Magnetic properties of ternary chromium sulfides, V,Cr, -,S4 (0 <x <1.0) Anthony V. Powell* and Sascha Oestreicht Department of Chemistry, Heriot- Watt University, Riccarton, Edinburgh, UK EH14 4AS A series of phases V,Cr3 -,S4 (0.0d x d 1.0) have been prepared by high-temperature synthesis and characterised by thermogravimetry, energy dispersive X-ray microanalysis and powder X-ray diffraction in conjunction with Rietveld profile analysis. Data are consi:tent with the formation of single-phase products which all adopt the Cr3S4 structure (space group 12/m: a M 5.9, b =3.4, c M 11.2 A, 91.4"). Magnetic susceptibility data indicate that spin-glass behaviour persists in the range 0.4d x <1.0, whilst data for x =0.2 suggest that there is a slow freezing of spins prior to the onset of long-range magnetic ordering observed for x =0.0.A large number of binary transition-metal chalcogenides of stoichiometry M3X4 adopt the Cr3S4 structure (Fig. 1). This structure may be considered to be derived from that of CdI,. In the latter structure, cations (M) occupy octahedral sites between alternate pairs of layers in a hexagonally close-packed array of anions (X); the resulting stacking sequence may be represented schematically as MXXMXX. In the Cr3S4 struc- ture, additional cations are accommodated in half of the vacant octahedral sites in the X.-.X van der Waals gap in an ordered fashion resulting in an XMXM,.,XMX stacking sequence. The structure of Cr3S4 may therefore be viewed as an ordered defect structure intermediate between those of CdI, and NiAs.The presence of two crystallographically distinct cation sites suggests that a more appropriate formulation is (M)[M,]X,, where parentheses and square brackets denote sites in the vacancy layer and the fully occupied layer, respectively. When a second cation is present, two extreme cation arrange- ments corresponding to the normal (M')[ M,] X4 and inverse structures (M)[M'M]X4 have been ident5ed.l In addition, a number of non-stoichiometric phases have been and found to exhibit interesting variations in their physical properties as a function of composition. The precise structure adopted by non-stoichiometric phases will depend on the competing site-preferences of the constituent cations and in a small number of cases, studies of cation distributions have been carried out5-' We have recently commenced an investi- gation of structural and magnetic properties of such non-stoichiometric phases, and here present magnetic and structural data for the system V,Cr3 dxS4 (0.0dx <1.0).The end-member phases exhibit contrasting properties.VCr2S4 has been shown to be a semiconductor,* consistent with the presence of localised moments and formal oxidation states of V" and Cr"'. These properties are in agreement with predictions based on one- electron energy-level diagrams.* By contrast, Cr3S4 is an itiner- ant electron antiferromagnet. On the basis of powder neutron diffraction data,g the NCel temperature TNwas estimated to be 280 K.Subsequently, other workers have suggested" that the presence of impurity phases might result in an overestimate of the Nee1 temperature. More recent susceptibility and specific heat measurements" indicate TNto be in the range 200-220 K. The series V,Cr3 -,S4 therefore provides an opportunity to investigate the competition between itinerant and localised electron behaviour with changing chemical composition. Tazuke', has suggested, on the basis of magnetic susceptibility measurements, that phases in this system show a comparatively rare13314double transition from a paramagnetic to an antiferro- t Present Address: Max-Planck Institute for Colloid and Interface Science, Kanstr. 