Electrostatic potential calculations on crystalline TiO2 : the
surface reducibility of rutile and anatase
Citation for published version (APA):
Woning, J., & Santen, van, R. A. (1983). Electrostatic potential calculations on crystalline TiO2 : the surface
reducibility of rutile and anatase. Chemical Physics Letters, 101(6), 541-547.
https://doi.org/10.1016/0009-2614%2883%2987030-4
DOI:
10.1016/0009-2614%2883%2987030-4
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Published: 01/01/1983
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Volume 101. number 6 CHEMICAL PHYSICS LETTERS 4 November 1983
ELECTROSTATIC POTENTIAL CALCULATIONS ON CRYSTALLINE TiO2: THE SURFACE REDUCIBILITY OF RUTILE AND ANATASE
J. WONING and R.A. VAN SANTEN *
Koninkl~ke/~hell-Laboratorium, Amsterdam (Shell Research B. V.). P.0. Box 3003.1003 AA Amsterdam, The Netherlands
Received 23 March 1983; in final form 22 hlay 1983
From calculations of the electrostatic potential at the most densely packed rutile (110) and anatase (001) crystal faces.
greater reducibility of the coordinatively unsaturated Ti4’ _ Ions at the rutile surface than at the anatase surface is predicted.
Consequently, the intrinsic hewis acidity of coordinatively unsaturated Ti?’ - Ions at the (110) face of rutile is larger than that of the T14+ ions at the anatase face. Thii may relate to some esperimentaily observed differences in catalytic activity between rutile and anatase.
1. Introduction
In the following sections we present the results of
* Present address: Shell Dev. Co., Westhollow Research
Centre, P-0. Box 1380, Houston, Texas 77001, USA.
electrostatic potential calculations on mtile and an-
atase. Rutile and anatase are both crystal modifica- tions of TiO,, which show markedly different catalyt-
ic activities in chemical reactions. Several examples of this phenomenon have been reported in the literature
[l-3].
Table 1
Crystallographic data and bulk chemical properties of rutile and anatase
space group a) packing mode a)
a (nm) a)
c (nm) a) u a)
coordination number Ti4’ ccordination number O*- Ti-0 bond lengths (nm) b)
lattice energy (kJ mol-‘) c) Mtq 298_15 K (kJ mol-‘) d) AS;98 15 K (J mol-’ K-l) d) density & ml-‘) d) Rut& Anatase p42/mnm @ah) 142m (Dz,j) hexagonal cubic 0.459375 0.3785 0.295812 0.9514 0.3053 0.2066 6 6 3 3 O.19461 0.1937o 0.19834 0.19656 -13623 -13669 -943.5 -912.5 49.92 50.25 4.2? 3.90
a) Ref. 141. b) Calculated using Wyckoffs [4] data. c, See ref. IS]. d) Ref. [6].
Vohime 101, number 6 CHEMICAL PHYSICS LETTERS 4 November 1983
Fig. 1. Srrucrurc of the wile (110) face. AI rhe surface (Z = 0) five- (type I. C,) and six-coordinated (type II. &h) Ti4* ions are
prrsrnt. Surbcc O”- ions appear in ta o- (type IV) Jnd in three-coordinated (type III, V) environment. * = Ti. o = 0. a = surface
o\vcL‘n x JGlIlC\ -_ _-
In the reaction referred to rutile is a far more active cdt&st than anatase. This seems at first sight rather surprising. since the crystallographic data and bulk chemical properties (see table 1) of rutile and anatase
are very similar. However, differences occur in the sec- ond and higher coordination shells of Ti. It is the pur- pose of this letter to show how this affects the surface electrostatic potentials of the most densely packed
f=o__
trt -
i-2 _ _. . - - - _.
f=, _ __--.. *
&5-.
Fig. 2. Structure of the anatase (001) face. At the surface (f = 0) both two- (type II) and three-coordinated (type I) O*- ions are
presenr. Surface Ti4+ ions appear exclusively in five-coordinated (Dzd) environment. l = Ti, o = 0, I= surface oxygen vacancy.
