3. Discussion

Measurement of vacancy motion in solid state materials is a challenging work. There are not so many experimental methods. In situ HVEM has been proven to be one of the powerful tools to obtain vacancy migration energy by measuring the temperature dependence of the growth speed of a dislocation loop during electron irradiation. A reasonable phenomenological model of the loop growth could be selected and applied to extract the vacancy migration energy from the experimental data. Kiritani et al. firstly proposed one linear model to calculate the vacancy migration energy. Then, Wan et al. derived a new formula by considering the surface effect. In this chapter, a new nonlinear model was developed by considering the other sink effects such as surface, small void, small precipitates, and grain boundary, and the numerical method was rediscussed. When the measured experimental data are ideal, not affected by the surface or other defect sinks, the vacancy migration energy value calculated by the three methods should be the same. One experimental example for calculating the vacancy migration energy by using the three methods was given here. The sample was Fe-10Cr model alloy which was preimplanted by He and H ion sequentially. Then electron irradiation and in situ observation were carried out in HVEM at 573, 673, and 773 K. At a corresponding temperature, the growth rates of dislocation loop were measured [15]. But, the ln (dR/dt) and 1/T calculated from the experimental data were not strict linear that means there may be influences from the sample surface or other sinks. Thus, three assumed ideal values of the growth rate which are close to the three experimental values were selected to test the three methods, which are about 1.1 nm/min at 573 K, 3.5 nm/min at 673 K, and 8.1 nm/min at 773 K, respectively. According to these values, the ln(dR/dt) and 1/T followed a strict linear relationship, which means an ideal situation without the effect of other sinks. Then, the three methods were used to calculate the vacancy migration energy in this ideal case, and the results were shown in Figure 1. Figure 1(a) showed the result calculated by the linear method where blue squares are the experimental data and red pentagrams are the ideal values. The result calculated by the numerical method was shown in Figure 1(b); the solving process example of the Eq. (17) was given in the Appendix. Figure 1(c) showed the result calculated by the nonlinear method where the horizontal axis

#### Figure 1.

Measurement of vacancy migration energy in sequential-(He+H) ion implanted Fe-10Cr samples according to the ideal values by using linear method (a), numerical method (b), and nonlinear method (c), respectively.


Measurement of Vacancy Migration Energy by Using HVEM DOI: http://dx.doi.org/10.5772/intechopen.87131

#### Table 1.

The characteristics of three methods for measuring vacancy migration energy.

represents the inverse of the growth rate and the vertical axis represents the inverse of temperature. These results indicated that the vacancy migration energy value calculated by the three methods according to ideal values in He+H pre-implanted Fe-10Cr sample was the same which was about 1.52 eV, while the vacancy migration energy values calculated by a different method according to the experimental data were different because of the different characteristics of the method. The characteristics of three methods for measuring vacancy migration energy were listed in Table 1.

In addition, if the linear fitting degree is larger than 0.9 which means the effect of other sinks was not dominated, linear model was preferred to fitting the experimental data and obtaining the value of vacancy migration energy because it is very simple. Otherwise, nonlinear model or numerical method should be used in considering the surface effect and other sink effect intrinsically. And, the overall influence of other sinks was also given as an influence factor (B) in the nonlinear model. It is worth to note that the "nonlinear method" has one more parameter than "linear method," which means there is a bigger possibility for overfitting problem to arise. Thus, one should notice that parameter B should be negative according to Eq. (31) to avoid the overfitting problem. Another thing which needs to be noted is that Mi >> Mv is appropriate for pure metals, but Mv > Mi may exist for some alloys [11, 16, 17]. The anti-noise property and the result reliability of different methods were also discussed in Ref. [18] and listed in Table 1. Then, one can choose an appropriate method to measure the vacancy migration energy according to the anti-noise property, result reliability, and other characteristics of the three different methods.
