Question

3. The nitridation of a silicon particle can be described by a simple binary diffusion of oxygen through the nitride film and a fast reaction at the silicon/nitride interface, i.e., a diffusion-controlled process; 2N2+3Si—>Si3N4. A typical model, based on a quasi-steady state assumption, leads to the silicon radius Rf being a function of time (t); initial particle size is R0. For a small silicon particle, the film thickness of not to small as compared with the particle size. In such a case, the nitrogen concentration profile may not be linear. With this, please derive a model to simulate the consumption of silicon particle (Rf (t)). The solubility of oxygen in the film is CO and the molar density of the film is Cf .

Answer 1

This question is related to silicon chemistry.

The nitridation of a silicon particle is described by a simple binary diffusion of oxygen through the nitride film and a fast reaction at the silicon/nitride interface that is a diffusion-controlled process which is given by the following reaction:

2N₂+3Si --------—> Si₃N₄.

A typical model, based on a quasi-steady state assumption, leads to the silicon radius R_f being a function of time (t); initial particle size is R₀. Quasi-steady state means that the concentration become constant at a particular time.

For a small silicon particle, the film thickness is not too small as compared with the particle size. In that case, the nitrogen concentration profile is not be linear.

Si₃N₄ is very interested to associate with the desire and for developing a suitable ceramic for high-temperature applications which is particularly used for gas turbines.
Si₃N₄ is a covalently bonded compound which decomposes above 1800 °C temperature. So, it is impossible to densify this Si₃N₄ without sintering material or we can say additives. With the presence of a large degree of porosity, it is solve by the help of hot-pressing of formed silicon nitride with many sintering additives. After that we can observe that the self-diffusivity become relatively low. The low self diffusivity is very important for the intended application for gas turbines at high temperatures. The additives are important because they are not only improve the mechanical properties but as well as process the Si₃N₄. So, in this model, it is realizes the importance of diffusion studies.The importance of this model is not only the self-diffusion studies but also the diffusion of solutes. Si₃N₄ plays a important role as diffusion barriers in silicon device technology.