Adsorption of N2 and H2 at AlN(0001) Surface - ACS Publications

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Adsorption of N2 and H2 at AlN(0001) Surface: Ab Initio Assessment of the Initial Stage of Ammonia Catalytic Synthesis Pawel Strak, Konrad Sakowski, Pawel Kempisty, Izabella Grzegory, and Stanislaw Krukowski J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05009 • Publication Date (Web): 10 Aug 2018 Downloaded from http://pubs.acs.org on August 13, 2018

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The Journal of Physical Chemistry

Adsorption of N2 and H2 at AlN(0001) Surface: Ab Initio Assessment of the Initial Stage of Ammonia Catalytic Synthesis Pawel Strak, Konrad Sakowski, Pawel Kempisty, Izabella Grzegory, Stanislaw Krukowski* Institute of High Pressure Physics, Polish Academy of Sciences, Sokolowska 29/37, 01-142 Warsaw, Poland, ABSTRACT Adsorption of molecular nitrogen and molecular hydrogen at Al-terminated AlN(0001) surface was investigated using ab initio simulation methods. It was shown that both species undergo dissociation during attachment to the surface, i.e. the adsorption is dissociative. Despite high bonding energies of both molecules, the dissociative adsorption is energetically highly favorable. In addition, both processes have negligible, close to zero, energy barriers. The adsorption sites were identified for both H and N adatoms. High adsorption energy is related to contribution from electron donation by partially occupied Al broken bond state. The electron contribution terminates at the coverage equal to ¼ and ¾ monolayers (ML) for N and H, respectively. This is in accordance with the extended electron counting rule (EECR). Thus the electron charge transfer role in ammonia catalysis at the surface is elucidated. Further, as shown by ab initio calculations, the adsorbed species may react creating N-H radicals, and the ammonia admolecules which desorbs from the surface. The ab initio modelling provides indication that AlN(0001) is powerful catalyst for high pressure – high temperature synthesis of ammonia, indicating that AlN may be a candidate for industrial applications in ammonia synthesis.

* Corresponding author. Email: [email protected]

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INTRODUCTION. Platinum as ammonia synthesis catalyst was invented by Fritz Haber more than a century 1

ago. The invention was honored by the Nobel Prize in Chemistry, awarded to Haber in 1919.2 Soon it was realized by Haber and his coworkers that iron also may be a good candidate for effective catalysis in the ammonia synthesis. Later on, the significant contribution to development of the iron-based catalysts were made by Haber’s assistant Alwin Mittasch. Working with Swedish-produced Gallivare magnetite iron he discovered the optimal composition of the catalyst, based on fused iron with small addition of alumina, calcium oxide and potassium.3 Subsequently, industrial synthesis was implemented by Carl Bosch, the achievement that earned him Nobel Prize in Chemistry in 1931.4 Much more later, the other, metal based catalysts were developed, including cobalt and ruthenium or osmium containing catalysts developed in seventies,5,6 and nineties7-9 , respectively. Significant

improvement brought use of combined ruthenium-

molybdenum catalyst, developed recently.10-12 A new step in this direction towards the use of a combined catalyst was to study barium hydride (BaH2) – molybdenum (Mo) - carbon nanotubes (CNT) catalysts that showed promising characteristics, both in terms of the energy savings and the temperature.13 Also ruthenium nanoparticles combined with calcium amide or electride may facilitate synthesis.14,15 According to Robert Schlogl in prophetically entitled paper, “Catalytic Synthesis of Ammonia - a Never-Ending Story?”, the ammonia research continues.16 Generally, the invention of ammonia catalytic synthetic reaction is one of the greatest achievements of the chemical sciences, in terms of the scientific value and of beneficial contribution to the mankind.1 The discovery paved the way to famine reduction on the global scale. In addition, the synthesis of nitrogen compounds is important for other industry branches, including fabrication of plastic materials or explosives.1 The success story of the ammonia synthesis has his own price. The synthesis is energy and hydrogen consuming. Even at small facilitation of the process, the scale of the gains in the production, and also reduction of the costs is enormous. That is why, after a century, the search of better, more effective catalysts is still very active. The investigations brought significant progress in terms of the pressure used for synthesis which dropped from original 100 MPa to 10-15 MPa. Simultaneously, the energy spending was reduced from 78 GJ to 27.2 GJ, fairly close to theoretical limit of 20.1 GJ.17


