Hydrogen embrittlement is the degradation of structural properties of solids due to hydrogen. Its primary impact on metals takes the forms of loss of ductility and reduced load carrying capacity. Hydrogen embrittlement occurs in most metals, but not usually in copper, gold, silver or tungsten.
The effects of hydrogen embrittlement can take be observed in many forms. A few of these forms will be discussed in this section.
1.1 Hydrogen-induced cracking
Hydrogen-induced cracking occurs when two H atoms form an H2 molecule inside the metal matrix. When this happens in abundance, it results in a local increase in pressure. If the pressure increase is located near the surface of the material, the result will be blistering of the surface. If the pressure increase is remote from surface, the material will experience crack formation and growth. The cracking may resemble steps (“stepwise cracking”) if the steel has inclusions in parallel planes. Stepwise cracking is a series of events whereby the crack-front region of one void connects with the crack-front of another void on a parallel plane. 
1.2 Delayed failure
Steel may undergo “delayed failure” when exposed to a sustained load, even at a relatively low level, and/or a hydrogen environment, or if there was hydrogen pick-up during the forming process, thereby pre-charging the material with hydrogen. Delayed failure is a phenomenon whereby a steel containing hydrogen fails at a lower stress level than its tensile stress as measured in a notched tensile test; this happens when increased diffusion of hydrogen yields high concentrations in regions of localized stress. It is also referred to as hydrogen-stress failure and low-stress brittle failure. 
1.3 Flaking and shatter cracking
Flakes and shatter cracks (internal fissures) may occur during forging of steel. This is caused by hydrogen being picked up during the melting and precipitating at voids. 
1.4 Hydrogen attack
Hydrogen attack is a phenomenon related to hydrogen embrittlement. It occurs at elevated temperature (above 200⁰C) and pressure. Hydrogen combines with carbon to form methane at grain boundaries, and the internal pressure caused by the methane leads to enlarged pores or fissures in the metal. The damage caused by hydrogen attack cannot be reversed by a low-temperature annealing process; the reduction of strength and ductility are permanent. 
My current research involves the corrosion and subsequent mechanical testing of metal bipolar plate materials. Tensile and bending tests are performed before and after corrosion in a 70⁰C H2SO4 environment sparged with hydrogen. These conditions were chosen because they mimic the anodic environment of a polymer electrolyte fuel cell, and there is abundant literature with which to compare results. Many of the effects mentioned in section 1 above are especially prone to occur in a sulfuric acid environment. Stainless steels are the main metals being used for the experiments, but nickel and aluminum and also being considered. Because of the susceptibility of metals to hydrogen pick-up and subsequent embrittlement, various coatings will be tested to prevent corrosion and to prevent hydrogen from entering the material. Some of the coatings are proprietary, and so they will not be discussed in detail.
Having examined some effects of hydrogen embrittlement and the motivation for studying them, we now focus on the mechanisms at the microscopic and atomic levels. Figure 1 presents a Venn diagram of the many factors that interact to create a situation of hydrogen embrittlement. The categories into which these factors fall are (i) material (crystal structure, phase stability interfacial aspects), (ii) environmental (electrolytic or gaseous environment, fugacity), and (iii) mechanical/electromechanical (stress states, electrochemical driving forces). The purpose of this diagram is simply to show the many factors that must be taken into consideration when choosing a material for an application such as a bipolar plate.
Fig. 1. Hydrogen embrittlement interaction aspects. 
Despite extensive study, the mechanism(s) behind hydrogen embrittlement remain unclear. Three schools of thought are hydride-induced embrittlement, interstitial mechanisms and grain boundary mechanisms, although there are other possible areas as well. There is most likely a combination of mechanisms at work in any given embrittlement situation.
3.1 Hydride-induced embrittlement
Hydride-induced embrittlement is a second-phase mechanism that involves the nucleation and growth of an extensive hydride field ahead of a crack. It has been observed that hydrides first nucleate in the stress field of a crack and then grow to large sizes not by the growth of individual hydrides but by the nucleation and growth of new hydrides in the stress field. The auto-catalytic process of hydride nucleation and growth together with their brittle nature seems to be the main cause of embrittlement of V, Nb, Ti and Zr. 
3.2 Interstitial mechanisms
Two interstital mechanisms have been widely considered: hydrogen-enhanced decohesion and hydrogen-enhanced localized plasticity.
