Tip-growth model

However, it is unclear what the growth mechanisms are because no Si feedstock was fed in the gas form, which is required for the tip-growth model to work. In the following, we will discuss the composition and growth mechanisms of the nanowires made in this work, and show that the Co nanoparticles may play a dual-catalytic role by helping form gaseous silicon species and catalyze the growth of Si-based nanowires. 

CNTs continue to grow. The reaction ceases if the metal tip gets encapsulated with excess carbon. The CNT growth operated according to the above-described mechanism is called tip-growth model. ... 

Growth Mechanisms. Growth mechanisms have been investigated, andsev-eral theories have been proposed. There are two general models that are used to explain catalytic synthesis of nanowires or nanotubes. The first is called tip growth, in which... 

Proposed Growth Models. Summarizing the results given above, the growth mechanisms are proposed as follows. Because of the location of nanoparticles at the tips of SiNW, we conclude that growth must occur in the gas phase. More precisely, we think that Co silicide SAN play a role here. They help convert Si and H2 into SiH4 (gas). Unreacted Co nanoparticles left on the surface, possibly due to the... 

Several growth mechanisms of nanotubes have been proposed so far—e.g., open-end growth model (54), quasi-liquid tip model (29), and so forth. Here, we describe the quasi-liquid tip model for the growth of MWNTs. 

An expression of the same linear form will be obtained for the growth of a needle if the tip is modeled as a hemisphere. Further results bearing on the diffusion- or interface-limited growth (and shrinkage) of particles have been reviewed by Sutton and Balluffi [6]. 

Crack growth models in monolithic solids have been well document-ed. 1-3,36-45 These have been derived from the crack tip fields by the application of suitable fracture criteria within a creep process zone in advance of the crack tip. Generally, it is assumed that secondary failure in the crack tip process zone is initiated by a creep plastic deformation mechanism and that advance of the primary crack is controlled by such secondary fracture initiation inside the creep plastic zone. An example of such a fracture mechanism is the well-known creep-induced grain boundary void initiation, growth and coalescence inside the creep zone observed both in metals1-3 and ceramics.4-10 Such creep plastic-zone-induced failure can be described by a criterion involving both a critical plastic strain as well as a critical microstructure-dependent distance. The criterion states that advance of the primary creep crack can occur when a critical strain, ec, is exceeded over a critical distance, lc in front of the crack tip. In other words... 

Two types of crack growth have been considered. One is intermittent, or stop-start crack growth, for which case the crack tip fields applicable to the static crack have been used to develop crack growth models.32 An example of intermittent crack growth in an alumina ceramic is shown in Fig. 10.3,46 and these results are supported also by work in glass-ceramics.8,47 The other mode of crack growth advance is continuous crack growth for which case the HR-fields are taken into account. 

Recently, genotypic variation in mature cotton fiber surface components, presumably from the cuticle, has been reported [51]. In the cytoplasm, smaller vacuoles coalesce into one large central vacuole leaving only a thin ribbon of cytoplasm between the vacuole membrane and the cellular membrane (plasmalemma). Organelles are distributed in the cytoplasm in a manner that is consistent with a model for cell expansion occurring by intercalation rather than tip growth [52,53]. The random orientation of cell wall polymers in the primary cell wall... 

Two growth models are postulated depending on whether or not catalyst particles are found in the tips of the tubes obtained. In the so-called tip-growth, the metal is situated at the nanotubes tip, whereas in the base- or bottom-growth it remains stuck to the substrate. Experimental examples have been observed for both mechanisms. The tip-growth variant ensues from the catalyst being pushed upward by the growing tube. This may only occur upon rather weak adhesion of the metal particle to the substrate, and its size must not exceed a certain limit... 

Equation 6.14 provides a formal connection between creep crack growth and the kinetics of creep deformation in that the steady-state crack growth rates can be predicted from the data on uniaxial creep deformation. Such a comparison was made by Yin et al. [3] and is reconstructed here to correct for the previously described discrepancies in the location of the crack-tip coordinates (from dr/2 to dr) with respect to the microstructural features, and in the fracture and crack growth models. Steady-state creep deformation and crack growth rate data on an AlSl 4340 steel (tempered at 477 K), obtained by Landes and Wei [2] at 297, 353, and 413 K, were used. (AU of these temperatures were below the homologous temperature of about 450 K.) The sensitivity of the model to ys, N, and cr is assessed. 

The growth rate of the dendritic tip is modeled using the available results for low Peclet number growth in unbounded liquid. The model used by Rappaz and Thevoz [152] is... 

Overmann, J. and Schubert, K. (2002). Phototrophic consortia model systems for symbiotic interrelations between prokaryotes. Arch. Microbiol. 177, 201-208. Palanivelu, R. and Preuss, D. (2000). Pollen tube targeting and axon guidance parallels in tip growth mechanisms. Trends Cell Biol. 10, 517-524. 

In the craze-growth model an advancing craze-tip process zone of extent A, as depicted in Fig. 11.17, develops a craze-tip opening displacement in a... 

In the craze-growth model the craze-tip opening displacement S of eq. (11.44) is taken as a reinterpretation of the crack-opening displacement of the Argon and Salama (1976) perturbation model, but properly downscaled by the attenuation factor a described above, giving... 

Dumais, J., Shaw, S.L., Steele, C.R., Long, S.R., Ray, P.M. (2006). An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth. International Jourtml of Developmental Biology, Vol.50, pp. 209-222. 

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