Extreme values of the shear modulus for hexagonal crystals

Goldstein, R. V.; Городцов, В. А.; Komarova, M.A.; Lisovenko, D. S.

doi:10.1016/j.scriptamat.2017.07.002

Cited by 13 publications

(6 citation statements)

References 9 publications

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“…The analysis of variability of shear modulus presented in ref. showed that for hexagonal structures four stationary values can be found:

G_{1} = \frac{1}{s_{44}}

for

θ = 0

and any

ψ

angles, and also at

θ = π / 2

ψ = 0

;

G_{2} = \frac{1}{{normals}_{44} true(1 + Π_{3} true)} = \frac{1}{s_{66}}

is obtained at

θ = ψ = π / 2

;

G_{3} = \frac{1}{{normals}_{44} true(1 + Π_{03} true)} = \frac{1}{s_{11} + s_{33} - 2 s_{13}}

is achieved at

θ = π / 4

ψ = 0

, and

θ = 3 π / 4

ψ = 0

;

G_{4}^{- 1} = s_{44} true(1 + Π_{3} - \frac{Π_{3}^{2}}{{4 Π}_{03}} true)

possible for

θ_{0}

ψ_{0}

0 \leq {normalcos}^{}

…”

Section: Resultsmentioning

confidence: 97%

“…For the structures with hexagonal anisotropy Young's modulus and Poisson's ratio are defined as:

\frac{1}{s_{11} E} = 1 + true(Π_{1} - Π_{01} {sin}^{2} θ true) {cos}^{2} θ

- \frac{ν}{s_{13} E} = 1 + true(Π_{2} {sin}^{2} ψ + Π_{02} {cos}^{2} θ {cos}^{2} ψ true) {sin}^{2} θ

\frac{1}{s_{44} G} = 1 + true(Π_{3} {sin}^{2} ψ + 4 Π_{03} {cos}^{2} θ {cos}^{2} ψ true) {sin}^{2} θ

Π_{01} \equiv \frac{δ}{s_{11}}, Π_{02} \equiv \frac{δ}{s_{13}}, Π_{03} \equiv \frac{δ}{s_{44}}

…”

Section: Resultsmentioning

confidence: 99%

“…For example, in ref. it was shown that Cd has negative Poisson's ratio, which was proved to be wrong . This mistake is connected with the wrong calculation of the compliance coefficients and it was shown that Poisson's ratio of Cd ranges from 0.1 to 0.7 …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Elastic Properties of Fullerites and Diamond‐Like Phases

Rysaeva

Baimova

Lisovenko

et al. 2018

Physica Status Solidi (b)

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Diamond‐like structures, that include sp2 and sp3 hybridized carbon atoms, are of considerable interest nowadays. In the present work, various carbon auxetic structures are studied by the combination of molecular dynamics (MD) and analytical approach. Two fullerites based on the fullerene C60 and fullerene‐like molecule C48 are investigated as well as diamond‐like structures based on other fullerene‐like molecules (called fulleranes), carbon nanotubes (called tubulanes) and graphene sheets. MD is used to find the equilibrium states of the structures and calculate compliance and stiffness coefficients for stable configurations. Analytical methods are used to calculate the engineering elastic coefficients (Young's modulus, Poisson's ratio, shear modulus and bulk modulus), and to study their transformation under rotation of the coordinate system. All the considered structures are partial auxetics with the negative value of Poisson's ratio for properly chosen tensile directions. It is shown that some of these structures, in a particular tension direction, have a very high Young's modulus, that is, 1852 GPa for tubulane TA6.

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“…The analysis of variability of shear modulus presented in ref. showed that for hexagonal structures four stationary values can be found:

G_{1} = \frac{1}{s_{44}}

for

θ = 0

and any

ψ

angles, and also at

θ = π / 2

ψ = 0

;

G_{2} = \frac{1}{{normals}_{44} true(1 + Π_{3} true)} = \frac{1}{s_{66}}

is obtained at

θ = ψ = π / 2

;

G_{3} = \frac{1}{{normals}_{44} true(1 + Π_{03} true)} = \frac{1}{s_{11} + s_{33} - 2 s_{13}}

is achieved at

θ = π / 4

ψ = 0

, and

θ = 3 π / 4

ψ = 0

;

G_{4}^{- 1} = s_{44} true(1 + Π_{3} - \frac{Π_{3}^{2}}{{4 Π}_{03}} true)

possible for

θ_{0}

ψ_{0}

0 \leq {normalcos}^{}

…”

Section: Resultsmentioning

confidence: 97%

“…For the structures with hexagonal anisotropy Young's modulus and Poisson's ratio are defined as:

\frac{1}{s_{11} E} = 1 + true(Π_{1} - Π_{01} {sin}^{2} θ true) {cos}^{2} θ

- \frac{ν}{s_{13} E} = 1 + true(Π_{2} {sin}^{2} ψ + Π_{02} {cos}^{2} θ {cos}^{2} ψ true) {sin}^{2} θ

\frac{1}{s_{44} G} = 1 + true(Π_{3} {sin}^{2} ψ + 4 Π_{03} {cos}^{2} θ {cos}^{2} ψ true) {sin}^{2} θ

Π_{01} \equiv \frac{δ}{s_{11}}, Π_{02} \equiv \frac{δ}{s_{13}}, Π_{03} \equiv \frac{δ}{s_{44}}

…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Elastic Properties of Fullerites and Diamond‐Like Phases

Rysaeva

Baimova

Lisovenko

et al. 2018

Physica Status Solidi (b)

Self Cite

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show abstract

“…The engineering elastic coefficients (Young's modulus E, Poisson's ratio ν and shear modulus G) depend on the orientation of the deformed crystal. In the case of the hexagonal crystal family, the expressions for Young's modulus E, Poisson's ratio ν and the shear modulus G have the forms [44]: where s ij are matrix compliance coefficients. Dimensionless parameters Π 1 , Π 2 , Π 3 , Π 01 , Π 02 , Π 03 and dimensional coefficient δ are the characteristics of the degree of crystal anisotropy.…”

Section: Elastic Properties Of the Cef 3 Crystalsmentioning

confidence: 99%

Bridgman Growth and Physical Properties Anisotropy of CeF3 Single Crystals

et al. 2021

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“…The elastic properties of hexagonal crystals are analyzed in [3][4][5][6][7][8][9][10]. Young's modulus, Poisson's ratio and shear modulus for hexagonal Tl and Cd crystals are studied for some particular orientations in [3].…”

Section: Introductionmentioning

confidence: 99%

Variability of Young’s modulus and Poisson’s ratio of hexagonal crystals

Komarova

Городцов

Lisovenko

2018

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. In this paper, the variability of elastic characteristics (Young's modulus and Poisson's ratio) of hexagonal crystals has been studied. Analytic expressions for Young's modulus and Poisson's ratio are obtained. Stationary values for these elastic characteristics are found. Young's modulus has three stationary values, and Poisson's ratio has eight stationary values. Numerical analysis of these elastic characteristics for hexagonal crystals is given based on the experimental data from the Landolt-Börnstein handbook. Global extrema of Young's modulus and Poisson's ratio for hexagonal crystals are found. Crystals are found in which the maximum values exceeds the upper limit for isotropic materials.

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Extreme values of the shear modulus for hexagonal crystals

Cited by 13 publications

References 9 publications

Elastic Properties of Fullerites and Diamond‐Like Phases

Elastic Properties of Fullerites and Diamond‐Like Phases

Bridgman Growth and Physical Properties Anisotropy of CeF3 Single Crystals

Variability of Young’s modulus and Poisson’s ratio of hexagonal crystals

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