Bubble nucleation and migration in a lead–iron hydr(oxide) core–shell nanoparticle

Significance

An understanding of gas bubble formation in a solid and the materials’ responses at the nanoscale is of technological importance. Tracking nanobubble evolution in a solid during chemical reactions involving a solid, a gas, and a liquid is rarely achieved. Here, we show a breakthrough in materials characterization by monitoring gas bubble nucleation and migration and the associated strain evolution in a lead–iron hydroxide core–shell nanoparticle during dehydration reaction using liquid cell transmission electron microscopy. We found strain coupling can be used to remove gas bubbles from nanostructures, which sheds light on strategies for nanomaterials engineering and novel materials synthetic routes.

Abstract

Iron hydroxide is found in a wide range of contexts ranging from biominerals to steel corrosion, and it can transform to anhydrous oxide via releasing O₂ gas and H₂O. However, it is not well understood how gases transport through a crystal lattice. Here, we present in situ observation of the nucleation and migration of gas bubbles in iron (hydr)oxide using transmission electron microscopy. We create Pb–FeOOH model core–shell nanoparticles in a liquid cell. Under electron irradiation, iron hydroxide transforms to iron oxide, during which bubbles are generated, and they migrate through the shell to the nanoparticle surface. Geometric phase analysis of the shell lattice shows an inhomogeneous stain field at the bubbles. Our modeling suggests that the elastic interaction between the core and the bubble provides a driving force for bubble migration.

Gas bubble formation in a solid is commonly observed and its migration dynamics is of both scientific and engineering importance (1, 2). For instance, in recent years there has been increasing interest in solution processing of materials for energy conversion and storage applications (3). Dehydration of as-synthesized materials to form anhydrous phases is a critical step (4), where gaseous species are often generated during the reaction. As a consequence, materials may become porous or deformed, and properties can be altered accordingly. Gas bubble formation is key to many other materials processes as well, including embrittlement and cracking in the nuclear reactor cladding due to neutron radiation (5), food preservation (6), seismic events in the earth’s mantle (7), etc. Gas bubbles in a liquid can be released easily to the surface through a pressure gradient (8). However, high temperature annealing is often needed (i.e., up to 1,400 °C) to remove bubbles from a solid (9), because it involves a large number of atoms’ correlated movements. To understand how bubbles propagate and migrate through a crystal lattice, it is necessary to monitor the processes in situ and quantify the structural evolution dynamics. So far, however, there have been limited real-time studies on the bubbles propagation in solid materials, especially while the materials are under chemical reactions in a liquid environment.

Here, we made Pb–FeOOH core–shell nanoparticles in a liquid cell under transmission electron microscopy (TEM) (10–12). The iron hydroxide shell undergoes dehydration reaction upon electron irradiation and release gaseous species. Because different phases of gas, solid, and liquid are involved in such a dehydration reaction, it is a challenge to visualize the bubble evolution with high spatial resolution and to map dynamic strain distribution within the crystal lattice. In this work, we have been able to monitor the evolution of gas bubbles during the dehydration process using homemade liquid cells under TEM. By tracking the dynamic strain distribution in the core–shell nanoparticle, we have obtained an unprecedented level of details on the evolution and migration of nanobubbles in the nanoparticle while the chemical reactions are proceeding in a wet environment. Geometric phase analysis (GPA) of the shell lattice reveals an inhomogeneous stain field at the bubbles. Our computational modeling suggests that the elastic interaction between the core and the bubble provides a driving force for bubble migration.

Results and Discussion

Bubble Nucleation and Growth.

We synthesized Pb–FeOOH (β) core–shell nanoparticles inside a liquid cell as the model system. A precursor solution of Pb(acetylacetonate)₂ and Fe(acetylacetonate)₂ (molar ratio of Pb:Fe is 1:2) dissolved in triethylene glycol was used. The growth of nanoparticles was achieved by the electron beam irradiation at lower magnification under TEM with a beam current density of ∼500 electrons⋅Å⁻²⋅s⁻¹. The Pb–FeOOH (β) core–shell nanoparticles were obtained through the phase separation of lead and iron species (note that Pb and Fe are immiscible on Pb–Fe phase diagram). An TEM image of the core–shell nanoparticle is shown in Fig. 1A, where the 10-nm Pb core is off-centered in the 30-nm iron hydroxide matrix. The structural identification of the as-synthesized nanoparticle using high-resolution TEM images is shown in Fig. S1 and Table S1. Under continuous electron beam irradiation with a beam current density of ∼1,000 electrons ⋅ Å⁻² ⋅ s⁻¹, the iron hydroxide is not stable and transforms into iron oxide (13, 14), where gas bubbles containing H₂O, O₂, and H₂ are generated from the dehydration of the hydroxide and the radiolysis of water under the electron beam (Supporting Information).