3.2.a. Hydrogen-enhanced decohesion (HEDE)
This mechanism occurs due to the increased solubility of hydrogen in tension field of an edge dislocation. There is a decrease in atom binding forces of the metal lattice, which results in premature brittle fracture. The brittle fracture may be in the form of either intergranular or transgranular cleavage. This is depicted in Figure 2.
Fig. 2. Schematic of Hydrogen-Enhanced Decohesion (HEDE) mechanism. 
3.2.b. Hydrogen-enhanced localized plasticity (HELP)
In this mechanism, dislocation movement is initiated by external stresses. Hydrogen eases dislocation movement by shielding the dislocation stress fields against each other as well as against other grid defects. This local drop of yield stress due to hydrogen causes local dislocation movement at low levels of shearing stress. See Figure 3.
Sliding localization occurs, leading to a microcrack caused by the formation of micro pores and shearing action. Once the crack leaves the area of reduced yield stress, it will not propagate any further.
Fig. 3. Schematic of Hydrogen-Enhanced Localized Plasticity (HELP) mechanism. 
3.3 Grain boundary mechanisms
There are two main mechanisms by which hydrogen embrittlement occurs at grain boundaries. In one scenario, hydrogen in the metal can diffuse to the grain boundaries and lower intergranular cohesion. In another scenario, alloying or impurity elements can segregate at the grain boundaries and contribute to decohesion. Such elements would be, for example, Mn, Si, S or P. An intergranular crack can form, and hydrogen will be attracted, further accelerating the fracture. 
Some experimental research has been performed on special grain boundaries which are engineered to resist the effects of hydrogen. In particular, research was done in 2009 on engineered twin boundaries that are resistant to hydrogen-induced intergranular embrittlement in Ni-201. Embrittlement could not be completely avoided, of course, but with a fraction of 75% of special (principally twin) boundaries, the material had almost twice the tensile ductility and 20 to 30% higher fracture toughness than microstructures containing 46% special fractions. 
4. Literature Search
Several articles are summarized below, especially with regard to the application of DFT to hydrogen embrittlement mechanisms.
4.1 Tateyama and Ohno (2002)
In their work, this research team treated spin-polarization, since the calculated energy of vacancy formation is affected by spin configuration. They used a 54-atom cell with 27 k-points. As shown in Table 1, the lattice constant, bulk modulus and magnetic moment of α-Fe obtained computationally are in close agreement with experiments.
Table 1. Comparison of fundamental properties of pure α-Fe, as well as vacancy and hydrogen in α-Fe, obtained in ab-initio calculations versus other calculations and experiments. 
Before continuing the discussion of the findings of Tateyama and Ohno, Figure 4 is supplied as a reminder of the octahedral and tetrahedral sites of the bcc unit cell. The sites are represented by the red circles. In addition, a monovacancy in bcc Fe is represented in Figure 5.
Fig. 4. Interstitial sites in bcc unit cell. [6,7]
Fig. 5. Monovacancy in bcc Fe. (Open circles represent the six octahedral sites.) 
Hydrogen trapping energy Etrap(n) for VHn is defined as the energy gained by trapping an interstitial hydrogen atom into VHn-1. Tateyama and Ohno found that, at ambient condition, the lowest energy configuration of hydrogen in a monovacancy in bcc occurs in the VH2 monovacancy-hydrogen complex. This revises previous theory, which had concluded that VH6 was the major complex in α-Fe at ambient condition. The hydrogen trapping energies appear in Figure 6. The two arrows on the right of the figure indicate experimental values of 60.8 kJ/mol-H, corresponding to VH and VH2 formation, and 41.5 kJ/mol-H, corresponding to VH3 formation.
Fig. 6. Hydrogen trapping energies in α-Fe. 
The electronic states of VHn were examined in an effort to understand why the VH2 configuration had the lowest trapping energy. As seen in Figure 7, the density of states in VH2 shows that a new state appears below the 4s band by trapping two H atoms. The arrows indicate new states appearing in the VH2 system. The energy origin is set to the Fermi energy. Large hydrogen trapping energies for VH and VH2 formations are caused by the termination of broken Fe bonds. Fe 3d-H 1s hybridization is shown in Figure 8.
Fig. 7. Density of states for up and down spins in pure α-Fe and the VH2 complex system. 
Fig. 8. Partial electron density of the new states on the (001) plane. 
This new state consists mainly of H 1s orbitals and is doubly occupied by electrons. Electrons are transferred from the Fe atoms to the regions around H atoms, and the negatively charged H atoms repel. As the number of H atoms in the region increases, the repulsive interaction is more dominant, causing a decrease in H trapping energies for VH3, VH4, etc. So VH2 becomes the major complex at ambient condition. 
