Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (2): 219-232.doi: https://doi.org/10.1007/s10483-022-2814-6
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Ye XIAO1,2, J. SHANG1,3, L. Z. KOU3, Chun LI1,2
Received:
2021-09-10
Revised:
2021-11-23
Published:
2022-01-25
Contact:
Chun LI, E-mail:lichun@nwpu.edu.cn
Supported by:
2010 MSC Number:
Ye XIAO, J. SHANG, L. Z. KOU, Chun LI. Surface deformation-dependent mechanical properties of bending nanowires: an ab initio core-shell model. Applied Mathematics and Mechanics (English Edition), 2022, 43(2): 219-232.
[1] NELA, L., MA, J., ERINE, C., XIANG, P., SHEN, T. H., TILELI, V., WANG, T., CHENG, K., and MATIOLI, E. Multi-channel nanowire devices for efficient power conversion. Nature Electronics, 4, 284-290 (2021) [2] FAN, S. Q. and CHEN, Z. G. Electric potential and energy band in ZnO nanofiber tuned by local mechanical loading. Applied Mathematics and Mechanics (English Edition), 42(6), 787-804 (2021) https://doi.org/10.1007/s10483-021-2736-5 [3] YANG, Y. and NI, Y. Elastic interaction between inclusions and tunable periodicity of superlattice structure in nanowires. Applied Mathematics and Mechanics (English Edition), 41(10), 1461-1478 (2020) https://doi.org/10.1007/s10483-020-2654-6 [4] LU, Z. X., XIE, F., LIU, Q., and YANG, Z. Y. Surface effects on mechanical behavior of elastic nanoporous materials under high strain. Applied Mathematics and Mechanics (English Edition), 36(7), 927-938 (2015) https://doi.org/10.1007/s10483-015-1958-9 [5] MENG, J. P. and LI, Z. Schottky-contacted nanowire sensors. Advanced Materials, 32, 2000130 (2020) [6] KIM, J., LEE, H. C., KIM, K. H., HWANG, M. S., PARK, J. S., LEE, J. M., SO, J. P., CHOI, J. H., KWON, S. H., BARRELET, C. J., and PARK, H. G. Photon-triggered nanowire transistors. Nature Nanotechnology, 12, 963-968 (2017) [7] ZUO, K., MOURIK, V., SZOMBATI, D. B., NIJHOLT, B., WOERKOM, D. J., GERESDI, A., CHEN, J., OSTROUKH, V. P., AKHMEROV, A. R., PLISSARD, S. R., CRA, D., BAKKERS, E., PIKULIN, D. I., KOUWENHOVEN, L. P., and FROLOV, S. M. Supercurrent interference in few-mode nanowire Josephson junctions. Physical Review Letters, 119, 187704 (2017) [8] ELSNER, B. A. M., MULLER, S., BARGMANN, S., and WEISSMULLER, J. Surface excess elasticity of gold: ab initio coefficients and impact on the effective elastic response of nanowires. Acta Materialia, 124, 468-477 (2017) [9] PISHKENARI, H. N., AFSHARMANESH, B., and AKBARI, E. Surface elasticity and size effect on the vibrational behavior of silicon nanoresonators. Current Applied Physics, 15, 1389-1396 (2015) [10] ZHUO, X. R. and BEOM, H. G. Atomistic study of the bending properties of silicon nanowires. Computational Materials Science, 152, 331-336 (2018) [11] CUENOT, S., FRETIGNY, C., CHAMPAGNE, S. D., and NYSTEN, B. Surface tension effect on the mechanical properties of nanomaterials measuredby atomic force microscopy. Physical Review B, 69, 165410 (2004) [12] CHEN, Y. X., DORGAN, B. L., MCLLROY, D. N., and ASTON, D. E. On the importance of boundary conditions on nanomechanical bending behavior and elastic modulus determination of silver nanowires. Journal of Applied Physics, 100, 104301 (2006) [13] TAN, E. P. S., ZHU, Y., YU, T., DAI, L., SOW, C. H., TAN, V. B. C., and LIM, C. T. Crystallinity and surface effects on Young's modulus of CuO nanowires. Applied Physics Letters, 90, 