Strain thinning

When a mismatch is inevitable, as in the combination Gej-Sii j. — Si, it is found that up to a value of jc = 0.4, there is a small mismatch which leads to a strained silicide lattice (known as commensurate epitaxy) and at higher values of jc there are misfit dislocations (incommensurate epitaxy) at the interface (see p. 35). From tlrese and other results, it can be concluded that up to about 10% difference in the lattice parameters can be accommodated by commensurately strained thin films. 

As an indication of the changes in deformation modes that can be produced in ionomers by increase of ion content, consider poly(styrene-co-sodium methacrylate). In ionomers of low ion content, the only observed deformation mode in strained thin films cast from tetra hydrofuran (THF), a nonpolar solvent, is localized crazing. But for ion contents near to or above the critical value of about 6 mol%, both crazing and shear deformation bands have been observed. This is demonstrated in the transmission electron microscope (TEM) scan of Fig. 3 for an ionomer of 8.2 mol% ion content. Somewhat similar deformation patterns have also been observed in a Na-SPS ionomer having an ion content of 7.5 mol%. Clearly, in both of these ionomers, the presence of a... 

Crystal defects, crystal orientations, accurate lattice parameter measurements, local strain, thin foil thickness can be identified from CBED and LACBED [7],... 

Let us examine the instability oi strained thin films. In Fig. 3, thin films of30 ML are coherently bonded to the hard substrates. The film phase has a misfit strain, e = 0.01, relative to the substrate phase, and the periodic length is equal to 200 a. The three interface energies are identical to each other = yiv = y = Y Both phases are elastically isotropic, but the shear modulus of the substrate is twice that of the film (p = 2p). On the left-hand side, an infinite-torque condition is imposed to the substrate-vapor and film-substrate interfaces, whereas torque terms are equal to zero on the right. In the absence of the coherency strain, these films are stable as their thickness is well over 16 ML. With a coherency strain, surface undulations induced by thermal fluctuations become growing waves. By the time of 2M, six waves are definitely seen to have established, and these numbers are in agreement with the continuum linear elasticity prediction [16]. 

Figure 3. Moiphological evolution of strained thin-films under the infinite- and zero-torque conditions. Thin films of 30 ML and are coherently bonded to the hard substrates whose shear modulus is twice that of the film (q =2q). The film phase has amisfit strain, e= 0.01, relative to the substrate phase.

Girgsdies F, et al. Strained thin copper films as model catalysts in the materials gap. Catal Lett. 2005 102(l-2) 91-7. 

From TEM studies on strained thin films, Donald and Kramer shown... 

LLDPE similar to LLDPE-A polymer, the LPX-30. For PP a strain thinning effect may be suspected. In Fig. 22 the steady state viscosities for PP and BL ngCe) 3n(oi) were reported. For the other samples... 

Doughs with different protein contents (13.2, 16.0, and 18.8% based on 14%MB) showed different biaxial extensional viscosities (Huang and Kokini, 1993). Figure 31 shows that the biaxial extensional viscosity approached 6tj at an extensional rate of 7.3 x 10 sec . Strain thinning behavior was observed in dough during biaxial extension. 

Colored Engineering Resins for High Strain/Thin... 

Cciored Engineering Resins fcr High Strain/Thin Walled Applicaticms 263... 

Gosnet, A. M. H. Koubaa, M. Santander-Syro, A. F. Lobo, R. P. S. M. Lecoeur, R Mercey, B. (2008). Metallic nature of strained thin single-crystal La2/3Sri/3Mn03 films. Physical Review B, Vol. 78, No. 11, (September 2008), Article Number 115118, pp. (1-5), ISSN 1098-0121... 

Below we demonstrate that the surface PM and PE effects coupled with the surface (nanoparticles) or mismatch strains (thin films on substrates) lead to the appearance of built-in magnetic and electric fields. These fields generate the magnetization or polarization and hence alter the corresponding phase diagrams. 

The meaning of strain hardening and strain thinning is more clearly seen, when the effects of the linear-viscoelastic spectrum of relaxation times and the nonlinear strain measure Q on the elongational viscosity are separated. In the tube model, the strain measure can be represented by the second rank orientation tensor (describing the orientation of tube segments) and a molecular stress function f [6],... 

Keywords elongational viscosity, melt strength, extensibility, strain hardening, strain thinning, molecular stress function, flow induced crystallization, fiber spinning, blow molding, foam extrusion. 

Piezoelectric materials of thicknesses of 1 mm or more require applied voltages in excess of 100 V to reach maximum strain, depending on the frequency of excitation and the nature of the piezoelectric material. To reduce the voltages needed for full strain, thin ( 50 um) layers of piezoelectric material may he stacked with Pt electrodes in a green, presintered state and then sintered to form a complete piezoelectric element with internal electrodes. 

For the case of a strained thin film of mean thickness / on a relatively thick unstrained substrate, the depth of the valleys in this equilibrium configuration determine whether the material separates into distinct islands or it reaches equilibrium before doing so. The valley depth in this two degree of freedom idealization is a distance ai - - a2 below the mean film thickness. Therefore, the material will separate into islands if h < ai + a2 and it will not do so otherwise. For the case of A = Acr, this depth is approximately 0.135A = O.lSAcr- This observation implies that a strained film will divide up into islands only if the mean thickness is less than about 18% of the system specific critical wavelength. The particular model is too idealized... 

Figure 42 Schematic diagram of four types of LAOS behavior (a) type 1, strain thinning (b) type II, strain hardening (c) type III, weak strain overshoot and (d) type IV, strong strain overshoot. Reproduced from Kyu Hyun, S. Kim, K.H. Ahn, S.J. Lee, J. Non-Newtonian Fluid Mech. 107(2002)51...

Several processes contribute to the mobility behavior in the alloy. The mobility is reduced by alloy scattering due to fluctuations in the atomic core potentials. Also, in biaxially strained thin films the cubic symmetry of the solid is eliminated by the strain field, and individual branches of the band structure are split to different energies. This reduces scattering from one band to another near the band minimum and consequently increases mobility. Alloy scattering dominates the behavior overall. 

---