**4. Discussion**

**4. Discussion**  The crystal structures of the t and m phases of PSZ are shown in Figure 6 [24]. This phase transformation is considered to be a martensitic transition. Generally, an athermal diffusionless martensitic transition occurs quickly, with the motion of the phase boundary as high as the speed of sound [25]. The overall transition proceeds in two major stages [26]. First, the transition of the lattice structure from tetragonal to monoclinic occurs by the shearing displacement of zirconium ions. The second stage involves the sliding of oxygen ions to the oxygen sites in the monoclinic lattice. The displacement of oxygen ions from the ideal fluorite positions along the c-axis was investigated by X-ray diffraction (XRD) [27]. Therefore, the 100 keV electron is considered to cause the shearing displacement of zirconium ions and the sliding of oxygen ions. In [9], the reported activation energies for the phase transition are close to 100 kJ/mol (~1 eV), which is similar to the activation energy for the sliding of oxygen ions to oxygen sites. In order to find the mechanism of the phase transition, the factor of the sliding of oxygen ions to oxygen sites should be considered.

be considered.

equation:

**Figure 6.** Crystal structure of monoclinic and tetragonal partially stabilized zirconia [24]. **Figure 6.** Crystal structure of monoclinic and tetragonal partially stabilized zirconia [24].

One of the factors is the kinetic energy transfer due to the elastic collision between the electron and target atoms. The kinetic energy of the target atom from the incident electron is expressed as follows: One of the factors is the kinetic energy transfer due to the elastic collision between the electron and target atoms. The kinetic energy of the target atom from the incident electron is expressed as follows:

The crystal structures of the t and m phases of PSZ are shown in Figure 6 [24]. This phase transformation is considered to be a martensitic transition. Generally, an athermal diffusionless martensitic transition occurs quickly, with the motion of the phase boundary as high as the speed of sound [25]. The overall transition proceeds in two major stages [26]. First, the transition of the lattice structure from tetragonal to monoclinic occurs by the shearing displacement of zirconium ions. The second stage involves the sliding of oxygen ions to the oxygen sites in the monoclinic lattice. The displacement of oxygen ions from the ideal fluorite positions along the c-axis was investigated by X-ray diffraction (XRD) [27]. Therefore, the 100 keV electron is considered to cause the shearing displacement of zirconium ions and the sliding of oxygen ions. In [9], the reported activation energies for the phase transition are close to 100 kJ/mol (~1 eV), which is similar to the activation energy for the sliding of oxygen ions to oxygen sites. In order to find the mechanism of the phase transition, the factor of the sliding of oxygen ions to oxygen sites should

$$E\_p = \frac{2M\_\varepsilon}{M\_\Gamma} \cdot \frac{1}{M\_\varepsilon c^2} \left( E + 2M\_\varepsilon c^2 \right) E \text{ } \sin^2 \frac{\theta}{2} \tag{4}$$

where *E*, , *c*, *M*T, and *Me* denote the energy of the incident electron, scattering angle, speed of light, mass of the target atom, and electron mass, respectively. Therefore, in the case of = 0°, *E*p takes the maximum value (*E*p, max), which is represented by the following where *E*, *θ*, *c*, *M*T, and *M<sup>e</sup>* denote the energy of the incident electron, scattering angle, speed of light, mass of the target atom, and electron mass, respectively. Therefore, in the case of *θ* = 0◦ , *E<sup>p</sup>* takes the maximum value (*Ep,max*), which is represented by the following equation:

$$E\_{p,\max} = \frac{2E\left(E + 2M\_{\ell}c^2\right)}{M\_{\Gamma}c^2} \tag{5}$$

Figure 7 shows the *Ep,max* for Zr, Y, and O atoms, as a function of the energy of the incident electron. The result shows that the value of *Ep,max* for the O atom is 1 eV at the energy of the 7.2 keV incident electron. This suggests that a 100 keV electron can cause the migration of oxygen ions to oxygen sites, by elastic scattering, to trigger the phase transition. Figure 7 shows the *Ep,max* for Zr, Y, and O atoms, as a function of the energy of the incident electron. The result shows that the value of *Ep,max* for the O atom is 1 eV at the energy of the 7.2 keV incident electron. This suggests that a 100 keV electron can cause the migration of oxygen ions to oxygen sites, by elastic scattering, to trigger the phase transition. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 7 of 9

**Figure 7.** Kinetic energy transfer for Zr, Y, and O atoms due to elastic scattering as a function of the energy of the incident electron. **Figure 7.** Kinetic energy transfer for Zr, Y, and O atoms due to elastic scattering as a function of the energy of the incident electron.