Volume 1 01 = number 6 CHEMICAL PHYSICS LETTERS 4 November J983
Fig- 3. Structure
of
the rut& (001) face, At the surface (I= 0) X4’ _ 1s esctusively four coordinated (C,) and O*- is exclusivelytr\ o coordinated_ l = Ti, o = 0. Pp = surface oxygen vacancy.
faces of anatase and rutile and hence the Lewis acidity of the cations or basicity of surface anions. The calcu- lations predict that one may expect a distinct differ- ence in reducibility of the Ti4* ions at these surfaces.
Calculations have been carried out on the stable, most densely packed rutile (110) and anatase (001) faces and on the stable rutile (001) face.
At the rutile (1 IO) surface both five- and six-coor- dinated Ti4+ are present (fig. I). At the anatase (001) surface Ti4+ is five coordinated (fig. 3) and at the rutile (001) surface Ti3+ is four coordinated by oxygen
ions (fig. 3).
2. Calculation procedure
For the calculation of the electrostatic potential several methods have been developed [7-l O] _ For our calculations we selected the method originally devised by Evjen [S] for bulk potential calculations. Unliie the other methods, the Evjen method allows simple programming, and, what is most important is easily modified to facilitate potential calculations in semi-infinite crystals. Madelung constants M(ro) were calculated according to the definition:
in which U is the electrostatic lattice energy; IZ is the
number of molecules in the unit cdl; G&k) is the electrostatic potential of ion k, at position rk and with charge ,&e, generated by ah other ions (charac- terized by position vectors ri + ri f rk and charges
qie) in the lattice; k runs over the ions making up the unit cell; r. is the nearest-neighbouring distance, and z is the largest common factor of the qk_ For a TiOz lattice, eq. (I) reduces to:
M(ro) = (ro/2e)[@(Ti4*) - $(O’-)] . f3 As far as the quantities M(ro) and also ET [see eq. (S)] are concerned, the calculated results are very accu- rate; the accuracy solely being determined by the accu- racy of the input data @4 significant digits in ah cases), The calculated electrostatic potentials 9, however, are considerably less accurate (estimated absolute accuracy =0.05).
3. Results and discusdon
The results of our electrostatic potential calculations are given in tables 2,3 and 4 for the rutile (PO]), the r-utile (110) and the anatase (001) faces, respectively. A comparison of the Maddung constantsBf(ro) as a function of the layer number I * shows that it behaves roughly in the same way for the rutile (001) and the
* 1 counts the number of layers. start@ from the surface (Z = 0). See also figs. 1,2 and 3.
\rohm~e 101. number 6 CHEMICAL PHYSICS LETTERS 4 November 1983
Table 2
Elecrrosraric porenrials 0 (X4’, and o(O’-) and Madelung constantsM(q,) (r,-, = 0.1946, nm) as a function of the layer number 1. for the rutile (001) face
rutile (110) face. In both casesAl exhibits a mini- mum at the surface (Z = 0), a maximum at the layer immediately below the surface (Z = 1) and converges to an intermediate bulk value of 4.7718,. The mini-
1 0 Cri4+) (e nm-‘) 0
(o’-)
-1 (enm 1 M (ro) -27~~ b) -31.99 -31.2, -31.21 -31.2, -31.23 -31.14 -31.25 -31.26 c) 2.34 3) 15.4,b)
l&l& 17.8, 17&q 1 7.Sz 17.61 17.80 17.79 17.76 =) 4.1632, b) 4.6802~ 1.75946 4.77353 4.7716, 4.77187 4.77l84 4.771g4 4.7718zt c,mum at the surface is of course due to coordinative unsaturation. The fact that in the case of rutile the (110) surface (M(r,) = 4.61313) is electrostatically more stable than the (001) surface (Af(r,) = 4.1632,) reflects the larger degree of coordinative saturation and the denser packing of the ions at the (110) surface.