Fig. 1.

Nucleation and growth dynamics of bubbles in lead–iron (hydr)oxide core–shell nanocrystal. (A) TEM image of the Pb–FeOOH(β) core–shell nanoparticle formed in a liquid cell. (B) Sequential images showing three growing bubbles at the core–shell interface and coalesce into one bubble later. (C) TEM image of the Pb–iron oxide core–shell nanoparticle resulted from the phase transition of the initial Pb–FeOOH(β) core–shell nanoparticle under the electron irradiation. (D) Sequential images showing a growing bubble at the core–shell interface. (E) Evolution of the growing nanobubble in D and the Inset is the trajectory of contours of the bubble. (F) Change in area of the projected shape of the growing bubble with time.

Fig. S1.

Structural mapping and identification using FFT. (A) A series of TEM images from Movie S1. (B) The overlapped original images in A with the inversed FFT images using the diffraction spots circled in (C) FFT patterns of the corresponding TEM images in A.

Table S1.

Lattice parameters of β-FeOOH, Fe₃O₄, and Pb from the experiments and standard powder diffraction database

β-FeOOH		Fe3O4		Pb
Measured lattice spacing (Å)	Powder diffraction database (PDF) 34–1266 (Å)	Measured lattice spacing (Å)	PDF 26–1136 (Å)	Measured lattice spacing (Å)	PDF 04–0686 (Å)
3.72 ± 0.02	3.728	4.60 ± 0.03	4.67	2.85 ± 0.03	2.8550
3.38 ± 0.03	3.333		2.86	2.40 ± 0.03	2.4750
		2.42 ± 0.03	2.439		1.7500
		2.33 ± 0.03	2.335	1.45 ± 0.03	1.4930
2.65 ± 0.02	2.6344		2.023		1.4290
2.48 ± 0.02	2.5502		1.651		1.2380
	2.3559		1.557		1.1359
	2.2952		1.43		1.1069
	2.1038		1.234		1.0105
	2.0666				0.9526
1.98 ± 0.02	1.9540				0.8752
	1.7557				0.8369

A large number of bubbles are observed in the nanoparticle at the core–shell interface (Fig. 1B and Fig. S2; Movies S1 and S2). It is expected that the gaseous reaction products, including O₂ and H₂O, could accumulate at the core–shell interface or inside the iron (hydr)oxide lattice, which is intrinsically a highly defective material (15). The as-generated H₂O molecules can further undergo radiolysis to produce radicals (e_aq⁻, H˙, and ˙OH) and molecular products (H₂ and H₂O₂) under electron beam irradiation (16, 17). Therefore, the propagating nanobubbles should be filled with gaseous molecules of O₂, H₂O, or H₂. Most bubbles nucleate at the core–shell interface, which has lower energy barrier for the bubble nucleation and growth (18, 19). The bubbles grow and migrate rapidly through the shell, and coalescence of bubbles is also observed (Movie S3). The elastic interaction between the core and the shell may provide a driving force for bubble migration. The role of core–shell interface in bubble migration including the elastic energy estimation has been provided in the later section of this paper.

Fig. S2.

Image contrast analysis to determine the mass loss inside a bubble. (A) TEM image of the Pb–Fe₃O₄ core–shell nanoparticle with a bubble at the core–shell interface. The area used for contrast analysis is highlighted. (B) Image intensity profile of the outlined area in A. (C) Fitting curves of the liquid and crystal from the image intensity shown in B. (D) Fitting curve of the bubble generated in the liquid.

Fig. 1 C and D illustrates the process where a bubble nucleates at the core–shell interface and grows to 13 nm in diameter. Meanwhile, a deformation of the shell is observed, where a phase transition from iron hydroxide to iron oxide (likely Fe₃O₄; see detailed analysis in Supporting Information) occurs. The shell is flattened (thinner in the vertical direction) from the drastic atom rearrangement of the crystal lattice during the phase transformation and bubble propagation, as shown by the lighter contrast of the particle in its sequential images. Detailed analysis of the bubble formation at interfaces shows that the bubble changes its shape dynamically while it is pinned at the interface. The bubble growth trajectories show stepwise propagation characteristics (Fig. 1 E and F). It is clear that bubble enlargement involves the movement of a large number of atoms and the accumulation of vacancies and gas molecules. When the edge of the bubble reaches the nanoparticle surface, it disappears rapidly.

Strain Analysis.

