*1.3.2 Ostwald ripening (OR) mechanism*

The classical crystal growth mechanism is the Ostwald Ripening (OR) that describes the smaller crystals grow into the larger crystals through the diffusion to reduce the total surface free energy (**Figure 4**) [54–56]. It is a concentration gradientinduced process around the surface of particles that follows the Gibbs-Thompson relation, as shown in Eq. (1) [56, 57]. Therefore, it results in spherical particles most often, which are in the micrometer size diameter range. However, this mechanism is most often unable to describe the crystal growth in the nanoscale. Further, the particles with similar crystal symmetries can also obtained due to the similar crystal facet surface energies [56].

#### **Figure 3.**

*TEM images of seed-mediated growth-assisted Au nanorods after one round of purification having (a) aspect ratio 18 at pH = 3.5, and (b) aspect ratio 25 at pH = 5.6. These images were reproduced from Brantley* et al*. [53] with permission from Willey Online Library.*

**Figure 4.** *Schematic representation of OR-based crystal growth.*

*Oriented Attachment Crystal Growth Dynamics of Anisotropic One-dimensional Metal/Metal… DOI: http://dx.doi.org/10.5772/intechopen.107463*

$$C\_r = C\_\epsilon \exp\left[\frac{2\gamma\Omega}{RTr}\right] \tag{1}$$

where *Cr* is the equilibrium concentration at the surface of the particle, *Ce* is the equilibrium concentration at a plane interface, *γ* is the surface free energy, R is the universal gas constant, *Ω* is the molar volume of the particle, T is the temperature, and r is the radius of the particle.

Since there is no involvement of crystal facets between the neighboring crystals, in the OR process the crystal defects are less than OA based structures. Although OA and OR the growth processes involve the growth of nanocrystals, the size gradually increases in OR mechanism, while particle size increment is stepwise in OA. Most often, both OR and OA mechanisms involved during the many synthesis processes and determine the final morphology.

#### **1.4 OA and OR kinetic models**

The kinetics of crystal growth of nanostructures are dependent on the nature of the material, the type of crystal facet interface, the solvent, temperature, and concentration of the surfactant [28]. Both OR and OA crystal growth mechanisms can occur simultaneously, and their kinetic models were developed with respect to the diameter growth of a nanostructure. However, it is possible to change the crystal growth into an OA mechanism by hindering OR mechanism initially by introducing surfactants [28, 58]. It is very important to know the characteristics of the OR crystal growth mechanism to distinguish from the OA mechanism. As the OR mechanism is a diffusion-controlled process, it is favored thermodynamically with saturated solution that dissolves nanoparticles. In contrast, OA mechanism dominates in undersaturated conditions [59]. The crystal growth kinetic models of these OR and OA mechanisms also behave differently. OR mechanism-based kinetics models follow first-order kinetics while OA-based kinetic models follow second-order kinetics [60, 61].

The OR kinetic model was proposed by Lifshitz, Slyozov, and Wagner named as LSW kinetic model [2, 62]. The first-order equation for the linear crystal growth rate can be expressed by an exponential function as follows [57].

$$\mathbf{D}^{\mathbf{n}} - \mathbf{D}\_0^{\mathbf{n}} = \mathbf{k}(\mathbf{t} - \mathbf{t}\_0) \tag{2}$$

where D and D0 are the mean particle sizes at time t and t0, k is a temperaturedependent rate constant, n is an exponent related to the coarsening mechanism through the diffusion.

The crystal growth kinetic process in OA is complicated than in OR kinetics since nanocrystals in the different stages of the reaction go through the collision and coalescence during the attachment. Therefore, three kinetic models have developed to explain the OA-based crystal growth of nanocrystals [2, 61]. They are: (1) primary particle-primary particle model (A1+A1), (2) primary particle-multilevel particle (A1+Ai) model, and (3) multilevel particle-multilevel particle (Ai+Aj) model, developed by Smoluchowski based on the collision between number of particles [2]. **Table 1** demonstrates the population growth matrixes of these three OA kinetic models. However, these modified Smoluchowski equations can describe the nanoparticle's diameter growth of the reaction. The kinetic models that describe the elongational growth of 1D nanostructures are essential to explain the controlled


*Crystal Growth and Chirality - Technologies and Applications*

**Table 1.**

*Three basic kinetic models OA-based crystal growth of nanoparticles [2].*

*Oriented Attachment Crystal Growth Dynamics of Anisotropic One-dimensional Metal/Metal… DOI: http://dx.doi.org/10.5772/intechopen.107463*

fabrication of anisotropic nanostructures. Very few metal oxide/hydroxides anisotropic structures were explained by fitting the existing three kinetic models to understand the OA crystal growth mechanism, and they are not satisfactory enough to understand the growth rates.

