Bulk Diffusion-Controlled Thermal Desorption Spectroscopy with Examples for Hydrogen in Iron
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GASEOUS species released by thermal desorption spectroscopy (TDS) may be detected easily and with high sensitivity by mass spectrometry. Thus, the technique is widely used for detecting hydrogen in iron base alloys or steels.[1–8] Besides yielding reliable values for the gas-content within the ppm and sub-ppm range, TDS also provides information about the binding energy via the temperature Tm where the maximum desorption rate is detected. Often more than one desorption peak is observed during temperature scans indicating the presence of sites or regions of different binding energies within the bulk. The activation energy of the rate determining desorption process Ed is obtained from the following equation derived by Kissinger[9] in the framework of reaction rate theory and by imposing a linear change of temperature h @ ln h=T2m Ed ¼ : ½1 @ð1=Tm Þ R
REINER KIRCHHEIM, Professor, is with the Institut fu¨r Materialphysik, Georg-August-Universita¨t Go¨ttingen, FriedrichHund-Platz 1, 37077 Go¨ttingen, Germany, and also with the International Institute for Carbon-Neutral Energy Research (WPII2CNER), Kyushu University, Fukuoka, Japan. Contact e-mail: [email protected] Manuscript submitted February 10, 2015. Article published online November 18, 2015 672—VOLUME 47A, FEBRUARY 2016
Thus, in a semi-logarithmic plot of h=T2m vs 1/Tm, straight lines with the slope Ed/R will be obtained. Depending on which process is rate determining, the energy Ed could be (i) the desorption energy from a surface state, (ii) the activation energy for bulk diffusion, if the desorbed atoms or molecules have to migrate from the interior of a sample to the surface, or (iii) the reaction energy of the decomposition of a compound releasing the gaseous species. These or part of these processes are treated in References 5 through 8,10. Lee et al.[5,10] proposed a model as shown in Figure 1 for a hydrogen atom being bound to a special lattice site called trap, in order to include the activation barrier for desorption from the trap site. The binding energy in the trap site is Et and hydrogen entering the trap site from a normal lattice site (labeled f in Figure 1) has to overcome a barrier of height Es. Hydrogen not bound in traps is referred to as free and moves from an f-site to adjacent sites by jumping over a barrier of height Q. Very often Es is set equal to Q and Eq. [1] becomes @ ln h=T2m Et þ Q ; ½2 ¼ R @ð1=Tm Þ if the release rate from trap sites is the rate determining step for thermal desorption. This is equivalent with the assumption of local equilibrium between free and trapped hydrogen as shown below. Very often the position of a desorption peak depends on sample thickness[10] indicating that diffusion through the sample contributes to the rate of desorption. METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 1—Schematic potential trace for an atom (i.e., hydrogen). Lattice sites labeled t are traps and hydrogen moves freely along f-sites with an activation barrier Q. Binding energy to traps is denoted by Et and the activation en
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