We map the local strain distribution within the nanoparticle using GPA on the sequential high-resolution TEM images acquired from the in situ experiments. A circular mask with certain radius is chosen in reciprocal space, such that its boundary is tangential to a Brillouin zone boundary, to maximize the resolution of GPA (20). We take the reference with the reciprocal lattice g vectors that best optimize the signal-to-noise ratio to calculate the geometric phase images P_g(r). Any displacement of the lattice fringes with respect to the selected reference will result in a phase shift, i.e., a change in the value of the phase at the position corresponding to the displacement. The geometric phase obtained here is related to one-dimensional lattice displacement field u_x(r) along the x direction, where u_x(r) = −(1/2π) · P_g(r) · g, and the g vector (111) is used for the displacement field determination in iron oxide. The x direction is normal to (111) plane of iron oxide (Fe₃O₄). The local distortion of the lattice around the core–shell interface, ε, is given by the gradient of the displacement field (ε_x = δu_x(r)/ δx), which indicates the corresponding strain field, ε_x, along the x direction. In Fig. 2, the GPA maps show that the shell lattice around the bubble has a tensile strain up to 1.5% ± 0.3% (discussions on the measurement error is provided in Supporting Information, and Figs. S3–S5). The tensile strain is observed before the bubble is visible, which suggests that H₂O and O₂ molecules accumulate in the local area (Fig. 2 and Fig. S3). The shell lattice around the core shows a compressive strain of about 1.0% ± 0.3%. During bubble growth, strain distribution around the bubble and the core changes, where the shell lattice maintains a positive strain around the bubble and a negative strain around the core (Movie S4). The same trend has been observed in other bubbles and the tensile stain likely results from the gas pressure inside the bubble (Supporting Information).

Fig. 2.

Strain distribution maps of the core–shell nanoparticle during nucleation and growth of a bubble at the interface. (A–C) TEM image series and the corresponding strain field (ε_x) calculated from the (111) Bragg reflection of the iron oxide (Fe₃O₄) shell during the bubble propagation. The white lines in the TEM images define the selected shell lattice for GPA; the arrows mark the same positions in the particle as references.

Fig. S3.

Strain mapping at the Pb–Fe₃O₄ core–shell interface. Strain field (ε_x) around the Pb–Fe₃O₄ interface during the bubble propagations. (A–E) The selected lattice area of the nanoparticle for GPA is highlighted with white line. The analysis shows that the bubble nucleates at the core–shell interface and a tensile strain in the shell lattice around the bubble is achieved. Contours of the Pb core and the bubble are highlight to guide the eyes.

Fig. S5.

Determination of the strain measurement precision. (A) The calculation of root-mean-square error of the strain measurement precision, which is determined as ±0.17%. (B) Line profiles of the strain as a function of the position along the black line in the Inset strain map.

Bubble Migration Dynamics.

The sequential high resolution TEM images in Fig. 3 show the shape evolution of two bubbles migrating through the shell, during which the shell experiences phase transition and shape deformation. In both cases, the shell maintains a single crystal lattice during bubble migration. As shown in Fig. 3 A and B, the surface configuration of the bubble changes with periodic enhancements in the isotropy of the shapes as bubble migrates inside the shell lattice. Here, isotropy (0∼1.0) is measured by the ratio of the perimeter of the bubble to that of a circular object with the same size, with a value of 1.0 corresponding to a circular projected shape. Because the bubble can absorb nearby vacancies (or small bubble precipitates) during migration (21), possible concentration fluctuations of vacancies (bubble precipitates) in the bubble peripheral area may contribute to the shape changes. On the other hand, the accompanying strain close to the bubble could also facilitate the shape changes, as well as the deformation of the particle. The approximately circular average projected shape suggests that surface energy is approximately isotropic. When a bubble moves out of the lattice (Fig. 3 C–E), curvature of the bubble is gradually reduced until a perfect crystal lattice is restored. The high structural flexibility of nanoparticles has been observed in other liquid processing of materials (22). The process of bubble nucleation and migration out of the particle represents an effective mechanism for transport of gas species in a solid.

Fig. 3.

Shape evolution of two bubbles during migration through the nanocrystal lattice. (A) Snapshot TEM images of a migrating bubble in FeOOH with average size of about 4.8 nm. The starting time is arbitrary. (B) Migration trajectory and shape changes of the bubble displayed in A and the roundness defines the shape factor of the bubble. (C) Snapshot TEM image series of a bubble migrating out of the iron oxide shell from Movie S3. R is the radius of the bubble, and the starting time is arbitrary. (D) Trajectory of the migrating bubble in C. (E) Curvature evolution of the bubble corresponding to D.

We measure the speed of bubble migration and its dependence on bubble sizes (Fig. 4). Trajectories of five bubbles with the diameters of 3.1, 4.0, 4.8, 5.4, and 5.8 nm (marked as 1, 2, 3, 4, and 5, respectively) show that all of the bubbles migrate directly from the core–shell interface to the particle surface. Each bubble has a near constant speed of migration and an average velocity of 2.56, 2.81, 1.90, 1.74, and 1.46 nm/s are observed. The larger bubbles moves slightly slower than the smaller ones, however, the size effect on bubble migration is not significant. The speed of migration increases when a bubble moves near the crystal surface before it vanishes (captured for bubbles 4 and 5).

