Vai trò của tính đàn hồi ở ranh giới trong sự không ổn định hình thái của giao diện heteroepitaxy

Abadias, G., Chason, E., Keckes, J., Sebastiani, M., Thompson, G., Barthel, E., Doll, G., Murray, C., Stoessel, C., Martinu, L.: Stress in thin films and coatings: current status, challenges, and prospects. J. Vac. Sci. Technol. A 36, 020801 (2018) Altenbach, H., Eremeyev, V.A., Morozov, N.F.: Surface viscoelasticity and effective properties of thin-walled structures at the nanoscale. Int. J. Eng. Sci. 59, 83–89 (2012) Andrews, A.M., Speck, J.S., Romanov, A.E., Bobeth, M., Pompe, W.: Modeling cross-hatch surface morphology in growing mismatched layers. J. Appl. Phys. 91, 1933–1943 (2002) Angheluta, L., Mathiesen, J.: Thermodynamics of stressed solids: Slow deformation and roughnening of material interfaces. Eur. Phys. J. Special Topics 178, 123–132 (2009) Angheluta, L., Jettestuen, E., Mathiesen, J.: Thermodynamics and roughening of solid-solid interfaces. Phys. Rev. E 79, 031601 (2009) Angheluta, L., Jettestuen, E., Mathiesen, J., Renard, F., Jamtveit, B.: Stress-driven phase transformation and the roughnening of solid-solid interfaces. Phys. Rev. Lett. 100, 096105 (2008) Aqua, J.-N., Favre, L., Ronda, A., Benkouider, A., Berbezier, I.: Configurable Compliant Substrates for SiGe Nanomembrane Fabrication. Cryst. Growth Des. 15, 3399–3406 (2015) Avouris, P.: Manipulation of matter at the atomic and molecular levels. Acc. Chem. Res. 28, 95–102 (1995) Asaro, R.J., Tiller, W.A.: Interface morphology development during stress-corrosion cracking: Part I. Via surface diffusion. Metall. Mater. Trans. 3, 1789–1796 (1972) Benveniste, Y., Miloh, T.: Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech. Mater. 33, 309–323 (2001) Berrehar, J., et al.: Surface patterns on single-crystal films under uniaxial stress: Experimental evidence for the Grinfeld instability. Phys. Rev. B 46, 13487–13495 (1992) Bochkarev, A.O., Grekov, M.A.: Influence of surface stresses on the nanoplate stiffness and stability in the Kirsch problem. Phys. Mesomech. 22, 209–223 (2019) Cahn, J.W.: On spinodal decomposition. Acta Metall. 9, 795–801 (1961) Cahn, J.W., Larche, F.: Surface stress and the chemical-equilibrium of small crystals. II. Solid particles embedded in a solid matrix. Acta Metall. 30, 51–56 (1982) Cammarata, R.C.: Surface and interface stress effects in thin films. Prog. Surf. Sci. 46, 1–38 (1994) Chiu, C.-H., Poh, C.T., Huang, Z.: Morphological stability of the Stranski-Krastanow systems under an electric field. Applied Physics Letters 88, 241906 (2006) Chen, L.-Q., Wang, Y.: The continuum field approach to modeling microstructural evolution. JOM 48, 13–18 (1996) Chen, T., Chiu, M.-S., Weng, M.-S.: Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids. J. Appl. Phys. 100, 074308 (2006) Colin, J., Grilhe, J., Junqua, N.: Morphological instabilities of a stressed pore channel. Acta Mater. 45, 3835–3841 (1997) Colin, J., Thilly, L., Lecounturier, F., Peyrade, J.P., Grilhé, J., Askenazy, S.: Axial and radial interface instabilities of copper/tantalum cylindrical conductors. Acta metall. 47, 2761–2768 (1999) Collins, J.B., Levine, H.: Diffuse interface model of diffusion-limited crystal growth. Phys. Rev. B 31, 6119 (1985) Dai, M., Li, M., Schiavone, P.: Plane deformations of an inhomogeneity-matrix system incorporating a compressible liquid inhomogeneity and complete Gurtin-Murdoch interface model. Journal of Applied Mechanics 85, 121010 (2018) Dai, M., Gharahi, A., Schiavone, P.: Analytic solution for a circular nano-inhomogeneity with interface stretching and bending resistance in plane strain deformations. Appl. Math. Model. 