Morphology of supported nanoparticles

Progress in Surface Science 80 (2005) 92–116 www.elsevier.com/locate/progsurf

Review

Morphology of supported nanoparticles Claude R. Henry CRMCN1-CNRS, Campus de Luminy, Case 913, 13288 Marseille Cedex 09, France

Abstract An short review of the shape of supported nanoparticles is presented. In the first part of this review the basic theoretical concepts governing the shape of crystals are given. The validity of the concepts of equilibrium shape for crystals with nanometer dimensions is discussed as well as the influence of the support. The effect of the growth kinetics on the particle shape is also discussed. In the second part, several examples of metal (Au and Pd) nanoparticles supported on MgO, mica and graphite substrates are given to demonstrate the utility of the main experimental techniques (TEM, STM, AFM, GISAXS) used to observe the morphology of nanocrystals.
2005 Elsevier Ltd. All rights reserved. Keywords: Nanoparticles; Size effects; Equilibrium shape; Morphology

Contents 1. 2.

3.

4.

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Theoretical aspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2.1. Equilibrium shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2.2. Kinetic shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Experimental aspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 3.1. Electron microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 3.2. Scanning tunnelling microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.3. Atomic force microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 3.4. X-ray diffraction techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Conclusion and future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

E-mail address: [email protected] CRMCN is associated to the Universities of Aix-Marseille II and III.

0079-6816/$ - see front matter
2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.progsurf.2005.09.004

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Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

1. Introduction Controlling the morphology of nanoparticles is of key importance for exploiting their properties in several emerging technologies. For example, selective optical filters [1], bio-sensors [2] are among the many applications that use optical properties of gold nanoparticles related to surface plasmon resonances which depends strongly on the anisotropy of the particle shape, larger shapes produce greater plasmon losses [3]. Application of magnetic nanoparticles in data storage is limited by the superparamagnetism that precludes their use at room temperature (RT) [4]. One way to circumvent this problem is to increase the magnetic anisotropy, by for example, growing very anisotropic shapes [5]. In catalysis the shape of the catalyst particles plays often an important role [6]. Despite the great importance of the morphology of nanoparticles, it is generally not well characterized and practically never controlled. This situation is not due to the negligence of the scientists but rather to the intrinsic difficulty to accurately characterize the morphology of nanoparticles and to the limited number of ways known for controlling shape. In this short review, I will try to describe, with the help of practical examples, how it is possible to give a detailed characterization of the morphology of nanoparticles, using a combination of several techniques. Some of the techniques, such as transmission electron microscopy (TEM) are relatively old, but others, like scanning tunnelling microscopy (STM), atomic force microscopy (AFM), and grazing incidence small angle X-ray scattering (GISAXS) are new. In addition to describing methods of characterization, I will draw some basic ideas on how to control the shapes of particles by controlling their growth. 2. Theoretical aspect 2.1. Equilibrium shape The equilibrium morphology of crystals is an old problem [7,8] which was solved over 100 years ago by Wulff [9]. The problem is to minimize the total free surface energy of a crystal at constant volume at constant temperature, T. If the surface energy is isotropic (as for a liquid) the problem is simply to minimize the surface and the solution is a sphere. In crystalline solids the surface energy is anisotropic and the energy-minimizing shape is found using the limiting planes of the lowest possible surface energy. Assuming that the equilibrium shape of a crystal is a polyhedron, Wulff found the solution which is expressed by the so called Wulff theorem (a general demonstration of the Wulff theorem was given for the first time in 1944 by Dinghas [10]): ci =hi ¼ constant

ð1Þ

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Fig. 1. Equilibrium shape at 0 K of a f.c.c.: truncated octahedron (a) and a b.c.c.: rhombic-dodecahedron (b).

ci and hi are the surface energy and the central distance of to the facet of index i. For an f.c.c. structure the equilibrium shape is a truncated octahedron containing eight hexagonal (1 1 1) facets and six square (1 0 0) facets and for a b.c.c. structure it is a rhombic-dodecahedron presenting twelve lozenge (1 1 0) faces. These shapes are shown in Fig. 1. The regular polyhedron shapes are valid only at 0 K where the surface energy anisotropy is maximal. At high temperatures, the surface energy anisotropy decreases, and rounded parts appear in the equilibrium shape [11]. Near the melting point, the equilibrium shape becomes a complete sphere. In this paper we are interested in particles with nanometer dimensions, so we can question the validity of the Wulff theorem in this size range. Several factors can change the equilibrium shape when going to nanometer size range. First, both the surface energy and the surface stress increase [12]. Second, different structures (e.g., icosahedral structure) can become more stable [13]. Finally, the proportion of edges atoms becomes no longer negligible. Even if the crystal structure remains bulk-like, the equilibrium shape can change. This can be seen using simple first neighbour two-body interactions [14]. Taking the case of a f.c.c. structure, a Wulff shape limited by (1 1 1) and (1 0 0) facets (see Fig. 1a) is determined by 2 integers n and m which represent, respectively, the number of atoms on the long edge of the (1 1 1) facets and p on the (1 0 0) facets. The anisotropy of the surface energy (c(1 0 0)/c(1 1 1)) is equal to ( 3) Æ (n + m)/ (n + 2m). For a given number of atoms one can calculate the value of n/m that minimizes thep surface energy. For a macroscopic crystal, n = m, and the anisotropy factor is 2/ 3
1.15. If we go to nanometer sizes n/m tends to infinity because m tends to zero, corresponding to the disappearance of the (1 0 0) facets: i.e., at very small sizes the p equilibrium shape is an octahedron. In these conditions, the anisotropy factor tends to 3. An octahedral shape is also produce p when we apply the Wulff construction using an anisotropy factor equal or greater than 3 (see Ref. [15]). In practice, nanoparticles must be supported. Hence, we will now examine the equilibrium shape of supported crystals. This problem of the equilibrium shape was first solved by Kaischew [16]. It is expressed by the Wulff–Kaischew theorem: Dh=hi ¼ Eadh =ci

ð2Þ

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Fig. 2. Schematic representation of the equilibrium shape of a supported crystal. The Wulff shape of the free crystal is truncated at the interface by Dhs, which is proportional to the adhesion energy.

