Stability of β-Mo2C Facets from ab Initio Atomistic Thermodynamics

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Stability of β-Mo2C Facets from ab Initio Atomistic Thermodynamics Tao Wang,† Xingwu Liu,† Shengguang Wang,‡ Chunfang Huo,† Yong-Wang Li,† Jianguo Wang,† and Haijun Jiao*,†,§ †

State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan, Shanxi 030001, People's Republic of China ‡ Synfuels China Co., Ltd., Taiyuan, Shanxi 030032, People's Republic of China § Leibniz-Institut f€ur Katalyse e.V. an der Universit€at Rostock, Albert-Einstein Strasse 29a, 18059 Rostock, Germany

bS Supporting Information ABSTRACT: The stability of β-Mo2C surfaces has been computed at the level of density functional theory under the consideration of the temperature, pressure, and molar ratios of CH4/H2 and CO/CO2 gas mixtures by using ab initio atomistic thermodynamic calculations. It was found that the (001) surface is most stable at low temperature, whereas (101) becomes dominant at high temperature with CH4 as carbon source, and the computed surface stability is supported by the experimental X-ray diffraction pattern and intensity. For CO as carbon source, the (101) surface has the smallest surface Gibbs free energy at temperatures up to 1000 K and is most stable. On the basis of the Wulff-type particle shapes from surface Gibbs free energies the (101) facet represents the largest surface area of β-Mo2C. Our findings are in perfect agreement with the results of high-resolution transmission electron microscopy.

’ INTRODUCTION Transition metal carbides have attracted great interests in both experiment and theory because of their special properties, e.g., high hardness and melting point, good thermal stability, and excellent electric conductivity.1 These physical properties have facilitated transition metal carbides as cutting tools and hardcoating materials.2 In addition, early transition metal carbides also have catalytic activities similar to those of Pt group metals3,4 which make them promising catalysts in chemistry. As one of the important transition metal carbides, molybdenum carbide (Mo2C) has been widely studied. Mo2C mainly has two crystalline structures, i.e., the orthorhombic phase and the hexagonal phase. The orthorhombic phase has a structure with Mo atoms slightly distorted from their positions in close-packed planes and carbon atoms orderly occupying one-half of the octahedral interstitial sites.5 In the hexagonal phase, Mo atoms form a hexagonally close packed structure with carbon atoms randomly filling half of the octahedral interstitial sites.6 However, the definition of α-Mo2C and β-Mo2C phases is not consistent in literature. In this paper we have followed the way applied in experimental literature4,7,8 and called the hexagonal phase βMo2C and the orthorhombic phase α-Mo2C. Mo2C has been reported to have catalytic activities as noble metals in hydrogenation,8 dehydrogenation,9 hydrogenolysis,10 aromatization, 11,12 hydrodesulfurization,13 hydrodenitrogenation,14 and hydrogen production from reforming of oxygenated compounds.15 The activity of a water
gas shift (WGS) reaction16,17 on Mo2C has also been widely investigated experimentally. Xiang r 2011 American Chemical Society

et al.18 reported CO hydrogenation on Mo2C and discussed the selectivity of alcohol formation under different experimental conditions. Compared with the great efforts denoted to the experiments, less theoretical reports for this system are known. Liu et al.19 studied the interaction of sulfur containing molecules with αMo2C and the role of carbon in desulfurization using density functional theory (DFT) calculations and found that carbon in Mo2C not only was a ligand but also played a key role in the dissociation of S-containing molecules. The hydrogenolysis mechanism of thiophene20 and indole21 on clean β-Mo2C was also systematically investigated on the basis of DFT calculations. The chemisorption and decomposition of simple molecules22 such as nitrogenous compounds, aromatic hydrocarbons, and CO were extensively examined on both α-Mo2C and β-Mo2C phases. Pistonesi et al. theoretically discussed the chemical properties of methanol23 and methyl iodide24 and the promoting effect of potassium on β-Mo2C5 (α phase in this paper) based on their surface experiments and proposed that the incorporation of potassium atoms enhanced the dissociation ability of the C
I and C
O bonds. Tominaga and Nagai25 built a schematic potential energy surface of the WGS reaction and concluded that the final process of the reaction of O with CO to form CO2 was the rate-limiting step. Liu et al.26 also calculated the WGS Received: June 24, 2011 Revised: September 5, 2011 Published: October 06, 2011 22360