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The quest for better catalyst was significantly changed from original Mittasch thousands of trials method to advanced surface investigations based on molecular scattering or ab initio simulations. The experiments of Ertl and Somorjai greatly enhanced understanding of surface reaction pathways and prediction of transition states controlling the reaction rates.18-24 These contribution were fundamental to general understanding of the surface reactions for which Gerhard Ertl was awarded Nobel Prize in Chemistry in 2007.25 A different approach was inaugurated by Norskov with the collaborators, who applied ab intio calculations to surface reaction pathways.26-31 Using ab initio data they proposed interpolation in the periodic table to create an alloy consisting of the elements very active and very inactive with nitrogen to create very active surface of the optimal performance. This assumption proved to be very fruitful as showed by Co-Mo catalysts, being more effective than ruthenium or osmium catalysts.29-31 A comparative ab initio study of activity of metal catalysts was undertaken recently showing distinctively different temporal behavior of metal wool catalysts: Pt, Pd, Ag, Cu and Ni increased their activity while Au, Fe, Mo, Ti, W and Al remained constant.33 The difference was attributed to initial nitridation of metal surface and creation of Me3N units at the surface.29 This path is presently used in the search of the possible new family of ammonia synthesis catalysts. First, the catalyzing surface has to be effective in decomposition of molecular nitrogen as preliminary, most difficult step in ammonia synthesis.28 The bonding energy of nitrogen molecule, equal to 9.76 eV (941.636 ± 0.60 kJ/mole),34 is the highest of all diatomic molecules, therefore the catalytic influence has to be exceptionally strong. In this respect, aluminum nitride is one of the best candidates, as it was shown recently. The energy gain in dissociative adsorption of N2 molecule at clean AlN(0001) surface is about 6 eV,35 much higher than for any metal catalysts.36 The N adatoms are located at H3 sites at AlN(0001) surface. The energy gain remain almost unchanged up to the critical θN = 0.25 ML coverage. For higher coverages nitrogen is adsorbed molecularly with small energy gain of about 1 eV, not suitable for ammonia synthesis. As identified relatively early, dissociation of N2 molecule is rate limiting step of ammonia synthesis.37-39 In contrast to the typical pattern, where the considerable energy barrier is encountered,36 the adsorption of molecular nitrogen at Al surface is barrier-free.35 The semiconductor surfaces are generally very active. They catch any species from the vapor, most frequently oxy-


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gen or water. In consequence of oxidation they become inactivated. Aluminum nitride has the largest bonding energy of all nitrides, it is exceptionally hard, capable to withstand most harsh conditions, far superior to any refractory metals. In addition, the oxidized AlN(0001) surface could be reactivated by nitridation in ammonia flow at 1000°C. The opposite, nitrogen terminated AlN(0001) surface is less resistant to etching by hydrogen or atomic nitrogen, therefore it is not suitable for long high temperature synthesis process and it is not considered in this paper. Thus the AlN(0001) surface is an excellent candidate for the ammonia synthesis catalyst. Based on these findings, the patent for use of AlN as catalysts for ammonia synthesis was submitted to the patent office.40 Thus the method is legally protected at the moment. Application of aluminum nitride as perspective catalyst is also related well to known use of sapphire (Al2O3) as substrate for growth of AlN and GaN based devices. Sapphire crystals are nitrided in ammonia flow, in temperature close to 1000°C.41 In the result, the AlN layer is obtained, indicating that Al-O bonds and oxygen can be removed. Thus, the poisoning of the catalyst by oxygen can be avoided and the catalysts could be regenerated. Finally, the additional steps should lead to creation and desorption of ammonia molecule, or suitable radicals. The question is whether presence of hydrogen leads to creation of chemical species favoring detachment of ammonia molecules, or ammonia building block such NH or NH2 radicals. As possible indication can be drawn from parallel investigations of the properties of GaN(0001) surface in ammonia ambient. As it was shown, at high pressures, the dominant role is played by NH2 radicals and NH3 admolecules that could be detached from the surface.,42,43 Thus a possible path exists, and the present publication is devoted to elucidation of thermodynamic and kinetic aspects of the reaction using recently formulated determination procedure of the equilibrium pressures at semiconductor surfaces.44

CALCULATION METHODS A freely-accessible ab initio code SIESTA, based on density functional theory (DFT) formalism, was used in the reported calculations.45,46 The solution procedure used in GGA calculations employs norm conserving pseudopotentials, in the determination of the wavefunction approximations as a finite combinations of local basis functions. The norm-conserving Troullier-


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Martins pseudopotentials, in the Kleinmann-Bylander factorized form47,48 for Al, H and N atoms were generated using ATOM program provided by the authors of SIESTA code. The atomic basis sets are: Al - 3s: DZ (double zeta), 3p: TZ, 3d DZ; N - 2s: DZ, 2p: TZ, 3d: SZ and H (real plus termination atoms) 1s: TZ, 2s DZ, 2p: SZ. The exchange-correlation functional was adopted in revised modification of Perdew, Burke and Ernzerhof (PBE)49,50 functional for solids and surfaces (PBEsol).51,52 A convergence criterion for the termination of the self consistent field (SCF) loop was that the maximum difference between the output and the input of each element of the density matrix was to be equal or smaller than 10-4. Relaxation of the atomic position was terminated when the force acting on any atom becomes smaller than 0.005 eV/Å. The ab initio lattice parameters of bulk AlN were: aAlN = 3.116 Å and cAlN = 4.97 Å, reasonably not far from the experimental values: aAlN = 3.111 Å and cAlN = 4.981 Å.53 The reaction path was determined using Born-Oppenheimer approximation employing nudged elastic band (NEB) method.54-56 In the present formulation NEB module of Atomistic Simulation Environment57 was linked to SIESTA package paving the way to fast determination of the energy and conformation of the species along the optimized pathways. Doping simulation was conducted by adding a charge density with SIESTA native routine that determines the charge of the system, and adds a compensating uniform background charge that makes the system neutral. The surface is represented by (4 x 4) AlN slab of the thickness of 8 Al-N double atomic layers (DALs). The periodic boundary conditions are enforced in the plane parallel to the surface. The thickness of the slab is sufficient to avoid the significant overlap of wavefunctions of the atoms on both surfaces of the slab: the real and termination one. The broken bonds at the opposite side of the slab were saturated by fractional (Z = 0.75) charge hydrogen atoms. This construction is sufficient to remove most drastic effect related to the arbitrary termination of the solid body. RESULTS. Properties of clean AlN(0001) surface.