55, P-14513Teltow-Seehof, Germany. n Fig. 1 Ball-and-stick representation of the structure of Cr,S,.Large filled circles represent chromium ions in the fully occupied layer, small open circles represent chromium ions in the vacancy layer and large open circles represent sulfide ions. magnetic to a spin-glass state and has described these materials as antiferromagnetic re-entrant spin-glasses. However, doubts remain as to the phase purity of the samples used in these experiments: for example, large uncertainties in TNwere attri- buted to imperfections in the sample. We have endeavoured to produce well characterised single-phase samples of these materials and here present magnetic data which show differ- ences to those previously presented. In particular we find no evidence for the double transition.Experimental Appropriate quantities of vanadium, chromium and sulfur powders (all Matthey Catalogue Sales) were ground in an agate mortar. All reaction mixtures were prepared with a slight deficiency of sulfur, corresponding to compositions of AB2S3.93, as it has been shown15 that the phase range of the Cr3S4 structure does not extend to the fully stoichiometric composi- tion. Reaction mixtures were sealed into evacuated, silica ampoules and fired at a temperature of 850°C for 4 days with one intermediate regrinding; a further regrinding was followed by a final firing in a silica ampoule at 950°C for 3 days. Samples were cooled to 300°C prior to removal from the J. Muter. Chem., 1996, 6(5),807-813 807 furnace Reaction progress was momtored by powder X-ray Quantum Design MPMS2 SQUID susceptometer Samples diffraction using a Philips PA2000 diffractometer with nickel- were loaded into gelatin capsules at room temperature and filtered Cu-Ka radiation Powder X-ray diffraction data for data were collected over the temperature range 6-296 K both subsequent Rietveld refinement were collected in step-scan after cooling the sample in zero applied field (zfc) and after mode using a step sue of 28=0 02" and a counting time of 5 s cooling in the measunng field (fc) Measuring fields of 0 1, 1 step-Energy dispersive X-ray microanalysis to determine and 10 kG were used All magnetic data were corrected for V Cr ratios was performed using a JEOL 200FX electron diamagnetism of the gelatin capsule and for intrinsic core microscope fitted with a Tracor Northern analysis system diamagnetism VCr04 was used as an intensity standard Sulfur contents were determined thermogravimetncally by oxidation in a flow of Resultsdry oxygen on a Stanton Redcroft TG-750 thermobalance The mass loss on conversion to the corresponding oxides was The results of the analysis of chemical composition are shown related directly to the sulfur content Magnetic susceptibility in Table 1 Data are in good agreement with the stoichiometry measurements on powdered samples were made using a of the initial reaction mixtures, consistent with the formation Table 1 Results of thermogravimetry and energy dispersive X-ray microanalysis for V,Cr3 -,S4 (0 0 <x <1 0) nominal nominal expenmentally expenmentally expenmentally determined composition V Cr determined V Cr determined S (V +Cr) composition cr3s3 93 --1 31( 1) Cr3S3 94 vO zCr2 $3 93 0 07 0 07(1) 1 31( 1) vO zCr2 $3 93 vO 4cr2 gS3 93 0 15 0 15( 1) 1 30( 1) vO 4cr2 6% 91 vO 6Cr2 4s3 93 0 25 0 23( 1) 1 31( 1) vO 56cr2 44s3 93 0 36 0 39( 3) 1 32( 1) vO 84cr2 16s3 97vO BCr2 2s3 93 VCr2S3 93 0 50 0 47(2) 1 36( 1) vO 92cr1 97s3 93 I I I I I 1 1 I I I r 1 I I I I I I 0 r(CrJS4 %'o 2cr28% 0 * .-I Y) 0 I I I I I I I I I I 1 I 1 I I I 1 I 02 03 04 05 06 07 08 09 10 02 03 04 05 06 07 oe 09 10 1 1 I 1 I 1 1 1 I I I I 1 I 1 I I I 1 - 0 Ic.v) Va 4CrZ 6s4 0 VO 6cr14s4 5 a-so 4 9 0-O D $ e-c Ya," rn 0 - E c.4- 0 0 Q 0 0 .I I I I I 1 I I I I 1 I I I I I I I ri I I I I I I I 1 n . I I I I I 1 1 I I - VO8Cr22% 0 4 0 4 v,vr 0 0 ...8 . .*I --.-I--..I.*..111). 111.1 .I--., .*0 II u, Ia.n .I$ ,in i-mi ma.