Tritium Migration Analysis Program Research Articles

Toward a high-fidelity tritium transport modeling for retention and permeation experiments

Tritium Migration Analysis Program version 8 (TMAP8), the latest version of TMAP, was developed within the framework of the Multiphysics Object-Oriented Simulation Environment (MOOSE). Created at Idaho National Laboratory (INL), MOOSE is an open-source, dimension-agnostic, fully coupled, and fully implicit multiphysics platform featuring massively parallel computation capabilities. Using TMAP8, tritium transport in a divertor monoblock was analyzed to elucidate the effects of pulsed operation (up to fifty 1,600 s plasma discharge and cool-down cycles) on the tritium in-vessel inventory source term and ex-vessel release term (i.e., tritium retention and permeation) for safety analysis. With its built-in Message Passing Interface capability, TMAP8 can, in under 2 h, simulate tritium transport in three different layered materials (i.e., tungsten, copper, and copper-chromium-zirconium alloy) in 2D geometry, using a single device/computer with 10 cores. The MOOSE-based TMAP8 code can leverage other MOOSE tools developed under the Nuclear Energy Advanced Modeling and Simulation program to perform tritium and thermal transport in complex geometries and multiphysics environments. And via its massively parallel computation, MOOSE will enable the fusion pilot plant designers to conduct high-fidelity multiphysics modeling for the design of the divertor and blanket systems as well as for the safety analysis.

Deuterium retention in cyclic transient heat loaded tungsten with increasing cycle numbers

Surface damage and microscopic defect evolution of tungsten (W) armor under transient heat loads are key factors for fuel retention in fusion reactors. In this work, experiments were conducted to investigate the effects of cyclic thermal shocks on deuterium (D) retention and surface blistering in W. Thermal shock experiments were conducted on recrystallized W using an electron beam with a power density of 0.15 GW m−2 across 100–1500 cycles, followed by D plasma exposure with high-fluence (∼1 × 1026 D m−2). The results demonstrate that samples subjected to 500 and 1500 cycles exhibit a significant presence of sub-grains within 90 μm. Notably, the inhibition of blistering induced by thermal shock leads to a substantial reduction in D retention (5.45 × 1019 D m−2) at lower cycle numbers (100 cycles) compared to the reference sample (2.35 × 1020 D m−2) which was only exposed to D plasma. When cycle numbers increase to 500 and 1500, D retention reaches 1.98 × 1020 D m−2 and 4.56 × 1020 D m−2, respectively. Based on the tritium migration analysis program, we propose that total D retention is a consequence of the competition between defects reduced by thermal shock-induced suppression of blistering and defects generated by plastic deformation induced by thermal stress. D retention initially decreases with the increase in cycle numbers, followed by a subsequent rise, with the inflection point slightly higher than 500 cycles. Additionally, due to the extensive scope of thermal stress, an escalated exposure period will result in substantial D captured by heat-induced defects, consequently intensifying the D retention. Whether there exists an upper limit to D retention induced by the increasing thermal shock cycles necessitates further experimental analysis. Nonetheless, it is evident that thermal shock significantly contributes to D retention within a profoundly deep bulk region under high cycles.

Tritium Transport Modeling at the Pore Scale in Ceramic Breeder Materials Using TMAP8

Fusion reactors depend on the blanket material to breed and release tritium at the same rate or faster than it is consumed by the fusion reaction. Cellular ceramic breeders (CCBs) are dense materials that can maintain a high tritium breeding ratio while promoting tritium release because of highly connected pores. Assessing the tritium breeding capabilities of these materials requires a combination of extensive experimental and modeling efforts. In this work, we develop and calibrate a multiphysics model of tritium transport. This novel model accounts for ceramic and pore diffusion, trapping and detrapping, and several surface reactions at the pore surface. We perform a sensitivity analysis and calibrate the model by comparing its predictions against experimental measurements of deuterium absorption. The calibrated model is then used to model tritium absorption in samples with different pore microstructures to investigate the effect of pore interconnectivity on tritium absorption. The model is part of the development of the multiscale, multiphysics framework for tritium transport [i.e., the Tritium Migration Analysis Program (TMAP8)], which is itself built on top of the finite-element multiphysics framework multiphysics object-oriented simulation environment (MOOSE). This study demonstrates some of TMAP8’s capabilities and is the first step toward assessing the tritium breeding capabilities of ceramic breeder material designs.

