Letter pubs.acs.org/JPCL
Cite This: J. Phys. Chem. Lett. 2018, 9, 961−969
Direct Atomic-Scale Observation of Intermediate Pathways of Melting and Crystallization in Supported Bi Nanoparticles Junjie Li,† Zhongchang Wang,†,‡ and Francis Leonard Deepak*,† †
International Iberian Nanotechnology Laboratory (INL), Avenida Mestre Jose Veiga, Braga 4715-330, Portugal Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
‡
S Supporting Information *
ABSTRACT: Uncovering the evolutional pathways of melting and crystallization atomically is critical to understanding complex microscopic mechanism of first-order phase transformation. We conduct in situ atomic-scale observations of melting and crystallization in supported Bi nanoparticles under heating and cooling within an aberration-corrected TEM. We provide direct evidence of the multiple intermediate state events in melting and crystallization. The melting of the supported nanocrystal involves the formation and migration of domain boundaries and dislocations due to the atomic rearrangement under heating, which occurs through a size-dependent multiple intermediate state. A critical size, which is key to inducing the transition pathway in melting from two to four barriers, is identified for the nanocrystal. In contrast, crystallization of a Bi droplet involves three stages. These findings demonstrate that the phase transformations cannot be viewed as a simple single barrier-crossing event but as a complex multiple intermediate state phenomenon, highlighting the importance of nonlocal behaviors.
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processes are fairly slow and the size is comparatively large,23,24 bismuth (Bi) has also been reported as an ideal inorganic model material suitable for gaining insights into nucleation dynamics due to its low melting point (even down to room temperature due to size effect).25−30 Recently, Wang et al. used conventional transmission electron microscopy (TEM) to investigate a phase transformation induced by point defects in supported Bi nanoparticles under high electron dose irradiation at room temperature and highlighted the fundamental role of defects in the phase transformation.31 The present study, however, reveals melting (due to heating) and crystallization (due to cooling) because high electron dose not only provides energy to the nanoparticles but also transports momentum to atoms, giving rise to vacancies that may induce prenucleation.32−34 Furthermore, local atomistic details of defects and how they play a precise role in phase transformations are still unknown due to the limited spatial resolution of a conventional TEM as well as due to the strain and atomic vibrations that may blur the observations to obtain precise details.35−38 Here we report in situ atomic-scale observations of a real dynamic process of melting or crystallization in supported Bi nanoparticles under heating or cooling conditions using a heating holder within an aberration-corrected (scanning) transmission electron microscope. We provide direct evidence that prenucleation in either melting or crystallization takes places via multiple intermediate state pathways involving the
elting and crystallization are considerably fundamental and practically important first-order phase transitions in condensed-matter physics,1,2 material science,3−5 and climate change,6 yet a detailed understanding of their relevant kinetic pathways is still evolving.1,7 For over a century, scientists have speculated on how crystalline solids melt and how droplets freeze.7−12 To date, many theoretical models have been developed from homogeneous classical nucleation theory (CNT) model, but they rarely address the exact preferential nucleating sites and the potentially relevant role played by defects,13−16 surfaces,17,18 dimensionality, and their combinations in phase transformations.19,20 Such models apply an ideal single free-energy barrier-crossing process only to describe the phase transformations mainly due to lack of information on nucleation evolution.7 Recently, Samanta et al. conducted largescale atomistic calculation of a phase-transformation process of a metal from solid to liquid and predicted that the process takes place via multiple competing pathways involving the formation and migration of point defects or dislocations.21 Furthermore, each pathway is characterized by multiple barrier-crossing events arising from multiple intermediate states within the solid basin.21 Although these calculations indeed provide a rare look at real-phase transformations, much confusion still exists regarding the atomistic understanding of a dynamic process of a phase transformation due to the lack of direct experimental observations on the atomic scale as well as due to the experimental intricacies in tackling such a challenging topic.22 In addition to the application of colloidal crystals to experimentally probe dynamical process of a phase transformation on a micrometer scale, for which the crystallization © XXXX American Chemical Society
Received: December 24, 2017 Accepted: February 1, 2018 Published: February 7, 2018 961
DOI: 10.1021/acs.jpclett.7b03403 J. Phys. Chem. Lett. 2018, 9, 961−969
Letter
The Journal of Physical Chemistry Letters
Figure 1. Sequential HRTEM images showing multiple intermediate states in the melting pathway of interfacial nanocrystal with a size of 42.9 nm. (a−f) HRTEM image showing the structure of supported Bi nanocrystal before melting (a), premelting at domain boundary (b), premelting at interface (c), premelting at dislocation (d), and a catastrophic transformation from a solid−liquid intermediate state to a liquid droplet as a whole (e,f). The electron dose rate was 2.5 × 103 e/Å2s.
