We detected NaCl particles yielded from an acetone solution of dissolved NaClO₃ powder crystals. The solution contained molecular sieves as a desiccant to eliminate residual water, which substantially lowered the amount of dissolved NaClO₃ because of the large difference in solubility [36 g in 100 g water vs. 4.2 × 10^–5 g in 100 g acetone (Burgess, 1978)], thereby increasing the waiting time for nucleation of NaCl crystals. The magnification was 2000×, and the dose rate was 310 electrons nm⁻²s⁻¹. Examples of the detection of NaCl particles are shown in Figure 1, where the image size is 12 μm × 12 μm. We conducted a continuous observation, and the view was fixed at time t = 0 s. In the dark area at the edge of the image, the electron beam was blocked by the aperture. The bright circular region was filled with the saturated acetone solution of NaClO₃. Until 19 s, no apparent change was observed and there was no detection (Figure 1A). The first particle was detected at t = 19.1 s (Figure 1B) and exhibited a radius of ∼150 nm. The second, third, and fourth particles were detected at t = 22.4 s (Figure 1C), t = 24.5 s (Figure 1D), and t = 28.4 s (Figure 1E), respectively. In all cases, the radius of the particles was ∼200 nm at the beginning of the detection in the 12 μm × 12 μm image.

Figure 2 shows the change in the number of detected particles as a function of time. The red solid line and the green broken line show the number of detections and that of labeling by the human eye. Because the human-eye observations involve repeated observations and adjustments to the contrast, tiny particles can be labeled. The machine learning algorithm used in present study can detect particles with a delay of ∼3 s compared with the data labeling by the human eye. The delay in detection by the standard YOLOv5 algorithm is comparable to the delay when a person observes a particle when watching a video directly the first time.

In the video, the view is almost motionless until t = 45 s. At t > 45 s, the view shifts to the upper left. Thus, the particles appear to have moved to the lower right, as shown in Figure 1F. The number of particles in the image also decreases. Even though part of the particle is hidden by the aperture and its shape appears to not be circular, it is still detected. Immediately before t = 50 s, one half-moon-shaped particle is detected momentarily in the video.

Although some detection failures occurred, no false positive were detected. In this video, the total recall score was 0.82 (Table 4). When particles became large (40 s < t < 50 s), the recall score was 0.93. This recall value is approximately the same as that of the validation data shown in Table 3.

From the obtained data of corresponding to the detected boxes, we obtained time changes of the radii of five particles (Figure 3). Each box is slightly larger than their corresponding particles. The systematic deviation does not strongly affect the study of its time change. The shape of particles is assumed to circular, and the radius of particles is estimated on the basis of the geometric average of one-half the height and one-half the width of the box. The growth rates of each particle were obtained by fitting the data in the region 35 s < t < 45 s (solid lines in Figure 3); these values are summarized in Table 5. The radius of the fifth particle may not be accurate because the window prevented us from observing the entire particle. The average growth rate excluding the fifth particle was 9.5 nm s⁻¹.

The growth rate V(r) can be predicted by classical nucleation theory. When a circular particle with radius r grows in a system, the growth rate V(r) is obtained as V r = V ∞ 1 − r c r , (3) where r _c is the critical radius and V _∞ is a constant, that depends on the concentration and the temperature. When the radius of the particle is larger than the critical radius, the growth rate is close to a constant asymptotically. The radius increases linearly with time. From our data, the value of the growth rate V _∞ is ∼9.5 nm s⁻¹.

The growth rate V of the stem of the NaCl crystals under the dose rate F is written as V = K′F ^1/2, where the effective kinetic coefficient K′ is ∼8.5 electron^−1/2 nm² s^1/2 (Figure 6 in Yamazaki and Kimura (2021)]. When the dose rate is substituted as 310 electrons nm^{−2 s−1}, the growth rate is obtained as 150 nm s⁻¹, which is very different from our observed growth rate of 9.5 nm s⁻¹. The effective dose rate appears to be reduced by the presence of molecular sieves in the solution. Because the crystal shown in Figure 6 in Yamazaki and Kimura (2021) is sufficiently large, the effective dose rate in Figure 1 is estimated as 1.2 electrons nm⁻²s⁻¹, using a obtained growth rate of 9.5 nm s⁻¹. Thus, the effective electron dose rate becomes 1/250 as a result of molecular sieves.

In classical nucleation theory, small particles grow slower than large particles because of the surface tension, which is well known as the Gibbs-Thomson effect. However, our data for particles 1 and 4 suggest the opposite trends: the growth rate of a small particle is larger than that of a large particle. The growth rates of particles 1 and 4 with radii less than 400 nm are 24.7 nm s⁻¹ and 21.6 nm s⁻¹, respectively. The magnitude of the growth rate of particles with a radius smaller than 400 nm is twice larger than that of the same particle with a radius larger than 400 nm. The particles do not rotate because they are formed on a membrane. In addition, our observed particle is approximately circular, and the orientational dependence of the growth rate is negligible. The growth rate is almost the same for particles 1 and 4, even though the timing of their formation is different. The degree of supersaturation does not change through the volume diffusion of materials.

