First principle investigation of the exposed surfaces and morphology of β-ZnMoO 4

Crystal shape is a critical determinant of the physical and chemical properties of crystalline materials; hence, it is the challenge of controlling the crystal morphology in a wide range of scienti ﬁ c and technological applications. The morphology is related to the geometry of their exposed surfaces, which can be described by their surface energies. The surface properties of β -ZnMoO 4 have not yet been well explored, either experimentally or theoretically. Thus, the ﬁ rst-principle calculation at the density functional theory level was carried out for di ﬀ erent low-index surfaces of β -ZnMoO 4 , speci ﬁ cally (001), (010), (110), (011), (101), and (111), and the surface energy values (E surf ) were reported. The surface stability was found to be controlled by the undercoordinated [MoO n . .. yV xO ] and [ZnO n .. . yV xO ] (n = 4 and 5; y = 1 and 2) clusters, i.e., their local coordination of Mo and Zn cations at the exposed surfaces, respectively, with the (111) surface being the most stable. A complete map of investigated β -ZnMoO 4 morphologies was obtained using the Wul ﬀ construction and changing the values of the calculated energy surfaces. The ﬁ nal geometries from this map were compared with ﬁ eld emission-scanning electron microscopy images showing excellent agreement, prevising rectangular and hexagonal plates. Our ﬁ ndings will promote the use of facet engineering and might provide strategies to produce β -ZnMoO 4 -based materials for achieving morphology-dependent technological applications.


I. INTRODUCTION
][9][10][11][12][13][14] Studying surface properties and morphologydependent properties can help to better control and achieve the functionality of specific material surfaces.To this end, it is mandatory to study their exposed surfaces and to know how the atoms located on the exposed surfaces of a crystal are coordinated to their nearest neighbors and, thus, the landscape of the surface electronic structure. 8,15,16n general, the properties and functions of any crystal are highly dependent on its surface composition, geometry, morphology and electronic structures, and the morphology results from the relative stability of the exposed surfaces.The equilibrium morphology of a crystal and its evolution can be predicted by the classical Wulff construction, and its generalizations have been well-recognized procedures for a long time [17][18][19][20][21][22] to obtain the morphology of materials [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and require surface energies to be known. 23,24][27][28][29] First-principle calculations are well-suited to obtain the values of the surface energies for different exposed surfaces. 300][41][42][43][44][45] Better understanding and control of the exposed surfaces would bring innovative capabilities to design adequate structures with enhanced applications.7][48][49][50][51][52] Nevertheless, theoretical frameworks providing fresh insight into the structure and stability of surfaces are vital steps toward realizing the true potential of complex materials and thin films.][66][67][68][69][70][71] The multifunctional properties of ZnMoO 4 complex ternary oxides are influenced by the surface structure.Therefore, their surface controlled synthesis is not only a rational route to study the relationship between the morphology and the surface structuredependent properties but also a feasible approach for developing highly active materials such as catalysts and sensors.However, the importance of exposed surfaces, morphology, and their evolution has not been systematically taken into account to the best of our knowledge.Herein, first-principle calculations are carried out to explore the morphology of β-ZnMoO 4 surface properties, such as atomic configurations and stabilities, broken surface bonds, their cleavage nature, and the degree of surface relaxation for six lowindex (001), (010), (110), (011), (101), and (111) surfaces.We have provided a further detailed analysis of the relationship between the surface structures and their stabilities.Finally, the equilibrium shape and a complete map of available morphologies of the β-ZnMoO 4 crystal were drawn using the Wulff construction.Our findings provide useful insights into the basic understanding of the anisotropic surface properties of β-ZnMoO 4 and represent an important step toward rationalizing their morphology control.
The monoclinic crystalline structure of bulk β-ZnMoO 4 , as depicted in Fig. 1, was built based on experimental results (Rietveld refinement) 70 and fully relaxed (lattice parameters and atomic positions).][83] Different surfaces were modeled in the second step by using unreconstructed (truncated bulk) slab models with calculated equilibrium geometries.The (001), (010), ( 110), (011), (101), and (111) surfaces of β-ZnMoO 4 were simulated considering symmetrical slabs (with respect to the mirror plane).All surfaces were terminated with O planes, and the resulting slab models after the corresponding optimization process and thickness convergence tests consisted of four molecular units containing 24 atoms, as shown in Fig. 1.
The E surf was calculated by using the following equation: 32 In this case, n is the number of surface molecular units, E bulk is the total energy of the bulk, E slab is the total energy of the surface slab per molecular unit, and A is the surface area.The equilibrium shape of a crystal can be calculated by utilizing Wulff constructions that minimize the total surface free energy at a fixed volume, providing a simple relationship between the E surf of a (hkl) plane and its distance from the crystallite center in the normal direction. 84The Visualization for Electronic and Structural Analysis (VESTA) program was used to obtain morphologies of the ZnMoO 4 crystals. 85

