Atomistic Simulations of Formation of Elementary Zr-I Systems

doi:10.4236/ojpc.2011.13014

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Open Journal of Physical Chemistry, 2011, 1, 104-108

doi:10.4236/ojpc.2011.13014 Published Online November 2011 (http://www.SciRP.org/journal/ojpc)

Atomistic Simulations of Formation of

Elementary Zr-I Systems

Matthew L. Rossi, Christopher D. Taylor

Materials Scie nce an d Tech nol o gy , MST-6, Los Alamos Na t ional La b, Los Alamos, USA

E-mail: [email protected]

Received August 6, 2011; revised September 8, 2011; accepted October 14, 2011

Abstract

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 re-

action schemes through atomistic simulations to better understand the nature of Zr-I interactions through iso-

lated 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 pre-

dict condensation of volatile ZrI4 with ZrI2 to form Zr2I6.

Keywords: Nuclear Chemistry, Quantum Chemistry, Computational Modelling

1. 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 initia-

tion 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 [5-7].

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 cross-

section of zirconium with respect to thermal neutrons.

However, these materials can undergo significant corro-

sion 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 combi-

nation of both effects on the exposed Zr surface, and

investigation is required to better understand the initia-

tion 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 zir-

conium 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:

Zr+2I2 ↔ ZrI4 (1)

2I ↔ I

2 (2)

with the combination of the impure Zr and I2 gas

forming volatile ZrI4, which then deposits on a filament,

and can decompose under the equilibrium of (1), result-

ing in pure zirconium. This same mechanism is sus-

pected to be a means of I-SCC in Zr cladding [11]. For-

mation of zirconium iodides, however, can occur in mul-

tiple stoichiometries. There are structures provided in the

Inorganic Crystal Structure Database (ICSD) for ZrI2

[12], ZrI3 [13], in addition to ZrI4 [14]. One must con-

sider each of these molecular crystals in the effort to un-

derstand 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 ZrIx stoich-

iometry. Shown in Equation (2), evolution of free iodine

atoms occurs during fission, which can combine to form

I2 gas, in cooperative equilibrium with (1).

105

M. L. ROSSI ET AL.

The formation of zirconium iodides are important due

to observations seen in previous research [15-17], which

can lead to pit formation and nucleation [5,11], followed

by material failures. A suspected mechanism of pit for-

mation 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 ZrxI1-x to a locally saturated

state approaching stoichiometric ZrI4. While this sort of

mechanism may not describe the bulk surface, such ag-

gregation 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 iso-

lated systems.

2. Methodology

In an effort to understand the mechanistics of Zr-I inter-

actions, simple ZrIx molecular species were constructed

and energy structure calculations were performed. These

molecular species were chosen due to their correspond-

ing stoichiometries as given by the ICSD structures

[12-14]. In addition, mapping the potential energy of

dissociation for Zr2I6 was performed. ZrI4 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. ZrI2 is expected to exist in the

singlet state, while ZrI3 is in the doublet state and ZrI4 is

a singlet. The dimerized system, Zr2I6, 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):

ZrI2 + ZrI4 ↔ Zr2I6 (3a)

2ZrI3 ↔ Zr2I6 (3b)

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 re-

action 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 ZrI4 species, which has been

observed to cause pitting and corrosion [5,11]. Elemen-

Figure 1: Reaction schematic for the decomposition of Zr2I6

into disproportionation (upper) and comproportionation

(lower) components. Electronic structure calculations pre-

dict formation of Zr2I6 from both the D and C materials.

tary formations of higher-valency iodides were formed

under the following reactions:

Zr + I2 ↔ ZrI2 (4a)

ZrI2 + I2 ↔ ZrI4 (4b)

2ZrI2 + I2 ↔ 2ZrI3 (5a)

2ZrI3 + I2 ↔ 2ZrI4 (5b)

All calculations were performed with the GAMESS

[18,19] software package using the hybrid B3LYP

[20-22] functional with the SBKJC [23-25] basis set.

3. Results and Discussion

ZrI2 was calculated in both the singlet and triplet state,

based on the ground state electron configuration of Zr

(3F2). In the case of ZrI2, 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 occu-

pied Zr s-orbital.

By computation of (3a), we observe that the equilib-

rium favors the product, Zr2I6, and does not undergo dis-

proportionation. The energy change of the forward reac-

tion (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 ZrI3, with an energetic favor-

ing of 1.54 eV relative to the disproportionation prod-

ucts.

Formation of Zr2I6 from component materials, as

shown in (3a,b), is of primary interest. As originally re-

ported by Busol [26], there are two possible mechanisms

in ZrIx formation:

3ZrI4 + Zr ↔ 4ZrI3 (7a)

ZrI4 + Zr ↔ 2ZrI2 (7b)

Busol [26] determined that the rate limited step in ZrI3

formation was not I2 concentration, but rather, the diffu-

M. L. ROSSI ET AL.

106

sion rate at which I2 can pass through surface ZrIx layers

to reach pristine Zr. Observations from their work have

shown that formation of ZrI3 is the primary reaction,

with little or no formation of ZrI2. This is consistent with

the energetic barrier we observe to the formation of ZrI2

from Zr2I6, which at high temperature the latter can de-

compose. This, however, does not preclude volatilization

of ZrI4, which can form when the exposed Zr surface is

sufficiently saturated with iodine, such that the dispro-

portionation reaction (Equation (3a)) need not occur to

yield ZrI4.

