General trends in surface stability and oxygen adsorption behavior of transition metal diborides (TMB2)

Accepted Manuscript Title: General trends in surface stability and oxygen adsorption behavior of transition metal diborides (TMB2 ) Authors: Wei Sun, Fuzhi Dai, Huimin Xiang, Jiachen Liu, Yanchun Zhou PII: DOI: Reference:

S1005-0302(18)30269-X https://doi.org/10.1016/j.jmst.2018.10.012 JMST 1379

To appear in: Received date: Revised date: Accepted date:

6-8-2018 2-10-2018 3-10-2018

Please cite this article as: Sun W, Dai F, Xiang H, Liu J, Zhou Y, General trends in surface stability and oxygen adsorption behavior of transition metal diborides (TMB2 ), Journal of Materials Science and amp; Technology (2018), https://doi.org/10.1016/j.jmst.2018.10.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

●Research Article

General trends in surface stability and oxygen adsorption behavior of transition metal diborides (TMB2)

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Wei Sun1,2, Fuzhi Dai1, Huimin Xiang1, Jiachen Liu2, Yanchun Zhou1,* Aerospace Research Institute of Materials & Processing Technology, Beijing 100076,

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China

School of Materials Science and Engineering, Tianjin University, Tianjin 300072,

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China

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*Corresponding author. Tel.: +86 10 68382478; Fax: +86 10 68383237; E-mail

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address: [email protected], [email protected] (Y.C. Zhou).

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[Received 6 August 2017; revised 2 October 2017; accepted 30 October 2017]

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Abstract The potential applications of transition metal diborides (TMB2) in extreme environments are particularly attractive but still blocked by some intrinsic properties such as poor resistances to thermal shock and oxidation. Since surface plays a key

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role during grain growth and oxygen adsorption, an insight into the surface properties of TMB2 is essential for understanding the materials performance and accelerating the

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development of ultra-high temperature ceramics. By employing two-region modeling method, the stability and oxygen adsorption behavior of TMB2 surfaces were

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investigated by first-principles calculations based on density functional theory. The

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effects of valance electron concentration on the surface stability and oxygen

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adsorption were studied and the general trends were summarized. After analyzing the

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anisotropy in surface stability and oxygen adsorption, the observed grain morphology

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of TMB2 were well explained, and it was also predicted that YB2, HfB2 and TaB2 may

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have better initial oxidation resistance than ZrB2.

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Key words: Transition metal diborides, First-principles calculation, Surface energy,

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Grain morphology, Oxidation resistance.

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1. Introduction Transition metal diborides (TMB2) based ultrahigh temperature ceramics have been regarded as candidates of materials for nose tips and sharp leading edges of hypersonic vehicles and hot structure components of scramjet engine, due to the

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combination of properties including high melting point, high hardness, high strength, high thermal conductivity and absence of phase changes in the solid state [1,2].

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Among them, ZrB2 and TiB2 based materials are intensively investigated, however, some intrinsic properties, such as brittleness, poor thermal shock resistance, poor oxidation resistance and easily microcraking, are still barriers for their extensive

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applications [3-5]. Besides tailoring the properties of ZrB2 and TiB2, researchers also

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tried to dig out more satisfactory performances from other TMB2. It was found that

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investigation on the properties of a series of TMB2 is very useful in scanning the properties of intrigued UHTCs and accelerates the materials development and

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application process [6]. Ivanovskii presented various examples of successful use of ab

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initio approaches for examination of elastic properties of metal borides and their relations to electronic, cohesive and bonding characteristics of these materials [7].

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Zhou et al. investigated the mechanical properties of TMB2 bulk materials from a chemical bonding point of view, and predicted that YB2 and MnB2 have good thermal

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shock resistance while MnB2, MoB2 and WB2 are more ductile or damage tolerant [8]. Xu et al. also suggested that 4d- and 5d-TMB2 compounds are good candidates for high-temperature structural applications through studying the stability, electronic structure and elastic constants of the early-transition-metal diborides [9]. It is well believed that, from a microstructure perspective, grain size and morphology have 3

strong effects on the mechanical properties and oxidation resistance of materials. Since surfaces play key roles during the grain growth and oxygen adsorption, an insight of the intrinsic surface properties is very helpful in understanding the performance of TMB2. However, experimental investigations on TMB2 surfaces are

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blocked by the development levels of preparation techniques and test methods. Opportunely, theoretical prediction previews a promising way for the surface study.

