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The interaction between mechanics and chemistry plays an essential and critical role in the surface segregation and relaxation in nanoscale alloys. Following the thermodynamics analysis based on surface eigenstress, the present study takes the free-standing nanometer thick films of Ni1–xCux solid solutions with face-centered cubic (fcc) crystalline structures as an example to investigate surface segregation of Cu and relaxation of the films. Hybrid Monte Carlo and Molecular Dynamics (MCMD) simulations are conducted on free-standing Ni1–xCux alloys of (100) and (111) nanofilms. The MCMD simulations verify the theoretical analytic results and determine the values of parameters involved in the theoretical analysis. Especially, the parameter of the differentiation in reference chemical potential behaves like the molar free energy of segregation in the McLean adsorption isotherm, and the differentiation in chemical composition induced eigenstrain plays also an important role in surface segregation and relaxation. The integrated theoretical and numerical study exhibits that both surface excess Cu concentration and apparent biaxial Young's modulus of Ni1–xCux nanofilms depend on the nominal Cu concentration and the film thickness. [ABSTRACT FROM AUTHOR]

The equilibrium morphology of misfit twins in an epilayer with different elastic constants from its substrate is systematically investigated by energy minimization based on the dislocation mechanism of twinning. Explicit formulas for period arrays of misfit twins with the same orientation and with alternating orientations are derived by superposition of the solutions reported in Part I of this series. The equilibrium morphology for a periodic array of misfit twins is characterized by the twin width and the twin mean spacing. The effects of elastic mismatches between the epilayer and the substrate on the equilibrium morphology of twins are also studied comprehensively. The theoretical predictions agree with experimental observations. [ABSTRACT FROM AUTHOR]

Abstract: Theoretical analysis and molecular dynamics simulations were conducted to study systematically surface eigen-displacement and surface Poisson’s ratios of solids, which play essential roles in surface energy, surface strain and surface stress. Face-centered cubic (001) Au thin films were taken as typical examples to illustrate the physical picture. The surface eigen-displacement is a critical surface strain at the equilibrium state after normal relaxation and thus an intrinsic surface property. Surface Poisson’s ratios are also intrinsic surface properties. Combining surface eigen-displacement and surface Poisson’s ratios with surface eigen-stress and surface tangential elastic constants lays foundations of surface elasticity of solids. [Copyright &y& Elsevier]

The indentation stress is the key and fundamental parameter in indentation delamination tests, which are widely used in characterization of the interfacial fracture toughness (or adhesion) between a thin film and its substrate. The indentation stress was analyzed in the present work by using the finite element method for microwedge indenters of different wedge angles and with various other geometrical and mechanical parameters including the penetration depth, film thickness, delamination size, Young's modulus, and yield strength of the indented film. The analysis exhibited the stress field under an indentation load and the stress field after unloading caused by plastic deformation, which resulted in the loading indentation stress and the unloading indentation stress, respectively, expressed by empirical formula in terms of the indenter geometry, the indentation depth, and the film thickness and mechanical properties. The energy release rate was also calculated for the indentation-induced interfacial crack. [ABSTRACT FROM AUTHOR]

Abstract: In the present work, we describe a novel microbridge testing method for thin films. The single-layer, bilayer and trilayer thin film microbridge samples were prepared with the microelectromechanical fabrication technique such that they were easy to handle. The microbridge test was conducted with a load- and displacement-sensing nanoindenter system equipped with a microwedge probe. In the mechanics analysis, we considered residual stress in each layer, modeled the substrate deformation with three coupled springs and derived the load–deflection formula in a closed form. For brittle thin films, the microbridge testing method allows us to evaluate simultaneously the Young''s modulus, the residual stress and the bending fracture strength. In addition, the microbridge test can characterize the yield strength for ductile thin films. [Copyright &y& Elsevier]

The depth and spacing of cracks in a tensile residual stressed thin film bonded on a brittle substrate are analyzed thermodynamically using the minimum energy theorem on the basis that the film has the same mechanical properties as the substrate. The results show that the cracks penetrate into the substrate. Simple and approximate relationships between three dimensionless parameters, i.e., the normalized crack depth and spacing, and the cracking resistance number, are derived, which determine the fracture behavior of the film. [Copyright &y& Elsevier]

