Distribution of Cations and Vacancies in TaFe1. 25Te3 Studied by

8712

J. Phys. Chem. B 1998, 102, 8712-8718

Distribution of Cations and Vacancies in TaFe1.25Te3 Studied by Mo1 ssbauer Spectroscopy C. Pe´ rez Vicente,*,† M. Womes, and J. C. Jumas Laboratoire de Physicochimie de la Matie` re Condense´ e (UMR 5617 CNRS), CC-003, UniVersite´ Montpellier II, Place Euge` ne Bataillon, 34095 Montpellier Cedex 5, France

L. Sa´ nchez and J. L. Tirado Laboratorio de Quı´mica Inorga´ nica, Facultad de Ciencias, UniVersidad de Co´ rdoba, AVda. San Alberto Magno, s/n, 14004 Co´ rdoba (Spain) ReceiVed: April 30, 1998; In Final Form: July 14, 1998

125Te and 57Fe Mo ¨ ssbauer spectroscopy are used to assess the tellurium sublattice and iron clustering in the pseudo two-dimensional structure of 57Fe-enriched TaFe1.25Te3. The 125Te spectrum reveals two quadrupole signals in 1:2 intensity ratio ascribable to two sets of unequivalent tellurium atoms in a highly distorted electronic environment. The basic features of the 57Fe Mo¨ssbauer spectra at 77 and 5 K were accounted for by a Markov chain treatment of short-range ordering (SRO) of iron atoms, while a model based on random distribution fails to describe the complex hyperfine structure of the spectra.

Introduction Tantalum iron telluride TaFe1.25Te3 is an interesting compound not only from the point of view of its structure but also because of electric, magnetic,1 and insertion2 properties. The structure has been recently reported1 showing the presence of an unusual Ta-Fe bonded network in Ta-Fe-Fe-Te ribbons, which define a pseudo-layered structure. This structure strongly differs from the classical layered chalcogenides with their close packed arrangement of chalcogen atoms and metal atoms occupying the octahedral interstices between consecutive chalcogen layers. In TaFe1.25Te3, iron atoms are placed in two nonequivalent crystallographic sites. One of them is fully occupied while the other one is partially filled by iron atoms, three-fourths of the sites remaining vacant. Although the crystal structure of TaFe1.25Te3 seems now to be completely understood due to the detailed X-ray diffraction study by Badding et al.,1 one question still remains. The fact that the existence of a single-phase compound is limited to a very narrow range of stoichiometry, between Fe1.25 and Fe1.29, despite the large number of crystallographically identical sites remaining vacant, led Badding et al. to the hypothesis of an ordering of Fe atoms. However, the authors found no indications of a possible superstructure. In cases where eventual short-range ordering effects are to be investigated, experimental methods that are (unlike diffraction techniques) not based on coherence phenomena can give better results. Mo¨ssbauer spectroscopy, for example, has proven to be very sensitive to variations of the local environment of the probing atom, with each environment giving rise to an individual spectrum. The presence of two active Mo¨ssbauer isotopes in TaFe1.25Te3 (125Te and 57Fe) makes this compound an ideal candidate for a complete Mo¨ssbauer characterization. In this paper, we report on the results obtained by Mo¨ssbauer spectroscopy for these two isotopes. The occurrence of a magnetic ordering at low temperature facilitated * Author to whom correspondence should be addressed. † Permanent address: Laboratorio de Quı´mica Inorga ´ nica, Facultad de Ciencias, Universidad de Co´rdoba, Avda. San Alberto Magno, s/n, 14004 Co´rdoba (Spain)