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Since the properties of clean AlN(0001) surface were already determined, they are only mentioned here.35 According to the ab initio simulations, the clean AlN(0001) surface undergoes no reconstruction. The Fermi level at AlN(0001) surface is pinned by a highly dispersive Al broken bond surface state of the energy located below conduction band minimum (CBM). The surface electric neutrality energy level is located about 0.4 eV below CBM.58 AlN(0001) surface under H coverage

In ammonia synthesis the molecular nitrogen (N2) and the molecular hydrogen (H2) are used. Therefore, hydrogen coverage of AlN(0001) surface is important in the context of catalysis of NH3 synthesis. In recent period, hydrogen coverage of similar GaN(0001) surface was intensively investigated.43,59 As it was shown, hydrogen is adsorbed dissociatively at GaN(0001) surface with the adsorption energy equal to 2.24 eV/molecule and -2.38 eV/molecule for θH ≤ 0.75 ML and θH ≥ 0.75 ML, respectively.43 The difference stems from the jump of the Fermi level which is pinned at Ga-broken bond state and at valence band maximum for low and high hydrogen coverage of the surface, respectively. At low coverage, transitions of electron from Ga broken bond state contribute to adsorption energy. The effect is absent for high coverage as, according to extended electron counting rule (EECR), all Ga broken bond states are empty.42 Therefore the energy gain for adsorption at high coverage is negative, i.e. the hydrogen at the surface is unstable. Similar analysis is made here for adsorption of hydrogen at clean AlN (0001) surface. Similarly to GaN(0001) surface, as it is shown in Figure 1, the configuration of hydrogen at AlN(0001) surface depends on the coverage: for low coverage, θH ≤ 0.75 ML the hydrogen molecules dissociates upon adsorption that leads to H atom localization in the site on-top of Al surface atom. For higher coverage (above 0.75 ML), the adatom configuration is energetically unstable, hydrogen is attached in the molecular form. The H2 admolecule is located on-top of the Al surface atom, oriented parallel to the surface.


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Figure 1. Energetically stable configuration of hydrogen at AlN(0001) surface: (a) – at 1/16 ML (top view), (b) – at 15/16 ML (top view) and (c) – at 15/16ML (side view) coverage. The surface is represented by (4 x 4) AlN slab of the thickness of 8 Al-N double atomic layers (DALs). In order to saturate broken hydrogen atom bonds at the bottom, hydrogen pseudo-atoms are attached


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of the Z = ¾ fractional charge. Al, N, H atoms and H pseudoatoms are denoted by yellow, blue, small cyan and small green balls, respectively.

It will be shown below that the Fermi level position plays decisive role in the configuration of the H adatom at AlN(0001) surface. In order to illustrate this influence the band diagrams for AlN(0001) surface under various coverage are plotted in Figure 2, creating the basis for electron counting rule (ECR) analysis.


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Figure 2. Electronic properties of a 4 x 4 slab representing an AlN(0001) surface under various H coverage: dispersion relations (left), space alignment of the bands derived from atom projected density of states (P-DOS) on the row of atoms (middle), and DOS, total - solid line and projected on H adatom and H pseudoatom– dashed and dotted line, respectively (right). The diagrams present a slab and: (a) single H adatom, i.e. θΗ = 0.0625 ML (b) 12 H adatoms, i.e. θ H = 0.75 ML ; (c) 14 H adatoms i.e. θ H = 0.875 ML. The red lines in the band dispersion diagram indicate the H-Al bonding states.

From Figure 2 it follows that the H-Al bonding state is located about 0.5 eV above valence band maximum (VBM). The state is fully occupied for low hydrogen coverage as long as the Fermi level is pinned by Al broken bond state. For very high H coverage, the Al broken bond is empty, the Fermi level is pinned by H-Al bonding state. Therefore it is interesting to determine at which H coverage the transition takes place. In standard electron counting rule (ECR) analysis,60 the Al broken bond state contributes ¾ electrons and the hydrogen adatom single electron.42 The critical H adatom concentrations may be deduced using the recently formulated extended electron counting rule (EECR) for adsorbed species.42 In this formulation, for the Fermi level not pinned at the surface, the EECR condition requires the number of electrons donated by hydrogen adatoms and broken bond states (left side of Eq. 1) to be equal to the number of electrons occupying the quantum states. The concentration of the Al top atoms with no H adatoms is denoted by β. Denoting a normalized concentration of H adatoms by α, the following charge balance is obtained:

1 + + = 2 + 0

(1a)

where it is accounted that the two electrons occupy H-Al states and the Al broken bond state is empty. This condition has to be supplemented by normalization condition: + =1

(1b)

which gives the following solution: = = and = . The solution describes the state of the surface in which the Fermi level is not pinned, it is located in the gap between Al broken bond state and Al-H state. For coverage lower than specified above, the Fermi level is pinned by Al


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broken bond state, for higher it is pinned by Al-H bonding state. As it may be verified from Figure 2, the ab initio data confirm the EECR predictions. The electron donation effect is visible in the molecular adsorption energy, presented in Figure 3. As it is shown the H2 adsorption energy is approximately equal to 2.60 eV. The energy

is almost constant for coverage , with slight fluctuations which are related to the ad sorbate configurational contributions. It does not depend on the doping in the bulk. In the vicinity

of the critical coverage = , the adsorption energy depends on the doping in the bulk.61,52 This is consistent with the electron donation scenario, as in the case of Fermi level not pinned the transition is from Fermi level, i.e. depends on the doping in the bulk.