Phase field simulations were conducted to investigate the effects of unequally biaxial misfit strains on domain stability diagrams and equilibrium domain structures in an epitaxial ferroelectric PbTiO3 thin layer, which is sandwiched in a nonferroelectric medium. The simulations reveal a multidomain structure in the layer and allow constructing “misfit strain-misfit strain” and “temperature-misfit strain” phase diagrams. It is found that unequally biaxial misfit strains may lead to the presence of a single tetragonal variant, either a-domains or b-domains, which do not exist if the misfit strains are equally biaxial. [ABSTRACT FROM AUTHOR]

The present work uses Raman spectra to measure residual stresses in Pb(Zr[sub 0.53]Ti[sub 0.47])O[sub 3] thin films. Based on thermodynamic analysis, a linear relationship is found between the stress and the square of the Raman frequency in the A[sub 1] [transverse optical[sub 3] (TO[sub 3])] and E [longitudinal optical[sub 3] (LO[sub 3])] modes. We calibrate the linear relationship by measuring the Raman spectra of stressed bulk Pb(Zr[sub 0.53]Ti[sub 0.47])O[sub 3] samples. Then, we assess residual stresses in the lead zirconate titanate thin films at different thicknesses and different annealing temperatures. The residual stresses extracted from the A[sub 1](TO[sub 3]) mode are consistent with those from the E(LO[sub 3]) mode, which are more or less the same as those measured by the x-ray diffraction sin[sup 2] ψ method. © 2001 American Institute of Physics. [DOI: 10.1063/1.1426271]. [ABSTRACT FROM AUTHOR]

Abstract: A delamination buckling model is proposed for the assessment of the interfacial fracture toughness by the microwedge indentation delamination test on a film/substrate system. The delamination buckling model is based on Von Karman nonlinear plate theory and considers the elastic deformation in the substrate and the impression on the film. The substrate deformation is modeled by employing three-coupled springs and the effect of the impression free-surfaces is modeled by using two-coupled springs. A closed form solution is derived with the spring compliances obtained from the dimension analysis and numerical calculations. The energy release rate and the phase angle are given for a variety the elastic mismatch between the film and the substrate. The results show that in some cases, the energy release rate can be two orders in magnitude larger than that derived from the clamped end condition. [Copyright &y& Elsevier]

Abstract: Indentation stresses in single- and multi-layer delaminated thin films made of elastic–perfectly plastic materials in microwedge indentation delamination tests are analyzed via finite element calculations with different wedge angles and other geometrical and mechanical parameters. Based on the formula for a single-layer thin film under indentation loading [Zhao et al. J Mater Res 2009;24:1943] and by introducing the equivalent material parameters, we developed simple analytical formulae for the loading indentation stress (as well as the energy release rate) in each layer of the multi-layer thin film, in terms of the residual stress, elastic modulus, Poisson’s ratio, yielding strength, and thickness of each layer. Our analytical solution is validated by the finite element calculations and should be useful to thin-film delamination tests. [Copyright &y& Elsevier]

Abstract: The present work conducts crystal characterization by High Resolution Transmission Electron Microscopy (HRTEM) on Cu/Sn-nanolayer/Ni sandwich structures associated with the use of Energy Dispersive X-ray (EDX) analysis. The results show that DO22–(Cu,Ni)3Sn intermetallic compound (IMC) ordered structure is formed in the sandwich structures at the as-electrodeposited state. The formed DO22-(Cu,Ni)3Sn IMC is a homogeneous layer with a thickness about 10nm. The DO22–(Cu,Ni)3Sn IMC nanolayer is stable during annealing at 250°C for 810min. The formation and stabilization of the metastable DO22–(Cu,Ni)3Sn IMC nanolayer are attributed to the less strain energy induced by lattice mismatch between the DO22 IMC and fcc Cu crystals in comparison with that between the equilibrium DO3 IMC and fcc Cu crystals. [Copyright &y& Elsevier]

A formula is derived to calculate the phase angle of interfacial mixed mode fracture in the indentation delamination test, in which the delaminated film buckles. Interfacial fracture toughness depends on the phase angle and calculating the phase angle is necessary for the determination of mode I interfacial fracture toughness. [Copyright &y& Elsevier]