Another factor to consider are the excitation-related processes [28]. The amorphousto-crystalline phase transition via the excitation-related processes is often observed in amorphous ceramics such as Al*2*O*3*, ScPO*4* and LaPO*4*[29]. The behavior of phase transition Another factor to consider are the excitation-related processes [28]. The amorphousto-crystalline phase transition via the excitation-related processes is often observed in amorphous ceramics such as Al2O3, ScPO<sup>4</sup> and LaPO<sup>4</sup> [29]. The behavior of phase transi-

via excitation-related processes is known to have an approximate relationship with the

 ቌඨ℮ 2 

> 58.5 ̅

ቍ (6)

.ଵଽ, (7)

െ

ൌ 2ସ

is opposite, the influence of kinetic energy application is considered to be large.

ൌ 9.76̅

where e is the elementary charge, *NA* is the Avogadro number, is the mass density, *Z* is the atomic number, *A* is the atomic weight, *E* is the electron energy, ℮ is the base of natural logarithm, *I* is the mean excitation energy, and ̅ is the mean atomic number.

Figure 8 shows the calculation result of the stopping power for electron in ZrO2 as a function of the energy of the incident electron. The result indicates that the stopping power increases with the decreasing incident electron energy. This tendency is in contrast to the kinetic energy of the elastic collision as shown in Figure 7. The possible factors that cause the phase transformation are the transfer of kinetic energy or the electronic excitation effect. In further research, in order to investigate the mechanism of the m→t phase transition in PSZ, it is important to determine the energy dependence of the phase transformation by low-energy electron beams. If the phase transformation rate increases with decreasing incident electron energy, the electronic excitation effect is the main factor. On the other hand, when the tendency between the energy and the phase transformation rate

Bethe formula [30], which is as the following:

tion via excitation-related processes is known to have an approximate relationship with the Bethe formula [30], which is as the following:

$$-\frac{dE}{d\mathbf{x}} = 2\pi e^4 N\_A \frac{\rho Z}{AE} \ln\left(\sqrt{\frac{\tau}{2}} \frac{E}{I}\right) \tag{6}$$

$$I = 9.76\overline{Z} + \frac{58.5}{\overline{Z}^{0.19}} \tag{7}$$

where e is the elementary charge, *N<sup>A</sup>* is the Avogadro number, *ρ* is the mass density, *Z* is the atomic number, *A* is the atomic weight, *E* is the electron energy, is the base of natural logarithm, *I* is the mean excitation energy, and *Z* is the mean atomic number.

Figure 8 shows the calculation result of the stopping power for electron in ZrO<sup>2</sup> as a function of the energy of the incident electron. The result indicates that the stopping power increases with the decreasing incident electron energy. This tendency is in contrast to the kinetic energy of the elastic collision as shown in Figure 7. The possible factors that cause the phase transformation are the transfer of kinetic energy or the electronic excitation effect. In further research, in order to investigate the mechanism of the m→t phase transition in PSZ, it is important to determine the energy dependence of the phase transformation by low-energy electron beams. If the phase transformation rate increases with decreasing incident electron energy, the electronic excitation effect is the main factor. On the other hand, when the tendency between the energy and the phase transformation rate is opposite, the influence of kinetic energy application is considered to be large. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 8 of 9

**Figure 8.** Stopping power for incident electrons normalized at 100 keV electron energy in ZrO2. **Figure 8.** Stopping power for incident electrons normalized at 100 keV electron energy in ZrO<sup>2</sup> .

