Phosphorous Diffusion Through Ni2PâLow Energy Diffusion Path

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Phosphorous Diffusion Through NiP # Low Energy Diffusion Path and Its Unique Local Structure Jose L. Contreras-Mora, Hiroko Ariga-Miwa, Satoru Takakusagi, Christopher T Williams, and Kiyotaka Asakura J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12367 • Publication Date (Web): 23 Feb 2018 Downloaded from http://pubs.acs.org on March 3, 2018

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The Journal of Physical Chemistry

Phosphorous Diffusion Through Ni2P ― Low Energy Diffusion Path and its Unique Local Structure José Contreras-Mora 1,2, Hiroko Ariga-Miwa,1 Satoru Takakusagi1, Christopher T. Williams* 2, Kiyotaka Asakura* 1 1 2

Institute for Catalysis, Hokkaido University, Kita 21-10 Kita, Sapporo 001-0021, Japan Department of Chemical Engineering, University of South Carolina, Columbia 29208, SC, USA

* corresponding authors: [email protected], [email protected] Abstract Phosphorous (P) diffusion in bulk Ni2P was investigated by density functional theory (DFT) to find the origin of the low temperature P diffusion into the surface. The Ni2P bulk structure consists of two types of layers, Ni3P2 and Ni3P1, stacked along the [0001] direction. Two types of P vacancies in Ni2P were studied: VP1 (P deficient in N3P2), and VP2 (P deficient in N3P1). VP1 was a somewhat more stable point defect than VP2 by 0.20 eV. The P diffusions to vacancies (VP1 and VP2) had large diffusion barriers of more than 1 eV, except the P diffusion path along [0001] direction through an interstitial site in Ni3P1 (IP12) and then to VP1, which showed the lowest energy barrier of about 0.18 eV. The DFT calculations suggested that the two adjacent vacancies (both VP1) allow the local rearrangement of the structure to form a tetrahedral structure at the intermediate state. We have proposed a new diffusion mechanism in the intermetallic compound named interstitial–vacancy diffusion mechanism.

Introduction Ni2P is an intermetallic compound whose bonding has covalent, ionic and metallic character and shows unique properties especially in catalysis.

Over the past decade, the

catalysis of Ni2P has been investigated for a variety of industrially important reactions, including

hydrodesulfurization

(HDS)

1–7

,

hydrodenitrogenation

(HDN)

3,8

,

hydrodeoxygenation (HDO)9–11 and the electrocatalytic hydrogen evolution reaction (HER)

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12,13

. Although operando spectroscopies have provided information about the catalytic active

sites

1,6,14,15

, the detail structure and activity relation requires surface scientific investigation

using single crystal surfaces and surface science techniques such as XPS, LEED, STM and DFT 16–33. The Ni2P single crystal surfaces showed interesting features 33. The phosphoruspoor surface created by Argon sputtering recovers original Ni2P stoichiometry by diffusion of phosphorus at low temperature (450 K)

17

. Further high temperature annealing induced the

segregation of the phosphorus to produce a phosphorus-rich well-defined reconstructed surface

29–31,33

.

The surface-segregated phosphorus atom termination stabilizes the

reconstructed surfaces, which is related to the reduction of the density of state at the Fermi level by the P adsorption on the Ni dangling bond 29,31. The P segregation and the P diffusion to the surface occur from the bulk at relatively low temperature (~450 K). However, little is known about diffusion in bulk Ni2P. The diffusion of atoms through materials is mainly discussed in three mechanisms

34

:

interstitial, vacancy and interstitialcy mechanism. The interstitial mechanism requires a large diffusion barrier and occurs at the higher temperature. Vacancy model is the easiest way for the diffusion. However, in Ni2P, the simple vacancy model rarely occurs because the P vacancy is only surrounded by Ni atoms. In binary compounds, another vacancy diffusion process called the “six-jump cycle mechanism” has been proposed for vacancy diffusion (See Fig. S1c) 35,36. To understand the low temperature P diffusion in Ni2P, the diffusion process was investigated by density function theory (DFT) calculations. The present work provides a new insight on P low temperature diffusion where intermediate interstitial structure is stabilized by the local reconstruction to create tetrahedral structure around Ni atoms that reduces the activation energy tremendously.


