In Situ Measurement of Stresses and Phase Compositions of the Zirconia Scale During Oxidation of Zirconium by Raman Spectroscopy

Abstract

Raman spectroscopy was used to determine the stress and phase compositions of the zirconia scale in situ during the oxidation of zirconium at 600–900 °C in ambient air. The results show that the compressive stresses in the zirconia scale vary with the oxidation temperature and the oxidation time. The tetragonal (t) phase forms at the metal/oxide interface and the t to monoclinic phase transformation occurs far away from the interface during the oxide scale growth. The compressive growth stress at the oxidation temperature is favourable to the formation of t phase.

Appendix: Determination of the Piezospectroscopic Tensor of Zirconia Scale

To obtain the stress from the Raman peak shift, the piezospectroscopic tensor П _ij should be determined. Therefore, a designed four-point bending test, in which the strain can be applied precisely, was carried out. A schematic view of the experiment setup is shown in Fig. 6a. A strain gauge was located at the bottom oxide layer and used to precisely measure the applied strain. As illustrated in Fig. 6b, the biaxial stresses around the strain gauge are:

$$ \left\{ \begin{gathered} \sigma_{x} = \sigma_{0} + \varepsilon E, \hfill \\ \sigma_{y} = \sigma_{0} - \upsilon \varepsilon E, \hfill \\ \end{gathered} \right. $$

(4)

where σ ₀ is the original stress inside the oxide scale, ε is the applied strain, υ is the Poisson ratio and E is the Young’s modulus of the zirconia scale. Therefore, the stress due to the applied strain in the bottom oxide layer is:

$$ \sigma = \overline{\sigma } - \sigma_{0} = \frac{{\sigma_{x} + \sigma_{y} }}{2} - \sigma_{0} = \frac{1 - \upsilon }{2}\varepsilon E. $$

(5)

Fig. 6

a A schematic view of the four-point-bending test on the zirconia layer, b an illustration of the biaxial stresses around the strain gauge, and c variation of the wavenumber around 330 cm⁻¹ (black rectangular symbols) and its peak shift as a function of the applied strain. The solid lines are the linear fittings of the wavenumbers and the peak shifts

The top oxide layer, where the Raman spectra were collected from, was under compressive stress, which has the same magnitude with the tensile stress in the bottom oxide layer. Thus, the compressive stress in the top oxide layer due to the applied strain is written as:

$$ \sigma = - \frac{1 - \upsilon }{2}\varepsilon E. $$

(6)

Combining Eq. (6) and (1), the Raman peak shift has a linear relationship with the applied strain:

$$ \Updelta \nu = - \Uppi \cdot \frac{1 - \upsilon }{2}E \cdot \varepsilon. $$

(7)

Figure 6c shows the variation of the Raman peak position and its peak shift as a function of the applied strain. From the slope of the linear relationship, using E = 194 GPa (measured by nano-indentation [MTS Systems Corp., USA]) and ν = 0.25, the constant П is obtained as −3.21 cm⁻¹ GPa⁻¹. Therefore, the relationship between peak shift and the stress state is established as:

$$ \Updelta \nu = - 3.21\sigma. $$

(8)

Unless otherwisely indicated, the stresses of the oxide scale were all calculated based on the peak shift of the 330 cm⁻¹ peak according to Eq. (8) in this study.