- Email: [email protected]
Modelling the shape and orientation of ZnO nanobelts
Chemical Physics Letters 419 (2006) 313–316 www.elsevier.com/locate/cplett
Modelling the shape and orientation of ZnO nanobelts A.S. Barnard
a,*
, Y. Xiao b, Z. Cai
b
a
b
Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK Advanced Photon Source, Argonne National Laboratory, 9700 S Cass Avenue, Argonne, IL 60439, USA Received 13 October 2005; in final form 29 November 2005 Available online 20 December 2005
Abstract At the nanoscale, zinc oxide forms in many different shapes, the dimensions of which are often closely related to specific properties. Although much attention is focussed on finding methods for controlling the morphology, explanations of phenomena such as the change in crystallographic orientation of the principle axis of one-dimensional nanostructures (with size) are still largely empirical. We have used a shape-dependant thermodynamic model to identify the relationship between size, structure and orientation in zinc oxide nanobelts, and present results showing that growth in the ½1 2 1 0 direction is a decisive factor in determining the orientation. Published by Elsevier B.V.
Zinc oxide (ZnO) is an extremely widely studied nanomaterial, in part due to many properties promising new applications in a variety of nanodevices. One-dimensional structures have already been used in Schottky contacts [1] and logic circuits [2], but nanoscale ZnO may be synthesised in many different shapes and structures [3]. Even in one-dimension recent examples may be cited of nanorods [4], nanowires [5], nanocombs [5], nanosheets [5] and nanobelts [6,7] as well as more exotic branched structures such as tetrapods [8] and multipods [9]. ZnO nanostructures may be grown using templates [10], physical vapour deposition [11], electrodeposition [12] thermal evaporation [13] or hydro-thermal [14,15] and solvo-thermal [16] methods. Increasingly it has been found that particular (desirable) properties are intrinsical linked to the morphology of a given ZnO nanostructure [17], making a fundamental knowledge of the factors affecting the shape (as well as size) of great importance. Although much attention is being given to finding methods of controlling the morphology [11,15,16,18–20], explanations of phenomena such as the change in orientation of the principle axis of one-dimensional nanostructures (with size) are still largely empirical.
*
Corresponding author. E-mail address: [email protected] (A.S. Barnard).
0009-2614/$ - see front matter. Published by Elsevier B.V. doi:10.1016/j.cplett.2005.12.003
The zinc oxide nanobelts used as part of our studies were synthesised using thermal evaporation of ZnO powders (purity: 99.99%; melting point: 1975 K) at 1400 C for 2 h. The result was white wool-like products, that formed in high yield on the surface of the alumina plate under controlled conditions, without the presence of a catalyst. The experimental conditions include a chamber pressure of 300 torr, and an Ar flowing rate of 50 standard cubic centimeters per minute [21]. The synthesised nanobelts have a rectangular cross-section with a typical width of 30–300 nm. The typical thickness and width-to-thickness ratios of the ZnO nanobelts are in the range of 10–30 nm and about 2–10, respectively, with lengths up to a few millimetres. Putting the as-synthesised nanobelts into ethyl-alcohol solvent made a suspension in which the nanobelts were fully dispersed by ultrasonic agitation. Then, a proper amount of the suspension was transferred onto a silicon nitride membrane window. The nanobelt density on the membrane was checked with an optical microscope. High-resolution scanning electron microscopy (SEM) was used to characterize the samples in terms of dimensions, isolation, and coordinates prior to X-ray experiments. For accurate measurement, a thin layer of amorphous carbon (10 nm) was vaporized on the silicon nitride membrane window to reduce the electron charging effect.