163112 (2007) [14] CELIK, E., GUVEN, I., and MADENCI, E. Mechanical characterization of nickelnanowires by using a customized atomicforce microscope. Nanotechnology, 22, 155702 (2011) [15] NAM, C. Y., JAROENAPIBAL, P., THAM, D., LUZZI, D. E., EVOY, S., and FISCHER, J. E. Diameter-dependent electromechanical properties of GaNnanowires. Nano Letter, 6, 153-158 (2006) [16] GAVAN, K. B., WESTRA, H. J. R., VAN DER DRIFT, E. W. J. M., VENSTRA, W. J., and VAN DER ZANT, H. S. J. Size-dependent effective Young's modulus of silicon nitride cantilevers. Applied Physics Letters, 94, 233108 (2009) [17] SADEGHIAN, H., YANG, C. K., GOOSEN, J. F. L., VAN DER DRIFT, E., BOSSCHE, A., FRENCH, P. J., and VAN KEULEN, F. Characterizing size-dependent effective elastic modulus of silicon nanocantilevers using electrostatic pull-in instability. Applied Physics Letters, 94, 221903 (2009) [18] SADEGHIAN, H., YANG, C. K., GOOSEN, J. F. L., BOSSCHE, A., STAUFER, U., FRENCH, P. J., and VAN KEULEN, F. Effects of size and defects on the elasticity of silicon nanocantilevers. Nanotechnology, 20, 064012 (2010) [19] GURTIN, M. E. and MURDOCH, A. I. A continuum theory of elastic material surfaces. Archive for Rational Mechanics and Analysis, 57, 291-323 (1975) [20] GURTIN, M. E. and MURDOCH, A. I. Surface stress in solids. International Journal of Solids and Structures, 14, 431-440 (1978) [21] STEIGMANN, D. J. and OGDEN, R. W. Plane deformations of elastic solids with intrinsic boundary elasticity. Proceedings of the Royal Society A, 453, 853-877 (1997) [22] CHHAPADIA, P., MOHAMMADI, P., and SHARMA, P. Curvature-dependent surface energy and implications for nanostructures. Journal of the Mechanics and Physics of Solids, 59, 2103-2115 (2011) [23] CHIU, M. S. and CHEN, T. Y. Effects of high-order surface stress on static bending behavior of nanowires. Physica E, 44, 714-718 (2011) [24] WANG, G. F. and FENG, X. Q. Effects of surface elasticity and residual surface tension on the natural frequency of microbeams. Applied Physics Letters, 90, 231904 (2007) [25] HE, J. and LILLEY, C. M. Surface stress effect on bending resonance of nanowires with different boundary conditions. Applied Physics Letters, 93, 263108 (2008) [26] SONG, F., HUANG, G. L., PARK, H. S., and LIU, X. N. A continuum model for the mechanical behavior of nanowires including surface and surface-induced initial stresses. International Journal of Solids and Structures, 48, 2154-2163 (2011) [27] LI, X. F., ZHANG, H., and LEE, K. Y. Dependence of Young's modulus of nanowires on surface effect. International Journal of Mechanical Sciences, 81, 120-125 (2014) [28] NIX, W. D. and GAO, H. J. An atomic interpretation of interface stress. Scripta Materialia, 39, 1653-1661 (1998) [29] SUN, C. Q., TAY, B. K., ZENG, X. T., LI, S., CHEN, T. P., ZHOU, J., BAI, H. L., and JIANG, E. Y. Bond-order-bond-length-bond-strength (bond-OLS) correlation mechanism for the shape-and-size dependence of a nanosolid. Journal of Physics: Condensed Matter, 14, 7781-7795 (2002) [30] SUN, C. Q., TAY, B. K., LAU, S. P., SUN, X. W., ZENG, X. T., LI, S., BAI, H. L., LIU, H., LIU, Z. H., and JIANG, E. Y. Bond contraction and lone pair interaction at nitride surfaces. Journal of Applied Physics, 90, 2615-2617 (2001) [31] OU-YANG, G., TAN, X., and YANG, G. W. Thermodynamic model of thesurface energy of nanocrystals. Physical Review B, 74, 