**3. Results**

Figure 1 shows the XRD pattern of 3Y-PSZ before and after irradiation with a 100 keV electron beam. In Figure 1a, the main XRD peaks are assigned to all measurement regions. This result indicates that the t (111) phase dominates the 3Y-PSZ specimen at approximately 2*θ* = 30◦ , before and after irradiation [16]. The peaks of the m (11 − 1) and (111) phases at approximately 2*θ* = 28◦ and 31.5◦ do not appear because the signal intensity is much lower than that of the t phase. A peak is known to exist in the m (11 − 1) phase. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 3 of 9

**Figure 1.** XRD patterns of a PSZ specimen before and after irradiation with 100 keV electron beams. The black line is before irradiation. (**a**) is the spectrum of the measured range shifted up by 100; (**b**) is the spectrum focused on m (11 − 1) between 27 and 29°. **Figure 1.** XRD patterns of a PSZ specimen before and after irradiation with 100 keV electron beams. The black line is before irradiation. (**a**) is the spectrum of the measured range shifted up by 100; (**b**) is the spectrum focused on m (11 − 1) between 27 and 29◦ .

ൌ 0.82 ൈ

phase transformation in 3Y–PSZ is caused by electron irradiation.

The fraction *C*M of the m phase to the t phase can be evaluated from the peak areas of

୲ሺ101ሻ ൈ 100%, (1)

sin <sup>൰</sup> (2)

୫ሺ11 െ 1ሻ ୫ሺ111ሻ

where *I*m and *I*t are the peak intensities of m and t, respectively. Figure 2 shows the fractional content of the m phase as a function of the electron fluence. This result indicates that the fractional content of m increases as the absorbed dose increases. Therefore, the

**Figure 2.** Fraction of monoclinic zirconia as a function of the fluence of 100 keV electrons.

layer of depth , can be expressed using the following [17,18]:

Because the phase transition is detected by XRD, the absorbed dose should be calculated in the shallow surface region that is probed by XRD. This region was determined by the X-ray penetration depth. The fraction ሺሻ of the total diffracted intensity, due to a surface

ሺሻ ൌ 1 െ exp ൬െ2

[13]:

27 and 29°.

In Figure 1b, to focus on the m (11 − 1) peak, the diffraction angle was set between 27◦ and 29◦ . The results show that the intensity of the peak monotonically increases after irradiation, depending on the fluence of 100 keV electrons. irradiation. (**a**) is the spectrum of the measured range shifted up by 100; (**b**) is the spectrum focused on m (11 − 1) between The fraction *C*M of the m phase to the t phase can be evaluated from the peak areas of

*Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 3 of 9

**Figure 1.** XRD patterns of a PSZ specimen before and after irradiation with 100 keV electron beams. The black line is before

The fraction *C*<sup>M</sup> of the m phase to the t phase can be evaluated from the peak areas of the most intense signals of t (101), m (11 − 1), and t (111), using the following equation [13]: the most intense signals of t (101), m (11 − 1), and t (111), using the following equation [13]:

$$\text{C}\_{\text{M}} = 0.82 \times \frac{I\_{\text{m}}(11-1) + I\_{\text{m}}(111)}{I\_{\text{t}}(101)} \times 100\% \tag{1}$$

where *I*<sup>m</sup> and *I*<sup>t</sup> are the peak intensities of m and t, respectively. Figure 2 shows the fractional content of the m phase as a function of the electron fluence. This result indicates that the fractional content of m increases as the absorbed dose increases. Therefore, the phase transformation in 3Y–PSZ is caused by electron irradiation. where *I*m and *I*t are the peak intensities of m and t, respectively. Figure 2 shows the fractional content of the m phase as a function of the electron fluence. This result indicates that the fractional content of m increases as the absorbed dose increases. Therefore, the phase transformation in 3Y–PSZ is caused by electron irradiation.

**Figure 2.** Fraction of monoclinic zirconia as a function of the fluence of 100 keV electrons. **Figure 2.** Fraction of monoclinic zirconia as a function of the fluence of 100 keV electrons.

Because the phase transition is detected by XRD, the absorbed dose should be calculated in the shallow surface region that is probed by XRD. This region was determined by the X-ray penetration depth. The fraction ሺሻ of the total diffracted intensity, due to a surface layer of depth , can be expressed using the following [17,18]: Because the phase transition is detected by XRD, the absorbed dose should be calculated in the shallow surface region that is probed by XRD. This region was determined by the X-ray penetration depth. The fraction *G*(*x*) of the total diffracted intensity, due to a surface layer of depth *xx*, can be expressed using the following [17,18]:

$$G(\mathbf{x}) = 1 - \exp\left(\frac{-2\mu\mathbf{x}}{\sin\theta}\right) \tag{2}$$

where *µ* is the absorption coefficient and −2*µx*/ sin *θ* is the effective path length for X-rays to penetrate to a depth *x* at a given Bragg angle *θ*. For the PSZ, the path length of Cu Kα X-rays incident at *θ* = 28◦ is approximately 9 µm, as shown in Equation (2), with *G*(*x*) = 0.99. The electrons are known to have a short flight distance in the materials. To investigate the range of the flight distance, the Monte Carlo calculation for radiation behavior was conducted, using the particle and heavy ion transport code system (PHITS) [19].