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A.S. Barnard et al. / Chemical Physics Letters 419 (2006) 313–316
A recently developed X-ray nanodiffraction technique [22] was used to determine the orientation of a group of ZnO nanobelts with different dimensions. The experiment was performed at the 2ID-D beamline at the Advanced Photon Source. Using the extremely high brightness of a third-generation synchrotron radiation source and hard X-ray zone-plate optics, we focused hard X-rays to a microbeam of less than 200 nm so that significant diffraction can be measured from a single ZnO nanobelt. This X-ray nanodiffraction technique allows nondestructive structural characterization of individual nanobelts with the advantages of high structural sensitivity. The experimental results show ZnO nanobelts with two different growth directions. Two nanobelts with cross-sections of 220 nm · 26 nm and 200 nm · 23 nm were found to grow along ½1 0 1 0 and were enclosed by ð1 2 1 0Þ and ±(0 0 0 1) facets. Independently, two with cross-sections of 65 nm · 43 nm and 35 nm · 17 nm were found to grow along ±[0 0 0 1] and were also enclosed by ð1 0 1 0Þ and ð1 2 1 0Þ facets. The ZnO nanobelts with principle axes oriented in the ½1 0 1 0 and ±[0 0 0 1] directions have been denoted as Type I and Type II, and are shown schematically in Fig. 1a,b, respectively. The observation of these different morphologies in such specific size ranges indicates that a relationship exists between the dimensions of the nanobelts and direction of the principle axis. These ZnO nanobelts are particularly interesting, not only because they have such distinctively different shapes, but also because they share the same surface facets. This suggests the possibility for a Type I–Type II size-dependent Ôorientational transitionÕ during growth, that is also dependent in some way upon the shape of the nanobelts. To investigate the possibility of an orientational transition between Type I and Type II nanobelts, and identify the underlying shape-dependent factor, we have used a multi-scale, shape-dependent thermodynamic model based on a summation the Gibbs free energy [23], that has proven very successful in describing the shape of oxide nanomaterials in the past [24]. The (truncated) version of the model [25] (used here) is applicable only to isolated structures in
Fig. 1. The experimental results show that there are three types of ZnO nanobelts: (a) Type I and (b) Type II, each with different growing directions and cross-sections. The growing directions are dependent on the size of the nanobelts, and the lengths can be up to a few millimetres.
the range 3–100 nm in average diameter (since edge and corner effects have been ignored), so that the total free energy G is described in terms of the surface energy ci for each crystallographic surface i, weighted by the factors fi, P (such that i fi ¼ 1): " # X M G ¼ Df G þ ð1 eÞ q fi ci ; ð1Þ q i where DfG is the standard free energy of formation of the bulk (macroscopic) material, M is the molar mass, q is the density and e is the volume dilation induced by the surface stresses ri (as defined in reference [23]). As input into the model, we have used the ab initio (all-electron) surface energies of cð1 0 1 0Þ ¼ 2:32 J=m2 , cð1 2 1 0Þ ¼ 4:1 J=m2 and c(0 0 0 1) = 5.4 J/m2 calculated by Wander and Harrison with the hybrid B3LYP density functional [26]. It is important to point out that since each of the spatial dimensions the nanobelts exceeds 10 nm (a size at which the affect of the surface stress induced dilation on the total free energy has been found to be practically insignificant), the effects of surface stress have been ignored, so that e = 0. The validity of this approximation was confirmed for the ZnO nanobelt morphologies investigated here, by comparing results calculated with ri = 0 and ri = ci "i. In general, the surface to volume ratio q and the weighting factors fi provide the shape dependence and must be calculated explicitly for each morphology and the facets therein. The morphology of Type I and Type II nanobelts was defined geometrically in terms of the nanobelt length, width and thickness (assuming a rectangular cross-section), and the model in Eq. (1) was used to calculate the total free energy. The energy was calculated as a function of each of the three spatial dimensions, which were tested independently while keeping all other parameters constant. In varying the nanobelt length, the width and thickness were held constant at the average experimental values (as listed above). In this case, although the total free energy was found to change dramatically with increasing length (corresponding to an overall increase in size) both Types were found to be similar in energy (differing only in total surface area) as shown in Fig. 2a, and no orientational transition was predicted. When varying the thickness (while keeping the length constant at 100 lm, and the width constant at the average experimental values listed above) Type II nanobelts were predicted to be consistently lower in free energy than Type I nanobelts (as a function of thickness) as shown in Fig. 2b; but still without an orientational transition. Finally, when varying the width (with the length at 100 lm, and thickness at the average experimental values) Type II nanobelts were predicted to be lower in free energy than Type I nanobelts above 1340 m2/mol. Below this point the situation is reversed, as shown in Fig. 2c. This crossing indicates an orientational transition at a Type II width of 76 nm (or a Type I width of 176 nm), in excellent agreement with the experimental observations.
