Fe interfaces: A first principles study

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Citation for the published paper: Kádas K., Eriksson O., Skorodumova N. "Highly anisotropic sliding at TiN/Fe interfaces: A first principles study" Journal of Applied Physics, 2010, Vol. 108, Article No. 113511 URL: http://dx.doi.org/10.1063/1.3518048

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Highly anisotropic sliding at TiN/Fe interfaces: a first principles study K. K´adas1,2 , O. Eriksson1 , and N. V. Skorodumova1 1

Division for Materials Theory, Department of Physics and Astronomy, Uppsala University, Box 530, SE-751 21, Uppsala, Sweden and 2

Research Institute for Solid State Physics and Optics, H-1525 Budapest, P.O.Box 49, Hungary (Dated: July 28, 2010)

Abstract By means of first principles density functional theory, we investigate the properties of the TiN(001)/fcc Fe(111) and TiN(001)/bcc Fe(110) interfaces. We demonstrate that along certain directions Fe slides with negligible energy barriers against TiN at both interfaces, whereas sliding along other directions is involved with significant energy barriers. The interface between bcc Fe and TiN has a low energy barrier for sliding along the [110] direction of the TiN lattice, as does sliding along the [010] direction at TiN(001)/fcc Fe(111). For fcc Fe on TiN, a large energy barrier is found for sliding along the [100] direction of the TiN lattice. We show that this phenomenon and the stability of these interfaces are determined by the interplay between N-Fe bonding and Ti-Fe antibonding interactions.

1

I.

INTRODUCTION

TiN is a common coating material used for cutting tools and steel machining. Cutting is an extremely complex process imposing severe conditions on both working and tool materials. It invariably includes sliding of steel against TiN and the eventual separation of the two materials. Therefore, an atomic level understanding of the interaction between TiN and the working material is of primary importance, both for improving machinability of steels and controlling adhesion between the cutting tool and steel. As a first step towards an atomistic understanding of the complex processes taking place during cutting we study the sliding and separation of the TiN(001) surface against the most close-packed surfaces of bcc and fcc iron, i.e. the base phases for ferritic and austenitic steels. The bulk and surface properties of TiN and Fe are well studied both experimentally [1, 2] and theoretically [2–7]. However, the reported research on the TiN/Fe interfaces consists of only few studies of the separation of the TiN(001)/bcc Fe(001) system [8–11]. Here we study the interfaces between the most stable surface of TiN, (001), and the most stable surfaces of bcc Fe, (110), and fcc Fe, (111) (see Fig. 1). We show that although chemical bonds are formed between Fe and TiN, Fe can slide along certain directions on TiN with almost negligible energy barriers. The analysis of the electronic structure of the interfaces reveals that whereas Fe atoms form a bond with the N atoms of TiN, the interaction of Fe with Ti is of essentially antibonding character. This interplay of bonding and antibonding interactions is responsible for the observed almost barrierless sliding of close-packed surfaces of Fe along the TiN(001) surface. As the interface slides some bonds are broken and some are newly formed, therefore, the balance is preserved.

II.

COMPUTATIONAL DETAILS

The calculations were done in the framework of density functional theory (DFT) using the projector augmented wave (PAW) method [12] (as implemented in VASP [13]). The exchange-correlation interaction was calculated within the generalized gradient approximation (GGA) using the Perdew-Wang parametrization [14]. DFT-based methods are known to provide reliable surface energies for metals [15, 16] and compounds [17, 18]. The TiN and Fe surfaces were fitted together as shown in Fig. 1. The TiN(001)/fcc