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Figure 1. Unit cell of β-Mo2C with an eclipsed configuration (Mo/blue ball and C/black ball).

mechanism and emphasized the oxygen importance on the Mo2C surface. In order to study the intrinsic WGS activities of Mo2C, Schweitzer et al. loaded Pt on Mo2C27 and found Mo2C to play the role of both support and catalyst. For studying the surface properties of Mo2C within the scope of DFT calculations, the most frequently used surfaces are βMo2C(001) and α-Mo2C(0001). They have unified active centers, are flat, and can be easily used for studying the reaction mechanisms. In addition, the stability of other Miller index surfaces has been calculated.28,29 It showed that the β-Mo2C(011) facet was the most stable in the whole range of carbon chemical potential (μC). However, the stabilities of these reported surfaces and some high Miller index surfaces in connecting with the effects of Mo2C formation conditions were not considered. In this work, we present an atomistic thermodynamic study of the stabilities of different β-Mo2C surfaces under CH4/H2 and CO/ CO2 atmospheres by considering the temperature and pressure on the basis of periodic DFT calculations. On the basis of the computed surface free energies, the equilibrium shape of the catalyst at defined conditions can be made from the Wulff construction.

’ COMPUTATIONAL MODEL AND METHOD a. Model. There is no uniform model for β-Mo2C available. Haines et al.30 proposed an eclipsed configuration with a Mo
C
Mo
C stacking pattern on the basis of their X-ray diffraction and ab initio calculation. Tominaga and Nagai25 employed a structure with a Mo
Mo
C
Mo stacking pattern. Recent DFT calculations by Shi et al.28 verified the eclipsed configuration with a Mo
C
Mo
C stacking mode to be the most stable, and Han et al.29 have employed this model for their study. In this paper, we used this most stable eclipsed configuration in a slightly different way, as our model shows in Figure 1. For example, Shi et al.28 removed the four carbon atoms along orientation B, while we removed the four carbon atoms along orientation A. Consequently, our (101) facet is the reported (011) facet by Shi et al.28 Our benchmark calculations show that both models are equal in energy. The right reason for our choice is the experimental X-ray diffraction (XRD) data of Mo2C,31 which always show a very intense peak assigned to the (101) surface. In addition, high-resolution transmission electron microscopy (HRTEM) reported the images of β-Mo2C(101). Wang et al.32 found that the HRTEM of the supported β-Mo2C yields d-space