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315
tion of the width and thickness. We can see from Fig. 2d,e that while the total free energy of Type I and Type II nanobelts decreases with decreasing surface area, no orientational transition is predicted in either case. This clearly verifies that it is the width of the Type I and Type II nanobelts that is the critical spatial parameter. Looking again to Fig. 1a,b, we can see that for both Type I and Type II nanobelts the width is oriented in the ½1 2 1 0 direction; and that this dimension does not alter during the orientational transition identified in Fig. 2c. Given that the growth rates normal to surfaces are inversely proportional to the surface free energy (of the surface), we can see from the results of Wander and Harrison [26] that this is likely to be the secondary growth direction of the ZnO nanobelts. In general, there is still ongoing debate as to the growth mechanism responsible for the formation of belt-like nanostructures. ZnO nanostructures (such as the nanobelts under consideration here) are synthesized by controlling the processing conditions; indicating that the kinetics are important in their morphological evolution [3]. The twodimensional nucleation probability P on the surface of a belt-like nanostructures is given by 2
P ¼ B expfðp= ln½aÞðE=kT Þ g;
Fig. 2. Total Gibbs free energy of Type I and Type II ZnO nanobelts (as defined in Fig. 1). The decreasing surface area corresponds to an increase in: (a) length, (b) thickness, (c) width, (d) total cross-sectional area, and (e) the width-to-thickness ratio. The cross over in (c) at a Type II width of 76 nm indicates the size dependence of the orientational transition.
In addition to these parameters the total cross-sectional area (perpendicular to the principle axis of the nanobelts) and the width-to-thickness ratio was also varied, each with the length set to 100 lm. These results are shown in Fig. 2d,e, respectively, and were added to determine if the width was the only spatial dimension controlling the orientational transformation, or if it was in fact a combina-
ð2Þ
where B is a constant, E the surface energy of the solid nanostructure, k the BoltzmannÕs constant, T the absolute temperature, and a the supersaturation ratio determined by a = p/p0 (with p the actual vapor pressure and p0 the equilibrium vapor pressure corresponding to temperature T) [27]. Usually, a > 1. Thus, E is dependent upon the orientation of the nanobelt, and directly affects the nucleation probability. For example, a low-index crystal plane gives rise to a lower surface energy, but a larger 2-D nucleation probability. Moreover, it is energetically unfavorable for a partial layer to form on a low-energy surface, and an atom (or molecule) adsorbed on a low-energy surface has a high probability of desorption. It is therefore likely that a combination of kinetics and thermodynamics are responsible for the formation of the initial nanobelt morphology (via parameters such as the temperature and the supersaturation ratio) [3]. We may logically speculate that the nanobelts examined herein begin as Type II (with the length growing kinetically in the primary ±[0 0 0 1] direction) and once the kinetic growth in the secondary ½1 2 1 0 direction reaches a critical width of 76 nm the thermodynamic driving forces dominate, and the orientation changes. This change increases the surface area of the {0 0 0 1} facets, and facilitates a lowering of the total surface energy. The dimensions of the Type I nanobelts are different following this transition due to crystallographic restrictions. In conclusion, results of the shape-dependent model used herein have identified the secondary ½1 2 1 0 growth direction as a decisive parameter in determining the orientation of the principle axis of the Type I and Type II ZnO nanobelts (with axes in the ½1 0 1 0 and ±[0 0 0 1],
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respectively). These results are in excellent in agreement with the experimental findings presented here, and highlight how simple thermodynamic arguments may assist in understanding the relationship between the size and morphology of ZnO nanostructures. Acknowledgements This work has been supported by the Glasstone Benefaction at the University of Oxford and the US Department of Energy, Office of Basic Energy Sciences, under Contract W-31-109-ENG-38. The ZnO nanobelt samples were provided by Zhong-Ling Wang from the School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332. References [1] W.I. Park, G.-C. Yi, J.-W. Kim, S.-M. Park, Appl. Phys. Lett. 82 (2003) 4358. [2] W.I. Park, J.S. Kim, G.-C. Yi, H.-J. Lee, Adv. Mater. 17 (2005) 1393. [3] Z.L. Wang, Mater. Today 7 (2004) 26. ¨ , Physica E 28 (2005) 76. [4] L. Wu, Y. Wu, W. LU [5] J.-H. Park, Y.-J. Choi, J.-G. Park, J. Eur. Ceram. Soc. 25 (2005) 2037. [6] X. Wen, Y. Fang, Q. Pang, C. Yang, J. Wang, W. Ge, K.S. Wong, S. Yang, J. Phys. Chem. B 109 (2005) 15303.
