Ternary chalcogenides of vanadium and chromium

J. Phys. Gem. Solids

Pergamon

TERNARY

Press 1966. Vol. 27, pp. 755-759.

CHALCOGENIDES

Printed in Great Britain.

OF VANADIUM

AND

CHROMIUM* S. L. HOLT, R. J. BOUCHARD Department

and A. WOLD

of Chemistry and Division of Engineering, Providence 12, Rhode Island

Brown University

(Received 9 September 1965)

number of compounds with the defect nickel arsenide structure have been prepared. Their crystallographic parameters and electrical properties were determined, including electrical resistivity as a function of temperature and Seebeck voltage. The properties observed for particular metal ions present is discussed and schematic one-electron one-molecule energy level diagrams for these compounds are presented. In all cases, the predictions made are consistent with the electrical properties observed.

Abstract-A

INTRODUCTION

RECENTLY(~)four monoclinic compounds of the type NiBa!&, where B is V+s or Cr+s and X is S or Se were prepared. Their crystallographic parameters and electrical properties including electrical resistivity as a function of temperature and Seebeck voltages were determined. The compounds NiCrsSJ exhibited semiconducting properties with low activation energies. The Seebeck voltage of NiCrsSed was reported to be in the range usually assigned to metallic materials (-2lpV/“C), while that of NiCrsS4 was much larger ( - 117pV/“C), which is more characteristic of semiconducting behavior. However, the two vanadium compounds were reported to be metallic as indicated by the positive temperature coefficient of resistivity and their extremely low Seebeck voltages. It was suggested that if the conduction observed in NiCr& and NiVsS4 is caused at least in part, to direct overlap of metal ion orbitals, then NiVsS4 should appear to be more metallic than NiCr&. This was found to be consistent with the observed transport properties. GOODENOUGH(~~~) has indicated that bands can also occur as a result of covalent mixing of anion wave functions into the cationic d-wave functions. * This work has been number AF 19(628)-3837

supported by ARPA and Grant from the Air Force. 755

This mixing is strongest for the d-orbitals with o-band symmetry. According to this model, metallic or semiconducting properties depend upon the manner in which these bands are occupied. For compounds with completely filled or empty bands, semiconductor behavior is observed whereas partially filled bands give rise to metallic behavior. Several of the monoclinic ternary metal chalcogenides of the type MBsS4 (where M is a divalent transition metal ion, B is V+3 or Cr+s and X is S or Se) show semiconducting behavior whereas the majority are metallic. It appears that the scheme proposed by Goodenough can be applied to explain these properties.

EXPERIMENTAL Preparation

These compounds were prepared by a hightemperature combination of the elements. High purity (99.99%) materials were used and the reactions were carried out in evacuated silica tubes at 800-1000°C. Several firings were necessary with grinding under dry nitrogen (up to one hour in a mechanical mortar grinder) between firing to achieve homogeneity. For electrical resistivity and Seebeck measurements, the samples are pressed at about 30,000 psi into bars approximately 0.8 x 0.15 x 0.15 in. These

756

S. L.

HOLT,

R. J. BOUCHARD

were fired in evacuated silica tubes for a period of several days. Physical measurements

Electrical resistivity as a function of temperature was determined on the bars previously described over a temperature range from - 180°C to + 150°C at 10-30” intervals. A Keithley Model 503 milliohmeter was used to measure resistance by the fourprobe technique to eliminate contact resistance. For the compounds that appear to be semiconductors these measurements were correlated by means of the equation p = pa exp(q/kT), where yn ;E +h* ““_ bVII>LaIILD ^^-\“&^..&- al&u -,A q is the resistivity, ps and K ale conduction. It can be seen activation energy for that a plot of log p vs. l/T gives 4 as the slope. The . c 4 values were reproducible for various samples or $e same compdsition within narrow limits. The variation of resistivity with temperature was shown to be reversible within experimental error. Seebeck measurements were taken at room temperature using an ice bath as the cold junction. The Seebeck voltage was reproducible from sample to sample. For the purpose of this investigation a compound is classified as a metal if its resistivity shows a positive temperature dependence and its Seebeck voltage is less than 50 ~LV/‘C. Crystallographic parameters were determined on powder samples with a Norelco diffractometer using monochromatic radiation (AMR-202 Focusing Monochrometer) and high intensity copper source. A computer program designed to calculate d values for all possible h k I values was used in conjunction with an IBM 70 70 computer. I”

LILU

RESULTS AND DISCUSSION

The compounds VsS4, CrsS4, TiCrsS4, NiCrsS4 and CrVsS4 have been prepared, and their structures were found to be monoclinic with similar cell parameters. For these compounds only reflections with h + k+ 1 = 2n were observed, indicating a body centered unit cell of the type reported by JELLINEIC.(~)The X-ray data for the six singlephase materials are presented in Table 1. The compounds CrVsS4, VCrsS4 and TiCrsS4 have not been prepared previously, All the compounds were analyzed by both chemical and X-ray techniques and found to be single phase with the composition MBsX4. All the peaks in the diffraction

and

A.