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values (0.18 and 0.23 nm) for the (102) and (101) surfaces, respectively. In addition, Nagai et al.33 acquired the HRTEM data of the supported β-Mo2C when discussing the WGS reactivity, and their HRTEM images clearly showed the crystal phase and two types of crystal phase distances (0.229 and 0.237 nm) corresponding to the (101) and (002) surfaces, respectively. All these HRTEM data demonstrated the existence of the (101) surface as a stable facet of Mo2C. The calculated lattice parameter of the cell is a = 6.075 Å, b = 6.069 Å, and c = 4.722 Å, in good agreement with the experiment: a = b = 2  3.011 Å and c = 4.771 Å.34 The thickness of our slabs for different surfaces is 9
14 Å, thick enough to avoid significant influence on the surface energies from our benchmarks. A vacuum layer of 10 Å was set to exclude the interactions among the periodic slabs. b. Method. All calculations were performed using the planewave periodic DFT method as implemented in the Vienna ab initio simulation package (VASP).35,36 The electron ion interaction was described with the projector augmented wave (PAW) method37 implemented by Kresse and Joubert.38 The electron exchange correlation energy was treated within the generalized gradient approximation in the Perdew
Burke
Ernzerhof formalism (GGA-PBE).39 The calculations were performed with cutoff energy of 400 eV and Gaussian electron smearing method with σ = 0.05 eV to ensure accurate energies with errors due to smearing of less than 1 meV per unit cell. For bulk optimization, the lattice parameters for β-Mo2C were determined by minimizing the total energy of the unit cell using a conjugated-gradient algorithm to relax the ions. A 5  5  5 Monkhorst
Pack k-point grid was used for sampling the Brillouin zone. The geometry optimization was done when the convergence criterion on forces becomes smaller than 0.02 eV/Å and the energy difference is lower than 10
4 eV. Ab initio atomistic thermodynamics, proposed by Scheffler and Reuter40 connects the surface stability with temperature and pressure of gas phase. This method, to some extent, combines the DFT total energy and experiment conditions and uses the Gibbs free energy as criterion for chemical problems. On the basis of this method, the stabilities and properties of several metal oxides under certain gas phases were reported.41 The edge structure of MoS2 under the consideration of temperature, pressure and H2S/H2 ratio was also reported42 and the method used was similar with the ab initio atomistic thermodynamics. Aray et al.43 investigated the effects of temperature and gas-phase partial pressure on the stability of low Miller index RuS2 surfaces. For carbides, Sautet and Cinquini44 discussed some carbon sources in the carburization process and defined the way to depict the carbon chemical potential (μC). By using CO as the carbon source to describe the μC, de Smit et al.45 compared the relative stability of iron carbide phases under different catalytic and pretreatment conditions. In addition, de Smit et al.46 also calculated the stability of their chosen surfaces of χ-Fe5C2 with synthesis gas as the carbon origin to describe the μC. According to Scheffler and Reuter40 the stability of a given surface can be determined by the surface free energy γ(T, pi) within the general scheme 1 γðT, pi Þ ¼ ½G
A

∑i Ni μi ðT, pi Þ

Here G is the Gibbs free energy of a solid surface, A stands for the total surface area of two equilibrium surfaces (top and bottom sides), μ(T, pi) is the chemical potential of the species i, and Ni is the number of atoms of the ith type element. For the Mo2C 22361

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Figure 2. Surface energies (J/m2) of different terminations (ter) of β-Mo2C by using graphite bulk energy as (μC) carbon chemical potential (Mo/blue ball and C/black ball).

surface, the above equation can be rewritten as γðT, pÞ ¼

The Gibbs free energy is associated with Helmholtz free energy, F, via

1 slab ½G
NMo μMo ðT, pÞ
Nc μc ðT, pÞ A Mo2 C

ð1Þ

Gslab Mo2C is the Gibbs free energy of a solid Mo2C slab composing two equivalent surfaces and μMo and μC are the chemical potentials of Mo and C. Ni represents the atom numbers of the corresponding element. In a general sense, the bulk Mo2C and its components satisfy the following relation in eq 2. bulk 2μMo þ μC ¼ gMo 2C

ð2Þ

gMo2C is the Gibbs free energy of the bulk Mo2C (per formula unit), inserting eq 2 into eq 1 to eliminate μMo, the Gibbs free energy of the slab with two equivalent surfaces becomes a function of the μC as shown in eq 3: "

γðT, pÞ ¼

#

bulk NMo gMo 1 slab NMo
2NC 2C þ μC ðT, pÞ GMo2 C
2 2 A

GðT, p, NMo , NC Þ ¼ FðT, p, NMo , NC Þ þ pV ðT, p, NMo , NC Þ

Also F can be written as FðT, p, NMo , NC Þ ¼ Etotal DFT ðV , NMo , NC Þ þ F vib ðT, V , NMo , NC Þ Etotal DFT(V, NMO, NC) is the electron contribution which can be calculated by VASP. Then Fvib can be divided into two parts F vib ðT, V , NMo , NC Þ ¼ Evib ðT, V , NMo , NC Þ
TSvib ðT, V , NMo , NC Þ Further