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Computational Method The DFT calculations were performed using the Vienna ab initio Simulation Package code (VASP 5.4.1)

37,38

. The Perdew-Burke-Ernzerhof exchange-correlation functional with a

generalized gradient approximation was used

39,40

. Projector-augmented wave approach

41,42

has been used together with plane wave basis sets with a 4×4×4 k-points mesh Brillouin-zone integration to obtain the optimized structures and a 8×8×12 k-points mesh for the density of state (DOS) calculation. Spin-polarized calculations were performed for all the systems with an energy convergence tolerance of 1 × 10−8 eV/atom. The density of states for α and β spins did not show any differences, and thus the spin effect on diffusion was not discussed in this paper. The transition and intermediate steps were analyzed with the climbing-image nudgedelastic-band (cNEB) method 43. The optimized bulk Ni2P lattice constants were a = b = 0.589 nm, c = 0.337 nm, α= β = 90°, γ = 120°. These are consistent with the previous work (Table S2) 16,17,23. The unit cell was increased to a 2×2×3 supercell with a = b = 1.178 nm, c = 1.011 nm for the present studies. The formation energies for each structure are defined as:

Ni P = Ni P + P − Ni P

(1)

where Ni P , Ni P and P are the total energies for the super cell with a phosphorus vacancy, of the perfect Ni2P and a gas-phase P4 molecule, respectively. Results and Discussion (1) Stable Structures of P Vacancies The Ni2P crystal has a space group P62m 44. Figure 1a illustrates the Ni2P of (2 × 2 × 3) supercell. Two types of layers are alternatively stacked along the [0001] direction; one is called as “Ni3P2 layer” (Figure 1b) and the other is “Ni3P1 layer” (Figure 1c). coordinates of all atoms are listed in Table S1 in the supporting information.


The

A set of


Page 4 of 17

different Ni and P sites in each layer are named Ni (1) and P (1) (blue and pink spheres in Fig. 1b) for the Ni3P2 layer and Ni (2) and P (2) (green and orange spheres in Fig. 1c) for the Ni3P1 layer. Nickel atoms in the Ni3P1 and Ni3P2 layers have different local structures. Ni (1) in Ni3P2 layer has a near-tetrahedral P coordination while Ni (2) in Ni3P1 has a square-base pyramidal P coordination, as shown in Figs. 1b and c. The Ni-P distances in crystallographic data were well reproduced by DFT calculations shown in Table S3.

Since sputtering

selectively removes P 17, the discussion in this paper is only about P vacancy and P diffusion. There are two types of P vacancies in Ni2P: VP1 (P (1) deficient, pink dotted circle in Figure 1d) and VP2 (P (2) deficient, orange dotted circle in Figure 1e). The formation energies in Table 1 show that the VP1 was energetically more favorable than VP2 by 0.20 eV. The local structures of the perfect Ni2P structure and vacancies (VP1, VP2) are shown in Figure 1f, 1g and 1h, respectively. Numbers at subscripts were given to identify the different Ni and P sites, while the number in parentheses indicated the different types of Ni and P in Ni3P2 and Ni3P1 layers. Removal of the P20 (1) atom generates the vacancy, VP1, as shown in Figure 1g. Figure S2 shows the displacement directions of the Ni atoms around the vacancy. The vacancy was surrounded by 9 Ni atoms. The three Ni in the lower Ni3P1 (in this case Ni16,17,18 (2)) and the three Ni atoms in the upper Ni3P layer (Ni40,41,42 (2)) moved away from the vacancy VP1, as shown in Figure S2. The three Ni atoms in the same plane (Ni3P2; Ni37,38,39 (1)) also moved away from the VP1, although only a small degree. Interestingly, Ni (2) atoms around the VP1 which originally had the square-base pyramid geometry became a near-tetrahedral (tetrahedrality was 0.028 discussed later). In contrast, the VP2 (Figure 1h) that is created by the lack of P (2) showed smaller displacements than 0.1 Å of the Ni (2) (the same layer) or Ni (1) in adjacent layers (Table S4). The most significant displacement was the Ni40 (2) where Ni40 (2)-P (1) distances reduced to 2.42 Å from 2.47 Å.