2

Fe(111) unit cell used in the calculations contains a 2x1 unit cell of TiN, parallel to the interface, (Fig. 1, thick black line). The unit cell contains 20 Ti, 20 N, and 72 Fe atoms. The unit cell of the TiN(001)/bcc Fe(110) interface contains 4 Ti and 4 N atoms in the TiN interface layer, and 6 Fe atoms in the Fe interface layer (Fig. 1, thick dashed red line). The whole unit cell has 20 Ti, 20 N, and 54 Fe atoms. The interfaces were modelled by slabs of 5 layer thick TiN and 9 layer thick Fe films, and the slabs were separated by 5 ˚ A of vacuum. The side views of the calculated TiN(001)/fcc Fe(111) and TiN(001)/bcc Fe(110) interfaces are shown in Fig. 2. To determine the work of separation, we changed the size of the interface unit cells in the [001] direction (dc in Fig. 2), and calculated the total energies of the interfaces at each dc . In these calculations, three layers of TiN and six layers of Fe closest to the interface were relaxed along the surface normal, while the rest two layers of TiN and three layers of Fe were kept fixed. The thickness of vacuum, dvac in Fig. 2, was also kept fixed in the calculations. The calculated lattice parameter of bulk TiN (4.253 ˚ A) was used in the slab calculations. This is justified by the fact that TiN is a much harder material than iron or steel. The Vickers hardness of TiN is 1900 [19], while it is only 608 for Fe [19]. This, in turn, also means that during a cutting process, the iron (steel) is distorted to a significantly larger extent, compared to the TiN coated cutting tool. Fitting fcc Fe(111) with TiN as shown in Fig. 1, results in a lattice mismatch of -2.54% in Fe, i.e. the Fe slab is compressed. The angles ∠(Fe7 -Fe5 -Fe3 )=53.1◦ , and ∠(Fe5 -Fe3 -Fe6 )=126.9◦ differ from their ideal values (60◦ and 120◦ ) by -11.5% and 5.75%, respectively. In the TiN(001)/bcc Fe(110) interface the lattice mismatch is 0.2% along the [110] direction (Fig. 1), and 6.3% along the [110] direction, i.e. the Fe slab is stretched along both directions. The bcc phase of Fe was calculated allowing for spin polarization. As austenitic steels are known to be non-magnetic, we performed non-magnetic calculations for TiN(001)/fcc Fe. The 3p6 3d2 4s2 (Ti), 2s2 2p3 (N) and 3d6 4s2 (Fe) valence orbitals and 875 eV cutoff energy were used. The Monkhorst-Pack k-point grids of 2x4x1 and 2x8x1 were used for TiN(001)/fcc Fe(111) and TiN(001)/bcc Fe(110), respectively.

III.

RESULTS AND DISCUSSION

The work of separation of the interface (W ), i.e. the work per area, required to separate the interface, is characteristic of the strength of the chemical interaction between the two 3