# mm om0-no-*-il..l........,-:-4 .I--:-:-I I I I I t I I I I I I I I I I I I 02 03 04 05 06 01 OR 09 10 02 03 04 05 06 07 oe 09 10 Fig. 2 Final observed (points), calculated (full line) and difference (lower full he) profiles for V,Cr3 .S4 (00 <x < 1 0) phases 808 J Muter Chem, 1996, 6(5),807-813 of single-phase products. For the phase with nominal composi- behaviour may be divided into one of three types, according tion VCr,S,, results indicate a slight deficiency of metal, to composition.In the compositional range 1.0<xd0.4, zfc suggesting that some attack of the silica ampoule has taken and fc data overlie each other in the temperature range place. This is consistent with energy dispersive X-ray micro- Tp d T d296 K. A maximum in susceptibility is observed in the analysis data which indicated, for all phases prepared, the zfc curve at Tg whilst the fc curve continues to rise. This indicates presence of trace amounts of silicon. The levels of the resulting magnetic frustration, in agreement with the previous description minor impurity phase are extremely low and below the limits of these materials as spin-glasses. Spin-glass behaviour persists of detection by powder X-ray diffraction.to x=0.4,the glass transition temperature, <,increasing linearly Initial examination of powder X-ray diffraction patterns with decreasing vanadium content. At x=O.2, zfc data show a indicated that all phases could be indexed on the basis of a broad ill-defined maximum at Tz 14 K. However, zfc and fc monoclinic unit cell with parameters similar to those for Cr,S4. data overlie each other only over the range 126d TG296 K However, in view of the existence of a number of phases with and start to diverge at 126 K, a temperature considerably above and that at which there is a susceptibility maximum. This may closely related structures and differing stoi~hiometriesl~ because of the significant influence that such impurities can correspond to a slow freezing of the spins resulting in magnetic have on magnetic properties, it was desirable to obtain further clusters of finite size, with associated uncompensated magnetic evidence of phase purity.Diffraction data were analysed by moments, prior to the onset of long-range antiferromagnetic the Rietveld16 method of profile analysis as incorporated in ordering which has been observed for Cr3S4. Data for x=O.O the GSAS suite of programs.” Starting models for all phases (Cr,S,) are in agreement with those reported previously and were derived from the previous X-ray diffraction study of indicate an apparently antiferromagnetic transition at Tz50 K. Cr,S, .I5 Recent work on VCr2S418 demonstrates that vanadium However, deviations from a modlfied Curie-Weiss law begin at is evenly distributed between sites in the vacancy and fully significantly higher temperatures (Tz220 K): in the region to occupied layers.However, since the difference in X-ray scat- which TNhas been assigned previously. tering power between vanadium and chromium is insufficient Attempts to fit magnetic susceptibility data in the high- to discriminate between them in the mixed phases, and as temperature region to a Curie-Weiss law resulted in relatively Rietveld refinement was carried out solely to establish phase poor agreement. However, introduction of a temperature-purity, in this work, vanadium was arbitrarily introduced at independent term, xo, in a modified Curie-Weiss law of the the metal site in the vacancy layer such that overall stoichi- form x =xo + C/(T-Q), led to a significant improvement in the ometry was maintained.fit in the high-temperature region as exemplified by Fig. 4 in The background was modelled using a cosine Fourier series which reciprocal observed data for VCr,S, are compared with with the coefficients introduced as refinable parameters. Initial calculated data derived from the fit to the modified Curie- refinement of background, zero-point, cell parameters and Weiss law. Derived magnetic parameters are given in Table 3. atomic positions proceeded smoothly. Isotropic temperature factors when introduced into the refinement became unstable Discussionfor phases with 0.4dxd 1.0. Thermal parameters for these phases were subsequently fixed at those refined values appro- All peaks in the powder diffraction patterns are fitted by the priate to Vo.2Cr2.8S4, prior to the introduction of peak shape