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(2) In-plane Diffusion First, we considered the in-plane diffusion of P. The intermediate states of P diffusion to the VP1 or VP2 were denoted as IP11 and IP22, shown in Figures 2a and 2b, respectively, which corresponded to the interstitial sites surrounded by Ni atoms. Red balls in these figures are diffusing P atoms which are denoted as P (1’) and P (2’) hereafter. The IP11 and IP22 were unstable with a relative energy of 1.81 eV and 3.08 eV, respectively. Since the relative energies are so high, in-plane diffusions are less likely. The shortest distances between the diffusing P and the surrounding P atoms in the intermediate states are 3.20 Å and 2.41 Å for IP11 and IP22, respectively, which are smaller than the sum of van der Waals radius and result in the large diffusion barrier.

Other P-P distances (dpp) are summarized in the

supporting information (Table S5). (3) Inter-plane Diffusion Three phosphorus inter-plane (or interlayer) diffusion paths between P (1) and P (2) were considered for this work. One type of interlayer diffusion path is the P vertical diffusion along [0001] direction from P (1) and P (2) site to another corresponding P site, denoted as IP12 and IP21, respectively. The energy difference between the initial state VP2 and the intermediate state IP21 is 4.86 eV, in which the P (2) diffuses through a P-rich Ni3P2 layer. Here, the diffusing P (2’) interacts repulsively with the surrounding P (1) atoms in Ni3P2 layer at the intermediate IP21 step, where the dpp was found at 2.70 Å. In contrast, the energy difference was 0.18 eV for the diffusion from P (1) to the intermediate state IP12, where the shortest dpp was 3.41 Å. We calculated the energy change along the diffusion path through the IP12 using the cNEB method as shown in Figure 2g. The Roman numbers in Figure 2g correspond to the P pathway in IP12 (Roman numbers) in



of Figure S1. The diffusion barrier between IP12 and VP1 was a little more than 0.18 eV, indicating the easy diffusion path of the P (1). Another type of inter-plane diffusion was the P (2) diffusing to the VP1. The transition state (TSP21) as shown in Figure 2f was calculated by cNEB method because it was difficult to determine the intermediate structure. The details of the diffusion pathway were illustrated in Figure S1, corresponding to the Arabic numbers (1-6) in Figure 2g. Figure 2f shows the TSP21 where the P24 (2’) diffused to an interstitial site in Ni3P1 layer and then diffuses to VP1, and creating a new VP2. During the P24 (2’) diffusion, local structures were modified, especially, with a drastic displacement of P32 (1) varying the P32 (1)-Ni40 (2) distance from 2.47 Å to 3.40 Å at TSP21, indicating the breaking of the bond as shown in Figure 2f. More details can be seen in Figure S2d. The energy barrier for the diffusion path is 1.81 eV as shown in Table 1. (4) Six-jump Cycles Diffusion Pathway The six-jump cycles diffusion pathway was considered as a possible mechanism for the diffusion of intermetallic compounds as shown in Fig.S1. First, VP1 or VP2 was filled with Ni instead of P, and the energy of Ni at VP1 or VP2 was low. However, the second step hardly occurred where Ni vacancy was filled with P. The P surrounded by 8 P atoms was quite unstable and its structures were unrealistic, therefore, the six-jump cycles mechanism was ruled out as the diffusion pathway in Ni2P. (5) Intermediate Structure of IP12 and Easy Diffusion Path Here we discuss the high stability of the intermediate structure IP12 where the diffusing P32 (1) (P32 (1’) for simplicity) is in between two vacancies. In the IP12 structure, we found Ni40 (2) to form a new tetrahedral geometry during the P32 (1’) diffusion. The Ni40 (2)-P32 (1’)


