# ICME overview of zirconium oxide degradation

## Contents |

### ICME overview of zirconium oxide degradation

#### Problem description

Zirconium alloys due to their low neutron absorption have an important usage in nuclear power plants as a fuel cladding tubes. During operation the fuel corrodes to form ZrO2, which causes a build up of oxide on the cladding outer surface which grows to several microns in thickness. The oxide which forms first is the tetragonal zirconia phase in the form of nano-crystals, these crystals are under very high compressive stresses of the order of up to 2-3 GPa due to the volume increase on oxidation of the metal surface. As oxide growth continues a layer of monoclinic oxide starts to form and oxide damage occurs increasing the corrosion rate.#### Macroscale

At component scale we can see some cracks to study these cracks we need crack growth and coalescence mechanism from macroscale, so at macroscale we need a continuum polycrystalline finite element model for crack growth and coalescence. The crack growth at this scale needs crack nucleation and loading from lower scales.

#### Microscale

Macroscale needs crack nucleation and loading from this scale so, we need a microscale polycrystalline finite element model using Cohesive Interface Law that allow the investigation of crack nucleation and a phase field model which predict the oxidation rate and stresses. The first model needs deformation kinematics and the second one needs oxygen diffusion coefficient from lower scales.

#### Nanoscale

This scale must give the deformation kinematics of zirconia so, we need a crystal plasticity model to account for the crystal slip and twining. In addition at this scale we need a phase field model which predicts the tetragonal to monoclinic phase transformation and its induced stresses. Mobility, interfacial energy and elastic moduli are the inputs of this scale.

#### Atomistics Scale

Atomistic calculations (MD) can give us diffusion coefficients for microscale and mobility for Nanoscale, besides atomistic calculations can give high rate mechanism to component scale. It is crucial that the interaction potential used in the MD simulations be assessed for suitability in describing this system. It is equally important that the simulation supercell adequately depicts the physical system.

#### Electronic scale

At this scale by using DFT we can calculate interfacial energy and elastic moduli for zirconium, tetragonal zirconia and monoclinic zirconia. Because the transformation stress and oxidation stress is high the effect of pressure on elastic moduli must be studied.

#### References

[1] Leistikow S, Schanz G, Berg H, Aly AE. Comprehensive presentation of extended zircaloy-4/steam oxidation results 600–1600 c. In: Proc. OECD-NEACSNI/IAEA Specialists Meeting on Water Reactor Fuel Safety and Fission Product Release in Off-Normal and Accident Conditions, Risø Nat. Lab., Denmark. 1983.

[2] Leistikow S, Schanz G. Nuclear engineering and design 1987;103:65–84.

[3] W. Qin, C. Nam, H. Li, and J. Szpunar, “Tetragonal phase stability in ZrO2 film formed on zirconium alloys and its effects on corrosion resistance,” Acta materialia, vol. 55, no. 5, pp. 1695–1701, 2007.

[4] X. S. Zhao, S. L. Shang, Z. K. Liu, and J. Y. Shen, “Elastic properties of cubic, tetragonal and monoclinic ZrO2 from first-principles calculations,” Journal of Nuclear Materials, 2011.

[5] Nuclear Fuel Behaviour in Loss-of-coolant Accident (LOCA) Conditions, State-of-the-art Report, © OECD 2009 NEA No. 6846

[6] Multiscale Modeling of Armor Ceramics: Focus on AlON, by G. A. Gazonas, J. W. McCauley, I. G. Batyrev, D. Casem, J. D. Clayton, D. P. Dandekar, R. Kraft, B. M. Love, B. M. Rice, B. E. Schuster, and N. S. Weingarten. Proceedings of the 27th Army Science Conference, Orlando, FL, 29 November 2010.