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Previous works mainly focused on the (0001) surfaces of TMB2. Han et al. revealed the different relaxations and charge accumulations within the top three atomic layers

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for both Ti- and B-terminated (0001) surfaces of TiB2 [10]. Suehara et al. predicted

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the stable structures of (0001) surfaces in NbB2 and ZrB2 based on surface energy

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calculations [11]. Gamallo et al. simulated the adsorption of atomic and molecular

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oxygen on (0001) surfaces of ZrB2, and also predicted the minimum energy path for

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the molecular adsorption [12]. However, the other surfaces of TMB2 were seldom mentioned, the systematic investigation on the surface properties of TMB2 is still

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absent, and the general trends in surface stability and oxygen adsorption behavior of

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TMB2 are also not clear.

To make up this deficiency, the surface stability and oxygen adsorption behavior

of TMB2 (TM = Sc, Y, Ti, Zr, Hf, V, Nb and Ta) are investigated by first-principles

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calculations in this work. Due to the analogous crystal structure, these TMB2 have similar surface constructions. By employing two-region modeling method, six types of surfaces, including (0001)-TM and (0001)-B (TM- and B-terminated (0001) surfaces), (11 2¯ 0), (10 1¯ 0)-TM (TM-terminated (10 1¯ 0) surface), (10 1¯ 0)-B(TM) 4

(B-terminated (101¯0) surface with TM as the second layer) and (101¯0)-B(B) ((101¯0) surface terminated by two layers of B) surfaces, are simulated and the surface energies and oxygen adsorption energies are accurately calculated. The effects of valance electron concentration (VEC) on the surface stability and oxygen adsorption

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are investigated and general trends are given. By analyzing the anisotropy in surface stability and oxygen adsorption, the grain morphology and initial oxidation resistance

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are also predicted. 2. Calculation methods

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First-principles calculations are carried out based on the density functional

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theory using the Cambridge Serial Total Energy Package (CASTEP) code [13],

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wherein the Vanderbilt-type ultrasoft pseudopotentials [14] are adopted to represent

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the interactions between the ionic cores and the valence electrons. The

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exchange-correlation energy is treated under generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) scheme [15]. The plane-wave basis set

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cut-off energy is fixed at 450 eV for all calculations. The special point sampling

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integration over the Brillouin zone is employed by using the Monkhorst Pack method [16], and the k-points separations are set as 0.04 Å-1. To obtain the accurate surface properties,

the

surface

models

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Broyden-Fletcher-Goldfarb-Shanno

are

(BFGS)

optimized minimization

by scheme

using [17].

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tolerances for geometry optimization are difference on total energy within 5  10-6 eV/atom, maximum ionic Hellmann-Feynman forces within 0.01 eV/Å, maximum stress within 0.02 GPa and maximum ionic displacements within 5  10-4 Å. Zhou et 5

al. [8] had demonstrated that the lattice constants of bulk TMB2 optimized with this calculation method are close to the experimental data and also agree with the calculated values reported in other theoretical works [18,19]. These bulk geometries are used as the initial input for the surface optimizations.

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Surface energy γ is defined as the excess energy at the surface of a material

 

1 Eslab  Ebulk  A

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compared to the bulk:

(1)

where A is the surface area, Eslab is the total energy of the surface slab and Ebulk is the

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energy of the bulk material with the same component. Since the accurate γ can only

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be calculated when the surface model has the same stoichiometry as the bulk material,

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the two-region modeling method is adopted [20]. Taking the surface models of ScB2 as examples, each model employs a two-dimensional slab which contains layers of Sc

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and B atoms and is separated by a 15 Å vacuum gap, as shown in Fig. 1. The slab has

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been divided into two regions. Region 1, the surface slab, contains the surface and several atomic layers below it, while region 2 is assumed as the inside part of the bulk

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material. The initial model is built according to bulk crystal structure. The atoms in region 1 are free to relax during geometry optimization, in the meantime, those atoms