materials. For TiN(001)/fcc Fe(111) and TiN(001)/bcc Fe(110) the calculated values of W are 2.482 J/m2 and 1.548 J/m2 , respectively, demonstrating a substantial chemical interaction across the interface (Table I). However, the surface energies of fcc(111) and bcc(110) Fe, calculated for comparison, 2.678 and 2.371 J/m2 , respectively, indicate that the bonding in Fe is stronger than that between TiN and Fe, especially in the case of TiN(001)/bcc Fe(110). Therefore, in the act of separation one would expect the rupture to occur at the interface rather than through iron. Further, we consider the energy cost of interfacial sliding, i.e. moving the entire Fe slab with respect to the TiN slab along different crystallographic directions. In the case of TiN(001)/fcc Fe(111), the iron slab was first shifted along the [100] direction of TiN by half a Ti-N bond distance, i.e. by 1/4 of the lattice parameter of the (1x1) TiN unit cell (Fig. 1, b1 vector). We note that in the presence of the interface with iron the [100] and [010] directions of TiN(001) become nonequivalent (Fig.1). In the initial structure (Fig. 1), Fe1 , and Fe2 are situated above Ti atoms (Ti1 and Ti2 , respectively), i.e. they have top(Ti) positions. Fe5 , and Fe6 are in top(N) positions, while Fe3 , Fe4 , Fe7 , and Fe8 possess bridge positions above TiN. After shifting the Fe slab above TiN by b1 , Fe1 , Fe2 , Fe5 , and Fe6 will be in bridge positions, and Fe3 , Fe4 , Fe7 , and Fe8 will have hollow positions. We find that a significant energy barrier, 0.950 J/m2 (Fig. 1 (a), and Table I), is needed to be overcome for sliding in this direction. Next, iron was shifted on TiN along the [010] direction by 0.25dTi−N , i.e. by 1/8 of the lattice parameter of the (1x1) TiN unit cell (Fig. 1, b2 vector). After this shift, all Fe atoms will possess positions that are between a top and a bridge position. Fe1 , Fe2 , Fe3 , and Fe4 will be close to Ti atoms, while Fe5 , Fe6 , Fe7 , and Fe8 will be close to N atoms. We obtain an almost negligible energy barrier, 0.129 J/m2 , for sliding along this direction (Fig. 1, curve (b)). At the TiN(001)/bcc Fe(110) interface, iron was shifted along the [110] TiN direction by 1/24 of the lattice parameter of the interface unit cell (Fig. 1, b3 vector). In the initial structure Fe1 is situated above N1 , in a top(N) position, and Fe5 is in a hollow position. After shifting the iron slab above TiN along b3 , Fe1 will move away from the top(N) position. Fe2 will be in a hollow position, and Fe3 moves towards N4 . Fe4 moves away from Ti1 , Fe5 moves towards Ti3 , and Fe6 will have a top(Ti) position above Ti4 . For this shift we obtain an even smaller energy barrier, 0.052 J/m2 (Fig. 1, curve (c)). To understand the physical reasons for the observed behaviour we have analysed the relaxation pattern and electronic structure of the interfaces. In Fig. 3 we show the near4

est neighbor N-Fe and Ti-Fe distances at both interfaces. In the initial geometry of the TiN(001)/fcc Fe(111) interface, the Fe atoms lying above N atoms (e.g. the atoms labeled Fe5 , Fe6 in Fig.1) relax towards the N atoms (N3 , N4 ), forming bonds with them (dN−Fe =1.847 ˚ A, see upper left panel of Fig. 3). N1 and N2 , however, do not have Fe atoms in their vicinity, consequently have no possibility for bond formation. This leads to a very anisotropic relaxation pattern. The average nearest neighbor distance for Fe atoms ˚ to N is dav N−Fe =2.290 A. Fe atoms above Ti (Fe1 , Fe2 , see upper right panel of Fig. 3) relax away from Ti, indicating that the Ti-Fe interaction in this case is of antibonding nature and energetically unfavorable, and resulting in a less anisotropic relaxation pattern regarding the Fe-Ti distances compared to the Fe-N distances. The total energy of the TiN(001)/fcc Fe(111) interface with the Fe slab shifted by vector b2 is slightly lower than that of the initial configuration (Fig. 1). For this lowest energy structure we also find a shorter dav N−Fe = 1.916 ˚ A compared to that of the initial structure. This improved bonding of Fe to N atoms appears to be the stabilizing factor for this interface. Shifting Fe along the [100] directions (vector b1 ) gives the least stable structure, which corresponds to the largest dav N−Fe of 2.648 ˚ A. A similar relaxation pattern is observed for the TiN(001)/bcc Fe(110) interface. In this case only the atom labeled Fe1 in Fig.1 forms a bond with atom N1 in the initial geometry. ˚ Here dav N−Fe is 2.327 A(see lower left panel of Fig 3). Shifting of the Fe slab along the [110] direction by vector b3 leads to a slight increase of dav N−Fe . This shift also brings Fe6 closer to Ti4 . This represents an energetically unfavorable situation, and hence the Fe6 atom relaxes away from Ti4 along the surface normal with 0.3 ˚ A. In the shifted structure, the av increased dav Ti−Fe (see lower right panel of Fig. 3) compensates the small increase of dN−Fe ,