the identification of several environments around Fe atoms and allowed an interpretation of the results on the basis of a Markov chain theory. Thus, our paper is organized as follows: after two short sections on experimental details and the crystal structure of TaFe1.25Te3, we shall present and discuss results obtained by Mo¨ssbauer spectroscopy in two sections, separately for each isotope. The last section will be devoted to a short description of Markov’s theory and to an evaluation of our results in the frame of this theory. Experimental Section Powder samples of TaFe1.25Te3 were synthesized as described elsewhere.1 For reducing the recording time of 57Fe Mo¨ssbauer spectra, enriched 57Fe was used to synthesize the samples. The X-ray diffraction patterns (XDP) were obtained on a Siemens D-5000 diffractometer using CuKR radiation and graphite monochromator. The XDP confirmed that the sample was single-phased. 57Fe Mo ¨ ssbauer spectra were recorded in the constantacceleration mode on an ELSCINT-AME40 spectrometer at 77K and 5 K. The velocity scale was calibrated with the six-line spectrum of a high-purity iron foil absorber. The source was 57Co(Rh). Lorentzian profiles were fitted to the recorded spectra by the least-squares method.3 The spectrum at 77 K was recorded in a 1024-channel configuration instead of the classical 512-channel configuration in order to increase the resolution and to facilitate the identification of the various components. In light of the results obtained at 77 K, the spectrum at 5 K was also refined. The Mo¨ssbauer spectrum of 125Te was recorded at 4 K, using Mg3125mTeO6 as source, prepared by activation of Mg3124TeO6 under a flux of 3 × 1014 n cm-2 s-1.4 Structure TaFe1.25Te3 has a monoclinic structure (space group P21/m). The structural parameters and atomic position extracted from ref 1 are included in Table 1. There are three sites for

10.1021/jp982070m CCC: $15.00 © 1998 American Chemical Society Published on Web 10/08/1998

Cations and Vacancies in TaFe1.25Te3

J. Phys. Chem. B, Vol. 102, No. 44, 1998 8713

Figure 1. Structure of TaFe1.25Te3. Projection perpendicular to (010) direction.

TABLE 1: Unit Cell Parameters and Atomic Coordinates of TaFe1.25Te3a a ) 7.416(9) Å b ) 3.628(2) Å atom Ta Fe1 Fe2 Te1 Te2 Te3

Unit Cell Parameters c ) 10.011(9) Å β ) 109.01(9)°

Atomic Coordinatesb occupancy (%) x 100 100 25 100 100 100

0.8340(1) 0.3853(2) 0.7686(11) 0.4392(1) 0.0165(1) 0.2179(1)

z 0.3007(1) 0.9110(3) 0.9953(7) 0.1860(1) 0.8411(1) 0.4970(1)

Figure 2. Structure of a ribbon, the building block of the TaFe1.25Te3 structure. Projection perpendicular to (010) direction. The different crystallographic sites of Te are noted 1, 2, and 3.

a All atoms are placed in 2e site (x, 1/4, z) space group P2 /m. b From 1 ref 1.

accommodating Te atoms: two for iron atoms (one of them 100% occupied, noted Fe-1, the other one only 25% occupied, noted Fe-2), and only one for Ta atoms. This structure consists of Ta-Te-Fe-Te-Ta ribbons, bridged at right and left by two Te atoms as (Ta-...-Ta) - Te3 - (Ta-...-Ta). It creates pseudo-layers (as illustrated in Figure 1), which are linked to each other by Fe2-Te bonds and Te-Te van der Waals forces. It is worth noting that the Fe2-Te interactions are not very important because only 25% of the theoretical positions of Fe2 are really occupied by iron atoms. Thus, this structure presents tunnels that make this compound an interesting candidate for intercalation studies.2 Figure 2 shows a zoom on one ribbon and the bridging Te atoms. We easily observe the three different Te sites (noted 1, 2, and 3). Although Te1 and Te2 do not belong to the same set of symmetry equivalent sites, they are both included in the ribbon and their environments are similar (coordinated by Ta and Fe atoms). This is not the case of Te3, located between two ribbons and coordinated only by Ta atoms. The structure of a ribbon is shown in Figure 3. If only the Fe and Te atoms present in a single ribbon are considered, Fe2 atoms are coordinated by 4 Te in a slightly distorted squareplanar configuration and Fe1 atoms are found to be in a triangular-planar coordination, also slightly distorted [see Figure 3 (left)]. Figure 3 (right) shows the direct interactions between

Figure 3. Structure of a ribbon, the building block of the TaFe1.25Te3 structure. Projection along (010) direction. Ta and Te3 atoms have been excluded. (Left) Showing the Te-Fe interactions. (Right) Showing the Fe1-Fe2 interactions.

Fe1 and Fe2 atoms. Fe2 atoms always have three neighboring Fe1 atoms. The situation is different for Fe1 atoms. They have two neighboring Fe1 and three Fe2 atoms. Because the latter can be occupied or empty we can find four different environments for Fe1, depending on the local occupancy of Fe2 around the Fe1 atoms. Thus, they can have two, three, four, or five neighbors. Table 2 summarizes the number of neighbors and distances between them.

8714 J. Phys. Chem. B, Vol. 102, No. 44, 1998

Pe´rez Vicente et al.

