Optimization of chemical vapor infiltration with simultaneous powder formation
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B.W. Sheldon Division of Engineering, Brown University, Providence, Rhode Island, 02912 (Received 8 July 2000; accepted 30 August 2000)
A key difficulty in isothermal, isobaric chemical vapor infiltration is the long processing times that are typically required. With this in mind, it was important to minimize infiltration times. This optimization problem was addressed here, using a relatively simple model for dilute gases. The results provided useful asymptotic expressions for the minimum time and corresponding conditions. These approximations were quantitatively accurate for most cases of interest, where relatively uniform infiltration was required. They also provided useful quantitative insight in cases where less uniformity was required. The effects of homogeneous nucleation were also investigated. This does not effect the governing equations for infiltration of a porous body; however, powder formation can restrict the range of permissible infiltration conditions. This was analyzed for the case of carbon infiltration from methane.
I. INTRODUCTION
A variety of materials are produced by infiltration processes. In these techniques a fluid phase (i.e., a gas or a liquid) is transported into a porous structure, where it then reacts to form a solid product. These methods are particularly important for producing composite materials, where the initial porous preform is composed of the reinforcement phase (i.e., fibers, whiskers, or particles) and infiltration produces the matrix.1,2 A detailed assessment of the relevant reaction and mass transport rates during infiltration requires mathematical modeling, using a minimum of two coupled partial differential equations which describe changes in the reactant concentration and the solid structure as a function of both position and time. This type of modeling can also be extended to analyze the optimization and control of infiltration processes. The research presented here specifically considers optimization for a set of two equations which describe isothermal, isobaric chemical vapor infiltration (CVI). In this process a vapor-phase precursor is transported into the porous preform, and a combination of gas and surface reactions leads to the deposition of the solid matrix phase. During infiltration the formation of the solid product phase eventually closes off porosity at the external surface of the body, blocking the flow of reactants and effectively ending the process. This is a key feature of a)
Research supported by United States Department of Energy 98ER25346. J. Mater. Res., Vol. 15, No. 12, Dec 2000
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most infiltration processes. Isothermal, isobaric CVI often requires extremely long times, so it is generally important to minimize the total processing times. This paper considers the problem of determining the optimal pressure and temperature which correspond to the minimum infiltration time. From a practical perspective, the nature of the porous preform is often predetermined by the intended applications (e.g.,
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