There are two possibilities of the change of the growth rate. One is the occurrence of the phase transition of a particle at the radius of 400 nm. Another is the heterogeneous nucleation of the stable phase on the metastable phase. Our observations do not allow us to distinguish between them. We speculate that the non-linear function arises from the crossover between the growth of the metastable phase and the growth by the heterogeneous nucleation of the stable phase on the surface of the metastable phase. Thus, the larger growth rate indicates that a metastable phase appears in the early stages of the nucleation process. This conclusion suggests that the nucleation of NaCl from a saturated solution of NaClO₃ in acetone is not a single-phase process. We therefore found an example of the two-step nucleation process of simple circular precipitates.

We investigate the detectability of dendritic crystals that exhibit rapid growth. The magnification was 3,000× and the dose rate was 2.0 × 10² electron nm⁻²s⁻¹. The solution was the same as that studied in the previous section but without the addition of molecular sieves. The outline of the video is as follows: The observation starts at t = 0 s and many nanoparticles emerge within 1 s. At t = 1 s, the nucleation of nanoparticles is almost completed and each nanoparticle grows. Moreover, nanoparticles also coalesce with their neighbors. The production of nanoparticles stops because the solute is consumed by the nucleation and growth of the nanoparticles.

Examples of the detection by machine learning of dendritic crystals are shown in Figure 4. Here, t = 0 s corresponds to when the shutter was opened. Immediately after the shutter was opened (Figure 4A), no objects were observed. At t = 0.4 s, numerous tiny particles emerge although there is no detection by machine learning (Figure 4B). Our detection by machine learning often overlooks small nuclei. The first detection is at t = 0.6 s (Figure 4C). As time passes, the number of detections increases (Figures 4D–F). To check the detectability, we counted the number of dendritic crystals by adjusting the contrast. Figure 5 shows the numbers of particles suggested by YOLOv5 (red square) and counted by the human eye (green cross). The numbers increase in the period t < 1 s, and a difference is observed between the result obtained by YOLOv5 and that by the human eye. Both results show that the number of particles was steady at t > 3 s, and both results are consistent. In the steady region (t > 3 s), the dendritic crystals become large and are clearly observed and the change in the image is relatively small. In this case, the number of dendritic crystals counted by YOLOv5 is consistent with that of counted by the human eye. During steady growth, the standard YOLOv5 algorithm can detect crystals at the same level as the human eye, as mentioned in the preceding subsection.

As we characterize the change of the number of particles over time, we can estimate the nucleation rate. The nucleation rate indicates how many nuclei are yielded per unit area and unit time. The observed nuclei appear on amorphous silicon nitride membranes on the top and the bottom of a silicon tip (Yamazaki and Kimura, 2021). The nucleation occurs in two dimensions and the area is ∼ 88 μm², when both the top and bottom surfaces of the membrane are considered. By fitting the data, we can estimate the nucleation rate as 0.3 μm⁻²s⁻¹ (solid line) and 0.8 μm⁻²s⁻¹ (broken line) on the basis of detection using the standard YOLOv5 algorithm and detection by the human eye, respectively. Although the number of particles by YOLOv5 is less than one-half of that detected by the human eye, the estimated nucleation rates are of the same order. In most discussions concerning crystallization, determining the order of the nucleation rate is sufficient. If we need to estimate physical quantities such as the nucleation rate more accurately, improving the detectability by preprocessing the images is worthwhile.

In the preceding subsection, we detected circular shaped particles in a video in which the particles slowly changed. In this subsection, we detect dendritic particles whose size and shape change rapidly under a dose rate of 2.0 × 10² electron nm⁻²s⁻¹. As reported in (Yamazaki and Kimura, 2021), the growth rate depends on the dose rate in a solution without molecular sieves. Although the dose rate is smaller than that in Figure 1, numerous dendrites are formed. The shape of the nanoparticles depends on the degree of supersaturation. When the degree of supersaturation is low, the shape is similar to the equilibrium shape, which is compact. When the degree of supersaturation is high, the shape becomes dendritic because fast growth proceeds before sufficient relaxation of the shape can occur. Because the amount of water is related to the precipitation of NaCl crystals, the effect of water loss due to molecular sieves strongly affects the degree of supersaturation. The decrease in the degree of supersaturation is attributed to a decrease in the amount of dissolved chlorate ions, which become chloride ions (Yamazaki and Kimura, 2021). In Figure 2, we observe the appearance of five particles in the 126 μm² solution area in 10 s and the nucleation rate is estimated as 0.004 μm⁻² s⁻¹. This rate is 200 times smaller than the value obtained in Figure 4. It is a conventional result because of the same aforementioned conclusion deduced from the crystal shape.