As we can see in Fig. 2 the Wulff shape is truncated at the interface by an amount Dh. hi and ci are the central distance to the facet parallel to the interface and the corresponding surface energy. Eadh is the adhesion energy (or the work of adhesion) which is equal to the work necessary to separate the crystal from the support by an infinite distance. It is useful to know the relationship between the Young–Dupre´ equation and the Wulff– Kaischew theorem. In the case of a droplet in equilibrium on a support, the mechanical equilibrium is expressed by the Young equation (see Fig. 3): cs ¼ cd cos h þ cint

ð3Þ

cs is the surface free energy of the substrate, cd is the surface free energy of the deposited droplet, cint is the interfacial energy and h is the contact angle. The adhesion energy is related to the interfacial energy cint by the following formula: Eadh ¼ cs þ cd  cint

ð4Þ

Combining Eqs. (3) and (4), one gets the Young–Dupre´ equation Eadh ¼ cd ð1 þ cos hÞ

ð5Þ

When the contact angle is zero the droplet spreads on the surface to form a 2D layer, corresponding to the perfect wetting that results with an adhesion energy larger or equal to 2cd. At the other extreme case, the contact angle is 180 and the droplet is a sphere corresponding, to the non-wetting, that results with an adhesion energy of zero. It is important to note that the contact angle is defined only for an isotropic medium like a liquid

Fig. 3. Schematic representation of a droplet in equilibrium on a flat surface. The longer dotted line represents the interface.

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droplet. In the case of a supported crystal, the angle between the substrate and the bottom side facets (see Fig. 2), is defined by crystallography and has nothing to do with the thermodynamic equilibrium. In Fig. 3 the droplet is a truncated sphere of radius R, and the amount of the truncation (at the interface) is equivalent to the truncation Dh of a supported crystal (see Fig. 2). The relationship between R and Dh can be expressed as Dh ¼ Rð1 þ cos hÞ

ð6Þ

Now combining Eq. (6) with Eq. (5) one gets: ð7Þ

Dh=R ¼ Eadh =cd

Formally, Eq. (7) is equivalent to Eq. (2), representing the Wulff–Kaischew theorem. To summarize, the equilibrium shape of a supported (macroscopic crystal) is defined by the surface energy of the facets and the interaction with the substrate as quantified by the adhesion energy. We will see in Section 3 that, as for a non-supported crystal, when the particle size is reduced to the nanometer range, the equilibrium shape is modified due to the nonnegligible edge energies. However, even for macroscopic supported crystals several factors can modify the equilibrium shape e.g., the adsorption on foreign atoms or molecules, and the presence of strain at the interface due to a misfit between the lattices of the support and of the deposited crystal. From Gibbs [7], it is known that adsorption decreases the surface free energy. For a surface at temperature T in equilibrium with gases the variation of surface energy is X dc ¼  Ci dli ð8Þ li and Ci are the chemical potential and the concentrations of the ith species. Let us take as an example the case of a single gaseous species at pressure P. The variation of the surface energy in response to a variation of pressure will be ð9Þ

dc ¼ kT Cg dP =P

k is the Boltzmann constant and Cg is the concentration of adsorbed molecules given by the adsorption isotherm. Considering the case of a Langmuir isotherm for a dissociative adsorption: Cg ¼ ðC s h0 Þ=½1 þ ðP =P 0 Þ

1=2



ð10Þ

Cs is the surface concentration of adsorption sites, h0 is the saturation coverage and P0 is the gas pressure at saturation which is related to the adsorption energy. From relations (9) and (10), and after integration, the surface energy as a function of the gas pressure is c ¼ c0  2h0 C s kT ln½1 þ ðP =P 0 Þ

1=2



ð11Þ

P0 can be evaluated from adsorption kinetics. A practical example has been treated for oxygen on Pd [17]. If different facets yield different adsorption energies, the change in surface energy will depend on the type of facet, leading to modifications in both the surface energy anisotropy and the equilibrium shape. Calculated equilibrium shapes for Pd particles in UHV and in oxygen are represented in Fig. 4. These calculations are in good agreement with experimental results obtained from 10 nm Pd particles supported on MgO(1 0 0) [17]. In the derivation of the equilibrium shape of a supported crystal, Kaischew [16] implicitly assumed that the lattice of the crystal was the same as that of the support. This

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Fig. 4. Effect of adsorption on the equilibrium shape of Pd crystals calculated at (a) T = 550 C, P O2 ¼ 105 mbar and (b) T = 450 C, P O2 ¼ 105 mbar. The surface energy anisotropies (c(1 0 0)/c(1 1 1)) are 0.96 and 0.85, respectively (from Graoui et al. [17]).

assumption is generally not true and, when the crystal structures are the same, there is a misfit between the two lattices defined by m ¼ ðad  as Þ=as

ð12Þ

where as and ad are the lattice parameter of the substrate and of the bulk deposit, respectively. This problem has been only recently addressed, first by Markov [18] who gave an atomistic formulation of the Wulff–Kaischew theorem assuming that the deposited crystal was uniformly strained. At the same time Mu¨ller and Kern [19,20] gave an analytic solution to the problem using a simple parallelepiped shape and continuum elasticity theory. Fig. 5a shows the cross-section of half of the crystal for various values of the misfit m. For zero misfit, edges between the top facet (parallel to the substrate) and the lateral facets (perpendicular) follow a straight line with crystal growth, meaning that the shape is self-similar

Fig. 5. Effect of strain on the equilibrium coverage of a supported crystal (from Mu¨ller and Kern [20]). (a) Equilibrium shape of a parallelepiped crystal with different value of misfit (m) between the lattices of the crystal and of the support. The continuous curves represent the trajectory of the crystal edge. (b) Effect of the generation of dislocations on the equilibrium shape (N is the order of the appearance of the dislocations). The continuous curves represent the edge trajectories for different misfits. The arrowed curve represents the trajectory followed by the crystal when its size increases.