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in region 2 and the lattice parameters of model cell are totally fixed. There is only one surface that needs to be considered in this model, and the numbers of atomic layers for each region are freely to be chosen to construct a stoichiometric surface slab. It must be pointed out that the energy in region 2 should not be included in the surface energy, but the energy change of region 2 induced by the atoms in region 1 still 6

contributes to the total energy. Therefore, the surface slab energy only contains the interaction energy within region 1 and half of the interaction energy between the two regions [20]:

1 1 E12  Etotal  E11  E22  2 2

(2)

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Eslab  E11 

where Etotal is the totoal energy of the surface model, E11 and E22 represent the internal

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energies within each region, and E12 corresponds to the interaction energy between the two regions. The reliability and accuracy of the two-region model on surface energy calculations have already been demonstrated in the investigation of ZrB2 surfaces

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[21].

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Oxygen adsorption energy (Eads) is defined as the reverse energy of separating an

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adsorption system into a bare surface and an isolated oxygen molecule [21]:

1 EO 2 2

(4)

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Eads  Esys  Ebare 

where Esys and Ebare are the total energies of the final adsorbed system and the bare

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surface, respectively, and EO2 is the total energy of an isolated oxygen molecule in

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the ground state. To diminish the interaction between adsorbed oxygen atoms, each surface model is constructed in supercell mode. The model of (112¯0) surface was enlarged for one time along [0001] direction, while every other surface model

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employed a 2  2 repeated surface slab. 3. Results 3.1. Geometry optimization and surface energy Due to the surface effect, the atomic arrangements near the surface, especially 7

the interlayer distances, are different from those in the bulk. In general, the relaxation of surface structure decreases inward. The outermost interlayer distance changing can reflect the extent of relaxation, and the innermost value presents the convergence. For the sake of accuracy, it is necessary to insure that both the two regions of the surface

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model are thick enough, because the properties of the innermost layer of region 1 must converge to those of the bulk. Then a convergence test on the interlayer distance

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changing, ∆=d/dbulk-1, of the surface models with different layer numbers is carried out. The layer configurations of the surface models and the relaxation results are listed

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in Table 1. For the sake of brevity, only the outermost and innermost interlayer

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distances are given. It is obvious that the relaxations of the innermost distances of all

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models are less than 0.20%, which indicates that the chemical environments of the

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innermost atoms in region 1 are very close to those in the bulk and the surface effect

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almost disappears. In other words, the influence of slab thickness on the modeling accuracy is converged. The models used in the following calculations on surface

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energies and adsorption energies are generated according to these layer configurations.

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There are significant differences of relaxations among the six types of surfaces in each TMB2, the relaxations of (101¯0) surfaces are much larger than those of (0001) and (112¯0) surfaces. It can also be found that with the increasing number of valance

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electron of TM, the relaxations of B-type surfaces decrease, while those of TM-type surfaces become larger. Then, surface energies of each TMB2 are calculated through these models, as listed in Table 2. Generally, lower surface energy indicates that the surface is 8

energetically more stable. It can be seen that the more stable (0001) surface is the B-terminated one in IIIB and IVB transition metal diborides instead of the TM-terminated one in VB transition metal diborides. Meanwhile, (101¯0)-B(B) surface is always more stable than (101¯0)-TM and (101¯0)-B(TM) surfaces. In addition, there

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are also substantial differences among surface energies of TMB2. To give a virtual view on the general trend of surface energies with the number of valence electrons of

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TM, the surface energies of TMB2 are plotted versus the valence electron

concentration (VEC), as shown in Fig. 2. For simplicity, only the stable surfaces along

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each direction are involved. The surface energies first increase when VEC increases

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from 3 to 3.33, and then decrease with VEC further increases. The surface energies

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also tend to decrease when the TM locates in the higher periods. These changing rules

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of the surface energies are very similar to those of the Young’s modulus and shear

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modulus of TMB2 bulk materials [8]. It is also obvious that for each surface type, TiB2 surface always exhibits the highest surface energy, while the energy of YB2

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surface usually displays the lowest value. Higher surface energies indicate less stable

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surfaces, i.e., the grain with high surface energies tends to grow larger to reduce the surface area. Then, it can be predicted that grain coarsening may easily occur in TiB2 and the grain sizes of YB2 are easier to be controlled. Additionally, the surface

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stability sequences in these diborides are also different, and the resulting differences of anisotropy in surface stability will be discussed in the 4.1 section. 3.2. Oxygen adsorption energy The adsorption of oxygen on the surface can be regarded as the very first step of 9

oxidation reaction. An insight into oxygen adsorption is helpful to reveal the initial oxidation behavior of TMB2. The adsorption tendency on a surface can be evaluated by the adsorption energy. In general, negative adsorption energy, i.e., decrease of the system energy, indicates strong adsorption and energetically stable adsorbed system.