structural model and there is no evidence to suggest the parameters as variables in the refinement.Final observed, presence of any significant impurity phases. Weighted profile calculated and difference profiles are shown in Fig. 2 and the R factors were of the order of 4-7%. A detailed discussion of resulting parameters are given in Table 2. the structures of these phases will not be given here, as results Magnetic susceptibility data for a measuring field of 1000 G of a recent structural study utilising a combination of powder are presented in Fig. 3. In all cases, field-cooled (fc) and zero- neutron and powder X-ray diffraction data will folloy in due field-cooled (zfc) susceptibilities overlie each other completely at course.19 Mean cation-anion separations of ca.2.4A are in higher temperatures. No appreciable field dependence was reasonable agreement with sums of respective ionic radii,20 observed over the range of applied field strengths investigated. whilst cation-cation separations relevant to the discussion of A broad maximum is observed at low temperatures (T,)for all magnetic properties which follows are summarised in Table 4. compositions. The insets to Fig. 3 show the differing behaviours The variation of cell parameters with composition is shown in of the fc and zfc susceptibilities below this transition.Magnetic Fig. 5. There is an overall decrease in each of the unit-cell edge Table 2 Parameters resulting from Rietveld refinement of powder X-ray diffraction data for V,Cr3-,S4 (0.0bx < 1.0)” x in V,Cr, -xS4 0.0 0.2 0.4 0.6 0.8 1.o 5.9538(4) 3.4211 (3) 11.2407( 7) 91.526(3) 5.9609( 4) 3.4164( 3) 11.2322(7) 91.428(3) 5.9762( 2) 3.4211 (1) 11.3145(5) 91.281 (3) 5.9 6 12(4) 3.4032( 2) 11.2172(7) 91.364( 2) 5.9488 (4) 3.3920( 3) 11.2026(8) 91.377(2) 5.9381 (5) 3.3827(3) 11.2086(8) 91.437(3) 0.85(9) 0.2586(3) 0.85(9) 0.33 72( 8) 0.3643 (4) 0.29(8) 0.3350(8) 0.8800(4) 0.29(8) -0.0238(5) 0.83(8) 0.2588( 3) 0.83(8) 0.3387(8) 0.3651(4) 0.52(8) 0.3361(8) 0.8807 (4) 0.52(8) -0.02 18( 5) 0.83(-) -0.0196( 6) 0.83(-) 0.2576(3) 0.3382( 9) 0.3684( 4) 0.3421(9) 0.8824(4) 0.52(-) 0.52(-) 0.83(-) -0.0222(5) 0.2579( 3) 0.3381(7) 0.3665( 3) 0.3388(7) 0.8809( 4) 0.52(-) 0.83(-) 0.52(-) 0.83(-) -0.0238( 5) 0.83(-) 0.2574( 3) 0.3357( 7) 0.3663 (4) 0.3396( 7) 0.8819(4) 0.52(-) 0.52(-) 0.83(-) -0.0262( 5) 0.2571(3) 0.3367(8) 0.3647( 4) 0.3369(9) 0.8830(4) 0.83(-) 0.52(-) 0.52(-) 4.4 4.7 5.5 5.1 5.7 6.8 3.3 3.4 4.0 3.7 4.2 5.1 a Space group: Z2/m, M on 2a (O,O,O), site occupancy factors: (1 -x)Cr, (x)V, Cr on 4i (x,O,z), S( 1) on 4i (x,O,z),S(2) on 4i (x,O,z).J. Muter. Chem., 1996, 6(5),807-813 809 I a a oxk O k 00 OaOn0 OOaOaO 6 J , . I . , . , . , . , . , o so 100 150 zoo 250 300 vcr,s4 -,S, (00 <x < 1 0) phases measured in a field of tion data show that solid-solution behaviour exists over the entire compositional range studied, it is evident from Fig 5 that changes in cell parameters with increasing vanadium content do not follow Vegard's law In particular, there are anomalies in all four plots at a composition of Vo4Cr2,S4 It is notable that this composition corresponds to that at which marked changes in the magnetic properties occur and may be indicative of changes in relative site preferences of the vanadium and chromium cations Powder neutron diffraction measure- ments have been used to investigate the site preferences of cations in the related systems Fe,V3-,S45 and CrxTi3-,Se4 In both systems, the partitioning of cations between sites in the fully occupied and vacancy layers was found to be incom- plete, although in the latter system, chromium was found to show a marked preference for sites in the vacancy layer Recent l'work,lg using a combination of X-ray and neutron scattering, has shown that a more complete randomisation of the two cations over the two types of site is found for VxCr3-,S4 Moreover, a marked change in the distribution of vanadium a cations between the two types of site occurs in the region in which anomalies in