A comparative study on the hydrogen dissolution and release behaviors in the zirconate proton conductors by TDS and TMAP4 analysis

Proton-conducting oxides are potential materials for electrochemical devices such as fuel cells, hydrogen pumps, hydrogen sensors, and the tritium purification and recovery system in nuclear fusion reactors. The hydrogen concentration in oxide materials is important, but its precise measurement is difficult. In this study, thermal desorption spectroscopy (TDS) was used to investigate hydrogen dissolution and release behavior in proton-conducting oxides, yttrium (Y), and cobalt (Co) doped barium-zirconates in the temperature range of 673-1273 K using deuterium (D2) and heavy water (D2O). Specimens were prepared with conventional powder metallurgy: the powder of three zirconates, BaZr0.9Y0.1O3-a (BZY), BaZr0.955Y0.03Co0.015O3-a (BZYC), and CaZr0.9In0.1O2.95 (CZI) was pressed into discs and fired in the air at 1873 K for 20 h. The densities of the sintered BZY, BZYC, and CZI specimens were 98 percent, 99.7 percent, and 99.5 percent of the theoretical densities respectively. XRD, SEM, and EDX were performed for the structural and morphological analysis of the sintered samples. From TDS measurement, a similar trend of temperature-dependent hydrogen solubility was obtained for all samples compared to the tritium imaging plate (TIP) methods literature data of HT- and DTO-exposed samples. To compare the experimental results of the deuterium desorption profile derived by TDS analysis, the simulation code of the tritium migration analysis program, version 4 (TMAP4) was employed.

Comparative Studies of Hydrogen Dissolution and Release Behavior in Zirconate Oxides by TDS and TMAP4 Analysis

Proton-conducting oxides are potential materials for electrochemical devices such as fuel cells, hydrogen pumps, hydrogen sensors, and the tritium purification and recovery system in nuclear fusion reactors. The hydrogen concentration in oxide materials is important, but its precise measurement is difficult. In this study, thermal desorption spectroscopy (TDS) was used to investigate hydrogen dissolution and release behavior in proton-conducting oxides, yttrium (Y), and cobalt (Co) doped barium-zirconates in the temperature range of 673-1273 K using deuterium (D2) and heavy water (D2O). Specimens were prepared with conventional powder metallurgy: the powder of three zirconates, BaZr0.9Y0.1O3-a (BZY), BaZr0.955Y0.03Co0.015O3-a (BZYC), and CaZr0.9In0.1O2.95 (CZI) was pressed into discs and fired in the air at 1873 K for 20 h. The densities of the sintered BZY, BZYC, and CZI specimens were 98 percent, 99.7 percent, and 99.5 percent of the theoretical densities respectively. XRD, SEM, and EDX were performed for the structural and morphological analysis of the sintered samples. From TDS measurement, a similar trend of temperature-dependent hydrogen solubility was obtained for all samples compared to the tritium imaging plate (TIP) methods literature data of HT- and DTO-exposed samples. To compare the experimental results of the deuterium desorption profile derived by TDS analysis, the simulation code of the tritium migration analysis program, version 4 (TMAP4) was employed.

Hydrogen isotope dissolution and release behavior in Y‐doped BaCeO3

AbstractOxides having a perovskite structure are known to exhibit good proton conductivity in a high‐temperature region, which makes them potential candidates in the tritium recovery and purification system of the electrochemical devices of fusion reactors such as hydrogen pumps, hydrogen sensors, and tritium monitoring systems. But the dissolution of hydrogen into the proton conductor and its release behavior is not well known yet. In this study, the dissolution and release behavior of hydrogen was investigated in BaCe0.9Y0.1O3−α proton conductor by exposing deuterium gas (D2) and heavy water vapor (D2O) at 600 or 700°C for 5 h. The dissolved deuterium amount in the sample was measured using a temperature‐programmed desorption analysis (TDS) method. The relationship between the amount of deuterium dissolved in the sample with the exposure pressure was also investigated. At room temperature (RT), the diffusivity of hydrogen (e.g., deuterium) was calculated from the change of the amount of residual hydrogen in the exposed sample due to the change of storage time. The Tritium Migration Analysis Program, Version 4 (TMAP4) simulation code was used to simulate and compare the experimental value of the obtained diffusivity. Although diffusivity at RT has not been reported in the past, the diffusivity is close to the extrapolation value of the literature data. From the comparison of this research results with literature, it may consider that the dominant diffusion mechanism does not change regardless of the temperature range.

