Morphology of Zinc Oxide Nanoparticles and Nanowires: Role of

Article pubs.acs.org/JPCC

Morphology of Zinc Oxide Nanoparticles and Nanowires: Role of Surface and Edge Energies Hugh F. Wilson,*,†,‡ Chunguang Tang,§ and Amanda S. Barnard† †

CSIRO Virtual Nanoscience Lab, 343 Royal Pde, Parkville, Victoria 3052, Australia School of Applied Sciences, RMIT University, Melbourne, Victoria 3000, Australia § School of Materials Science and Engineering, University of New South Wales, Kensington, NSW 2052, Australia ‡

ABSTRACT: Although zinc oxide (ZnO) is a widely studied nanomaterial and a useful photocatalyst, the structures predicted by traditional morphology models, such as the Wulff construction, are largely inconsistent with experimental observations. As well as being scientifically perplexing, this disparity hinders our ability to predict the conditions requires to produce specific ZnO nanostructures on demand. Using density functional theory calculations we compute and compare the surface and edge energies for surfaces of zinc oxide and their intersections, and use a nanomorphology model to predict the thermodynamically optimal shape of zinc oxide nanoparticles and nanowires as a function of size and aspect ratio. We find that edge energies play a significant role in determining the optimal morphology of small nanowires, with hexagonal cross sections preferred for cross sectional areas below 10 nm2 and dodecagonal cross sections thermodynamically stable for larger nanostructures.

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are hexagonal or sometimes dodecagonal/cylindrical prisms, extended along the (0001) direction and exhibiting (1010) and/or (1120) facets on the sides. Nanowire geometries are also readily formed, which are essentially extended versions of the nanoparticles, extended arbitrarily in the (0001) direction with hexagonal or dodecagonal cross sections. Tetrapod shapes consist of four prism-shaped wurtzite legs, surrounding a central core which is believed to exhibit a zincblende structure.11 A rather different class of ZnO nanoparticles is known as a nanobelt or nanosheet, consisting of ribbonlike or sheetlike quasi-two-dimensional structures with rectangular cross sections.12,13 Many derivative nanostructures are based on curved nanosheet geometries, including nanorings,14 nanobows14 and nanoflowers. Many studies have focused on the creation of different nanostructures by control of growth parameters,11,15−18 however a more predictive understanding of the principles at work has been lacking. The morphology of nanostructures is determined by the combination of kinetic effectsthat is, the growth rates of different surfacesand thermodynamic effectsthe energetic stability of the overall nanostructure. Understanding how thermodynamic formation conditions can be tuned to create tailored nanostructures will require a comprehensive understanding of both the growth rates and energetics of zinc oxide surfaces under different thermodynamic and chemical conditions. In this work, as an initial step toward this goal, we

inc oxide is a highly versatile material with a unique combination of electronic, catalytic, piezoelectric and pyroelectric properties, which lend it to a vast number of emerging technological applications.1−5 Zinc oxide may be fabricated in a wide variety of possible nanostructures,1,5,6 and nanostructured ZnO lends itself to a wide range of possible applications including nanogenerators,7 sensors,8 and photovoltaics.9 The combination of nanostructured ZnO’s diverse physical properties with the enormous variety of achievable morphologies opens up interesting possibilities for creating tailored ZnO nanostructures whose physical properties may be tuned via control of morphology by controlling the thermodynamic conditions under which the nanoparticles are formed. Tuning of the catalytic properties of ZnO nanoparticles via tuning of the portion of exposed facets has already been demonstrated.10 Practical realization of improved thermodynamic shape control of ZnO nanostructures requires a detailed knowledge of both the kinetics and thermodynamics of the morphology of nanostructured ZnO. Under ambient and near-ambient conditions, ZnO forms with a wurtzite crystal structure. The wurtzite structure has three primary cleavage planes, the {1010}, {1120}, and {0001}. Cleavage along the {0001} axis results in two polar surfaces, the (0001)-Zn terminated and (0001)-O terminated surfaces, while cleavage along the (1010) and (1120) planes results in nonpolar surfaces. A broad range of ZnO nanostructures may be formed using different methods and thermodynamic conditions, with the nanostructures almost always solely presenting some combination of the above four surfaces. The most frequently observed morphologies for ZnO nanoparticles © XXXX American Chemical Society