Fig. 4.

Migration dynamics of five bubbles. (A) Snapshot TEM images of the bubble migration events. (B) Migration trajectories of five bubbles with different sizes. (C) Average velocity of different bubbles.

It is noted that the observed bubble migration in this work is different from those solely under high-temperature heating (23, 24), where Brownian motion occurs. In the present work, bubbles migrate with a nearly constant speed along one direction toward the surface. Based on the analysis of bubble evolution after coalescence, we propose that bubble migration is primarily mediated by the surface diffusion (Fig. S6; Supporting Information). The bubble migration observed here is also different from other reported irradiation-induced bubbles (or voids) by high-energy particles under high temperatures, such as neutrons, α-particles, and electrons (Tables S2 and S3), where bubbles (or voids) mostly stay inside the solid (25–27). It has been reported that the temperature rise in a liquid cell induced from the electron beam irradiation is small (only a few degrees or less) (28–30), therefore, we consider a critical factor, i.e., the elastic strain contribution to the observed bubble migration rather than the electron beam heating.

Fig. S6.

Coalescence of two bubbles. (A) TEM images series of two coalescing bubbles. (B) Power law relation of the diameter of the neck (d) with time (t).

Table S2.

Particle-radiation–induced bubble formation in different materials

Materials	Radiation source	Irradiation conditions	Results	Source
Stainless steel (type 316)	Dounreay Fast reactor	Neutron dose:	Spherical or polyhedral cavities (voids) ranging in size from the smallest observable to 150 nm	(41)
		> 10−22 n · cm−2;
		400–610 °C;
Stainless steel (type 316)	Commercial liquid–metal fast breeder reactor	Neutrons formed by nuclear fission;	Bubble form and grow, giving rise to swelling of the steel	(42)
		0.2–2 MeV;
		400–600 °C;
Molybdenum	Van de Graaff accelerator	Nitrogen ions;	Bubble array with body-centered-cubic superlattice structure	(43, 44)
		dose: 7 × 1017 n · cm−2;
		2 MeV;
		870 °C
Molybdenum	Dounreay Fast reactor	Neutron dose:	Bubbles initially grow and then shrink as the irradiation proceeds	(45–48)
		> 10−22 n · cm−2;
		450 °C;
Cu foil containing 0.1% of helium	Cyclotron	α particles;	Fine dislocation network was observed initially under an JEM 6A electron microscope; then tiny bubbles formed on the grain boundaries and dislocation lines in the heating temperature range 450–550 °C	(21)
		dose: 7 × 1017 n · cm−2;
		38 MeV;
		<250 °C;

Table S3.

Voids formation in different materials by electron irradiation

Materials	TEM	Irradiation conditions	Results	Sources
Nickel (prebombarded with 130 kV argon ions with fluence of 2 × 1018 m−2)	Hitachi high voltage electron microscope	1 MeV;	First observation of void formation by electron irradiation	(49)
		430 °C;
		40 min;
α-Al2O3 thin foil	Hitachi 650 keV electron microscope	650 keV;	Dislocation loops at dose of ∼2.0 × 10−8 C m−2; voids detected in the region of dislocation loops at dose of ∼3 × 10−9 C m−2	(50)
		800 °C;
		2 h;
Ca5(PO4)3F	JEM200C× electric microscope	200 KeV	<5 min, voids with roughly hexagonal shape; 10 min, CaO nanoparticles formed besides the voids; >20 min, local amorphization	(51, 52)
TiO2	Hitachi H-9000 electron microscope	300 keV;	Irradiation-direction-dependent: at <101> direction, phase change to TiO; at <101> direction, void formation, growth and coalescence; at <110> direction, voids formation; at <111> direction, surface phase change to α-Ti2O3.	(25)
		4.3 × 10−8;
		55 min.

The Role of Elastic Energy in Bubble Migration.

We use molecular statics calculations to investigate the nature of the elastic interaction between the core particle and bubbles. To explore the generic behavior, we created a core–shell particle with interactions between atoms described by a simple model interatomic potential for a metal. Uniform 1% compressive and tensile strain was applied to two cylindrical regions inside the particle to mimic the core and the bubble, respectively. Details of the modeling are available in Methods and Supporting Information. The long-range elastic strain generated by the core and the bubble is illustrated in Fig. 5A. The calculated elastic energy as a function of the core–bubble distance is plotted in Fig. 5B for the bubbles with different sizes. The elastic energy decreases with the core–bubble distance. Therefore, it is energetically favorable for the bubble to move out from the lattice. Without the core, the bubble located far away from the surface would not experience the driving force and would stay in the middle of the particle. Fig. S7 shows the evolution of the gradient of the elastic energy as the core–bubble distance increases. The elastic interaction energy decreases more rapidly as the bubble approaches the surface. Therefore, a bubble should accelerate near the surface as observed in the TEM experiment. The simulated results are in qualitative agreement with our in situ experimental observations.