Verification and validation of mHIT code over TMAP for hydrogen isotopes transport studies in fusion-relevant environments

The accurate prediction of tritium inventory and permeation fluxes in the breeding blanket of a D-T fusion reactor is a key aspect for future thermonuclear power plants licensing. Tritium permeation into structural materials could give rise to potential issues concerning the fuel self-sufficiency and can be lost into the environment with resulting radiological risks for the population. In the frame of hydrogen isotopes transport modelling, the Tritium Migration Analysis Program (TMAP) code is considered a referred code for the safety design of nuclear fusion power plants. It is mainly applied to Plasma Facing Components (PFCs), which are subjected to intense particles implantation and surface heat fluxes.Due to some code limitations and to the need of having a more easy-to-use computer code in a multiphysics framework, in the last years the commercial software COMSOL Multiphysics has been used to assess tritium transport studies as an application to ITER, DEMO and CFETR fusion reactors, but it was never validated against TMAP. Within this paper, a COMSOL-based code named mHIT (multi-trapping Hydrogen Isotopes Transport code) is presented. A set of verification and validation (V&V) problems were addressed, with the aim of substantiating the capabilities of the code in common fusion-relevant experimental set-ups and to include different physics according to the level of detail needed for a given application.

Effect of tungsten deposition thickness on hydrogen isotope permeation through RAFM steel

Deuterium (D) plasma-driven permeation (PDP) experiments through reduced activation ferritic/martensitic (RAFM) steel with and without tungsten (W) deposition layer have been performed. The results confirm that W deposition does not always work as D permeation barrier, but enhances D permeation flux through the structural material under certain conditions. The steady state PDP fluxes through RAFM steel with a thin (~30 nm) W deposition layer have been found to be larger than those of bare RAFM steel, whereas the RAFM steel membrane with a thick (6.0 μm) W deposition layer exhibits lower permeation fluxes than those of bare steel sample. Tritium Migration Analysis Program (TMAP) calculation indicates that the steady state permeation flux is determined by the D concentration accumulated at the interface between W layer and RAFM steel, which is highly relevant to the W deposition thickness. Only when the W thickness is larger than ~2 μm, the steady state permeation flux will be controlled by diffusion in W deposition layer.

Isolating the detrapping of deuterium in heavy ion damaged tungsten via partial thermal desorption

Partial Thermal Desorption Spectrometry (pTDS) progressively depopulated trapped deuterium (D) from heavy-ion damaged tungsten (W) to determine spatial location and detrapping energies. W samples were prepared identically: 5 MeV Cu2+ damaging ions (0.12 peak dpa dose) before D2 plasma loading (1024D/m2 fluence) held at 373 K. Each sample reached one of six pTDS peak-and-hold temperatures. Nuclear Reaction Analysis (NRA) measured the D spatial profile remaining after pTDS, before final TDS.NRA and TDS measured total D retention were in good agreement. NRA displayed three zones of D-populated defects: (I) near-surface (below 0.1 μm), (II) heavy-ion damage (peaked ∼1 μm), and (III) uniform intrinsic (bulk). D concentration in zone I reduced by ∼97% in samples with pTDS at 597 K and higher, indicating near-surface traps have low detrapping energy. The Stopping and Range of Ions in Matter (SRIM) predicts a displacement profile for zone II that coincided with measured D profile for samples with pTDS at 597 K and higher. Samples prepared with pTDS below 597 K display a distinctly different D profile in zone II. The complete cycle of D2 plasma loading, pTDS, NRA, and final TDS was modeled with Tritium Migration Analysis Program (TMAP) using a recently developed Pseudo Trap and Temperature Partition (PTTP) scheme. Differences in TDS profiles isolated traps that release between consecutive pTDS temperatures, demonstrating 6 distinct release peaks. The best fit was found with detrapping energies near 1.0, 1.2, 1.4, 1.6, 1.8, and 1.9 eV. These results show that heating at 762 K for 2.5 h released ∼99% of retained D in heavy-ion damaged W.

