Tritium can bond to microstructural features within metals, including vacancies, interfaces, grain bound­aries, and dislocations. This phenomenon is generally referred to as ‘trapping.’15-18 The trapping of hydro­gen and its isotopes is a thermally governed process with a characteristic energy generally referred to as the trap binding energy Et. This characteristic energy represents the reduction in the energy of the hydro­gen relative to dissolution in the lattice16,19 and can be thought of as the strength of the bond between the hydrogen isotope and the trap site to which it is bound. Oriani16 assumed dynamic equilibrium between the lattice hydrogen and trapped hydrogen

Ут _ $l Et

1 — yT = 1 — yL exp rt)

where Ут is the fraction of trapping sites filled with tritium and 0L is the fraction of the available lattice sites filled with tritium. According to eqn [9], the frac­tion of trap sites that are filled depends sensitively on the binding energy of the trap (Et) and the lattice con­centration of tritium (0L). For example, traps in ferritic steels, which are typically characterized by low lattice concentrations and trap energy <100kJ mol-1, tend to be depopulated at high temperatures (>1000 K).

For materials with strong traps and high lattice con­centration of tritium, trapping can remain active to very high temperatures, particularly if the trap energy is large (>50kJ mol-1). The coverage of trapping sites for low and high energy traps is shown in Figure 1 for two values of K one material with relatively low solubility of hydrogen and the other with high solubility.

The absolute amount of trapped tritium, ct, depends on 0T and the concentration of trap

15

sites, nT :

ct = a»T$T [10]

where a is the number of hydrogen atoms that can occupy the trap site, which we assume is one. If multiple trapping sites exist in the metal, cT is the sum of trapped tritium from each type of trap. A similar expression can be written for the tritium in lattice sites, cL:

Cl = Ь»ьУь [11]

where nL is the concentration of metal atoms and b is the number of lattice sites that hydrogen can occupy per metal atom (which we again assume is one). Substituting eqns [10] and [11] into eqn [9] and recognizing that 0L ^ 1, the ratio of trapped tritium to lattice tritium can be expressed as

cl [cl + nLexp(-£t/RT)]

Therefore, the ratio of trapped tritium to dissolved (lattice) tritium will be large if cl is small and Et is large. Conversely, the amount of trapped tritium will be relatively low in materials that dissolve large amounts of tritium. The transport and distribution of tritium in metals can be significantly affected by trapping of tritium. Oriani16 postulated that diffusion follows the same phenomenological form when hydrogen is trapped; however, the lattice diffusivity (D) is reduced and can be replaced by an effective diffusivity, Deff, in Fick’s first law. Oriani went on to show that the effective diffusivity is proportional to D and is a function of the relative amounts of trapped and lattice hydrogen:

D

1 + —(1 — 0t)

c l

If the amount of trapped tritium (ct) is large relative to the amount of lattice tritium (cl), the effective diffusivity can be several orders of magnitude less than the lattice diffusivity.20 Moreover, the effective diffusivity is a function of the composition of the hydrogen isotopes, depending on the conditions of the test as well as sensitive to the geometry and microstructure of the test specimen. Thus, the intrin­sic diffusivity of the material (D) cannot be measured directly when tritium is being trapped. Equation [13] is the general form of a simplified expression that is commonly used in the literature:

D

«t

1 + exp

«L

Equation [14] does not account for the effect of lattice concentration, and is therefore inadequate when the concentration of tritium is relatively large. For materials with high solubilities of tritium (such as austenitic stainless steels), trapping may not affect transport significantly and Deff « D as shown in Figure 2. For materials with a low solubility and relatively large Et, the effective diffusivity can be substantially reduced compared to the lattice diffu — sivity (Figure 2). The wide variation of reported diffusivity of hydrogen in a-iron at low temperatures is a classic example of the effect of trapping on hydrogen transport2,2 : while the diffusivity of hydro­gen at high temperatures is consistent between studies, the effective diffusivity measured at low tem­peratures is significantly lower (in some cases by orders of magnitude) compared to the Arrhenius relationship established from measurements at ele­vated temperatures. Moreover, the range of reported values of effective diffusivity demonstrates the sensi­tivity of the measurements to experimental technique and test conditions. For these reasons, it is important to be critical of diffusion data that may be affected by trapping and be cautious of extrapolating diffusion data to experimental conditions and temperatures
different from those measured, especially if trapping is not well characterized or the role of trapping is not known.