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As illustrated in the previous work [21], there are multiple adsorption sites on each type of TMB2 surfaces. Generally, adsorptions occur at the sites with the

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strongest interaction. So, the favorable adsorption sites are the three-fold hollow site on (0001)-TM surface, bridge site on (0001)-B surface, hollow site surrounded by one

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B and two TM atoms on (112¯0) surface, bridge site along [12¯10] direction on (101¯

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0)-TM and (101¯0)-B(TM) surfaces and bridge site along [0001] direction on (101¯

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0)-B(B) surface, respectively. For conciseness, only the favorable adsorption energies

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on each surface are listed in Table 3. As shown in Fig. 3, the adsorptions tend to be

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weakened from IIIB to VB transition metal diborides. This is because the TM-B and B-B interactions are enhanced by the increasing VEC, which results in an extra

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energy barrier for the change of electronic structure during the adsorption.

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It can also be found that there are general differences of adsorption among six types of surfaces in each TMB2. (0001)-TM surface exhibits the strongest adsorption among six surfaces, while the adsorption on (0001)-B and (101¯0)-B(B) surfaces are

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relatively weaker than the others. This results from the differences of bonding characteristics among the six types of surfaces after adsorption. Taking HfB2 as an example, as shown in Fig. 4(a), the adsorption at the hollow site on (0001)-Hf surface is the strongest due to the formation of three Hf-O bonds. As can be seen from Fig. 10

4(b), the adsorption at bridge site on (101¯0)-Hf surface is also strong owing to the two strong Hf-O bonds. Since the B-O bonds are enhanced by the conjugation system in the B-plane (in Fig. 4(c-d)), the adsorption energies on (112¯0) and (101¯0)-B(Hf) surfaces are similar to that on (101 ¯0)-Hf surface. As shown in Fig. 4(e), there are large

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displacements of B atoms on (101¯0)-B(B) surface after adsorption, which leads to the weakening of surrounding B-B covalent bonds and elevates the system energy. Then,

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the adsorption on (0001)-B surface is the weakest since the strong B-B covalent bond need to be broken (in Fig. 4(f)).

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However, there are also several exceptions, including the (0001) surfaces of YB2

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and the (101¯0)-B(B) surface of VB2, as marked in Fig. 3. Due to the small radius of V

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atom, VB2 has the smallest distance between surface B atoms on (101¯0)-B(B) surface.

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Thus, as shown in Fig. 5(a), the B-O-B bond angle can be much smaller than those in

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other TMB2, which is beneficial to disperse the lone pair electrons of O atom and reduce the repulsions among them. Besides the B-O interactions, the two surface B

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atoms can also form a three-center bond with the V atom in the third layer by using

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the pz orbitals while their sp2 hybridization forms are maintained during the adsorption, which is helpful to compensate the electron deficiency of surface B atoms. These all lead to the strong adsorption on (101¯0)-B(B) surface of VB2. Different from

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VB2, YB2 has the biggest lattice size and much weaker B-B interactions. Therefore, when oxygen is adsorbed on (0001)-B surface of YB2, the energy required for breaking the B-B bond is relatively low. Moreover, due to the relatively larger interspace between surface B atoms, the O atom almost locates in the B plane (in Fig. 11

5(b)), which results in the enhancement of B-O interactions from the conjugation system. Hence, the adsorption energy on (0001)-B surface can be comparable with those on (112¯0) and (101¯0) surfaces. However, with less valance electrons and smaller electronegativity, the surface Y atom has insufficient electrons to bond with O atom

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and the adsorption becomes much weaker on (0001)-Y surface. 4. Discussion

