Proceedings of the 3rd Japan-Korea Joint Workshop
on First-Principles Electronic Structure Calculations

Tsukuba, Japan (2000)

First-principles study of the TiX(X = B, C, O, N, F) surfaces
Kazuaki kobayashi1
1 National Institute for Research in Inorganic Materials, Namiki 1-1, Tsukuba-shi, Ibaraki
305-0044, Japan

Abstract. TiX(X = B, C, N, O, F) bulk and surface systems as a rock salt structure areinvestigated by using the rst-principles molecular dynamics (FPMD) method. The purposeof this study is to investigate a change of the electronic properties in a series of systems forTiX(X = B, C, N, O, F) systematically.

1 Introduction
In this study, bulk and surface systems of TiX(X = B, C, N, O, F) are focused. TiC andTiN are known to be extremely hard and high melting point materials (for example, coatingmaterials). Technologically, they are very important as highly stable eld electron emittersand catalysts for various chemical reactions on the surfaces. The TiC and TiN surfaces havebeen studied [1, 2] for their electronic and structural properties. The purpose of this study
is to investigate electronic properties (energy band structure, electron charge density, work
function, etc.) of them and an e ect due to a di erence of anions(B, C, N, O, F). The (001)surfaces of them are non polarized, in which the outermost layer of an ideal (001) surface
consists of an equal number of cation (Ti) and anion (B, C, N, O, F) atoms.

2 Method of calculation
The calculation is based on the local density approximation(LDA) in the density functional
theory [3, 4, 5]. Troullier and Martins type optimized pseudopotentials [6] with separable
forms of Kleinman-Bylander approximation [7] are used in this calculation. A partial corecorrection (PCC) [8] is considered for Ti pseudopotential. As for Ti, a 3p core state is notconsidered as a valence state in this study. A supercell model is adopted and a repeated slab
geometry is used. The detailed calculation is similar to that of our previous work [1, 2] forthe transition metal carbide (TMC) and nitride (TMN) surfaces.

3 Results and discussion
The lattice properties of the bulk are tabulated in Table 1. The lattice properties for TiCand TiN agree with the experimental results [9, 10, 11]. The lattice constant of TiO is larger
by 2 % than that of experiment [12]. All electronic structures of bulk are metallic as shownin Fig. 1.
The TiX(X = B, C, N, O, F) ideal surfaces are calculated. Their electronic states arefound to be metallic as shown in Fig. 2.
1

(eV)

(eV)

(eV)

WLΓ

X W KTiB(NaCl,pcc) a = 8.529 a.u.

(eV)

(eV)

WLGX W K
TiC(NaCl,pcc) a=8.2a.u.

W

L

Γ

X W K

TiN(NaCl,pcc) a = 8.03 a.u.

WL

Γ

X W K

TiO(NaCl,pcc) a = 8.074 a.u.

WL

Γ

X W K

TiF(NaCl,pcc) a = 8.000 a.u.

Figure 1: Energy band structures of TiX(X = B, C, N, O and F) bulk as a rock salt. TheFermi level is indicated by the horizontal line.
Table 1: Calculated bulk properties (equilibrium lattice constants[A], bulk moduli[GPa])and deviation of the present work and experiment for the lattice constant [%].
Bulk Present work [A][GPa] Exp. [A][GPa] Deviation [%]TiB
4.50 186
TiC
4.33 262
4.33 [9]0.0TiN
4.25 282
4.238 [10] 288 [11]+0.2
TiO
4.27 238
4.177 [12]+2.2
TiF
4.58 103
The work function for the TiC and TiN surfaces have been studied in the previous
work [1, 2] with a structural optimization as shown in Table 2. As for the TiX(X = B, C,N, O, F) ideal surfaces, it is found as follows.
(1)The values of the work function for the TiB, TiC and TiN ideal surfaces are decreasing
in order of B ! C ! N.
(2)The values of the work function for the TiN, TiO and TiF ideal surfaces are increasing inorder of N ! O ! F.
(3)The value of the work function for the TiN ideal surface is lowest in those for the TiX(X= B, C, N, O, F) ideal surfaces.
Energy band structures of the TiX(X = B, C, N, O, F)(001)-121 ideal surfaces as shownin Fig. 2. A position of the Fermi energy for the TiN surface as indicated by a horizontalline in Fig. 2 is the highest in the three energy band structures for TiB, TiC and TiN. Thevalue of the work function is determined as an energy di erence between a vacuum level andthe Fermi energy. A decrease in the value of the work function from TiB to TiN is causedby the position of the Fermi energy as schematically shown in Fig. 2, although the actual
vacuum levels of the above three surfaces are not equal to each other. It is not clear thereason why the values of the work function from the TiN to TiF increase.

2Table 2: Calculated work function [eV] for the TiX(X = B, C, N, O, F) ideal surfaces. A
value of 3.86 eV [14] in the parentheses is for the unrelaxed surface.
Relaxed Unrelaxed
Theory
Exp.
TiB
4.93
TiC 4.62
4.19
4.7 [13]
3.8 [15]
TiN 3.25
3.03
2.92 [16]
TiO
3.27
TiF
3.35
TaC 4.16
3.85
4.24(3.86) [14]4.3 [17]
TaN 3.45
3.79
4.0 [16]
HfC 4.28
3.86
4.5 [17]
HfN 2.79
3.13
3.85 - 3.90 [16]NbC 4.26
3.85
4.2 [17]
NbN 3.333.59
3.92 [16]ZrC 4.30
3.94
4.0 [17]ZrN 2.79
2.84
2.92 [16]4 SummaryThe electronic properties for TiX(X = B, C, N, O, F) bulk and ideal surface systems arecalculated by the FPMD method. It may be not enough to explain the work function changeof them in this study. It needs more detailed analysis of the electronic properties (chargedensities and energy band structures, etc.). In this study, the surface structures for TiB, TiOand TiF are not optimized by using the FPMD method. It is very important to investigate
the work function change due to a structural optimization in a future next task.

Acknowledgements
The author wishes to thank Prof. K. Yamamoto for his helpful advice in calculating thework function. The valuable discussions and advice for this study of Dr. M. Arai aregratefully acknowledged. The author thanks the sta of The Supercomputer Center(Fujitsu
VPP500 and System A, B), Institute for Solid State Physics(ISSP), University of Tokyo for
the facilities provided by them.

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(eV)

(eV)

(eV)

Slab(eV)(eV)

VacuumVW
Ef(TiN)Ef(TiC)Ef(TiB)XΓM

TiB(001)-1x1 ideal surface

X

Γ

X

M

TiC(001)-1x1 ideal surface

ΓX

ΓM

X

X

TiN(001)-1x1 ideal surface

ΓM

TiO(001)-1x1 ideal surfaceXXΓM

TiF(001)-1x1 ideal surface

X(a.u.)

A potential(V) curve in the slab model[V = V(Hartree) + V(Local PS)]

Figure 2: Energy band structures of the TiX(X = B, C, N, O, F) ideal surfaces and schematical view of the potential curve for Hartree + local pseudopotential terms for the TiB, TiCand TiN surfaces. A number of k-points is 16 in the whole surface Brillouin zone. The Fermi
level is indicated by the horizontal line. Ef(TiB), Ef(TiC) and Ef(TiN) is the Fermi energiesof the TiB, TiC and TiN surfaces, respectively. \W" is the work function.
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