ð3Þ

Evib ¼ 22362

R1 k2

ðhv Þeð
hvi =kTÞ

∑i hvi þ k ∑i ½1
i eð
hv =kTÞ  R

i

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Further Svib ¼ R

∑i

ðhvi =kTÞeð
hvi =kTÞ
R ½1
eð
hvi =kTÞ 

∑i ln½1
eð
hv =kTÞ i

The contribution of the pV term to the surface free energy is negligible compared with the Helmholtz free energy. In the Mo2C slab, the contribution of Fvib to the surface energy is calculated from the frequency of slabs by VASP and we found that the range was 0.1
0.25 J/m2. This contribution becomes more obvious at high temperature and is not negligible in the surface free energy calculations. Therefore, we included this contribution in our calculations. To relate the μC to the gas phase reservoirs, we consider CH4/ H2 and CO/CO2. According to Sautet,44 the μC can be calculated as follows: For the formal CH4 dissociation CH4 f C þ 2H2

ðr1 Þ

It follows that μC ¼ μCH4
2μH2

ð4Þ

The formal reaction for CO 2CO f C þ CO2

ðr2 Þ

μC ¼ 2μCO
μCO2

ð5Þ

The chemical potential of the gas molecule i (e.g., CH4) can be related with the temperature and pressure as follows: ! p i ð6Þ þ μ~i ðT, p0 Þ þ kB T ln 0 μi ðT, pi Þ ¼ Etotal i p stands for the DFT total energy of the isolated gas phase Etotal i molecule (including zero point vibrations) and μ ~i(T,p0) is the change of chemical potential at different temperatures, and it also includes the contribution from vibrations and rotations of the molecule. We also used the experimental values from thermodynamic tables as Reuter et al. did.40 Inserting eq 6 into eqs 4 and 5 the μC values under CH4/H2 and CO/CO2 gas phases are ! respectively pCH4 0 total μC ðT, pÞ ¼ ECH4 þ μ~CH4 ðT, p Þ þ k B T ln p0 "


2

Etotal H2

pH þ μ~H2 ðT, p Þ þ k B T ln 02 p

"

ð7Þ




pCO þ 2μ~CO ðT, p0 Þ þ 2k B T ln p0

Etotal CO2

pCO2 þ μ~CO2 ðT, p Þ þ k B T ln p0

!#

0

ð8Þ

8 2 bulk 0 NMo gMo 1 < slab0 N
2N Mo C C 2 4ðEtotal
2Etotal Þ G þ γðT, pÞ ¼
CH4 H2 A: Mo2 C 2 2

pCH4 p0 þ ðμCH4 ðT, p Þ
2μ~H2 ðT, p ÞÞ þ kB T ln p2H2 0

8 2 bulk NMo gMo 1 < slab NMo
2NC 4 total 2C G þ ð2ECO
2Etotal γðT, pÞ ¼
CO2 Þ A: Mo2 C 2 2

p2CO þ 2μ~CO ðT, p0 Þ
μ~CO2 ðT, p0 ÞÞ þ kB T ln pCO2 p0

!#)

Here we fix the energy of the spin polarized free carbon atom μC = EC = 0 as the energy reference. Since the μC cannot vary without bounds, we constrain it in a suitable range. First, if the μC becomes too low, the molybdenum carbide will not steadily exist, and decompose into metal Mo and C atoms. Thus bulk bulk ð0, 0Þ
2gMo ð0, 0Þ min½μC ðT, pÞ ¼ ½gMo 2C

On the other hand, the maximum μC can be defined as the point beyond of which the gas carbon atom condensed. So the high limit of the μC is max½μC ðT, pÞ ¼ Eatom C

Inserting eqs 7 and 8 into eq 3, the surface free energy under CH4 and CO gas environment comes to

0

and

!#

0

! μC ðT, pÞ ¼ 2Etotal CO

Figure 3. Relationship of carbon chemical potential (μC) to total pressure (p) and temperature.