Received: February 11, 2016 Revised: April 5, 2016

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DOI: 10.1021/acs.jpcc.6b01479 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Table 1. Computed Surface Energies in J/m2 of Defect-Free ZnO Surfaces According to the DFT-PBE Results of Tang et al.,21,22 the DFT-LDA and DFT-PBE Results of Meyer and Marx,23 the DFT-LDA Results of Cooke et al., and the DFT-PBE + U Results of Na and Park.26 a surface

Tang et al.

Meyer/Marx (LDA)

Meyer/Marx (PBE)

Cooke et al.

Na and Park

(1010) (1120) (0001)-Zn (0001)-O γ(1010)/γ(1120)

0.839 0.872 2.39 0.96 0.962

1.94 2.17 − − 0.894

1.26 1.38 − − 0.913

1.19 1.23 − − 0.967

1.12 1.06 2.25 2.04 1.056

a The polar (0001) and (0001) surfaces were not considered by Meyer and Marx or Cooke et al. The ratio between the surface energies of the (1010) and (1120) surfaces is also shown for each set of calculations.

the nondefective, stoichiometric-ratio surfaces, under oxygenrich conditions are shown in Table 1. The nonpolar (1010) surface was found in this work to have a formation energy of 0.839 J/m2, and the nonpolar (1120) to have a formation energy of 0.872 J/m2. The Zn-terminated nondefective polar (0001) surface has by far the highest formation energy of 2.39 J/m2, while the O-terminated polar (0001) surface has a formation energy of 0.96 J/m2. For the purposes of comparison, surface energies computed in several previous studies are also shown in Table 1. The first set of energies is from the density functional theory calculations of Meyer and Marx,23 using two different exchange-correlation functionals: the local density approximation (LDA) and the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE).24 The second is the DFT results of of Cookeet al.25 using the LDA. The third is the PBE+U results of Na and Park26 which use the PBE GGA, but also include a U term representing the on-site Coulomb energy. We have not included in our table the early DFT calculations of Wander and Harrison,27,28 who find a surface energy of 1.16 J/m2 for the (1010) surface energy and 2.05 J/m2 for the (1120) surface energy, but who do not relax all degrees of freedom for the (1120) surface.28 Consistently, and significantly, all methods except the work of Na and Park find the (1010) surface to have slightly lower surface energy than the (1120), with the difference between the (1010) and (1120) surface energies being between four and ten percent. The PBE+U calculations of Na and Park find instead the (1120) surface to be more stable by around six percent. Values of the ratio between the (1010) and (1120) surface energies range from 0.894 to 1.06, with our own calculations giving 0.962.

determine theoretically the thermodynamic ground state morphology of pure zinc oxide nanoparticles and nanowires as a function of nanoparticle size and thermodynamic conditions. We combine surface energy calculations with newly calculated edge energies for several different types of facet intersection and show that edge energies play a significant role in selecting the cross-sectional shape for nanoparticles and nanowires smaller than a few nanometres in diameter.