Figure 3 shows the depth distribution of the dose from the surface of the PSZ, in the case of irradiation with one of the 100 keV electrons. This result indicates that the value of the dose rate peaks at approximately 5 µm, and continues to 30 µm. Therefore, the flight range of a 100 keV electron was considered to be longer than the observation range of the XRD analysis.

When charged particles, e.g., electrons and ions, pass through materials, the radiation effect is expressed as a loss of energy, due to an interaction called total stopping power (*S*). One type of S is collision stopping power (*S*col), e.g., electronic stopping power (*S*e), nuclear stopping power (*S*n), and radiative stopping power (*S*rad). S<sup>n</sup> is the main factor that causes the displacement and migration of atoms.

Cu Kα X-rays incident at

[19].

XRD analysis.

θ

**Figure 3.** Calculation result of dose rate as a function of the depth from surface. **Figure 3.** Calculation result of dose rate as a function of the depth from surface.

When charged particles, e.g., electrons and ions, pass through materials, the radiation effect is expressed as a loss of energy, due to an interaction called total stopping power (*S*). One type of S is collision stopping power (*S*col), e.g., electronic stopping power (*S*e), In an effort to describe the fraction of energy that moves into displacements such as the *S*n, due to radiation, the non-ionizing energy loss (NIEL) was developed and is expressed as follows [20–22]:

where is the absorption coefficient and െ2/sin is the effective path length for Xrays to penetrate to a depth at a given Bragg angle . For the PSZ, the path length of

ሺሻ = 0.99. The electrons are known to have a short flight distance in the materials. To investigate the range of the flight distance, the Monte Carlo calculation for radiation behavior was conducted, using the particle and heavy ion transport code system (PHITS)

Figure 3 shows the depth distribution of the dose from the surface of the PSZ, in the case of irradiation with one of the 100 keV electrons. This result indicates that the value of the dose rate peaks at approximately 5 μm, and continues to 30 μm. Therefore, the flight range of a 100 keV electron was considered to be longer than the observation range of the

= 28° is approximately 9 μm, as shown in Equation (2), with

$$\text{NIEL}\left(E\right) = \frac{N\_A}{A} \int\_{\theta\_{\text{min}}}^{\pi} L\left[T(\theta, E)\right] T(\theta, E) \frac{\text{d}\sigma(\theta, E)}{\text{d}\Omega} d\Omega \tag{3}$$

the *S*n, due to radiation, the non-ionizing energy loss (NIEL) was developed and is expressed as follows [20–22]: NIEL ሺሻ ൌ න ሾሺ, ሻሿሺ, ሻ dሺ, ሻ d ఏ , ሺ3ሻ (3) where *NA* is Avogadro's number, *A* is the atomic mass, *E* is the energy of the incident where *N<sup>A</sup>* is Avogadro's number, *A* is the atomic mass, *E* is the energy of the incident particle, *θ* is the scattering angle, *σ* is the scattering cross-section, and Ω is the solid angle of scattering. The equation also requires information regarding the differential cross-section for atomic displacements (d*σ*(*θ*, *E*)/dΩ), the average recoil energy of the target atoms (*T*(*θ*, *E*)), and the Lindhard partition factor (*L*[*T*(*θ*, *E*)]), which partitions the energy into ionizing and non-ionizing events.

particle, *θ* is the scattering angle, \_\_\_\_ is the scattering cross-section, and is the solid angle of scattering. The equation also requires information regarding the differential cross-section for atomic displacements (dሺ, ሻ/d), the average recoil energy of the target atoms (ሺ, ሻ), and the Lindhard partition factor (ሾሺ, ሻሿ), which partitions the energy into ionizing and non-ionizing events. Figure 4 shows the NIEL vs. energy for Zr, Y, and O atoms for electrons. The result shows that the NIEL value for each element rapidly increases above a certain energy threshold (*E*th). An increase in the NIEL value means that the kinetic energy given by the electron beam to the atom exceeds the displacement threshold energy (*E*d) and causes the production of a primary knock-on atom (PKA). *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 5 of 9

Figure 4 shows the NIEL vs. energy for Zr, Y, and O atoms for electrons. The result

effect, similar to PKA.

