Atomistic Simulations of Formation of Elementary Zr-I Systems

We report results of simulations on the formation of simple zirconium iodide molecules. Previous work by Wimmer et al. [1] explored the relationship between iodine and a zirconium surface. We investigate the reaction schemes through atomistic simulations to better understand the nature of Zr-I interactions through isolated molecules. The computed energy values of varying Zr-I systems suggests a strong binding mechanism between zirconium and iodine, and offer predictions of likely reaction products. The computed results predict condensation of volatile ZrI4 with ZrI2 to form Zr2I6.


Introduction
Considerable amounts of research have been performed regarding zirconium and zirconium-based alloys in the past few decades, due to usage in cladding for light water nuclear reactors (LWR).Stress-corrosion cracking (SCC) of the cladding has been observed [2] over the course of fuel-cycle lifetimes in nuclear reactors; the exact initiation of which, however, remains yet unclear [3,4].Much research has been done regarding iodine-influenced SCC, (I-SCC), which regards iodine as a strong accelerating factor in the corrosion of the zirconium cladding [5][6][7].
In LWRs, the uranium fuel pellets are enclosed within a zirconium-based alloy, such as Zircaloy-4 or Zirlo.These materials are chosen due to the very low crosssection of zirconium with respect to thermal neutrons.However, these materials can undergo significant corrosion due to stress cracking and fission product reactivity, in addition to other sources such as radiation or hydrogen embrittlement.The effect of iodine, a fission product of uranium, can affect the system in several ways.The first is direct chemical interaction and changes to the basal layer morphology characteristics due to bonding; the second, a physical localized stress induced via iodine adsorption.It is likely that I-SCC is caused by a combination of both effects on the exposed Zr surface, and investigation is required to better understand the initiation and nucleation mechanics of I-SCC.Physical stress on the system can be caused by gas pressure of the fis-sion products on the cladding walls.The internal fuel rod pressures can range from 1 -14 MPa during standard operating conditions, up to 1 GPa in contained "bubbles", [8] with pressure increasing [9] with burn-up.The focus of this research is the chemical interactions between zirconium and iodine.
The Zr cladding is expected to react strongly with the released iodine during fission; iodine is indeed used to purify Zr metal in a filament method [10].Under this scheme, iodine is used such that: (2) with the combination of the impure Zr and I 2 gas forming volatile ZrI 4 , which then deposits on a filament, and can decompose under the equilibrium of (1), resulting in pure zirconium.This same mechanism is suspected to be a means of I-SCC in Zr cladding [11].Formation of zirconium iodides, however, can occur in multiple stoichiometries.There are structures provided in the Inorganic Crystal Structure Database (ICSD) for ZrI 2 [12], ZrI 3 [13], in addition to ZrI 4 [14].One must consider each of these molecular crystals in the effort to understand I-SCC, as it is likely that as iodine gas evolves from the fuel pellet, the surface concentration of iodine increases, and the surface Zr atoms undergo changes in crystal morphology to reflect the current ZrI x stoichiometry.Shown in Equation (2), evolution of free iodine atoms occurs during fission, which can combine to form I 2 gas, in cooperative equilibrium with (1).
The formation of zirconium iodides are important due to observations seen in previous research [15][16][17], which can lead to pit formation and nucleation [5,11], followed by material failures.A suspected mechanism of pit formation is due to weakening of Zr-Zr bonds [7] at and around the site of iodine adsorption.Once these bonds are sufficiently weakened, it is likely that the zirconium surface undergoes a period of iodine aggregation, where the material proceeds from Zr x I 1-x to a locally saturated state approaching stoichiometric ZrI 4 .While this sort of mechanism may not describe the bulk surface, such aggregation is indeed likely to occur at or near grain boundaries, where Zr-Zr bonding is significantly weaker than along a pristine surface.
The research contained within this paper investigates the agglomeration of iodine on zirconium atoms in isolated systems.

