J. Phys. Chem. 1995, 99, 2696-2700
2696
Origin of Nonstoichiometry in ScS and Other Early Transition Metal Chalcogenides? Jeremy K. Burdett” and Slavi C. Sevov Department of Chemistry, The James Franck Institute, and The NSF Center for Superconductivity, The University of Chicago, Chicago, Illinois 60637
Oleg N. Mryasov Department of Physics and Astronomy, and The NSF Center for Superconductivity, Northwestern University, Evanston, Illinois 60208-31I 2 Received: June 8, 1994; In Final Form: August 4, 1994@
First principles linear muffin-tin orbital (LMTO) calculations are used to explore the origin of the electronic driving force behind the stabilization associated with metal atom loss in ScS leading to nonstoichiometric Scl-,S. On oxidation of the remaining Sc atoms, the d-band drops in energy, leading to a stabilization of the occupied sulfur p-band by enhanced metal-sulfur orbital interaction or covalency. Such a mechanism is only applicable for early chalcogenides where the energy of the metal d-band is strongly sensitive to variations in charge.
Introduction The origin of the electronic driving force which provides the stabilization associated with the formation of vacancies in solids is a long-standing question. In recent years the problem has received renewed attention with the unraveling of some of the complex chemistry associated with the high-temperature superconducting cuprates. Here a critical oxidation state for the copper atoms of the superconducting Cu02 sheets is often achieved during synthesis conditions by the partial occupancy of some of the metal sites. Thus for example Pb2Sr2RECu308 compounds are superconductorsfor RE = Eu, Dy, and Y, where there are around 9% vacancies on the RE site, but are insulators for RE = La, Pr, and Nd, where these sites are completely occupied.’ The topic of the present paper is an exploration, using first principles theoretical methods, of the electronic reasons behind the loss of metal on heating from a much simpler system, that of ScS and other early transition metal chalcogenides. Although both the cuprates and chalcogenides contain defects, in the latter their concentrationis so large (20%or more) that they have been termed “massively defective”.2 Our studies are the forerunner of attempts to see if the same electronic mechanism for defect formation in ScS is behind the formation of defects in the structurally more complex cuprates. The removal of metal atoms from the stoichiometric structure leads to oxidation of the remaining metal atoms, in ScS, formally some Sc2+ Sc3+ and, in the cuprates, some Cu2+ Cu3+. Nonstoichiometry in rock salt oxides and chalcogenides is widespread. In some cases the missing atoms are highly ordered to give what might be regarded as a new structure type. For example NbO is a line phase, but the structure contains defects at both metal and oxygen sites such that the material is best described as Nb0.75Oo.75.~ Although the chalcogenides of the early transition metals form a variety of ordered and disordered phases extending to either side of the stoichiometric 1:l composition, the fact that Sc leaves the solid on heating ScS rather than sulfur is somewhat surprising. Chemists “explain” such a result by stating that the Sc3+ generated by metal atom loss is “more stable” than the Sc2+ it replaces, but there is a considerable theoretical challenge in defining what is actually
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’Dedicated to Stuart Rice on the occasion of his 60th birthday. @
Abstract published in Advance ACS Abstracts, February 1, 1995
0022-365419512099-2696$09.00/0
Energy Atomic Levels
1 Energy Bands
‘a ’ Increasing Charge on Metal
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Figure 1. First-order (left) and second-order (right) effects of metal oxidation on energy levels in molecules and solids. Notice the increased mixing of metal d-character into the anion p-band on the right-side panel.
meant by such a statement in electronic terms. Misemer and Nakahara4 used the KKR method to study the problem and concluded from studies on ScS and SqS4 that no simple picture of vacancy stabilization emerged from their electronic structure results. Denker5 suggested that the calculated change in Fermi level was behind these observations in Scl-,S but, in addition to other c ~ n c e m s ,noted ~ that a shift in the Fermi level is expected in a rigid band model as the average oxidation state of the metal atoms increases with x. Franzen, Nakahara, and Misemer’ found increased covalent interactions between the metal and the square planar coordinated sulfur in the defect structure. (As we will see later this coordination geometry is not in fact the one found experimentally.) There is, however, a mechanism which has been proposed as one which could lead to stabilization of vacancies. One of us has shown how such a stabilization could occur in principle via the mechanism in Figure 1.6 As noted already, loss of metal but not of chalcogen leads to an increase in the oxidation state of the remaining metal atoms. The levels at the very bottom of the metal d-band are almost entirely metallic in character and thus are expected to become more tightly bound as a result of this change in oxidation state, by analogy with the variation of atomic ionization energy with charge. This brings the metal and chalcogen levels closer together in energy and leads to an increase in their mutual interaction and a stabilization of the filled, largely sulfur, levels. The latter, if large enough, leads to a stabilization associated with metal atom loss. Later 0 1995 American Chemical Society
ScS and Other Transition Metal Chalcogenides
J. Phys. Chem., Vol. 99, No. 9, 1995 2697
transition metal chalcogenides such as FeS and MnS will not exhibit the same behavior. By these electron counts the filled “metal” levels contain a significant amount of sulfur character and such movement with the change in metal oxidation state is small. Tight-binding calculations using self-consistent charge iterations support the broad features of this picture.6 However, tight-binding theory, while frequently of utility in the study of a variety of chemical problems, has serious deficiencies in the evaluation of the energetic details associated with bond breaking. The heat of sublimation of a mole of ScS is 240 kcaUm01.~ These are not weak bonds, and thus there must be some considerable electronic relaxation or rearrangement to compensate for such atom loss. Although tight-binding calculations give interesting insights, a more quantitative examination of this problem using first principles methods is highly appropriate.
