Mechanism of Morphology Transformation of Tetragonal Phase

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Mechanism of Morphology Transformation of Tetragonal Phase LaVO4 Nanocrystals Controlled by Surface Chemistry: Experimental and Theoretical Insights Pan Li,† Xian Zhao,‡ Chun-Jiang Jia,§ Honggang Sun,‡ Yanlu Li,‡ Liming Sun,‡ Xiufeng Cheng,‡ Li Liu,‡ and Weiliu Fan*,† †

School of Chemistry and Chemical Engineering and ‡State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China § Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany ABSTRACT: Morphology and exposed facets control are a hot and challenging topic in the design and synthesis of small-sized materials. Starting by studying the surface structure and surface energy of nanostructures is an important way to achieve this goal. In our experimental work, tetragonal phase LaVO4 (t-LaVO4) nanocrystals are prepared via the hydrothermal method by tuning the pH of the growth solution. The products are characterized by X-ray diffractometry, transmission electron microscopy, and high-resolution transmission electron microscopy, and the results show that the aspect ratios and exposed facets of the nanocrystals changed with the variation of pH values. By combining the experimental findings, first-principles calculations are used to investigate the effect of surface chemistry on the morphology transformation of t-LaVO4 nanocrystals. Equilibrium geometries, surface energies, and surface tensions are calculated for selected low-index surfaces of t-LaVO4 under the different surface passivated conditions. The surface energies of (100) and (101) surfaces increase first and then decrease, while the (001) surface decreases monotonously with the fraction of hydrogen in the adsorbates decreased. The equilibrium shapes of t-LaVO4 nanocrystals can be obtained according to the Wulff law. Our results indicate that surface energy has an important role to control the morphology and exposed facets of the nanocrystals; the effect of surface chemistry on the morphology of t-LaVO4 nanocrystals is obvious, which is consistent with our experimental findings. Besides, a modified Wulff construction model that considers the effect of surface tension is used and draws the same conclusions. Our investigations provide a useful approach to predict and evaluate the effect of surface chemistry on the shape of the nanocrystals, which is for better understanding the shapecontrolled nanocrystal growth.

1. INTRODUCTION Shape control of nanocrystals is an important objective in nanocrystal synthesis as different shapes of the particles can induce different electronic, optical, and catalytic properties.1−3Hence, understanding the mechanisms that determine crystal morphology is a major challenge in the field of nanoscience, which has driven intensive research toward this direction.4−9 The morphologies of nanocrystals depend on a number of surface chemistry factors such as the solvent,10,11 surface-active agents,12 and pH value of the solution.13−15 A better understanding of the underlying processes of how these factors affect the shape could lead to the optimization and control of the nanocrystal morphology. However, studies on the nanocrystal shape evolution mechanism have mostly been given based on some experimental speculation;10−15 the ultimate relationships between the experimental factors and the resulting nanocrystal shape are still unclear and require further clarification. © 2012 American Chemical Society

Surface energies of the featured facets of nanocrystals are a key factor in the free energy and consequently determining the nanocrystal morphology. In thermodynamic equilibrium, the crystal shape is determined by minimizing the surface energy for a given volume according to the Wulff construction.1,9,16,17 Since surface energies are not readily acquired by experiments, computer modeling and simulation provide a helpful approach to predict and evaluate the effects of surface chemistry on the surface energies and the resulting nanocrystal shape. Lanthanide orthovanadates are important rare-earth compounds and widely used as catalysts, polarizers, laser host materials, and phosphors.18−21 Lanthanide orthovanadates crystallize in two polymorphs, that is, monoclinic (m-) phase and metastable tetragonal (t-) phase. Yan et al. realized the selective synthesis of m- and t-LaVO4 nanocrystals via a Received: July 17, 2012 Revised: August 16, 2012 Published: September 17, 2012 5042

dx.doi.org/10.1021/cg3009927 | Cryst. Growth Des. 2012, 12, 5042−5050

Crystal Growth & Design

Article

each atom to be smaller than 0.05 eV/Å. For all slabs considered in the present work, both the top and bottom surfaces were passivated for they have identical termination.