Modifications to the MELCOR-TMAP code to simultaneously treat multiple fusion coolants

This paper describes recent progress at Idaho National Laboratory (INL) in developing the MELCOR-TMAP computer code for fusion. The MELCOR-TMAP for fusion computer code is being developed by INL’s Fusion Safety Program (FSP) by modifying the US Nuclear Regulatory Commission’s (NRC’s) MELCOR computer code for fission reactor severe accident analyses. Recently the INL FSP completed the process of merging INL’s Tritium Migration Analysis Program (TMAP) with MELCOR to provide the US fusion community with a more comprehensive tool for analyzing accidents in future fusion reactors. However, prior to the present modifications, a MELCOR-TMAP user could only substitute one of a number of available fusion coolants for MELCOR’s default coolant of water. This new capability corrects this modeling gap needed for safety assessments of fusion reactors that contain more than a single coolant. In this article, we discuss the present code modifications, benchmark MELCOR-TMAP against predictions from previous versions of the MELCOR code, illustrate the application of the code to analysis of an accident in a multiple fluids reactor concept, and describe future plans for the MELCOR-TMAP code.

Deuterium retention in neutron-irradiated single-crystal tungsten

Six single crystal tungsten specimens were neutron irradiated to a dose of 0.1 displacements per atom (dpa) at three different irradiation temperatures (633 K, 963 K, and 1073 K) at the High Flux Isotope Reactor in Oak Ridge National Laboratory under the US-Japan PHENIX project. A pair of neutron-irradiated tungsten specimens was exposed to deuterium (D) plasma to D ion fluence of 5.0 × 1025 m−2 at three different exposure temperatures (673 K, 873 K, and 973 K) at the Tritium Plasma Experiment in Idaho National Laboratory. A combination of thermal desorption spectroscopy, nuclear reaction analysis, and rate-diffusion modeling code (Tritium Migration Analysis Program, TMAP) were used to understand D behavior in neutron-irradiated tungsten. A broad D desorption spectrum from the plasma-exposure temperature up to 1173 K was observed. Total D retention up to 1.9 × 1021 m−2 and near-surface D concentrations up to 1.7 × 10−3 D/W were experimentally measured from the 0.1 dpa neutron-irradiated single crystal tungsten. Trap density up to 2.0 × 10−3 Trap/W and detrapping energy ranging from 1.80 to 2.60 eV were obtained from the TMAP modeling.

Expanding the capability of reaction-diffusion codes using pseudo traps and temperature partitioning: Applied to hydrogen uptake and release from tungsten

Simulating the implantation and thermal desorption evolution in a reaction-diffusion model requires solving a set of coupled differential equations that describe the trapping and release of atomic species in Plasma Facing Materials (PFMs). These fundamental equations are well outlined by the Tritium Migration Analysis Program (TMAP) which can model systems with no more than three active traps per atomic species. To overcome this limitation, we have developed a Pseudo Trap and Temperature Partition (PTTP) scheme allowing us to lump multiple inactive traps into one pseudo trap, simplifying the system of equations to be solved. For all temperatures, we show the trapping of atoms from solute is exactly accounted for when using a pseudo trap. However, a single effective pseudo trap energy can not well replicate the release from multiple traps, each with its own detrapping energy. However, atoms held in a high energy trap will remain trapped at relatively low temperatures, and thus there is a temperature range in which release from high energy traps is effectively inactive. By partitioning the temperature range into segments, a pseudo trap can be defined for each segment to account for multiple high energy traps that are actively trapping but are effectively not releasing atoms. With increasing temperature, as in controlled thermal desorption, the lowest energy trap is nearly emptied and can be removed from the set of coupled equations, while the next higher energy trap becomes an actively releasing trap. Each segment is thus calculated sequentially, with the last time step of a given segment solution being used as an initial input for the next segment as only the pseudo and actively releasing traps are modeled. This PTTP scheme is then applied to experimental thermal desorption data for tungsten (W) samples damaged with heavy ions, which display six distinct release peaks during thermal desorption. Without modifying the TMAP7 source code the PTTP scheme is shown to successfully model the D retention in all six traps. We demonstrate the full reconstruction from the plasma implantation phase through the controlled thermal desorption phase with detrapping energies near 0.9, 1.1, 1.4, 1.7, 1.9 and 2.1 eV for a W sample damaged at room temperature.

The effect of high energy ion beam analysis on D trapping in W

High energy ion beam analyses (IBA) are invaluable for measuring concentration depth profiles of light elements in solid materials, and important in the study of fusion fuel retention in tokamaks. Polycrystalline W specimens were implanted at 300 and 500 K, 5–10 × 1023 D m−2 fluence, with deuterium-only and simultaneous D-3%He ion beams. Selected specimens were analysed by elastic recoil detection analysis (ERDA) and/or nuclear reaction analysis (NRA). All specimens were measured by thermal desorption spectroscopy (TDS). The D TDS spectra show an extra peak at 900–1000 K following ERDA and/or NRA measurements. The peak height appears to correlate with the amount of D initially trapped beyond the calculated IBA probe beam peak damage depth. Similar to pre-implantation damage scenarios, the IBA probe beam creates empty high energy traps which later retrap D atoms during TDS heating, which is supported by modelling experimental results using the Tritium Migration Analysis Program.