4.2 Lu and Kaxiras (2005)
This research group has studied hydrogen embrittlement of aluminum, and like Tateyama and Ohno three years earlier (section 4.1 above), the group’s primary focus was the role of vacancies. A supercell with 108 atomic sites was used for the VASP calculations. The formation energy of a single vacancy and the binding energy for a nearest-neighbor divacancy in Al that were obtained computationally are in good agreement with theory and experiments. This is shown in Table 2.
Table 2. Vacancy formation energies. 
To understand the mechanisms of hydrogen atoms’ interaction with vacancies, the preferred vacancy sites for hydrogen atoms first had to be determined. (As a reminder of the vacancy sites in an fcc unit cell, see Figure 9.) The preferred site was found by calculating the total energy of a single H atom near the vacancy, and the total energy of a single H atom at a tetrahedral interstitial site and at an octahedral interstitial site. It was found that the tetrahedral interstitial site in bulk Al was slightly favored over the octahedral site, and the vacancy site is the most favored of all three positions. Figure 10 shows the vacancy site and the lowest energy position for an H atom. Note that the lowest energy position is not at the center of the vacancy site.
Thus the group established that a single H atom is stable near a vacancy site in Al. Next, the stability of an H2 molecule was studied, since H2 is responsible for bubble formation and subsequent hydrogen embrittlement. The binding energy of an H2 molecule was compared at the vacancy and in vacuum using the equation Eb = Ec(VAl + H2) + Ec(VAl) - 2Ec(VAlH), where Ec(VAl + H2) is the cohesive energy of a system with an H2 molecule at the center of the vacancy, Ec(VAl) is the cohesive energy of a system with a single vacancy in the absence of the H2 molecule, and Ec(VAlH) is the cohesive energy of a system with a single H atom in the position shown in Figure 10. It was found that there was a weak repulsion between the two H atoms in the molecular configuration at the vacancy site (+0.06 eV versus -6.67 eV binding energy in vacuum). So, the H atoms prefer not to be at a single vacancy site together, but rather at two separate vacancy sites. 
Fig. 9. Vacancy sites in fcc unit cell. [6,7]
Fig. 10. Vacancy site in fcc unit cell with 12 nearest neighbors. 
The group also did calculations using the vacancy concentration in Al (CV) and the hydrogen concentration (CH). They concluded that if CV > CH, then each vacancy prefers not to contain more than one H atom. However, if CH > CV the answer was not so clear. The trapping energy Etrap of multiple H atoms at a single vacancy site needed to be calculated using this equation:
Etrap(n) = 1/n[Ec(VAl + nH) - Ec(VAl)] - (Ec0(H) - Ec0)
where Ec(VAl + nH) is the cohesive energy of a system with n H atoms all at a single vacancy site, Ec0(H) is the cohesive energy of bulk Al with an H atom at the tetrahedral interstitial site, and Ec0 is the cohesive energy of the ideal bulk with hydrogen.
It was found that, if only one vacancy site is considered, then the trapping energy is lowest when only one H atom is trapped at that single site. However, when more than one vacancy site is considered, it is energetically more favorable for more than one H atom to be trapped at that single site, versus having one H atom at each of several sites. It was also found that up to twelve H atoms can become trapped at a single vacancy.  This configuration is shown in Figure 11. The trapping energies are shown in Figure 12.
Fig 11. Four of the six H2 molecules surrounding a vacancy on a (100) plane. The other two molecules lie directly above and below the plane, in the center of the figure. 
Fig. 12. Trapping energy per H atom versus number of H atoms trapped at a single vacancy site. The zero energy corresponds to the energy of an H atom at the tetrahedral interstitial site. 
The results of Lu and Kaxiras shed light on why hydrogen embrittlement can occur in a material such as Al, which has an extremely low equilibrium hydrogen concentration in bulk. Since there is significant H trapping at vacancies, a drastic increase of local H concentration is possible without the accumulation of H at bulk interstitial sites, which would be unlikely in Al. This is in accordance with Tateyama’s and Ohno’s work.  In addition, hydrogen-rich microvoids are created along slip planes when vacancies that have trapped H coalesce. Hydrogen enhances dislocation motion along slip planes and is strongly bound to dislocation cores, so hydrogen is able to move rapidly to the crack front. Finally, the fact that multiple H atoms can be trapped at a single vacancy increases the lattice mobility of hydrogen. 