hydrothermal method by using chelating ligands EDTA, and they found that t-LaVO4 nanocrystals exhibited an improved luminescent and catalytic performance.22,23 In our previous experimental work,24,25 the controlled synthesis of m- and tLaVO4 was realized by tuning the pH value of the growth solution, and the transformation from monoclinic to the tetragonal phase resulted in a prominent improvement of the luminescent properties. For the potential excellent properties of the metastable t-LaVO4, therefore, investigating the morphology transformation of t-LaVO4 nanocrystals is crucial for optimizing the synthesis to obtain better performance materials. In this work, we investigated the mechanism of morphology transformation of t-LaVO4 nanocrystals controlled by surface chemistry using experimental and theoretical calculation methods. In Section 3.1, t-LaVO4 nanocrystals with different morphologies were prepared via the hydrothermal method by tuning the pH of the growth solution and were characterized by powder X-ray diffractometry (XRD) and transmission electron microscopy (TEM). In Section 3.2, the relaxed structure of all surfaces with adsorbates modeling different surface conditions were discussed. Then, the surface energies and surface tensions were calculated, and the effect of surface chemistry on the shape was studied in Section 3.3.

3. RESULTS AND DISCUSSION 3.1. Characterization of the t-LaVO4 Nanocrystals. Figure 1 shows the XRD patterns of t-LaVO4 nanocrystals

Figure 1. XRD patterns of t-LaVO4 nanocrystals prepared under different pH conditions: (a) pH = 3.0; (b) pH = 3.5; (c) pH = 4.0; (d) pH = 5.5.

2. EXPERIMENTAL AND COMPUTATIONAL DETAILS The tetragonal phase t-LaVO4 nanocrystals were prepared by the hydrothermal method based on our previous work.24 In a typical synthesis, 1.6 mmol of La(NO3)3·6H2O was dissolved in 4 mL of deionized water to form a solution. A 8 mL portion of 0.2 M NaVO3 solution was then added dropwise into the above solution under stirring. The mixture solution turned yellow immediately. To investigate the effect of pH on the morphology of the final product, the amount of added NaOH (1.0M) was varied to adjust the pH value of the solution while other parameters were kept constant. Then, the suspension was stirred for another 10 min. After dilution with deionized water, the mixture was transferred into a 25 mL autoclave with an inner Teflon lining and maintained at 190 °C for 48 h. After the reaction was completed, the final pH of the growth solution was measured. The products was collected by filtration, washed several times with deionized water and absolute alcohol, and finally, dried in an oven at 80 °C for 8 h. The samples were characterized structurally by X-ray diffraction (XRD; Bruker D8, Cu Kα, λ = 0.15418 nm) and transmission electron microscopy (TEM; JEOL JEM-2100, 200 kV). The calculations were performed using the plane-wave pseudopotential density functional theory (DFT) method as implemented in the CASTEP code.26 The generalized-gradient approximation with the Perdew−Wang (PW91)27 forms was used to describe the exchange and correlation potential. Ultrasoft pseudopotentials are used to deal with core electrons. The pseudopotentials for La, V, and O atoms represented 5s25p65d16s2, 3s23p63d34s2, and 2s22p4 electron configurations, respectively. A Monkhorst Pack k-point mesh of 3 × 3 × 4 yielded well-converged bulk results. To verify the accuracy of the pseudopotentials and computational method, bulk t-LaVO4 calculations were performed. The calculated a and c lattice constants were 7.61 and 6.61 Å, respectively, in good agreement with experimental values.28 The bulk modulus B0 = 110 GPa calculated by using the Birch−Murnaghan equation of state29 was in good agreement with the value calculated by Zhang et al.30 Surfaces of the t-LaVO4 were described by using a slab model, and a 2 × 1 supercell was used for all the surface passivation. The thickness of the slab was three bulk lattice units for the (100) surface and four bulk lattice units for the (101) and (001) surfaces. A vacuum region of 16−20 Å was placed above the slabs in order to avoid any spurious interaction between adjacent slabs along the slab surface normals. The Monkhorst Pack grids used were 1 × 3 × 1 for the (100) and (001) surfaces and 2 × 2 × 1 for the (101) surface. Relaxation of the surface structures was accomplished by requiring the forces experienced by