The ma..imum value ofM(ro) at the layer imme- diately below the surface (i= 1) is inherent in the hexagonal structure of rutile. It is explained by the fact that the layer immediately below the surface (L = 1) suffers significant repulsion from only one neigh-
3) Electrostatical potential o(v) at the surface o\)gcn vacancy. b) Surface \JIUC. Ir) Uulk value.
bouring layer (Z = 3), while deeper layers (Z = i. i > 2) suffer significant repulsion from two neighbouring
Table 3
Electrostatic potentials 0(T14’) .md 0(0’-) and hlsdelung constantsAf(ro) (ro = 0.19461 mn) as .I function of the layer number I. for the rutile (110) face
I ,jG)p-$4+) a) o(6) mi4+) b) lg3)(ot-) c)
(e mn-’ ) (c mn -1 -1 M(r,)(5) a) M(Q,)@) b) ) (e nm ) 7.9
d)
0 -20.5,a
-24.16 C) 2&S,c)
%61313 C) 4.96642 e, 1 -1’.6s --a1.53 26.4t 4.77649 4.7623 t 2 -22.64 -22.67 16.40 4-77163 4.77524 3 -22.6, -21.67 26.3, 4.7718s 4.77182 4 --2?.lo -22.7 t 26.33 4.77184 4.77184 5 -22.74 0 -22.74 1‘) 16.30 f) 4.77164 0 4.77164 0J) SW Iis. 1. type I. b) SW I&_ 1. type II. c) See I&_ 1, type Ill.
d, Illcctro\tattc potcntkl o(t) at the surf302 oxyssn vacancy. e) Surface value. f) Bulk value. T.ible 4
Elecrro\rAc potonriA PI.TI~‘) And 0(03-) and Madelung constantsM(ro) (r. = 0.19371 mn) as a function of the layer number I. for the m.na.c (001) face
I ocr14+) (e mn -1 &)&-) a) ) (e nm -1 .+(3)(&-) b) ) (e mn --1 M (ro) (2) a) I b) ) 0 -2S.6, d) 2.30 c) I 7.~~ d) 19.g2 d) 4.4505~ d) 4.7051~ d) 1 -19.56 19_66 19_63 z 1.76646 4.76335 -19.57 l9.63 l9.63 4.76539 3 -19.59 4.76532 19.6, 19.61 4.7653t 1 -29.59 4.7653, 19.6t 19.6t 4.7653, 4.76531 5 -19.59 -29.5s c) l9.63 1 9.62 c, l9.63 6 1 9.63 e) 4.76531 4.7653, 4.76531 e) 4.7653, e,
a) See tig. 1. type II. b) Set fii_ 2, type I.
c, Electrostatic potential 0(v) at the surface oxygen vacancy. d) Surface va~uc. e) Bulk value.
Volume 101, number 6 CHEMICAL PHYSICS LETTERS 4 November 1983 Table 5
A comparison of the Madelung constantsM(ro) calculated
from Watson’s data [5], with our results, for the rutile (001) face
1 hiadelurg constant Ibf(ro)
Watson’s work our work
0 4-1623 4-1632s
1 4.881 t 4.88022
2 4.7608 4.75946
3 4.7746 4.77353
4 4.772, 4.7716,
layers characterized by I = i - 2 and I = i -t 2 respective- ly. The layers in cubic structures like anatase do not suffer significant repulsion from any neighbouring lay. ers, and therefore the relation between M(ro) and I does not show a maximum at I = 1. The calculated bulk Madelung constants for both rutile (ni(r,) = 4.771 S4) and anatase (ni(r,) = 4.76531) are in excel- lent agreement with the results of van Go01 [I l] (nf(r,) = 4.7720 for rutile.M(ro) = 4.765, for auatase, Ewald method). Very recently, Watson [5] calculated the difference between the electrostatic potentials at the Zth layer and the bulk as a function of I, for the mtile (001) face. Transformation of these potential differences into Madelung constants reveals a satisfac- tory agreement with our results, as can be seen from table 5. The slight deviations occurring in table 5 can be attributed to the fact that Watson used slightly dif- ferent unit cell parameters for rutile in his calculation.