Fig. 5.

Core–bubble interaction through an elastic field calculated using molecular statics. (A) Atomistic calculations of the migration of a bubble in a lattice with 1% compressive strain applied at the core (dark blue area) and 1% tensile strain applied to the bubble. The elastic interaction between the core and the bubble provides a driving force for the bubble to be expelled from the shell lattice. The colors correspond to strain, which is the component parallel to the line connecting the core and the bubble. It is calculated as the difference between the local lattice spacing between 100 planes and stress-free lattice parameter, divided by stress-free lattice parameter. (B) The change in the elastic energy with bubble migration is plotted for bubbles with a diameter of 2.5, 3.3, 5.0, and 6.0 nm; the dashed line shows the approximate surface of the shell.

Fig. S7.

Molecular statics calculation of core–bubble interaction through elastic field. (A) Elastic energy gradient for different sizes of the bubble as function of core–bubble separation distance. (B) Elastic energy gradient at ∼15 nm separation as function of the bubble diameter.

Conclusions

In conclusion, we have observed directly the bubble nucleation and migration in a lead–iron (hydr)oxide core–shell nanoparticle during dehydration reaction induced transformation from iron hydroxide to iron oxide. In situ high-resolution TEM imaging and the dynamic strain analysis allow us to map the strain distribution inside the nanoparticle as it undergoes chemical reactions involving solid, liquid, and gas phases. It is remarkable that bubbles can be pumped out of the solid, during which the single crystal lattice is maintained. Computational modeling illustrates that elastic strain interaction can drive a bubble to move out of the nanoparticle. These findings shed light on strategies of using strain to design defect-free anhydrous materials. The dynamics of bubble nucleation and migration in a crystal lattice may share some similarities with that of the bubbles generated in liquids (8, 17) or in biological systems (31). For instance, precipitation and growth of bubbles induced by gas diffusion and supersaturation have been found in those systems.

Methods

Pb-FeOOH (β) Core–Shell Nanoparticle Synthesis, Bubble Formation, and Movie Acquisition.

All chemicals including Pb(acetylacetonate)₂ (99%, Aldrich), Fe(acetylacetonate)₂ (99%, Aldrich), Triethylene Glycol (99%, Aldrich) are used as received. The Pb–FeOOH (β) core–shell nanoparticles were synthesized by electron beam initiation inside a liquid cell under an TEM in situ. The precursor solution was prepared by dissolving Pb(acetylacetonate)₂ and Fe(acetylacetonate)₂ (Pb:Fe molar ratio of 1:2) in triethylene glycol at 60 °C. When the electron beam (200 kV; beam current density of about 500 electrons ⋅ Å⁻² ⋅ s⁻¹) passes through the silicon nitride window (3 × 50 μm) irradiating the solution, growth of nanoparticles in the liquid was initiated at low magnification under TEM. The bubble formation in a core–shell nanoparticle was initiated under an electron current density of 1,000 electrons ⋅ Å⁻² ⋅ s⁻¹. The study of the kinetics of reaction and phase transition was under the same electron beam current density. It is noted that a stronger electron beam current (above 1,500 electrons ⋅ Å⁻² ⋅ s⁻¹) introduces undesirable deformation and damage of the core–shell nanoparticle. The movie was recorded at a rate of five frames per second by the open-sourced software VirtualDub embedded in the DigitalMicrograph software. The as-recorded movie was compressed to reduce the file size (480 × 480 pixels), and the movie plays 4 times faster than the original movie. However, all image analysis was done on the original images extracted from the as recorded movie. All movies were acquired using a JEOL 2100 transmission electron microscope with a high-resolution pole piece and a LaB₆ filament. A Gatan Orius CCD camera was used for in situ imaging.

Image Analysis.

We used ImageJ software to track the movements of each bubble. The image coloring was performed using the Photoshop software. All original images are available in Supporting Information. Further image processing such as image contrast analysis was done using Gatan Digital Micrograph. The stain analysis was conducted using geometric phase analysis.

Molecular Statics Calculations of Core–Bubble Interaction Through Elastic Field.