[7] D.-F. Zhang, L.-D. Sun, J.-L. Yin, C.-H. Yan, R.-M. Wang, J. Phys. Chem. B 109 (2005) 8786. [8] Z. Chen, Z. Shan, M.S. Cao, L. Lu, S.X. Mao, Nanotechnology 15 (2004) 365. [9] J. Wang, L. Gao, J. Cryst. Growth 262 (2004) 290. [10] H.J. Fan, W. Lee, R. Scholz, A. Dadgar, A. Krost, K. Nielsch, M. Zacharias, Nanotechnology 16 (2005) 913. [11] X.Q. Meng, D.X. Zhao, J.Y. Zhang, D.Z. Shen, Y.M. Lu, Y.C. Liu, X.W. Fan, Chem. Phys. Lett. 407 (2005) 91. [12] L. Xu, Y. Guo, Q. Liao, J. Zhang, D. Xu, J. Phys. Chem. B 109 (2005) 13519. [13] Y. Zhang, L. Wang, X. Liu, Y. Yan, C. Chen, J. Zhu, J. Phys. Chem. B 109 (2005) 13091. [14] M. Guo, P. Diao, S. Cai, J. Solid-State Chem. 178 (2005) 1864. [15] U. Pal, P. Santiago, J. Phys. Chem. B 109 (2005) 15317. [16] D. Wang, C. Song, J. Phys. Chem. B 109 (2005) 12697. [17] L. Liao, J.C. Li, D.F. Wang, C. Liu, Q. Fu, Mater. Lett. 59 (2005) 2465. [18] J. Zhang, L.-D. Sun, X.-C. Jiang, C.-S. Liao, C.-H. Yan, Cryst. Growth Des. 4 (2004) 309. [19] H. Wang, C. Xie, D. Zeng, J. Cryst. Growth 277 (2005) 372. [20] J. Du, Z. Liu, Y. Huang, Y. Gao, B. Han, W. Li, G. Yang, J. Cryst. Growth 280 (2005) 126. [21] Z. Pan, Z. Dai, Z. Wang, Science 291 (2001) 1947. [22] Y. Xiao, Z. Cai, B. Lai, Nanotechnology 16 (2005) 1754. [23] A.S. Barnard, P. Zapol, J. Chem. Phys. 121 (2004) 4276. [24] A.S. Barnard, L.A. Curtiss, NanoLetters 5 (2005) 1261. [25] A.S. Barnard, L.A. Curtiss, Rev. Adv. Mater. Sci. 10 (2005) 105. [26] A. Wander, N.M. Harrison, Surf. Sci. Lett. 468 (2000) 851. [27] J.M. Blakely, K.A. Jackson, J. Chem. Phys. 37 (1962) 428.
Modelling the shape and orientation of ZnO nanobelts A.S. Barnard
a,*
, Y. Xiao b, Z. Cai
b
a
b
Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK Advanced Photon Source, Argonne National Laboratory, 9700 S Cass Avenue, Argonne, IL 60439, USA Received 13 October 2005; in final form 29 November 2005 Available online 20 December 2005
Abstract At the nanoscale, zinc oxide forms in many different shapes, the dimensions of which are often closely related to specific properties. Although much attention is focussed on finding methods for controlling the morphology, explanations of phenomena such as the change in crystallographic orientation of the principle axis of one-dimensional nanostructures (with size) are still largely empirical. We have used a shape-dependant thermodynamic model to identify the relationship between size, structure and orientation in zinc oxide nanobelts, and present results showing that growth in the ½1 2 1 0 direction is a decisive factor in determining the orientation. Published by Elsevier B.V.