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(we are in fact in the Wulff–Kaischew case). For non-zero misfit, the height-to-width aspect ratio is not constant because the particle grows faster in height than laterally. The equilibrium shape then deviates from the Wulff–Kaischew case, with the larger misfits giving larger aspect ratios (i.e., taller crystal). Qualitatively, one can understand this evolution because the crystal is strained at the interface (it can relax more easily at the top), and therefore prefers to decrease the interface area. However, the elastic energy increases with the size of the crystal, and at a given size the system will partially relax the strain by introduction of dislocation. This situation is depicted in Fig. 5b. Just after introduction of the first dislocation the misfit is decreased and the height of the crystal decreases until it reached another edge-curve corresponding to the new misfit. The aspect ratio then increases again until the introduction of a second dislocation. This process is repeated, introducing more dislocations until the crystal is fully relaxed. It is worth noting that the calculation predicts an oscillation of the height of the crystal around a mean value. Such a behaviour has been observed experimentally for Ge/Si(0 0 1) [21]. 2.2. Kinetic shape In practice, when we grow a crystal we are not at the equilibrium because the supersaturation is larger than one. The supersaturation S is equal to the ratio of the (actual) pressure around the growing crystal and the equilibrium pressure at the same temperature. If S is larger than one the crystal grows, and it evaporates if S is smaller than one. In general (especially at large supersaturations) the shape of the crystal depends on the growth rate of the different facets. Three types of facets can be considered a flat one (F-face), a stepped one (S-face) or a kinked one (K-face). A K-face can grow spontaneously because every adatom is in a growing site. An S-face can grow if adatoms are on the ledge of a step— if they are not, the temperature must be increased to allow the diffusion of an adatom towards the step. The growth of an F-face cannot occur spontaneously at low supersaturation. If the supersaturation is large enough to stabilize a 2D nucleus, the face can grow. At low supersaturation, an F-face can grow if a screw dislocation emerges on the surface to produce stable steps. Elementary mechanisms of crystal growth have were derived by Burton, Cabrera and Frank and coworkers in 1951 [22]. Thanks to the invention of the STM [23], these mechanisms have since been observed, albeit five decades after their discovery. In this review, it is not our intention to develop the basic theory of crystal growth that one can find in text books [24,25]. Rather, we qualitatively discuss how and why the growth shape of crystals changes and how it is related (or not) to the equilibrium shape. The shapes of crystals have intrigued scientists for a long time. From observations of minerals, one finds that the same substance can appear with different shapes. For example, Fig. 6 shows various shapes taken by natural pyrite (FeS2). Despite the fact that the same faces are present, the observed polyhedral shapes are very different. This is in striking contrast with the equilibrium shape of a macroscopic crystal which is unique (at a given temperature). All these shapes, in Fig. 6, are isotropic and are due to various relative growth rates of the different facets. The growth rate of a crystal face depends primarily on the supersaturation but also on other factors that we will examine later. As we have seen, closed-packed faces (F-faces) grow more slowly than stepped (S-faces) or kinked faces (K-faces). Thus, a growing crystal will be limited only by F-facets that correspond to the lowest surface energy. However, the kinetically limited shape is not necessarily the equilibrium shape. Take, for example, an f.c.c. structure, and assume that

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Fig. 6. Common shapes of natural pyrite that are formed by a(1 0 0), o(1 1 1) and e(2 1 0) facets (from Sunagawa [26]).

Fig. 7. Cubic, acicular or platelet habits for a cubic crystal presenting different development of the equivalent a {1 0 0} faces (from Sunagawa [26]).

the growing crystal is limited, at a given time, by (1 0 0) and (1 1 1) facets. If for particular conditions, the (1 1 1) facets grow slower than the (1 0 0) facets, the final shape of the crystal will be an octahedron. At an intermediate stage, it can eventually get a truncated octahedron shape, similar to the equilibrium shape, but it is fortuitous. Another characteristic of growth shapes is that they can be very anisotropic. As seen in Fig. 7, crystals can exhibit an

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isotropic cubic habit, or anisotropic acicular or platelet habits that are due to different growth rates of the {1 0 0} faces. The primary source of anisotropy in the growth shape is the anisotropy of the environment that produces different flows of material to the different facets. For example, a crystal growing in solution and placed at the bottom of a vessel will grow anisotropically. In the case of vapor growth on a substrate, if the main flux comes from diffusion on the substrate, and if the surface diffusion is anisotropic, the growth shape will also be anisotropic. However, several other sources of anisotropy can exist. One very common source is the presence of defects. For example, an acicular form can be generated by the presence of a screw dislocation that increases the growth rate in one direction. Likewise, a platelet can be generated by the presence of dislocations in two perpendicular directions. Impurities can also dramatically change the growth shape of a crystal. In fact, as early as in 1783, Rome´ de L
Isle observed that the presence of urea, during the growth in solution of NaCl, changed the morphology from a cube to an octahedron [27]. Between 1950 and 1970, systematic experiments showed that the presence of foreign metal ions changes the shape of ionic crystals between a cube, a truncated octahedron or an octahedron, depending on the impurity concentration and on the supersaturation [28]. This phenomenon was explained by Stranski [29] and later by Hartman [30]. Impurity ions adsorb preferentially on the {1 1 1} faces, which are of K-type on NaCl crystals, and drastically reduce their growth rate. In other words, the K-faces become of F-type with foreign adsorption. Twinning is a source of crystal shape anisotropy identified long ago [31]. Twinning generates reentrant corners that are repeatable growth sites. Twinned crystals are elongated in one direction or flat. Successive twinning in a h 1 1 1 i direction gives rise to platelet triangular f.c.c. nanocrystals [32–34]. The origin of this peculiar shape has been explained by Ming and Sunagawa [35]. Another common source of anisotropy is coalescence. If two growing crystals touch each other they will produce an anisotropic form that will persist unless the temperature is elevated so as to increase surface diffusion to the extent that matter is redistributed between the different facets (such examples will be provided in Section 3.4). This last phenomenon is connected to an important question: what ere the kinetics of the transformation of a growth shape into the equilibrium shape by annealing at a given temperature? This problem was first addressed by Herring in 1951 [36]. Equilibrium is established by the transport of matter, on the surface of a crystal through surface diffusion (for a crystal in an open system, an equilibration from evaporation from one facet to condensation on another facet is unlikely). Herring showed that the relaxation time is proportional to the particle radius (R) and inversely proportional to the surface diffusion coefficient (Ds): s
R4 =Ds