195408 (2006) [32] DIAO, J., GALL, K., and DUMN, M. L. Atomistic simulation of the structure and elastic properties of gold nanowires. Journal of the Mechanics and Physics of Solids, 52, 1935-1962 (2004) [33] LEE, B. and RUDD, R. E. First-principles study of the Young's modulus of Si(001) nanowires. Physical Review B, 75, 041305(R) (2007) [34] CHEN, S. H. and YAO, Y. Elastic theory of nanomaterials based on surface energy density. Journal of Applied Mechanics, 81, 121002 (2014) [35] SYREITZ, F. H., CAMMARATA, R. C., and SIERADZKI, K. Surface-stress effects on elastic properties, I: thin metal films. Physical Review B, 49, 10699-10706 (1994) [36] LIANG, H. Y., UPMANYU, M., and HUANG, H. C. Size-dependent elasticityof nanowires: nonlinear effects. Physical Review B, 71, 241403 (2005) [37] OLSSON, P. A. T. and PARK, H. S. On the importance of surface elastic contributions to the flexural rigidity of nanowires. Journal of the Mechanics and Physics of Solids, 60, 2064-2083 (2012) [38] OU-YANG, G., LI, X. L., TAN, X., and YANG, G. W. Surface energy of nanowires. Nanotechnology, 19, 045709 (2008) [39] LIU, L. G. and BASSETT, W. A. Compression of Ag and phase transformation of NaCl. Journal of Applied Physics, 44, 1475-1479 (1973) [40] KLUG, H. P. A. Redetermination of the lattice constant of lead. Journal of the American Chemical Society, 68, 1493-1494 (1946) [41] HUBBARD, C. R., SWANSON, H. E., and MAUER, F. A. A silicon powder diffraction standard reference material. Journal of Applied Crystallography, 8, 45-48 (1975) [42] LEE, B. J., SHIM, J. H., and BASKES, M. I. Semiempirical atomic potentials for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, Al, and Pb based on first and second nearest-neighbor modified embedded atom method. Physical Review B, 68, 144112 (2003) [43] WORTMAN, J. J. and EVANS, R. A. Young's modulus, shear modulus, and Poisson's ratio in silicon and germanium. Journal of Applied Physics, 36, 153-156 (1965) [44] SIMMONS, G. and WANG, H. Single Crystal Elastic Constants and Calculated Aggregate Properties, M. I. T. Press, Cambridge (1971) [45] ROLNICK, H. Tension coefficient of resistance of metals. Physical Review, 36, 506-512 (1930) [46] JING, G. Y., DUAN, H. L., SUN, X. M., ZHANG, Z. S., XU, J., LI, Y. D., WANG, J. X., and YU, D. P. Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy. Physical Review B, 73, 235409 (2006) [47] MILLER, R. E. and SHENOY, V. B. Size-dependent elastic properties of nanosized structural elements. Nanotechnology, 11, 139-147 (2000) [48] YAO, Y. and CHEN, S. H. Surface effect in the bending of nanowires. Mechanics of Materials, 100, 12-21 (2016) [49] PARK, S. H., KIM, J. S., PARK, J. H., LEE, J. S., CHOI, Y. K., and KWON, O. M. Molecular dynamics study on size-dependent elastic properties of silicon nanocantilevers. Thin Solid Films, 492, 285-289 (2005) [50] PARK, H. S. and KLEIN, P. A. Surface stress effects on the resonant properties of metal nanowires: the importance of finite deformation kinematics and the impact of the residual surface stress. Journal of the Mechanics and Physics of Solids, 56, 3144-4166 (2008) [51] MOHAMMADI, P. and SHARMA, P. Atomistic elucidation of the effect of surface roughness on curvature dependent surface energy, surface stress, and elasticity. Applied Physics Letters, 100, 133110 (2012) |
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