TABLE 2: Number of Neighbors and Distances between Fe Atoms in TaFe1.25Te3 neighbors central atom

Fe1

Fe2

Fe1

2 at 2.720 Å

2 at 2.491 Å 1 at 2.694 Å

Fe2

2 at 2.491 Å 1 at 2.694 Å

Figure 4. 125Te Mo¨ssbauer spectrum recorded at liquid He temperature and the proposed fitting.

TABLE 3: Hyperfine Parameters of 125Te Mo1 ssbauer Spectrum of TaFe1.25Te3 at Liquid He Temperature: Isomer Shift (IS), Quadrupole Splitting (QS), Line Width (LW), Contribution and Attribution of the Doublets IS (mm/s)

QS (mm/s)

LW (mm/s)

contribution

attribution

1.49(9) 1.34(6)

0.67(9) 7.4(9)

7.28(5)a 7.28(5)a

67.3(7) 32.7(9)

Te1 + Te2 Te3

a

Constrained to be equal.

125Te

Mo1 ssbauer Spectroscopy

Figure 4 shows the 125Te Mo¨ssbauer spectrum of TaFe1.25Te3 recorded at liquid He temperature. The results of the refinement are included in Table 3. Irrespective of the large natural line width of the 125Te transition (5.20 mm/s), two different components could be resolved in the spectrum. Thus the complex signal decomposed in two quadrupole-split components. This behavior differs from that previously reported for binary tellurides, such as VTe2, TiTe2, and TaTe2, in which multiple components were not resolved in the 125Te Mo¨ssbauer spectra.5,6 The values of the isomer shift (IS) obtained for each component are significantly different. It is well established that the electron density at the nucleus depends on the population of the valence shell orbital. For MTe2 compounds, where TeTe interactions play an important role, as the deficit in 5p orbital population near the nucleus increases, the isomer shift values increase according to6

IS (mm/s) ) IS0 - 2.4R + 0.4β

we find a higher IS for TaFe1.25Te3 as compared to ditellurides, although the shortest Te-Te distance in TaFe1.25Te3 is larger than in TaTe2 (3.742 and 3.595 Å, respectively). However, IS values are also very sensitive to the chemical environment of Te atoms. This effect was particularly evident in (R-MoTe2, where although having an undistorted 2H structure, values of IS as high as 1.66 mm/s have been reported.6 The electron density at the nucleus is also dependent on the population of the valence shell orbital, which may differ from that of the hypothetical Te2- ion by covalent interactions. From the above discussion it can be concluded that the IS values obtained from the 125Te Mo¨ssbauer spectrum of TaFe1.25Te3 should be interpreted in terms of two markedly different chemical environments of the tellurium atoms, while Te-Te interactions such as those found in layered 1T ditellurides can be considered negligible. On the other hand, the quadrupole splitting (QS) values give information about the average deviation of the electronic states of tellurium from cubic symmetry. According to the previous structural description, from the three sets of 2e sites occupied by Te atoms, two types of atoms can be distinguished: those directly coordinating the Ta-Fe metal ribbons, Te1 and Te2, and those bridging adjacent ribbons, Te3 (see Figure 2). The two types can be correlated with the results in Table 3. Thus, the lower-intensity component (32.7%) which displays the larger QS value (7.4 mm/s) can be assigned to the bridging sites (Te3, for which a theoretical contribution of 33.3% is expected), while those sites having direct interactions with Fe atoms lead to the component with a higher intensity and a lower QS (Fe1 and Fe2, with a theoretical contribution of 66.6% vs the obtained value, 67.3%). 57Fe

Mo1 ssbauer Spectroscopy

Figure 5 shows the 57Fe Mo¨ssbauer spectrum of TaFe1.25Te3 recorded at room temperature. The spectrum is complex, with the presence of an asymmetric doublet. To facilitate the interpretation, the spectrum has also been recorded at 77 K (see Figure 6). It has a complex profile, with the presence of two kinds of components, one doublet and several sextets. The hyperfine parameters of the refinement are included in Table 4. In theory, five sextets are expected, corresponding to the four different environments of Fe1 (with two, three, four, or five Fe neighbors) plus Fe2 (which always has three neighbors). Assuming that Fe1 with three neighbors and Fe2 are indiscernible, only four sextets are expected. If the vacancies are randomly distributed in the Fe2 site, the probability of Fe1 having n + 2 neighbors (where n is the number of Fe2, with 0 e n e 3) can be calculated by a simple binomial distribution as