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4.1. Effect of surface stability on grain morphology

It is obvious that the surface stability is anisotropic in each TMB2, which is very

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helpful in understanding the anisotropic grain morphology of TMB2. In the course of

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solid-state reaction, the crystal growth rates are strongly influenced by surface

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crystallization and mass transport. Generally, higher surface energy indicates lower

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surface stability and faster crystallization rate along the direction normal to the

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surface. Since the three types of (101¯0) surfaces and two types of (0001) surfaces alternately stack during the grain growth of TMB2, the overall stabilities of (101¯0) and

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(0001) surfaces should be concluded by considering the stabilities of each surface,

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respectively. Although accurate weighted average method is still unavailable, the anisotropy in grain growth can be qualitatively analyzed. Due to the much higher energies of (101¯0)-TM and (101¯0)-B(TM) surfaces, the

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equivalent energies of (101¯0) surfaces should be higher than that of (101¯0)-B(B) surface. Consequently, the (101¯0) surfaces could display better stability than the others only when the energy of (101¯0)-B(B) surface is low enough. According to the hexagonal crystal structures of TMB2, the difference in orientation between (101¯0) 12

and (112¯0) surfaces is small, which leads to an intense competition during the crystal growth. It is worth noting that the mass transport rates along [101¯0] and [112¯0] directions are similar [22]. Then, according to the Wulff construction [23], the difference in crystal growth rates along these two directions is dominated by the

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surface energy ratio between (101¯ 0) and (112¯ 0) surfaces. When there is little difference of stability between them, the prismatic surfaces around [0001] direction

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are covered by these two surfaces simultaneously, and the (0001) cross sections of

grain may appear with dodecagonal or nearly circular shapes. If one of the surfaces is

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much more stable, the other will disappear rapidly, which results in hexagonal grain

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morphologies. As shown in Fig. 6(a), comparing to (101¯0)-B(B) surface, the (112¯0)

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surface becomes more stable with the increasing VEC. Consequently, (112¯0) surface

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is much more stable than (101¯0) surfaces and the grains are expected to be covered by

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(112¯0) surface and exhibit a hexagonal shape in TiB2, VB2, NbB2 and TaB2. However, in ScB2, YB2, ZrB2 and HfB2, (101¯0) surfaces may display better stability and appear

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in the grain morphology.

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For further understanding of the anisotropic morphology, the surface energy ratios between the more stable (0001) surface and the most stable prismatic surfaces are also calculated. As shown in Fig. 6(b), the (0001) surfaces and prismatic surfaces

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present similar stability in TiB2, and the (0001) surfaces exhibit better stability in VB2, while the prismatic surfaces are more stable in the other TMB2. It is noticeable that both (0001) surfaces in VB2 are very stable and those in TiB2 keep similar surface energies. In other words, the anisotropy in surface stability is slightly influenced by 13

the surface energy difference between two (0001) surfaces. It is also worth noting that the mass transport within the (0001) plane is faster than that along [0001] direction [22], which could accelerate the growth of prismatic surfaces. Therefore, the grain morphologies of VB2 and TiB2 are usually plate-like, and those of ScB2, YB2 and

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ZrB2 often display rod-like shape, while the grains of HfB2, NbB2 and TaB2 may appear with moderate aspect ratios. These predictions coincide with the observations

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in the as-synthesized TMB2 powders [24-29]. 4.2. Initial oxidation resistance

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Due to the different oxygen adsorption behaviors, the resistances of each surface

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to the initial oxidation are dissimilar, which result in anisotropic resistances of TMB2

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grains. Hence, controlling the grain morphology may be a promising way to improve

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the initial oxidation resistance of TMB2. As shown in Fig. 7(a), besides the peculiar

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adsorption energy on (0001)-B surface of YB2, the adsorption on (0001) surfaces are also very strong in VB2, NbB2 and TaB2 since (0001)-TM surfaces become more

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stable. Thus, rod-like grain morphologies along [0001] direction are beneficial to

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resist the initial oxidation of YB2, VB2, NbB2 and TaB2. Meanwhile, the (0001) surfaces are more inert for adsorption in ScB2, TiB2, ZrB2 and HfB2, which suggests that grains with plate-like shapes perpendicular to [0001] direction may have better