III. RESULTS AND DISCUSSIONS
A. Crystal structure, energy surface, and electronic properties An analysis of the results reported in Table I shows good agreement with both experimental and theoretical studies available in the literature.In addition, the obtained results confirm that both octahedral From now, we briefly analyze the geometrical distribution of the (001), (010), ( 110), ( 011), (101), and (111) surfaces of β-ZnMoO 4 (Fig. 1).The cutting process connected to the surface structures can generate different kinds of undercoordinated centers from the existence of dangling bonds; an inherent process associated with the symmetry-adapted cutting strategy that can be associated with the presence of neutral oxygen vacancies (V x O ) along the exposed surfaces.In this case, the exposed local geometries were notably different compared to the bulk (Fig. 1).
The atomic arrangement of the (001) and ( 111

Journal of Applied Physics
broken bonding density (D b ) index proposed by Gao et al. 87 as the relation between the number of bonds broken per surface area as calculated from Eq. ( 2), where N b is the number of broken bonds per unit cell area on a particular surface, and A is the surface unit cell area, The calculated values of E surf for the (001), ( 010), ( 110), ( 011), (101), and (111) surfaces of β-ZnMoO 4 and its D b are summarized in Table II.
The calculated E surf values reveal that the stability order is as follows: (111) < (010) < (110) < (011) < (001) < (101).In addition, the D b values are intrinsically connected to the E surf resulting in overall stability in comparison to the surfaces with reduced density of defects.
The electronic properties of bulk and surfaces of β-ZnMoO 4 are analyzed by calculating the density of states (DOS) and band structure pictures, as presented in Fig. 2.
The analysis of the main components of the atomic orbitals (AOs) for selected bands shows that the bulk β-ZnMoO 4 [Fig.2(a)] valence band (VB) mostly consists of the 2p orbitals of the O anions hybridized with the 3d and 4d valence orbitals of Zn and Mo cations, respectively.On the other hand, the conduction band (CB) shows the dominant composition of Mo valence states hybridized with oxygen orbitals.This profile indicates that the vertical excitation associated with the electronic transfer of electrons from valence band maximum (VBM) to conduction band minimum (CBM) is associated with the electron transfer from O (2p) states to empty orbital of Mo through the Mo-O bond path.Looking at the band structure, the vertical excitation was calculated as direct bandgap energy of 3.58 eV between X-X points, which is in agreement with previous experimental (3.17 eV) and theoretical (3.22 eV) results. 70he electronic profiles of the (001), (010), (110), (011), (101), and (111) surfaces are shown in Figs.2(b)-2(g).In this case, the calculated bandgap for each surface is presented in Table II.It was observed that the calculated bandgap for β-ZnMoO 4 surfaces is higher than the bulk value in all cases, which can be associated with the presence of structural defects along the surfaces that affect both the CBM and VBM resulting in increased excitation energies.

B. Crystal morphology
The precise control of crystal morphology is an effective tool to tailor material properties.In the case of β-ZnMoO 4 , a series of experimental works have been developed in order to elucidate the shape-dependent properties of the monoclinic wolframite material, especially in the photoluminescence and photocatalysis fields. 64,67,69,71,88However, the reasons behind the shape-dependent properties remain unclear, with the combination of theory and simulation being an alternative tool in this research area that can guide the efficient synthesis of outstanding materials.The Wulff construction was employed in this study in order to rationalize the crystal morphologies, which is related to the relative stability of the exposed surfaces.The complete set of morphologies for the β-ZnMoO 4 structure has been depicted in Fig. 3.The morphology evolution can be obtained by changing the ratio between the values of E surf for each surface, where the rate of each individual surface change is dependent on different E surf values.
The equilibrium morphology of β-ZnMoO 4 displays a cornertruncated hexagonal shape that predominantly exposed the (110),   010), (011), and (001) surfaces.Using the Wulff construction renders that the (110), ( 111), ( 010), (011), and (001) facets account for 30.0%,37.1%, 10.2%, 12.8%, and 10.0%, respectively.The two low-energy ( 110) and (111) surfaces dominate in the Wulff shape and make up almost 70% of the total crystal shape area.In addition, it was observed that different shapes were obtained by tuning E surf for β-ZnMoO 4 , such as truncated and nontruncated rectangular, hexagonal, octahedral, and rhombic shapes matching the experimental morphologies obtained by examining the FE-SEM images. 64,67,69,71,88These experimentally observed morphologies should be close to the equilibrium shapes under the experimental conditions.From a thermodynamic point of view, the morphology is controlled by relative stability of different surfaces, and the surface with the lowest E surf value is the main component of the corresponding morphology.Adjusting the ratio of the E surf values of the three surfaces enables obtaining different morphologies, and the corresponding reaction paths can be isolated and studied independently.This procedure can be considered an effective tool to investigate the morphology transformation and crystal growth mechanisms from a thermodynamic and kinetic point of view 55,89 and can provide useful insights for fabricating ZnMoO 4 materials with suitable morphologies for a wide variety of specific devices and purposes.
In this study, we were able to calculate the energy profiles of the paths connecting different morphologies from the values of the polyhedron energy (E pol ) by a function of the form as follows: 89,90 where C i is the percentage contribution of the surface area to the total surface area of the polyhedron, C i = A i /A polyhedron and E i surf is the surface energy of the corresponding surface.The energy profiles were calculated by decreasing and/or increasing the E surf values of a given surface of the polyhedron.
Two pathways connecting the ideal morphology with those displaying excellent agreement with the experimental morphologies were calculated.Polyhedron energy (E pol ) calculated from Eq. (3) for the selected morphology of β-ZnMoO 4 is summarized in Table III.