P(n + 2) )

()

3 n 3-n pq n

(2)

(1)

where IS0 is the isomer shift of the hypothetical Te2- anion and R and β are the deficits in 5s and 5p populations in the true electronic structure of tellurium atoms (5s2-R 5p6-β). On the other hand, it has been demonstrated that the presence of Te-Te interlayer interactions in group 5 transition metal-layered ditellurides increases the p-block band energies, thereby leading to partial electron transfer from the top portion of the Te p-block bands to the d-block bands of the metals.7,8 It was also shown that the shorter the Te-Te distances, the larger the rise in energy of the p-block bands, the larger the deficit in 5p population, and the larger the IS value.5 In contrast to these considerations,

where p is the probability to find an Fe2 atom and q is the probability of a vacancy. Because only one-fourth of the site Fe2 is occupied, p ) 0.25 and q ) 0.75. The results of these calculations are included in Table 5. The agreement between the calculated values and the observed experimental contribution is poor. It means that the applied model does not represent reality and that Fe2 atoms and vacancies are not exactly randomly distributed. This in turn can take place in two different ways: first, Fe2 atoms are ordered in the structure in a long-range order, creating a superstructure, and second, they are isolated or forming clusters, with a short-range order. Because no peaks ascribable to a superstructure have been



TABLE 4: Hyperfine Parameters of 57Fe Mo1 ssbauer Spectrum of TaFe1.25Te3 at 77 K and at 5 K: Isomer Shift (IS), Quadrupole Splitting (QS), Line Width (LW), Hyperfine Field (HF), the Contribution (%) of Each Multiplet and Their Attribution subspectra temperature

1

77 K

hyperfine parameters (mm/s)

5K

hyperfine parameters (mm/s)

attribution

central atom neighbors

3

4

5

IS QS LW HF

0.533(2) 0.496(4) 0.54(1) 31.6(3)

0.505(5) 0.092(2) 0.53(1) 3.39(1) 32.5(6)

0.522(7) 0.046(4) 0.50(1) 4.95(2) 22.3(8)

0.41(3) 0.23(1) 0.51(4) 6.42(4) 2.5(9)

0.69(1) -0.223(8) 0.53(3) 8.04(3) 11.1(9)

IS QS LW HF

0.53(1) 0.66(2) 0.53(3) 20.6(3)

0.55(1) 0.069(5) 0.48(4) 3.08(2) 39.4(3)

0.44(2) 0.16(1) 0.51(4) 4.92(3) 24.7(5)

0.50(9) 0.18(6) 0.48(3) 6.65(14) 3.5(8)

0.54(6) -0.05(4) 0.54(3) 8.21(7) 11.8(5)

Fe1

Fe1/Fe2 2Fe1 + 1Fe2 3Fe1

Fe1

Fe1

2Fe1 + 2Fe2

2Fe1 + 3Fe2

contribution

contribution

2

small particles 2 Fe1

On the other hand, it is well know that the particle size plays an important role in magnetic properties. In the case of R-Fe2O3, when the particles were smaller than 10 nm only a doublet is observed in the 57Fe Mo¨ssbauer spectrum. As the particle size increases, new signals appear corresponding to a sextet, and for particle sizes greater than 40 nm only a sextet is observed.10 This phenomenon is well know as superparamagnetism.11 The energy (E) of displacement of oriented-spin direction through an angle θ can be expressed as

E ) KV sin2θ

Figure 5.

57Fe

Mo¨ssbauer spectrum recorded at room temperature.

observed in the X-ray diffraction pattern, we can neglect the first option. To analyze the second possibility in more detail, a Markov chain-based study will be applied. It is worth noting the constant increment of the hyperfine field (HF), of about 1.5-1.6 mm/s, from one sextet to the next one. Dividing all the HF values by the highest one (8.04 mm/ s) we obtain the sequence 0.42:0.62:0.80:1.00 and reporting them to a maximum value of 5, the new sequence is 2.11:3.08: 3.99:5.00, which is the number of neighbors of the different iron environments (2:3:4:5), as exposed above. Thus, the four sextets can be attributed to the different Fe-Fe coordinations found in the network, as shown in Table 4. The doublet can be attributed to the presence of nonmagnetic Fe atoms in the ribbons. In a first working hypothesis, one can suppose that the nonmagnetic atoms are Fe2, but they represent only 20% of the total Fe atoms (0.25 Fe2/1.25 Fe1 + Fe2) and the contribution of the doublet is 31.6%. Thus, at least 15% of the Fe1 atoms have to be nonmagnetic. Additionally, if all Fe2 atoms are nonmagnetic we could not find Fe atoms either with five or with four magnetic neighbors. So, an important amount of Fe2 has to be magnetic, and the quantity of nonmagnetic Fe1 has to be strongly increased from the initial 15%. Thus, there must be a nonnull probability of finding another sextet with HF ≈1.6-1.7 mm/s that corresponds to Fe1 where the five neighbors are three vacancies, one magnetic Fe1, and one nonmagnetic Fe1. To test the hypothesis, we have tried to fit the 57Fe Mo¨ssbauer spectrum (at 77 K) adding to the fit the presence of the new sextet. But unfortunately, all attempts were unsuccessful, and during all the fitting procedures it came back to the solution with only four sextets.