In the preceding paragraphs we have seen that for
both the (110) and the (001) face of rutile, the Madelung constant M(ru) converges to a common bulk value at large 1. This is not true, however,-for the potentials $(Ti4’) and r$(O*-) of the Ti4+ and O’- ions. From tables 3 and 4 it can be seen that these dif- fer by a factor:
A@ = Qfli43(1 10) - @(-t,i43(OOl)
= @(02-)(1 10) - cp(o~-)(ool), (3) which converges to a constant value of 8.52 e nm-’ for the bulk electrostatic potentials. This implies that either the rutile (001) or the rutile (110) should have a finite dipole moment. From the surface structures (figs. 1 and 3) it is evident that the rutile (110) surface exhibits a dipole moment, perpendicular to the surface_
.4ccordmg to electrostatic theory, A$, when evalu- ated for the limiting case of the bulk electrostatic po- tentials, is proportional to the electric dipole density
p/A at the surface:
A@(bulk) = 2np/A _ (4)
Substituting A@(bulk) = 8~5~ e nm-I, we arrive at a dipole density of 1.36 e nm-’ at the rutile (110) sur- face. This result is in reasonable agreement with a value of 1 .4g e nm-’ calculated from the surface structure of fig. 1.
Within an electrostatic model, one can calculate the energy ET to transfer an electron from an oxygen atom adsorbed to a surface Ti ion at a surface oxygen coordi- nation site towards thii Ti ion by calculating the differ- ence in the electrostatic potential of the surface Ti ion with a fomral charge equal to +4 and a point charge -1
Fig. 4. Pauling valencies for nearest-neighbouring Ti4+ and O*- -
Cc) mile (001). sates at different TiOz surfaces: (a) rutile (I IO), @) anatase (OOl),
Volume 101, number 6 CHEMICAL PHYSICS LETTERS 4 November 1983
at the adsorbed surface osygen location and the sur- face Ti ion with a formal charge equal to +3 and the point charge removed.
This quantity is only indirectly related to the re- duction energy. since no driving force, i.e. the differ- ence between the ionization potentials of 02- and the electron affinity of the Ti”’ ion itself, is accounted ior. However. as long as the non-electrostatic terms contributing to the reduction energy are constant. the surfxe reducibility is proportional to ET ‘_ As far as
the rutile (110) and anatase (001) surfaces are con- cerned. this approximation seems reasonable. since the local environments of five-coordinated Tii”+ ions at the rutile (110) and the anatase (001) surfaces are virtually the same (see figs. 1. 2 and also 4).
Since ET relates to the energy differences due to electron donation from the adsorbate to the surface Ti ion. it will also relate to the Lewis acidity of the Ti surface ion.
We calculated ET(T?) for a coordinatively unsat- urated Til+ ion at the different TiOz surfaces. Ex- pressed in terms of electrostatic potentials. E-r-(T?) becomes
E-L(Tia+)= e[o(v) - pu(T?)] . (3
where Q(v) and ou(Ti”+) are the electrostatic poten- tials at the vacant surface oxygen coordination site location and its neighboring surface T@’ ion. respec- tively. The results. calculated from the data in tables 2-I. are collected in table 6. From these results, it cdn be concluded that it should be far easier to re- duce the five-coordinated Ti’l+ at the rutile (110) than at the anatase (001) surface. As the Til+ ion at the rutile (001) surfxe is four coordinated the quan- tity ET’ is not necessarily proportional to the redu- cibility in this case. Therefore. no definite conclusion
rutilc (00 1) rutite (I 10) amtasr (001) e0 W (rydberg) 0.347 0.797 0.213 coo (Ti43 ET (rydbcrg) (rydberg) -2.897 3.1446S -2.173 2.9696a -3.032 3_286g8 546
about the reducibility of a Ti4+ ion at the rutile (001)
surface can be drawn although the ET value of table 6 strongly suggests. that the reducib%ty of a Ti4’ site at the rutile (001) surface can be intermediate be- tween that of the rutile (110) and anatase (001) sur- faces.
