Fig. 4. Defect clusters evolution in Na_2/3Fe_1/2Mn_1/2O₂ under Kr ion irradiation.

Grayscale bright-field two-beam images are acquired to study the defect clusters distribution and evolution. a Scheme presenting the calculation of the gradient vector from a certain pixel of a bright-field two-beam image. The gradient vector points to the overall directional change in pixel value. Gradient vector calculated and superimposed on the bright-field two-beam image of a Na_2/3Fe_1/2Mn_1/2O₂ particle irradiated at the total fluence of b 6.25 × 10¹³ Kr²⁺/cm², c 1.88 × 10¹⁴ Kr²⁺/cm², d 4.38 × 10¹⁴ Kr²⁺/cm², and e 5.0 × 10¹⁴ Kr²⁺/cm² at room temperature. Bright-field two-beam image of a Na_2/3Fe_1/2Mn_1/2O₂ particle irradiated at the total fluence of f 6.25 × 10¹⁴ Kr²⁺/cm² at room temperature. The bright-field images are taken from the [100] zone axis. All the scale bars in the image b–f correspond to a length of 100 nm. g Distribution of the gradient vectors of image b–e against the angle of the gradient vector. The inset shows the scheme of how the angle of the gradient vector is defined. Dynamic defect evolution in a Na_2/3Fe_1/2Mn_1/2O₂ particle with increasing fluence of Kr ion irradiation  (h–j). The dynamic defect evolution is studied through the subtraction of the image acquired at higher irradiation dose from that of the lower irradiation dose (e.g., image c subtracted from image b). Defect evolution from h image b–c, i image c–d, and j image d–e. All the scale bars from images h–j correspond to a length of 100 nm. The color bar shows the corresponding values of the subtracted pixels after the subtracted grayscale image is converted to an RGB image. k Distribution of the gradient vectors of images h–j against the angle of the gradient vector.