WOLD

pattern could be indexed on the basis of the monoclinic unit cell chosen. The cell parameters reported have been obtained by a least-squares best fit of all the major diffraction peaks. This was carried out with a program developed for the 70 70 computer, Table

1. Cell parameters for monoclinic ternary chalcogenides

Compound V& c&34

TiCraS4

Vcras4 NiCr&

,-TTI n Lr v 234

a

b

5.86 5.94 5.96 5.95 5.94

3.28 3.42 3.41 3.38 3.42

e “A

J'OY

n -I) 3.33

C

B

11.36 11.24 11.35 11.22 11.14

I. n,-, II'LY

92.04 91.60 91.38 91.5 91.3

fin Aa YL'"‘

The transport properties of these compounds are summarized in Table 2. It can be seen that NiCrsS4 and VCrsS4 exhibit semiconducting properties with low activation energies. The Seebeck voltage of VCrsS4 is somewhat higher Table 2. Hectricalparameters for monoclinic ternary chalcogenides

Compound

v3s4

Cr3S4 TiCrzS4 VCr2S4 NiCrzS4 CrV2S4

qH.T.(eV)*

Metallic Metallic Metallic 3x10-2 4.3 x 10-Z Metallic

qLT(eV)t

3x10-2 9.3 x 10-3

Seebeck coefficient at 25”C(V/“C) +13.1 -36.0 -18.4 - 58.9 -117.0 -3.0

+ High temperature activation energy. t Low temperature activation energy.

than most metals but is still in the range assigned to metallic materials, while that of NiCrsS4 is much larger and more characteristic of semiconducting behavior. The remaining compounds, as illustrated by the positive temperature coefficient of resistivity and the extremely low Seebeck voltages, are metallic. GOODENOUGH has shown that for compounds of the type ABsX4 (spinel, where X = S, Se) the

TERNARY

CHALCOGENIDES

OF

covalency of the anion-cation bond is sufficient to form antibonding o* band states with cationic d-orbrtals of a-band symmetry, Goodenough’s theory may be represented by a one-electron energy diagram for the transition metal electrons. A simple diagram can be constructed for the monoclinic chalcogenides since all the metal ions are situated on octahedral or B-sites. On the basis of the one-electron picture, the B-site d-levels are split into a less stable doublet of eg symmetry and a more stable triplet of t3a symmetry. For oxides and probably also for sulfides the difference in the Madelung and ionization energies is sufficient that broad valence and conduction bands of s,p states are split by a large energy gap. Therefore, these states are not considered, since the lower bonding band is always full and the upper antibonding band is always empty. Whereas there is considerable admixing of anion s,p wave functions into es states (which have o symmetry), the extent of admixing into tzs states is much less since the tzg orbitals point away from the anion. For the purpose of this discussion, it is assumed that the tzg orbitals remain localized, so that their levels remain sharp. However, the tzsr levels can be broadened into a band of collective electron states if the interatomic separation is less than a critical distance Rc. This apparently occurs for Ti+3 and Vf3.(5) Where the distance between B-site ions is greater than R,, the electrons remain localized in the tgo levels. For sulfides, Goodenough replaces the e, levels by narrow energy bands of antibonding e* collective-electron states. The electron occupancy of these states determined the nature of the electrical properties of the compounds under consideration. The ternary chalcogenides of the type MB 3x4, having the defect nickel arsenide structure, contain transition metal ions which are all located on octahedral sites of the sulfur sublattice, The structure is illustrated in Fig. 1. Here the M+3 ions occupy the planes containing the ordered defects while the B ions occupy filled alternate planes. This structure was originally proposed by JELLINEK@)and confirmed by B~RTAUT.(~For both the M and B ions, the tzs levels (or broadened bands if R < Rc) are in a lower energy state than the eg levels which have been transformed by covalency into o* collective bands. The relative energies of the electronic levels (or bands) of the M and B ions

VANADIUM

AND

757

CHROMIUM

with respect to each other, are dependent upon how far they are separated in the periodic table, e.g. the tzg level of Ni+3 would be lower than the corresponding tzg level of Cr+?

-

I 2/m

C 2/m

-I---

0

Nit20r

Crt2

0

vt30r

0

vacancy

cr+s

sulfur atoms (or selenium) in hexagonoi array omitted

FIG. 1. The metal sublattice of the monoclinic NiAs structure.

defect

Schematic one-electron energy level diagrams can be drawn for the ternary chalcogenides of the type MB3X*, which have the monoclinic Cr3S4 structure. In these compounds there is no ambiguity possible for the spin states of the various ions, except Cr+3(d4). It is assumed that for Crf3, the exchange energy is large enough to result in the high-spin state. For metal ions with unpaired d-electrons, an inn-a-atomic exchange splitting exists which removes the spin degeneracy. In a one-electron energy diagram, this results in the formation of two different spin states which can be labeled t&a) and t&$). One level has its electron spins antip~~lel to the other. Sim~~ly, the eg levels are split into e,(g) and e&3) states. Figures 2-4 represent conventional one-electron, onemolecule energy-level diagrams of the d-states for Cr3S4, NiCr3Se and VCr3S4. Numbers in brackets refer to the total degeneracy of a

758

S.

