Dependence on Temperature of the Interlayer Spacing in Carbons of Different Graphitic Perfection

Steward, E. G.; Cook, B. P.; Kellett, E. A.

doi:10.1038/1871015a0

Cited by 95 publications

(37 citation statements)

References 4 publications

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“…The present calculation results of in-plane and out-of-plane CTE are shown in Figures 10 and 11, respectively, which are in good agreement with experimental data [27,35,36]. [35,36] are also shown.…”

Section: Cte Of Graphitesupporting

confidence: 76%

A continuum thermal stress theory for crystals based on interatomic potentials

Tang

Wang

2014

Sci. China Phys. Mech. Astron.

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This paper presents a new continuum thermal stress theory for crystals based on interatomic potentials. The effect of finite temperature is taken into account via a harmonic model. An EAM potential for copper is adopted in this paper and verified by computing the effect of the temperature on the specific heat, coefficient of thermal expansion and lattice constant. Then we calculate the elastic constants of copper at finite temperature. The calculation results are in good agreement with experimental data. The thermal stress theory is applied to an anisotropic crystal graphite, in which the Brenner potential is employed. Temperature dependence of the thermodynamic properties, lattice constants and thermal strains for graphite is calculated. The calculation results are also in good agreement with experimental data. Citation:Liu X L, Tang Q H, Wang T C. A continuum thermal stress theory for crystals based on interatomic potentials.

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Section: Cte Of Graphitesupporting

confidence: 76%

A continuum thermal stress theory for crystals based on interatomic potentials

Tang

Wang

2014

Sci. China Phys. Mech. Astron.

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“…In particular, graphite is known to have NTE at not too high temperatures [29], which may be explained quantitatively within a quasiharmonic theory [2][3][4][5][6] via first-principles calculations of phonon spectra and Grüneisen parameters [26]. The same calculations predicted that graphene should have NTE at any temperatures.…”

Section: Introductionmentioning

confidence: 84%

“…(D14) and (D18) we obtain the renormalization group equations (29) and (30) of the main text. We see that q uv ∼ min{λ, µ}/κ is a natural ultraviolet cut-off for the renormalization group equations (29) and (30).…”

mentioning

confidence: 99%

Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

et al. 2016

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We explore thermodynamics of a quantum membrane, with a particular application to suspended graphene membrane and with a particular focus on the thermal expansion coefficient. We show that an interplay between quantum and classical anharmonicity-controlled fluctuations leads to unusual elastic properties of the membrane. The effect of quantum fluctuations is governed by the dimensionless coupling constant, g0 ≪ 1, which vanishes in the classical limit ( → 0) and is equal to ≃ 0.05 for graphene. We demonstrate that the thermal expansion coefficient αT of the membrane is negative and remains nearly constant down to extremely low temperatures, T0 ∝ exp(−2/g0). We also find that αT diverges in the classical limit: αT ∝ − ln(1/g0) for g0 → 0. For graphene parameters, we estimate the value of the thermal expansion coefficient as αT ≃ −0.23 eV −1 , which applies below the temperature Tuv ∼ g0κ0 ∼ 500 K (where κ0 ∼ 1 eV is the bending rigidity) down to T0 ∼ 10 −14 K. For T < T0, the thermal expansion coefficient slowly (logarithmically) approaches zero with decreasing temperature. This behavior is surprising since typically the thermal expansion coefficient goes to zero as a power-law function. We discuss possible experimental consequences of this anomaly. We also evaluate classical and quantum contributions to the specific heat of the membrane and investigate the behavior of the Grüneisen parameter.

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“…(a) (b) Figure 5: (a) CTE for graphite [48] and SGI matrix [49]. (b) Equivalent CTE calculated for the nodule model with different number of internal conical sectors subjected to free cooling without external matrix constraints.…”

Section: Equivalent Cte For the Nodulesmentioning

confidence: 99%

A micro-mechanical analysis of thermo-elastic properties and local residual stresses in ductile iron based on a new anisotropic model for the graphite nodules

Andriollo¹,

Thorborg²,

Tiedje³

et al. 2016

Modelling Simul. Mater. Sci. Eng.

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In this paper, the thermo-elastic behavior of the graphite nodules contained in ductile iron is derived on the basis of recent transmission electron microscopy investigations of their real internal structure. The proposed model is initially validated by performing a finite element homogenization analysis to verify its consistency with the room-temperature elastic properties of ductile iron measured at the macro scale. Subsequently, it is used to investigate the formation of local residual stresses around the graphite particles by simulating the manufacturing process of a typical ferritic ductile iron grade, and the results are compared with preliminary measurements using synchrotron X-rays. Finally, the obtained accurate description of the stress & strain field at the micro scale is used to shed light on common failure modes reported for the nodules and on some peculiar properties observed in ductile iron at both micro and macro scale.

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Dependence on Temperature of the Interlayer Spacing in Carbons of Different Graphitic Perfection

Cited by 95 publications

References 4 publications

A continuum thermal stress theory for crystals based on interatomic potentials

A continuum thermal stress theory for crystals based on interatomic potentials

Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

A micro-mechanical analysis of thermo-elastic properties and local residual stresses in ductile iron based on a new anisotropic model for the graphite nodules

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