Page 6 of 17

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distance was 2.17 Å, Ni40 (2)-P13 (1) and Ni40 (2)-P25 (1) decreased by 0.20 Å to be 2.17 Å and Ni40 (2)-P24 (2) remained the same distance (2.34 Å). The most considerable change in dpp is found with P13 (1)-P25 (1) and P13 (1)-P9 (2) in which the distance increases by about 0.44 Å and decreases about 0.10 Å, respectively, from the original structure.

We calculated the tetrahedrality defined as

=

!" # %$

$

(2)

where &' and & ̅ are the i-th edge of tetragon and the average tetrahedral. T=0.18 when it is square planar.

45

. T=0 when it is perfect

The original Ni (1) had a near-tetrahedral

structure that gave the tetrahedrality as 0.0067.

When VP1 was created, the Ni40 (2) was

surrounded by 4 P atoms and its tetrahedrality was 0.028.

The tetrahedrality of Ni40 (2) in

the IP12 was 0.0046, therefore the tetrahedrality increased compared to the original Ni (1) near-tetrahedral structure. The original lattice positions of P25 (1) and P13 (1) made it possible for Ni40 (2) to form the tetrahedral coordination. was 0.0077 in the IP12. with 0.0046.

In addition, the tetrahedrality of Ni37 (1)

Ni41 (2) and Ni42 (2) had the same tetrahedrality as that of Ni40 (2)

The rearrangement to tetrahedral local structures might be responsible of

making the IP12 the most favorable diffusion path. Local DOS (LDOS) and electron distributions were calculated in the tetrahedral local structure of the IP12. Figure 3a shows a total DOS of the IP12. The DOS from -0.6 to -4 eV were mostly composed of a Ni-Ni 3d band bonding (Figure S3). The states of P3p and Ni3d from around -5 to -9 eV are mostly derived from the Ni-P bonds. Projected LDOS of P32(1’) p orbital and Ni40 (2) d orbital in the IP12 structure both have a bonding state at -4.7 eV. The energy indicates the Ni-P bonding in the IP12 structure is as stable as the Ni-P bonds in the perfect structure. Figure 3b shows an electron density distribution around Ni40 in the IP12 in the energy around -4.7 eV which indicates the formation of 4 Ni-P bonds in the tetrahedron.



The bond state around P32 (1’) is surrounded by 3 Ni (2) and making bonds with 3 Ni atoms illustrated in Figure 3c.

In addition, the anti-bonding state of Ni40 (2) and P32 (1’) exist

higher than -0.6 eV (Figure 3 and S4). The present diffusion path is a combination of interstitial and vacancy diffusion mechanism, and thus is designated as the interstitial-vacancy diffusion mechanism. First, a P diffuses from a lattice site to an interstitial site, when a vacancy VP1 exists in another Ni3P2 layer. Moreover, the IP12 is largely stabilized because of the tetrahedral geometry formation. Our results showed the characteristic low diffusion barrier (about 0.18 eV) of the P in the interstitial-vacancy model. We have revealed an easy diffusion path of P vacancy along the [0001] direction. The diffusion process was accompanied by the local structure change to a tetrahedral arrangement. It has been shown that the Ni2P (0001) surface is stabilized by P termination that forms tetrahedral coordination around the Ni 30. Conclusion We compared the stability of two types of vacancies and found that VP1 in the Ni3P2 layer was the most stable. When analyzing the different kinds of intermediate diffusion steps, IP12 was the most favorable step studied, with a diffusion barrier of only 0.18 eV. Such a low barrier could explain the low temperature recovery of surface P concentration by the diffusion of P from the bulk