prepared at different pH values. All of the diffraction peaks are well indexed to the tetragonal t-LaVO4 (JCPDS card no. 320504), and no traces of other phases are examined. The sharp peaks in each XRD pattern indicate the good crystallinity of the samples. A close examination shows that the ratio of the intensity of the (200) peak to that of the (101) peak decreases gradually. This trend is expected considering the growing fractions of (101) facets. To further confirm the morphologies of t-LaVO4 nanostructures, a detailed TEM analysis has been performed on the products synthesized. Figure 2 shows the TEM images of tLaVO4 nanocrystals and an individual t-LaVO4 nanocrystal prepared under different pH conditions. From Figure 2a, we can see that the nanorods had a low aspect ratio at pH= 3.0. The widths changed in the range 10−20 nm, and the lengths were in the range 20−60 nm. When the pH was increased to 3.5, the rod-shaped crystals grew longer, and the lengths of the nanorods were 50−80 nm (Figure 2b). Adjusting pH to 4.0 will favor the lengthwise growth and increase the aspect ratios. The widths of the nanorods were decreased to 10−15 nm while their lengths were increased to 70−90 nm. When the pH was raised to a higher value (5.5), the widths of the nanorods were 10−30 nm, and the lengths of the nanorods were decreased obviously in the range 30−40 nm. Moreover, it is noted that the shape of the tips of the nanorods varied under the different pH conditions. Typical TEM images of an individual t-LaVO4 nanocrystal are shown in Figure 2a 1, b1, c1 , and d1 , corresponding to the area marked in Figure 2a, b, c, and d. It can be observed that the nanorods had flat basal facets at lower pH, as shown in Figure 2a1 and b1. However, the shape of the tips of the nanorods changed from flat to sharp when the pH was increased (Figure 2c1 and d1). The above results suggest that the pH value of the growth solution not only has an impact on the aspect ratios of the nanocrystals but also on their exposed facets. 5043



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Figure 2. TEM images of t-LaVO4 nanocrystals prepared under different pH conditions: (a, a1) pH = 3.0; (b, b1) pH = 3.5; (c, c1) pH = 4.0; (d, d1) pH = 5.5.

surfaces can be also created by cutting through the La, V, and O atoms. For these surfaces, we found that the termination by La and O atoms was energetically favorable compared to that by La, V, and O atoms (1.56 J/m2 versus 2.58 J/m2 for (101) surface and 2.61 J/m2 versus 3.90 J/m2 for (001) surface). Therefore, these surfaces composed of La and O atoms are investigated in our study. The (101) surface is made up of La atoms with three dangling bonds and O atoms with one dangling bond. The O atoms on the surface can be divided into three classes (labeled with subscript) as shown in Figure 4 (e).There are two kinds of La and O atoms on the (001) surface. The La(1) atoms display two dangling bonds, and the La(2) atoms display four dangling bonds. The O(1) and O(2) atoms have two or one dangling bonds, respectively. From the experiments, water adsorbates appeared in the tLaVO4 nanocrystals under the different pH conditions.31 Therefore, the La atoms on the surface were terminated with water for the fact that the water is more likely to bind to La ions in the growth solution. Different degrees of surface acidic conditions were modeled by varying the amount of hydrogen adsorbed on the surface O atoms. All of the O atoms terminated with hydrogen surfaces were used to stand for most acidic conditions, whereas H poor surfaces were used to stand for weakly acidic conditions. Stoichiometric noncharged systems were employed in all our models. 3.2.1. Clean Surfaces. First, we calculated the relaxed geometry for these clean surfaces. Figure 4 shows the top and side views of the relaxed (100), (101), and (001) surfaces. For the (100) surface, the La ions exhibited a small inward relaxation of 0.01 Å, and the O ions underwent an inward relaxation of about 0.05 Å. In the case of the (101) surface, the La ions exhibited an evident inward displacement of 0.30 Å. The O(1) ions exhibited an inward relaxation of about 0.03 Å, while the O(2) and O(3) ions maintained their position. For the (001) surface, the inward displacement of the 4-fold coordinated La(2) ions was 0.19 Å that was larger than that of the 6-fold coordinated La(1) of 0.12 Å. The O(1) ions underwent