Interaction between bubble and particle is investigated using molecular static simulations. We used Cu as a model material with atomic interactions described by embedded atom method (EAM) potential (32). It is noted that the details of interaction will not be accurate due to choice of model Cu system instead of real lead–iron oxide core–shell structure. However, the calculations can address a general question whether there is a driving force for bubble migration due to elastic interactions. First, we created a perfect crystal with [100] type crystallographic directions parallel to the x, y, and z directions of the simulation block. The dimensions of the block were 40.0 × 40.0 × 0.3615 nm³. Then a cylindrical region of 20.0-nm radius was cut out from the original crystal. To mimic the core particle, we uniformly scaled the x and y positions of the atoms inside the cylindrical region with radius 5 nm by 1%. Similarly, we modeled the bubble by applying 1% tensile strain to another cylindrical region located at different distances away from the core. After this core–shell structure with bubble was created the structure was statically relaxed to minimize the total energy using conjugate gradient method implemented in Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) (33). During the minimization, the positions of atoms belonging to the core particle remain fixed, and the atoms belonging to the bubble moved as a rigid body. To visualize the elastic field in the particle after the relaxation we colored the atoms according to local strain e_xx = (a_xx-a₀)/a₀, where a_xx is the local lattice parameter in the x direction and a₀ is the stress-free parameter of perfect lattice. The x direction is parallel to the line connecting the centers of the core particle and the bubble.

Supporting Information

Liquid Cells for in Situ TEM Study.

Liquid cells were fabricated by following the similar process as described in previous publications (22, 34, 35). We used ultrathin silicon wafers (100 μm, 4-in., P-doped) purchased from Virginia Semiconductor, and deposited low stress silicon nitride membranes with a thickness of 10 nm on the silicon wafers. Here, the use of ultrathin silicon nitride membrane has effectively improved the spatial resolution of the liquid cell to subnanometer range. The subsequent fabrication processes include lithographic patterning, wet KOH etching of silicon, liquid cell bonding using an indium thin film spacer. The indium thin film was deposited by thermoevaporation, and it acts as a spacer as well as the sealing material for the liquid cell. A 100-nm spacing was used for the current experiments, although different thickness can be achieved. All of the fabrication processes were conducted at the Nanofabrication Laboratory of the University of California, Berkeley. The liquid loading was facilitated by a syringe and Teflon nanotube (Cole-Parmer) to control the size of liquid droplet. A droplet of 100-nL liquid was directed into the liquid reservoir without contaminating the electron transmission window. We estimated that there was only 30 pL of liquids drawn by capillary force into the gap between two silicon nitride membranes for imaging. After liquid was loaded into the liquid cell, we covered the cell using a single slot copper TEM grid (TEM grids are purchased from Ted Pella, Inc.) and sealed the liquid cell using epoxy. Properly sealing the liquid cell can assist maintaining the liquid inside the liquid cell for an extended period, which is critical for enabling the nanoparticle shape evolution.

Image Contrast Analysis to Determine the Mass Loss Inside a Bubble.

Bubbles generated inside the crystal was examined by image contrast analysis. Based on mass–thickness contrast in the transmission electron microscopy, the transmitted intensity (I) of an electron beam penetrating through an object with density of ρ and thickness of t is related to the initial electron intensity (I₀) and given by Beer’s Law:

$$\text{I}=I_0{e}^{-{\mu }_m\cdot \rho t},$$

where µ_m = µ/ρ, is the mass attenuation coefficient, and µ is the linear attenuation coefficient. The contrast K is defined as:

$$\text{K}=\ln \frac{I_0}{I}{\mu }_m\cdot \rho t\text{.}$$

For the Fe₃O₄ (crystal) and triethylene glycol (liquid) in current study, the mass attenuation coefficient for the two substances can be calculated as 0.1399 cm²/g and 0.1345 cm²/g. Assuming that the triethylene glycol layer is as thick as the Fe₃O₄ crystal and the crystalline contrast is negligible, the contrast differential in the two substances caused from equal-volume mass loss is give as:

$$\frac{K{\hspace{0.17em}}_{F{e}_3{O}_4}}{K{\hspace{0.17em}}_{Tri}}=\frac{{\mu }_{\text{m}1}\cdot \rho {\hspace{0.17em}}_{F{e}_3{O}_4}t}{{\mu }_{m2}\cdot {\rho }_{\text{Tri}}t}=\mathrm{4.64.}$$

To determine whether the bubble is propagating in the crystal or in liquid (outside the crystal), we carried out contrast analysis of TEM images with a bubble inside the particle (Fig. S2A). Fig. 5B is the image intensity profile derived from the highlighted area in the image. If the bump (Fig. S2B, arrows) is caused by a bubble in liquid (not in the crystal lattice), the calculated image intensity profile is shown as the green line in Fig. S2C. However, if an identical bubble is generated in the crystal, a much higher contrast deduction is achieved (Fig. S2D, blue dashed line) because the contrast differential between the crystal and liquid is about 4.64. Therefore, the contrast difference should be from bubble in the crystal lattice not in the liquid.