!#)

So the range of the μC is gMo2C
2gMo < μC < EC. The atomistic thermodynamic method has been successfully applied in many catalytic systems, and here we just applied it to Mo2C to discuss the relative thermodynamic stability of all surfaces under defined conditions although the morphology of the molybdenum precursor,47 the kinetics, and experimental issues are not considered. For example, for the comparison of the rate of carbon deposit and carbide formation, complex phase changes are referred to in the synthesis process when discussing the carbon sources. This is the advantage of the atomistic thermodynamic method, which can be easily used to discuss the thermodynamic properties of the catalyst without considering the mechanistic details. 22363

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’ RESULTS AND DISCUSSION I. Surface Structures and Stability from Surface Energy. For studying the surface structure and stability, we have chosen 11 βMo2C surfaces shown in Figure 2. The (001) surface has one Mo termination and one C termination. The (010) surface has one C

Figure 4. Relationship of carbon chemical potential (μC) to temperature and the molar ratios of CH4/H2 (a) and CO/CO2 (b).

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termination and two Mo terminations. The (100) surface has two Mo terminations and one C termination. The (111) surface has one Mo termination and one C termination. The (011), (101), (110), (112), and (201) surfaces have not only Mo and C terminations but also Mo and C mixed terminations. The (102) and (103) surfaces have very complex terminations and present step appearance. Since kink, ledge, and corner sites are always considered as active sites, it is interesting to link the active sites and the catalytic activities for defined surface structures. As referred by Burwell et al.48 and Dumeignil et al.49 the coordinative unsaturated sites (CUS) are active sites in catalysis, and the catalytic activities are related with the numbers of CUS on each surface. The saturated coordination numbers of Mo and C in Mo2C bulk are three and six, respectively; therefore, surface Mo and C having less than three and six coordination numbers, respectively, are CUS. For pure C terminated surfaces, surface Mo is coordinatively saturated, and surface carbon has CUS. For pure Mo terminated surface, surface carbon is saturated and surface Mo has CUS. For Mo/C mixed terminations, both Mo and C can be saturated or unsaturated. For the Mo/C mixed termination of (101) surface, for example, all the surface Mo atoms have saturated coordination and all the surface carbon atoms are coordinated with five Mo atoms. First, we have computed the surface energy of all terminations by using graphite bulk energy as the μC from eq 3, where the total electronic energies (E) from DFT calculations rather than the Gibbs free energies (G) are used, and this is also the same method used by Shi et al. The surface energy of the most stable termination of each surface has been used for ordering the relative stability of these surfaces. Among those surfaces, the Mo/C mixed termination of the (101) facet has the smallest surface energy (2.19 J/m2) and is therefore the most stable termination of the (101) facet, which also represents the most stable surface among all surfaces. The surface stability has the decreasing order of (101) > (011) > (201) > (001) > (100) > (112) > (111) > (010) > (103) > (102) > (110).

Figure 5. Relationship of surface Gibbs free energy (γ) of the terminations of the (010) and (101) surfaces to temperature. 22364

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Figure 6. Liner relationship of Gibbs free energy (γ) to carbon chemical potential (μC) of different surfaces at p = 1 atm: zone (a) for the μC range of CH4/H2; zone (b) for the μC range of CO/CO2, and the black dotted line for the μC of graphite bulk (the energy of spin polarized free carbon atom as energy reference).