the plots of cell parameters ZIS composition are observed (0 2 <x < 0 4) Data in Table 3 reveal that there is a temperature-indepen- dent contribution of ca 3 x emu to the paramagnetic susceptibility which is virtually independent of composition In addition, the negative Weiss constants indicate that the predominant cation-cation interactions in this system are antiferromagnetic The Curie constants decrease with increas- ing vanadium content, as would be expected for replacement of the Cr3+ d4 ion with V2+ d3 However, the values determined here are considerably lower than would be expected from the spin-only value for localised moments, which for example Table 3 Parameters denved from magnetic susceptibility data for V,Cr, ,S4 (0 0 < x < 1 0) x in V,Cr, ,S, 04 06 08 10 3 O(1) 2 7(1) 2 8(1) 20(1)1 66(4) 1 32( 3) 1 14(4) 0 82(2) -55(3) -33(2) -65(4) -65(4) 44 40 36 32 X -0 NE 20 18 16 14 12 10 0 6 Fig.3 Zero-field-cooled (zfc) and field-cooled (fc) molar magnetic susceptibilities for V,Cr, lo00 G Insets show detail around the transition measured with a field of 100 G 500-400 -3 1-E h r;." 300--E Y 7 rY 200-100-~ l ~ l ~ l ~ l ' ~ l 'l 0 50 100 150 200 250 300 TIK Fig.4 Observed (m) and calculated (-) reciprocal susceptibility plot for VCr,S4 The calculated plot is denved from the fit to modified Cune-Weiss law lengths on moving from Cr,S4 to VCr2S4 1on:c radii given by Shannon'' [r(V2')=0 79 A, r(Cr2+)=0 80 A] suggest that replacement of Cr2+ by V2+ would lead to very little change in the size of the unit cell However, examination of the one- electron energy-level diagrams presented by Holt et al reveals that the presence of Cr2+ d4 requires the population of e8 energy levels which are effectively antibonding in nature Replacement of Cr2+ d4 with V2+ d3 ions would lead to the removal of electrons from these levels and could account for the observed contraction in the unit cell Whilst X-ray diffrac- xo/10 emu C/emu K-' T,/K 810 J Muter 00 02 2 O(2) 24(1) 3 44(2) 2 03(6) -324(4) -97(4) -14 Chem, 1996, 6(5), 807-813 Table 4 Selected cation-cation distances (A)for V,Cr,-,S, (0.0<x <1.0) x in V,Cr,-,S4 0.0 0.2 0.4 0.6 0.8 1.o M-M 3.421 1(3) x 2 3.4164( 3) x 2 3.4211(1) x 2 3.4032( 2) x 2 3.3920( 3) x 2 3.3827(3) x 2 Cr-Cr 3.4211( 3) x 2 3.4164(3) x 2 3.4211( 1)x 2 3.4032( 2) x 2 3.3920( 3) x 2 3.3827( 3) x 2 3.193(5) x 2 3.214( 5) x 2 3.243(6) x 2 3.206( 5) x 2 3.182(5) x 2 3.151(5) x 2 3.691 (5) x 2 3.672( 5) x 2 3.656( 6) x 2 3.672( 5) x 2 3.680( 5) x 2 3.697(6) x 2 Cr-Ma 2.914(3) x 2 2.913(3) x 2 2.920(4) x 2 2.899( 3) x 2 2.890( 3) x 2 2.889(4) x 2 Cr-Mb 4.494(2) x 4 4.489(2) x 4 4.498(2) x 4 4.471(2) x 4 4.556(2) x 4 4.449( 2) x 4 4.423(3) x 4 4.417( 3) x 4 4.439( 3) x 4 4.423(3)~4 4.424( 3) x 4 4.428( 3) x 4 4.329( 3) x 4 4.333( 3) x 4 4.364( 3) x 4 4.330(2) x 4 4.320( 3) x 4 4.310( 3) x 4 MS, and CrS, octahedra with a common face.MS, and CrS, octahedra with common vertices. M is defined in Table 2. O0 o0 O0-3A2 397--3A1 o0 O oo 0. -3M 0596 --339 5 -Q -33 oc' 0 0. 0 oo59s --337 SW --336 o0 i4 I . 1 . , . 1 . , . I !335 O i 0uIb OD 02 OA I6 oa ID 1132 -oo-91s 1130--913 iim--91.45 $ 0 0 o0 !?! 1126-b, -91.40 3 IIW- .Q -9135 1122-' -Y130 1120- 4 I ou - , 03 . 0.4 0.6 , , 08 . , ID !913 x in V, Cr,-,S Fig. 5 Compositional variation of lattice parameters: (a) a and b parameters (b)c and parameters predicts C=6.75 for Cr,S,, and differ from those obtained in earlier work" where Curie constants close to those predicted for spin-only moments were obtained from data in the range 295 < T <800 K. This discrepancy probably indicates that the high-temperature limit for collection of magnetic data in this work is insufficiently high for the moments to be non-inter- acting. In addition, electron delocalisation may contribute to the lowering of Curie constants.One of the chromium ions in Cr,S4 is formally present as Cr" d4. In a crystal field of regular octahedral symmetry, this would result in a t2,3eg1 configur- ation. Whereas the tag levels in