55, 160–170 (2018) Dai, M., Schiavone, P.: Edge dislocation interacting with a Steigmann-Ogden interface incorporating residual tension. Int. J. Eng. Sci. 139, 62–69 (2019) Dhankhar, M., Ranganathan, M.: Quantum dot molecule formation in Si-Ge heteroepitaxy on pit-patterned Si(001) substrate: A theoretical study. J. Cryst. Growth 535, 125508 (2020) Du, D., Srolovitz, D.: Electrostatic field-induced surface instability. Applied Physics Letters 85, 4917 (2004) Duan, H.L., Wang, J., Karihaloo, B.L.: Theory of elasticity at the nanoscale. Advances in Applied Mechanics 42, 1–68 (2008) Duan, H.L., Weissmüller, J., Wang, Y.: Instabilities of core-shell heterostructured cylinders due to diffusions and epitaxy: spheroidization and blossom of nanowires. J. Mech. Phys. Solids 56, 1831–1851 (2008) Eremeyev, V.A.: On effective properties of materials at the nano- and microscales considering surface effects. Acta Mech. 227, 29–42 (2016) Fischer, F.D., Waitz, T., Vollath, D., Simha, N.K.: On the role of surface energy and surface stress in phase-transforming nanoparticles. Prog. Mater. Sci. 53, 481–527 (2008) Fitzgerald, E.A., Ast, D.G.: Structure and recombination in InGaAs/GaAs heterostructures. J. Appl. Phys. 28, 693–703 (1988) Fleury, V.: Un possible lien entre la croissance dendritique en physique et la morphogenese des plantes. Compt. Rendus. Acad. Sci. III Sci. Vie. 322, 725–734 (1999) Freund, L.B.: Evolution of waviness on the surface of a strained elastic solid due to stress-driven diffusion. Int. J. Solids Struct. 28, 911–923 (1995) Freund, L.B., Suresh, S.: Thin film materials: stress, defect formation and surface evolution. University Press, Cambridge (2003) Gao, H.: Some general properties of stress-driven surface evolution in a heteroepitaxial thin film structure. J. Mech. Phys. Solids 42, 741–772 (1994) Gibbs, J.W.: The Scientific Papers of J. Willard Gibbs. Longmans-Green, London (1906) Goldstein, R.V., Makhviladze, T.M., Sarychev, M.E.: Instability of the interface between joint conducting materials under electrical current. Mater. Lett. 6, 98–101 (2016) Goldstein, R.V., Makhviladze, T.M., Sarychev, M.E.: Electromigration-induced instability of the interface between solid conductors. Phys. Mesomech. 21, 275–282 (2018) Gorbushin, N., Eremeyev, V.A., Mishuris, G.: On the stress singularity near the tip of a crack with surface stresses. Int. J. Eng. Sci. 146, 103183 (2020) Grekov, M.A., Kostyrko, S.A.: Surface effects in an elastic solid with nanosized surface asperities. Int. J. Solids and Struct. 96, 153–161 (2016) Grekov, M.A., Sergeeva, T.S.: Interaction of edge dislocation array with bimaterial interface incorporating interface elasticity. Int. J. Eng. Sci. 149, 103233 (2020) Grekov, M.A., Sergeeva, T.S., Pronina, Y.G., Sedova, O.S.: A periodic set of edge dislocations in an elastic solid with a planar boundary incorporating surface effects. Eng. Fract. Mech. 186, 423–435 (2017) Grinfeld, M.: Instability of the equilibrium of a nonhydrostatically stressed body and a melt. Fluid Dyn. 22, 169–173 (1987) Grinfeld, M.A.: Thermodynamic methods in the theory of heterogeneous systems. Longman, Sussex, UK (1991) Grinfeld, M., Grinfeld, P.: Towards thermodynamics of elastic electric conductors. Philos. Mag. A 81, 1341–1354 (2001) Grinfeld, M.A., Hazzledine, P.M.: Rearrangement at coherent interfaces in heterogeneous solids. Philos. Mag. Lett. 74, 17–23 (1996) Gurtin, M.E.: Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance. Physica D 92, 178–192 (1996) Gurtin, M.E., Jabbour, M.E.: Interface evolution in three dimensions with curvature-dependent energy and surface diffusion: Interface-controlled evolution, phase transitions, epitaxial growth of elastic films. Arch. Ration. Mech. Anal. 163, 171–208 (2002) Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Rat. Mech. Anal. 57, 291–323 (1975) Gurtin, M.E., Murdoch, A.I.: Surface stress in solids. Int. J. Solids Struct. 14, 431–440 (1978) Gurtin, M.E., Voorhees, P.W.: The continuum mechanics of coherent two-phase elastic solids with mass transport. Proc. R. Soc. A 440, 323–343 (1993) Gurtin, M.E., Voorhees, P.W.: The thermodynamics of evolving interfaces far from equilibrium. Acta Mater. 