Methodology
In an effort to understand the mechanistics of Zr-I interactions, simple ZrI x molecular species were constructed and energy structure calculations were performed.These molecular species were chosen due to their corresponding stoichiometries as given by the ICSD structures [12][13][14].In addition, mapping the potential energy of dissociation for Zr 2 I 6 was performed.ZrI 4 volatilizes at relatively low temperature [7] and can evolve from an iodine-saturated Zr surface during reactor operation.Therefore, understanding the iodine aggregation on the Zr surface can provide insight to pitting and cracking [11] which occur during cladding failure.
It is notable that Zr-I species undergo changes to spin state due to bonding.ZrI 2 is expected to exist in the singlet state, while ZrI 3 is in the doublet state and ZrI 4 is a singlet.The dimerized system, Zr 2 I 6 , is once again a singlet.This can introduce problematic convergence in systems due to crossover from triplet-to-singlet states as the isolated materials approach.The reaction schemes are as follows (shown in Figure 1): Note that in (3b), the reactants are in the triplet state; while this triplet state is caused by the presence of two doublets, a singlet state is also possible.The reverse reaction of 3a and 3b are disproportionation (dis) and comproportionation (com), respectively.
Additional reaction schemes were investigated to study the propagation of iodizing zirconium.These schemes were used to simulate the means by which Zr metal results in the volatile ZrI 4 species, which has been observed to cause pitting and corrosion [5,11].Elemen- tary formations of higher-valency iodides were formed under the following reactions: All calculations were performed with the GAMESS [18,19] software package using the hybrid B3LYP [20][21][22] functional with the SBKJC [23][24][25] basis set.

Results and Discussion
ZrI 2 was calculated in both the singlet and triplet state, based on the ground state electron configuration of Zr ( 3 F 2 ).In the case of ZrI 2 , the singlet state is preferred by a value of 1.24 eV.This is consistent with bonding to the d-orbital and the presence of a non-bonding fully occupied Zr s-orbital.
By computation of (3a), we observe that the equilibrium favors the product, Zr 2 I 6 , and does not undergo disproportionation.The energy change of the forward reaction (3a) is 3.32 eV.The reaction pathway between the products and reactants in (3b) is also exothermic, with computed value of 1.79 eV.Therefore, in the event of dissociation, the overwhelmingly favored product would be comproportionation to ZrI 3 , with an energetic favoring of 1.54 eV relative to the disproportionation products.
Formation of Zr 2 I 6 from component materials, as shown in (3a,b), is of primary interest.As originally reported by Busol [26], there are two possible mechanisms in ZrI x formation: 3ZrI 4 + Zr ↔ 4ZrI 3 (7a) ZrI 4 + Zr ↔ 2ZrI 2 (7b) Busol [26] determined that the rate limited step in ZrI 3 formation was not I 2 concentration, but rather, the diffu-sion rate at which I 2 can pass through surface ZrI x layers to reach pristine Zr.Observations from their work have shown that formation of ZrI 3 is the primary reaction, with little or no formation of ZrI 2 .This is consistent with the energetic barrier we observe to the formation of ZrI 2 from Zr 2 I 6 , which at high temperature the latter can decompose.This, however, does not preclude volatilization of ZrI 4 , which can form when the exposed Zr surface is sufficiently saturated with iodine, such that the disproportionation reaction (Equation (3a)) need not occur to yield ZrI 4 .
In a system containing a pair of ZrI 3 molecules, separated at 6Å beyond the equilibrium separation of Zr atoms in Zr 2 I 6 (from here on, denoted eq + 6Å), the preferred electronic state is to remain as two doublets which combine for an overall triplet state, energetically favored by 1.43 eV relative to that of the singlet state.This energy difference is evidence of errors within Hartree-Fock (HF) methods, as two isolated ZrI 3 molecules should exhibit identical energies regardless of being in the singlet or triplet state.Upon inspection of the atomic charges, it does not appear that any ionization of species occurred, but that the ZrI 3 molecules were essentially symmetric in charge distribution.Examination of the molecular orbitals (Figures 2-3) show the loss of degeneracy in the isolated ZrI 3 -ZrI 3 singlet state, as is expected.However, the population of the non-degenerate HOMO shows electron density primarily in the d-orbitals, suggesting a delocalized, higher energy orbital occupation which does not occur when the system is allowed to exist in the triplet state, as a sum of two doublets.
Higher level theory was implemented (MCSCF [27][28][29][30][31]/SBKJC) to investigate this deviation, with resultant energy between the singlet and triplet states showing negligible (4.55 × 10 -5 eV) difference.Regardless of choosing restricted or restricted open-shell Hartree-Fock, HF-based methods fail to properly describe two isolated doublets, as these methods do not properly handle the multi-configurational spin states involved.Therefore, the energy difference predicted between singlet and triplet isolated ZrI 3 pairs is an artifact of Hartree-Fock theory.However, MCSCF is significantly more computationally expensive than DFT, and therefore is useful for the investigation of the difference between singlet and triplet states, but impractical for the high volume of calculations required to determine the potential energy curve mapped in Figure 4.The energy of the dissociated ((eq) + 6Å) disproportionation products was also computed to make a comparison between the dis and com lowest-energy products relative to the DFT results shown in Figure 4, with an energy difference of 2.05 eV favoring the comproportionation products.This energy is slightly larger than DFT-predicted result of 1.54 eV, both favoring  formation of 2ZrI 3 in the dissociation of Zr 2 I 6 .
Mapping of the potential energy curve for the reaction coordinate (Figure 4) for combination/dissociation of Zr 2 I 6 to the comproportionation and disproportionation products shows that at approximately Zr-equilibrium (eq) + 1Å separation, the Zr 2 I 6 system undergoes a spin transformation from the singlet Zr 2 I 6 to a roughly associated triplet ZrI 3 -ZrI 3 pair.
The combination schemes (3a, 3b, shown in Figure 4) reveal that in the region between the equilibrium Zr-Zr separation of Zr 2 I 6 to a separation of ~2Å, both the dis and com behave identically, reaching a stable, loosely bound Zr 2 I 6 when the iodines are allowed to relax during a constrained Zr-Zr distance optimization.However, as the separation increases, the asymptotic limit is reached for the dis and com products, respectively, which differ slightly in energy.It can be noted, however, that due to the preference for the singlet-triplet transition of the com products at a separation of ~eq + 1Å, the com reaction will instead follow the dashed (low) path (Figure 4).
The reactions show in Equations ( 4)-( 5) yielded exothermic results, consistent with increasing iodine coordination to the Zr central atoms.The associated energies of these reactions is shown in Table 1.The computed enthalpies of Equations (4b) and (5a) are lower the energy change associated with 5b.The data suggests that there is a preference to the formation of ZrI 3 , rather than ZrI 4 , again, supported by the report by Busol [26]。