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NANOPARTICLE MORPHOLOGY MODEL The free energy of formation of a nanoparticle can be expressed in terms of contributions from the bulk, surface, edges, and corners.19 As nanoparticle size increases, corner energies stay constant, edge energies increase linearly, and surface energies increase quadratically with the linear scale of the nanoparticle, leading to the surface energy dominating the nanoparticle morphology for nanoparticles with diameters of more than a few nm. Zinc oxide nanoparticles reported in the literature have been formed with a diameter as small as 4 nm,18 but the majority of observations are of nanoparticles and nanowires on the scale of tens to hundreds of nanometres. Given that we are only interested in nanoparticles whose smallest linear dimension is at least 4 nm, we may safely neglect corner energies. We also in this case neglect surface tension terms, which are also found to be important only for smaller particle sizes.19 Edge energies are often also ignored for nanoparticles on this scale, however considerations specific to ZnO nanoparticle morphology mean that they may be expected to play an outsize role in the case of ZnO, since the two main competing structures are hexagonal and dodecagonal prisms, one of which has nearly twice the total edge length of the others. We thus include edge energies in our model. We ignore the temperature-dependent vibrational terms in the energy of formation. Vibrational terms were recently shown to be insignificant even for the energetics of hydrogenterminated ZnO surfaces,20 and should be even less so for the bare surfaces where hydrogen is not present.

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EDGE ENERGIES There are five different edge types which we have considered. We exclude the possibility of planes meeting at acute angles based on the earlier work of Haffad et al. which showed small triangular-prism nanowires to be substantially less stable than hexagonal-prism nanowires.29 We also ignore the edges between the (0001)/(0001) end-cap surfaces and the side (1010)/(1120) planes, which will have only a small influence on shape. Images of the five edge types considered in this work are shown in Figure 1; we will refer to the (1010)-equivalent and (1120)-equivalent planes as “zigzag” and “armchair” respectively due to their appearance when viewed along the (0001) axis. Armchair−armchair and zigzag−zigzag plane intersections occur at an obtuse angle of 120°. The armchair−armchair intersection may adopt one of two different types of geometries depending on whether there is a single extremal hexagon at the corner or not, which we shall call

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SURFACE ENERGIES Surface energies of the four high-stability ZnO surface facets have been the study of several previous works. Although the surface energies of the (1010) and (1120) surfaces are relatively straightforward to calculate theoretically and have been the subject of extensive study, the energies of the polar (0001) and (0001) surfaces are substantially more difficult to compute. Recently the present authors and a subset thereof have computed surface energies of both the polar21 and nonpolar22 ZnO surfaces with and without defects as a function of oxygen chemical potential. These computed surface energy values for B

DOI: 10.1021/acs.jpcc.6b01479 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Figure 1. Illustration of the five different types of corners involved in the studied nanowire geometries: (a) the zigzag−zigzag corner, (b) armchair−armchair corner of the “in” type, (c) zigzag−zigzag corner of the “out” type, (d) the 150° armchair−zigzag intersection, and (e) the 90° (1010)-(1120) intersection.

respectively the “in” and “out” configurations. Only one type of 120° zigzag−zigzag intersection exists. There are two types of nonacute (1010)-(1120) intersection, one at 90° and one at 150°. The five types of corner give only three different angles, and thus imply only three different regular nanoparticle cross sectional shapes−hexagonal prisms with 120° corners, rectangular prisms with 90° corners, and dodecagonal prisms with 150° corners. Total energies for optimized geometries were computed for a set of 17 nanowire geometries with sizes ranging from 48 to 444 atoms per crystal length unit, corresponding to crosssectional areas between 1.0 and 9.7 nm2. The set includes seven rectangular prisms, four hexagonal prisms with zigzag−zigzag edges, four hexagonal prisms with armchair−armchair edges, and two dodecagonal prisms with zigzag-armchair corners. The data set includes an exhaustive collection of hexagonal and dodecagonal nanowires with less than 450 atoms, and a less exhaustive set of rectangular geometries. Each calculation was undertaken in periodic boundary conditions with 10 Å of vacuum included in the x and y directions and the periodicity of the lattice in the z direction. Increasing the vacuum spacing to 20 Å was found to change the total energy by less than 0.01 eV for the smallest 1.0 nm2 nanowire. The DFT calculations used pseudopotentials of the PAW type30 and the exchange-correlation functional of Perdew, Burke and Ernzerhof.24 A plane-wave basis set was used with a cutoff of 500 eV, and four k-points in the (0001) direction, which had a periodicity of 5.3005 Å, found to be optimal for the bulk. These parameters are identical in every respect to those applied in the our earlier works from which we take the surface energies,21,22 allowing energies from the two sets of calculations to be compared directly. The optimized nanowire geometries are shown in Figure 2 (hexagonal and dodecagonal cross sections) and Figure 3 (rectangular cross sections). Inspection of the geometry of the