L.

HOLT,

R.

J.

BOUCHARD

level per ‘molecule’. These are obtained by multiplying the number of orbital8 per atom contributing to a level or band by the number of atoms per molecule, then doubling to include the spin degeneracy. When an exchange energy is considered, as it must be in the three compounds shown in Figs. 2-4, the spin degeneracy

and

A.

WOLD

up by the addition of electrons, one at a time, to the available energy states until the desired number of d-electrons has been reached. Although the t&d) and asp levels represent schemati~ly the removal of the spin degeneracy, in a complete, multielectron solution all the tsg electrons have the Same energy. However, addition of the fourth electron in a tzg level is done only at the cost of intra-atomic exchange energy, since the @spin electron is forced to occupy the same orbital as an a-spin electron. The one-electron energy diagrams therefore are schematic representations of the correlation effects of the d-electrons.

FIG. 2. Schematic one-molecule, one-electron energy level diagram of the d*-state manifold of CrsS4. The levels to the left correspond to the divalent ion: the levels to the right correspond to both trivalent ions, which are degenerate in energy, so for simplicity are not differentiated. FIG. 4.

5=

1 egW)

FIG. 3. Schematic one-molecule, one-electron energy level diagram of NiCrsk. Note Ni+s levels are more stable than Cr+3 levels.

is removed by splitting into ol and j3 states. The broad valence and conduction band of s,p states presumably form occupied and empty bands below and above the d-state manifold and are therefore omitted from the figures for simplicity. The occupancy of an electron in one of the energy states is represented by either f or 4 depending upon the spin state. These one-electron diagrams like the one-electron diagrams of band theory are built

Schematic one-electron, one-molecule level diagram of VCraS4.

energy

It can be seen from Fig. 2 that the err(a) level of the Cr+s ion is half-filled and therefore CrsS4 should be a metal. However, it should be emphasized that Fig. 2 is a one-electron, one-molecule diagram. Therefore, gross magnetic properties should not be implied from it. The magnetic properties have been discussed by BERTAUT(~) who found a magnetic unit cell doubled in the a and c direction as shown in Fig. 5. The chromium ions are aligned in ferromagnetic sheets parallel to the 101 planes, where only divalent ions or only trivalent ions are in any one plane. These sheets are coupled antiferromagnetitally with respect to each other. Hence in Fig. 2 the divalent ion is assigned an antiparallel spin state with respect to the trivalent ions. For NiCrsS4 the t:;(a) and plevels, as well as the efi (ti) band are filled, while the e:’ (tc) is empty. Therefore NiCrsS4 should be a semiconductor, since there is an energy gap between a full band and the next empty available level. For VCrsS4 the &b) is filled and all other levels are empty. Therefore, it should also be a semiconductor. These predictions

TERNARY

CHALCOGENIDES

OF VANADIUM

AND

CHROMIUM

759

G b

l

Cr+* 0 Cr+3 0

vacancy

FIG. 5. Part of magnetic unit cell of CrsS4, showing doubling of chemical unit cell along (I axis only. Doubling along c axis is not shown. based on Goodenough’s model are consistent with the results tabulated in Table 2. It should be noted that for VCraS4 the vanadium tss levels are represented as bands (because of metal-metal overlap) yet they are still split by an exchange energy even though there are no localized vanadium electrons. The splitting, in this case, is a result of antiferromagnetic inter-atomic exchange with the localized Cr+a electrons. Schematic diagrams similar to Figs. 2-4 can be drawn for other compounds with the defect nickel arsenide structure. In all cases, the predictions made are consistent with the electrical properties observed.

Acknoruledgment-The authors would like to thank Dr. John B. GOODENOUGH for his helpful discussions pertaining to this research.

REFERENCES 1. BOUCHARDR. J. and WOLD A., J. Phys. Chem. Solids 27, 591 (1966). 2. GOODENOUGH J. B., Bull. Sot. Chim. Fr. 4, 1200 (1965). 3. GOODENOUGH J. B. (to be published). 4. JELLINEK F., Acta Crystullogr. IO, 620 (1957). 5. GOODENOUGHJ. B., Magnetism and the Chemical Bond, Interscience Publishers (1963). 6. BERTAUTE. F., ROULT G., ALEONARDR., PAUTHENET R., CHEVRETONM. and JANSEN R., Jtd. Physique 25, 158 (1964).