formation and migration of domain boundaries, dislocations, and the ordering of interface and surface on the atomic scale. The premelting of the nanoparticles initiates at a grain boundary and expands to interfaces and dislocations and finally
undergoes a catastrophic transformation from a solid−liquid structure to a liquid droplet as a whole in a rather short time when their size exceeds a threshold value. When the size is smaller than the threshold value, the melting of nanocrystals 962
DOI: 10.1021/acs.jpclett.7b03403 J. Phys. Chem. Lett. 2018, 9, 961−969
Letter
The Journal of Physical Chemistry Letters
Figure 2. HRTEM images showing premelting at grain boundary and dislocation. (a−l) Sequential HRTEM images showing detailed premelting at domain boundary in a nanocrystal in Figure 1b (a−f) and at the dislocation (labeled as T in panel g) in Figure 1d (g−l). The electron dose rate is 2.5 × 103 e/Å2s.
The SrBi2Ta2O9 (SBTO) platelets are synthesized by the molten salt method.39 X-ray diffraction (XRD) analysis and TEM imaging (Figures S1 and S2, Supporting Information) demonstrate a successful preparation of SBTO platelets with an orthorhombic structure (JCPDS card no. 49-0649). It is known that Bi tends to diffuse out of SBTO platelets under electron irradiation to form Bi nanoparticles.29−31 Hence the Bi
takes place via two barrier-crossing pathways, that is, premelting at grain boundary and a catastrophic solid−liquid transformation. Interestingly, precrystallization in a droplet occurs first at a solid−liquid interface and subsequently at the liquid surface, and eventually the droplet undergoes a fast complete transformation to a solid nanocrystal when undercooled. 963
DOI: 10.1021/acs.jpclett.7b03403 J. Phys. Chem. Lett. 2018, 9, 961−969
Letter
The Journal of Physical Chemistry Letters
Figure 3. Sequential HRTEM images showing multiple intermediate states in the melting pathway of the interfacial nanocrystal with a size of 21 nm. (a) HRTEM image showing structure of the supported Bi nanocrystal before melting. (b,d) HRTEM images showing the premelting at domain boundary. (c,e) HRTEM images showing recrystallization induced by atomic rearrangement. (e,f) Sequential HRTEM images showing a fast solid− liquid transformation with no interfacial premelting. The electron dose rate is 2.5 × 103 e/Å2s.
To uncover the melting pathways, a Bi nanocrystal with size (D) of ∼42.9 nm is heated at a rate of 0.1 °C/s from room temperature to 254 °C. Figure S4 (Supporting Information) shows sequential TEM images from room temperature to 235 °C. With the rise of temperature, the nanocrystal experiences an atomic rearrangement resulting in evolution of the faceted structure. However, there is no premelting taking place in the Bi nanocrystal until this temperature. As the temperature further increases, the premelting occurs in the solid structure. Figure 1 shows sequential TEM images, which reveal multiple intermediate states during premelting of interfacial nanocrystal at domain boundaries, solid−liquid interfaces, and dislocations. Eventually, a catastrophic transformation occurs from a solid−
nanoparticles used for the following experiments are obtained by irradiating the SBTO platelets under an electron dose of ∼1.15 × 104 e/Å2s at room temperature, as confirmed by energy-dispersive X-ray spectroscopy (EDS) analysis (Figure S3, Supporting Information). In situ heating/cooling experiments are performed in a Cs-corrected TEM equipped with a NanoEx-i/v single-tilt TEM holder, which exhibits negligible thermal drift and allows a very rapid heating and cooling rate. To minimize the electron-beam-induced effect and to accurately measure melting temperatures, an electron dose rate of ∼2.5 × 103 e/Å2s and a low heating (cooling) rate of ∼0.1 °C/s are adapted. 964
DOI: 10.1021/acs.jpclett.7b03403 J. Phys. Chem. Lett. 2018, 9, 961−969
Letter
The Journal of Physical Chemistry Letters
Figure 4. Sequential HRTEM images showing multiple intermediate states in the crystallization pathway of a supported droplet driven by undercooling. (a−c) Sequential HRTEM images showing the precrystallization at a solid−liquid interface. (e−g) Sequential HRTEM images showing the precrystallization at surface. (d,h) HRTEM images showing catastrophic transformation from an order−disordered intermediate state to an ordered nanocrystal in a nanodroplet. The electron dose rate is 2.5 × 103 e/Å2s.