Figure 2. Optimized nanowire geometries with hexagonal and dodecagonal cross sections. The first four geometries are hexagonal prisms with zigzag−zigzag corners. The next two geometries are hexagonal prisms with armchair−armchair corners of the “in” type. The following two geometries are hexagonal prisms with armchair− armchair corners of the “out” type. The final two geometries are dodecagonal prisms with armchair−zigzag corners. C

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Table 2. Computed Total Energies and Inferred Edge Energies per Unit Length per Edge, for Hexagonal and Dodecagonal Nanowire Geometriesa cross section area [nm2]

ZnO per cell

1.0 2.3 4.2 6.5 3.6

24 54 96 150 84

4.9

114

7.8

180

9.6

222

6.0 8.9

138 204

edge type

inradius (Å)

Hexagons zz−zz 4.74 zz−zz 7.59 zz−zz 10.43 zz−zz 13.28 ac−ac 9.86 (in) ac−ac 11.50 (out) ac−ac 14.79 (in) ac−ac 16.43 (out) Dodecagons ac−zz 13.21 ac−zz 16.26

Etot (eV/cell)

Eedge (eV/nm)

−204.00 −466.34 −835.73 −1312.40 −729.58

0.37 0.37 0.41 0.41 0.21

−991.71

0.98

−1576.67

0.33

−1946.18

0.96

−1206.22 −1789.89

0.29 0.29

a The inradius is defined as the distance from the centre of the wire to the middle of the outermost plane of atoms in the as-truncated geometry.

Table 3. Computed Total Energies and Inferred Edge Energies for Rectangular Cross Section Nanowiresa cross sectional area [nm2]

ZnO per cell

S (1010) [Å]

S (1120) [Å]

Etot [eV/cell]

Eedge [eV/nm]

1.4 1.8 2.3 2.9 3.9 4.5 8.2

36 42 52 66 90 104 190

13.14 9.86 19.72 16.44 23.00 19.72 29.58

9.48 15.18 9.48 15.18 15.18 20.92 26.56

−307.14 −359.16 −446.29 −569.73 −780.28 −903.79 −1662.77

0.71 0.75 0.73 0.93 0.82 0.61 0.87

a

S (1010) and S (1120) denote the width in Å of the (1010) and (1120) facets. The surface energy is inferred from the spatial extents of the unreconstructed wire geometry in the x and y directions and the values in Table 1. The edge energy is assumed to be the remaining term and is divided by the length and number of edges present.

hexagon or dodecagon geometry; the surface area for all facets per unit length is then given by S = 6.928r for a hexagonal nanowire and S = 6.431r for the regular dodecagon. For the rectangular nanowires, the surface area of the (1010) and (1120) facets are determined separately based on the spatial extent of the nanowire in the x and y directions. Subtracting bulk and surface terms from the total energy gives a remaining term, which is assigned to the edge energy. Although other terms influencing the energy exist, these can be expected to decrease as the size of the nanowire increases. The edge energy term is found to be quite consistent for each edge type as the size of the nanowire increases, validating the calculational approach used. All edge energies are found consistently to be between 0.25 and 1.0 eV per linear nanometre for each edge type. There is a large difference between the energies of the “in” and “out” types for the armchair−armchair corner, with the “out” type edge (1 eV/nm) being several times higher in energy than the in edge type (0.3 eV/nm). The zigzag−zigzag corner energy is consistent across all nanowires, with a value of approximately 0.4 eV/nm. The 150° armchair−zigzag edges of the dodecagonal nanowires

Figure 3. Optimized geometries for nanowires with rectangular cross sections. Each nanowire has four 90° corners between a (1010) plane and a (1120) plane.