Since the carbon sources are usually carbon containing gases such as hydrocarbon compounds and CO in experiment rather than graphite, and the μC is associated with the gas compositions and experimental conditions, we discuss the stability of different surfaces upon the change of the μC. II. Surface Structures and Stability from Surface Gibbs Free Energy. For studying the surface stability under experimental conditions, we use CH4/H2 and CO/CO2 as carbon sources, and this is because the CH4/H2 mixture is commonly applied as carburization gases in Mo2C synthesis. In order to compare the effects of a carbon source on the stability of the Mo2C surfaces, we also used CO/CO2 as carburization gases, although they are not commonly used under experimental conditions because they are prone to cause carbon deposits. On the other hand, they are either starting materials or intermediates in Fischer
Tropsch synthesis and in the synthesis of alcohols by using Mo2C as catalysts. At first we have computed the change of the μC upon the change of reaction conditions, i.e., temperature, pressure and the molar ratios of CH4/H2 and CO/CO2. The calculated μC ranges from
11.71 to 0.00 eV. The calculated μC values at CH4/H2 and CO/CO2 gas phase are within this range. A less negative μC indicates a higher carbon chemical potential and also the higher thermodynamic driving force of the reaction.

At first we fixed the molar ratio of CH4/H2 = 1/4 and the molar ratio of CO/CO2 =2/1 under the variation of temperature and pressure (Figure 3). By raising the temperature under a given pressure, the μC becomes higher under CH4/H2 and lower under CO/CO2. These trends are in line with the results of Sautet.44 When the pressure is allowed to rise at a given temperature, the μC becomes lower under CH4/H2 but higher under CO/CO2. This shows that temperature has a much stronger effect on μC than pressure. Now we fixed the total pressure at 1 atm and varied the temperature and molar ratios of CH4/H2 and CO/CO2 (Figure 4). When the temperature is allowed to rise at a given gas molar ratio the μC becomes higher under CH4/H2 but lower under CO/CO2. When the gas molar ratio is allowed to rise under a given temperature, the μC become slightly higher. It shows that temperature has a much stronger effect on μC than the gas molar ratios. Comparison in Figures 3 and 4 shows that temperature has much stronger effect on μC than pressure and the gas molar ratio, and CO/CO2 as a carbon source has a stronger influence on μC than CH4/H2. On the basis of these results, we discuss the temperature influence on the stability of different surfaces at 1 atm and molar ratios of CH4/H2 = 1/4 and CO/CO2 = 2/1. For studying the influences of the temperature on the stability of different terminations, we calculated the surface Gibbs free 22365

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Figure 7. Relative stability of the Mo2C surfaces at three temperatures at p = 1 atm in CH4/H2 = 1/4 (a) and CO/CO2 = 2/1 (b) (vertical axis for the Gibbs free energy (γ) and equatorial axis for the Miller index [hkl] of the surfaces.

energies of all terminations. For discussion we use the (010) and (101) surfaces as examples, and each surface has three different terminations, e.g., the two Mo terminations and one carbon termination for the (010) surface and two Mo terminations and one Mo/C mixed termination for the (101) surface. These results are shown in Figure 5 and the results for other surfaces are given in the Supporting Information. At CH4/H2 = 1/4, Mo-ter-1 of (010) is the most stable at the temperature up to 1000 K, followed by Mo-ter-2, with the carbon termination being the least stable. It also shows that the stability of Mo-ter-1 decreases as the temperature rises, while the stability of the Mo/C mixed termination increases. However, under CO/ CO2 = 2/1 up to 1000 K, the carbon termination of (010) is most stable, followed by Mo-ter-2, with Mo-ter-1 being the least stable. Raising the temperature decreases the carbon termination stability and increases the Mo-ter-1 stability. Such trends have also been found for other surfaces as given in the Supporting Information. For (101) under CH4/H2, we found that Mo-ter-2 below 300 K has the smallest surface free energy and is therefore most stable. As the temperature rises, Mo-ter-2 stability decreases and Mo-ter-1 and the Mo/C mixed termination stabilities increase. At higher than 300 K, the Mo/C mixed termination becomes dominant with relative low surface free energy. At CO/CO2 up to 1000 K, however, the Mo/C mixed termination is most stable. As discussed above, the stability of the Mo termination is favored under CH4/H2, while the stability of the carbon-containing termination is favored under in CO/CO2. III. Relationship between Surface Free Energy and μC. Since the μC is the function of temperature and gas composition as revealed in Figure 4 and eqs 7 and 8, the change in the μC, to a certain extent, reflects the change of surrounding conditions of the β-Mo2C surface. It is therefore interesting to study the dependence of the surface stability on the μC. As shown in Figure 6, the surface stability of the terminations shows obvious changes within a broad range of the μC.

