Iterations of the sawtooth map as a dynamical model for CVD/CVI SiC polytype growth

Gerard L. Vignoles (1)

1 LCTS - Laboratoire des Composites Thermostructuraux

In order to describe silicon carbide polytype growth under CVD/CVI conditions, a dynamical model based on iterations of the sawtooth map has been studied. A two-parameter bifurcation diagram has been computed for a simple logistic-like family, and its structure has been studied in more detail by means of kneading theory and study of the skeleton. All the routes to chaos are shown to derive from the application of a central theorem involved in the construction of the skeleton. A comparison, under a combinatorial point of view, between this mathematical model and the reported data on known SiC polytypes is carried out and discussed. Indeed, the model is able to generate any periodic or chaotic polytypic sequence.

Mots clés: Dynamical system; symbolic dynamics; silicon carbide; polytypism

Domaines: Systèmes dynamiques [math.DS]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Cristallographie; Matériaux

Gerard L. Vignoles. Iterations of the sawtooth map as a dynamical model for CVD/CVI SiC polytype growth. International journal of bifurcation and chaos in applied sciences and engineering , 1993, 3, pp.1177-1194. ⟨10.1142/S0218127493000970⟩. ⟨hal-00327300⟩