It should be noted that the same conclusions can be reached via a very simple consideration using Pauhng valencies [ 12]_ Taking into account nearest- neighbour interactions only, and assuming that in both rutile and anatase all Ti-0 and Ti-vacancy distances are equal. we can easily deduce the potentials @,(Ti4+) at the (coordinatively unsaturated) surface Ti4+ ions from fig. 3. The resulting @u(Ti4+) values are -1 O/3, -12/3 and -14/3 (units e ‘cl) for Ti4+ sites at the rutile (I 10). the rutile (001) and tlte anatase (001) sur-
face_
A comparison with table 4 reveals that the +,(Ti4+)
values
occur in exactly the same order as the negativesof the ET(Ti’+) Vahres. This implies that, within the
assumption that -ET(Ti3’) and qo(Ti4+) are propor- tional. a calculation of the electrostatical potential &,(Ti4+) using Pauling valencies. predicts the correct order of ET(Ti4+) values and surface reducibilities for the (coordinatively unsaturated) Ti4+ ions at the sur- face of anatase and r-utile. The assumption involved is consistent. since in the comparison of the ET(Ti4’) values using Pauling valencies. only the nearest-neigli- bour interactions have to be taken into account. As a consequence, o(v) in eq. (5) is a constant and -ET(Ti4’) and Go(Ti4+) become proportional to each other.
Of course. the electrostatic theory as it has been applied here is very simple, and thus by no means per- fect_ It completely neglects important factors like polarization lattice deformation (especially at
the sur-
face) and quantum-mechanical effects. However,
oursimple electrostatic model leads to the prediction that coordinatively unsaturated Ti4+ ions at the most dense- ly packed plane of rutile can be more readily reduced than those on the most densely packed plane of ana- tase. And a similar prediction can be made for the order of intrinsic Lewis activities. From the correlation with Pauling valencies it appears the differences are deter- mined primarily by the different surface arrangement of the Ti4+ and Oz- ions. The differences in surface potential are dominated by the local environment of
Volume 101, number 6 CHEMICAL PHYSICS LETTERS 4 November 1983 the electrostatic potential. This conclusion does not [3] Y. O&hi and T. Hamamura, Bull. Chem. Sot. Japan only agree with the results presented in this report, 43 (1970) 996;
but is also supported by the results of electrostatic Y. Onishi, Bull. Chem. Sot. Japan 44 (1971) 1460. potential calculations on the bonding of surface oxy- [4] R.W.G. Wyckoff, Crystal structures (Interscience, New gen at non-stoichiometric metal oxide phases [ 131 [S] R.E. Watson, York, 1963) p. 250. J.W. Davenport, ML. Perlman and
and on the acidity of natural and synthetic mica-
montn~orillonites [ 141. T.K. Sham. Phvs. Rev. B24 (1981) 1791. . _ [61 I71
[81
191
[lOI
1111
1121
1131 1141R.J.H. Clark, DC. Bradley and P. Thornton, Pergamon texts in inorganic chemistry. Vol. 19 (Pegamon Press, Oxford, 1973) p_ 376.
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[l] J. Cunningham, B.K. Hodnett, hf. Ilyas, J. Tobin, E.L. Leahy and J.L.G. Fierro, Faraday Discussion 72/17 (1981).
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E. hiadelung, Physik. Z. 19 (1918) 524. P.P. Ewald. Ann. Phys. 64 (1921) 253. H.M. Evjen, Phys. Rev. 39 (1932) 625. F. Berthaut, J. Phys. 13 (1952) 499.
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