°C, a catastrophic transformation converts the solid−liquid structure to a complete liquid droplet in a very short time. Thus the melting of the supported Bi nanocrystal encounters energy barriers: melting at grain boundary (Figure 1b), liquid−solid interface (Figure 1c), dislocation (Figure 1d), and perfect structure (Figure 1f). Interestingly, liquid nucleation at interfaces is stable, while premelting at defects is accompanied by the formation and migration of defects in the nanocrystal (Figure 1a−e). The premelting undergoes a pathway from grain boundaries to the interface between solids and finally to the dislocations. We confirmed this point with more than 10 individual set of experiments, and Figure S6 shows yet another example for the multiple intermediate state event. Moreover, the nanoparticle turns increasingly symmetric in shape in the whole evolution process, implying that the formation and migration of its interior domain boundaries and dislocations are attributed to atomic rearrangements driven by minimizing total energy. To shed further light on the premelting at the domain boundaries in Figure 1b, we present sequential TEM images (enlarged for clarity) and their corresponding Fourier trans-
liquid structure to a liquid droplet as a whole in a very short time (see also Video S1, Supporting Information). As we can see, the nanocrystal is crystalline at 237 °C and has an orientation relation [01̅0]Bi//[001]SBTO with substrate (Figure 1a). As the temperature reaches ∼237.6 °C (Figure 1b), premelting takes place at two domain structures (inset of Figure 1b), which is accompanied by atomic rearrangement upon further increase in temperature. With further increase in temperature, the newly formed disordered area grows up and migrates to other locations due to atomic rearrangement (Figure 1c−e). To rule out the potential influence of different heights on the image contrast (albeit that this is negligible on the atomic scale), we implement an fast Fourier transform (FFT) analysis at the premelting boundary, revealing the formation of the liquid (Figure S5, Supporting Information). Once the temperature reaches ∼250 °C, premelting initiates at the edge of the interfacial area (marked by blue arrows in Figure 1c) and grows up (Figure 1d−e), which is similar to the premelting at grain boundary precipitates of Pb in Al under heating.40 Subsequently, premelting takes place at dislocations (marked by yellow box in Figure 1d) at ∼251.9 °C. At ∼ 253.1 965
DOI: 10.1021/acs.jpclett.7b03403 J. Phys. Chem. Lett. 2018, 9, 961−969
Letter
The Journal of Physical Chemistry Letters
Figure 5. Statistical analysis of size-dependent melting, crystallization, and their multiple intermediate states. (a−d) Statistical analysis of the sizedependent melting and crystallization temperature (a,b) and the phase transformation pathways of supported nanoparticles in melting and crystallization (c,d). The red stars represent the nanoparticle (size less than ∼40 nm) experiencing two barriers during melting and the green ones a four barrier-crossing pathway (nanoparticles with size more than ∼40 nm).