leading to a slightly more stable structure than the initial one. Therefore, the structure analysis indicates that the nature of the N-Fe interaction is essentially bonding whereas the Ti-Fe interaction is of antibonding character. The overall stability of the different interface structures is determined by the interplay between these two interactions. This conclusion finds further support from the analysis of the electronic structure of these interfaces. Here we use the TiN(001)/bcc Fe(110) interface as an example to show how the charge density is redistributed due to the interface formation. We examine the charge density difference, ∆ρ=ρTiN/Fe -ρTiN -ρF e for this interface, where ρTiN/Fe is the charge density of the interface, ρTiN and ρF e are charge densities of separated TiN and Fe slabs, 5

of the same geometries as in the interface structure (Fig. 4). ∆ρ demonstrates that charge builds up between atoms N1 and Fe1 clearly indicating a bond formation between them. Areas with small but noticeable charge excess, ∆ρ, can also be observed between atoms N2 and Fe2 , as well as atoms N4 and Fe3 . Fig. 5 shows the density of states (DOS) for interface atoms and bulk-like atoms, i.e. atoms from the middle of the corresponding slabs, of the TiN(001)/bcc Fe(110) interface. Ti and N atoms become slightly magnetic in the spin polarized calculations, due to hybridization with the Fe 3d states. We obtain magnetic moments of 0.13-0.20 µB for Ti and 0.01-0.06 µB for N atoms. In Fig. 5 we show both the spin-up and spin-down DOSs for Fe, but for simplicity only the spin-up DOS of Ti and C projected states are displayed. Comparing the DOS of surface atoms to that of the corresponding bulk atoms, we can identify changes in the electronic structure upon interface formation. For surface Ti and N atoms the most pronounced difference is observed at around -5 eV, where the peak, corresponding to the bonding component of the covalent Ti 3d - N 2p bond, is shifted towards higher energies. This indicates a reduction in the strength of the covalent Ti-N bonding at the interface. N1 and Fe1 form a bond at the interface, which shows up as peaks at -5.5 eV in the DOS of both atoms. Detailed analysis shows that a bond is formed by N pz and Fe dz2 orbitals. The Fe4 atom, which is situated close to Ti1 , has a large peak at the Fermi level (EF ), built up by dz2 and dyz orbitals. This corresponds to the antibonding interaction between Fe4 and Ti1 . In Fig. 5 we also compare the DOSs for the initial structure to those with Fe shifted by vector b3 (Fig. 5, left and right panels, respectively). No significant changes can be seen in the DOS around EF for the interface Ti and N atoms. Regarding Fe atoms, the peak at -5.5 eV is still present in the DOS of Fe1 of the shifted structure, though it is smaller than for the initial geometry. This shows that Fe1 still has some bonding interaction with N1 . In the shifted structure the DOS of Fe4 and Fe6 differ significantly at EF . Fe6 , that lies right on Ti4 in the shifted structure, still has a peak at EF , that is slightly larger here, than in the initial geometry, in line with its closer distance to Ti4 . For Fe4 , however, the peak at EF disappears in the shifted geometry, since it moves away from Ti1 , stabilizing the shifted structure. In the entire unit cell, however, the changes in DOS on the whole are small, resulting in that the total energy of the shifted structure is very close to that of the initial geometry. 6