Figure 8. The Wulff shapes and proportion of surfaces areas of hexagonal Mo2C under different conditions: (a) for the shape at 0, 600, and 1000 K under CH4/H2 = 1/4 at 1 atm, and (b) for the shape at 0, 600, and 1000 K under CO/CO2 = 2/1 at 1 atm.

Figure 6 can be divided into different zones: zone a represents the change of the stability upon the μC change at CH4/H2 = 1/4; zone b represents the change of the stability upon the μC change at CO/CO2 = 2/1, both at 1 atm pressure. For comparison the black dotted line for the μC of graphite is given. In zone a, the surface stability presents conspicuous changes. At low μC, for example, the (001)-Mo termination is most stable, while the (101)-Mo/C mixed termination becomes most stable at high μC. The crossing point is at μC close to
10, where both terminations are possible. In zone b, the (101)-Mo/C mixed termination is most stable in the whole range of the μC. As shown in Figure 2 and the dotted line in Figure 6, the Mo/C mixed termination of (101) is most stable within a wide range of the μC. It is now interesting to compare the relative surface stability from DFT total energy and Gibbs free energy when the value of μC is the bulk energy of graphite. The surface stability has the decreasing order of (101) > (001) > (201) > (011) > (103) > (010) > (100) > (111) > (112) > (102) > (110) from Gibbs free energy (the orders along dotted line in Figure 6) and the decreasing order of (101) > (011) > (201) > (001) > (100) > (112) > (111) > (010) > (103) > (102) > (110) from DFT total energy (Figure 2). It shows that both methods do not give the same stability order; and this difference indicates that the thermal contributions to the surface free energy can not be simply neglected. IV. Surface Stability Order at Typical Temperatures. Since the μC has a close relationship to temperature, pressure, and gas mixture, we mainly discuss the stability of these surfaces at concerned temperatures under experiment conditions. For our analysis we 22366

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The Journal of Physical Chemistry C used the most stable termination of each facet. Here we mainly considered three sample temperatures, 0, 600, and 1000 K:. 0 K is the temperature applied in DFT calculation, 600 K stands for the reaction temperature (573 K) usually used in alcohol synthesis,50 and 1000 K is close to the upper limit of experimental carburization temperature from 573 to 1033 K.51 Since Mo2C cannot be synthesized at low temperature under experimental conditions, it is unreasonable to discuss the stability of Mo2C at 0 and 600 K, but our comparison can show the systematic changes upon the change of temperature. The most stable termination of each facet at the given temperature is taken to represent the corresponding surfaces, and the results are shown in Figure 7. Figure 7a shows the surface stability at three different temperatures under CH4/H2. At 0 K, the most stable surface is (001), which has been frequently used for studying the reaction mechanism of Mo2C. At 600 K, (001) still represents the most stable surface despite some obvious changes of other surfaces. At 1000 K, (101) has the lowest surface Gibbs free energy and becomes most stable. Indeed, this result is supported by the XRD data of βMo2C,52 which was synthesized under CH4/H2 gas environment at 973K. For example, a very strong peak of the (101) crystal plane was always observed, and the reported XRD intensity order of the surfaces is (101), (002), (100), (102), (103), and (110). Our calculated stability of the surfaces is (101), (001), (100), (102), (103), and (110), which was the same as the experimental results with the facet that the (002) surface is equal to (001). Figure 7b shows the surface stability at three different temperatures under CO/CO2, and the change is far less conspicuous in CO/CO2 than in CH4/H2. In the whole temperature range, (101) is most stable and much more stable than the other surfaces. V. Catalyst Surface Morphology. The surface Gibbs free energies as an indicator for surface stability provide the basis for analyzing the surface morphology on the basis of Wulff construction. Wulff shape possesses the lowest surface energy for a fixed volume and represents the ideal shape that the crystal would take in the absence of other constrains. More generally, Wulff shape is a polyhedron with faces corresponding to crystal planes low in energy. Therefore we perform Wulff constructions by applying the Wulffman53 module installed in Geomview54 to discuss the β-Mo2C morphology under different conditions. It also should be pointed out that the contribution of a crystal facet to exposed surface area depends not only on its surface energy but also on its orientation. Furthermore, the Wulff shape of the catalyst, constructed on the basis of the calculated surface free energies, provides an ideal shape of the catalyst morphology. As shown in Figure 8, the morphology of β-Mo2C presents some changes at different temperatures. Under CH4/H2 (Figure 8a) at 0 K six facets of β-Mo2C catalyst can exhibit; (101) has the largest surface ratio (33%), followed by (201) (22%), (001) (21%), (100) (13%), and (102) (10%). At 600 K, (101) has the largest surface ratio (35%), followed by (201) (32%), (001) (17%), and (102) (12%), while (100) disappears at 600 K. At 1000 K, (101) covers the largest surface ratio (83%), followed by (001) (13%). This indicates that at the typical carburization temperature (973 K) (101) represents the major ratio of the surface area of the β-Mo2C. Under CO/CO2 (Figure 8b), the (101) surface has the ratio to total surface area by more than 96%, while that of (001) is less than 4%. Therefore, the (101) facet represents the largest part of the surface area of the catalyst. At this stage it is interesting to compare our results with the available HRTEM images of β-Mo 2 C. As reported by Nagai et al,33 the clearly detected (101) and (002) surfaces with the crystal