Further HRTEM and fast Fourier transform (FFT) characterizations provide us more information on the structural details of these t-LaVO4 samples. As shown in Figure 3a, the tLaVO4 nanorod prepared at pH = 3.5 had flat basal facets. The corresponding HRTEM image in Figure 3a1 exhibited lattice spacings of about 0.330 and 0.374 nm, corresponding to the interplanar distance of (002) and (200) plane of t-LaVO4. Studies of the HRTEM image and FFT pattern (Figure 3a2) demonstrated that the t-LaVO4 nanorods grow along the [001] direction. Therefore, the basal planes of the t-LaVO4 nanorods are {001} planes, and its dominating side surfaces are {100} planes. At pH = 4.0, the shape of basal facets of t-LaVO4 nanorod became much sharper (Figure 3b). The lattice spacings (Figure 3b1) of 0.495 nm is well indexed to the (101) plane of the t-LaVO4. The dominating surfaces of the tLaVO4 nanorod are the {100} and {101} planes, while the fraction of {001} planes to the whole surface decreases dramatically. When the pH value was tuned to 5.5, the tLaVO4 exhibited a low aspect ratio; however, its exposed planes are only the {100} and {101} planes. Above structural characterization results demonstrate that the t-LaVO4 samples prepared under different pH conditions have various aspect ratios and exposed surfaces. The contribution of (101) planes to the shape increases with increasing the pH value of the growth solution, which is consistent with the XRD analysis. 3.2. Surfaces Structure. Due to the large specific surface area of the nanocrystals, studying on the surface science, especially the surface thermodynamic has a very important significance to clarify the growth mechanism and to control the exposed surfaces of the nanocrystals. Here, the surface thermodynamic properties of (100), (101), and (001) surface planes that are exposing planes of the prepared t-LaVO4 nanocrystals were investigated. The relaxed surface structures are presented for the (100), (101), and (001) surfaces, as shown in Figure 4. The (100) surface is composed of La and O atoms with one dangling bond. The (101) and (001) surfaces are created by cutting through the La and O atoms, whereas the 5044



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Figure 3. TEM images, HRTEM images, and the corresponding FFT patterns of t-LaVO4 nanocrystals prepared under different pH conditions: (a) pH = 3.5; (b) pH = 4.0; (c) pH = 5.5. Insets: schematic drawing of the morphology of t-LaVO4 nanocrystals.

molecules and La(2) ions (denoted as La(2)−OH2,a) were 2.65 Å. The water molecules adsorbed on the La(1) ions showed a trend to bond with the 4-fold coordinated La(2) ions for its stronger coordination ability, which resulted in the bond lengths between the water molecules and La(2) ions (denoted as La(2)−OH2,b) to be 2.73 Å. The O(1) ions underwent an outward relaxation of 0.19−0.27 Å, while the O(2) ions exhibited a stronger outward relaxation of 0.26−0.38 Å. The O−H bond lengths were found to be about 1.00 Å. 3.2.3. Highly Acidic Conditions. To represent ‘‘highly acidic conditions’’, three-quarters of the oxygen sites were terminated with hydrogen ions, and the other oxygen sites were left vacant. Figure 6 shows the surface geometry of the (100), (101), and (001) surfaces after relaxation. The (100) surface underwent a similar relaxation to the most-acidic conditions described above, except for the vacant oxygen ion maintained its position. The La−OH2 bond lengths were 2.72−2.76 Å, and the O−H bond lengths were 0.98 Å. It is should be noted that the formation of the hydrogen bond occurs between the hydrogen atom of the water molecule and the unpassivated oxygen ion on the surface. The length of the hydrogen bond was about 1.59 Å. For the (101) surface, the La ions capped with water and the O