The electronic structure indicates that the stability of the examined interfaces is determined by the interplay between the N-Fe bonding and Ti-Fe antibonding interactions. This interplay results in almost barrierless sliding along the [010] direction of the TiN lattice at the TiN(001)/fcc Fe(111) interface, and along the [110] direction at the TiN(001)/bcc Fe(110) interface. We note that real interfaces are more complicated than the calculated structures. One restriction of our calculations was the necessity to fit the Fe and TiN lattices together in one unit cell that led to slightly distorted (compressed at the TiN(001)/fcc Fe(111) interface, and stretched at the TiN(001)/bcc Fe(110) interface) Fe slabs. Knowing the nature of Fe-TiN interaction we can expect the work of separation of interfaces between non-distorted TiN and Fe crystals to be a bit smaller than our calculated values, because in that case fewer N-Fe bonds, which actually bind the interface together, could be formed. In addition, dislocations can occur at real interfaces to accommodate the lattice misfit, which we did not consider in our study, but which might influence the stability of the interfaces. However, our study indicates that the energetics of sliding at TiN/Fe interfaces is determined by the interplay between N-Fe bonding and Ti-Fe antibonding interactions and, therefore, one can expect the anisotropy of sliding to be present in real systems.

IV.

CONCLUSIONS

The performed analysis reveals the nature of the interaction between Fe and TiN. Although, TiN(001)/bcc Fe(110) was discussed here in detail, our findings are also valid for other TiN/Fe systems. In particular, the interplay between bonding N-Fe and antibonding Ti-Fe interactions explains the interface energies and barriers obtained for the TiN(001)/fcc Fe(111), as well as TiN(001)/bcc Fe(001) interfaces. An interesting consequence of this peculiar bonding situation is the almost frictionless sliding of interfaces formed by TiN(001) and close packed surfaces of bcc and fcc Fe along certain crystallographic directions. Despite the limitation of the performed study by the number of considered geometries, misfits, and ideal, non-defective interfaces, our investigation has revealed new, general aspects of the interface chemistry between TiN and fcc and bcc Fe, and possibly also the interface between TiN and steel.

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Acknowledgement

˚ Angstr¨om Materials Academy, the Swedish Research Council, and SSF are acknowledged for financial support. The calculations were performed on UPPMAX and HPC2N resources. Valuable discussions with U. Wiklund, M. Collin, S. Hedberg, K. Leifer, S. Rubino, A. Olsson, H. Engqvist, S. Jacobsson and U. Jansson are acknowledged.

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72, 235423 (2005). [17] N. V. Skorodumova, K. Hermansson, B. Johansson, Phys. Rev. B, 72, 125414 (2005). [18] A. V. Ponomareva, E. I. Isaev, N. V. Skorodumova, Yu. Kh. Vekilov, I. A. Abrikosov, Phys. Rev. B, 75, 245406 (2007). [19] W. Martienssen and H. Warlimont, Springer Handbook of Condensed Matter and Materials Data, Springer, 2005.

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˚2 in parenthesis) of TiN(001)/fcc Fe(111) TABLE I: Work of separation (W , in J/m2 , and in eV/A and TiN(001)/bcc Fe(110) interfaces in their relaxed initial geometries, and after sliding the Fe slabs (see translation vectors in Fig. 1). Interface

geometry

W

TiN(001)/fcc Fe(111)

initial

2.482 (0.155)

TiN(001)/fcc Fe(111)

Fe slided along [100]

1.532 (0.096)

TiN(001)/fcc Fe(111)

Fe slided along [010]

2.611 (0.163)

TiN(001)/bcc Fe(110)

initial

1.548 (0.097)

TiN(001)/bcc Fe(110)

Fe slided along [100]

1.600 (0.100)