Proposed Chemical Reactions for Bubble Generation.

Based on our analyses of the shell structure (Table S1; Fig. 3), both Fe₂O₃ and Fe₃O₄ can be transformed from the original hydroxide phase upon electron irradiation. Due to the reductive nature of electron irradiation, it is likely that Fe₃O₄ is the dominant phase when the hydroxide shell underwent continuous electron beam irradiation. Both the dehydration of the hydroxide shell and the radiolysis of the water molecules can generate gaseous species. Accordingly, we propose the possible reaction pathways for the bubble generation as below:

$$12\hspace{0.17em}\mathrm{FeOOH}\stackrel{{\mathit{e}}^{\mathrm{-}}}{\to }6\hspace{0.17em}\mathrm{F}{\mathrm{e}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{3}}+6\hspace{0.17em}{\mathrm{H}}_{\mathrm{2}}\mathrm{O}$$ [S1]

$$12\hspace{0.17em}\mathrm{FeOOH}\stackrel{{\mathit{e}}^{\mathit{-}}}{\to }4\hspace{0.17em}\mathrm{F}{\mathrm{e}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{4}}+{\mathrm{O}}_{\mathrm{2}}+6\hspace{0.17em}{\mathrm{H}}_{\mathrm{2}}\mathrm{O}$$ [S2]

$$6\hspace{0.17em}\mathrm{F}{\mathrm{e}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{3}}\stackrel{e^{\mathrm{-}}}{\to }4\hspace{0.17em}\mathrm{F}{\mathrm{e}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{4}}+{\mathrm{O}}_{\mathrm{2}}$$ [S3]

$$2\hspace{0.17em}{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\stackrel{{\mathit{e}}^{\mathrm{-}}}{\to }{\mathrm{O}}_{\mathrm{2}}+2\hspace{0.17em}{\mathrm{H}}_{\mathrm{2}}\text{.}$$ [S4]

Analysis of the Gas Pressure Inside a Nanobubble.

The image contrast indicates that the light contrast domains generated in the crystal. It is estimated that they are a void space filled with gaseous reaction products, i.e., O₂, H₂O and H₂ (from radiolysis of H₂O). The gas pressure can be estimated from the ideal gas law:

$$PV=nRT,$$

where $P$ is the gas pressure, $V$ is the bubble volume, $b$ is the van der Waals constant, $R$ is the gas constant, and $T$ is temperature.

Consider the core–shell nanoparticle with the lead diameter of 10 nm and outer β-FeOOH shell diameter of 30 nm, about 4.6 × 10⁻²⁰ mol of oxygen gas could be generated after the complete phase transition to the cubic Fe₃O₄ phase. Based on our observation of the bubble propagation, the total bubble volume could be estimated as 7 × 10⁻²⁵ m³. If all of the O₂ gas molecules are released inside the nanoparticle without counting other gases generated from H₂O, an average pressure of 1.6 × 10⁷ Pa can be achieved. In reality, the gas pressure in each individual bubble can be larger or smaller depending on different stages of reaction, bubble size, etc. We consider the quantitative estimate of stain generated from the gases inside the bubble is not applicable at the moment; however, it can be a topic of future study. The formation of bubbles or voids under radiation by high-energy particles or an electron beam can be found in materials as summarized in Tables S2 and S3.

Geometric Phase Analysis of Strain Field at the Interface of the As-Grown Lead–Iron Hydr(oxide) Core–Shell Nanoparticle.

The strain determination is derived from the lattice displacement made by the GPA. The GPA has been used widely to map the distortion of lattices and retrieve local structural information from high-resolution transmission electron microscopy (HRTEM) images, which would be hard to be picked up by bare eyes. There have been reports on using GPA of one-dimensional lattices to determine the uniaxial strain distribution along certain directions. For instance, the bending of carbon nanotubes (36), lattice distortion in SrTiO_3-x:Ny single crystal (37) and local structure of algal cellulose microfibrils (38), etc., have been investigated. In our experiments, the one-dimensional strain field can be mapped out from the selected high signal/noise ratio TEM images, where the relative strain distribution in the nanoparticle can be compared. To perform GPA on the selected TEM images, we use a mask on selected a set of diffraction spots in fast Fourier transform (FFT) patterns of the original images. The size of the mask affects the resolution of the strain map. As a simple argument, it has been shown that increasing the mask size could induce larger error to a phase image, which eventually brings impacts on the strain field (36). We carefully selected proper mask size and the error bar of the measurement (±0.31%) has been included (Fig. S4).

Fig. S4.

