Electronic structure analysis of two crystalline phases of Fe3O2BO3

Electronic Structure Analysis of TwoCrystalline Phases of Fe3O2BO3

MARIA MATOS,1 ANIVALDO X. SOUZA2

1Departamento de Fısica, PUC-Rio, CP38071, Gavea, Rio de Janeiro, RJ, CEP 22453-970, Brazil2Ctur, Universidade Federal Rural do Rio de Janeiro, Rio de Janeiro, RJ, Brazil

Received 9 January 2004; accepted 5 April 2004Published online 22 March 2005 in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/qua.20554

ABSTRACT: A theoretical electronic structure analysis was performed on twocrystalline phases of the homometallic Fe ludwigite, appearing in a structural transitionrecently found experimentally to occur at 283 K. The extended Huckel method was usedto study different subunits of the compound, which is known to present lowdimensionality in magnetic properties. Total energy calculations show an electronicstability of the low-temperature (distorted) phase, in agreement with experiment. Alongitudinal Fe2�-Fe2� interaction (perpendicular to the flat planes of the orthorhombicunit cell) appears to be mainly responsible for the stabilization. A contribution ofanother Fe2� ion was seen to be related to an enhancement of Fe-O interaction. Aremarkable result is the reversal of these results when high spin FeO6 monomers areconsidered. In that case, it is the Fe-O interaction in an Fe3�-Fe2�-Fe3� triad whichseems to drive the stabilization of the distorted phase. It is suggested that spin effectsmight be important to the structural transition in Fe3O2BO3. © 2005 Wiley Periodicals,Inc. Int J Quantum Chem 103: 562–571, 2005

Key words: Fe ludwigite; structural phases; extended Huckel; electronic structure

Introduction

D ue to its interesting physical properties, thehomometallic Fe ludwigite [1] has stimulated

both experimental and theoretical studies in the lastfew years [2–7]. The material presents a rich mag-netic behavior, with an antiferromagnetic orderingassociated with two independent Fe subsystems [2].Specific heat measurements indicated the existenceof a Wigner glass phase and of a charge order-

ing state below 200 K [3]. More recently, a roomtemperature structural transition was found inFe3O2BO3, which lowers the crystal symmetry witha consequent duplication of the unit cell [4].

Theoretical studies in Fe3O2BO3 have includedinvestigations of charge distribution [5] and a de-tailed analysis of the magnetic properties of thecompound [6]. In another theoretical article [7], thestructural transition was analyzed through a com-parison between one 1D subunit of Fe3O2BO3 witha three-leg-ladder hydrogenic chain. The Fe-lud-wigite is a mixed valency compound, having beenreasonably established [2, 6] that Fe3� and Fe2� ionsCorrespondence to: M. Matos; e-mail: [email protected]

International Journal of Quantum Chemistry, Vol 103, 562–571 (2005)© 2005 Wiley Periodicals, Inc.

are in high spin states, S � 5/2 and S � 2, respec-tively.

The ludwigites are members of a class of mate-rials which could be characterized as metallic oxo-borates. The general formula can be written asM2M’O2BO3, in which M and M’ are di- and triva-lent metals, respectively. The crystalline structurewas first obtained for the MgFe ludwigite [8] andsince then a number of other compounds were syn-thesized and structurally characterized (see, for ex-ample, Refs. 9 and 10). The crystal is formed bycorrugated planes of metal containing oxygen octa-hedra, held together by strong BO3 units, with fourformula units in a flat orthorhombic unit cell (seeFig. 1). There are four distinct octahedral sites, andit is well accepted that sites 1, 2, and 3 are occupiedmost probably by the divalent metal, M2�, whilesite 4 more likely bears M’3�. Lattice parameters arenot very different among the ludwigites, being a �9Å, b �12 Å and c �3 Å. Ludwigites are related to

another oxo-borate, the warwickite, which crystal-lizes in the general formula MM’OBO3, with M andM’ di- and trivalent metals, respectively [11–14].The warwickite contains infinite straps of O octa-hedra, instead of the corrugated planes of the lud-wigite.