Journal of Applied Physics
The first one, reaction path (A), considers the increase of the E surf value for (010) and a posterior decrease of E surf for (001), which induces forming a rectangular (C) shape that predominantly exposes the (001) surface plane, and is in agreement with experimental findings.On the other hand, the reaction path (B) moves from the ideal path with an increase in the E surf value for (001), and a posterior decrease of E surf for (010) generates a hexagonal plate (E) that predominantly exposes the (010) surface plane.It is important to point out that both theoretical morphologies labeled C and E herein correspond to a minimum in the reaction coordinate diagram as depicted in Fig. 4, indicating that both reaction paths are thermodynamically favorable, as proven by the experimental reproduction of such morphologies.
From the experimental point of view, the authors state that distinct surfactants changed the shape and average size of β-ZnMoO 4 microcrystals.In addition, they point out that the chemical nature of the surfactants (cationic, anionic, and nonionic) can interact differently with the Zn 2+ and [MoO 4 ] 2− ions in solution, influencing the formation and growth process of the microcrystals. 59In looking at the geometrical characteristics of both (010) and (001) surfaces, the distinct exposed clusters can interact with the surfactants to generate different crystal morphologies.For example, the (010) surface shows a smaller broken bond density (Table I) in comparison to the (001) surface, thus suggesting a more negative charge character for the (010) surface due to the presence of a high number of saturated bonds along the exposed plane.On the other hand, it is expected that the (001) surface shows a more positive charge concentration due to the increased unsaturation degree observed for this plane.Those facts can be directly compared to the interaction between cationic and anionic surfactants that results in the obtained shapes.
Therefore, the obtained morphological map is a fundamental tool to understand the morphological transformation associated with β-ZnMoO 4 , with the additional morphologies proposed in this study constituting alternative possibilities that can guide experimental studies toward enhanced technological properties.The next step will be to use the present results to establish correlation between the morphology, properties, and applications, such as those which our group have developed for Co 3 O 4 , 33 MnTiO 3 , 91 CaZrO 3 :Eu 3+ , 92 ZnO, 93 Ag 3 PO 4 , 94 α-Ag 2 WO 4 , 89,95 PbMoO 4 , 60 and ZnWO 4 . 96,97.CONCLUSIONS Motivated by the interest in the β-ZnMoO 4 material, its exposed surface and morphology are studied in detail by the first-principle calculations at the density functional theory level.The values of the energy surfaces and their atomic and electronic arrangement of different low-index surfaces (001), (010), (110), (011), (101), and (111) of β-ZnMoO 4 are calculated.Analysis of the surface structures showed that the surface energies and electronic properties were associated with the presence of undercoordinated [MoO n . . .yV x O ] and [ZnO n . . .yV x O ] (n = 4 and 5; y = 1 and 2) clusters.A complete map of the available morphologies was obtained based on these results and by using the Wulff construction, and it was revealed that the theoretical morphologies match with previously reported experimental morphologies when the surface energy values of the (010) and (001) surfaces were 0.2 J/m².The present findings will help us to further understand and control the available morphologies of β-ZnMoO 4 crystals and suggest potential strategies to indicate the morphology transformation.
First, let us analyze the structural properties of bulk and surfaces of β-ZnMoO 4 based on the constituent clusters and existence of structural defects.The β-ZnMoO 4 crystallizes in a wolframitetype monoclinic structure, space group P2/c and point group symmetry C 4 2h .In the monoclinic structure, the Zn and Mo cations are sixfold coordinated by oxygen anions to form the distorted octahedral [ZnO 6 ]/[MoO 6 ] clusters, as presented in Fig. 1.The calculated lattice parameters and M-O (M = Zn, Mo) distances are presented in Table I and compared with previous experimental and theoretical results.
[ZnO 6 ] and [MoO 6 ] clusters are distorted, showing three different values of M-O bond lengths, with the Mo-O always being shorter than Zn-O.

TABLE I .
Lattice parameters and M-O (M = Zn, Mo) bond distances for β-ZnMoO 4 .The available experimental and theoretical results were inserted for comparative purposes.

TABLE III .
Values of E surf (J m −2 ), contribution of the surface area by the total area (C i , %), and the polyhedron energy (E pol , J m −2 ) calculated for selected morphologies of β-ZnMoO 4 .Schematic representation of the energy profile for different β-ZnMoO 4 morphologies.Intermediate morphologies were obtained by a decrease/increase in E surf values involved in the process.The experimental FE-SEM images from Ref. 69 (inset) are included for comparison.Reprinted from L. S. Cavalcante, J. C. Sczancoski, M. Siu Li, E. Longo, and J. A. Varela, Colloids Surf.A 396, 346-351.Copyright (2012) with permission from Elsevier.The experimental FE-SEM images (inset) are included for comparison.