Determination of the measurements error by GPA. (A) The lead–iron oxide core–shell nanoparticle and the strain map calculated using GPA. (B) The calculated root-mean-square error of the strain measurement. A value of ±0.31% is achieved.

Determination of the Strain Measurement Precision.

GPA is “general to all HRTEM images, and can be adapted to cope with differing noise levels and misalignments” (39). For a given TEM image, “the inherent accuracy and spatial resolution of GPA depends greatly on the mask size, the strain profile direction, and width, but not on the image resolution” (40). Increasing the noise of the image will not impose artificial distortion of the lattices.

Regarding to the strain at the top surface of the particle and the strain at the bubble formation area, we have provided the root-mean-square error of the strain measurement, ±0.31% (Fig. S4). Moreover, we have also done additional strain measurement independent of GPA by a method which has better control of the mask and smoothing Kernel [developed by Dr. Colin Ophus at National Center for Electron Microscopy (NCEM) in Lawrence Berkeley National Laboratory]. We estimate the displacement of fringes from the known spacing as a function of the spatial coordinate $\overrightarrow{r}$, and then compute the numerical derivative of the fringe displacement to obtain the strain.

First, to obtain the fringe displacement, we generate a filter for the convolution of the original TEM image to determine the intensity and position of the lattices. The filter was defined as:

$$H\left(\overrightarrow{r},\overrightarrow{q}\right)=\exp \left(-\frac{{\left|\overrightarrow{r}\right|}^2}{2{\sigma }^2}\right)\exp \left(-2\pi i\hspace{0.17em}\overrightarrow{r}\cdot \overrightarrow{q}\right),$$

where the reference wave $\overrightarrow{q}=$(0.148, 0.186) px⁻¹ was refined from a Bragg peak.

Second, we obtain the fringe displacement map, where the strain field perpendicular to the fringes is calculated as the numerical derivative of the fringe displacement along the perpendicular vector. As a result, strain field ranging from −1.1 to 1.6% is achieved (Fig. S5A). The strain maps are consistent with the results achieved by our GPA measurement.

Third, to approximate the error of this measurement, we calculated the root-mean-square strain derivation in an expected flat region of the sample (Fig. S5A, dashed frame), which takes into account both random fluctuations due to shot noise, and systematic errors due to noise correlation, filtering artifacts, compression, etc. Consequently, a measurement error of ±0.17% has been obtained (Fig. S5B).

The strain maps (Fig. S5A) determined by this method basically agree with the calculation using the GPA. Both the strain at the top surface and the strain at the bubble formation area are larger than the measurement error, thus, are reliable. The origin of strain at the top nanoparticle can be from defects in the nanoparticle. During the growth of nanoparticles inside a liquid cell, defects formation in a nanoparticle is common. However, to identify the type of defects and how they are formed requires more measurements, which is beyond the scope of this work. The strain at the bubble formation area is the interest and the focus of this study, and the calculated strain maps and the root-mean-square strain derivation show that strain field at the bubbles and the top surface of the nanoparticle are both reliable measurement, which is consistent with those calculated using GPA.

The Diffusion Mechanisms for Bubble Migration.

We did additional experimental analysis to examine the mechanisms of bubble migration. We track the bubble evolution after the coalescence of two migrating bubbles (Fig. S6A). The neck of the two connecting bubbles changes with time and the diameter of the neck (d) as a function of time (t) is plotted in Fig. S6B. With power-law fitting, d ∼ t^α, we found the bubble evolution has two regimes, i.e., α ∼0.15 at the early stage and α∼2.50 at the later stage.

To interpret the result, we consider the diffusion mechanism of two bubbles after coalescence can be similar as that of two particles coalescence. According to the early studies, when the particles are smaller than 1 µm and at a temperature below their bulk melting point, surface diffusion is considered as the dominant mass transport route (53). A characteristic power law d ∼ t^α is expected, where d is the diameter of the neck of two particles after coalescence, t is time, and α is a constant. For surface diffusion, the constant α of 0.143 or 0.167 was achieved (54, 55).

In our experiment, the constant α (∼0.15) for bubble evolution lies in the range of the 0.143∼0.167. Therefore, we propose that a surface-diffusion–controlled mechanism is dominated for the atom arrangement around the bubbles, which facilitates the fast migration of the gas bubbles. It is also noted that, at the later stage, the neck cannot be clearly identified thus this estimation may not be applicable.

Molecular Statics Calculations of Core–Bubble Interaction Through Elastic Field.

Interaction between void and particle is investigated using molecular static simulations. Fig. S7A shows the elastic energy gradient calculated as function of core–bubble separation for bubbles with diameters ranging from 2.5 to 6 nm. Fig. S7B shows the value of the elastic energy gradient calculated for 15-nm core–bubble separation as a function of the bubble diameter.