edges at the atomic scale shows a behavior consistent with the reconstruction behavior of the facets, with oxygen atoms displaced outward and zinc atoms inward from their ideal lattice positions, consistent with the behavior at surfaces.23,25 Computed total energies of the optimized ZnO nanowire geometries are given in Table 2 and Table 3. To determine the values of the edge energies, we first compute the portions of the total energy of each nanowire attributable to the bulk and surface. The bulk term was −8.92831 eV per ZnO unit, taken from a bulk calculation using identical parameters. To compute the surface energy term, we first determine the equivalent surface area of each facet; this was determined geometrically by using the distance from the center to of the outermost plane of atoms in the preoptimization geometry as the inradius r for a regular D

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A constructed minimum surface energy shape for a crystal computed using the Tang et al. surface energies from Table 1 is shown in Figure 5. The shape is an irregular dodecagonal prism,

have energies similar to the hexagonal corners, again around 0.3 eV/nm. For the right-angle corners, a somewhat larger range of values is found among the structures, from 0.6 to 0.9 eV/nm; as we shall show, this variation is unimportant for the determination of optimal nanoparticle geometries. We assign energies of 0.27 ± 0.1 eV/nm for armchair−armchair corners, 0.41 ± 0.1 eV/nm for zigzag−zigzag corners, 0.29 ± 0.1 eV/nm for armchair−zigzag corners, and 0.8 ± 0.1 eV/nm for the right-angled corners (Figure 4).

Figure 5. Rendered view of a ZnO crystal with a shape that minimizes the surface energy, based on the surface energy values of Table 1. Cyan facets are equivalent to (1010), magenta facets are (1120) and the (0001) facet is green. The (0001) facet is not visible from this angle.

with the (1010) facets of the prism being somewhat larger than the (1120) facets, due to the slightly smaller surface energy of the (1010) facet. The ratio of the surface area of the (1010) facets to the (1120) facets is 1.73:1. Using the nondefective (0001) and (0001) surface energies in Table 1, the aspect ratio of the particle (that is, the ratio of the length in the (0001) direction to the thinnest width) is 2.0:1. The true thermodynamic ground state of the (0001) and (0001) surfaces is dependent upon oxygen chemical potential and involves either defects or long-range reconstructions. The exact ground state structure is in general unknown, however Tang et al. show that the accumulation of short-range ordered defects on the surface reduces the summed surface energy of the two facets by around 1.1 eV,21 which would imply an aspect ratio of approximately 1.4:1. Although the surface energies computed using different methods in Table 1 differ somewhat from each other, the result that dodecagonal nanoparticles minimize surface energy compared to hexagonal ones is the same for all five sets of values since the ratio of the smaller to the larger energy is larger than (3/4) in each case. The results of Na and Park imply a dodecagonal shape in which the (1120) surfaces are slightly larger than the (1010) facets, while all other values predict a dodecagon with (1010) facets larger than the (1120) facets. We now consider the effect of the inclusion of edge energy terms. Figure 6 plots the relative formation energies, including surface and edge terms, of (regular) dodecagonal and hexagonal prisms with both (1010) and (1120) facets, including surface and edge terms, as a function of aspect ratio for three volumes, 10 nm3, 60 nm3 and 1000 nm3. For small volumes below 60 nm3, a hexagonal cross section with (1010) facets is preferred. At approximately 60 nm3, a crossover occurs to greater stability of dodecagonal nanoparticles. The optimal aspect ratio also decreases with decreasing size as the edge energy applies a penalty to length. At the crossover volume of 60 nm3, the optimal aspect ratio gives a diameter of approximately 3.5 nm, close to the cross section of the smallest observed ZnO nanoparticles.

Figure 4. Computed edge energies in eV per linear nanometer, for the set of nanowire geometries as a function of cross sectional area and corner type.