Zinc oxide (ZnO) is an extremely widely studied nanomaterial, in part due to many properties promising new applications in a variety of nanodevices. One-dimensional structures have already been used in Schottky contacts [1] and logic circuits [2], but nanoscale ZnO may be synthesised in many different shapes and structures [3]. Even in one-dimension recent examples may be cited of nanorods [4], nanowires [5], nanocombs [5], nanosheets [5] and nanobelts [6,7] as well as more exotic branched structures such as tetrapods [8] and multipods [9]. ZnO nanostructures may be grown using templates [10], physical vapour deposition [11], electrodeposition [12] thermal evaporation [13] or hydro-thermal [14,15] and solvo-thermal [16] methods. Increasingly it has been found that particular (desirable) properties are intrinsical linked to the morphology of a given ZnO nanostructure [17], making a fundamental knowledge of the factors affecting the shape (as well as size) of great importance. Although much attention is being given to finding methods of controlling the morphology [11,15,16,18–20], explanations of phenomena such as the change in orientation of the principle axis of one-dimensional nanostructures (with size) are still largely empirical.
*
Corresponding author. E-mail address: [email protected] (A.S. Barnard).
0009-2614/$ - see front matter. Published by Elsevier B.V. doi:10.1016/j.cplett.2005.12.003
The zinc oxide nanobelts used as part of our studies were synthesised using thermal evaporation of ZnO powders (purity: 99.99%; melting point: 1975 K) at 1400 C for 2 h. The result was white wool-like products, that formed in high yield on the surface of the alumina plate under controlled conditions, without the presence of a catalyst. The experimental conditions include a chamber pressure of 300 torr, and an Ar flowing rate of 50 standard cubic centimeters per minute [21]. The synthesised nanobelts have a rectangular cross-section with a typical width of 30–300 nm. The typical thickness and width-to-thickness ratios of the ZnO nanobelts are in the range of 10–30 nm and about 2–10, respectively, with lengths up to a few millimetres. Putting the as-synthesised nanobelts into ethyl-alcohol solvent made a suspension in which the nanobelts were fully dispersed by ultrasonic agitation. Then, a proper amount of the suspension was transferred onto a silicon nitride membrane window. The nanobelt density on the membrane was checked with an optical microscope. High-resolution scanning electron microscopy (SEM) was used to characterize the samples in terms of dimensions, isolation, and coordinates prior to X-ray experiments. For accurate measurement, a thin layer of amorphous carbon (10 nm) was vaporized on the silicon nitride membrane window to reduce the electron charging effect.
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A.S. Barnard et al. / Chemical Physics Letters 419 (2006) 313–316
A recently developed X-ray nanodiffraction technique [22] was used to determine the orientation of a group of ZnO nanobelts with different dimensions. The experiment was performed at the 2ID-D beamline at the Advanced Photon Source. Using the extremely high brightness of a third-generation synchrotron radiation source and hard X-ray zone-plate optics, we focused hard X-rays to a microbeam of less than 200 nm so that significant diffraction can be measured from a single ZnO nanobelt. This X-ray nanodiffraction technique allows nondestructive structural characterization of individual nanobelts with the advantages of high structural sensitivity. The experimental results show ZnO nanobelts with two different growth directions. Two nanobelts with cross-sections of 220 nm · 26 nm and 200 nm · 23 nm were found to grow along ½1 0 1 0 and were enclosed by ð1 2 1 0Þ and ±(0 0 0 1) facets. Independently, two with cross-sections of 65 nm · 43 nm and 35 nm · 17 nm were found to grow along ±[0 0 0 1] and were also enclosed by ð1 0 1 0Þ and ð1 2 1 0Þ facets. The ZnO nanobelts with principle axes oriented in the ½1 0 1 0 and ±[0 0 0 1] directions have been denoted as Type I and Type II, and are shown schematically in Fig. 1a,b, respectively. The observation of these different morphologies in such specific size ranges indicates that a relationship exists between the dimensions of the nanobelts and direction of the principle axis. These ZnO nanobelts are particularly interesting, not only because they have such distinctively different shapes, but also because they share the same surface facets. This suggests the possibility for a Type I–Type II size-dependent Ôorientational transitionÕ during growth, that is also dependent in some way upon the shape of the nanobelts. To investigate the possibility of an orientational transition between Type I and Type II nanobelts, and identify the underlying shape-dependent factor, we have used a multi-scale, shape-dependent thermodynamic model based on a summation the Gibbs free energy [23], that has proven very successful in describing the shape of oxide nanomaterials in the past [24]. The (truncated) version of the model [25] (used here) is applicable only to isolated structures in
Fig. 1. The experimental results show that there are three types of ZnO nanobelts: (a) Type I and (b) Type II, each with different growing directions and cross-sections. The growing directions are dependent on the size of the nanobelts, and the lengths can be up to a few millimetres.