(3)

where K is the energy for changing the spin direction per unit volume and V is the volume. When KV/kBT > 10, the spin fluctuations are small. The characteristic time of fluctuation is longer than the lifetime of the excited 57Fe Mo¨ssbauer state for the magnetic interactions, and the hyperfine field is detected. On the contrary, when KV/kBT < 1, the fluctuations take place through 180°, the hyperfine flied is averaged to zero, and one doublet is observed in the spectrum. Besides the particle size (or volume), the temperature also has an important influence. In the case, for example, of ferritin, for a given particle size, the sextet is detected only at low temperatures and for T > 40 K only a doublet is observed.12 Finally, at high temperatures, the spectrum shows a doublet which is often asymmetric due to surface effects leading to numerous different environments. Usually, in the 57Fe Mo¨ssbauer spectra of samples with a distribution of particle size, both sextet and doublet components are observed.11 There are relatively few particles with the critical size for an intermediate situation between the sextet (corresponding to the hyperfine interaction) and the doublet (corresponding to the collapsed components of the sextet), and the relaxed spectrum is usually not visible. In fact, scanning electron microscopy images show the presence of two sets of particles in TaFe1.25Te3: the first one is characterized by a large particle size (10-50 µm). On the surface of these large particles, small particles are adhered, with a size of about 50 nm. Such complex texture allows us to attribute the magnetic and superparamagnetic behavior to large and small particles, respectively. We can now reanalyze the 57Fe Mo¨ssbauer spectra at 77 K and room temperature. According to the results of Badding et al.,1 the sample is paramagnetic at room temperature. The different doublets in the spectrum correspond to different Fe environments. The close values of the doublets (in IS and QS) make the refinement very difficult. As T decreases below the Neel temperature of 200 K,1 the larger particles give rise to


Figure 6.

57Fe


Mo¨ssbauer spectra recorded at 77 K (top) and at 5 K (bottom) and the proposed fitting.

TABLE 5: Contribution of the Different Fe Environments as a Function of the Number of Neighbors (a) Calculated from a Classical Binomial Distribution, and (b) Observed in the 57Fe Mo1 ssbauer Spectrum of TaFe1.25Te3 Recorded at 77 K and at 5 K contribution (%) to multiplets

2

number of neighbors 3 4

5

binomial distribution

Fe1 Fe2 Total

42.19 33.75

42.19 100 53.75

14.06 11.25

1.56 1.25

Mo¨ssbauer spectrum at 77 K Mo¨ssbauer spectrum at 5 K

Fe1 Fe2 Total Fe1 Fe2 Total

59.4 47.5 62.0 49.6

15.7 100 32.6 13.9 100 31.1

4.6 3.7 5.5 4.4

20.3 16.2 18.6 14.9

sextets in the 57Fe Mo¨ssbauer spectrum, while small particles still appear as doublets due to superparamagnetism. To confirm this interpretation, a new 57Fe spectrum was recorded at 5 K, shown in Figure 6. As at 77 K, one doublet and four sextets are observed. Calculating the ratio between the hyperfine field of the different sextets one obtains 1.88: 3.00:4.05:5.00 which is the number of neighbors of the different iron environments (2:3:4:5), as shown above. It is worth noting the decrease of the contribution of the central doublet. As it

