Estimation of diffusion-related parameters using genetic algorithm from desorption rates obtained from thermal desorption spectroscopy

抄録

Introduction

In the field of materials science, it has been attempted to create stronger and lighter materials by controlling the amount and bonding state of incorporated hydrogen in metallic materials. One of the methods to investigate diffusion properties of the hydrogen atoms in the metallic materials and their desorption behavior at the material surface is the thermal desorption spectroscopy (TDS), in which a time varying desorption rate is measured while heating the material linearly, so that the desorption spectrum is measured. However, it is difficult to determine several parameters related to the diffusion and the desorption from a single measured spectrum because the internal state of the material changed during the TDS measurement. In this study, we are developing an inverse analysis method to determine the several parameters from a single TDS measurement. For the method of the inverse analysis, a real number genetic algorithm (RGA) with adaptive domain method (ADM) [1] has been employed.

Analysis model

At time t in the TDS, the concentration distribution of dissolved hydrogen C(z,t) at depth z in the target material follows the diffusion equation with the diffusion coefficient D =D₀ exp(-E_d/kT) in the metal sample, where D₀ is the frequency factor of diffusion, E_d is the activation energy of diffusion, k is the Boltzmann constant, and T is the absolute temperature which depends on time during TDS measurement. The hydrogen atoms recombining at the surface and desorbed as molecules are represented by dC/dt=-2k_surfC²(0,t), where k_surf is the recombination coefficient. If the initial concentration distribution is given by C (z,0)=A z exp(-(z-z_c)²/(2w² )), the desorption rate v(t)=k_surfC²(0,t) can be expressed by the 6 parameters of A, z_c, w, D₀ , E_d, and k_surf. To determine these parameters, RGA with ADM was used, in which many parameter sets are examined, and the domains of the parameters are narrowing according to the differences between the measured spectrum and the spectrum of the forward analyses from the parameter sets. For the fast forward analysis, the boundary integral equation is adopted by using the fundamental solution of the diffusion equation. To evaluate the performance of the inverse analysis system, we used a simulated spectrum which was prepared from given parameters instead of an actual measured spectrum.

Results and Discussion

Inverse analyses by RGA cooperated with ADM for different initial random seeds were performed on the simulation data. In most of results, the desorption rate spectrum could be expressed with small differences from the simulated data by the inverse analyses with difference seeds as shown in Fig.1; however, the estimated parameters were not unique. The activation energy E_d in the diffusion coefficients converged within a range close to the given true value, but other parameters were different for each random seed.

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