44, 235–247 (1996) Gurtin, M.E., Weissmüller, J., Larché, F.: A general theory of curved deformable interfaces in solids at equilibrium. Philos. Mag. A 78, 1093–1109 (1998) Ishiguro, H., Rubinsky, B.: Mechanical Interactions between ice crystals and red blood cells during directional solidification. Cryobiology 31, 483–500 (1994) Javili, A., McBride, A., Steinmann, P.: Thermomechanics of solids with lowerdimensional energetics: On the importance of surface, interface, and curve structures at the nanoscale. A Unifying Review. Appl. Mech. Rev. 65, 010802 (2013) Javili, A., Ottosen, N.S., Ristinmaa, M., Mosler, J.: Aspects of interface elasticity theory. Math. Mech. Solids 23, 1004–1024 (2018) Jonsdottir, F.: Computation of equilibrium surface fluctuations in strained epitaxial-films due to interface misfit dislocation. Modelling Simul. Mater. Sci. Eng. 3, 503–520 (1995) Junqua, N., Grilhé, J.: Instabilities of planar interfaces between two stressed materials. Philos. Mag. Lett. 69, 61–70 (1994) Kim, J.-H., Vlassak, J.J.: Perturbation analysis of an undulating free surface in a multi-layered structure. Int. J. Solids Struct. 44, 7924–7937 (2007) Kitamura, T., Hirakata, H., Sumigawa, T., Shimada, T.: Fracture Nanomachanics. Pan Stanford, New York (2011) Klinger, L., Levin, L., Srolovitz, D.: Morphological stability of a heterophase interface under electromigration conditions. J. Appl. Phys. 79, 6834–6839 (1996) Komarov, I.A., Antipova, O.M., Kalinnikov, A.N., Orlov, M.A., Bogachev, V.V., Buyanov, A.D., Onoprienko, E.A.: Coupling of short DNAs with reduced graphene oxide for electronic and sensing applications. Fuller. Nanotub. Car. N. 28(7), 526–532 (2020) Kostyrko, S.A., Grekov, M.A.: Elastic field at a rugous interface of a bimaterial with surface effects. Eng. Fract. Mech. 216, 106507 (2019) Kostyrko, S., Grekov, M., Altenbach, H.: Stress concentration analysis of nanosized thin-film coating with rough interface. Continuum Mech. Thermodyn. 31, 1863–1871 (2019) Kostyrko, S., Shuvalov, G.: Surface elasticity effect on diffusional growth of surface defects in strained solids. Continuum Mech. Thermodyn. 31, 1795–1803 (2019) Larché, F.C., Cahn, J.C.: The interaction of composition and stress in crystalline solids. Acta Metall. 33, 331–357 (1985) Leo, P.H., Lowengrub, J.S., Jou, H.J.: A diffuse interface model for microstructural evolution in elastically stressed solids. Acta Mater. 46, 2113–2130 (1998) Lu, W., Suo, Z.: Dynamics of nanoscale pattern formation of an epitaxial monolayer. J. Mech. Phys. Solids 49, 1937–1950 (2001) Lurie, S., Belov, P.: Gradient effects in fracture mechanics for nano-structured materials. Eng. Fract. Mech. 130, 3–11 (2014) McBride, A.T., Javili, A., Steinmann, P., Bargmann, S.: Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion. J. Mech. Phys. Solids 59, 2116–2133 (2011) Miller, R.E., Shenoy, V.B.: Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11, 139–147 (2000) Mogilevskaya, S.G., Crouch, S.I., Stolarski, H.K.: Multiple interacting circular nano-inhomogeneities with surface/interface effects. J. Mech. Phys. Solids 56, 2298–2327 (2008) Mullins, W.W.: Theory of thermal grooving. J. Appl. Phys. 28, 333–339 (1957) Mullins, W.W., Sekerka, R.F.: Morphological stability of a particle growing by diffusion or heat flow. J. Appl. Phys. 34, 323–329 (1963) Murphy, S., Osing, J., Shvets, I.V.: Irreversible nanoscale morphology transformation of an Fe film on Mo(110) induced by a magnetic STM tip. Surf. Sci. 547, 139–148 (2003) Nazarenko, L., Bargmann, S., Stolarski, H.: Closed-form formulas for the effective properties of random particulate nanocomposites with complete Gurtin-Murdoch model of material surfaces. Continuum Mech. Thermodyn. 