Abstract
The lattice strain ε(D) function of nanocrystals within different interface environments was modeled. For nanoparticles and nanocrystals embedded in incoherent interfaces, the lattice shrinks with the decrease of size, resulting in the reduction of ε(D). For nanostructure materials and the nanocrystals embedded in the coherent interfaces, ε(D) increases due to lattice expansion. These changes in interfacial lattice parameters depend on the sign of interfacial stress fss, i.e., the lattice contracts when fss > 0 and expands when fss < 0. In addition, we also give a criterion to judge the sign of fss, fss is negative when the surface stress f of the matrix is larger than that of the embedded nanocrystals, and vice versa. The variation in the sign of fss is also applicable to explain the thermal stability of the interface.
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References
Xu Z, Xiao FS, Purnell SK, Alexeev O, Kawi S, Deutsch SE, Gates BC (1994) Size-dependent catalytic activity of supported metal clusters. Nature 372(6504):346–348
Zhou SM, He LF, Zhao SY, Guo YQ, Zhao JY, Shi L (2009) Size-dependent structural and magnetic properties of LaCoO3 nanoparticles. J Phys Chem C 113(31):13522–13526
van Buuren T, Dinh LN, Chase LL, Siekhaus WJ, Terminello LJ (1998) Changes in the electronic properties of Si nanocrystals as a function of particle size. Phys Rev Lett 80(17):3803–3806
Liu W, Zhao YH, Li Y, Jiang Q, Lavernia EJ (2009) Enhanced hydrogen storage on Li-dispersed carbon nanotubes. J Phys Chem C 113(5):2028–2033
Xiao BB, Jiang XB, Yang XL, Jiang Q, Zheng F (2016) The segregation resistance of the Pt2ML/Os/Pd3Al sandwich catalyst for oxygen reduction reaction: a density functional theory study. Phys Chem Chem Phys 18(43):30174–30182
Wang X, Su J, Chen H, Li GD, Shi ZF, Zou HF, Zou XX (2017) Ultrathin In2O3 nanosheets with uniform mesopores for highly sensitive nitric oxide detection. ACS Appl Mater Inter 9(19):16335–16342
Mays CW, Vermaak JS, Kuhlmann-Wilsdorf D (1968) On surface stress and surface tension: II. Determination of the surface stress of gold. Surf Sci 12(2):134–140
Wasserman HJ, Vermaak JS (1970) On the determination of a lattice contraction in very small silver particles. Surf Sci 22(1):164–172
Wasserman HJ, Vermaak JS (1972) On the determination of the surface stress of copper and platinum. Surf Sci 32(1):168–174
Montano PA, Schulze W, Tesche B, Shenoy GK, Morrison TI (1984) Extended X-ray-absorption fine-structure study of Ag particles isolated in solid argon. Phys Rev B 30(2):672–677
Montano PA, Zhao J, Ramanathan M, Shenoy GK, Schulze W, Urban J (1989) Structure of silver microclusters. Chem Phys Lett 164(2):126–130
Medasani B, Park YH, Vasiliev I (2007) Theoretical study of the surface energy, stress, and lattice contraction of silver nanoparticles. Phys Rev B 75(23):235436
Solliard C, Flueli M (1985) Surface stress and size effect on the lattice parameter in small particles of gold and platinum. Surf Sci 156:487–494
Liang LH, Li JC, Jiang Q (2003) Size-dependent melting depression and lattice contraction of Bi nanocrystals. Physica B 334(1):49–53
Kellermann G, Craievich AF (2002) Structure and melting of Bi nanocrystals embedded in a B2O3-Na2O glass. Phys Rev B 65(13):134204
Yu XF, Liu X, Zhang K, Hu ZQ (1999) The lattice contraction of nanometre-sized Sn and Bi particles produced by an electrohydrodynamic technique. J Phys D: Appl Phys 11(4):937–944
Apai G, Hamilton JF, Stohr J, Thompson A (1979) Extended X-ray-absorption fine structure of small Cu and Ni clusters: binding-energy and bond-length changes with cluster size. Phys Rev Lett 43(2):165–169
da Silva EZ, Antonelli A (1996) Size dependence of the lattice parameter for Pd clusters: a molecular-dynamics study. Phys Rev B 54(23):17057–17060
Lamber R, Wetjen S, Jaeger NI (1995) Size dependence of the lattice parameter of small palladium particles. Phys Rev B 51(16):10968–10971
Tsunekawa S, Ishikawa K, Li ZQ, Kawazoe Y, Kasuya A (2000) Origin of anomalous lattice expansion in oxide nanoparticles. Phys Rev Lett 85(16):3440–3443
Nafday D, Sarkar S, Ayyub P, Saha-Dasgupta T (2018) A reduction in particle size generally causes body-centered-cubic metals to expand but face-centered-cubic metals to contract. ACS Nano 12(7):7246–7252
Manuel DP, Péter Á, Karsten A (2012) Size-dependent lattice expansion in nanoparticles: reality or anomaly? ChemPhysChem 13(10):2443–2454
Qin W, Szpunar JA (2005) Origin of lattice strain in nanocrystalline materials. Phil Mag Lett 85(12):649–656
Shen TD, Zhang JZ, Zhao YS (2008) What is the theoretical density of a nanocrystalline material? Acta Mater 56(14):3663–3671