Assuming the cap-edge energies, at the intersection between the (0001)/(0001) prism caps and the (1010)/(1120) planes, to be on the same order of magnitude as the other edge energies, we may estimate that the cap-edge energy will be a contribution order of magnitude smaller than the cap energy for a prism with a 4 nm diameter, and 2 orders of magnitude smaller for a prism of 12 nm diameter. The effect of the cap edge energy is to slightly increase the cost of the cap, lessening the ideal aspect ratio, however the effect is small compared to the (not precisely known) effect of defects and reconstruction on the polar surfaces.

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OPTIMAL MORPHOLOGY Nanoparticles. We begin by considering the limit of a large nanoparticle, in which only the surface energy term is important. The problem in this case reduces to the Wulff construction,31 in which the optimal shape is given by a polyhedron in which the center of each facet is connected to a central point by a vector with length proportional to the surface energy of that facet. From geometric construction, it is easy to see that the surface-energy minimizing shape for a ZnO nanoparticle bounded by the four surfaces in question has three possible shapes. If the ratio between the (1010) and (1120) surface energies is less than (3/4) (approximately 0.866), the optimal shape is a hexagonal prism with six (1010)-equivalent facets on the sides and (0001) and (0001) facets on the end. If the γ(1010)/γ(1120) ratio is between (3/4) and (4/3) the optimal shape is a dodecagonal prism with both (1010) and (1120) facets. Finally, if the γ(1010)/γ(1120) ratio greater than (4/3) , the shape is again a hexagon, but with (1120) edge facets. E

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Figure 7. Computed relative formation energies per unit length of the side walls of ZnO nanoprisms with cross sections of (1010)- and (1120)-faceted hexagons, rectangles, and dodecagons with (1010) and (1120) facets, including surface and edge energies.

idealized 1.73:1 (1010):(1120) surface area ratio are found to be stable for cross sectional areas in excess of 10 nm2, corresponding to a diameter of approximately 4 nm. For cross sectional areas smaller than 10 nm2, hexagonal cross sections with (1010) facets are the most stable configuration. The crossover between hexagonal and dodecagonal stability represents the point at which the cost of the extra edges of the dodecagonal prism crosses over with the cost of the extra surface area of the hexagonal prism.

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DISCUSSION The calculations in this work imply that dodecagonal prisms, with a (1010):(1120) sidewall surface area ratio of 1.73:1, are the thermodynamically optimal shape for ZnO nanoparticles and nanowires with a cross section of more than a few nm. Edge energy terms are sufficient to cause hexagonal prisms to become stable at or near the cross sectional areas of the smallest ZnO nanostructures observed in practice, however have very little influence on the shape for cross sectional areas above 10 nm2. An optimal aspect ratio of approximately 2 is predicted; however, stabilization of the (0001) and (0001) surfaces by defects and reconstruction can be expected to reduce this aspect ratio somewhat. Despite the thermodynamic stability of the dodecagonal shape, nanoparticles and nanowires with hexagonal cross sections are very frequently observed in the literature.2 Observations of nanoparticles and nanowires with the dodecagonal shape are rarer. Nanowires with dodecagonal cross sections were observed by Dai et al. via a vapor-phase method32 with a substrate temperature of 1000 °C and Nobis et al. by pulsed laser deposition.33 Dodecagonal cross sections, however, are often difficult to distinguish from cylindrical cross sections, and careful observation of high-resolution TEM images of cylindrical nanowires may show them to exhibit some faceting, for example;34 we thus suggest that many of the observed cylindrical shapes in the literature may turn out upon closer examination to be dodecagonal. It is interesting to consider whether higher temperatures, which tend to promote the movement of atoms into the thermodynamic ground state, will cause the creation of dodecagonal over hexagonal nanoparticles. There are some

Figure 6. Nanoparticle formation energy as a function of aspect ratio, including surface and edge energies, for hexagonal prisms with both (1010) and (1120) facets, and regular dodecagonal prisms, for three volumes.