ð13Þ

More recently, Kern [37] showed that, starting from a cubic shape, the relaxation time expressed as 4=3

s ¼ 2kTR4 =v0 Ds c

ð14Þ

k is the Boltzmann constant, v0 the atomic volume and c the mean surface energy. The relaxation time is strongly size dependent. Taking the case of a gold crystal at 1300 K (c ffi 1 J/m2, v0 = 8 · 1030 m3, Ds ffi 107 m2 ), s is 106 s for a particle of 1 lm while it is only 1 ls for a particle of 1 nm. However, the previous calculation assumes that there is no nucleation barrier to form a new layer on a flat facet. Taking into account this

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nucleation barrier, the relaxation time increases considerably [38]. Simulations using kinetic Monte–Carlo methods have shown that the Herring model is valid only at high temperatures. These simulations showed that the relaxation time follows the Herring predictions at high temperature but not at low temperatures. Fig. 8 shows the energy of a crystal containing 1728 atoms as a function of time for two temperatures, starting with an elongated shape (aspect ratio of 20) [39]. At a high temperature (700 K) the energy decreases smoothly (in agreement with Mullins) while at a lower temperature (300 K) the energy curve has several plateaus, which indicate that the particle is stable. Visualizations of the particle shape during the simulation (see Fig. 8d) show that the plateaus correspond to fully facetted particles where the reshaping process is blocked until, by a fluctuation, a 2D nucleus appears on one facet. At high temperatures (Fig. 8c), many kinks and steps are present on the surface of the particle, and they act as sources of atoms or growth sites for diffusing adatoms. These simulations are in agreement with predictions of Mullins and Rohrer [38]. The nucleation barrier increases with the size of the

Fig. 8. Simulation of the evolution of the shape of an elongated crystal (aspect ratio: 20, 1728 atoms) towards the equilibrium. The total energy is calculated as a function of time at 700 K (a) and 300 K (b). The arrows in (b) represent the transition between a faceted shape to the next. (c,d) Show snapshots of the simulation during the annealing at 700 K, and 300 K, respectively. The grey scale corresponds to the number of neighbouring atoms (from Combe et al. [39]).

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facets [38]. Eventually, at a given temperature, the nucleation barrier is such that the particle retains the same shape practically indefinitely. 3. Experimental aspect 3.1. Electron microscopy In this experimental section, we will show practical examples of how the morphology of nanocrystals can be determined. First, we consider the most commonly used technique— transmission electron microscopy (TEM). TEM samples must be thin enough to be transparent to the electron beam, so nanoparticles on bulk supports need special preparation techniques, such as ion etching, transfer to a thin carbon film or microcleavage [40]. If nanoparticles are in solution or supported on nanometric oxide particles they can be collected on a thin carbon film. Conventional TEM gives the size distribution and the number density of the particles easily and accurately (see Figs. 9 and 10).

Fig. 9. TEM analysis of gold particles supported on an MgO(1 0 0) surface. The particles were obtained by vapor growth at 600 C under UHV. (a) Bright field image, A, B and C indicate the three kinds of particles present on the sample. (b) Diffraction diagram obtained from a large area of the sample. The four 002 spots (close to the centre) correspond to particles A that are in (1 0 0) epitaxy. The twelve 022 spots on the second circle are due to particles A, B and C. The four strong 022 spots are due to A particles and also to B or C particles that are in (1 1 1) epitaxy. The weak 022 spots are only due to particles B and C that are both in (1 1 1) epitaxy but with two perpendicular azimuthal orientations. (c) Dark field image obtained with a 002 spot that corresponds to particles A (see A circle in b). (d) Dark field image obtained with a 022 spot that corresponds only to particles B (see B circle in b).

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Fig. 10. Pd particles (mean size 40 nm) grown in epitaxy at 400 C on MgO(1 0 0). (a) Bright field TEM image, (b) electron diffraction pattern, (c) weak beam dark field TEM image.

The outline of the particles gives only partial information on the particle shape. For example, Fig. 9a is a TEM picture of gold nanoparticles supported on MgO(1 0 0). There are basically three types of particle outlines in the figure: square, rectangle or triangle (more or less truncated at the edges). Without any other information it is dangerous to precise a 3D particle shape. For example, a square outline can mean a cube or square pyramid. In Fig. 9a picture, particles with square outline have the same orientation because they have grown in epitaxy on the substrate. Triangular particles are also in epitaxy but with two azimuthal orientations at 90 to each other. The electron diffraction diagram from the same sample (Fig. 9b) shows that the particles are in epitaxy because only isolated spots are present. By selecting a particular spot with an objective aperture one images the particles corresponding to this spot. These images are called dark field images because the particles that are in Bragg condition, for this spot, appear bright on a dark field (see Fig. 9c and d). In this manner, we find that the square particles have a (1 0 0) plane parallel to the substrate while the triangles have a (1 1 1) plane parallel to the substrate and two azimuthal orientations. From a (h k l) dark field position, a weak beam condition is produced by tilting the sample about an axis parallel to the (h k l) planes. The Bragg condition is no longer fulfilled and the contrast of the visualized particles decreases. Such a weak beam dark field (WBDF) image is seen in Fig. 10 for large Pd particles supported on MgO. The diffraction pattern the Pd particles (Fig. 10b) shows that they are in (1 0 0) epitaxy. The weak beam dark field image (see Fig. 10c) was obtained by tilting the sample from the Bragg condition for a 0 0 2 spot. An examination of the contrast of the particle shows that it is modulated by fringes running parallel to the particle edges. In fact, these fringes are