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Figure 3. Molecular hydrogen adsorption energy at AlN(0001) surface in function of hydrogen coverage. The two regimes are clearly identified: for low coverage the atomic configuration is stable. For very high coverage, molecular hydrogen has lower energy.

For higher coverage the energy gain is sharply reduced so that it becomes negative. Thus overall configuration of separate atom is not stable. As it turned out, the more stable configuration is H2 admolecule attached to the AlN(0001) surface which is 0.58 eV lower than the molecule at far distance from the surface. Thus the stability order is as follows: the most stable is molecule attached at the surface, then molecule in the vapor, and the least stable are atoms attached at the surface. From Figure 3 the hydrogen equilibrium pressure could be obtained. The formalism was derived in Ref. 44 in which the chemical potential equality was used to derive the equilibrium pressure as:

= = −∆

3

3

123 + ∆!"#$% + ∆&'(!"#$% + &$#) + ∆&*+,- . = −∆/0#) −

47 5 − 5) 6 + + ∆8) + 43 8 − 8) 6 + 4 9) 6: − 2 θ /1 − θ

(2)

( is Boltzmann constant) where these terms describe: •

the vaporization enthalpy ∆

123 = ∆/0#) assumed to be equal to the energy of desorp-

tion determined from ab initio calculations, •

thermal enthalpy difference in the range between 0K and To = 25°C = 298.15 K 3

: ∆!"#$% = 47 5 − 5) 6, where 5 and 5) denote specific heat at constant pressure in the vapor and at the surface, respectively, •

3

the entropy related free energy difference ∆&'(!"#$% = + ∆8) + 43 8 − 8) 6, where

first term is related to vaporization entropy at standard state of substance used in thermodynamics and the second is analogous entropy difference temperature integral, •

the pressure dependent term usually &$#) = 4 9) 6:, where 9) is the volume at the sur

face, is small and will be neglected here,

44


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•

the configurational contribution, calculated for the adsorbed gas only: ∆&*+,- =

−2 θ /1 − θ .

The specific heat and the entropy could be obtained directly from ab initio phonon calculations using the following formulae: 5>? = ∑F A

ABC #ADAB E

C

#ADAB E(.

B G>? = ∑F H − 1 − IJ:D−JF E.K #ADA E(

where JF =

ħωB

MN 3

B

(3a)

(3b)

and ħ, kB and ωj are the reduced Planck constant, the Boltzmann constant and the

frequency of j-th mode of vibration, respectively. The specific heat obtained for the clean slab and the slab with the hydrogen adatom attached is presented in Figure 4.


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Figure 4. Specific heat of AlN(0001) slab, clean (red dashed line), and the slab with the attached H adatom (blue dashed line). The solid lines represent approximations for To < 298.15 K: magenta – clean slab, cyan – the slab with H adatom.

In the low temperature interval, the ab initio calculated temperature dependence was approximated by the following relations (in eV/K): i/ for clean slab 5>? =

O.7Q×7ST USV 3 V

(4a)

O.QZ×7ST USV 3 V

(4b)

X X Q.QW7.77US YC 3 YC

ii/ for the slab with attached H atom 5>? =

X X O.[W7.77US YC 3 YC

Finally, for the ideal hydrogen vapor, a weakly temperature-dependent heat capacity is approximated by parabolic function: 5 [ = 2.92 × 10( + 1.31 × 10(Z ^ ( + 8.96 × 10([ ^ ([ [

(4c)

Using these expressions the thermal enthalpy difference in the range between 0K and To = 25°C 3

= 298.15 K : ∆!"#$% = 47 5 − 5) 6 can be obtained by direct integration. The result is:

∆!"#$% = −0.203Ia. Thus this contribution is not large as it was already noticed.44

The second contribution stems from the entropy related free energy difference, equal to 3

∆&'(!"#$% = −+ ∆8) − 43 8 − 8) 6

(5)

where the first term is related to vaporization entropy at standard state used in thermodynamics and the second is entropy temperature integral. The vaporization entropy at normal conditions will be calculated using the formalism developed earlier, expressing entropy change for the vaporization reaction


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8 ↔

C

(6)

[

for single hydrogen atom in the vapor as:59

∆8) = 2 c d[ρe − 1g − [ρe d1 − ρ

ρ

f

f

[ρf

ρe

g + 2h

(7)

The vaporization entropy has to be scaled with the volume associated with the adsorbed atom. The volume associated with pair of Al-N atoms in AlN lattice is VAlN = 20.915 Å3. Assuming that the area is the same, the volume associated by pair of hydrogen atoms is the volume associated with the AlN atom pair scaled by the bond length which is equal to 1.91 Å and 1.62 Å for Al-N and Al-H respectively. Therefore the volume associated to a pair of H adatoms is:

ρ)( [ =

ρeSijk 0ijSk 0ijSl

=

0ijSk

mijk 0ijSl

(8)

which gives the adsorbate density of H2 ρ)( [ = 5.6 × 10([ Å( . This has to be compared with

the density of H2 vapor at normal conditions, that is ρ( [ = 2.69 × 10(O Å( . Substituting this

density ratio in Eq. 7 gives the vaporization entropy for single hydrogen atom: ∆8) = 17.30 Iq,

i.e. ∆8) = 1.49 × 10( Ia/^. This is the reference value for the entropy at normal conditions,

from which the entropy change is obtained for higher temperatures, as presented in Figure 5.