has been attributed to a superparamagnetic effect due to the small size of some particles, one can expect a decrease of its contribution with temperature, as experimentally observed. Anyway, there are about 20% of particles (in mass) for which the size is not large enough to ensure a coherent internal magnetic field, even at 5 K. Finally, although the magnetic interactions between iron atoms are evident, the nature of the magnetism is not clear. Thus, one possible model has been proposed1 based on a ferromagnetic exchange between intraribbon iron atoms, which are the closer and expected to have stronger exchange, and an antiferromagnetic exchange between ribbons. The nature of the exchange (direct exchange or superexchange by Te atoms) is also unknown. Markov Chains The theory of Markov chains enables us to simulate atomic distributions with a given short-range order, like cluster formation. When it is applied to an A-B distribution in a linear chain, the obtained information is proportional to the configurational entropy of a mono-dimensional AxB1-x solution, where the cluster formation has been evaluated by combinatorial methods.13 It has also been shown that it is possible to define stochastic processes in two dimensions, applied to the cation order in structures of band and layer silicates.14 More recently, the theory of Markov chains has been used to obtain informa-



O2O1 V2O1 O2V1 V2V1 Figure 7. Schema of a ribbon, where only Fe atoms are present. Consecutive Fe1 and Fe2 positions are noted A, B, and C, and 1, 2, 3, 4, and 5, respectively.

tional models for the configurational entropy of regular solid solutions.15 It has also been applied to express algebraically the mechanism of sequential crystal growth.16,17 In the present work, this theory will be used to analyze the possible trend of Fe2 atoms to create clusters, with a short-range order, working with a pseudo-one-dimensional model. The structure of a ribbon can be simplified according to the schema shown in Figure 7, where A, B and C represent consecutive atoms of Fe1 and 1, 2, 3, 4 and 5 the second site which can be vacant (V) or occupied by an Fe2 atom (O). On the contrary, sites A and B are always occupied. For site number 1, one can find an atom, with a probability P(O), or a vacancy, with a probability P(V). From the stoichiometric composition of the solid, we can define P(O) ) 0.25 and P(V) ) 0.75. We study now the second site (2). Consider the transition matrix

O1 V1

O2 V2 R 1-R β 1-β

This matrix defines a first-order Markov chain, where each element Pij of the matrix represents the probability of finding O or V in site 2 after O or V has been placed in site 1. Thus, P(O/O) ) R corresponds to the probability of finding O in site 2 when O has been previously placed in site 1, and it describes the degree of interactions of short-range between Fe2 atoms. Three different special situations can be defined: (a) R ) 0, which implies that O are always surrounded by V (Fe2 atoms are isolated from each other); (b) R ) 1, where an infinite chain of O is found; (c) R ) 0.25, which corresponds to perfect random distribution. Values of R between 0 and 0.25 indicate the tendency of O to isolate themselves, while 0.25 < R < 1 corresponds to the trend to cluster formation. The limiting distribution P(O) and P(V) can be calculated as

P(O) ) P(O/O) P(O) + P(O/V) P(V)

(4a)

P(V) ) P(V/O) P(O) + P(V/V) P(V)

(4b)

Again because of the stoichiometry of the solid, and taking into account that the absolute probabilities of finding V or O in any position are always 0.75 and 0.25, respectively, one can write

0.25 ) R0.25 + β0.75

(5a)

1 ) R + 3β

(5b)

This equation implies that if the composition is fixed (it means that if the final global configuration is known) only one of the transition probabilities is independent. We now add the third position, noted 3 in Figure 7. The next matrix combines the transition probabilities between the configuration of sites 1 and 2 and the configuration in 2 and 3:

O3O2 V3O2 O3V2 V3V2 x 1-x 0 0 0 0 y 1-y z 1-z 0 0 0 0 t 1-t

If O is placed in sites 1 and 2 (O2O1), the probabilities finding V3V2 and O3V2 are zero, since in site 2 we cannot find O and V at the same time. Thus, P(VV/OO) ) 0, and so on for the other cases. Taking into account the expression for the limiting distribution, one can write:

P(O/O) ) P(OO/OO) P(O/O) + P(OO/OV) P(O/V)

(6a)

P(O/V) ) P(OV/VO) P(V/O) + P(OV/VV) P(V/V) (6b) P(O/O) ) xR + zβ

(6c)

P(O/V) ) y(1 - R) + t(1 - β)

(6d)

Taking into account expression 4a, we can write

P(O) ) P(O/O) P(O) + P(O/V) P(V)

(7a)

1 ) [xR + zβ] + 3[y(1 - R) + t(1 - β)]

(7b)