The regular crystalline structure of the homome-tallic Fe ludwigite has been found to belong to thePbam space group [1, 2, 4, 12]. In this work, we usethe lattice parameters a � 9.462 Å, b � 12.308 Å, andc � 3.075 Å, given in Ref. 4. The new structure,found below 283 K [4], was fitted to the lowersymmetry space group Pbnm, with a � 9.449 Å, b �12.282 Å, and c � 6.150 Å, the latter indicating theduplication of the unit cell. Special attention hasbeen given [4, 7] to the effects of the structuraltransition upon the group Fe(4)-Fe(2)-Fe(4), the Fetriad, which provides the shortest Fe–Fe distance(2.787 Å, in the high temperature, regular, phase).During transition, Fe(4) moves towards or awayfrom Fe(2), alternately along the c-axis, creating twodistinct crystallographic positions, 4a and 4b. TheFe(2)-Fe(4a) distance is shortened to 2.755 Å, whilethe Fe(2)-Fe(4b) distance increases to 2.806 Å (seeTable I). Due to the alternancy, the structural tran-sition duplicates the unit cell in the c direction.

In this study we use the extended Huckel ap-proach to analyze the electronic structure of thenew (distorted) crystal phase of Fe3O2BO3, aiming atestablishing a comparison between the latter andthe regular phase of the material. The energetics ofeach phase was examined in order to determinepossible electronic mechanisms related to the stabi-lization of the lower symmetry phase.

Theoretical Method

Extended Huckel theory [15] is a well-knownLCAO one electron quantum theoretical method.When applied to a crystal [16], it is a tight-bindingapproach with overlap, whose reciprocal spaceHamiltonian H(k) is built from empirical parame-ters Hii and Hij; Hii are given by valence state ion-ization potentials and Hij are calculated accord-ing to the Wolfsberg-Helmholz formula, Hij �K/2(Hii � Hjj)Sij; we use a weighted formula K �k � �2 � �4(1-k), where � � (Hii - Hjj)/(Hii � Hjj)and k � 1.75 [17]. Sij are overlap integrals betweenthe Slater Type Orbitals (STO) of the atomic basisset. The empirical parameters used in the presentwork are shown in the Appendix. Total and pro-jected density of states (DOS) and crystal orbital

FIGURE 1. The unit cell of Fe3O2BO3, seen along thec axis. Different Fe sites are indicated as 1–4. Note the424 triad surrounded by Fe(3) atoms. Big spheres: Fe;medium: B; small: O.

CRYSTALLINE PHASES OF FE3O2BO3

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 563

overlap population (COOP) curves can also be ob-tained. The latter provide the strength and nature(bonding, antibonding) of a given orbital or atominteraction. Wave vectors k, necessary to obtainband dispersion, DOS and COOP were chosen inthe first Brillouin zone (BZ) [16].

In the estimate of total average electronic energyof the 1D and 2D crystalline systems considered inthis work, a convergence study was made, by vary-ing the number of k-points of the Brillouin zone(BZ). For 1D the convergence is faster than for 2D,but for both cases one obtains very good conver-gence for the energy difference between two struc-tures, regular and distorted. For convenience, a setof 250 (225) points was chosen for the 1D (2D)models. For 3D calculations, due to the large size ofthe duplicated unit cell (408 orbitals), a speciallydesigned set of 192 k-points was used, built such asto fill the primitive orthorhombic BZ with equallyspaced points. In this set, the k-points density in-creases as one goes from y to x to z directions, giventhat b�a�c (increasing intercell bonds). It has beenused in the Fe3O2BO3 system [5] and in a study ofthe Ti2MgOBO3 warwickite [18], providing a gooddescription of the DOS curves.

The unit cell atomic coordinates for both theregular and distorted crystalline structures weretaken directly from X-ray data [4]. The extendedHuckel method is very convenient in the study ofcrystalline and electronic structure relationships

and was successfully used in the study of chargedistribution of Fe3O2BO3 [5].