In a system containing a pair of ZrI3 molecules, sepa-

rated at 6Å beyond the equilibrium separation of Zr at-

oms in Zr2I6 (from here on, denoted eq + 6Å), the pre-

ferred 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 en-

ergy difference is evidence of errors within Hartree-Fock

(HF) methods, as two isolated ZrI3 molecules should

exhibit identical energies regardless of being in the sing-

let or triplet state. Upon inspection of the atomic charges,

it does not appear that any ionization of species occurred,

but that the ZrI3 molecules were essentially symmetric in

charge distribution. Examination of the molecular orbi-

tals (Figures 2-3) show the loss of degeneracy in the

isolated ZrI3-ZrI3 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 trip-

let state, as a sum of two doublets.

Higher level theory was implemented (MCSCF

[27-31]/SBKJC) to investigate this deviation, with resul-

tant 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 ZrI3 pairs is an artifact of Hartree-Fock theory.

However, MCSCF is significantly more computationally

expensive than DFT, and therefore is useful for the in-

vestigation 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 com-

proportionation products. This energy is slightly larger

than DFT-predicted result of 1.54 eV, both favoring

Figure 2. Molecular orbital diagram of ZrI3-ZrI3 singlet

system at eq + 6.0Å separation. Black indicates occupied

orbitals, grey indicates virtual (unoccupie d) orbitals.

Figure 3. Molecular orbital diagram of ZrI3-ZrI3 triplet

system at eq + 6.0Å separation. Black indicates occupied

orbitals, grey indicates virtual (unoccupie d) orbitals.

formation of 2ZrI3 in the dissociation of Zr2I6.

Mapping of the potential energy curve for the reaction

coordinate (Figure 4) for combination/dissociation of

Zr2I6 to the comproportionation and disproportionation

products shows that at approximately Zr-equilibrium (eq)

+ 1Å separation, the Zr2I6 system undergoes a spin trans-

formation from the singlet Zr2I6 to a roughly associated

triplet ZrI3-ZrI3 pair.

The combination schemes (3a, 3b, shown in Figure 4)

reveal that in the region between the equilibrium Zr-Zr

separation of Zr2I6 to a separation of ~2Å, both the dis

and com behave identically, reaching a stable, loosely

bound Zr2I6 when the iodines are allowed to relax during

a constrained Zr-Zr distance optimization. However, as

the separation increases, the asymptotic limit is reached

107

M. L. ROSSI ET AL.

Figure 4. Energy curves for disproportionation (diamonds)

and comproportionation in the singlet (squares) and triplet

(triangles) states relative to displacement from the equilib-

rium position. The dashed line indicates the suspected path

which includes conversion from the isolated triplet (two

doublet) state of ZrI3 to combination resulting in the singlet

Zr2I6.

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 co m

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 exo-

thermic results, consistent with increasing iodine coor-

dination 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 en-

ergy change associated with 5b. The data suggests that

there is a preference to the formation of ZrI3, rather than

ZrI4, again, supported by the report by Busol [26]。

4. Conclusions

It is apparent that aggregation of ZrIx species will form

larger systems as shown in structures from the ICSD

[12-14]. The choice of studying Zr2I6 was based on the

analogous structure of bulk ZrI2 [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 ex-

ample, the next largest structure, Zr3I8, with each Zr atom

having two bridging iodines, and maintaining a tetrahe-

dral geometry of the Zr cores, consistent with the bulk

ZrI2 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 clad-

ding material, and enabling the growth of poly

crystalline ZrI2. It is expected that upon reaching some

Table 1. Energy change table for reactions 4-5.

Reaction Reactants Products ΔE (eV)

4a Zr + I2 ZrI2 –4.59

4b ZrI2 + I2 ZrI4 –6.78

5a 2ZrI2 + I2 2ZrI3 –9.50

5b 2ZrI3 + I2 2ZrI4 –5.24

critical limit, the surface iodine saturation will cause

morphological changes to the Zr surface, resulting in a

mixture of ZrIx species, and ultimately to stoichiometric

ZrI4. Upon reaching iodine surface saturation, it is then

possible that molecular ZrI4(g) volatilization will be pos-

sible, resulting in pitting, and ultimately, corrosion of the

cladding.

5. Acknowledgements

This research was supported by the Consortium for Ad-

vanced Simulation of Light Water Reactors (www.

casl.gov), an Energy Innovation Hub (http://www.en-

ergy.gov/hubs) for Modeling and Simulation of Nuclear

Reactors under U.S. Department of Energy Contract No.

DE-AC05-00OR22725. The Los Alamos National Labo-

ratory is operated by Los Alamos National Security LLC

for the National Nuclear Security Administration of the

U.S. Department of Energy under contract DE-AC52-

06NA25396.

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