4.3 Johnson and Carter (2010)
This study involves assessment of protective coatings to inhibit H absorption into steel. Traditional corrosion resistant coatings for steel include Zn or Cr, but they are not effective under high temperature conditions or conditions of chemical attack. For this reason new coatings need to be explored. The research group used DFT to model absorption of H into FeAl and Fe3Si surfaces and also to model bulk diffusion of H through the same materials.
The calculations were performed using VASP software, and spin polarization was considered, except for H2 in vacuum. Similar to previous researchers’ work, Johnson and Carter used the lowest energy surfaces of the two coating materials, namely, the (100) and (110) surfaces. In both FeAl and Fe3Si, the (110) surface can only be terminated one way, but the (100) surface can be terminated two ways. For FeAl, this is either an Al surface or an Fe surface. The Al surface was chosen since it is has the lower surface energy. For Fe3Si, the choices for the (100) surface are a 100% Fe layer or a 50% Si and 50% Fe layer. The latter was chosen since Si was observed to segregate to the surface in experiments performed by Starke et al. in 2001. 
It was found that H prefers the tetrahedral site in both the bulk and subsurfaces of FeAl and Fe3Si, except in the case of the FeAl (110) surface, where H prefers an octahedral subsurface site. 
The dissolution energies for each alloy were calculated. See Figures 13 and 14. In each figure, the energy marked “Bulk” is for H in the bulk material. The H dissolution energies for each of the alloys (0.31 eV for FeAl and 0.79 eV for Fe3Si) are more endothermic than the H dissolution energy in pure Fe (0.20 eV). The group concluded that a protective coating of Fe3Si would be the most effective way to inhibit H dissolution since there is nearly a four-fold increase in endothermicity, from 0.20 eV to 0.79 eV.
Fig. 13. Energy landscape of H on FeAl surfaces and in bulk FeAl, neglecting zero-point energies. The reference state is the clean surface +1/2 H2. 
Fig. 14. Energy landscape of H on Fe3Si surfaces and in bulk Fe3Si, neglecting zero-point energies. The reference state is the clean surface +1/2 H2. 
It should be noted that the DFT calculations were done with perfect crystals. In experiments, bulk diffusivity will necessarily be different because of defect concentration and trapping behavior in a real sample. 
5. Proposed work
In an effort to minimize experimental time and materials in my current research, I would like to use DFT to model hydrogen diffusion in the following materials:
- Uncoated martensitic and ferritic stainless steels
- Al and Ni
- More costly base materials, such as Ti
- 3 to 5 µm thick coatings, such as nitrides and Au plating, on the above substrates
Once the most promising materials and substrates are determined, the next step will be to combine substrate with various coatings. In particular, I plan to use nitriding and gold plating. (No more specifics can be provided as to the coatings due to the proprietary nature of the project.) In any substrate/coating combination, the coefficient of thermal expansion of both materials needs to be taken into consideration. If the coefficients are not similar, the coating is likely to flake off from the substrate upon being subjected to the 70⁰C sulfuric acid environment.
DFT would provide quite an advantage over traditional experimental methods in that it would greatly reduce the amount of materials and time needed to perform actual experiments. In addition, assuming that the calculations are set up correctly, there is much less room for error than in traditional experiments. Finally, using DFT will allow more expensive materials and coatings to be tested than would otherwise be possible.
1. C.G. Interrante and G.M. Pressouyre, eds., Current Solutions to Hydrogen Problems in Steels, (Metals Park, OH, ASM, 1982), 9-13.
2. A.K. Das, Metallurgy of Failure Analysis, (Columbus, OH, McGraw-Hill, 1997), 134-135.
4. S. Bechtle et al., “Grain-boundary engineering markedly reduces susceptibility
to intergranular hydrogen embrittlement in metallic materials,” Acta Materialia 57 (2009) 4148–4157.
5. Y. Tateyama and T. Ohno, “Atomic-scale effects of hydrogen in iron toward hydrogen embrittlement: ab-initio study,” ISIJ International 43 (4) (2003), 573-578.
8. G. Lu and E. Kaxiras, “Hydrogen embrittlement of aluminum: the crucial role of vacancies,” Phys. Rev. Letters 94 (2005), 155501-1 – 155501-4.
9. U. Starke et al., "Structural and compositional reversible phase transitions on low-index Fe3Si surfaces," Europhys. Lett. 56 (2001), 822-828.
10. D. Johnson and E. Carter, "First-principles assessment of hydrogen absorption into FeAl and Fe3Si: towards prevention of steel embrittlement," Acta Mater. 58 (2010), 638-648.