Cr,S, are effectively localised, covalent mixing of the eg orbitals with anion s and p orbitals leads to a broadening of eg levels into a narrow band, thereby reducing the effective moment. All phases for which x>O.O have eg levels populated. Furthermore, for vanadium-rich phases, broadening oft,, states is possible, as found previously in binary vanadium sulfides.21,22 Previous work" found magnetic anomalies in the tempera- ture range 100d TG296 K which were ascribed to a double magnetic transition.Careful examination of our data in this region, including calculations of first derivatives of the x us. T O0 Fig. 6 Magnetic structure of Cr,S,. The crystallographic unit cell is outlined and anions are omitted for clarity. Light and dark circles denote cations with (-) or (+) spin, respectively. curves, provides no evidence for a transition to an antiferro- magnetic state above q.In addition, the data in this tempera- ture region were well fitted by a modified Curie-Weiss law and we therefore conclude that for our samples, the magnetic behaviour in this compositional range involves a change from a paramagnetic to a spin-glass state with decreasing tempera- ture. The existence of a spin-glass phase suggests some degree of electron localisation consistent with the known semiconduct- ing properties of VCr,S4 itself.However, the reduction in the values of the Curie constants below a value predicted on the basis of an ionic structure, together with the almost constant temperature-independent contribution to the susceptibility, suggests that localised and delocalised electrons are simul- taneously present. The magnetic structure of Cr3S4 (Fig. 6) determined by powder neutron diffraction measurements at 4.2 K9 consists of ferromagnetic sheets parallel to the (101) planes which in turn are coupled antiferromagnetically with respect to each other. This results in a doubling of the magnetic unit cell in the a and c directions. By considering the eB band to be infinitely narrow, application of the qualitative rules previously devel- oped by Go~denough~~ permits analysis of and Kanam~ri~~ the observed magnetic structure in terms of individual super- exchange interactions. In the fully occupied layer each Cr"' d3 ion has six nearest-neighbour Cr"' d3 ions (Fig.7). A 90" correlation superexchange via an anion p orbital is predicted J. Muter. Chem., 1996, 6(5), 807-813 811 (3.12) Crtn Cr, f Fig. 7 Illustration of interionic magnetic interactions in Cr& defining fully occupied layer; (b) interactions within the vacancy layer, and (c) cation-cation separations. to be ferromagnetic, whereas antiferromagnetic exchange results from direct cation-cation interactions. The latter decrease more rapidly with increasing cationic separation than do tee former.Hence, the two longer-range [d(Cr-Cr) =3.42, 3.69 A] interactions are dominated by correlation super-exchange resulting in &(2) >0 a,nd &b >0, whereas the relatively short-range [d(Cr-Cr) =3.19 A] interaction is dominated by direct cation-cation exchange resulting in JF(l) <0. The short separation betwoeen Cr"-and Cr"'-centred octahedra [d(Cr-Cr)=2.91 A] which share a common face results in direct cation-cation interactions dominating the JVFterm. As the d shell is less than half-full, these are predicted to be (JVFantiferr~magnetic~~ <O). In addition, each Cr" in the vacancy layer has six Cr'" neighbours, to which it is linked by a common anion, in each of the fully occupied layers above and below it (Crl-Cr12 in Fig.7). Whilst cation-anion-cation angles of ca. 130" lead to some uncertainty over the sign of correlation superexchange interactions, comparison with other systems23 suggests that they will carry the sign of the 180" interaction. The signs of correlation superexchange interactions involving Cr" are difficult to predict owing to the degenerate ground state of octahedral Cr" d4. One possible model may be derived in a similar manner to that applied to Mn"' oxides." The vacant d orbital can