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resistance for these TMB2. Since the most stable surface usually occupies the largest proportion in grain morphology, the oxygen adsorption on this surface may dominate the oxidation behavior of the whole grain. Then, the favorable adsorption energies on the most 14

stable surface in TMB2 are selected, as shown in Fig. 7(b). Comparing with that in ZrB2, the favorable adsorption in YB2, HfB2 and TaB2 are relatively weaker, which indicates the better intrinsic initial oxidation resistance of these three diborides. 5. Conclusions

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The general trends in stability and oxygen adsorption behaviors of TMB2 surfaces are investigated by first-principles calculations. By employing two-region

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modeling method, accurate surface energies and adsorption energies of TMB2

surfaces are obtained. Surface energies firstly increase with VEC, reaching the

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maximum at VEC = 3.33, and then decrease with further increase of VEC. A decrease

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tendency of surface energies is also found when the TM locates in the higher periods.

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It is predicted that, under equilibrium condition, hexagonal plate-like grain

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morphology with (112¯0) covered side surfaces will appear in TiB2 and VB2, and the

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grain morphologies of ScB2, YB2 and ZrB2 may display rod-like shape that are mainly covered by (101¯0) surfaces.

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The oxygen adsorptions tend to be weakened from IIIB to VB transition metal

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diborides. The adsorptions on (0001)-B and (101¯0)-B(B) surfaces are usually much weaker than those on the other surfaces, while the strongest adsorption often occurs on (0001)-TM surface. However, the distinctive atomic radius of V and Y lead to the

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exceptional adsorption energies on the (0001) surfaces of YB2 and the (101¯0)-B(B) surface of VB2. Considering grain morphology and oxygen adsorption, it is suggested that plate-like grain morphologies are beneficial to resist the initial oxidation of ScB2, TiB2, ZrB2 and HfB2, while rod-like morphologies will improve the resistance of YB2, 15

VB2, NbB2 and TaB2. It is also predicted that YB2, HfB2 and TaB2 may have better initial oxidation resistance than ZrB2. Acknowledgments This work was supported by the Natural Sciences Foundation of China under

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Technology Commission under Grant No. D161100002416001.

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Grant No. 51672064 and No. U1435206, and Beijing Municipal Science &

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References [1] D.M. van Wie, D.G. Drewry, E.D. King, C.M. Hudson, J. Mater. Sci. 39 (2004) 5915-5924. [2] M.M. Opeka, I.G. Talmy, J.A. Zaykoski, J. Mater. Sci. 39 (2004) 5887-5904.

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[3] W.G. Fahrenholtz, G.E. Hilmas, I.G. Talmy, J.A. Zaykoski, J. Am. Ceram. Soc. 90 (2007) 1347-1364.

Kriven, J. Eur. Ceram. Soc. 30 (2010) 2375-2386.

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[4] P. Sarin, P.E. Driemeyer, R.P. Haggerty, D.K. Kim, J.L. Bell, Z.D. Apostolov, W.M.

[5] S. Gangireddy, S.N. Karlsdottir, S.J. Norton, J.C. Tucker, J.W. Halloran, J. Eur.

A

[6] A. White, MRS Bull. 37 (2012) 715-716.

N

U

Ceram. Soc. 30 (2010) 2365-2374.

M

[7] A.L. Ivanovskii, Prog. Mater Sci. 57 (2012) 184-228.

285-294.

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[8] Y.C. Zhou, H.M. Xiang, Z.H. Feng, Z.P. Li, J. Mater. Sci. Technol. 31 (2015)

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[9] X.W. Xu, K. Fu, M. Yu, Z.M. Lu, X.H. Zhang, G.D. Liu, C.C. Tang, J. Alloys Compd. 607 (2014) 198-206.

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[10] Y.F. Han, Y.B. Dai, D. Shu, J. Wang, B.D. Sun, J. Phys.: Condens. Matter 18 (2006) 4197-4205.