#### **2. Characterization techniques to visualize OA crystal growth dynamics**

An in-depth understanding of the guiding principles of OA mechanism that dictates the attachment of adjacent nanocrystals toward a specific crystallographic orientation is still critical for the progress of miniaturization and high aspect ratio of anisotropic 1D nanostructures. The visualization tools including *in-situ* and *ex-situ* electron microscopy techniques and computational simulation methods have been investigated to reveal the OA crystal growth processes. It was found out multiple factors influence the OA process such as the type of the solvent or surfactant in the medium and their polarity, size and shape of the primary nanocrystal, temperature, and concentration of precursors [28, 58, 63]. The size and shape can be controlled by changing either surface energies of the crystal facets and the external growth environment [31]. However, the deeper understanding to obtain ultrathin 1D nanostructures is still in its infant stage. In this section, we discuss the main characterization tools that visualize the OA crystal growth process performed in different anisotropic nanomaterials and their findings.

#### **2.1 Ex-situ investigation techniques**

The *ex-situ* investigation is the technique that performs outside of the reaction process such as after the drying or processing. The disadvantage of this method is that artifacts induced to the system after the post process may affect the interpretation of the analysis. Therefore, it needs the careful analysis with other supporting techniques. Transmission electron microscopy (TEM) is an advanced, versatile, and standard *exsitu* tool to obtain the structural and chemical information of the nanocrystalline materials such as elemental composition and mapping, size, shape, and crystallinity [64]. Selective area electron diffraction (SAED) feature associated with the TEM is used to determine the crystal structure and their crystallographic orientation in a specific area of the nanostructure [65]. This high accelerated electron beam related technique is enable to characterize the uniformity of nanomaterials [64]. The scanning transmission electron microscope (STEM) mode is one of the recent advancements of TEM, which generates images by performing a raster scan on the surfaces of nanostructures [64]. This STEM detector is coupled with a high-angle annular darkfield (HAADF) detector and the energy-dispersive X-ray detector (EDX or EDS) that provides the elemental composition and mapping in the nanostructures [66].

Today's HR-TEM can provide atomic-resolution intrinsic structure, crystal lattice information combined with the chemical information of a single nanocrystal [67]. Therefore, it is one of the frontier-characterization tools that provide the understanding of the size and shape-controlled anisotropic nanostructures. One of the extensive studies of identifying the possible crystal growth mechanism of Ag nanowires was performed by Murph and her team utilizing both HR-TEM analysis and molecular dynamics (MD) simulations [9]. They have monitored the intermediate stages of the synthesis to visualize the coarsening process of similar crystallographic facets of neighboring nanocrystals. MD simulation results have suggested that the dipole-dipole attraction causes the preferential crystallographic attachment of hydroxide ions on the surfaces of nanocrystals to produce these ultra-long Ag nanowires.

HR-TEM provides crystal defect information such as twins, misorientation, tacking faults, and phase transformation, and it is an important visualization technique to identify OA crystal attachment process [64, 68]. The very early reports of Penn and Banfield demonstrated the crystal defects of TiO2 nanocrystals including the edge, screw, and mixed dislocations by looking at the lattice fringe details of crystals using HR-TEM [19]. They referred such defects as imperfect oriented attachment, which can be expected in natural and experimental conditions.

Time-dependent XRD technique is another important characterization tool used to investigate crystal growth planes during the OA growth process. Although it is not a standalone technique to identify a crystal growth mechanism, it provides a platform to track dynamics of crystal planes growth at different stages of OA process combined with the selective area electron diffraction (SAED) of TEM [69]. Our group reported such valuable investigation to observe the gradual coalescence, reorientation of crystal facets during the OA-based sol-gel-derived process of ultrathin Cu(OH)2 nanowires [44]. **Figure 5** shows the time-dependent SAED patterns and powder XRD traces of Cu(OH)2 nanoarrays and nanowires at the different stirring time intervals followed by aging in a base-catalyzed sol-gel chemical process.

#### **Figure 5.**

*Time-dependent SAED patterns along with powder XRD traces of Cu(OH)2 nanocrystals at different stirring and aging time. Reproduced from reference [44] with permission from the Royal Society of Chemistry.*

*Oriented Attachment Crystal Growth Dynamics of Anisotropic One-dimensional Metal/Metal… DOI: http://dx.doi.org/10.5772/intechopen.107463*

#### **2.2 In-situ investigation techniques**

The *in-situ* investigation tools are prominent techniques to accurately investigate the crystal growth mechanisms as it can perform real-time monitoring in the reaction solution without any further modifications. The recent advances of liquid-phase TEM is one of the leading tools for the direct visualization of different nanostructures [47, 70–73]. The high spatial and temporal resolution of the liquid-phase TEM allows to comprehensively understand the underlying growth mechanism at an atomic scale. It also provides the information about crystals orientation and crystal defect formation during the nanocrystal's attachment [74]. As a result, our understanding of nanocrystal nucleation, growth, and their dynamics has accelerated. However, it requires a careful interpretation as it has the electron beam effect, substrate effect, and some synthesis procedures are complex and incompatible with liquid phase-TEM [75, 76]. Therefore, this tool has been limited to few synthetic process and materials although it facilitates real- time monitoring. However, these *in-situ* techniques alone cannot be utilized to confirm the growth mechanisms. They should undergo the *exsitu* analysis as a supporting information to prove the direct observation analysis.