When a large number of nuclei are produced in a small area, the growth rate becomes small because the growth of each nucleus competes with other nuclei on the supplied material. Although this effect should be studied in detail according to the rate-limiting process, the limiting process of the present system, including the radical reaction, is unclear. However, the influence of the surrounding nuclei is relatively weak immediately after the nucleation occurs. From the classical nucleation theory, the nucleation rate J is written as J = ω*ΓZ ₁  exp (−ΔG*/k _B T) where ω is the frequency of the attachment of atoms to the critical nucleus, Γ is the Zeldovich factor, Z ₁ is the steady-state concentration of a monomer, and ΔG* is the free energy of the critical nucleus (Markov, 2003). The pre-exponential factor A = ω*ΓZ ₁ is not sensitive to the supersaturation in comparison with   exp (−ΔG*/k _B T) = exp (−B/Δμ ²). Therefore, we assume J = A ⁡ exp − B Δ μ 2 , (4) where B = 16πσ ³ v/(3k _B T), σ is the interfacial energy, k _B is the Boltzmann constant, and T is the temperature. The ratio of the nucleation rate in Figure 1 (J ₁) to that in Figure 4 (J ₄) is J 1 J 4 = exp − B 1 Δ μ 1 2 − B 4 Δ μ 4 2 ≃ exp − B 1 Δ μ 1 2 , (5) where Δμ ₁ and Δμ ₄ are the chemical potential of the solid phase in Figures 1, 4, respectively. Here, we ignore the term Δμ ₄ because the effective dose rate in Figure 1, as discussed in the previous subsection is sufficiently smaller than that in Figure 4. The lower limit of the ratio of the interfacial energy and the chemical potential is obtained as B 1 Δ μ 1 2 ≃ ln J 4 J 1 ≃ 5.3 , (6) where B ₁ depends on the interfacial energy of an unknown phase discussed in the previous subsection and J ₁ is the effective dose rate (1.2 electrons nm⁻² s⁻¹).

In Figure 2A of Yamazaki and Kimura (2021), two NaCl crystals appears in an area of 22 μm² in 10 s with an electron dose rate J ₂ = 37 electron nm⁻² s⁻¹. The crystal shape is dendritic, and its symmetry is reflected in the crystal symmetry. The precipitate is assumed to be crystalline, and it is not identical to that in Figure 1 because the particles are circular. Using the same approach, we obtain the relation of the interfacial energy B ₂ and the chemical potential to the solid Δμ ₂ as B 2 Δ μ 2 2 ≃ ln J 4 J 2 ≃ 4.5 . (7)

B ₂ depends on the interfacial energy of the solid phase of the NaCl crystal. Because the chemical potential Δμ depends on the 1/2 power of the dose rate, we can estimate the difference of the interfacial energy of the unknown phase σ ₁ and crystal phase σ ₂ as σ ₁ ≃ 0.33σ ₂. In general, the interfacial energy of a metastable phase is smaller than that of a stable phase; therefore, metastable crystals nucleate before stable crystals. The present system also conforms to this empirical rule.

We attempted to identify the unknown metastable phase of NaCl shown in Figure 1. The possible structures for the NaCl crystals are the NaCl-type structure and CsCl-type structure, and the NaCl-type is observed in the stable phase. The ratio of the interfacial energy of the CsCl-type to that of the NaCl-type can be roughly estimated by a bond counting method. On the (100) surface of the NaCl-type structure, the number of Na⁺ ions and Cl⁻ ions is 2 and 2, respectively, in a unit cell with a lattice constant 5.6 Å. On the (100) surface of the CsCl-type, the number of Na⁺ ions and Cl⁻ ions are 0.5 and 0.5, respectively, in one unit cell. Its lattice constant is assumed to be 3.3 Å on the basis of the ratio of the lattice constant of NaCl-type to CsCl-type of other crystals such as CsCl crystals and CsBr crystals (Kimura et al., 2002). The ratio of the interfacial energy of CsCl-type to NaCl-type is ∼0.71. Because the ratio of the interfacial energy of the unknown phase shown in Figure 1 to that of the NaCl crystal shown in Figure 4 is 0.33, the interfacial energy of the unknown phase is inconsistent with that of a CsCl-type NaCl crystal. In conclusion, we inferred that the unknown phase observed in Figure 1 is an amorphous phase of NaCl or dense-liquid after liquid-liquid phase separation because of the large growth rate, the circular shape, and the small interfacial energy.

Object detection algorithm have difficulty in detecting small objects, and first detection is inevitably delayed. Here, the difference is only 0.2 s, which is shorter than the detection delay in the previous section, where particles nucleated slowly. However, object detection is adequate for early detection because some recent TEM cameras can record several seconds before using the lookback function. By integrating the detection system into a transmission electron microscope, rare events such as nucleation phenomena will be captured within the limited resources for recording. The time necessary for the detection is within 10 ms without the CPU-GPU data transfer. Because the time required for real-time detection, which depends on the PC configuration, is approximately 15–35 ms including the CPU-GPU data transfer (Katsuno et al., 2021), object detection of nucleation phenomenon in in situ observation is possible when the image data are received directly through the software of a TEM camera.