubic materials are given for situations in which there is equi-biaxial strain within the plane. These formulae are relevant in the consideration of the deposition of thin films on single crystal substrates such as silicon. Within a particular (hkl), the directions defining these principal biaxial moduli are shown to be those along which there are the extreme values of the shear modulus and Poisson's ratio. Conditions for stationary values of the biaxial moduli are also derived, from which the conditions for the global extrema of the biaxial moduli are established.

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Existence of a negative Poisson ratio in fcc crystals

Cited by 167 publications

References 12 publications

Negative Poisson’s ratios in metal nanoplates

Negative Poisson’s ratios in metal nanoplates

Negative poisson’s ratio in single-layer black phosphorus

The Biaxial Moduli of Cubic Materials Subjected to an Equi-biaxial Elastic Strain

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