A

[11] S. Suehara, T. Aizawa, T. Sasaki, Phys. Rev. B 81 (2010) 085423. [12] P. Gamallo, R. Sayόs, J. Phys. Chem. C 117 (2013) 5831-5839. [13] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys. Condens. Matter 14 (2002) 2717-2744. [14] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. 17

[15] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [16] J.D. Pack, H.J. Monkhorst, Phys. Rev. B 16 (1977) 1748. [17] B.G. Pfrommer, M. Côté, S.G. Louie, M.L. Cohen, J. Comput. Phys. 131 (1997) 233-240.

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[18] P. Vajeeston, P. Ravindran, C. Ravi, R. Asokamani, Phys. Rev. B 63 (2001) 045115.

[20] J.D. Gale, A.L. Rohl, Mol. Simul. 29 (2003) 291-341.

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[19] I.R. Shein, A.L. Ivanovskii, J. Phys.: Condens. Matter, 20 (2008) 8106-8110.

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[21] W. Sun, J.C. Liu, H.M. Xiang, Y.C. Zhou, J. Am. Ceram. Soc. 99 (2016)

N

4113-4120.

A

[22] Z. Fan, Z.X. Guo, B. Cantor, Composites Part A 28 (1997) 131-140.

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[23] G.Z. Wulff, Z. Kristallogr, Mineral 34 (1901) 449–530.

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[24] Y. Zhang, R.X. Li, Y.S. Jiang, B. Zhao, H.P. Duan, J.P. Li, Z.H. Feng, J. Solid State Chem. 184 (2011) 2047-2052.

PT

[25] H.T. Liu, H.Y. Qiu, W.M. Guo, J. Zou, G.J. Zhang, Adv. Appl. Ceram. 114 (2015)

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418-422.

[26] S. Venugopal, D.D. Jayaseelan, A. Paul, B. Vaidyanathan, J.G.P. Binner, P.M. Brown, J. Am. Ceram. Soc. 98 (2015) 2060-2064.

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[27] S.H. Kang, D.J. Kim, J. Eur. Ceram. Soc. 27 (2007) 715-718. [28] L. Bača, N. Stelzer, J. Eur. Ceram. Soc. 28 (2008) 907-911. [29] S.B. Jin, P. Shen, D.S. Zhou, Q.C. Jiang, Cryst. Growth Des. 12 (2012) 2814-2824. 18

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Figures

Figure 1 Calculation models for (a) (0001)-Sc, (b) (0001)-B, (c) (112¯0), (d) (101¯0)-Sc,

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M

A

N

U

(e) (101¯0)-B(Sc), and (f) (101¯0)-B(B) surfaces of ScB2. (color online)

19

IP T SC R U N A M ED PT

Figure 2 Surface energies of (a) stable (0001), (b) (112¯0) and (c) stable (101¯0)

A

CC E

surfaces in each transition metal diborides. (color online)

20

Figure 3 Favorable oxygen adsorption energies on the surfaces of transition metal

M

A

N

U

SC R

IP T

diborides. (color online)

ED

Figure 4 Differential charge density of adsorbed (a) (0001)-Hf surface on (112¯0) plane, (b) (101¯0)-Hf surface on (0001) plane, (c) (112¯0) surface on (0001) plane, (d)

PT

(101¯0)-B(Hf) surface on (0001) plane, (e) (101¯0)-B(B) surface on (112¯0)

CC E

plane and (f) (0001)-B surface on (112¯0) plane in HfB2. The positive charges

A

are shown as blue, and negative ones are shown as red. (color online)

21

Figure 5 Differential charge density of adsorbed (a) (101¯0)-B(B) surface on (112¯0) plane in VB2 and (b) (0001)-B surface on (112¯0) plane in YB2. The positive

ED

M

A

N

U

SC R

IP T

charges are shown as blue, and negative ones are shown as red. (color online)

Figure 6 Ratio of surface energies between (a) (101¯0)-B(B) and (112¯0) surfaces, and

PT

(b) stable prismatic and basal surfaces of each transition metal diborides.

A

CC E

(color online)

22

IP T SC R U N

A

Figure 7 Favorable oxygen adsorption energies on (a) stable (0001), (112¯0) and stable

M

(101¯0) surfaces, and (b) on the most stable surface of each transition metal

ED

diborides. (color online)

PT

Table 1 Layer configurations and structural relaxations of transition metal diboride surface models. N1 and N2 represent the atomic layer numbers in region 1 and region 2.