Results and Discussion

For a general overview of the physical system,the band structure was obtained for the new, dis-torted phase (below 283 K), and compared with thatobtained for the regular structure (above 283 K) [5].Results are shown in Figure 2 for the 3d Fe bands.Dispersion along X�Z, principal points of the Bril-louin zone, are very similar in both structures. PointX is at the center of the orthorhombic BZ face per-pendicular to the a-axis of the unit cell; thus, inter-cell interaction is small in that direction [5]. Thisexplains why there is little dispersion along X�. Forthe sake of comparison of the two structures, in thecalculation of the regular phase, the unit cell wasdoubled. The formation of two groups of bands canbe noted, whose origin is the 3 below 2 splitting ofd levels in octahedral field. The Fermi level, definedas the highest occupied band orbital, stays at thetop of the t2g group and does not change from onestructure to the other, being, in both cases, EF �–12.04 eV. The first unoccupied narrow band is partof the t2g group and comes from a strong antibond-ing Fe–Fe �* combination of Fe(2) and Fe(4) [5], themost interacting pair. The Fe(2)–Fe(4) bonding (�)band spreads in the lower part of the 3d bands, one

TABLE I ______________________________________________________________________________________________Crystal lattice parameters, Fe–Fe distances, and Fe–O average radii (in Å) occurring in the regular anddistorted crystalline phases of Fe3O2BO3.

Crystal lattice parameters of the regular (distorted) phasea b c

9.462 (9.449) 12.308 (12.282) 3.075 (6.150)

Fe-Fe distances in regular structure1–4 2–3 2–4 3–4

dFe-Fe 3.101 3.176 2.787 3.191

Distorted structure1–4a 1–4b 2–3a 2–3b 2–4a 2–4b 3a–4b 3b–4a

dFe-Fe 3.085 3.116 3.155 3.194 2.755 2.806 3.174 3.192

Fe-O average radii in regular structure1 2 3 4

�dFe-O� 2.145 2.088 2.147 2.057

Distorted structure1 2 3a 3b 4a 4b

�dFe-O� 2.140 2.088 2.143 2.144 2.049 2.072

MATOS AND SOUZA

564 VOL. 103, NO. 5

branch of it clearly shown around –13 eV. Notefrom Table I that Fe(2)–Fe(4) distances are the short-est among Fe–Fe distances in the compound, forboth structures. For the distorted phase, there aretwo Fe3� sites, 4a and 4b, where Fe(4a) is closer toFe(2). This dimerization-like geometrical changecould suggest the existence of a Peierls-like transi-tion. However, as seen in Figure 2, it is evident thatboth phases present an insulating (or semiconduct-ing) character; the forbidden gap is found to be 0.20eV and 0.23 eV in the regular and distorted phases,respectively. It is also interesting to note that thegeometrical changes in the triad do not lead to aseparation in the � or �* bands, as could be ex-pected, since those bands mainly originate fromFe(2)–Fe(4) interactions. A closer examinationshows that �* (as well as the eg bands, above it) isslightly higher in energy in the distorted phase.

This is probably a result of a stronger Fe–O repul-sive effect. In fact, from Table I it can be seen thatthe average Fe–O octahedral radii are, with theexception of site 4b, smaller in the distorted phase,thus leading to a stronger Fe–O bond. This pointwill be discussed below. It is worth noticing that,since the �* band is unoccupied in the ground state,its upward shift in the distorted phase could favorthe regular phase at higher temperatures, a resultwhich would be in agreement with experimentalobservation. It remains, however, to be seen whichstructure is more stable in the zero temperaturelimit. This is discussed below.