17,30

observed in experiments. It was found that the type of

diffusion mechanism taking place was an interstitial-vacancy diffusion mechanism, since a vacancy (VP1) was needed for the P to diffuse to an interstitial site and then to a lattice site. The low diffusion barrier and stability of the intermediate step structure seemed to be due to the reconstruction of the local structures into tetrahedral geometries. When the geometrical


Page 8 of 17

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reconstruction took place in IP21, the combination of the vacancies and P diffusion helped the Ni-P bonding to become dominant.

Supporting information The coordinates derived from DFT calculations in the perfect crystal (Table S1), lattice parameter comparison (Table S2), calculated and experimental distances of Ni-P and P-P (Table S3), displacements of Ni from the calculated perfect structure (Table S4), P-P distances in I

P 11,

P

I

22

intermediate structure (Table S5), some diffusion pathways (Figure S1),

the Ni2P structure and displacement during the diffusion process (Figure S2), partial density of states (PDOS) for a) Ni and b) P (Figure S3).

Acknowledgments The travel and living expenses for J.C.M. in Japan were supported by NSF IGERT Fellowship (DGE-1250052). J.C.M. and C.T.W. gratefully acknowledge the Institute for Catalysis (ICAT) International Collaboration Program. The work was financially supported by CREST JST “Resolution Catalyst” and JSPS Grant-in-Aid for Scientiﬁc Research (Category S, No.16106010).



Page 10 of 17

Ni37(1)

Ni40(2)

Figure 1: Ni2P Structure: a) supercell containing 72 Ni and 36 P atoms, b) Ni3P2 layer with tetrahedral structure, c) Ni3P layer with square-base pyramid, d) vacancy in Ni3P2 layer and e) Ni3P layer. Local structure with the P P corresponding P and Ni for: f) Perfect structure,g) V 1, h) V 2. Diffused P is in red, Ni3P2 and Ni3P vacancies are in pink and orange doted circles, respectively.


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Table 1: Defect formation energy and relative energy barrier for structures

Name

Formation energy/ eV

Relative energy / eV

P

1.25

-

1.45

0.20

3.06

1.81

4.33

3.08

1.43

0.18

6.31

5.06

3.06

1.81

V

1

P

V

2

P

I

11

P

I

22

P

I

12

P

I

21 P

TS

21



),*→* − -,* = 1.81 12

Page 12 of 17

),$→$ − -,* = 3.08 12

),*→$ − -,* = 0.1812

),$→* − -,* = 5.06 12

67,$→* − -,* = 1.81 12

Figure 2: a) Intermediate state P diffusion in Ni3P2, b) intermediate state P diffusion in Ni3P, c) intermediate state P diffusion from Ni3P2 to Ni3P, d) intermediate state P diffusion from Ni3P to Ni3P2. Diffused P is in red, Ni3P2 and Ni3P vacancies are in pink and orange doted circles, respectively. Local structure with the corresponding P and Ni for: e) P P P P P I 12, f) TS 21 and g) cNEB diffusion energy barrier for TS 21 and I 12 (with a zoom in of the I 12). Arabic numbers P P represent the points and diffusion path of TS 21, Roman number indicates the points and diffusion path of I 12 (see Fig S1). Energies of intermediate states were given in the Figure 2a-d.


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P

Figure 3: (a) Total DOS for the I 1 2 and LDOS for the d orbital of Ni40 (2) and p orbital of P32(1’). (b) 3D representation of electron density around Ni40 for Ni-P bonding region (-4 to -8 eV) for the IP12 structure, which show tetrahedral coordination. (c) 2D slice of (b) parallel to (0001) plane including Ni40. Red circles represent the diffusing P.



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(3) (4) (5) (6)

(7)

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Phosphorous Diffusion Through Ni2PâLow Energy Diffusion Path

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