On the Thermodynamics and Experimental Control of Twinning in Metal Nanocrystals

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On the Thermodynamics and Experimental Control of Twinning in Metal Nanocrystals

Kyle D. Gilroy, Joël Puibasset, Madeline Vara, Younan Xia

To cite this version:

Kyle D. Gilroy, Joël Puibasset, Madeline Vara, Younan Xia. On the Thermodynamics and Ex-

perimental Control of Twinning in Metal Nanocrystals. Angewandte Chemie International Edition,

Wiley-VCH Verlag, 2017, 56 (30), pp.8647-8651. �10.1002/anie.201705443�. �hal-02109910�

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On the Thermodynamics and Experimental Control of Twinning in Metal Nanocrystals

Kyle D. Gilroy,

Joël Puibasset,

Madeline Vara,

and Younan Xia

a

The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, Georgia 30332, United States

b

Interfaces, Confinement, Matériaux et Nanostructures (ICMN), UMR 7374, CNRS et Université

d’Orléans, 1b rue de la Férollerie, 45071 Orléans cedex 02, France

c

School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, United States

d

School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States

*

Corresponding author. E-mail: younan.xia@bme.gatech.edu

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Abstract

This work demonstrates a new strategy for controlling the evolution of twin defects in metal

nanocrystals by simply following thermodynamic principles. With Ag nanocrystals supported on

amorphous SiO

as a typical example, we establish that twin defects can be rationally generated

by equilibrating nanoparticles of different sizes through heating and then cooling. We validate

that Ag nanocrystals with icosahedral, decahedral, and single-crystal structures are favored at

sizes below 7 nm, between 7 and 11 nm, and greater than 11 nm, respectively. This trend is then

rationalized by computational studies based on density functional theory and molecular dynamics,

which show that the excess free energy for the three equilibrium structures correlate strongly with

particle size. This work not only highlights the importance of thermodynamic control but also

adds another synthetic method to the ever-expanding toolbox used for generating metal

nanocrystals with desired properties.

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Metal nanocrystals have found use in a wide variety of applications, with ample examples in plasmonics, catalysis, electronics, sensing, and biomedical research.

It has been established that the performance of metal nanocrystals towards a specific application strongly depends on their size, shape, and composition.

More recently, it was further demonstrated that the value of metal nanocrystals could be greatly augmented by introducing twin defects into the crystal lattice. A twin defect is simply a plane of atoms that separates two single-crystal (Sc) domains mirroring each other crystallographically. When inserted in a nanocrystal, the twin defect not only affects the shape or symmetry but also defines the surface-energy landscape and determines the packing of surface atoms. In addition, it also controls the magnitude and direction of lattice strain within the volume and on the surface of a nanocrystal. All these features are of great importance because each one of them plays a critical role in defining the properties, including the surface electronic structure (e.g., the d-band center)

that regulates the nature of how molecules adsorb onto, react with, and desorb from catalytic sites.

Metal nanocrystals with twin defects have been explored in a range of different applications.

For example, many groups have demonstrated that nanocrystals lined with twin defects play a positive role in tuning the surface strain to favorably modify the binding strength of key intermediates in catalytic reactions. This phenomenon has been observed for OH* during the oxygen reduction reaction (ORR)

and for COOH* during the electrochemical reduction of CO

.

Outside from catalysis, others have exploited the unique symmetry of decahedral (Dh) seeds to fabricate one-dimensional nanostructures such as penta-twinned nanorods or nanowires, and accordingly, their anisotropy morphology for optical and electrical applications.

On the other hand, icosahedral (Ih) seeds have been used to template the formation of nanostars with sharp apexes for surface-enhanced Raman spectroscopy (SERS) and related applications.

Most recently, twin defects have been shown to weaken the structural integrity of Au Ih nanocages.

This unique feature allows the nanostructures to be fragmented ultrasonically, which is critical to in vivo applications as fragments with dimensions less than 6 nm are necessary to ensure excretion from the body post application.

The mechanism that guides the generation of twin defects in nanocrystals is still unknown and

perplexing. This is because twin defects are generally formed during homogenous nucleation -- a

rapid process that is currently unresolvable and still lacks a modernized model. This presents an

urgent need to develop synthetic strategies, while at the same time working towards determining

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how and why atoms assemble into a particular configuration during homogeneous nucleation. At the moment, the generation of nanocrystals with a particular twin-defect structure relies on what is referred to as the kinetic control.