an inward relaxation of about 0.13 Å, while the O(2) ions exhibited a stronger inward relaxation of 0.17 Å. 3.2.2. Most-Acidic Conditions. To represent “most-acidic conditions”, all the oxygen sites were terminated with hydrogen ions. Figure 5 shows the surface geometry of the (100), (101), and (001) surfaces after relaxation. For the (100) surface, the La ions capped with water molecules exhibited an inward relaxation of about 0.16 Å, while the H-terminated oxygen ions underwent an outward relaxation of about 0.18 Å. The bond lengths between oxygen of the water molecules and the surface La ions (denoted as La−OH2) were 2.88−2.93 Å, and the bond lengths between hydrogen and the surface oxygen ions (denoted as O−H) bond lengths were 0.98−0.99 Å. In the case of the (101) surface, the La ions underwent an inward displacement of 0.21 Å that was less pronounced than the clean surface. The O(1) and O(3) ions exhibited an outward relaxation of 0.18 and 0.22 Å, respectively, whereas the O(2) ions underwent a more stronger outward displacement of 0.43 Å. The La−OH2 bond lengths were 2.64 Å, and the O−H bond lengths were 0.99−1.04 Å. For the (001) surface, the La ions exhibited an inward relaxation very similar to the clean surface described above. The bond lengths between the water 5045



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Figure 4. Top and side views of the relaxed clean surfaces: (a, b) for (100) surface; (c, d) for (101) surface; and (e, f) for (001) surface. La atoms are colored blue, V atoms are colored gray, and O atoms are colored red.

Figure 6. Top and side views of the relaxed surfaces with adsorbates chosen to represent highly acidic conditions: (a, b) for the (100) surface; (c, d) for the (101) surface; and (e, f) for the (001) surface.

displacement of 0.12 Å, and the La(2) ions underwent an inward relaxation of 0.13 Å. The La(2)−OH2,a bond lengths were 2.62 Å, shorter than the (100) surface. The water molecules adsorbed on the La(1) ions bonded with the La(2) ions again, and the La(2)−OH2,b bond lengths were 2.68 Å. The O(1) ions all capped with hydrogen exhibited a similar outward relaxation to the most-acidic conditions. The O(2) ions capped with hydrogen exhibited an outward relaxation of 0.12−0.17 Å, whereas the vacant O(2) ions underwent an inward relaxation of about 0.13 Å. The O−H bond lengths were found to be about 1.00 Å. 3.2.4. Moderately Acidic Conditions. To represent “moderately acidic conditions’’, half of the oxygen sites were terminated with hydrogen ions, and the other oxygen sites were left vacant. Figure 7 shows the surface geometry of the (100), (101), and (001) surfaces after relaxation. For the (100) surface, one of the La ions exhibited an inward relaxation of 0.08 Å, and the other La ions exhibited a stronger inward relaxation of 0.15 Å. The H-terminated oxygen ions underwent an outward relaxation of about 0.17 Å, while the vacant oxygen ion exhibited a small inward relaxation of about 0.03 Å. The La−OH2 bond lengths were 2.68−2.90 Å, and the O−H bond lengths were 0.98−0.99 Å. The lengths of the hydrogen bonds were about 1.72−1.84 Å. The relaxation of the (101) surface was very similar to the highly acidic conditions and so were the lengths of the La−OH2 bonds and the O−H bonds. In the case of the (001) surface, the La(1) ions exhibited an inward displacement of 0.14 Å, and the La(2) ions underwent an inward relaxation of 0.19 Å. The La(2)−OH2,a bond lengths were 2.56−

Figure 5. Top and side views of the relaxed surfaces with adsorbates chosen to represent most-acidic conditions: (a, b) for the (100) surface; (c, d) for the (101) surface; and (e, f) for the (001) surface.

ions capped with hydrogen underwent a relaxation akin to the most-acidic conditions, whereas the vacant O ions relaxed slightly. The lengths of the La−OH2 bond and the O−H bond were almost identical as with the most-acidic conditions. In the case of the (001) surface, the La(1) ions exhibited an inward 5046



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Figure 7. Top and side views of the relaxed surfaces with adsorbates chosen to represent moderately acidic conditions: (a, b) for the (100) surface; (c, d) for the (101) surface; and (e, f) for the (001) surface.

Figure 8. Top and side views of the relaxed surfaces with adsorbates chosen to represent weakly acidic conditions: (a, b) for the (100) surface; (c, d) for the (101) surface; and (e, f) for the (001) surface.