the range 3–100 nm in average diameter (since edge and corner effects have been ignored), so that the total free energy G is described in terms of the surface energy ci for each crystallographic surface i, weighted by the factors fi, P (such that i fi ¼ 1): " # X M G ¼ Df G þ ð1 eÞ q fi ci ; ð1Þ q i where DfG is the standard free energy of formation of the bulk (macroscopic) material, M is the molar mass, q is the density and e is the volume dilation induced by the surface stresses ri (as defined in reference [23]). As input into the model, we have used the ab initio (all-electron) surface energies of cð1 0 1 0Þ ¼ 2:32 J=m2 , cð1 2 1 0Þ ¼ 4:1 J=m2 and c(0 0 0 1) = 5.4 J/m2 calculated by Wander and Harrison with the hybrid B3LYP density functional [26]. It is important to point out that since each of the spatial dimensions the nanobelts exceeds 10 nm (a size at which the affect of the surface stress induced dilation on the total free energy has been found to be practically insignificant), the effects of surface stress have been ignored, so that e = 0. The validity of this approximation was confirmed for the ZnO nanobelt morphologies investigated here, by comparing results calculated with ri = 0 and ri = ci "i. In general, the surface to volume ratio q and the weighting factors fi provide the shape dependence and must be calculated explicitly for each morphology and the facets therein. The morphology of Type I and Type II nanobelts was defined geometrically in terms of the nanobelt length, width and thickness (assuming a rectangular cross-section), and the model in Eq. (1) was used to calculate the total free energy. The energy was calculated as a function of each of the three spatial dimensions, which were tested independently while keeping all other parameters constant. In varying the nanobelt length, the width and thickness were held constant at the average experimental values (as listed above). In this case, although the total free energy was found to change dramatically with increasing length (corresponding to an overall increase in size) both Types were found to be similar in energy (differing only in total surface area) as shown in Fig. 2a, and no orientational transition was predicted. When varying the thickness (while keeping the length constant at 100 lm, and the width constant at the average experimental values listed above) Type II nanobelts were predicted to be consistently lower in free energy than Type I nanobelts (as a function of thickness) as shown in Fig. 2b; but still without an orientational transition. Finally, when varying the width (with the length at 100 lm, and thickness at the average experimental values) Type II nanobelts were predicted to be lower in free energy than Type I nanobelts above 1340 m2/mol. Below this point the situation is reversed, as shown in Fig. 2c. This crossing indicates an orientational transition at a Type II width of 76 nm (or a Type I width of 176 nm), in excellent agreement with the experimental observations.