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Figure 5. Adsorbate- vapor entropy difference for a single hydrogen adatom at AlN(0001) surface in function of the temperature. Solid blue line represents the data obtained from Eq. 3b, the broken line is an approximation (Eq. 9).

The entropy change obtained from ab initio calculations via Eq. 3b are approximated by the following relation

∆8) = 8)s

?

+ 8 − 8)s

?(

= G1 +

'[√3

'W'3

(9)

where G1 = 2.88 × 10( Ia/^, G2 = −4.33 × 10( Ia/^ /[, G3 = 1.28 × 10 and G4 =

12.24^ ( . The approximation is consistent with the vaporization entropy value obtained from


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Eq. 8, i.e. ∆8) = 1.49 × 10( Ia/^ at To = 298.16K. The entropy related free energy change may be obtained via direct integration: 3

∆&'(!"#$% = + ∆8) + + 43 ∆8) 6 = 0.455Ia + u − u+

(10a)

where u = G1 ∗ +

['[ '

'

'3

w√ − x' y zx ' {|

(10b)

that allows to calculate the entropy related free energy change for any temperature. Finally, the vaporization enthalpy have to be calculated as the adsorption energy, including zero point vibrational energy, according to the formula:

∆

123 123 = ∆/0#) + ∆/}~ = ∆/0#) + /}~()s

?(

− /}~()s

?

− [ /}~( [

(11)

The equilibrium pressure determined according to the following formula: : = :+

∆ f W∆ W∆S θl [ IJ: (θl MN 3

(12)

is presented in Figure 6. The reference pressure po = 1 bar. From the above calculations it follow that very low pressure, below 10-6 bar is sufficient to attain the coverage close to 0.7 ML. The higher coverage require much higher pressures.


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Figure 6. Equilibrium pressure of molecular hydrogen at AlN(0001) surface at T = 1000 K in function of the hydrogen coverage of the surface. The symbols denote: red stars – p-type, blue circles – n-type and green squares – semi-insulating material. The data presented in Figure 6 indicate that the high hydrogen equilibrium coverage of the AlN(0001) surface is attained at very low pressures. The important issue is the problem whether the energy barrier slows down the hydrogen attachment. Therefore, Born-Oppenheim calculation for hydrogen adsorption at clean AlN(0001) surface was conducted using NEB procedure.54-56 The adsorption path is presented in Figure 7 showing that hydrogen molecule decomposes during adsorption.


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Figure 7. The reaction path of hydrogen (H2) molecule approaching AlN(0001) surface. The molecule decomposes into separate H adatoms that are located on-top of the surface Al atoms. The energy – reaction path is presented in Figure 8. The data present its excess energy with respect of the far distance value in function of the reaction coordinate, i.e. the average distance from the initial point far away from the surface calculated along the reaction path. At close distance, the molecule decomposes into the single atoms, which are attached to the surface. As shown in Figure 7 the separated atoms move along the surface and the reaction coordinate cannot be translated into a function of the distance from the surface.


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Figure 8. The energy of hydrogen (H2) molecule approaching AlN(0001) surface: (a) along the reaction path, (b) in function of the distance from the surface. The zero point for the reaction path (0) is at the equilibrium position. The reaction path is measured as the sum of distance between


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the calculation points. The molecule decomposes into separate H adatoms that are located on-top of the surface Al atoms.

As it is shown in Figure 8, the H2 molecule decomposes at AlN(0001) surface without any energy barrier. Therefore this process will not be a rate controlling factor of the ammonia synthesis reaction at AlN(0001) surface.

AlN(0001) surface under N coverage

In addition to molecular hydrogen (H2), the molecular nitrogen (N2) is necessary in ammonia synthesis. Thus AlN surface may be potentially covered by some concentration of nitrogen adatoms, admolecules or derived adducts. The nitrogen coverage is defined as a ratio of nitrogen atoms attached to the surface to the number of Al top surface atoms, i.e. θ N ≡

NN NN = , where N Al N o

NN and NAl are the numbers of nitrogen adatoms and Al atoms. The latter is assumed to be equal to number of sites at the surface No. The adsorption of nitrogen already investigated using ab initio calculations was reported in Ref. 35. The results presented there will be shortly summarized. Nitrogen molecule adsorbs dissociatively at clean AlN(0001) surface with the net energy gain of 6.0 eV. The process is practically barrierless, the energy barrier is not larger than 0.1 eV, i.e. is of no importance to catalytic synthesis of ammonia. The single N atoms are located in H3 site, thus saturating three Al broken bonds. As it was shown, the Ns states of N adatoms preserve their molecular character, having their energy deep in valence band (VB). The Np states overlap with the neighboring Al atoms, creating states in the bandgap, higher energy for Npz state, lower for Npx and Npy states. These states accept electrons from broken bond states of Al surface atoms without coverage. At the crit

ical coverage θ = , the donating electron Al broken state become empty and no further transition is possible. The Fermi level is depinned from Al broken bond state and moves down, still above the upper Npz-Al state in the bandgap. This transition was confirmed by ab initio calculations. Since the number of electrons available is greater than 6, the Fermi level remains al-


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ways above the uppermost Npz-Al state. For the coverage above the critical one, i.e. θ = ,

the donation of the electrons, is not possible. It was shown that for coverage θ , the ni

trogen is adsorbed molecularly, with the energy gain of about 1 eV/molecule. The molecular regime is not presented in full extent as it is not suitable for application as a catalyst for ammonia synthesis reaction. Note also small difference between 16 and 12 atoms slabs, which is related to the error due to slab size.