participate in four dsp2 hybrid orbitals which form a square-plane directed towards those (5.42) the exchange constants discussed in the text. (a) Interactions within the interlayer interactions.Numbers in parentheses indicate corresponding sulfurs which are common to Crllll-Crgl'l (Fig. 7). All 180" superexchange interactions between Cr" and the latter will therefore be antiferromagnetic (JVF(2) <0). Con-c0, JVF(3) versely, the half-occupied d, orbital directed towards sulfurs common to Cr$'-Crlp1 will give rise to a ferromagnetic 180" correlation superexchange interaction with the latter (&(I) >0). The remaining interactions are the 90" cation- anion-cation intralayer Cr'I-Cr" interactions for which d,-p,/p,-d, coupling results in ferromagnetic exchange (Jv,>O). Allowing for a finite width to the eg band does not alter this analysis significantly as only interlayer Cr"-Cr"' 180" interactions via a common anion and intralayer Cr"-Cr" 90" interactions are affected by the width of the eg band.Weakening of these interactions does not change the overall magnetic structure which is primarily determined by the signs of JF(l), JF(2), JFb and JVF* The spin-glass behaviour of VCr2S, is a consequence of mag- netic frustration which prevents the establishment of long-range order. Extension of the above treatment permits rationalisation of this behaviour. It has been shown18 that this compound is more correctly formulated as (Vo.51Cro.49)[ S4.Vo.49Cr1.51] Whilst ambiguity exists regarding the oxidation state of vanadium in the fully occupied layer, Hayashi et uL7 have indicated that for TiCr2Se,, chromium is present as Cr"' irrespective of the type of site which it occ-812 J.Muter. Chem., 1996, 6(5),807-813 upies. Similar behaviour in VCr,S, would result on (Vo.5111Cro.4~11)[ S, with all ions being isoelec- Vo.4~1Cr1.511'1] tronic (d3). Cation-cation separations show little variation in traversing the series from Cr3S, to VCr2S, and the relative magnitudes of competing exchange mechanisms within the fully occupied layer would not be expected to vary from those of Cr3S,. The signs of JF(l)and JF(2)are therefore identical to those for Cr3S4. Intralayer 90" cation-anion-cation inter-actions between d3 ions are ferromagnetic leading to JFb>O and JVb>0. Furthermore, interlayer interactions, of the direct cationsation type, result in JVF<0. Other interlayer inter- actions of the 180" correlation type involve d3 ions only and all are predcted to correspond to antiferromagnetic exchange.Given the presence of both ferromagnetic and antiferromag- netic coupling in the fully occupied layer, it is immediately apparent that cations in the vacancy layer cannot be simul- taneously antiferromagnetically aligned with all six neighbours in each of the two neighbouring fully occupied layers. The model therefore predicts the magnetic frustration implied by the spin-glass behaviour of VCr,S,. Structural studies" demon- strate that a similar statistical distribution of vanadium persists in the compositional range 0.4,<x,< 1.0. The increase in with decreasing x can be associated with the corresponding increase in the amount of Cr" d4, permitting the growth of magnetically ordered regions.At some critical composition, x,, it is to be expected that exchange pathways exist which permit the establishment of long-range magnetic order. From this work, it would appear that x, ~0.2.Further investigation of the properties of phases with compositions close to x=O.2 are required. In particular, low-temperature neutron diffraction measurements would establish whether Vo.,Cr,$, is magneti- cally ordered. Financial support from the EPSRC (grants GR/J36075 and GR/J34231) is gratefully acknowledged. We wish to thank Dr A.M. Chippindale, University of Oxford who performed the energy dispersive X-ray microanalysis measurements and Mr D.C. Colgan of Heriot-Watt University for thermogravimetric measurements.References 1 A. Wold and K. 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