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thickness fringes and it has been shown that their width is related to the angle of the particle facets with respect to the substrate [40,41] through the following equation: W ¼ ðGh k l Dh tan /Þ

1

ð15Þ

Gh k l is the modulus of the vector of the reciprocal lattice associated to the (h k l) reflection, Dh is the tilt angle away from the Bragg position, and / is the angle of the facet with the plane of the substrate. In the presence of re-entrant angles at the interface, the width of the fringes is divided by 2. The accuracy in the determination of the / angle is limited (in the best case to about 5) but it is generally enough to determine the type of facets that are present on the particle. Knowing the orientation of the particle (as shown above) and assuming that it contains only dense planes one can identify the nature of the facets. For the case represented in Fig. 10 corresponding Pd particles, {1 1 1} and {1 0 0} facets are present. The shape is an octahedron that is more or less truncated. The particles are, in fact, big enough (around 50 nm) to see a contrast from the edges in the bright field image (Fig. 10a). The large flat particles result from coalescence, and their morphology is far from equilibrium. Reconsidering the Au particles (Fig. 9), the squares and the (truncated) triangles correspond to truncated octahedra with {1 1 1} and {1 0 0} facets seen along a [1 0 0] or [1 1 1] axis perpendicular to the sample. The observation of thickness fringes with the WBDF technique is limited to a resolution of about 2 nm because, for the thinner fringes, obtained at larger tilt angles, the contrast is too weak to allow an accurate measurement of the width. Thus, in practice the WBDF method is typically limited to particles larger than 7–10 nm. For smaller particles, the only way to obtain the 3D shape of the particles is to observe the particles in different orientations. Such is possible by bending the carbon film supporting the particles, but it is then difficult to accurately know the particle orientation. A more useful method is to use specimens where the particles sit on a microscopic support of known geometry. This is possible by growing directly the nanoparticles on MgO cubes (or other well defined nanooxides) [40]. Fig. 11 displays an HRTEM picture of 2 nm Pd particles grown on MgO microcubes [42]. Viewed from above, the Pd clusters have a square outline, and viewed in profile they have a trapezoidal outline. As the two projections are exactly 90 to each other, it is apparent that the Pd nanoparticles are truncated square pyramids (see Fig. 11b). If the MgO

Fig. 11. Pd particles (2 nm) grown, under UHV, on MgO microcubes. (a) HRTEM picture showing the corner of an MgO cube. The black and the white dotted circles represent 2 nm Pd particles seen in profile and in top view, respectively. (b) Ball model of the Pd clusters (from Giorgio et al. [42]).

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Fig. 12. Evolution of the equilibrium shape of Pd particles supported on MgO(1 0 0) with various sizes: (a) smaller than 2 nm, (b) in the range 4–6 nm, (c) larger than 10 nm (from Graoui et al. [44]).

crystal is well oriented relative to the electron beam, the HRTEM pictures show the atomic structure of both the support and the particles. In Fig. 11a, the two families of {2 0 0} MgO planes are seen, and it is possible to measure the lattice parameter of the different crystal planes parallel to the interface of the Pd particles seen in profile. Taking the lattice parameter in the MgO particle as that of the bulk, it was concluded that the Pd clusters, 2 nm in size or smaller expanded by 8% to accommodate the MgO lattice [43]. Particles of 4–8 nm are accommodated at the interface and progressively relax towards the bulk lattice of Pd after 3–4 atomic planes. Pd particles larger than 10 nm are fully relaxed and dislocations appear at the interface. The morphology of the particles of increasing sizes can be seen in Fig. 12. The Pd particles were grown at a high temperature to obtain the equilibrium shape. The lattice of the large particles is fully relaxed, and the shape is a truncated octahedron with re-entrant angles at the interface. The adhesion energy of Pd on MgO was obtained with the Wulff–Kaischew theorem (Eq. (2)) [44]. The measured value (0.91 J/m2) is in good agreement with recent molecular dynamics simulations, which gave 0.85 J/m2 [45]. For particles smaller or equal to 6 nm, the equilibrium shape is different: the re-entrant angles disappear, a modification that is equivalent to an increase of the adhesion energy. This increase in adhesion is probably due to the accommodation of the Pd lattice to that of the MgO substrate at the interface. Indeed, molecular dynamics simulations [45] show that the major contribution to the adhesion energy is the bonds between Pd and oxygen ions at the interface, which is maximized when the Pd lattice is accommodated to the MgO substrate. Particles smaller than about 2 nm have no (1 0 0) truncation at the top, meaning that they are perfect pyramids exposing only {1 1 1} facets. This modification in shape is due to the large fraction of edge sites for such small sizes, as discussed in Section 2.1. We have seen that combining different TEM techniques renders possible the full characterization of the morphology and the internal structure of nanocrystals down to 1 or 2 nm. However, TEM gives no information on the atomic structure of the outer surface of the nanocrystals. Even if the nature of the facets is identified, they can be reconstructed or relaxed, and it is important to understand their chemical reactivity [6]. We will see in the