Conclusions
It is apparent that aggregation of ZrI x species will form larger systems as shown in structures from the ICSD [12][13][14].The choice of studying Zr 2 I 6 was based on the analogous structure of bulk ZrI 2 [12], which is not stoichiometrically identical, but geometrically similar as the system size increases.(The excess of iodine in the stoichiometry is due to terminal iodine capping.)For example, the next largest structure, Zr 3 I 8 , with each Zr atom having two bridging iodines, and maintaining a tetrahedral geometry of the Zr cores, consistent with the bulk ZrI 2 structure.Such aggregation supports the idea that as iodine exposure increases, similar to what occurs within a nuclear reactor, the iodine will bind to the Zr cladding, causing changes to the surface morphology of the cladding material, and enabling the growth of poly crystalline ZrI 2 .It is expected that upon reaching some critical limit, the surface iodine saturation will cause morphological changes to the Zr surface, resulting in a mixture of ZrI x species, and ultimately to stoichiometric ZrI 4 .Upon reaching iodine surface saturation, it is then possible that molecular ZrI 4 (g) volatilization will be possible, resulting in pitting, and ultimately, corrosion of the cladding.

Figure 1 :
Figure 1: Reaction schematic for the decomposition of Zr 2 I 6 into disproportionation (upper) and comproportionation (lower) components.Electronic structure calculations predict formation of Zr 2 I 6 from both the D and C materials.

Figure 4 .
Figure 4. Energy curves for disproportionation (diamonds) and comproportionation in the singlet (squares) and triplet (triangles) states relative to displacement from the equilibrium position.The dashed line indicates the suspected path which includes conversion from the isolated triplet (two doublet) state of ZrI 3 to combination resulting in the singlet Zr 2 I 6 .