Figure 9. Molecular nitrogen adsorption energy at AlN(0001) surface in function of nitrogen coverage. The two regimes are clearly identified: for low coverage the atomic configuration is

stable. For high coverage (θ ), nitrogen is adsorbed molecularly.


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The equilibrium pressure was also determined, using adsorption energy and the configurational entropy only. Therefore the data were not precise. They showed the seven order difference in pressure for dissociative and molecular adsorption. These data need verification by ab initio

simulations close to the critical region > θ > , and also by the precise procedure of

the determination of the equilibrium pressure as the one applied above for hydrogen. Similarly to the case of hydrogen, the molecular nitrogen equilibrium pressure could be obtained from Eq. 2, with the change of configurational entropy term because N adatom occupies three sites while H adatom only one.

= = −∆ 3

3

123 + ∆!"#$% + ∆&'(!"#$% + &$#) + ∆&*+,- . = −∆/0#) −

47 5 − 5) 6 + + ∆8) + 43 8 − 8) 6 + 4 9) 6: − 2

θk ([θk C (θk V

(13)

The thermal enthalpy difference in the range between 0K and To = 25°C = 298.15 K : ∆!"#$% = 3

47 5 − 5) 6 may be obtained using the procedure described for the hydrogen above. The spe-

cific heat of the nitrogen adsorbed at the surface, obtained from Eq. 3a, is plotted in Figure 10.


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Figure 10. Specific heat of AlN(0001) slab, clean (red dashed line), and the slab with the attached N adatom (blue dashed line). The solid lines represent approximations for To < 298.15K: magenta – clean slab, cyan – the slab with N adatom.

In the low temperature interval, the ab initio calculated temperature dependence for the slab with attached N adatom was approximated by the following expression: 5>? =

O.7[×7ST USV 3 V

X X [.OW7.777QUS YC 3 YC

(14a)

Finally, for the ideal hydrogen vapor, a weakly temperature-dependent heat capacity is approximated by the parabolic function: 5[ = 2.94 × 10( + 2.44 × 10(Z K ( + 2.75 × 10( K ([ [ ACS Paragon Plus Environment

(14b)

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Using Eq. 4a and Eqs 14 the thermal enthalpy difference in the range between 0 K and To 3

= 25°C = 298.15 K : ∆!"#$% = 47 5 − 5) 6 can be obtained by direct integration. The result

is: ∆!"#$% = 0.059Ia. Thus this contribution is much smaller than the value obtained for hydrogen. The second contribution is due to the entropy related free energy difference 3

∆&'(!"#$% = −+ ∆8) − 43 8 − 8) 6

(15)

The first term is related to vaporization entropy at normal conditions ∆8) and the second is entropy temperature integral. The vaporization entropy at normal conditions will be calculated using formalism developed earlier, expressing entropy change for the vaporization reaction 8 ↔

C

(16)

[

for single nitrogen atom in the vapor phase:63

∆8) = 2 c d[ρe − 1g − [ρe d1 − ρ

ρ

f

f

[ρf

ρe

g + 2h

(17)

The vaporization entropy has to be scaled with the volume associated with the adsorbed nitrogen atom. The volume associated with pair of Al-N atoms in AlN lattice is VAlN = 20.915 Å3. Assuming that the area is the same, the volume associated by pair of hydrogen atoms is the volume associated by the AlN atom pair is scaled by the bond length. The Al-N distance is equal to 1.063 Å which has to be scaled by factor 3 due to the division of the tetrahedron height by the proportion 1:3. Hence the equivalent bond length is equal to 3.207 Å and 1.91 Å for N at the surface and AlN bulk, respectively. Therefore the volume associated to pair of N adatoms is:

ρ)([ =

ρeSijk 0ijSk 0ijk

=m

0ijSk

ijk 0ijk

(18)

which gives the adsorbate density of N2 ρ)([ = 2.9 × 10([ Å( . This has to be compared with

the density of ideal N2 vapor at normal conditions ρ([ = 2.69 × 10(O Å( . Substituting this density ratio in Eq. 7 gives the vaporization entropy for single hydrogen atom: ∆8) = 15.93 Iq, ACS Paragon Plus Environment

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i.e. ∆8) = 1.373 × 10( Ia/^. This is the reference value for the entropy at normal conditions, from which the entropy change is obtained for higher temperatures, as presented in Figure 11.

Figure 11. Adsorbate- vapor entropy difference for single nitrogen adatom at AlN(0001) surface in function of the temperature. Solid blue line represents the data obtained from Eq. 3b, the broken red line is an approximation (Eq. 19).