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next two sections that this missing information can be obtained by scanning probe microscopy. 3.2. Scanning tunnelling microscopy Scanning tunnelling microscopy (STM) was the first technique for imaging the atomic structure on extended surfaces [46]. It is very versatile, working under vacuum, in ambient conditions, or in air. The only requirement is that the sample be conducting. STM works well on planar surfaces but it is much more difficult on rough surfaces because there is an exponential variation in the tunnelling current with the tip-sample distance. However, in recent years, the use of STM with supported nanoparticles has increased. Fig. 13 displays an STM picture of Pd nanoparticles supported on a graphite single crystal together alongside a TEM image of the same sample. The STM and TEM pictures look similar, the density of particles is the same (1.2 · 109 cm2) and the particle outlines are triangles with variable degrees of truncation. However, careful examination reveals important differences. First, the mean size determined by STM is 91 nm while it is only 69.4 nm from TEM measurements. Second, the insets of Fig. 13 show that the edges of the particles appear round in the STM pictures and sharp in the TEM images. These differences are due to an effect common to all the scanning probe techniques: the distortion of the shape of the object by the shape of the imaging tip. If accurate measurements are necessary, we must correct this effect (we will come back on this important problem in the next section). The tip effect increases with the slope of the facets and with the radius of curvature of the tip apex. The advantage of STM over TEM is that the height of the particles is defined with an accuracy better than 0.1 nm. Thus, combining STM and TEM information, it is possible to obtain the morphology of large nanocrystals. For the Pd nanoparticles presented in Fig. 13, the morphology is a truncated tetrahedra exposing {1 1 1}, {1 0 0} and eventually {1 1 0} facets (see Fig. 14). If the sample is flat and only a single atom protruding at the apex of the tip is imaging, atomic resolution becomes possible. The first atomic resolution STM images of 3D nanoparticles were obtained from Pd clusters supported on graphite [48,49] (see Fig. 15). Several other types of nanoparticles have since been imaged at atomic resolution by STM e.g., Pd/MoS2 [49], Pd/Al2O3/NiAl(1 1 0) [50], Cu/Al2O3/NiAl(1 1 0) [51], Au/FeO(1 1 1)/ Pt(1 1 1) [52].

Fig. 13. Pd nanoparticles grown under UHV on a graphite (0 0 0 1) surface. (a) STM picture. (b) TEM micrograph from the same sample. The insets are enlargements to show more clearly the outline of the nanocrystals (from Chapon et al. [47]).

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Fig. 14. Schematic representation of the most frequent morphologies of Pd nanocrystals grown epitaxially on the basal plane of graphite, formed from a tetrahedron exposing {1 1 1} facets (a), or {1 0 0} facets (b).

Fig. 15. Atomically resolved STM pictures of Pd clusters supported on a graphite substrate obtained by epitaxial growth under UHV. (a,b) Correspond to particles exposing {1 1 1} and {1 0 0} facets, respectively, (c,d) are the corresponding ball models. On the {1 1 1} facets the dense h 1 1 0 i atomic rows are parallel to the edges while on the {1 0 0} facets they are parallel to the height of the triangular facets (from Humbert et al. [48] and Piednoir et al. [49]).

When the facets of the nanocrystals are atomically resolved, it is easy to derive their morphology. Taking the example of the Pd clusters on graphite in Fig. 15a, that the dense atomic rows are parallel to the edges, proves that they are {1 1 1} planes (compare Fig. 15a and c). In Fig. 15b, dense atomic rows are perpendicular to the edge parallel to the substrate that means that the lateral facets are{1 0 0} (compare with Fig. 15d). In both cases the basal plan is {1 1 1}. STM is a very powerful technique to image nanoparticles but atomic resolution cannot be routinely obtained. For effective imaging, it is thus necessary to have very sharp tips, probably nanotips, extending from the macroscopic apex of a standard tip. As a second limitation of the STM, it cannot work on bulk insulators. We will see in the next section that Atomic Force Microscopy can be used for this class of materials.

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3.3. Atomic force microscopy As a scanning probe technique, atomic force microscopy (AFM) is younger than STM [53]. AFM can be used in one of the two main modes: contact mode (c-AFM) or noncontact mode (nc-AFM, also known as dynamic mode) [54]. In contact mode the scanning tip is in contact with the surface, generally through several atoms, precluding true atomic resolution so that only lattice resolution can be obtained [55]. In the non-contact mode, the tip does not touch the surface, and true atomic resolution can be obtained on extended surfaces of semiconductors [56], metals [57] and insulators [58]. Atomic resolution is apparent through the visualization of atomic defects [59]. Fewer investigations of nanocrystal morphology have been undertaken by AFM because the technique is relatively new and, more significantly, because AFM tips are generally bigger than the STM tips, meaning that tip-sample distortion is large and even facetted nanoparticles appear round. To overcome this problem, one can grow a sharp carbon tip on the apex of the AFM tip [60] or attach a carbon nanotube [61]. Fig. 16 is an example showing an improvement in resolution with a shaper tip. With the normal tip the 20 nm Pd particles appear round and seem to touch each other, while with the carbon tip the facetting of the particles is visible and many small Pd particles appear between the large ones. Another way to overcome the tip-induced distortion problem is to reconstruct the distorted images. If the shape of the tip is known, the reconstruction of the image is possible [63]. An example of a 1D reconstruction is shown in Fig. 17. However, from Fig. 17 (bottom), it is apparent that some information is lost from the bottom of the particle. The shape of the tip can be obtained by electron microscopy (see inset of Fig. 16). However this is not always possible, and the tip can evolve during scanning. An approximate shape of the tip apex can be obtained in situ by analyzing the local curvature of AFM images of nanoparticles presenting different heights [64]. Fig. 18 shows the shape of the apex of an AFM tip obtained with this method [65]. It is interesting to note that the tip is asymmetric and the apex very sharp. Fig. 19 shows two images of Au nanoparticles supported on a mica surface: one is the normal AFM image (Fig. 19a) and the other is the reconstructed image. Clearly, the

Fig. 16. Effect of the sharpness of the tip in AFM imaging (in contact mode) of 20 nm Pd particles supported on MgO. (a) AFM image obtained with a commercial tip. (b) Image of the same sample with a carbon nanotip (radius of curvature of 10 nm) grown, inside a FEG-SEM, on the apex of a commercial AFM tip (see the SEM picture in the inset) (from Maier et al. [62]).