Theoretical Approach The ScS system has been the object of several earlier calculations as noted above. Misemer and Nakahara4 reported the results of calculations at the KKR level with the object of studying the electronic structure of the ScS parent and of the nonstoichiometric Sc& (Sc0.75S). The structure chosen in their study for the latter was not the experimentally observed one but one which contained a Sc atom missing from the center of the traditional cubic eight-atom cell. This defect pattem leads to the generation of scandium vacancies in every close-packed layer, and therefore square planar sulfur atoms, rather than the observed “octahedral cis-divacant” or butterfly sulfur coordination, are found in the real structure of this material. The experimental resultss for Scl-,S at 1650 K show Sc atom vacancies disordered over every other metal layer perpendicular to [ l l l ] . This leads to the same local butterfly sulfur coordination in addition to some sulfur atoms in square pyramidal coordination. Tight-binding results for a range of Scl-,S stoichiometriesshowed that the ordering pattem of the vacancies that is most stable is the observed one which avoids square planar coordination at s ~ l f u r .The ~ metal coordination remains octahedral for all x . The calculations reported here used the scalar-relativistic linear muffin-tin orbital (LMTO) method with the atomic sphere approximation (ASA).l0-l3 All calculations were performed until self-consistency was reached with the total energy converging to better than Rykell. The wave functions of the valence electrons within Sc and S were expanded through 1 = 2, and those within the vacancies, through 1 = 1, and core electrons were treated using the frozen core approximation. The Wigner-Seitz radii used for Sc and S were 3.24 and 2.82 a.u., respectively. The LMTO method requires a way to choose such radii, and these numbers are those which satisfy the local neutrality condition. Since the ScS structure is relatively well packed, the maximum overlapping of the spheres is about 15%, and this justifies the use of the atomic sphere approximation. Since the vacancies are at the scandium sites, their radius in Scl-,S was set equal to that of the metal. The density of states was computed using 146 nonequivalent points within the irreducible wedge of the Brillouin zone. All calculations were performed on a rhombohedral supercell of ScS (Figure 2a). This cell is derived from the NaC1-type structure of ScS (a = 5.1917 A) by choosing arh = 4 2 x a, and a = 60°, or in other words, the rhombohedral axes are the face diagonals of the cubic cell. The cell so constructed contains eight scandium and eight sulfur atoms. It is a more versatile choice for the study of the defect structures than the one of ref 4 and allows the study of the different ordering pattems of the vacancies leading to square planar and butterfly coordination at sulfur. The electronic
Figure 2. Rhombohedral supercells for Sc& used for the calculations: ( large crossed circles) S; (small open circles) Sc; (small filled circles) Sc vacancies. (a) Sc8& (ScS); (b) S C ~ S(Sc0.875S); S (c) s c & (sc0.75s-I)with vacancies in every close-packed layer of Sc; (d) s c & (Sc0.75S-11)with vacancies in every other close-packed layer of Sc.