The effect of inert gas pre-irradiation on the retention of deuterium in tungsten: A TMAP investigation combined with first-principles method

Thermal desorption of deuterium in tungsten pre-irradiated with the inert gas (helium, neon, argon) is modelled by TMAP (Tritium Migration & Analysis Program). Each TMAP model incorporates three activation energies linked with three types of traps respectively. First-principles method is performed to calculate the activation energies of deuterium detrapping from different kinds of defects. By comparing the activation energies modelled in TMAP with that obtained from first-principles method, the types of traps are determined. The pre-irradiation of helium can suppress the deuterium retention in vacancy clusters. Neon and argon pre-irradiation suppresses deuterium retention in mono-vacancies due to decreasing the number of mono-vacancies caused by the occupation of the inert gas atoms into mono-vacancies. The pre-irradiation of neon can facilitate deuterium retention in vacancy clusters through generating vacancy clusters during the injection process. Argon pre-irradiation facilitates deuterium retention mainly through generating voids, which are of a larger scale than vacancy clusters and can serve as effective traps.

Recent development and application of a new safety analysis code for fusion reactors

This paper describes the recent progress made in the development of two codes for fusion reactor safety assessments at the Idaho National Laboratory (INL): MELCOR for fusion and the Tritium Migration Analysis Program (TMAP). During the ITER engineering design activity (EDA), the INL Fusion Safety Program (FSP) modified the MELCOR 1.8.2 code for fusion applications to perform ITER thermal hydraulic safety analyses. Because MELCOR has undergone many improvements at SNL-NM since version 1.8.2 was released, the INL FSP recently imported these same fusion modifications into the MELCOR 1.8.6 code, along with the multiple fluids modifications of MELCOR 1.8.5 for fusion used in US advanced fusion reactor design studies. TMAP has also been under development for several decades at the INL by the FSP. TMAP treats multi-specie surface absorption and diffusion in composite materials with dislocation traps, plus the movement of these species from room to room by fluid flow within a given facility. Recently, TMAP was updated to consider multiple trap site types to allow the simulation of experimental data from neutron irradiated tungsten. The natural development path for both of these codes is to merge their capabilities into one computer code to provide a more comprehensive safety tool for analyzing accidents in fusion reactors. In this paper we detail recent developments in this area and the application of this new capability to a DEMO relevant water-cooled tungsten armored divertor.

Tritium transport calculations for the IFMIF Tritium Release Test Module

The IFMIF Tritium Release Test Module (TRTM) is projected to measure online the tritium release from breeder ceramics and beryllium pebble beds under high energy neutron irradiation. Tritium produced in the pebble bed of TRTM is swept out continuously by a purge gas flow, but can also permeate into the module's metal structures, and can be lost by permeation to the environment. According analyses on the tritium inventory are performed to support IFMIF plant safety studies, and to support the experiment planning. This paper describes the necessary elements for calculation of the tritium transport in the Tritium Release Test Module as follows: (i) applied equations for the tritium balance, (ii) material data from literature and (iii) the topological models and the computation of the five different cases; namely release of tritium from the breeder solid material into the purge gas, loss of tritium over the capsule wall, rig hull, container wall and purge gas return line in detail. The problem of tritium transport in the TRTM has been studied and analyzed by the Tritium Migration Analysis Program (TMAP) and the adapted fusion-devoted Tritium Permeation Code (FUS-TPC). TMAP has been developed at INEEL and now exists in Version 7. FUS-TPC Code was written in MATLAB with the original purpose to study the tritium transport in Helium Cooled Lead Lithium (HCLL) blanket and in a later version the Helium Cooled Pebble Bed (HCPB) blanket by [6] (Franza, 2012). This code has been further modified to be applicable to the TRTM. Results from the computations for the five computational cases concerning safety and experiment analyses are presented.

