electronic reprint Crystal structure and charge distribution of ... - CRM2

esearch papersTable 1Experimental details for YbFeMnO 4 .Crystal dataCell settingHexagonalSpace groupR3 ma (A Ê ) 3.4580 (1)c (A Ê ) 25.647 (3)V (A Ê 3 ) 265.59 (3)Z 3Radiation typeMo KWavelength (A Ê ) 0.71073No. of re¯ections for cell parameters 18 range ( ) 40.98±45.30Temperature (K) 293 (2)Crystal formSphereCrystal radius (mm) 0.055Crystal colourBlackData collectionDiffractometerEnraf±Nonius CAD-4Data collection method!± scansAbsorption correctionSphereT min 0.086T max 0.166No. of measured re¯ections 655No. of independent re¯ections 577No. of observed re¯ections 528Criterion for observed re¯ectionsI > 2(I)R int 0.0196 max ( ) 59.84Range of h, k, l 0 ! h ! 70 ! k ! 460 ! l ! 61No. of standard re¯ections 3Frequency of standard re¯ectionsEvery 240 minIntensity decay (%) 0.5Re®nementRe®nement on F 2s.o.f. (Yb) = 1 s.o.f. (Yb) = 0.963Chemical formula weight 347.83 341.49D x (Mg m 3 ) 6.524 6.405 (mm 1 ) 33.593 32.637R‰F 2 >2…F 2 †Š 0.0195 0.0175wR…F 2 † 0.0524 0.0437S 1.153 1.184No. of re¯ections used 577 577in re®nementNo. of parameters used 13 14…=† max 0.000 0.001 max (e A Ê 3 ) 3.39 at 2/3,1/3,0.1059(0.30 A Ê from Fe/Mn)2.55 at 0,0,0.1109(0.44 A Ê from O1) min (e A Ê 3 ) 6.20 at 0,0,0.0214(0.55 A Ê from Yb)4.88 at 0,0,0.0217(0.56 A Ê from Yb)Extinction method SHELXL (Sheldrick,1997)SHELXL (Sheldrick,1997)Extinction coef®cient 0.0237 0.0290 (11)tional homologous series, i.e. series in which the type(s) andthe general shapes of building blocks, as well as the principlesde®ning their mutual relationships, are preserved, but the sizeof these blocks increases with the number of coordinationpolyhedra in them (Makovicky, 1997).Ideal trigonal bipyramids, with two identical apical bonds,have been found only in compounds where the bipyramidshost a single type of cation, such as InGaO 3 (II) (Shannon &Prewitt, 1968). When different cations enter the bipyramids,these no longer have their two apical bonds identical and havebeen classi®ed into two types. Type I has the three basal MÐObonds shorter than the two apical ones: the cation is stillrelatively close to the basal plane, and the bipyramid is notmuch distorted. Type II has the cation signi®cantly off-centredfrom the basal plane, towards one of the corners: one of theapical bonds is shorter and the other is longer than the threebasal ones (Nespolo, Sato et al., 2000).The above compounds can be classi®ed into two accretionalhomologous series: (R 3+ M 3+ O 3 ) n M 2+ O, analogous to the(YbFeO 3 ) n FeO series (Kato et al., 1975, 1976; Malaman et al.,1975, 1976; Kimizuka et al., 1976), and R 3+ M 3+ O 3 (M 2+ O) m ,analogous to the LuFeO 3 (ZnO) m series (Isobe et al., 1994).The latter has recently drawn attention from differentresearch groups, because of the unusual features of highermembers. In particular, for R = In or Ga, M 3+ = Fe and M 2+ =Zn, extra re¯ections in the selected-area electron diffractionpattern were reported (Li et al., 1997, 1998, 1999a; Li, Bando,Nakamura, Kurashima & Kimizuka, 1999) and interpreted interms of superspace group analysis (Li et al., 1998). TEMobservations have revealed the existence of a modulationwave involving the octahedral cation (Li et al., 1997, 1998,1999a; Li, Bando, Nakamura, Kurashima & Kimizuka, 1999;HoÈ rlin et al., 1998; Wolf & Mader, 1999), whose origin is atpresent unclear. No modulated structure has been reported sofar in members with m < 6. The structure of this series hasbeen recently rationalized in terms ofm ˆ 2K ‡ L;…1†where K 0 and L =0or1(K and L are both integers). Theideal symmetry is P6 3 /mmc and R3Åm for L = 0 and L =1,respectively. In higher members with a modulated structurethe symmetry is actually reduced, at least locally, to orthorhombicand monoclinic, respectively (Li et al., 1998).Important insights into the structural details of thesecompounds can be obtained by the charge distribution (CD)analysis (Hoppe et al., 1989; Nespolo et al., 1999). The CDmethod is the most recent development of the classical theoryof bond strength (Pauling, 1929) and differs from the bondvalence (BV) approach (Brown, 1978) in exploiting the truebond distances in a kind of self-consistent computation ratherthan employing empirical curves. Differently from the BVmethod, in the CD approach the computed `charges' (Q) ofthe cations and of the anions convey different information. Inshort, by labelling q the formal oxidation number, the q/Qratio for the cations indicates the correctness of the structuredetermination, whereas the same ratio for the anionsmeasures the degree of over- or under-bonding. The analysisof the structural details on the basis of the strength of eachbond (called `bond valence' in the BVand `bond weight' in theCD) is meaningful only when the structure is correctly re®nedand the empirical method itself is applicable. The BV methoddoes not contain any internal criterion for such an evaluation,while the CD method has in the q/Q ratio for the cationsprecisely this kind of criterion (for details refer to Nespolo etal., 1999).The CD analysis of several compounds belonging to the twoaccretional homologous series described above has revealedthat those containing type II trigonal bipyramids have a q/Q806 Nespolo et al. YbFeMnO 4 Acta Cryst. (2000). B56, 805±810electronic reprint