In this approach, one or more of the experimental parameters are varied to alter the nucleation and growth pathways towards a desirable defect structure and facet expression. Our group recently illustrated this concept experimentally by showing that there was a strong correlation between the rate at which a Pd(II) precursor was reduced and the number and types of defects expressed in the resultant nanocrystals.

It was discovered that Sc, Ih, and stacking-fault-lined structures would form preferentially at fast, moderate, and slow reduction rates, respectively. In addition to wet-chemical modalities, others have demonstrated that similar correlations could be extended to nanocrystals formed using vapor-phase methods. By varying the substrate temperature during the vapor-phase deposition of Cu, for example, the twin-defect structure could be controlled between Sc and Ih nanocrystals.

Furthermore, it is also feasible to promote defect formation during seed-mediated growth, in which Sc seeds act as heterogeneous nucleation centers for atoms generated during the solution-phase reduction of a salt precursor.

Using this strategy, it was found that Sc Ag seeds could be employed to template the formation of Ag@Au Ih nanocrystals;

Sc Pt and Au seeds for Au and Cu penta-twinned nanorods, respectively;

and Sc Au seeds for the formation of triangular Ag defect-lined nanoplates.

In essence, maneuvering the kinetics during nanocrystal nucleation and/or growth, either in the vapor or solution phase, offers a viable route to the generation of nanocrystals with well-defined, yet unpredictable twin defects.

In this work, we demonstrate how, and then offer computational insights to explain why, metal

nanocrystals with well-defined twin defects can be rationally engineered by simply following the

guidelines defined by thermodynamics. For a face-centered cubic (fcc) metal, theory predicts that

the most stable arrangement of atoms, and thus the geometric shape, trends with the number of

atoms contained in the particle, with large, medium, and small sizes favoring the formation of Sc,

Dh, and Ih structures, respectively.

To see whether we could control the twin defect

thermodynamically, we devised a protocol that involves heating of Ag nanoparticles to 600

C,

followed by slow cooling (Figure 1). This strategy is analogous to what is often used for attaining

equilibrium phases in bulk materials,

albeit the Ag nanoparticles are supported on amorphous

SiO

(a-SiO

) and have additional energetic contributions such as surface, defect, and strain free

energies. When cooled down slowly from an elevated temperature, it is anticipated that the atoms

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contained in each particle would arrange such that the individual structure reached an equilibrium state in terms of internal defect structure (i.e., the number and orientation of twin defects) and external structure (i.e., facet expression or geometric shape).

To test this hypothesis, we prepared the supported Ag nanoparticles by thermally evaporating a small amount of Ag onto an a-SiO

substrate (see the Supporting Information for details). As expected for depositing a high-surface energy material (e.g., a noble metal) on a low-surface energy substrate (e.g., an oxide), the assembly of atoms on the surface follows the Volmer-Weber growth mode.

Because the self-organization of atoms occurred on a surface maintained at room temperature, it is inherently a non-equilibrium process, resulting in metastable particles with poorly defined defect structures and irregular shapes, as shown by the high-resolution transmission electron microscopy (HRTEM) images in Figures S1–S3 for the nanoparticles that were formed from Ag films prepared with effective thicknesses of 4, 7, and 15 Å, respectively.

To obtain such high-resolution images, the Ag films were directly deposited on TEM grids with electron-transparent a-SiO

windows (40 nm thick), as schematically illustrated in Figure 1A.

To ensure that all the atoms in each particle gained adequate kinetic energy to overcome the built-in diffusion barriers and thus descend in energy to a collective equilibrium state, the metastable Ag structures were heated to 600 °C in less than 1 min, held there for 2 min, and then passively cooled to room temperature, as illustrated in Figure 1B. This resulted in the formation of pseudo-spherical nanocrystals (see Fig. S4, A–C, for size histograms). After the heating process, we also analyzed the particle distribution and found that the areal particle density decreased exponentially with the effective film thickness while the average particle size increased logarithmically (Fig. S4C). We used these trends to generate nanocrystals with well-defined sizes simply by controlling the effective film thickness, or more directly, the deposition time. Figure 2A shows a TEM image of 5-nm Ag nanocrystals derived from the Ag film with an effective thickness of 4 Å. It was necessary to use HRTEM to identify the internal defect structure (see Fig.

