SHORT-RANGE AND LONG-RANGE ORDER OF TITANIUM IN Ti1+xS2

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SHORT-RANGE AND LONG-RANGE ORDER OF

TITANIUM IN Ti1+xS2

R. Moret, M. Huber, R. Comès

To cite this version:

R. Moret, M. Huber, R. Comès. SHORT-RANGE AND LONG-RANGE ORDER OF

TI-TANIUM IN Ti1+xS2. Journal de Physique Colloques, 1977, 38 (C7), pp.C7-202-C7-206.

JOURNAL DE PHYSIQUE Colloque C7, supplkment au no 12, Tome 38, dkcembre 1977, page C7-202

SHORT-RANGE AND LONG-RANGE ORDER OF TITANIUM

IN

Ti,+$,

R. MORET, M. HUBER

Laboratoire de Chimie Appliqute de 1'Etat Solide, E.N.S.C.P., l l , rue P.-et-M.-Curie, 75231 Paris Cedex 05, France

and R. COMES

Laboratoire de Physique des Solides, Universite Paris-Sud, 91405, Orsay, France

R b m C . - L'etude de Ti, +,S, par diffraction des rayons X et des electrons a montrk I'existence d'un ordre A courte distance des atomes de titane dans les couches metalliques incomplc?tes. Une interpretation de la distribution de l'intensitk diffusee est proposee. Le modele utilisk est base sur la coexistence de deux types de microdomaines et tient compte des corrtlations entre premiers, seconds

et troisiemes voisins.

Abstract. - Electron and X-ray diKuse scattering studies on Ti, +,S, have revealed the occurrence of short range ordering of titanium atoms in partly filled metallic layers. An ordering model is pro- posed allowing to explain the distribution of the diffuse scattering intensity. This model is based on the coexistence of two types of microdomains, taking account of first, second and third neighbour interactions.

1. Introduction. - In a recent paper we reported preliminary observations of diffuse scattering features on the X-ray and electron diffraction patterns for Ti, +,S, [l]. These diffuse features were attributed to

the ordering of titanium atoms in the partly occupied layers of the structure. This proposal is now confirmed and we present here a structural model for the short- range order state.

In the composition range : 0 X < 0.5 and parti-

cularly in the neighbourhood of X = 0.20 the tita- nium-sulfur system is very complicated from the structural point of view. For example it is known that . n o stable phase exists at 1 000 O C for compositions

varying from Ti,,,,S2 to Ti1.,,S2. This structural instability is revealed by the occurrence of polytypic modifications in the same batch and frequently in the same crystal. The structures of these polytypes are very similar to those of Cdl, and the extra titanium atoms are located in the Van der Waals gap. For a review of the various structures observed up to now and a mechanism proposed for their formation, one is referred to previous papers ([2] and references therein).

These structures consist of close-packed layers of sulphur atoms, the environnement of the titanium atoms being octahedral. In the composition range we consider (0

<

nately completely and partly filled. This contrasts with the structures observed for higher titanium

concentrations where the vacancies are no longer distributed in every other metallic layer.

The occurrence of polytypism in Ti, +,S, being closely related to the composition, there is an obvious, but still unknown, relationship between the presence of titanium atoms in the Van der Waals gap and the growing mechanism of the polytypes. Any attempt to elucidate this relationship requires an investigation of the real structure of these materials. This is one of the aims of the present paper.

2. Experimental. - The preparation of the samples has been described previously [3]. The compositions of the individual crystals were determined from unit cell volume and density measurements [l]. We assume this method to provide an accuracy of 0.02 on the X

value.

X-ray and electron diffractions have been used, and consistent features observed. In fact, considering the uncertainty about the composition homogeneity of the samples, it was easier to relate the diffuse scattering features to the composition using X-ray methods. So, only the X-ray diffraction results will be reported here. The X-ray patterns were obtained with stationary single crystals, a monochromatized MoKa radiation and a cylindrical camera [4]. Exposure times of about two days were required, due to relatively small crystal sizes.