2.59 Å, and the La(2)−OH2,b bond lengths were 2.67 Å. The O(1) ions all capped with hydrogen underwent an outward relaxation of about 0.22−0.36 Å. The vacant O(2) ions exhibited an inward relaxation of about 0.14 Å. The O−H bond lengths were 1.00 Å. The formation of the hydrogen bond occurs between the hydrogen atom of the water molecule and the unpassivated O(2) ion on the surface. The lengths of the hydrogen bonds were 1.57−1.58 Å. 3.2.5. Weakly Acidic Conditions. To represent ‘‘weakly acidic conditions’’, one-quarter of the oxygen sites were terminated with hydrogen ions, and the other oxygen sites were left vacant. Figure 8 shows the surface geometry of the (100), (101), and (001) surfaces after relaxation. For the (100) surface, half of the La ions exhibited an inward relaxation of 0.08 Å, and the other La ions exhibited a stronger inward relaxation of 0.15 Å. The H-terminated oxygen ion underwent an outward relaxation of 0.16 Å, while the vacant oxygen ions exhibited a small inward relaxation of about 0.01 Å. The La− OH2 bond lengths were 2.64−2.80 Å, and the O−H bond length was 0.99 Å. The lengths of the hydrogen bonds were about 1.71−1.81 Å. In the case of the (101) surface, the La ions underwent a similar relaxation to the other conditions described above. The H-terminated O(1), O(2), and O(3) ions exhibited an outward relaxation of 0.16, 0.19, and 0.32 Å, respectively, whereas the left vacant O ions was found to relax slightly. The La−OH2 bond lengths were 2.66−2.79 Å, and the O−H bond lengths were 0.99−1.00 Å. For the (001) surface, the relaxation of the La ions was similar to the moderately acidic conditions. The La(2)−OH2,a bond lengths were 2.62− 2.64 Å, and the La(2)−OH2,b bond lengths were 2.64 Å. The O(1) ions capped with hydrogen underwent an outward

relaxation of about 0.14 Å, while the vacant O(1) ions exhibited an inward relaxation of 0.07 Å and the vacant O(2) ions of 0.13 Å. The O−H bond lengths were 0.98 Å. Except for the hydrogen bonds formed by the hydrogen atom of the water molecule and the unpassivated O(2) ion, the unpassivated O(1) ion on the surface formed hydrogen bonds with the hydrogen atom of the water molecule in the same way. The lengths of the hydrogen bonds were 1.67−1.71 Å. 3.3. Surface Energies and Equilibrium Morphology. The surface energies γ for the t-LaVO4 surfaces under different passivated conditions described in Sections 3.2 were calculated. The value of the surface energy γ was calculated using the following expression: G 1 surface = (EN − NE bulk − Nadμad ) (1) A 2A where G is the surfaces free energy, A is the surface area, Esurface N is the total energy of the slab, N is the number of t-LaVO4 pairs in the slab, Ebulk is the total energy per LaVO4 pair of bulk tLaVO4, Nad is the number of adsorbates pairs, and μad is the chemical potential of the adsorbates. The factor 2 originates from the presence of two equivalent (top and bottom) surfaces. The chemical potential μad is computed from the chemical potentials of water and hydrogen: μad = n H2OμH O + nHμH (2) γrelaxed =

2

μ H O = E H 2O + 2

5047

hνH2O 2

⎡ ⎛ PV ⎞⎤ + kBT ⎢In⎜ ⎟⎥ ⎢⎣ ⎝ kBT ⎠⎥⎦

(3)



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Table 1. Surface Energies γi (and Surface Tension σi) of Clean and Passivated t-LaVO4 Surfaces (in J/m2) for Each Type of Surface Chemistry (100) (101) (001)

μH =

clean

most acidic

highly acidic

moderately acidic

weakly acidic

1.42(3.31) 1.56(−1.80) 2.61(1.78)

1.47(−0.18) 2.48(−7.03) 2.51(−4.89)

1.27(0.25) 2.08(−6.46) 2.32(−3.32)

1.15(0.65) 1.72(−4.54) 2.19(−1.60)

1.04(1.02) 1.36(−6.08) 1.97(−0.62)