29(1), 77–96 (2017) Nazarenko, L., Chirkov, A.Y., Stolarski, H., Altenbach, H.: On the modeling of carbon nanotubes reinforced materials and on influence of carbon nanotubes spatial distribution on mechanical behavior of structural elements. Int. J. Eng. Sci. 143, 1–13 (2019) Nazarenko, L., Stolarski, H., Altenbach, H.: Effective properties of short-fiber composites with Gurtin-Murdoch model of interphase. Int. J. Solids Struct. 97–98, 75–88 (2016) Nazarenko, L., Stolarski, H., Altenbach, H.: Effective properties of short-fiber composites with Gurtin-Murdoch model of interphase. Int. J. Eng. Sci. 126, 130–141 (2017) Otsuka, K., Karato, S.: Deep penetration of molten iron into the mantle caused by a morphological instability. Nature 492, 243–246 (2012) Povstenko, Yu.Z.: Theoretical investigation of phenomena caused by heterogeneous surface tension in solids. J. Mech. Phys. Solids 41, 1499–1514 (1993) Risler, T., Basan, M.: Morphological instabilities of stratified epithelia: a mechanical instability in tumour formation. New J. Phys. 15, 065011 (2013) Ru, C.Q.: Simple geometrical explanation of Gurtin-Murdoch model of surface elasticity with clarification of its related versions. Sci. China Phys. Mech. 53, 536–544 (2010) Sekerka, R.F.: Morphological stability. J. Cryst. Growth 3, 71–81 (1968) Sharma, P., Ganti, S., Bhate, N.: Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82, 535–537 (2003) Shenoy, V.B.: Atomistic calculations of elastic properties of metallic fcc crystal surfaces. Phys. Rev. B 71, 094104 (2005) Shodja, H.M., Ahmadzadeh-Bakhshayesh, H., Gutkin, MYu.: Size-dependent interaction of an edge dislocation with an elliptical nano-inhomogeneity incorporating interface effects. Int. J. Solids Struct. 49, 759–770 (2012) Shuttleworth, R.: The surface tension of solids. Proceedings of the Physical Society Series A 63, 444–457 (1950) Shuvalov, G.M., Vakaeva, A.B., Shamsutdinov, D.A., Kostyrko, S.A.: The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Sciences. Control Processes, 16(2), 165–176 (2020) Shuvalov, G.M., Kostyrko, S.A.: Surface self-organization in multilayer film coatings. AIP Conf. Proc. 1909, 020196 (2017) Srolovitz, D.J.: On the stability of surfaces of stressed solids. Acta Metall. 37, 621–625 (1989) Steigmann, D.J., Ogden, R.W.: Elastic surface-substrate interactions. Proc. R. Soc. A 455, 437–474 (1999) Steigmann, D.J., Ogden, R.W.: Plane deformations of elastic solids with intrinsic boundary elasticity. Proc. R. Soc. A 453, 853–877 (1997) Thornton, K., Ågren, J., Voorhees, P.W.: Modeling the evolution of phase boundaries in solids at the meso- and nano-scales. Acta Mater. 51, 5675–5710 (2003) Tian, L., Rajapakse, R.K.N.D.: Elastic field of an isotropic matrix with nanoscale elliptical inhomogeneity. Int. J. Solids Struct. 44, 7988–8005 (2007) Torii, R.H., Balibar, S.: Helium crystals under stress: the Grinfeld instability. J. Low Temp. Phys. 89, 391–400 (1992) Umeno, Y., Shimada, T., Kinoshita, Y., Kitamura, T.: Multiphysics in nanostructures. Springer, Japan (2017) Vakaeva, A.B., Krasnitckii, S.A., Grekov, M.A., Gutkin, M.Y.: Stress field in ceramic material containing threefold symmetry inhomogeneity. J. Mater. Sci. 55, 9311–9321 (2020) Wang, J., Huang, Z., Duan, H., Yu, S.W., Wang, G., Zhang, W., Wang, T.: Surface stress effect in mechanics of nanostructured materials. Acta Mech. Solida Sin. 24, 52–82 (2011) Xie, Z., Avila, R., Huang, Y., Rogers, J.A.: Flexible and Stretchable Antennas for Biointegrated Electronics. Adv. Mater. 32, 1902767 (2020) Xu, X., Aqua, J.-N.: Quantum dot growth on a stripe-pattern. Thin Solid Films 543, 7–10 (2013) Yoshino, T.: Penetration of molten iron alloy into the lower mantle phase. C. R. Geosci 351, 171–181 (2019) Zhang, J., Zhang, K., Yong, J., Yang, Q., He, Y., Zhang, C., Hou, X., Chen, F.: Femtosecond laser preparing patternable liquid-metal-repellent surface for flexible electronics. Colloid Interface Sci. 578, 146–154 (2020)