SHORT-RANGE AND LONG-RANGE ORDER OF TITANIUM IN Ti, +,S, C7-203

3. Diffraction observations: - Figure 1 shows X- ray diffraction patterns of single crystals whose compo- sitions run from Ti,.,,S2 to Ti,.,,S2. The c direction is approximately perpendicular to the figure. We note that the diffuse intensity is localized in the vicinity of hexagonal prisms running through the 2-D Brillouin zone boundary corresponding to the parent structure. Concerning this observation it is relevant to take into account that the reciprocal space section

is a spherical one. Accordingly, the honeycomb network noticed on figure lb is thus a conclusive piece of evidence for the prismatic nature of the diffuse scattering features.

We shall now examine the evolution of the diffuse scattering distribution as a function of the para- meter X which represents the titanium concentration

FIG. 1. -X-ray diffuse scattering patterns for Ti,+,S2 wlth inci- FIG. 2. -Schematic representation of the diffuse intensity streaks

dent X-ray beam approximately parallel to c. a) Ti,,,,S2 ; and maxima corresponding to the scattering patterns shown in

b) Ti1.,,S2 ; c) Ti1.23S2 ; d) Til,2,S2; e) Ti1.,,S2. figure 1. The (a, b) unit cell is that of the matrix.

maxima are referred to the reciprocal cell of the Brillouin zone sides and concentrates on the maxima matrix. and on the associated triangles. Moreover the maxima

a) For Ti,.,,S2 (figures la, 2a) diffuse segments are located in the middle of the hexagon sides and extend along the direction of these sides. Weaker diffuse streaks can be observed in the form of curved triangles which link the intensity maxima. These triangles are centered on positions of the type h = k = 113.

b) Figures Ib, 2b (Ti,.2,S2) show an increase of the length of the diffuse segments so that the honeycomb array is now completely drawn. Furthermore the diffuse intensity is almost constant along this locus.

c) Figures Ic, 2c (Ti!,,,S,) show a similar pattern but a closer examinatlon reveals the existence of intensity maxima on the hexagon sides. They stand at h = k # 0.42 positions. Once more, these maxima

are linked by curved triangles centered at the hexagon vertices.

d) For a higher titanium concentration (figures Id, 2d, Ti,.,,S2) the diffuse intensity decreases on the

are shifted towards the heiagon vertices and peak at

h = k # 0.36 positions.

e) Finally these maxima reach the hexagon ver- tices (figures le, 2e, Ti,.,,S,). They define a two- dimensional superstructure with lattice parameters

a' = b' = a J3 and (a, a') = 300 where a is the parameter of the-basic unit cell.

4. Interpretation. - Pis it was previously suggest- ed [l] the main features-of diffuse scattering can be attributed to short-range ordering of titanium atoms within the sublattice generated by the defective metallic layers. This contrasts with the case of the stoichiometric TiS, compound where electron diffrac- tion patterns show diffuse streaks passing through the main Bragg spots [5]. There, the defective layers are assumed to be empty [6] so the origin of the diffuse scattering cannot be the same.

SHORT-RANGE AND LONG-RANGE ORDER O F TITANIUM IN Ti,+,S, C7-205

possible to consider separately the interlayers and intralayers correlations. In the present paper we propose a qualitative structural model for the latter. Therefore the problem becomes a two-dimensional one. However, interlayers correlations actually occur and produce intensity modulations along the hexa- gonal prism faces. These correlations are well esta- blished for Ti,,,,S, and will be studied in a forthcom- ing paper [7].

Concerning the two-dimensional problem, our interpretation is derived from calculation of short- range order parameters assuming a somewhat idea- lized locus for the diffuse intensity [8]. The results.are briefly summarized here :

i) two titanium atoms never are first neighbours ;

ii) second and third neighbours predominantly occur.

Consequently we suggest a microdomain model which takes account of first, second and third near- neighbour correlations. Two kinds of microdomains, A and B, are involved and correspond to ordered arrangements of third and second neighbour titanium atoms, respectively. Indeed the microdomain B cor- responds to the superstructure obtained for Ti,.,,S,.

Figure 3a shows an example of atomic arrangement for the case represented in figures lb, 2b. The corres- ponding diffuse intensity is shown in figure 3b. It has been computed by Fourier transform and drawn in the reciprocal lattice cell according to the darkening scale which is given. Due to its limited size the model does not primitively reflect the hexagonal ,symmetry observed on the diffraction pattern. In order to

FIG. 3a). - Model for the arrangement of titanium atoms (black circles) in the Ti,,,,S, case. The hexagonal layer sites are repre-

sented by the honeycomb network and the vacancies stand in the centers of the unoccupied hexagons. One microdomain of each

kind is indicated.

reproduce this symmetry we have assumed the pre- sence of three symmetry related models in the crystal. The intensity shown in figure 3b is, in fact, the sum of the three corresponding intensities. The qualitative agreement between figures Ib and 3b seems satisfac- tory.Nevertheless, the atomic concentration of the model is slightly higher (0.26) than actually observed for this diffuse scattering case (0.20). In fact this compositional problem is not fully understood.