#### **5. Conclusions 5. Conclusions**

It was observed that the monoclinic phase in 3Y-PSZ increased with increasing electron-beam fluence. The calculation results using PHITS suggested that the energy deposited by a 100 keV electron to the PSZ lattice was not the main reason for the phase transition. The NIEL calculation indicated that the atoms in the PSZ only recoiled under electron irradiation at energies over 0.56 MeV; 100 keV electrons cannot cause displacement dam-It was observed that the monoclinic phase in 3Y-PSZ increased with increasing electronbeam fluence. The calculation results using PHITS suggested that the energy deposited by a 100 keV electron to the PSZ lattice was not the main reason for the phase transition. The NIEL calculation indicated that the atoms in the PSZ only recoiled under electron irradiation at energies over 0.56 MeV; 100 keV electrons cannot cause displacement damage.

age. However, the kinetic energy or the excitation-related processes from incident electrons in the PSZ might be higher than the energy needed to shift oxygen ions to oxygen However, the kinetic energy or the excitation-related processes from incident electrons in the PSZ might be higher than the energy needed to shift oxygen ions to oxygen sites, and is suggested to be the cause of the phase transition.

sites, and is suggested to be the cause of the phase transition. **Author Contributions:** Conceptualization, Y.O. and Y.O.; methodology, Y.O.; software, Y.O.; validation, Y.O.; formal analysis, Y.O.; investigation, Y.O.; resources, N.O.; data curation, Y.O.; writing—original draft preparation, Y.O.; writing—review and editing, Y.O.; visualization, Y.O.; supervision, N.O.; project administration, N.O.; funding acquisition, N.O. All authors have read and **Author Contributions:** Conceptualization, Y.O. and Y.O.; methodology, Y.O.; software, Y.O.; validation, Y.O.; formal analysis, Y.O.; investigation, Y.O.; resources, N.O.; data curation, Y.O.; writing original draft preparation, Y.O.; writing—review and editing, Y.O.; visualization, Y.O.; supervision, N.O.; project administration, N.O.; funding acquisition, N.O. All authors have read and agreed to the published version of the manuscript.

**Acknowledgments:** We would like to thank Takashi Oka and Shuichi Okuda (OPU) for supporting

**Conflicts of Interest:** The authors declare no conflict of interest.

1. Tsujimoto, K.; Oigawa, H.; Ouchi, N.; Kikuchi, K.; Kurata, Y.; Mizumoto, M.; Sasa, T.; Saito, S.; Nishihara, K.; Umeno, M.; Tazawa, Y. Research and Development Program on Accelerator Driven Subcritical System in JAEA. *J. Nucl. Sci. Technol.* **2007**,

2. Oigawa, H.; Tsujimoto, K.; Nishihara, K.; Sugawara, T.; Kurata, Y.; Takei, H.; Saito, S.; Sasa, T.; Obayashi, H. Role of ADS in the back-end of the fuel cycle strategies and associated design activities: The case of Japan. *J. Nucl. Mater.* **2011**, *415*, 229. 3. Kurata, Y. Corrosion experiments and materials developed for the Japanese HLM systems. *J. Nucl. Mater.* **2011**, *415*, 254. 4. Yeliseyeva, O.; Tsisar, V.; Benamati, G. Influence of temperature on the interaction mode of T91 and AISI 316L steels with Pb–

5. Schroer, C.; Skrypnik, A.; Wedemeyer, O.; Konys, J. Oxidation and dissolution of iron in flowing lead–bismuth eutectic at 450 °C.

6. Deloffre, P.; Terlain, A.; Barbier, F. Corrosion and deposition of ferrous alloys in molten lead–bismuth. *J. Nucl. Mater*. **2002**, *301*,

7. Fernandez, J.A.; Abella, J.; Barcelo, J.; Victori, L. Development of an oxygen sensor for molter 44.5% lead–55.5% bismuth alloy.

8. Schroer, C.; Konys, J.; Verdaguer, A.; Abellà, J.; Gessi, A.; Kobzova, A.; Babayan, S.; Courouau, J.-L. Design and testing of elec-

trochemical oxygen sensors for service in liquid lead alloys. *J. Nucl. Mater*. **2011**, *415*, 338–347.

agreed to the published version of the manuscript.

our electron irradiation tests.

Bi melt saturated by oxygen. *Corros. Sci.* **2008**, *50*, 1672.

**References** 

*44*, 483.

35–39.

*Corros. Sci*. **2012**, *61*, 63.

*J. Nucl. Mater.* **2002**, *301*, 47–52.

**Funding:** This research received no external funding.

**Acknowledgments:** We would like to thank Takashi Oka and Shuichi Okuda (OPU) for supporting our electron irradiation tests.

**Conflicts of Interest:** The authors declare no conflict of interest.