⎡ ⎛ PV ⎞⎤ hνH2 1 (E H 2 + + kBT ⎢In⎜ ⎟ ⎥) ⎢⎣ ⎝ kBT ⎠⎥⎦ 2 2

(4)

where kB is Boltzmann’s constant, T and P are the temperature and pressure, respectively, ν is the total of the vibrational frequencies in the reservoir,and V is the quantum volume:32

⎛ h2 ⎞3/2 V=⎜ ⎟ ⎝ 2πmkBT ⎠

(5)

Experimental values were used for ν, and the chemical potentials were calculated at ambient temperature T = 298.15 K and ambient pressure P = 101.33 kPa. EH2O and EH2 were the energies of a free water or H2 molecule in the gas phase separately. The calculated values γ of surface energies for each type of surface chemistry were given in Table 1. The thermodynamic sequence (100) < (101) < (001) for the clean surface was the same as the passivated conditions. With the fraction of hydrogen in the adsorbates decreased, the surface energies of the (100) and (101) surfaces increased first and then decreased, while the (001) surface continued to decrease. The equilibrium shapes of the nanocrystals can be obtained from the values of surface energies listed in Table 1 according to the Wulff construction. Figure 9 shows the defined aspect

Figure 10. Predicted shape of t-LaVO4 nanorods based on the surface energies under the conditions of (a) most-acidic, (b) highly acidic, (c) moderately acidic, and (d) weakly acidic.

Table 2. Relative Contribution (%) of Each Surface for the Shape of t-LaVO4 Nanocrystals (100) (101) (001)

most acidic

highly acidic

moderately acidic

weakly acidic

69.38 21.12 9.50

67.08 28.77 4.15

62.64 37.10 0.26

56.46 43.54 

(001) surface to the total surface area was reduced to 4.15%. For the moderately acidic conditions, the aspect ratio of the nanorods was up to 1.94. Moreover, the nanorod exhibited sharper tips for the (001) surface, its occupation of the total surface area was reduced down only to 0.26%, and there was more contribution of the (101) surface. For the weakly acidic conditions, the (001) surface was vanished in the shape, and 43.54% of the crystal shape was occupied by (101) surface. The aspect ratio of the nanorods was down to 1.71. It is clear to see that the surface chemistry has a fairly obvious effect on the shape and exposed facets of the t-LaVO4 nanocrystals. To determine if the equilibrium shape change with size, we used a modified Wulff construction model proposed by Barnard33 to optimize the nanoparticle shapes as a function of size, which considered the effects of surface tension. In this model, the total free energy G is described as follows:

Figure 9. Aspect ratio of the t-LaVO4 nanocrystal defined by the lengths labeled A and B.

ratio of the t-LaVO4 nanocrystal. The height of this rod is labeled A, and the width of the rod is labeled B. The morphology of the nanocrystal is defined by the size of A with respect to B. By using the results of surface energies given in Table 1, the predicted equilibrium shapes of the nanocrystals for each type of surface chemistry are shown in Figure 10. Table 2 shows the fraction area of each surface contributed to the shape of crystals. Under the most-acidic conditions, the nanoparticles had an aspect ratio of about 1.73. About 69.38% of the crystal shape was occupied by the (100) surface and 21.12% of the crystal shape was occupied by the (101) surface. The (001) surface had a contribution of 9.50% as basal facet of the nanoparticles. When the fraction of hydrogen in the adsorbates decreased, the contribution of the (101) surface to the total surface area was increased while that of the (100) and (001) surfaces was decreased. In the highly acidic conditions, the nanorods became elongated, and the contribution of the

G = ΔGf0 +

2 ∑i fi σi P ⎞ M⎛ ⎜⎜1 − + ex ⎟⎟[q ∑ fi γi] ρ⎝ B0 R B0 ⎠ i

(6)

where γi is the surface energy for surface i, weighted by the factors f i, (∑if i = 1), M is the molar mass, ρ is the density, q is the surface-to-volume ratio, σi is the surface stresses, and Pex is external pressure that resulted in the volume expansion expressed by the Laplace−Young equation.33a In all cases, atmospheric external pressure was supposed. The value of the surface tension σ was obtained using the expression

σ= 5048

∂G ΔG ≈ ∂A ΔA

(7)