The band dispersion did not show an evidence ofwhich structure should be the most stable. Theeffects of the structural transition are thus expectedto be small. Differences between the two structuralphases could, however, be found in the calculation

FIGURE 2. Extended Huckel 3d band structures of the regular and distorted crystalline phases of Fe3O2BO3. TheFermi level is indicated by dotted lines. Energies in eV.



of total electronic energies. It showed stabilizationof the distorted crystal, with an energy difference�E � –0.40 eV with respect to the regular phase.This quantity was defined as �E � Edist – Ereg,where E is the total electronic energy per unit cell.This stability of the distorted (low temperature)phase is in qualitative agreement with what isfound experimentally, since our calculation de-scribes the T � 0 limit.

In order to understand basic mechanisms relatedto the energetics found above, we analyzed differ-ent subunits, carved out of the ludwigite crystal.Since the 1D 424 triad chain encloses the nearest,more interacting, Fe–Fe pairs, it is natural to startthe analysis in the subunit formed by that chain.There are two such chains in the unit cell of eitherphase, with the 424 triad atoms aligning across twovertices of the corrugated plane (see Fig. 3a). In thedistorted phase, there is alternancy of 4a and 4bsites, creating zig-zag legs along the chain axis (par-allel to c) [4]. The 1D 424 triad band structures (notshown) present the same general aspect as the 3Dbands. Distorted empty bands are slightly abovethe regular ones, with no noticeable differences be-low EF. Nevertheless, total energy calculations give�E � 0.11 eV, showing the regular structure to bemore stable, a result opposite to that found in thebulk calculations above.

Given that 3D and 1D results predicted differentstructures as being the most stable, we consideredinvestigating intermediate subunits to clarify. Oneexpects identifying electronic mechanisms, presentin the 3D structure and absent in the 1D chain,which could be relevant to the stability found in thebulk. First, a 2D subunit was considered, formed bythe whole corrugated plane (Fig. 3a). Here one ob-tains �E � –0.16 eV, showing the distorted phase tobe more stable, thus qualitatively reproducing thebulk calculation. This result suggests that the inter-actions which contribute to the stabilization of thedistorted phase are not in the 424 triad.

To determine possible stabilizing interactions,different stoichiometries [5] were used in the 2Dsubunit. The corresponding physical models arerepresented in Figure 3b,c. As seen, different stoi-chiometries are represented by a unit cell whichlacks one (Fig. 3b) or two (Fig. 3c) Fe atoms. Actu-ally, Mg was used as a substituent of the missingatoms. The justification for the choice of Mg will bediscussed below. By extracting, e.g., Fe(1), whichconnects two Fe(4) atoms, one gets �E � –0.12 eV.Another stoichiometry which substitutes Fe(3) byMg, while keeping Fe(1) (as seen in Fig. 3c) gives

�E � –0.02 eV. Therefore, one could assume thatinteractions involving Fe(1) and Fe(3) are importantfor stabilizing the distorted phase. By comparingthe different values obtained for �E, one finds thatFe(1) contributes to a decrease of 0.13 eV in thisquantity, while Fe(3) is responsible by a decrease of0.23 eV, both with respect to the 1D-triad value.

Whether a dimensionality effect could explainthe stabilization of the distorted phase—note thatall 2D subunits provide stabilization—was betterclarified by another 1D calculation. Taking into ac-count that Fe(3) has the dominant role, a 1D 5-Fechain was considered, which was formed by the34243 Fe group (see Fig. 3d), giving �E � –0.08 eV.This result corroborates the role of Fe(3) in the

FIGURE 3. A representation of the corrugated planeof the distorted phase, seen along the c axis. The unitcell is shown inside a dotted square. The other half ofthe doubled cell is above the one shown, along c, withsites b(a) on top of a(b). (a): the whole plane; (b) and (c)different stoichiometries; (d) the 5-Fe 34243-Fe 1D sub-unit.

MATOS AND SOUZA

566 VOL. 103, NO. 5

stabilization and shows that dimensionality is not anecessary attribute to stabilize the distorted phase.Even though there is a dimensionality effect in �E,to be acknowledged by the difference in this quan-tity when one goes from the 2D-34243 (–0.12 eV) tothe 1D-34243 (–0.08eV) subunits.

