Mathematical Simulation of Phase Formation and Growth in Nickel Aluminizing
A mathematical model is developed for simulating the formation and growth of phases in the diffusion of aluminum through the nickel matrix of high-temperature alloys. The kinetic laws of diffusion processes in multiphase coatings deposited from a gaseous phase by the method of circulation are determined. The suggested mathematical model is tested experimentally.
Many physical phenomena can be described by biexponential curve. To study the physical phenomena, there is a need to obtain their mathematical expressions. Generally, the expressions are acquired based on the fitting of experimental data, and the general method to fit exponential curve is nonlinear least squares (NLLS). In the NLLS method, it is crucial to choose good enough starting values for the parameters, otherwise, the fitting might fail to converge. In this paper, one new method is proposed to solve the problem, which utilizes the Fourier transform to transform the non-linear exponential fitting model into a linear one. It makes the estimation of the parameters independent of the initial values and easy to converge. The fitting result shows that the proposed method can be used to fit the curve expressed by difference of double exponentials.