**Figure 4.** Non-ionizing energy loss (NIEL) vs. electron energy calculated for Zr, Y, and O atoms. The values of Ed for Zr, Y, and O are 80, 80, and 120 eV, respectively. **Figure 4.** Non-ionizing energy loss (NIEL) vs. electron energy calculated for Zr, Y, and O atoms. The values of E<sup>d</sup> for Zr, Y, and O are 80, 80, and 120 eV, respectively.

However, the *E*th values of Y, Zr, and O are higher than the energy of the incident electrons by approximately 2200, 1250, and 600 keV, respectively. Therefore, the phase However, the *E*th values of Y, Zr, and O are higher than the energy of the incident electrons by approximately 2200, 1250, and 600 keV, respectively. Therefore, the phase

From the calculation result in Figure 3, the deposition energy such as the *S*e is also estimated to be 1.9 × 10−14 eV when an electron passes the lattice of t-PSZ having a volume of 137 Å3, which might be much lower than the energy that causes the phase transition. The phase transition from t to m in the PSZ is also known to be a thermal effect which is between 150 and 300 °C, as shown in Figure 5 [23]. The electron beam that heats the sample surface is considered to be about 80 mW because the condition of electron beam is a defocus-beam, rather than a micro-focus beam. The region such as 25 μm from the surface, which is main energy deposition region indicated from Figure 3, is 11 K/s. The sample temperature between the electron irradiation was less than 40 °C. For the above reasons, in the irradiation, the sample temperature is lower than the annealing temperature which causes a phase transition from the t-to-m phase. Therefore, the observed phase transition caused by the irradiation with 100 keV electrons is not considered to be a radi-

**Figure 5.** Relationship between the amount of the monoclinic phase and annealing temperature in

ation effect such as the Se, the Sn and the thermal effect.

PSZ fabricated above 1500 ℃ [23]. The annealing time is 50 h.

**4. Discussion** 

1.E-07

10-7

1.E-06

10-6

NIEL(MeV cm2

 g-1)

1.E-05

10-5

1.E-04

10-4

transition is considered to be caused by the transfer of kinetic energy lower than the recoil effect, similar to PKA. transition is considered to be caused by the transfer of kinetic energy lower than the recoil effect, similar to PKA.

However, the *E*th values of Y, Zr, and O are higher than the energy of the incident electrons by approximately 2200, 1250, and 600 keV, respectively. Therefore, the phase

**Figure 4.** Non-ionizing energy loss (NIEL) vs. electron energy calculated for Zr, Y, and O atoms. The

*Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 5 of 9

values of Ed for Zr, Y, and O are 80, 80, and 120 eV, respectively.

012345

Zr O Y

Electron energy (MeV)

From the calculation result in Figure 3, the deposition energy such as the *S*<sup>e</sup> is also estimated to be 1.9 <sup>×</sup> <sup>10</sup>−<sup>14</sup> eV when an electron passes the lattice of t-PSZ having a volume of 137 Å<sup>3</sup> , which might be much lower than the energy that causes the phase transition. From the calculation result in Figure 3, the deposition energy such as the *S*e is also estimated to be 1.9 × 10−14 eV when an electron passes the lattice of t-PSZ having a volume of 137 Å3, which might be much lower than the energy that causes the phase transition.

The phase transition from t to m in the PSZ is also known to be a thermal effect which is between 150 and 300 ◦C, as shown in Figure 5 [23]. The electron beam that heats the sample surface is considered to be about 80 mW because the condition of electron beam is a defocus-beam, rather than a micro-focus beam. The region such as 25 µm from the surface, which is main energy deposition region indicated from Figure 3, is 11 K/s. The sample temperature between the electron irradiation was less than 40 ◦C. For the above reasons, in the irradiation, the sample temperature is lower than the annealing temperature which causes a phase transition from the t-to-m phase. Therefore, the observed phase transition caused by the irradiation with 100 keV electrons is not considered to be a radiation effect such as the Se, the Sn and the thermal effect. The phase transition from t to m in the PSZ is also known to be a thermal effect which is between 150 and 300 °C, as shown in Figure 5 [23]. The electron beam that heats the sample surface is considered to be about 80 mW because the condition of electron beam is a defocus-beam, rather than a micro-focus beam. The region such as 25 μm from the surface, which is main energy deposition region indicated from Figure 3, is 11 K/s. The sample temperature between the electron irradiation was less than 40 °C. For the above reasons, in the irradiation, the sample temperature is lower than the annealing temperature which causes a phase transition from the t-to-m phase. Therefore, the observed phase transition caused by the irradiation with 100 keV electrons is not considered to be a radiation effect such as the Se, the Sn and the thermal effect.

PSZ fabricated above 1500 ℃ [23]. The annealing time is 50 h.

**Figure 5.** Relationship between the amount of the monoclinic phase and annealing temperature in **Figure 5.** Relationship between the amount of the monoclinic phase and annealing temperature in PSZ fabricated above 1500 ◦C [23]. The annealing time is 50 h.