S5 for the representative structures), which revealed that more than 60% of the nanocrystals could

be readily identified as Ih, where the crystallographic orientation took on one of the three

orthogonal projections (e.g., vertex-, edge-, or face-oriented; see Fig. S6 for atomic models). The

majority of the particles took the face- and edge-oriented configurations, which were roughly

equal in population. We attribute the relatively low yield to the fact that many of the nanocrystals

could have been oriented along unfamiliar zone axes, making them unidentifiable. An individual

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Ag Ih nanocrystal is shown in Figure 2B, clearly showing a twin structure consistent with that of a face-oriented Ih bound by {111} facets. Upon close inspection, it became apparent that some atoms are missing from the vertex sites, a feature that has not been reported to the best of our knowledge. Taken together, our result points toward an equilibrium structure in the form of an Ih with an incomplete outer shell of atoms.

By simply increasing the effective thickness of the Ag film to 7 Å, while following the same heating/cooling regime, the average size of the nanocrystals was increased to 10 nm. In addition to the increase in size, a clear transition in internal defect structure from Ih to Dh was observed (Fig. 2C). We found that the Dh nanocrystals were primarily oriented with the five-fold axis perpendicular to the substrate or with a slight off-axis tilt, as shown in Figure S7. In contrast to the Ih nanocrystals, the Dh nanocrystals could be obtained with yields well over 90%, and could even be identified using conventional TEM. Figure 2D shows an HRTEM image of an individual Dh nanocrystal, which is consistent with that of the truncated Mark’s decahedral motif--a {111}

facet-bound structure with reentrant groves that expose ten {100} facets running parallel to the five-fold axis.

Reentrant groves are known in theory to increase structural stability by balancing surface and strain energy contributions.

Increasing the effective film thickness to 15 Å led to nanocrystals with an average size of 13 nm and a clear transition to Sc structures with yields well over 90% (Fig. 2E). The HRTEM image in Figure 2F shows a characteristic nanocrystal, which takes on a rounded (or weakly-faceted) shape with an internal structure devoid of twin defects. In addition, there were small proportions of Dh and singly-twinned particles. The presence of singly-twinned particles is not surprising because theoretical work often treats them as stable as Sc particles.

It is expected that the Sc structure should continue to be the favorable products for sizes >11 nm, as evident from the work carried out previously, where annealing sapphire-supported Ag films resulted in the formation of weakly-faceted, single-crystalline, Wulff-shaped nanocrystals for sizes ranging from 30 to 250 nm.

To investigate the crystallographic orientation of the nanocrystals relative to the substrate, we carried out X-ray diffraction measurements that resulted in a signal dominated by noise.

However, the top-view TEM images, as shown in Figure 2E, reveal that the nanocrystals have

six-fold hexagonal symmetry, suggesting that they are single-crystal Ag nanocrystals with their

[111]- or [100]-axis normal to the surface of the substrate.

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The strong correlation between the size of a nanocrystal and its internal defect structure follows theoretical calculations based on the equilibration of free-standing Ag clusters (see Figure 3A for a brief summary). As stated by Baletto and Ferrando, the stability of a structure comprised of N-atoms can be compared by calculating the excess energy (Δ):

Δ = E

− Nε

N

(1)

where ε

is the cohesive energy per atom in the bulk, and E

is the total energy of a given structure after relaxation. This expression can be further defined as:

Δ = a + bN

+ cN

+ dN

N

(2)

where the terms on the right side correspond to the energy contributions from the vertices (a), facets (bN

), edges (cN

), and volume (dN). For a Sc structure, Δ decreases with size until a steady-state value is reached, while the Δ for the Dh and Ih structures initially decreases, reaches a minimum, and then finally diverges at large sizes as N

.

The qualitative behaviors of Equation [2] for the three distinct structures are shown in Figure 3B, and the crossover points noted by N

and N

mark the numbers of atoms at which one structure becomes favorable over the other.

In the current study, the Ih-to-Dh crossover point (N

) was experimentally found to be around 7 nm (N ≈ 6,000) while the Dh-to-Sc crossover point (N

) was located at 11 nm (N ≈ 21,000).

Figure S8 shows how the size of each structure was converted to the number of atoms, N.

Comparing these values with theoretical calculations derived for free-standing clusters reveals that the experimental value for N

matches well with theory, albeit N

is much larger, see Table 1. At first, we thought that the discrepancy in N

could be attributed to the presence of the a- SiO

substrate, which accounts for the truncated structure with an asymmetric distribution of strain energy, and thus deviation from the predicted crossover points for free-standing clusters.