structures of the one-to-one compound and three Sc-deficient stoichiometries were calculated. Figure 2b shows the cell of s C 7 s S (sCO.875s) where one Sc atom is missing at the comers of the cell. This leads to two different types of sulfur atoms: six are five-bonded (those in the middle of the figure) and two are six-bonded. Parts c and d of Figure 2 show two different arrangements of the vacancies in a compound with stoichiometry SC6& (Sc0.75S). The vacancies in the former (sc0.7~S-I)are evenly distributed in all layers. Thus, there are six sulfur atoms with four Sc neighbors in square planar coordination and two sulfur atoms in octahedral coordination for this ordering pattem vacancies are in Figure 2c. In the second pattem (SCO,~~S-II), only present in every other layer of Sc. Now there are four sulfur atoms with four Sc neighbors in a butterfly coordination and four sulfur atoms with five Sc neighbors in Figure 2d. The stoichiometry and the vacancy arrangements in Figure 2c are essentially the same as those chosen by Misemer and Nakahara for their calculation^.^ Recall that experimentally the situation in Sc0.75S-I1is the one found.8
Results Figure 3 shows the density of states of the stoichiometric compound ScS plotted together with the densities of states of sc0.875s (Figure 3a), Sc0.75S-I (Figure 3b), and Sc0.75S-I1(Figure 3c). In accord with earlier studies the lowest band (between -1.2 and -1.0 Ry) is almost entirely made up of sulfur s-character, the middle band (between -0.7 and -0.3 Ry) is of both sulfur p-character and scandium d-character, and the upper band (above -0.3 Ry) is mostly of Sc d-character. The middle band therefore represents Sc-S bonding while the upper band involves Sc-Sc interactions and is Sc-S antibonding. It should be noted that metal-metal interactions are quite weak, since the Sc-Sc distance, 3.67 A, is rather long. Another important feature of the DOS is that the sulfur mixing with the Sc d-states
Burdett et al.
2698 J. Phys. Chem., Vol. 99, No. 9, 1995
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Figure 3. Total DOS of (a) SCO.&, (b) Sco,.i&I, and (c) SCO..~~S-II in the right-side panels compared with the total DOS of the stoichiometric ScS in the left-side panels. The positions of the Fermi levels are shown by horizontal lines.
is predominantly at the upper half of the Sc d-band. Thus the sulfur contribution to the states at the Fermi level (d') is negligible compared to that from Sc. On the basis of results from charge-iterated tight-binding calculations on ScS with similar supercells and stoichiometries, Burdett and Mitchell proposed the mechanism of Figure 1 to explain why vacancies are so easily formed on the scandium sites6 The broad features of the electronic density of states of the Sc,-,S compounds predicted by such a mechanism are in very good agreement with the results from the present calculations. First, we notice that the d-band becomes increasingly stabilized as Sc atoms are removed (Figure 3). This may be understood as being the result of the further oxidation of the remaining Sc atoms whose charge has to compensate for the charge of the extracted atoms. Since there is little sulfur
character in the filled part of the d-band, the stabilization is quite sensitive to changes in charge. As a result of this movement the d-band gets closer in energy to the predominantly S p-type middle band. In perturbation theory terms and using the language of tight-binding theory, since the interaction between two orbitals depends inversely on their energy separation, mixing of the Sc d-states with those on sulfur is enhanced. The result is stronger Sc-S bonding via this secondary stabilization of the middle band which lowers its energy. An increase in Sc-S covalency, namely stronger mixing between Sc and square planar S states, was noted by Franzen, Nakahara, and Misemer for the defect model they used. Here we reveal its origin. In order to illustrate this effect in more quantitative terms, we calculated the mean energy of the middle band by evaluating
ScS and Other Transition Metal Chalcogenides 0.2,
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DOS (states/Ry*Sc) Figure 4. DOS of Mno.,sS (Sco.~~S-II type) compared with the DOS of the stoichiometric MnS. The positions of the Fermi levels are shown by horizontal lines.
the expression Cnie(ni)lCni, where there are ni states with an energy ei. The results are -0.4626, -0.4659, -0.4649, and -0.4758 Ry for ScS, Sc0,875S,Sc0.75S-I,and Sc0.75S-11,respectively. It is clear then that in terms of lowering the energy of the middle band the order of the compounds is Sc0.75S-I1 > sco.875s > Sc0.75S-I > ScS. This shows too that Sc-S bonding becomes stronger when Sc is removed. Upon this removal the remaining Sc atoms become more oxidized. From our calculations the Sc positive charges are higher by 0.1 and 0.16 in Sc0.875Sand Sc0.75S,respectively, when compared to that in ScS. As mentioned above this higher positive charge leads to lowering of the Sc d-band, better mixing with the S p-band, and therefore stronger Sc-S bonding. The limit of the Sc removal is, of course, the known compound Sc2S3 (sCO.67s), in which all sulfur atoms are coordinated by four Sc neighbors in a butterfly arrangement. The Sc is now all present as Sc3+(do), and no more may be removed while keeping S as S2-. From these results it is also clear that