CC E

The relaxations of the outermost and innermost interlayer distances are denoted by Δout and Δin.

A

Surface

(0001)-TM

(0001)-B

ScB2

YB2

TiB2

ZrB2

HfB2

VB2

NbB2

TaB2

N1

6

6

6

6

6

6

6

6

N2

5

5

6

4

6

5

6

6

Δout, %

-2.76

-3.43

-4.70

-4.68

-2.64

-11.98

-10.46

-9.08

Δin, %

0.03

0.09

0.02

0.00

-0.04

0.13

-0.14

0.04

N1

6

6

8

6

6

6

6

6

23

(101¯0)-B(B)

5

6

6

4

6

Δout, %

-10.60

-9.72

-6.49

-7.06

-5.22

2.02

-0.12

1.54

Δin, %

0.13

-0.15

0.04

0.01

0.12

-0.08

-0.12

-0.15

N1

6

7

6

6

5

6

6

6

N2

5

6

5

5

4

5

4

4

Δout, %

-4.82

-7.70

-2.53

-4.15

-3.14

-2.51

-3.88

-3.37

Δin, %

-0.08

0.11

0.14

-0.02

-0.08

0.10

0.10

-0.01

N1

9

15

9

9

9

12

15

15

N2

9

12

9

6

6

9

13

13

Δout, %

-3.34

12.54

-15.81

-4.52

-6.77

-32.95

-23.31

-25.69

Δin, %

-0.17

-0.01

0.09

-0.05

0.08

-0.03

0.08

-0.16

N1

12

15

12

9

9

9

12

12

N2

9

12

9

8

6

U

9

10

10

Δout, %

-41.43

-75.58

-17.33

-25.18

-8.02

-20.33

-18.83

Δin, %

-0.02

0.00

-0.03

0.08

0.10

-0.16

0.07

0.09

N1

12

15

12

9

9

12

12

12

N2

10

10

9

6

6

11

12

11

Δout, % Δin, %

N

SC R

IP T

6

-29.07

A

(101¯0)-B(TM)

5

M

(101¯0)-TM

5

ED

(112 ¯0)

N2

-45.18

-50.90

-36.49

-41.75

-41.58

-35.60

-41.28

-44.56

0.03

-0.06

0.16

-0.12

-0.13

0.01

-0.20

0.08

A

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Surface

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Table 2 Calculated surface energies of transition metal diborides Surface energy (J∙m-2)

ScB2

YB2

TiB2

ZrB2

HfB2

VB2

NbB2

TaB2

(0001)-TM

3.336

2.844

4.233

3.914

3.931

3.147

2.877

2.565

(0001)-B

3.144

2.675

4.207

3.828

3.878

3.539

3.129

2.778

(112 ¯0)

2.983

1.998

4.112

3.475

3.640

3.710

2.684

2.415

(101¯0)-TM

3.787

3.034

4.861

4.330

4.514

3.954

3.684

3.490

(101¯0)-B(TM)

4.151

2.825

4.763

4.103

3.976

4.292

3.642

3.339

(101¯0)-B(B)

2.670

1.760

4.192

3.353

3.553

3.857

3.141

2.892

24

IP T

diborides

SC R

Table 3 Favorable oxygen adsorption energies on the surfaces of transition metal

Oxygen adsorption energy (eV)

VB2

NbB2

TaB2

U

YB2

TiB2

ZrB2

HfB2

(0001)-TM

-6.115

-4.861

-6.213

-6.138

-5.444

-5.234

-5.337

-4.566

(0001)-B

-4.262

-5.304

-3.457

-3.752

-3.066

-2.938

-3.069

-3.066

(112 ¯0)

-5.518

-5.254

-5.327

-5.518

-5.171

-4.454

-4.596

-4.319

(101¯0)-TM

-5.641

-5.327

-5.095

-4.462

-4.580

-4.139

(101¯0)-B(TM)

-5.823

-5.329

(101¯0)-B(B)

-4.625

-4.277

A

N

ScB2

M

Surface

-4.670

-5.053

-4.984

-4.569

-4.520

-4.377

-3.990

-4.664

-4.450

-4.215

-4.910

-3.955

-3.758

A

CC E

PT

ED

-5.497

25