10

Figure captions Figure 1: (Color online.) Relative positions of the surface layer atoms in the TiN(001)/fcc Fe(111) and TiN(001)/bcc Fe(110) interface unit cells (thick lines). Ti and N atoms are denoted by solid and empty black circles, resp. Fe atoms are displayed by large red circles. Energy cost (per surface area) of sliding Fe on TiN at the TiN(001)/fcc Fe(111) interface along the [100] and [010] directions are shown in curves (a) and (b), resp. The corresponding translation vectors, b1 and b2 are shown by green and blue arrows, resp. Energy of sliding Fe along the [110] direction (b3 translation vector) at the TiN(001)/bcc Fe(110) interface is shown in curve (c). Energies are given relative to the shown initial geometries, and the same energy scale is applied in all the curves. Figure 2: (Color online.) Side views of the TiN(001)/fcc Fe(111) (a), and TiN(001)/bcc Fe(110) interface unit cells (b), in their initial geometries, before relaxation. dc denotes the size of the unit cell in the [001] direction, and dvac is the thickness of vacuum. For the sake of clarity, only atoms in the (010) plane are shown for the TiN(001)/fcc Fe(111) interface, while for the TiN(001)/bcc Fe(110) interface, atoms in the (220) plane are displayed. The top views of the corresponding interface layers are shown in Fig. 1. Figure 3: (Color online.) Nearest neighbor N-Fe (left panels) and Ti-Fe distances (right panels) at the relaxed TiN/Fe interface structures. Distances at the TiN(001)/fcc Fe(111) interface (a) are shown in the initial geometry (solid black circles), and for the structure with Fe slab shifted by b1 (open green squares) and b2 (open red circles). For the TiN(001)/bcc Fe(110) interface (b) distances in the initial and in the shifted structures are displayed by solid black and open red circles, resp. Figure 4: (Color online.) Charge density difference (ρTiN/Fe -ρTiN -ρF e ) map (given in electrons) in the (010) plane of the relaxed TiN(001)/bcc Fe(110) interface (initial structure). Atomic labels correspond to those in Fig. 1. Figure 5: (Color online.) Electronic density of states of selected atoms of the TiN(001)/bcc Fe(110) interface for the initial geometry shown in Fig. 1 (left panels), and for the structure with Fe shifted on TiN along the [110] diraction respect to TiN. (right panels). Atomic numbers correspond to those in Fig. 1. Tibulk , Nbulk , and Febulk are bulk-like atoms from the middle layers of the TiN and Fe slabs. For Fe atoms both spin-up and spin-down chanels 11

are shown (the latter in the negative region). Notice that Ti1 and Ti4 , as well as Fe4 and Fe6 are equivalent in the initial geometry.

12

E/S (J/m2)

0.8

(a)

0.4 0.0

fcc Fe(111)

-0.4

b1

Fe 7

N3

Ti 3

b

(b)

Fe 5

Fe 3

Ti N Fe

Fe 8

N4

Ti 4

Fe 6

Fe 4

-0.4

0.0

0.4

b2 Ti 1

Ti 2 Fe 2

N1

Fe 1

E/S (J/m )

E/S (J/m2)

N2

2

bcc Fe(110) Ti 4 Fe 6 N4

Ti 3

(c) b

Ti 2

N3

0.0

[010]

/m

-0.

4

/S

E

(J

)

2

Fe 3

Fe 5

b3

Ti 1

Fe 4

Fe 2 N2

[100] N1 Fe 1

TiN(001)/fcc Fe(111) 11)

TiN(001)/bcc Fe(110) Ti N Fe

dvac

dc

Fe1

Fe2

Fe1 N1

Ti1 N1 Ti2 N2

Fe2 N2

N3

[001]

(a)

[100]

Fe3 N4

[001]

(b)

[110]

d (Å)

4 3

3

2

2

1 N1 4

d (Å)

4

fcc Fe(111)

N2

N3

1 N4 Ti1 (a) 4

bcc Fe(110)

3

3

2

2

1 N1

1 Ti1

N2

N3

fcc Fe(111)

N4

(b)

initial tr. [100] tr. [010]

Ti2

Ti3

bcc Fe(110)

Ti4

initial tr. [110]

Ti2

Ti3

Ti4

Fe3

Fe2

Fe1

N2

N1

N3

N4














DOS

2

Ti1 Ti4 Tibulk

1

DOS

0 N1 N3 Nbulk

0.4 0.2 0 2

Fe1 Fe4 Fe6 Febulk

N-Fe bond

DOS

1 0 -1 -2 -10

-8

-6

-4

-2 0 E-EF (eV)

2

4

6 -10

-8

-6

-4

-2 0 E-EF (eV)

2

4

6