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Fig. 17. Schematic reconstruction of a profile of a nanoparticle imaged by AFM. (Top) Actual profile and profile imaged by a parabolic tip. (Bottom) Reconstructed profile.

Fig. 18. Shape of the apex of an AFM tip determined in situ (see text) (from Ferrero [65]).

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Fig. 19. Reconstruction of an AFM image of Au nanoparticles supported on a mica substrate. (a) Actual AFM image, (b) reconstructed image. The profiles at the bottom correspond the arrows in the AFM images (from Ferrero [65]).

separation distance between the particles is enlarged after image reconstruction. The example profiles indicate a decrease of the mean particle width by 3 nm, which is in agreement with the 4 nm difference observed between the TEM and AFM size distributions [65]. If the particles are not too flat, the slope (i.e., angle) of the lateral facets can be determined from the reconstructed profiles. From those displayed in Fig. 19, the measured slopes correspond to angles of 54 and 70. Taking into account that the particles are in (1 1 1) orientation, it is clear that {1 0 0} and {1 1 1} facets have been imaged. The shape of the gold particles is thus a truncated octahedron with a h 1 1 1 i direction perpendicular to the mica sample (see Fig. 20c). Using c-AFM, the lattice of facets can be determined if the particles are large enough (
20 nm). Fig. 20 shows a gold nanoparticle of 27 nm grown epitaxially on mica (1 0 0) and imaged by c-AFM [66]. The outline of the particles is hexagonal because they are in (1 1 1) epitaxy. In Fig. 20b, the atomic lattice of the top {1 1 1} facet is shown. Resolution of the lateral facets is lost in the vicinity of the edge, and far from the edge parallel lines perpendicular to the edge appear (see top of Fig. 20b). From the separation distance of these lines, they are identified as h 1 1 0 i atomic rows of a {1 0 0} lateral facet. True atomic resolution by nc-AFM has not yet been reached on supported nanoparticles contrary to extended flat surfaces [56–58]. For gold nanoparticles supported on KBr (1 0 0), it has been shown recently that even if atomic resolution was obtained on the sub-

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Fig. 20. 27 nm gold particle in epitaxy on mica (1 0 0) imaged by AFM in contact mode. (a) Top view image. (b) High resolution AFM image on the particle close to a top edge (indicated by a white dotted line) showing atomic lattices of top (1 1 1) and lateral (1 0 0) facets. (c) Ball model of the particle. The dotted line indicates the displacement of the tip (from Ferrero et al. [66]).

Fig. 21. nc-AFM image of a 2 nm gold cluster supported on the (1 0 0) surface of KBr. (a) Topography image. (b) Detuning image showing atomic resolution on the KBr substrate. (c) Drawing presenting the main features of the AFM images (from Barth and Henry [67]).

strate at the vicinity of the particles, no atomic resolution was achievable on the particles [67]. Fig. 21 shows that the gold particle appears with a rounded shape. Closer inspection in the detuning image shows a lozenge in the middle of the particle. An interpretation is that the image of the cluster is formed by two components. The first one comes from the long range forces (Van der Waals and electrostatic) giving the round shape, while the second comes from short range forces (chemical) giving the top square facet of a truncated pyramid in (1 0 0) orientation. In this particular case the particle is smaller than the apex of the tip, meaning that the long range forces image the shape of the tip apex [67]. 3.4. X-ray diffraction techniques X-ray diffraction is a very accurate technique for the study of the crystallography of thin films and supported nanoparticles when it is used at grazing incidence: grazing incidence X-ray diffraction (GIXD). This technique has been used to study epitaxy and relaxation in metal islands growing epitaxially on MgO surfaces [68]. Another X-ray technique that can give information on the morphology of supported nanoparticles is: grazing

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Fig. 22. The GISAXS technique. The X-ray beam impinges on the sample with an angle of incidence ai. The scattered X-rays are recorded by a 2D-detector perpendicular to the incidence plane. A beam stop is placed in front of the direct and the reflected beams. The sample can be rotated along the normal to the sample (x rotation) (from Renaud et al. [70]).

incidence small angle X-ray scattering (GISAXS) [69,70]. This technique allows a quantitative analysis of the morphology of an assembly of nanoparticles during their growth [70,71]. Fig. 22 describes the basic principle of the GISAXS technique. To first order, the distance between the GISAXS peaks and the direct spot is inversely proportional to the mean distance D separating neighbouring particles. Their width and their height are inversely proportional to the mean diameter and the mean height of the particles, respectively [69]. To be more accurate it is necessary to simulate the GISAXS patterns taking into account the shape and the polydispersity of the nanoparticles [71]. When the particles are facetted, additional information can be gained from the GISAXS technique. Fig. 23 shows two GISAXS patterns recorded from Pd clusters supported on MgO(1 0 0) with the incidence plane parallel to the [1 1 0] and the [1 0 0] directions of the MgO crystal. It is known from TEM studies that, at high temperatures, the Pd particles grow as truncated octahedra, that are in the (1 0 0) orientation on the MgO(1 0 0) surface, and edges parallel to the substrate oriented in the h 1 1 0 i directions of MgO (see Fig. 23) [17,40,42,44]. When the incidence plane is parallel to the [1 1 0] direction (Fig. 23a) an additional peak is seen 54.7 from the surface normal. This peak corresponds to the reflection of the X-ray beam from the lateral {1 1 1} facets. In the [1 0 0] direction of the incidence

Fig. 23. GISAXS patterns from Pd nanoparticles growing at 650 K on MgO(1 0 0) taken with the incidence plane parallel to the [1 1 0] (a) and to the [1 0 0] (b) directions of MgO. (c) Mean size (d), height (h), interparticle distance (D) and aspect ratio (h/d) as a function of the average thickness of deposited Pd (from Renaud et al. [70]).