The entropy change obtained from ab initio calculations via Eq. 3b are approximated by the following relation

∆8) = 8)s

?

+ 8 − 8)s

?(

= G1 +

'[√3

'W'3

(19)

where G1 = 2.209 × 10( Ia/^, G2 = 2.447 × 10( Ia/^ /[, G3 = 2.822 × 10 and G4 =

9.773^ ( . This approximation is compatible with the vaporization entropy value obtained from

Eq. 8, i.e. ∆8) = 1.373 × 10( Ia/^ at To = 298.16K. Again the entropy related free energy


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change may be obtained via direct integration to calculate the entropy related free energy change for any temperature. These data allows us to obtain the equilibrium pressure of molecular nitrogen vapor at

AlN(0001) surface. These data are limited by the configurational entropy factor to θ for which all sites are covered.

Figure 12. Equilibrium pressure of molecular nitrogen at AlN(0001) surface at T = 1000 K in function of the hydrogen coverage of the surface. The symbols denote: red stars – p-type, blue squares – n-type and green circles – semi-insulating material.

As it could be seen the equilibrium pressure of nitrogen at AlN(0001) surface is much lower than the equilibrium pressure of hydrogen. This opens the possibility of use of relatively


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low pressure of nitrogen which could assure coverage of nitrogen of the surface sites. In addition, the excess of nitrogen is sufficient to protect AlN surface from reaction with the subsurface nitrogen atoms and erosion of the AlN(0001) surface. Thus, chemical stability of AlN(0001) catalyst may be assured so the catalyst may serve for a very long time. AlN(0001) surface under very low mixed N and H coverage could retain some fraction of the Al sites uncovered, i.e. their bond are broken. As shown above, at low coverage the molecular nitrogen and hydrogen are unstable, the adatoms have smaller energy. In the contact with the mixed N2 + H2 vapor, there exist possibility of creation of the radicals. From the point of ammonia synthesis reaction the critical is creation of NH radical. Such configuration was investigated by ab initio calculations. It was shown that the most stable configuration is NH radical located in H3 site in vertical orientation. The configuration is identical with N adatom located in H3 site. The difference is that hydrogen atom is located on-top of N adatom. Assume that the pair of N2 and H2 molecules is attached at AlN(0001) surface. The ab initio calculations were used to compare energies of the separate atoms and pair of NH radicals. The pair of NH radicals have its energy lower by 0.23 eV than the separated atoms. Thus the energy of single radical is 0.11 eV lower than the pair of separate N and H adatoms. Therefore the creation of NH radical is very likely, which constitutes first step in the synthesis of admolecule. The NH3 admolecule may be created by reaction of NH radical and H2 molecule from the vapor.

CONCLUSIONS Ab initio calculations were used to determine basic features of the adsorption reaction of molecular hydrogen (H2) and molecular nitrogen (N2) at clean AlN(0001) surface. It was shown that both molecular species disintegrate during adsorption at AlN(0001) surface without any energy barrier. The atomic adsorption takes place at relatively lower coverage, up to 0.75 ML of hydrogen and up to 0.25 ML of nitrogen. The adsorption site of hydrogen is on-top of AlN topmost surface, thus hydrogen adatom saturates single Al broken bond. The adsorption of nitrogen is at H3 sites, i.e. nitrogen adatom saturates three Al broken bonds. The adsorption energies for hydrogen is 2.60 eV/molecule. Due to triple bonding, the adsorption energy of nitrogen is much higher, about 6.05 eV/molecule. These high energies are achieved despite high bonding of the


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molecular nitrogen and hydrogen due to extremely strong bonding of adatoms by Al terminated AlN(0001) surface. These properties shows that AlN(0001) surface presents properties, which makes it ideal candidate for industrial ammonia synthesis. High energy of adatoms bonding is partially caused by the intrasurface electron transfer in which the Al broken bond partially filled surface state behaves as electron donor. The newly created surface states have much lower energies which located slightly above the valence band maximum. Due to wide bandgap of AlN, the energy effect of electron transfer is very substantial. For higher coverage, the Al broken bond state is empty, the Fermi level is no longer pinned and the electron transfer does not contribute to adsorption energy. Thus, the adsorption energy of molecular hydrogen becomes negative, close to 2.0 eV. The electron donation contribution reach 4.6 eV/molecule of hydrogen. In case of nitrogen, the electron donation by Al broken bond state is exhausted at 0.25 ML coverage, Fermi level is not pinned again, and any excess N adatom have no contribution from Al broken bond state. The molecular nitrogen adsorption energy decreases from 6.0 eV to 1.0 eV, hence the electron transition contribute to such high adsorption energy. From the above data it follows that adsorption of both hydrogen and nitrogen is energetically highly favorable/unfavorable for coverages below/above the critical values. Thus relatively high coverage may be attained that creates opportunity of use of AlN(0001) surface for catalysis. For higher coverage this is energetically costly and the molecular adsorption takes place with no application for catalysis. Equilibrium pressure of both hydrogen and nitrogen was obtained by full analysis, including energetic and entropic contribution. The entropy contribution is comparable for both species but the adsorption energy differs by more than 3 eV. The difference is translated into exponential ratio for the pressure. Therefore both species pressures are relatively low, but for hydrogen this is about 10-8 bar at 1000K while for nitrogen this is less than 10-20 bar. So larger ratio is very beneficial as it allows to prevent decomposition of the AlN lattice by hydrogen reaction. Thus these features could afford to keep the catalysts stable which is important for AlN applications. Naturally, full description of the surface reaction requires extensive investigations of interaction of co-adsorbed species. This will entail not only the site occupation effects and the elec-