Thus, from eqs 5b and 7b R and β can be calculated, when x, y, z and t are known. Let us consider now the coordination of Fe1 placed in sites A and B. We can see that they are not independent, since Fe2 neighbors in sites 2 and 3 are shared. We will then consider the transition matrix between the different possible configuration around A and B ((X3X2X1) and (X4X3X2), respectively). To simplify the problem, we assume that the cation and vacancy distribution is affected only by the closer atoms (or vacancies). Thus, the Fe2 atom (or vacancy) placed in site 4 is influenced only by atoms (or vacancies) in sites 2 and 3. On the contrary, the atom (or vacancy) placed in site 1 has no influence on the configuration in site 4. Under these conditions, it is evident that P(X4X3X2/X3X2X1) ) P(X4X3/ X3X2) ) P(X3X2/X2X1) and the transition matrix can be written as O4O3O2 V4O3O2 O4V3O2 V4V3O2 O4O3V2 V4O3V2 O4V3V2 V4V3V2 O3O2O1

x

1–x

0

0

0

0

0

V 3 O2 O1

0

0

y

1–y

0

0

0

0

O3V2O1

0

0

0

0

z

1–z

0

0

V3V2O1

0

0

0

0

0

0

t

1–t

O3O2V1

x

1–x

0

0

0

0

0

0

V3O2V1

0

0

y

1–y

0

0

0

0

O3V2V1

0

0

0

0

z

1–z

0

0

V3V2V1

0

0

0

0

0

0

t

1–t

0

which leads us to write the following equations:

P(OOO) ) x[P(OOO) + P(OOV)] P(VOO) ) (1 - x)[P(OOO) + P(OOV)] (8a) P(OVO) ) y[P(VOO) + P(VOV)] P(VVO) ) (1 - y)[P(VOO) + P(VOV)] (8b)



P(OOV) ) z[P(OVO) + P(OVV)] P(VOV) ) (1 - z)[P(OVO) + P(OVV)] (8c) P(OVV) ) t[P(VVO) + P(VVV)] P(VVV) ) (1 - t)[P(VVO) + P(VVV)] (8d) From eqs 8a and 8d we obtain

P(VOO) ) P(OOV)

P(VVO) ) P(OVV)

(9)

which is a logic result since these configurations are equivalent only by renaming the sites 1,2,3,4 as 4,3,2,1. As an additional hypothesis, we can also assume that

P(OVO) ) [P(VOO) ) P(OOV)] P(VOV) ) [P(VVO) ) P(OVV)] (10) It means that we have only four independent equations, which correspond to the four experimental data obtained from the 57Fe Mo¨ssbauer spectrum at 77 K as the relative contribution of the four sextet components. These observed relative contributions are 32.5:22.3:2.5:11.1 for two, three, four, and five neighbors, which correspond to the configurations 3V, 2V + O, V + 2O, and 3O, respectively (since the other two neighbors are fixed). Because in the stoichiometry of the compound there are 1.25 Fe atoms, we have to report the contributions to 125%. It gives 59.4:40.7:4.6:20.3. If we now take into account that the 0.25 Fe2 always have three neighbors and they are not affected by their own distribution, the relative final contributions of Fe1 atoms to the Mo¨ssbauer spectrum are 59.4:15.7:4.6:20.3 (as indicated in Table 5). In the same way, at 5 K, the obtained contributions are 62.0:13.9:5.5:18.6. The values at both temperatures are within the experimental error (statistical deviation in the spectra and typical deviations in the refinement). Thus, using an average value, we can write

P(OOO) ) 0.195

(11a)

P(OOV) + P(OVO) + P(VOO) ) 0.050

(11b)

P(OVV) + P(VOV) + P(VVO) ) 0.148

(11c)

P(VVV) ) 0.607

(11d)

The values of x, y, z, and t can be calculated, and from eqs 5b and 7b the values of R and β can be obtained. The first two matrixes can be now written as

O1 V1 O2O1 V2O1 O2V1 V2V1

O2 0.16 0.28

V2 0.84 0.72

O3O2 V3O2 O3V2 V3V2 0.92 0.08 0 0 0 0 0.25 0.75 0.25 0.75 0 0 0 0 0.07 0.93

The value of R ) 0.16 (compared to the random distribution value, 0.25) can be interpreted as a slight trend of Fe2 atoms to isolate themselves, surrounded by vacancies. On the contrary, if in site 1 there is a vacancy (V), the obtained value of β ) 0.28 (close to 0.25) indicates that the presence of this vacancy does not have a strong effect on the occupancy of the site number 2.