The relationship between real and reciprocal space distributions (figures 3a and 3b) can be examined in terms of different considerations. Among these, the antiphase concept is probably one of the most conve- nient. In this respect one can note that the real space model is composed of a packing of small micro- domains of the two kinds (A and B). Considering the various sizes of these microdomains it can be deduced that the antiphase relationships which occur between microdomains of each kind are essentially aperiodic. In reciprocal space this produces streaks passing through positions ofthe h = k = 112 and h = k = 113 types, i.e. reciprocal lattice points for the super- structures A and B.

By the variation of the A and B microdomains sizes and distribution it might be possible to repro- duce the diffuse intensity evolution as a function of composition.

5. Discussion. - In a recent paper [g] De Ridder

et al. suggested a cluster model in order to describe the substitutional disorder in binary alloys. This model applies to the case of well-defined diffuse intensity contours and appears to be successfull in view of a quite good correspondence between observed and predicted diffuse scattering features.

More recently [10], the cluster model was used to elucidate the state of order in Ti,+,S, and in some similar -systems (Fe,TaS, and - Ni,WbS, forexample)

where ordering of atoms and vacancies occurs within hexagonal layers of octahedral sites. Clusters formed by the second neighbours of a lattice site were consi- dered and a relation for the cluster site occupancies was derived. Then, these authors suggested a micro- domain model which involves microdomains B and antiphase boundaries of the (1 1 .O) type. The validity of this model was checked by comparison with an optical diffraction analogue.

With reference to our interpretation we would point out that supplementary conditions must be introduced to provide a satisfactory agreement between observed and calculated diffuse intensity distributions. Thus, the exclusion of first neighbour titanium atoms is particularly important as it leads to the diffuse plane extinction, i.e. the formation of the hexagonal prisms network. Moreover it is clearly evident that third neighbour atomic correlations are involved for low titanium concentrations.

R. MORET, M. HUBER AND R. COMES

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--..--

.--.--

...

...

+...+.

.I....%

+.+.+I

.E. . f 4 4 4 f f f 4 4

I<2 2 d < 3 k I < 4 4 6 1 ~ 5 5 d < 6 &I<7 7 d < 8 8 d < 9 9<1<10 1061

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Intensity

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FIG. 3b. -Diffuse intensity distribution in reciprocal space obtained by Fourier transform of the model. The darkening scale is shown beneath the figure.

within the defective metal layers is probably related tion of the relationship between the diffuse intensity to the occurrence of polytypic structures in the modulations, particularly along c*, and the stacking composition range we consider. So, a close investiga- sequence of the polytypes should be worthwhile.

References

[l] MORET, R., HUBER, M., COMES, R., Phys. Status Solidi (a)

38 (1976) 695.

[2] LEGENDRE, J. J., MORET, R., TRONC, E., HUBER, M., J. Appl.

Cryst. 8 (1975) 603.

[3] TRONC, E., HUBER, M,, J. Phys. Chem. Solids 34 (1973) 2045. [4] C O M ~ , R., LAMBERT, M., LAUNOIS, H., ZELLER, H. R., Phys.

Rev. B 8 (1973) 571.

[ 5 ] WILSON, J. A., DI SALVO, F. J., MAHAJAN, S., Adv. Phys. 24

(1975) 117.

[6] CHIANELLI, R. R., SCANLON, J. C. and THOMPSON, A. H.,

Mat. Res. Bull. 10 (1975) 1379.

[7] MORET, R., TRONC, E., HUBER, M., C o b , R., to be published. [S] MORET, R., Thbe, Universitk Paris M (1977).

[g] DE RIDDER, R., VAN TENDEWO, G., VAN DYCK, D., AME- LINCKX, S., Phys. Status Solidi (a) 38 (1976) 663.

[l01 DE RIDDER, R., VAN DYCK, D., VAN TENDELOO, G., AME-