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tron exhaustion of electron donating source, but also direct interaction of the species at the surface. A preliminary data obtained for mixed N-H coverage showed that NH radical has its energy 0.11 eV lower than pair of N and H adatoms, that confirms possibility of the efficient synthesis of ammonia at AlN(0001) surface. In summary, the presented results are interesting from basic point of view demonstrating crucial role of electrons in the surface catalysis. In addition, they present new class of catalysts for industrial applications. These results also prove the crucial role of the chemical state of the surface, i.e. absence of parasitic species.

ACKNOWLEDGMENT.

The research was partially supported by Polish National Science Centre grants number DEC2015/19/B/ST5/02136 and 2017/27/B/ST3/01899. The calculations reported in this paper were performed using computing facilities of the Interdisciplinary Centre for Modelling of Warsaw University (ICM UW).


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Figure 1. Energetically stable configuration of hydrogen at AlN(0001) surface: (a) – at 1/16 ML (top view), (b) – at 15/16 ML (top view) and (c) – at 15/16ML (side view) coverage. The surface is represented by (4 x 4) AlN slab of the thickness of 8 Al-N double atomic layers (DALs). In order to saturate broken hydrogen atom bonds at the bottom, hydrogen pseudo-atoms are at-tached of the Z = ¾ fractional charge. Al, N, H atoms and H pseudoatoms are denoted by yel-low, blue, small cyan and small green balls, respectively.



Figure 2. Electronic properties of a 4 x 4 slab representing an AlN(0001) surface under various H coverage: dispersion relations (left), space alignment of the bands derived from atom projected density of states (PDOS) on the row of atoms (middle), and DOS, total - solid line and projected on H adatom and H pseudoatom– dashed and dotted line, respectively (right). The diagrams pre-sent a slab and: (a) single H adatom, i.e. ΘH = 0.0625 ML (b) 12 H adatoms, i.e. ΘH = 0.75 ML ; (c) 14 H adatoms i.e. ΘH = 0.875 ML. The red lines in the band dispersion diagram indicate the H-Al bonding states. 293x516mm (300 x 300 DPI)


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Figure 3. Molecular hydrogen adsorption energy at AlN(0001) surface in function of hydrogen coverage. The two regimes are clearly identified: for low coverage the atomic configuration is stable. For very high coverage, molecular hydrogen has lower energy. 279x215mm (150 x 150 DPI)



Figure 4. Specific heat of AlN(0001) slab, clean (red dashed line), and the slab with the attached H adatom (blue dashed line). The solid lines represent approximations for To < 298.15 K: magenta – clean slab, cyan – the slab with H adatom. 279x215mm (150 x 150 DPI)


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Figure 5. Adsorbate- vapor entropy difference for a single hydrogen adatom at AlN(0001) sur-face in function of the temperature. Solid blue line represents the data obtained from Eq. 3b, the broken line is an approximation (Eq. 9). 279x215mm (150 x 150 DPI)



Figure 6. Equilibrium pressure of molecular hydrogen at AlN(0001) surface at T = 1000 K in function of the hydrogen coverage of the surface. The symbols denote: red stars – p-type, blue circles – n-type and green squares – semi-insulating material. 279x215mm (150 x 150 DPI)


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Figure 7. The reaction path of hydrogen (H2) molecule approaching AlN(0001) surface. The molecule decomposes into separate H adatoms that are located on-top of the surface Al atoms.



Figure 9. Molecular nitrogen adsorption energy at AlN(0001) surface in function of nitrogen coverage. The two regimes are clearly identified: for low coverage the atomic configuration is stable. For high coverage (θ_N≥1/3 ML), nitrogen is adsorbed molecularly. 279x215mm (150 x 150 DPI)


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Figure 8. The energy of hydrogen (H2) molecule approaching AlN(0001) surface: (a) along the reaction path, (b) in function of the distance from the surface. The zero point for the reaction path (0) is at the equilibrium position. The reaction path is measured as the sum of distance between the calculation points. The molecule decomposes into separate H adatoms that are located on-top of the surface Al atoms.



Figure 10. Specific heat of AlN(0001) slab, clean (red dashed line), and the slab with the at-tached N adatom (blue dashed line). The solid lines represent approximations for To < 298.15K: magenta – clean slab, cyan – the slab with N adatom. 279x215mm (150 x 150 DPI)


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Figure 11. Adsorbate- vapor entropy difference for single nitrogen adatom at AlN(0001) surface in function of the temperature. Solid blue line represents the data obtained from Eq. 3b, the bro-ken red line is an approximation (Eq. 19). 279x215mm (150 x 150 DPI)



Figure 12. Equilibrium pressure of molecular nitrogen at AlN(0001) surface at T = 1000 K in function of the hydrogen coverage of the surface. The symbols denote: red stars – p-type, blue squares – n-type and green circles – semi-insulating material. 279x215mm (150 x 150 DPI)


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Adsorption of N2 and H2 at AlN(0001) Surface - ACS Publications

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