Concerning the distribution X3X2/X2X1, the values of y and z ) 0.25 also indicate that when only one vacancy is present (VO and OV configurations in sites 1 and 2), the probability of finding an occupied site in 3 is 0.25, and the Fe2/vacancies distribution is close to the random distribution. This situation changes when the two first sites are occupied (OO) or empty (VV). Thus, for an OO configuration, the probability of finding another atom increases from 0.25 to 0.92, indicating the strong tendency toward cluster formation. In the same way, when a VV configuration is found, the probability of finding a third vacancy also increases from 0.75 to 0.93. These results lead us to interpret the iron/vacancy distribution in the ribbon as clusters of Fe (OOO) and clusters of vacancies (VVV), separated by transition regions between both configurations with an almost random distribution of iron atoms and vacancies. These clusters are also randomly distributed along the ribbons, since any reflections ascribable to a superstructure are detected neither in the X-ray diffraction pattern nor in the electron diffraction patterns.1 Conclusions We present here a new application of the Markov chain treatment of short-range ordering (SRO) of atoms in a 1D lattice to the interpretation of the 57Fe Mo¨ssbauer spectra of 57Feenriched TaFe1.25Te3. The relative intensities of several sextet signals emerging from the magnetic ordering of iron atoms in four possible distributions are clearly related with the partial clustering. LRO in the tellurium sublattice is revealed by the 125Te Mo ¨ ssbauer spectra of TaFe1.25Te3, which is dominated by the two different tellurium sites, which are found in the structure of this chalcogenide in a noncubic symmetry. Acknowledgment. C.P.V. is grateful to the European Community for financial support (TMR, contract ERBFMBICT 96.0768). References and Notes (1) Badding, M. E.; Li, J.; DiSalvo, F. J.; Zhou, W.; Edwards, P. P. J. Solid State Chem. 1992, 100, 313. (2) Sanchez, L.; Tirado, J. L.; Pe´rez Vicente, C.; Jumas, J. C. J. Solid State Electrochem. 1998, 2, 328. (3) Ku¨ndig, W. Nucl. Instrum. Methods 1969, 75, 336. (4) Elidrissi Moubtassim, M. L.; Aldon, L.; Lippens, P. E.; OlivierFourcade, J.; Jumas, J. C.; Ze´gbe´, G.; Langouche, G. J. Alloys Compd. 1995, 228, 137. (5) Stanek, J.; Khasanov, A. M.; Hafner, S. S. Phys. ReV. B, 1992, 45, 56. (6) Guzman, R.; Morales, J.; Tirado, J. L.; Elidrissi Moubtassim, M. L.; Jumas, J. C.; Langouche, G. Solid State Commun. 1995, 96, 911. (7) Whangbo, M. H.; Canadell, E. J. J. Am. Chem. Soc. 1992, 114, 9587. (8) Canadell, E.; Jobic, S.; Brac, R.; Rouxel, J.; Whangbo, M. H. J. Solid State Chem. 1992, 99, 189. (9) Guzman, R.; Morales, J.; Tirado, J. L. Chem. Mater. 1995, 7, 1171. (10) Ku¨ndig, W.; Bo¨mmel, H.; Constabaris, G.; Lindquist, R. H. Phys. ReV. 1966, 143, 327. (11) Thomas, M. F.; Johnson, C. E. Mo¨ ssbauer Spectroscopy, Dickson, D. P. E., Berry, F. J., Eds.; Cambridge University Press: New York, 1986; pp 191-197. (12) Bell, S. H.; Weir, M. P.; Dickson, D. P. E.; Gibson, J. F.; Sharp, G. A.; Peters, T. J. Biochim. Biophys. Acta 1984, 787, 227. (13) Kikuchi, R. A. Phys. ReV. 1951, 81, 988. (14) Lapides, I. L.; Lustenberg, E. Y. SoV. Phys. Crystallogr. 1992, 36, 773. (15) Kudo, T.; Hibino, M. Electrochim. Acta 1998, 43, 781. (16) Harris, K. D. M.; Jupp, P. E. Proc. R. Soc. London, Ser. A 1997, 453, 333. (17) Ko¨nig, O.; Bu¨rgi, H. B.; Armbruster, T.; Hulliger, J.; Weber, T. J. Am. Chem. Soc. 1997, 119, 10632.

Distribution of Cations and Vacancies in TaFe1. 25Te3 Studied by

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