In the distorted phase it is convenient to namesite 3 as 3a and 3b, neighboring 4b and 4a, respec-tively, as shown in Figure 3a–d. From Table I it canbe noted that Fe–Fe distances which involve Fe(3)are among the largest ones and, therefore, the cor-responding pairs are the least probable to cause asignificant effect, as compared to other pairs. How-ever, when one looks along the c direction of thecrystal, one finds one (3a)–(3b) pair (see Fig. 4a),which has a bond distance smaller than thoseshown in Table I, d3a–3b � 3.044 Å, and smaller thanthe corresponding distance in the regular phase,d3–3 � c � 3.075 Å. Other comparable distances inthe same direction are d3b–3a � 3.106 Å, d1–1 � 3.075Å, d4b–4a � 3.077 Å, and d2–2 � 3.083 Å.

We examined COOP curves for the two shorterdistance pairs, 1–1 and 3a–3b (note that Fe(2) andFe(4) have been discarded, as relevant to repro-duce the 3D stability). They are shown in Figure4b,c, respectively. While the curves are almostidentical in the 1–1 pair, differences could benoted in the Fe(3) pair, for the COOP area belowEF. The order of the bond, estimated by totalCOOP, gives – 0.001 for the Fe(1) pair and 0.002for the Fe(3) pair. These values are too small to beconclusive. However, they are qualitatively con-sistent with the relative importance of Fe(3) in theenergetics of stabilization. It should be noted thatno other pair is expected to give larger COOPthan the 3a–3b pair.

An isolated molecular 34243 subunit, the basicgroup that generates the 34243 1D chain (Fig. 3d),was considered as well in our study. By means ofthis chemical model, �E was found to be almostnegligible, –0.002 eV. Since this molecular unit doesnot contain the above-mentioned Fe(3a)–Fe(3b) lon-gitudinal interaction, this result helps one to believethe latter pair as having a significant role in thestabilization of the distorted structure.

Another mechanism of stabilization could comefrom Fe–O interactions. That is, an enhancement ofFe–O interaction—pushing upward the antibond-ing Fe–O bands (3d bands) and downwards thebonding low lying (O-2s, O-2p) bands—could bal-ance favorably in energy, leading to stabilization[19]. An estimate of oxygen octahedra contractionor distention, during the structural transition, as

given by the average Fe–O radii, is given in Table I.Note that, except for Fe(4b), all Fe–O average radiiare smaller in the distorted phase (with no changefor Fe(2)), suggesting a favorable situation for thestabilization to occur.

A differential DOS (DDOS) curve represents thedifference between density of states of distortedand regular calculations. Positive values of DDOScontribute negatively to �E, and thus to stabiliza-tion of the distorted phase. We then analyzedDDOS curves with an attempt to determinewhether Fe–O interactions could be reflected in itsbehavior. However, no clear or easily seen tenden-cies were found below EF. There is a constantlyoscillating pattern of the DDOS curve as the energyincreases. At the lower end of the O bands, how-ever, some nonoscillating positive values could beseen, as shown in Figure 5.

We decided then to examine the energetics ofindividual FeO6 monomer units, carved out fromthe ludwigite structures. Results of the calcula-tion of �Emon for the several Fe sites are shown inTable II. It can be noted that, with the exceptionof Fe(4b), all monomers contribute to the stabili-zation of the distorted phase (the Fe(2) monomeris inert in this respect), consistent with the con-traction of the corresponding octahedra. As forFe(4b), the distorted monomer is less stable (inthis case dFe–O� increases). Thus, in Fe3O2BO3,the energetics of individual Fe–O octahedra cor-relate well with their average radii. The summa-tion at the lower entry of Table II takes intoaccount that there is an equal number (2) of eachmonomer in the unit cell. These localized pictureresults are consistent with the behavior of theseveral crystalline subunits examined above.Note that if one considers only the contribution ofsites 2, 4a, and 4b, the resulting value of �E ispositive, leading to stabilization of the regularphase, in qualitative agreement with what wasfound in the 424 1D infinite chain.