the square planar geometry (not observed experimentally) found in Sc0.75S-Iis less stable than the butterfly arrangement found in Sc0.75S-11. Burdett and Mitchell have suggested6 that the stabilization of the sulfur p-band disappears for higher electron counts as d-levels which contain more sulfur character are occupied. This is indeed shown by the results for calculations on two manganese sulfides. Evaluation of the expression Cnie(ni)l&i gives -0.5538 and -0.5499 Ry for MnS and Mno.75S (Sc0.75SI1 type), respectively, indicating quantitatively that the strength of the Mn-S bonding in the stoichiometric compound is stronger than in the Mn-deficient one. Figure 4 shows the computed densities of states of the two manganese sulfides. The effect which we have described for ScS and shown in Figure 3 is clearly absent here. Another, even better way of assessing the stability of the compounds is to compare total energies, and in order to do that we calculated the energy change for the reaction SCS(S)
-
Sc,-,S(s)
+ xSc(s)
(1)
An additional calculation of the electronic structure and total energy of elemental Sc metal was performed using the same method and the reported lattice parameters. This combined with the total energies of the compounds involved led to values of -4.0, - 1.9, and -4.6 kcal for the reactions producing S C O . ~ ~ ~ S , Sc0.75S-I, and Sc0.75S-11, respectively. Therefore there is a driving force although relatively small which favors the Scdeficient compositions over the stoichiometric one. Moreover the order of the compounds arranged according to the energy change of reaction 1 is of course the same as when compared in terms of stronger Sc-S bonding (above): Sc0.75S-II > Sc0.875S > sco.75s-I > s c s . We can also compare the results of our calculations with experimental measurements. Franzen and co-workers have measured the heats of sublimation of ScS(s), sCO,8065s(S), and Sc(s) as 240.2 f 5, 223.4 f 4.5, and 90.3 f 1.0 kcal/mol, re~pectively.~ Using a simple Born-Haber cycle we find -0.7 & 6.7 kcal for the energy change of reaction 1. Unfortunately, the uncertainty is quite large and a useful comparison with our results not possible. We now focus attention on the locations of the vacancies. We first note that the ionic model fails9 miserably to match the experimental results, just as it does in Nb0.3 It is well-known that, when Scl-,S with x 2 ‘/6 is cooled, the vacancies order in such a way that they are contained only within every other closepacked layer of Sc. Note that in this range of stoichiometries there will be sulfur atoms with more than one Sc missing from the octahedral coordination. Evenly distributed vacancies in every close-packed layer would ultimately lead to the existence of square planar sulfur atoms. It has been pointed out by Misemer and Nakahara4 and by Burdett and Mitchell6 that such coordination leads to a nonbonding pz orbital on the sulfur atom. This orbital would have an energy significantly higher than those of the other sulfur orbitals and would make this configuration energetically unfavorable relative to a butterfly coordination. Our calculations confirm these results. Sc0.75S-Ihas six square planar sulfur atoms, and the density of states shows a relatively large peak (around 0.28 Ry) above the main part of the middle band in Figure 3c. This peak comes solely from the square planar sulfur atoms and is absent in the density of states of Sc0.75S-11,where all four-bonded sulfur atoms are in a butterfly coordination. Therefore the square planar sulfur and subsequently the higher-energy peak in the density of states are the reasons for the destabilization of the middle band (above) and the relatively low negative energy change of reaction 1 for the formation of this compound compared to the energies of formation of Sc0.875S and Sc0.75S-11. There is still an enhanced interaction between metal d-states and sulfur p-states in Sc0.75.S-I similar to that in Sc0.75S-11,as described above. This mechanism for stabilizing a nonstoichiometric compound is expected to apply also to the other early transition metal chalcogenides. We believe it is the first electronic mechanism proposed for any system which is able to provide insight into this problem.
Acknowledgment. We thank A. J. Freeman for helpful discussions. This Research was supported by the NSF Center for Superconductivity, Grant NSF DMR9120000. References and Notes (1 ) Xue, J. S.; Greedan, J. E.; Marik, M. J. Solid State Chem. 1993, 102, 501.
( 2 ) Franzen, H. F.; Nakahara, J. F.; Misemer, D. K. J. Solid State Chem. 1986,61, 338. (3) Burdett, J. K.; Hughbanks, T. J. Am. Chem. Soc. 1984, 106, 3101. (4)Misemer, D. K.; Nakahara, J. F. J. Chem. Phys. 1984,80, 1964.
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Denker, S. P. J. Less-Common Met. 1968, 14, 1. Burdett, J. K.; Mitchell, J. F. Chem. Muter. 1993, 5, 1465. Teunge, R. T.; Laabs, F.; Franzen, H. F. J. Chem. Phys. 1976.65. Dismukes, J. P.; White, J. G. Znorg. Chem. 1964, 3, 1220. Franzen, H. F.; Merik, J. A. J. Solid State Chem. 1980, 33, 371. Andersen, 0. K. Solid State Commun. 1973, 13, 133.
(11) Andersen, 0. K. Phys. Rev. B 1975, 12, 3060. (12) Andersen, 0. K. In The Electronic Structure of Complex Systems; Phariseau, P., Temmerman, W. M., Eds.; Plenum Press: New York, 1984. (13) Gunnarson, 0.;Jepsen, 0.; Andersen, 0. K. Phys. Rev. B 1983, 27, 7144. JF94 1400+
