Symmetry lowering and surface elasticity effects on Young’s modulus and Poisson’s ratio of nanofilms

Li, Jiangang; Narsu, B.; Yun, Guohong; Wang, Aoxuan; Gao, Zhixiang

doi:10.1007/s00339-018-2231-z

Cited by 11 publications

(13 citation statements)

References 35 publications

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“…This coupling characteristic is similar with the volume dependence c / a in the hexagonal crystal materials 28 . Since the vertical direction always behaves inverse relaxation comparing to in-plane directions, the additional surface elastic constant has different sign from other surface elastic constants 33 . This symmetry lowering effect is derived mathematically, but not only qualitative analysis here.…”

Section: Resultsmentioning

confidence: 98%

“…For example, surface stress compresses the film along in-plane directions while the vertical direction expands via Poisson’s effect. This equilibrium property makes lowered symmetry of nanofilms 33 . If top and bottom surface stresses are not balance, the nanofilm will bend even curl into a nanotube 27 .…”

Section: Resultsmentioning

confidence: 99%

“…In consideration of the rule of Poisson’s effect, the vertical relaxation procedure should be inversely. For example, if the in-plane direction is expanded (compressed) by intrinsic surface stress, the vertical direction will be relaxed inwards (outwards) 33 .…”

Section: Resultsmentioning

confidence: 99%

“…The lattice constant difference between in-plane and vertical directions introduces lowered symmetry of nanofilms. This lowered symmetry introduces an additional elastic constant which is no bulk counterpart 28,33 . And this additional elastic constant relates to the interactions of expansion and vertical lattice relaxation.…”

Section: Resultsmentioning

confidence: 99%

“…While, the vertical direction lattice constant is not only different from bulk material but also different from the in-plane direction counterpart. The lattice constant difference between these two directions induces a lowered symmetry of the nanofilm 33,34 . And the intrinsic surface stress makes the bending behavior of a nanofilm be very different from macroscopic thick film counterpart.…”

Section: Introductionmentioning

confidence: 99%

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Surface effects on the self equilibrium, self bending and symmetry lowering of nanofilms

Han

et al. 2019

Sci Rep

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A continuum theoretical scheme for self equilibrium, self bending and symmetry lowering of nanofilms was obtained by considering surface elasticity, surface stress and the corresponding surface slice thickness. When surface stress and surface elasticity are both balance, the nanofilm is simply compressed (or expanded). When the surface stress or surface elasticity is imbalance, the nanofilm will bend. On the other hand, surface stress and surface elasticity imbalances induce a nanofilm to curl into a nanotube when the nanofilm is very thin. The surface stress and surface elasticity balances induce uniform in-plane strain (the overall film relaxation), while the vertical direction of the nanofilm relaxes reversely due to Poisson’s effect. And then, the crystal lattice constants of in-plane and vertical directions are different from each other, the ratio of these two lattice constants decrease with film thickness increase. Hence, the symmetry of the nanofilm is lowered by the overall film relaxation.

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Section: Resultsmentioning

confidence: 98%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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