As an estimate of spin effects in the structuraltransition, we studied the stability of high spinmonomers, by occupying higher energy levelsaccording to the spin state of the Fe atom. ThusFe(1), Fe(2), and Fe(3) (S � 2) have the five 3dlevels singly occupied, with double occupancy inthe lower t2g energy level. On the other hand, inFe(4) (S � 5/2), there is one single spin-up elec-tron per 3d level (Table II). It is interesting to notethat the stability of the distorted phase is stillobtained, but the contributions to it are reversedin all Fe types. In this case, Fe(4b) gives the only



FIGURE 4. a: the 2D unit cell, seen along the a-axis (x direction), with four Fe sites indicated as 1, 3a and 3b. b: Fe(1)–Fe(1) projected COOP. c: Fe(3a)–Fe(3b) projected COOP. All projections were taken from the 2D subunit. Energies in eV.

MATOS AND SOUZA

568 VOL. 103, NO. 5

contribution to the stability of the distortedphase, which is large enough to counterbalancethe opposite contribution of other Fe atoms.

Finally, we analyzed charge transfer between Featoms caused by the structural transition. Mullikencharges were found to be 0.682, 1.516, 0.669, and1.029, in the regular phase, respectively, for Fe(1),Fe(2), Fe(3), and Fe(4). For convenience, they wereobtained from the 2D subunit, but good agreementis found with the bulk calculated charges [5]. In thedistorted phase, significant changes are obtainedonly in the triad, bearing the charges 1.546, 0.963,and 1.076 for Fe(2), Fe(4a), and Fe(4b), respectively.Hence, electron transfer from Fe(2) and Fe(4b) toFe(4a) occurs, leading to a spatial charge distribu-tion, on top of the underground regular phase,whose main energetic consequence is the long dis-tance electrostatic attraction between Fe(2) andFe(4a). We estimated the latter to be about –0.01 eVper 2–4a pair. This amount, even though favoringthe stabilization of the distorted phase, is notenough to change the conclusions presented aboveas to the role of the 424 triad in the structuraltransition.

The results discussed in this section point to aspecial role of Fe(3)–Fe(3) interactions in the stabil-ity of the distorted phase, with a contribution ofFe(1), as well, although no clear mechanism hasbeen identified which involved Fe–Fe interactionwith this site. The contribution of Fe(1) was betterseen in the localized picture. The relevant Fe(3)–Fe(3) interaction is along the c-axis and is caused bythe alternating character of the structural transition.For the ground state, no contribution of the stron-ger interacting 424 triad was found to the stabilityof the distorted phase of the compound. A some-what remarkable result was the reversal of behaviorof the several Fe ions when high spin is considered.In this case, it is the 424 triad which is responsible

TABLE II ______________________________________Total monomer energy difference between thedistorted and regular phases.

�Emon �E1

Fe(1) 0.042 0.005Fe(2) 0 0Fe(3a) 0.037 0.009Fe(3b) 0.027 0.005Fe(4a) 0.056 0.003Fe(4b) 0.145 0.036total 0.017 0.014

High spin monomers are shown. Energies in eV.

FIGURE 5. Differential DOS (DDOS) of the 2D subunitshown in the energy region of (a) O(2s) and (b) O(2p)bands. Energies in eV. See definitions in the text.



for the stabilization of the distorted phase, throughthe effect of relaxation of the 4b octahedron.

Mg

The use of Mg as a substituent of Fe is related tothe role of the former in breaking Fe–Fe bonds, asrequired to represent different stoichiometries. Thiscould be better understood by a comparison be-tween the 2D calculations shown in Figure 6 (for theregular phase). In this case, the band structure of anMg-containing system is compared with that of theFe-missing system. As can be noted, they are prac-tically identical in the relevant energy region. ACOOP calculation was done in order to determinethe amount of interaction between Mg and the twoneighboring Fe atoms. The total average COOP wasfound to be –0.0186 and –0.0187, respectively, thenegative sign indicating a mainly anti-bondingCOOP. This is confirmed in Figure 7 for the Mg–Fe(4) bond. It can be noted that the main interactionoccurs in the higher levels, indicating bonds with4s- and 4p-Fe orbitals [5], with no relevant contri-bution in the 3d band. One could then say that thesubstituent Mg isolates the two adjacent Fe(4) at-oms from each other, in the same way as the miss-ing Fe(1) does, thus providing the required stoichi-ometric effect. For the distorted phase, the sameconclusions can be drawn. It could be stressed inaddition that Mg is a natural substituent for Fe2� inthe ludwigite [8].