The direct observation of metal hydroxide/oxide growth is less as most common metal oxide synthesis methods are not compatible to observe under liquid-phase TEM. The important calculations of translational and angular speeds of iron oxyhydroxide nanoparticles were performed during the OA growth by Li and the team for the first time using liquid-cell TEM [47]. Furthermore, the Pb3O4 nanocrystals coalescence, and growth rates were determined by another group during the OA growth along the [002] crystal facet using liquid-cell TEM [77]. Another recent study demonstrated the fivefold twinned Au crystal domains formation using real-time HR-TEM imaging [78]. *In-situ* monitoring ZnO nanorod formation reached a milestone by providing new insights into the dynamics of OA [79]. The driving forces and torques for both aggregation and alignment were determined using the individual trajectories and attachment events of several ZnO nanoparticle pairs. The OA mechanism was confirmed using lattice fringes observations and its Fast Fourier transform (FFT) analyses. Investigation on oriented attachment of Au nanoparticles was performed by Zhu *et al* using direct observation of liquid TEM. In this ligand-controlled reaction, they observed that the overlapped ligands follow the rotation into {111} orientation. The calculated ligand binding energy on {111} crystal facets is lower than that of other crystal facets, which causes the preferential attachment of Au nanoparticles [14].

Small-angle X-ray scattering (SAXS) is another important *in-situ* tool to get qualitative and quantitative understanding of the OA mechanism at different stages of the process. It can accurately determine the shape and size of nanostructures [80]. Recently, the nucleation and growth of Au nanoparticles were successfully investigated to understand the mechanism and kinetics using SAXS technique in the solutions [81–83]. An early attempt of direct probing of TiO2 nanorods in the reaction solution was performed by Tsao and the group at different temperatures for different reaction times [84]. The time-dependent temporal evolution of SAXS profiles revealed the spontaneous alignment of the quasi-spherical particles with the time from initially formed spherical particles. They confirmed that this observation combines with the HR-TEM analysis.

#### **2.3 Computational simulations**

The computational simulation techniques are a growing field to interpret experimental observations to reveal the detailed information of key growth mechanisms.

The main simulation methods are molecular dynamics (MD), density functional theory (DFT), ab initio, and Monte Carlo (MC) calculations. These methods provide insight into the thermodynamics, kinetics, and driving forces of crystal growth mechanisms [85, 86]. Although computational simulations involved with faster timescales than experiments, they provide a valid approach to understand crystal growth dynamics with a good agreement with experimental results.

The current arguments of the driving force for OA mechanism are controversial. The main assumption of OA is the reduction of surface energy of nanocrystals that causes the thermodynamic driving factor for the spontaneous attachment of nearby nanocrystals [19, 87]. However, recently some research works have suggested that OA is driven by physical driving forces such as van der Waals interactions [88] and/or dipole-dipole interactions [89, 90]. Computational simulations are important to compare these different driving factors and then finally find out the primary contributing factor in different systems. Zhang and Banfield successfully analyzed these key factors separately by treating the system differently [86]. They demonstrated that Coulombic interactions are predominant when nanoparticles are close to each other in a solution, while van der Waals interactions are dominant when nanoparticles are far apart in a solution.

The main fortuitous advantage of combination of atomistic computer simulation techniques with experimental characterization methods is to validate the assumptions of crystal growth mechanism and controlling factors observed in the experiments. MD simulation is useful to explain the driving forces for the *ex-situ* TEM observations of different nanostructures. Zhang *et al* described the direction-specific interaction forces that can create torque to align adjacent ZnO nanocrystals and induce OA to form ZnO nanorods using MD simulations [91]. Very early studies of MD estimated the free energy changes of MgO nanoparticles due to the OA aggregation toward specific orientation in vacuum [92]. Another study used ab initio methods to calculate the surface energies of crystal faces of Sb-doped SnO2 nanocrystals to predict the final morphology, which is observed from *ex-situ* TEM [93]. Murph *et al* also used MD studies to validate their HR-TEM experimental data on Ag nanowires and describe the mechanism to form penta-twinned nanowires growth along the [110] facet [9].

Very recent work demonstrated the solvent effect for the probability of perfect and imperfect OA mechanism by mapping the crystal growth dynamics of Ag nanocrystals in contrast to the solid state without the solvent in the medium [94]. This study is useful to develop new solvent directed strategies to control the specific crystallization processes to obtain the desired final product. Furthermore, Sayle and the group predicted the mechanical properties of CeO2 nanorods and nanochains using atomistic computer simulation with the in detailed discussion of the effect of dislocations and grain boundaries for mechanical properties [95].