formation (FFT) analysis in Figure 2a−f. The nanoparticle initially shows a single-crystal structure (Figure 2a) and subsequently undergoes an atomic rearrangement upon heating, giving rise to the formation of two domain structures (labeled as domains A and B in Figure 2b; the corresponding FFT images confirm the small rotation between both the domains). At T = ∼237.6 °C, premelting takes place at the grain boundary which grows up (see red areas in Figure 2c,d). Subsequently, the liquid area migrates (Figure 2d,e) and finally moves out of the viewing area due to the structural rearrangement of the nanoparticle (Figure 2f). Figure 2g−l show the detailed evolution of the premelting at a dislocation involving the formation of dislocation, premelting at dislocation, and recrystallization. Figure 2g shows a formed edge dislocation, as confirmed by a Burgers circuit (see red box) and the extra half atomic plane (labeled as T). At ∼251.9 °C, the dislocation area starts to melt (Figure 2h−j), and the disordered structure finally moves out of this area, leaving behind the single-crystal structure in the viewing area. Further FFT analyses confirm the crystalline structure in the whole process (Figure S7, Supporting Information). To study the influence of size on melting pathways, a series of in situ melting experiments of Bi nanocrystals with different sizes are carried out. In contrast with the four barrier-crossing pathways in melting in Figure 1, Figure 3 presents sequential TEM images revealing two barrier-crossing pathway when the size of nanocrystal is smaller than ∼40 nm (see also Video S2, Supporting Information). Figure 3a shows a nanocrystal of ∼21 nm, which possesses an orientation relationship [421̅]Bi// [001]SBTO with the substrate. Figure 3b−d shows the
premelting at domain boundary (Figure 3b,d, inset) and the recrystallization-induced atomic rearrangement, and the detailed FFT analysis is given in Figure S8 (Supporting Information). Interestingly, at 234.3 °C, the nanoparticle experiences a fast solid−liquid transformation without interfacial premelting, and the melting of the small nanocrystal finishes after two energy barriers: melting at grain boundaries and perfect structure, indicative of size-dependent intermediate state pathways for the melting. To unravel the pathways of crystallization, a series of in situ crystallization experiment of Bi nanocrystals with different size are investigated. Figure 4 and Figure S9 (Supporting Information) show sequential TEM images revealing precrystallization at interface and surface when undercooled (see also Video S3, Supporting Information). Upon closer inspection of the evolution of precrystallization at interface, we observe direct evidence of the ordering of liquid atoms adjacent to the interface once undercooled. The interfacial ordered structure initially shows a discontinuous morphology (see the interfacial area between the two yellow dotted lines in Figure 4b) yet turns increasingly continuous when temperature reaches the liquid−solid transition point (Figure 4c). Such ordering of Bi atoms in the interfacial layers can be attributed to the template effect of substrate.41,42 In the meantime, surface ordering is also revealed (Figure 4e−g). On the basis of surface tension measurements, the formation of a crystalline structure at the surface can typically be characterized by a slope change in a surface tension versus temperature curve (γ(T) = dγ/dT), where γ(T) > 0 stands for a crystalline surface, while γ(T) < 0 stands for a liquid surface.11,43 The slope in our case is indeed 966
DOI: 10.1021/acs.jpclett.7b03403 J. Phys. Chem. Lett. 2018, 9, 961−969
Letter
The Journal of Physical Chemistry Letters positive for a Bi droplet on oxide support,44−46 which accounts for the surface crystallization of the Bi droplet. After precrystallization at interface and surface, the entire structure turns crystalline in a very short time (Figure 4d,h) when undercooled by more than a critical value of ∼90 °C. The orientation relationship between the newly formed nanocrystal and the substrate is [010]Bi//[001]SBTO (Figure S10). Because the temperature is far below the transformation point in equilibrium, undercooling is the major driving force for the liquid-to-solid transformation. To gain insights into how particle size affects the multiple intermediate states in both melting and crystallization, sizedependent melting temperature in Figure 5a is presented, where the calculated values based on Shi’s melting temperature model are also given. In Shi’s model, the relationship between melting point and size of a nanoparticle can be expressed as47
atomic scale. We provide direct experimental evidence of the multiple intermediate states in the melting and crystallization phase transformations. The melting of nanocrystal takes place via a solid-(liquid, solid)-liquid pathway involving four energy barriers (grain boundary to interface, dislocation, and to perfect crystal) when its size exceeds 40 nm, while two energy barriers (grain boundary to perfect crystal) are observed for smaller nanocrystals. The crystallization of droplets involves three energy barriers, that is, undergoes a pathway from liquid to ordered liquid at interface, ordered liquid at surface and interface, and to crystal. Consequently, a catastrophic transformation takes place in the melting and crystallization process once the size-dependent critical temperature of phase transformation is reached. These findings demonstrate that the melting/crystallization processes cannot be viewed as a simple single barrier-crossing event but as a complex multiple intermediate state phenomenon, which enhances our general understanding of nucleation and growth, melting/crystallization phenomena, and phase transformations and helps to clarify atomic origins of temperature-dependent behaviors in other nanomaterials and thin films.
⎡ ⎛ r ⎞−1⎤ Tm(r ) = Tm,bulk exp⎢ −(α − 1)⎜ − 1⎟ ⎥ ⎝ 3h ⎠ ⎦ ⎣
where r is radius of a particle, h is a characteristic length that represents the height of an atomic monolayer on a bulk surface and can be estimated by lattice constant, and α is the ratio of mean square displacement of surface to interior atoms. One can note that the calculated melting points match well with the experimental data when the particle size is larger than ∼20 nm, yet a discrepancy is clearly visible when the particle has a size