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plane the {1 1 1} facets are not seen. Moreover, the presence of several order of scattering peaks in the direction normal to the substrate indicates the presence of flat {1 0 0} facets on the top of the Pd particles. the aspect ration (h/d). An aspect ratio (h/d) can be obtained from the mean values of the width (d) and of the height (h) of the Pd particles. In Fig. 23c the evolution of the aspect ratio (h/d), as deduced from the GISAXS data, is plotted as a function of the amount of deposited Pd. The aspect ratio is equal to 0.62 and decreases steeply at larger amounts of Pd. The value of 0.62 is in excellent agreement with those determined by TEM (h/d = 0.68) from Pd particles larger than 10 nm having the equilibrium shape [17,44]. With the drop in the aspect ratio comes an increase of the inter-particle distance (D), corresponding to the beginning of the coalescence stage. After coalescence, the particles become flatter (i.e., the aspect ratio decreases) and they cannot spontaneously recover the equilibrium shape. The same phenomenon has been observed by AFM for the growth of Au nanoparticles on MgO(1 0 0) [72]. After coalescence the particles become anisotropic flat islands which are far from equilibrium. They cannot spontaneously recover the equilibrium shape because, at the deposition temperature, it is not possible to extract atoms from the flat lateral facets to grow a new layer on the top facets. The particles can eventually recover the equilibrium shape by further growth. 4. Conclusion and future prospects We have seen that that the morphology of nanocrystals depends on both kinetic (i.e., growth) and thermodynamic parameters. If the growth takes place far from equilibrium conditions (i.e., large supersaturation) the growth shape is not unique and depends on many parameters, such as: flux of growing material, structure of the support (if it is present), presence of defects (dislocations, twins), presence of impurities, confinement (i.e., template effect). Generally, these parameters are not well-controlled or not controlled at all. However, in the case of well-defined systems it is possible to reduce the number of growth parameters and attempt to control the shape of growing particles. In the case of 2D-growth, use of single crystal substrates with a known surface diffusion anisotropy, has enable the preparation of 2D-islands with shapes tunable by the growth conditions [73]. In the case of 3D-growth, it is much more complicated to control all growth parameters. Use of templates like micelles or inverted-micelles could favour one type of shape but it does not allow one to obtain a single shape [74]. Perfect shape control has recently been achieved by using light-induced ripening, which formed an assembly of silver nanoparticles with a unique triangular-prismatic shape and a sharp size distribution [75]. Specific adsorption of salts or polymers are promising ways to change the growth shape [74,76] but these processes are still not well understood and require further systematic studies. At first glance, playing with thermodynamics seems the most simple method of control. Indeed, if we are close to the thermodynamic equilibrium (i.e., low growth rate, high temperature (but not too high to avoid Ostwald ripening)) we can approach the equilibrium shape of the crystalline particles, which is unique for defined thermodynamic conditions. In the case of supported crystals the equilibrium shape is truncated in proportion to the adhesion energy (i.e., deposit/substrate interaction). Thus, choosing substrates with stronger adhesion energy will result in particles with smaller aspect ratios (height/lateral size). In epitaxial growth, the orientation of the crystal is defined, and it is therefore possible to obtain particles with different symmetry axes perpendicular to the substrate [77]. In the case of particles of a few nm in size, the presence of edges, which are by nature

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under-coordinated, increases the surface energy anisotropy such that only one type of facet is present on the equilibrium shape. In the case of epitaxial clusters, the presence of strain at the interface, can also modify the equilibrium shape. Thus, it is, in principle, possible to modify the shape of supported particle by applying a stress during growth. Another way to modify the equilibrium shape is to grow the particles in presence of a gas of foreign molecules that adsorb differently on the different facets. With this selective adsorption, surface energy is modified and the equilibrium shape is changed. However, if the change in the environment renders the shape metastable [78], a clever method of preserving the shape is by freezing it through a decrease in temperature. Another way to produce one type of nanocrystal morphology capitalizes on selecting the desired shape by elimination of the unwanted shapes. Such could be achieved by selectively absorbing light on particles with unwanted shapes to evaporate them—for example by adjusting to a plasmon loss specific to these particles. From the experimental point of view, several improvements of existing techniques will simplify the characterization of the 3D-shape of supported nanoparticles, or overcome some of their limitations. One is TEM tomography that allows to image an object in three dimensions, by taking automatically a series of pictures of the same particle at different tilt angles and using a computer assisted shape reconstruction [79]. Another improvement of TEM is environmental HRTEM that is able to image nanoparticles, with atomic lattice resolution, at various temperatures and under pressures up to 30 to 50 mbar. In this new type of microscopes, the sample is isolated from the vacuum of the microscope column either by several differentially-pumped apertures [78] or by two carbon windows, transparent to the electron beam, which seal the pressurized cell containing the sample [80]. These new developments are particularly important for catalysis. The determination of the 3D-shape of nanoparticles by AFM (especially in the dynamic mode) is hampered by the fact that both long range and short range forces are simultaneously probed, that produces rounding of the shapes in addition to the tip sample convolution effect (see Fig. 21). A new mode, called constant height mode dynamic-AFM, reduces considerably these effects and allows to visualize the actual shape of the particle top facets [81]. At the end, I want to recall that with the fast development of computers, it is now possible, to simulate the shape of supported nanoparticles up to sizes of about 10 nm, by using realistic many-body inter-atomic potentials [13]. Acknowledgments This review is dedicated to Alain Humbert, prematurely departed. Clemens Barth, Claude Chapon, Sylvain Ferrero, Suzanne Giorgio, Christine Mottet, Gilles Renaud, Georges Sitja are gratefully acknowledged for many enlightening discussions during the preparation of this review and Ellen Siem for critically reading the manuscript. References [1] [2] [3] [4] [5]

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