Oehl N, Michalowski P, Knipper M, Kolny-Olesiak J, Plaggenborg T, Parisi J (2014) Size-dependent strain of Sn/SnOx core/shell nanoparticles. J Phys Chem C 118(51):30238–30243
Lewin E, Råsander M, Klintenberg M, Bergman A, Eriksson O, Jansson U (2010) Design of the lattice parameter of embedded nanoparticles. Chem Phys Lett 496(1):95–99
Zhong J (2000) Thesis, Institute of Metal Research, Chinese Academy of Sciences
Jiang Q, Zhang Z, Li JC (2000) Melting thermodynamics of nanocrystals embedded in a matrix. Acta Mater 48(20):4791–4795
Jiang XB, Xiao BB, Lan R, Gu XY, Sheng HC, Yang HY, Zhang XH (2018) Definition of interface parameter and its application on estimating the thermal stability of metallic nanoparticles. J Phys Chem C 122(45):26260–26266
Buttard D, Dolino G, Faivre C, Halimaoui A, Comin F, Formoso V, Ortega L (1999) Porous silicon strain during in situ ultrahigh vacuum thermal annealing. J Appl Phys 85(10):7105–7111
Stoneham AM (1999) Comment on ‘The lattice contraction of nanometre-sized Sn and Bi particles produced by an electrohydrodynamic technique’. J Phys D: Appl Phys 11(42):8351–8352
Jiang Q, Liang LH, Zhao DS (2001) Lattice contraction and surface stress of fcc nanocrystals. J Phys Chem B 105(27):6275–6277
Ouyang G, Zhu WG, Sun CQ, Zhu ZM, Liao SZ (2010) Atomistic origin of lattice strain on stiffness of nanoparticles. Phys Chem Chem Phys 12(7):1543–1549
Sun CQ (2014) Skin bond relaxation and nanosolid densification. Springer, Singapore, pp 223–238
Sun CQ (2007) Size dependence of nanostructures: impact of bond order deficiency. Prog Solid State Ch 35(1):1–159
Omar MS (2013) Critical size structure parameters for Au nanoparticles. Adv Mater Res 626:976–979
Omar MS (2016) Structural and thermal properties of elementary and binary tetrahedral semiconductor nanoparticles. Int J Thermophys 37:11
Omar MS (2012) Models for mean bonding length, melting point and lattice thermal expansion of nanoparticle materials. Mater Res Bull 47(11):3518–3522
Abdullah BJ, Omar MS, Jiang Q (2018) Size dependence of the bulk modulus of Si nanocrystals. Sādhanā 43:174
Omar MS, Taha HT (2009) Lattice dislocation in Si nanowires. Physica B 404(23–24):5203–5206
Zhu YF, Zheng WT, Jiang Q (2009) Modeling lattice expansion and cohesive energy of nanostructured materials. Appl Phys Lett 95(8):083110
Jiang Q, Zhao DS, Zhao M (2001) Size-dependent interface energy and related interface stress. Acta Mater 49(16):3143–3147
Sheng HC, Gao R, Xiao BB, Jiang XB (2021) Prediction of the surface and interface stress of metallic elements. Vacuum 192:110428
Jiang XB, Xiao BB, Lan R, Gu XY, Zhang XH, Sheng HC (2019) Estimation of the solid-liquid interface energy for metal elements. Comp Mater Sci 170:109174
Yang CC, Jiang Q (2005) Size and interface effects on critical temperatures of ferromagnetic, ferroelectric and superconductive nanocrystals. Acta Mater 53(11):3305–3311
Lang XY, Zheng WT, Jiang Q (2006) Size and interface effects on ferromagnetic and antiferromagnetic transition temperatures. Phys Rev B 73(22):224444
Li XL (2014) Modeling the size- and shape-dependent cohesive energy of nanomaterials and its applications in heterogeneous systems. Nanotechnology 25(18):185702
Zhao M, Yao X, Zhu YF, Jiang Q (2018) Effect of the interface energy on the pressure-induced superheating of metallic nanoparticles embedded in a matrix. Scripta Mater 142:23–27
Wang YR, Tang K, Yao X, Jin B, Zhu YF, Jiang Q (2018) Interface effect on the cohesive energy of nanostructured materials and substrate-supported nanofilms. Dalton 47(14):4856–4865
Zhao M, Jiang Q (2004) Melting and surface melting of low-dimensional In crystals. Solid State Commun 130(1):37–39
Jiang Q, Liang LH, Li JC (2003) Thermodynamic superheating of low-dimensional metals embedded in matrix. Vacuum 72(3):249–255
Banerjee R, Sperling EA, Thompson GB, Fraser HL, Bose S, Ayyub P (2003) Lattice expansion in nanocrystalline niobium thin films. Appl Phys Lett 82(24):4250–4252
Qian LH, Wang SC, Zhao YH, Lu K (2002) Microstrain effect on thermal properties of nanocrystalline Cu. Acta Mater 50(13):3425–3434
Ohshima K, Yatsuya S, Harada J (1981) Characterization of ultra fine palladium particles with the mean size of 20 Å by X-ray diffraction. J Phys Soc Jpn 50:3071–3074
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Sheng, H., Yin, T., Xiao, B. et al. Modeling the lattice expansion and contraction of nanocrystals in different interface environments. J Nanopart Res 24, 255 (2022). https://doi.org/10.1007/s11051-022-05634-w
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DOI: https://doi.org/10.1007/s11051-022-05634-w