However, previous theoretical work showed that the value for N

was barely affected by the

presence of an atomically smooth a-SiO

substrate.

Nevertheless, when nanometric roughness

was introduced to the surface of the a-SiO

slab, both the thermodynamic trend and the position

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of the crossover points drastically changed. Specifically, the vertex-oriented Dh nanocrystals became the most stable structure over the full range investigated (0–1400 atoms) but where single crystal nanocrystal became favored at N

= 11,000 atoms (ca. 8 nm), as shown in Figure 4. It should also be noted that for N < 300, calculations show that the vertex-oriented Ih and Dh had similar excess energies.

As evident from the past and present theoretical results, along with the experimental data presented herein, it is clear that the position of the crossover point is indeed sensitive to the chemical and physical nature of the underlying support, and thus better agreement with theory may come about when more parameters are taken into account (e.g., roughness, surface termination, impurities). In the future, we hope to exploit this highly sensitive particle- substrate interaction to controllably modulate the thermodynamic trend.

In summary, we can add thermodynamic control as another means for the rational synthesis of metal nanocrystals with desired defect structures. By controlling the size of the Ag nanoparticles, we demonstrated that heating/cooling could transform the particles into Ih, Dh, and Sc structures at small, medium, and large sizes, respectively. Remarkably, we found that this trend agreed fairly well with theoretical calculations previously considered for both free-standing particles and those supported on a-SiO

, with the primary difference being the location of the crossover points. We believe that a closer match to theory will be achieved once the exact roughness present in the experiment is incorporated into the simulation environment. In all, this experimental system serves not only as a model system for the elucidation of the thermodynamic landscape of supported metal nanocrystals but also as model candidate for future investigations into how the size, shape, and structure of supported nanomaterials affect their expressed physicochemical properties. This approach not only advances our understanding of the nanoscale equilibration pathways but also provides a quantitative and deterministic approach for controlling the twin structure and shape of nanocrystal materials.

Acknowledgements.

This work was supported in part by a research grant from the NSF (DMR 1506018) and startup

funds from the Georgia Institute of Technology. High-resolution TEM imaging was performed at

the Georgia Institute of Technology’s Institute of Electronics and Nanotechnology (IEN)

characterization facilities. We would especially like to thank IEN’s personnel Walter Henderson,

Todd Walters, and Eric Woods for assistance.

9

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Figure 1. (A) Schematic illustration of the experimental setup used to deposit ultrathin films of

Ag onto the surface of TEM grids coated with electron-transparent windows made of 40-nm thick

a-SiO

. (B) Schematic illustration of a heated particle and the nanocrystal formed after cooling to

room temperature.

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Figure 2. (A, C, E) TEM and (B, D, F) HRTEM images of Ag nanocrystals with three distinctive

internal defect structures that were derived from Ag films with different effective thicknesses

using the standard heating and cooling procedures: (A, B) 4, (C, D) 7, and (E, F) 15 Å,

respectively. The nanocrystals took a (A, B) icosahedral, (C, D) decahedral, and (E, F) single

crystal structure. Scale bars in (A, C, E), (B, D), and (F) are 50, 4, and 10 nm, respectively.

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Figure 3. (A) Schematic illustration of three crystallization pathways that a free-standing particle

can take when cooled to room temperature from the molten state. Particles less than 7 nm, between

7 and 11 nm, and greater than 11 nm take on Ih, Dh, and Sc structures, respectively, upon

crystallization by cooling. (B) Qualitative plot representing the excess energy for free-standing

Ih, Dh, and Sc structures as a function of the total number of atoms. Symbols N

and N

in (B)

represent the crossover points.

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Table 1. Theoretical crossover points for Ag particles

state 𝐍_𝚫^𝛂 𝐍_𝚫^𝛃 ref.

un-supported ~200 20000 [8]

supported^a ~160 1000 [13a]

supported^b - 11000 This work supported ~6000 ~21000 This work

**Calculations based on smooth^a and rough^b a-SiO2 support

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Figure 4. Plot trending the theoretical excess energy for an axis-oriented Ag decahedron against a [111]-oriented Sc cuboctahedron supported on nanometer-scale rough a-SiO

as a function of the number of atoms (at T = 0 K). The crossover point (N

) represents the number of atoms at

which thermodynamic favorability switches between the Sc and Dh structures. The crossover

point was found to be about 11000 atoms (ca. 8 nm). The vertical dashed lines mark the number

of atoms at the theoretical cross-over points.

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