Conclusion

We analyzed different subunits carved out oftwo crystalline phases of the Fe3O2BO3 ludwigite,experimentally found to occur in a structural tran-sition of the material, at 283 K. Extended Huckelelectronic band and molecular level structures, den-sity of states, and COOP curves were used in theanalysis. Our results suggest a stability of the crys-tal phase of lower symmetry (Pbnm) (the distortedphase), found experimentally to occur at low tem-peratures.

By comparing the energetics of bulk (3D) with2D, 1D, and molecular subunits of the compound, itwas seen that the stability of the bulk is reproducedin all the subunits which contain Fe(1) and/or Fe(3),vhe latter being the dominant contribution. Thestability of the distorted phase is not due to thestrong interacting Fe 424 triad.

FIGURE 6. Fe-3d band structure calculation of sev-eral 2D structures in the regular phase. At left, the ac-tual 2D ludwigite; in the middle panel Fe(1) is missing;at right, Mg is used as substituent of Fe(1). Note thesimilarity in the band structures of the middle and rightpanels. Energies in eV.

FIGURE 7. The COOP curve for the interaction be-tween Fe(1)-substituent Mg and the nearest Fe(4) atom.Note the larger COOP intensity at higher energies. TheFermi level is shown by the broken line.

MATOS AND SOUZA

570 VOL. 103, NO. 5

We found that the bonding characterized by thenearest Fe(3)–Fe(3) pair, formed along the c-axis, isenhanced by the distorted phase, due to a decreasein the bond distance, which occurs in the alternat-ing distortions, characteristic of the structural tran-sition. This is the closest iron pair outside the triadand points longitudinally (parallel to the triadchain). For the next pair, no significant bondingchanges occur to contribute to the stabilization.

Fe–O interaction also appears to play a role inthe stabilization below 283 K. Due to a contractionof oxygen octahedra, the iron-oxygen lower levels,mainly oxygen, lose enough energy to counterbal-ance the increasing Fe–O repulsive effect in thepartially full 3d levels. In this localized picture, aninteresting reversal of the role of different Fe sitesarose when high spin monomer configurations wereanalyzed. In that case, it is the 424 triad that isresponsible for the stabilization of the distortedphase.

It is suggested that a more complete analysis,including spin effects, should be done for a defini-tive understanding of the thermal behavior of thecompound. Nevertheless, with the present studywe have provided a comprehensive description ofbasic electronic mechanisms involved in the struc-tural transition of the homometallic Fe ludwigite.

Appendix

The extended Huckel parameters used in all cal-culations of the present article were obtained fromstandard eHT tables [20], whose values for the di-agonal Hamiltonian matrix elements Hii and SlaterAtomic Orbitals exponents � are the following: a)for B, H2s,2s � –15.2 eV with �2s � 1.3, H2p,2p � –8.5eV with �2p � 1.3; b) for O, H2s,2s � –32.3 eV with�2s � 2.275, H2p,2p � –14.8 eV with �2p � 2.275 andc) for Fe, H4s,4s � –9.10 eV with � 4s � 1.9, H4p,4p �–5.32 eV with �4p � 1.9, H3d,3d� –12.6 eV with �1 �5.35 and �2 � 2.0 in a linear double zeta combina-tion with coefficients c1 � 0.5505 and c2 � 0.6260,respectively.

