Experiments to obtain diffusivity

The purpose of most experimental studies of diffusion is to obtain accurate diffusion coefficients as a function of temperature, pressure, and composition of the phase. For this purpose, the best approach is to design the experiments so that the diffusion problem has a simple anal3hical solution. After the experiments, the experimental results are compared with (or fit by) the anal3hical solution to obtain the diffusivity. The method of choice depends on the problems. The often used methods include diffusion-couple method, thin-source method, desorption or sorption method, and crystal dissolution method. 

After the experiment, the experimental charge is prepared for analysis of the diffusion component or species. The analytical methods include microbeam methods such as electron microprobe, ion microprobe, Rutherford backscatter-ing, and infrared microscope to measure the concentration profile, as well as bulk methods (such as mass spectrometry, infrared spectrometry, or weighing) to determine the total gain or loss of the diffusion component or species. Often, the analysis of the diffusion profile is the most difficult step in obtaining diffusivity. 

This section describes the experimental methods and focuses on the estimation of diffusivity after the experiment. The analytical methods are not described here. Estimation of diffusivity from homogeneous reaction kinetics (e.g., Ganguly and Tazzoli, 1994) is discussed in Chapter 2 and will not be covered here. Determination of diffusion coefficients is one kind of inverse problems in diffusion. This kind of inverse problem is relatively straightforward on the basis of solutions to forward diffusion problems. The second kind of inverse problem, inferring thermal history in thermochronology and geospeedometry, is discussed in Chapter 5. 

In the diffusion-couple method, two cylinders of the same radius and roughly the same length are prepared. Each cylinder (called a half) is uniform in com- 

The experimental duration and the length of the diffusion couple are designed such that the length of the diffusion profile is short compared to the total length of the diffusion couple. Hence, the diffusion medium may be treated as infinite, meaning that at the ends of the two halves, the compositions are still the initial compositions. If D does not vary with concentration or distance, the concentration profile (C versus x) would be an error function. Hence, the first step to try to understand the profile is to fit an error function to the profile (Equation 3-38)  

---