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plane distance of 0.229 and 0.237 nm cover the catalyst surface (the morphology of the (002) surface corresponds to our (001) surface). These results are in perfect agreement with our calculations.

4. CONCLUSION Ab initio atomistic thermodynamic calculations were applied to study the stability of the β-Mo2C surfaces by comparing their surface free energies under different conditions It shows that carbon chemical potential (μC) is an important parameter to connect surface Gibbs free energies with surrounding environments (e.g., T, p, and gas compositions). The calculated results reveal that μC is more sensitive to the temperature than to the pressure and molar ratio of gas mixtures. Furthermore, the carbon source also strongly affects μC. With temperature increase, μC presents an uptrend under CH4/H2 gas phase and a downshift under CO/CO2 gas phase. As the surface Gibbs free energy is tightly related with μC, the changing of μC reflects the changing of surrounding conditions and further affects the stabilities of β-Mo2C surfaces. Taking CH4/H2 as carbon source, the (001) surface has the lowest surface energy at lower temperature, while the (101) plane becomes most stable at higher temperature. The calculated surface stability agrees perfectly with the experimentally determined XRD pattern and intensity. Taking CO/CO2 mixture as carbon source, the (101) surface is most stable along the whole range of μC and temperature. Since surface energy determines the orientation of crystal growth and affects the morphology of crystal, the equilibrium shape of β-Mo2C surface is determined by using the Wulff construction on the basis of our calculated surface free energies. With the increase of temperature, the equilibrium of the (101) surface increases, while that of (001) decreases. That the (101) facet represents the largest surface area of β-Mo2C is in perfect agreement with the HRTEM results. This change might explain the different activities of catalysts from different preparation methods. The studies of catalytic activities on some main surfaces are our ongoing interest and will be discussed elsewhere. ’ ASSOCIATED CONTENT

bS

Supporting Information. Computed surface free energy of all terminations at three typical temperatures (S1) as well as the relative stability of different terminations in corresponding surface at different temperatures (S2). This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by Chinese Academy of Science, National Basic Research Program of China (No. 2011CB201406), and Synfuels CHINA. Co., Ltd. ’ REFERENCES (1) Kumashiro, Y. Electric Refractory Materials, Marel Dekker: New York, 2000. 22367

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