A First Simulation Study of Hydrogen Isotope Accumulation and Diffusion in Tungsten First Wall of HiPER Inertial Fusion Facility

The study of the retention and desorption of hydrogen isotopes and helium atoms in first-wall materials is key for the design of future fusion reactors, not only for the effect of the materials on the degradation of the wall properties but also for the implications in tritium management strategies.A diffusion model of the implanted H, D, T, and He species in a 1-mm-thick first wall of tungsten for the two initial phases of the proposed European laser fusion project HiPER (namely, phases 4a and 4b) has been implemented using the tritium migration analysis program TMAP7. The effects of the abrupt temperature increases, working temperatures, and the operational pulsing modes on the diffusion are studied. Although a detailed treatment of the different trapping mechanisms has been omitted, meaningful quantitative results on the accumulation, desorption, and time intervals to reach a stationary state are presented and discussed.

Reduced deuterium retention in self-damaged tungsten exposed to high-flux plasmas at high surface temperatures

We investigated the effect of surface temperature on deuterium retention in self-damaged tungsten exposed to high-flux deuterium plasmas. The retention saturates at a W4+ fluence of about 3 × 1017 m−2 and is strongly reduced for the present high surface temperatures of 800–1200 K as compared with previous experiments at 470–525 K. Combination of nuclear reaction analysis (NRA), thermal desorption spectroscopy and positron annihilation Doppler broadening (PADB) was used to investigate the reduction in deuterium retention. The NRA showed a strong reduction of retention at the surface at high surface temperatures. The PADB measurements suggest that during plasma exposure defects are mobile and cluster into larger clusters containing up to a few tens of vacancies. The Tritium Migration Analysis Program 7 simulations show that trapping and de-trapping rates are very high for defects with trapping energies below ∼1.5 eV. The strong reduction in retention seems to be caused by the reduced amount of mono-vacancies and small vacancy clusters in combination with their strong depopulation due to thermal trapping and de-trapping.

The deuterium depth profile in neutron-irradiated tungsten exposed to plasma

Tungsten samples (99.99% purity from A.L.M.T. Corp., 6 mm in diameter, 0.2 mm in thickness) were irradiated by high-flux neutrons at 50 °C to 0.025 dpa in the High Flux Isotope Reactor at Oak Ridge National Laboratory. Subsequently, the neutron-irradiated tungsten samples were exposed to high-flux deuterium plasmas (ion flux: 1021–1022 m−2 s−1, ion fluence: 1025–1026 m−2) in the Tritium Plasma Experiment at Idaho National Laboratory. This paper reports the results of deuterium depth profiling in neutron-irradiated tungsten exposed to plasmas at 100, 200 and 500 °C via nuclear reaction analysis (NRA). The NRA measurements show that a significant amount of deuterium (>0.1 at.% D/W) remains trapped in the bulk material (up to 5 μm) at 500 °C. Tritium Migration Analysis Program simulation results using the NRA profiles indicate that different trapping mechanisms exist for neutron-irradiated and unirradiated tungsten.

Modelling deuterium release during thermal desorption of D+-irradiated tungsten

Thermal desorption profiles were modelled based on SIMS measurements of implantation profiles and using the multi-trap diffusion code TMAP7 [G.R. Longhurst, TMAP7: Tritium Migration Analysis Program, User Manual, Idaho National Laboratory, INEEL/EXT-04-02352 (2004)]. The thermal desorption profiles were the result of 500eV/D+ irradiations on single crystal tungsten at 300 and 500K to fluences of 1022–1024D+/m2. SIMS depth profiling was performed after irradiation to obtain the distribution of trapped D within the top 60nm of the surface. Thermal desorption spectroscopy (TDS) was performed subsequently to obtain desorption profiles and to extract the total trapped D inventory. The SIMS profiles were calibrated to give D concentrations. To account for the total trapped D inventory measured by TDS, SIMS depth distributions were used in the near-surface (surface to 30nm), NRA measurements [V.Kh. Alimov, J. Roth, M. Mayer, J. Nucl. Mater. 337–339 (2005) 619] were used in the range 1–7μm, and a linear drop in the D distribution was assumed in the intermediate sub-surface region (∼30nm to 1μm). Traps were assumed to be saturated so that the D distribution also represented the trap distribution. Three trap energies, 1.07±0.03, 1.34±0.03 and 2.1±0.05eV were required to model the 520, 640 and 900K desorption peaks, respectively. The 1.34 and 1.07eV traps correspond to trapping of a first and second D atom at a vacancy, respectively, while the 2.1eV trap corresponds to atomic D trapping at a void. A fourth trap energy of 0.65eV was used to fit the 400K desorption peak observed by Quastel et al. [A.D. Quastel, J.W. Davis, A.A. Haasz, R.G. Macaulay-Newcombe, J. Nucl. Mater. 359 (2006) 8].