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tion of the width and thickness. We can see from Fig. 2d,e that while the total free energy of Type I and Type II nanobelts decreases with decreasing surface area, no orientational transition is predicted in either case. This clearly verifies that it is the width of the Type I and Type II nanobelts that is the critical spatial parameter. Looking again to Fig. 1a,b, we can see that for both Type I and Type II nanobelts the width is oriented in the ½1 2 1 0 direction; and that this dimension does not alter during the orientational transition identified in Fig. 2c. Given that the growth rates normal to surfaces are inversely proportional to the surface free energy (of the surface), we can see from the results of Wander and Harrison [26] that this is likely to be the secondary growth direction of the ZnO nanobelts. In general, there is still ongoing debate as to the growth mechanism responsible for the formation of belt-like nanostructures. ZnO nanostructures (such as the nanobelts under consideration here) are synthesized by controlling the processing conditions; indicating that the kinetics are important in their morphological evolution [3]. The twodimensional nucleation probability P on the surface of a belt-like nanostructures is given by 2
P ¼ B expfðp= ln½aÞðE=kT Þ g;
Fig. 2. Total Gibbs free energy of Type I and Type II ZnO nanobelts (as defined in Fig. 1). The decreasing surface area corresponds to an increase in: (a) length, (b) thickness, (c) width, (d) total cross-sectional area, and (e) the width-to-thickness ratio. The cross over in (c) at a Type II width of 76 nm indicates the size dependence of the orientational transition.
In addition to these parameters the total cross-sectional area (perpendicular to the principle axis of the nanobelts) and the width-to-thickness ratio was also varied, each with the length set to 100 lm. These results are shown in Fig. 2d,e, respectively, and were added to determine if the width was the only spatial dimension controlling the orientational transformation, or if it was in fact a combina-
ð2Þ
where B is a constant, E the surface energy of the solid nanostructure, k the BoltzmannÕs constant, T the absolute temperature, and a the supersaturation ratio determined by a = p/p0 (with p the actual vapor pressure and p0 the equilibrium vapor pressure corresponding to temperature T) [27]. Usually, a > 1. Thus, E is dependent upon the orientation of the nanobelt, and directly affects the nucleation probability. For example, a low-index crystal plane gives rise to a lower surface energy, but a larger 2-D nucleation probability. Moreover, it is energetically unfavorable for a partial layer to form on a low-energy surface, and an atom (or molecule) adsorbed on a low-energy surface has a high probability of desorption. It is therefore likely that a combination of kinetics and thermodynamics are responsible for the formation of the initial nanobelt morphology (via parameters such as the temperature and the supersaturation ratio) [3]. We may logically speculate that the nanobelts examined herein begin as Type II (with the length growing kinetically in the primary ±[0 0 0 1] direction) and once the kinetic growth in the secondary ½1 2 1 0 direction reaches a critical width of 76 nm the thermodynamic driving forces dominate, and the orientation changes. This change increases the surface area of the {0 0 0 1} facets, and facilitates a lowering of the total surface energy. The dimensions of the Type I nanobelts are different following this transition due to crystallographic restrictions. In conclusion, results of the shape-dependent model used herein have identified the secondary ½1 2 1 0 growth direction as a decisive parameter in determining the orientation of the principle axis of the Type I and Type II ZnO nanobelts (with axes in the ½1 0 1 0 and ±[0 0 0 1],
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respectively). These results are in excellent in agreement with the experimental findings presented here, and highlight how simple thermodynamic arguments may assist in understanding the relationship between the size and morphology of ZnO nanostructures. Acknowledgements This work has been supported by the Glasstone Benefaction at the University of Oxford and the US Department of Energy, Office of Basic Energy Sciences, under Contract W-31-109-ENG-38. The ZnO nanobelt samples were provided by Zhong-Ling Wang from the School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332. References [1] W.I. Park, G.-C. Yi, J.-W. Kim, S.-M. Park, Appl. Phys. Lett. 82 (2003) 4358. [2] W.I. Park, J.S. Kim, G.-C. Yi, H.-J. Lee, Adv. Mater. 17 (2005) 1393. [3] Z.L. Wang, Mater. Today 7 (2004) 26. ¨ , Physica E 28 (2005) 76. [4] L. Wu, Y. Wu, W. LU [5] J.-H. Park, Y.-J. Choi, J.-G. Park, J. Eur. Ceram. Soc. 25 (2005) 2037. [6] X. Wen, Y. Fang, Q. Pang, C. Yang, J. Wang, W. Ge, K.S. Wong, S. Yang, J. Phys. Chem. B 109 (2005) 15303.
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