As will be shown in the next section, the stability difference between the regular dodecagonal and optimal dodecagonal cross section is very small, justifying the use of the regular rather than optimal dodecagonal shape in this section. Nanowires. We now consider the optimal cross-sectional shape of a nanowire. Although a nanowire, with its extended aspect ratio, is not an overall surface energy minimizing shape, nanowires are readily grown in practice due to the higher growth rate of ZnO in the [0001] direction. It is reasonable to consider the optimal shape of a nanowire whose aspect ratio is constrained, since the rearrangement of atoms from side wall to side wall is kinetically much easier than the rearrangement of atoms from side wall to cap. If only the surface energy terms are included, it may be shown that the optimal shape for a nanoparticle of fixed aspect ratio is the shape with the same dodecagonal cross section as the nanoparticle in Figure 5, with a ratio of (1010) to (1120) surface area of 1.73:1. Inclusion of edge energies leads to a stability relationship which is dependent upon cross-sectional area. Figure 7 shows predicted side facet formation energies per unit area of hexagonal (1010)-faceted, hexagonal (1120)-faceted, regular dodecagonal (1010)-(1120)-faceted ZnO nanowires, and square nanowires. Dodecagonal cross sections with the F

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indications in the literature that this may be the case in the few works where nanoparticles of both shapes are formed. Wuet al.34 report forming hexagonal nanowires by deposition methods at 500 °C and 1 atm argon flow, and cylindrical nanowires at 950 °C and 200 Pa argon. Similarly, Dai et al. fabricate dodecagonal nanowires by evaporative techniques at the high temperature of 1100 °C.32 Future experimental work which more systematically studies the variation of nanoparticle cross section as a function of growth temperature may be valuable. This work has only considered bare ZnO surfaces. Termination with some other chemical species (for instance in solution-based processes) may change the relative surface energies of the (1010) and (1120) surfaces, changing the Wulffoptimal shape from. It should be noted, however, that the bonding behavior of the (1120) and (1010) surfaces is very similar; for instance the adsorption energy of hydrogen on the (1010) versus the (1120) form is found to differ by only 0.03 eV/atom.20 Further work may be able to better predict whether adsorbates may stabilize one facet over another.

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SUMMARY

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AUTHOR INFORMATION

Using a model which takes both surface and edge energies into account, we have computed the thermodynamic stability of ZnO nanoparticles as a function of size and shape. For crosssectional areas below 10 nm2, competition between avoidance of edges and minimization of surface area results in a hexagonal cross section being most stable, but for larger cross sections a dodecagonal cross section is found to be optimal. Although this work goes only a small way toward understanding the full diversity of zinc oxide nanostructures observed in practice, understanding the thermodynamically stable structure is an indispensible first step toward understanding how divergences from this structure occur.

Corresponding Author

*(H.F.W.) E-mail: [email protected]. Telephone: +61 3 9662 7349. Notes

The authors declare no competing financial interest.

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REFERENCES

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DOI: 10.1021/acs.jpcc.6b01479 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C (32) Dai, J.; Xu, C. X.; Wu, P.; Guo, J. Y.; Li, Z. H.; Shi, Z. L. Exciton and Electron-Hole Plasma Lasing in ZnO Dodecagonal WhisperingGallery-Mode Microcavities at Room Temperature. Appl. Phys. Lett. 2010, 97, 011101. (33) Nobis, T.; Rahm, A.; Czekalla, C.; Lorenz, M.; Grundmann, M. Optical Whispering Gallery Modes in Dodecagonal Zinc Oxide Nanocrystals. Superlattices Microstruct. 2007, 42, 333−336. (34) Wu, Z. Y.; Chen, I. J.; Lin, Y. F.; Chiu, S. P.; Chen, F. R.; Kai, J. J.; Lin, J. J.; Jian, W. B. Cross-Sectional Shape Modulation of Physical Properties in ZnO and Zn1−xCoxO Nanowires. New J. Phys. 2008, 10, 033017.

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DOI: 10.1021/acs.jpcc.6b01479 J. Phys. Chem. C XXXX, XXX, XXX−XXX