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4. CONCLUSIONS In summary, we have revealed in the present work the mechanism of morphology transformation of t-LaVO4 nanocrystals controlled by surface chemistry using experiments and theoretical calculations methods. The tetragonal phase t-LaVO4 nanocrystals were synthesized via the hydrothermal method. We found that the pH value of the growth solution had a very important effect on the aspect ratios and exposed facets of tLaVO4 nanorods. With the pH increased, the aspect ratio of the nanocrystals first increased then decreased, and the shape of the tip of the nanorods changed from flat to sharp for the growing fractions of (101) facets. First-principles calculations were used to examine the relaxed surface structures and to calculate surface energies and surface tensions of all surfaces under different passivated conditions. The surface energies of the (100) and (101) surfaces increased first and then decreased, while the (001) surface continued to decrease with the fraction of hydrogen in the adsorbates decreased. The predicted equilibrium shapes of t-LaVO4 nanocrystals for each type of surface chemistry were obtained according to the Wulff construction. Our results showed that the aspect ratio and the exposed facets of the nanocrystals changed with the acidity of the surface conditions varied, which was in good agreement with our experimental findings. The change of relative stability among the (100), (101), and (001) surfaces resulted in morphology difference of t-LaVO4 nanocrystals. The morphological transformation of t-LaVO4 nanocrystals revealed by this model was consistent with the Wulff construction. Our work showed that starting by surface thermodynamics is a helpful approach to predict and assess the morphology transformation of the nanocrystals. We expect that our work is beneficial to get a profound understanding of how to achieve shape-controlled nanocrystal synthesis.

The values of surface tensions for each type of surface chemistry were listed in Table 1. For the (100) surface, the surface tension varied from negative to positive when the acidity of the surfaces conditions was decreased. The surface tension σ of the (101) and (001) surfaces was found to remain negative, indicating a tendency for the surfaces to expand. By using the model above, the aspect ratio A/B of t-LaVO4 nanocrystals was optimized as a function of size for each type of surface chemistry with a side length B of 5−100 nm (see Figure 11). In both cases, the change of the aspect ratio with size is

Figure 11. Optimized aspect ratio A/B of t-LaVO4 nanocrystals as a function of size for each type of surface chemistry, with a side length B of 5−100 nm.

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very small, and as the crystal increased in size, the shapes converged to the Wulff construction. The aspect ratio of the nanocrystals was increased first and then decreased when the acidity of the surface conditions was decreased, which was consistent with the Wulff construction. This agrees with our experimental findings. The aspect ratio and exposed facets of t-LaVO4 nanocrystals largely depends on the pH value of the growth solution. With the acidity of the surface conditions decreased, the aspect ratio of the nanocrystals first increases then decreases, the contribution of the (101) planes to the shape increased and that of the (001) planes decreased, which is consistent with the results from XRD and HRTEM. Surface chemistry has an important effect on the resulting nanocrystal shape. The H+ ions with different concentrations in the solution are selectively adsorbed on the nanocrystal surfaces, making the surface energies of the (100), (101), and (001) surfaces differing distinctly. The change of relative stability among these surfaces results in the observed morphology difference of t-LaVO4 nanocrystals. In this study, some other factors influencing the growth of nanocrystals in our experiments, such as the temperature, pressure, and the kinetic factors are not taken into account in our calculations. Our work starts by thermodynamics, especially the surface thermodynamics to investigate the mechanism of morphology transformation of nanocrystals. Surface thermodynamics has an important role in controlling the final morphology and exposed facets of the nanocrystals, which provides a useful approach to predict and evaluate morphology transformation of the nanocrystals.

AUTHOR INFORMATION

Corresponding Author

*Phone: 86-531-88366330; fax: 86-531-88365174; e-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (grant nos. 21173131, 51172127, and 91022034), Excellent Youth Foundation of Shandong Scientific Committee (grant no. JQ201015), Youth Scientist (Doctoral) Foundation of Shandong Province of China (grant no. BS2009CL038), the Independent Innovation Foundation of Shandong University (grant no. 2012TS212), and the Graduate Innovation Foundation of Shandong University, GIFSDU, (grant no. yyx10033).

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Mechanism of Morphology Transformation of Tetragonal Phase

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