ACKNOWLEDGEMENTS

All calculations were done with the computa-tional code yaehmop, developed by Dr. Greg Land-rum (Chemistry Department of the University of

Cornell, Ithaca, NY). We thank Dr. Grigory Vaje-nine for providing the set of 192 k points, used in all3D calculations.

References

1. Swinnea, J. S.; Steinfink, H. Am Miner 1983, 68, 827.2. Guimaraes, R. B.; Mir, M.; Fernandes, J. C.; Continentino,

M. A.; Borges, H. A.; Cernicchiaro, G.; Fontes, M. B.; Can-dela, D. R. S.; Baggio-Saitovich, E. Phys Rev B 1999, 60, 6617.

3. Fernandes, J. C.; Guimaraes, R. B.; Continentino, M. A.;Ghivelder, L.; Freitas, R. S. Phys Rev B 2000, 61, R850.

4. Mir, M.; Guimaraes, R. B.; Fernandes, J. C.; Continentino,M. A.; Dorigueto, A. C.; Mascarenhas, Y. P.; Ellena, J.; Cas-tellano, E. E.; Freitas, R. S.; Ghivelder, L. Phys Rev Lett 2001,87, 147201, 1.

5. Matos, M.; Anda, E. V.; Fernandes, J. C.; Guimaraes, R. B. JMol Struct (Theochem), 2001, 539, 181.

6. Whangbo, M.-H.; Koo, H.-J.; Dumas, J.; Continentino, M. A.Inorg Chem 2002, 41, 2193.

7. Latge, A.; Continentino, M. A. Phys Rev B 2002, 66, 94113, 1.8. Takeuchi, Y.; Watanabe, T.; Ito, T. Acta Cryst 1950, 3, 98.9. Norrestam, R.; Nielsen, K.; Sotofte, I.; Thorup, N. Zeitschr

Kristallogr 1989, 189, 33. Norrestam, R.; Kritikos, M.;Nielsen, K.; Sotofte, I.; Thorup, N. J Solid State Chem 1994,111, 217.

10. Fernandes, J. C.; Guimaraes, R. B.; Continentino, M. A.;Borges, H. A.; Sulpice, A.; Jholence, T.-L.; Siqueira, J. L.;Zawislak, L. I.; da Cunha, J. B. M.; dos Santos, C. A. Phys RevB 1998, 58, 287, and references therein; a detailed descriptionof the ludwigite structure can be found in Jaffe, H. W.,Crystal Chemistry and Refractivity; Dover: New York; 1996,256.

11. Capponni, J. J.; Chenavas, J.; Joubert, J. C. J Solid State Chem1973, 7, 49.

12. Attfield, J. P.; Clarke, J. F.; Perkins, D. A. Phys B, 1992,180/182, 581.

13. Norrestam, R.; Kritikos, M.; Sjodin, A. J Solid State Chem,1995, 114, 311.

14. Attfield, J. P.; Bell, A. M. T.; Rodriguez-Martinez, L. M.;Greneche, J. M.; Cernick, R. J.; Clarke, J. F.; Perkins, D. A.Nature (Lond), 1998, 396, 655.

15. Hoffmann, R. J Chem Phys 1963, 39, 1397; Whangbo, M. H.;Hoffmann, R. J Am Chem Soc 1978, 100, 6093.

16. Hoffmann, R. Solids and Surfaces; VCH: New York, 1988.17. Ammeter, J. H.; Burgi, H. B.; Thibeault, J. C.; Hoffmann, R.

J Am Chem Soc 1978, 100:12, 3686.18. Matos, M.; Hoffmann, R.; Latge, A.; Anda, E. V. Chem Mater

996, 8, 2324.19. Whangbo, M. H. Crystal Chemistry and Properties of Mate-

rials With Quasi-One-Dimensional Structures; Rouxel, J. Ed.;D. Reidel: New York, 1986, 27.

20. Tables of Parameters for Extended Huckel Calculations, col-lected by Santiago Alvarez, Universitat de Barcelona, 1993.



Documents

Electronic structure analysis of two crystalline phases of Fe3O2BO3