1131 The Canadint Minerala gi st Vol.33, pp. I 131-1l5l (1995) BORATEMINERALS. I. POLYHEDMLCLUSTERS AND FUNDAMENTALBUILDING BLOCKS PETERC. BURNSE Departnuntof EanhSciences, tlniversity of Cambridge,Downing Street, Catnbridge CB2 iEQ, U.K. JOELD. GRICE ResearchDivisiaa Carudian.Mweum of Nature,P.O. Box 3443, Station D, Ottawa,Ontario KIP 6P4 FRANKC. HAWTHORNE Departmcntof GeologicalSciences, tlniversity of Manitoba,Wittnipeg, Manitoba R3T 2M ABSIRA T In general,the structuresof the borateminerals are ba$edon BQ3and B$a polyhedra,which occur as discreteoxyanions or polymerizeto form finite clusters,chains, sheets and frameworls. The B-Q bonds (Q: unspecifiedanion) are of much higber bond-valencethan the interstitial bonds,and thus borateninerals readily lend themselvesto hierarchicalclassification based on the topological characterof ttre FBB (fundamentalbuilding block) and the structuralunit. Here, we derive topologically and metrically possiblefinite clust€rsof the form [BnQ.], where 3 3 n 3 6, and identify those clustersthat occur as FBBs of the structues ofborate minerals.In addition,we havedeveloped graphical and algebraicdescriptors ofthe topologicaland chemical aspectsof tle clustersand their modeof polymerization.ln fhe structuresof the borafeminerals based on FBBs with 3 3 z 5 6, all FBBs arepolyhedral rings or decoratedpolyhedral rings. Moreover,three-membered polyhedral rings are almostcompletely dorninant;the only exceptionis the four-memberedpolyhedral ring in borcarite.Three-membered polyhedral rings occur in the following order of preference:<A2fl> >> 4Afl> > <3fl> > <34>. Only a small numberof the topologicaly and metrically possibleclustg$ occur as FBBs in borateminerals; Nature seemsto producesfiuctural diversity by using only a small number of FBBs and then polymerizingthem in many different ways. Keywords:borate minerals, hierarchy of structures,fundamental building block, crystalstructure, boron, structure classification. Sol,IIr,IaIRs En g6n6ral,les structuresdes min6rauxborat6s ont commeunit6s de basedes polybdresB03 et BO4,presents sous forme d'anionsdistincts ou en agencementspolym6ris6s, qui sont soit des regroupementslimit6s de polybdres,des chalnes,des feuillets ou des trames.I,es liaisons B-$ ($: anion non sp6cifi6) possOdentune valencede liaison beaucoupplus 6levdeque les liaisons interstitielles, de lelle sort€ que les min6rauxboratds se pret€nt tout natuellement tr un sch6made classification hidrarchiquefond6 sur le caractbretopologique du bloc structuralfondamental et de I'unite structuralede base.Nous d6rivons ici tous les agencementsfinis possiblesselon les critdrestopologiques et m6triquesapproprids pour les agencemetrtsde tylre ;BrQ.l, danslesquels 3 3 z 3 6, et nousidentifions les agencementsqui serventde bloc structuralfondamental dans les structures de mindraux borat6s. En plus, nous ddvelopponsles atnibuts graphiqueset alg6briquesrequis pow d6crire les aspects topologiqueset chimiquesdes agencemsnts et leur modede polymdrisation.Dans touts structured'un mindralborat6 impliquant un bloc structuralfondamental avec 3 3 n 3 6, ce bloc constitueun armeaude polybdres,ddcor6 ou non. De plus, les an:reauxi trois membressont fortement pr6dominants.La seule exception, en fai! est la borcarite, qui contient un anneaul quatre polybdres.Les anneauxi trois polybdresse rencontrentavec une fr6quencedans I'ordre <A2fF >> 4 D> > <3!> > <34>. ks min6rauxboratds ne contiennentqu'un nombrerestreint des agencementstopologiquement et m6triquementpossibles. La diversit6structurale s'explique donc par un petit nombrede blocs structuaux fondamentaux,qui sont polym6risdsde plusieurs fagonsdans les structures. (Traduit par la R6daction) Mots-cl€s: min6raux borat6s,hidrmchie des strucfires, bloc structural fondamental,strucn[e cristalline, bore, classification structurale. * Presentaddress: Department of Earth andPlanetary Sciences, Univenity of New Mexico, Albuquerque,New Mexico 87131- 1116.U.S.A. Ll32 TT{E CANADIAN MINERALOGIST IrrrnoousnoN structuresand, ultimately, the paragenesisof borate minerals. Boronhas an ionic radiusof 0.1I A (Shann611976;, and hencecan occur in both niangular and tetrahedral The schemzof Christ & Clark ( 1977) coordination where bonded to oxygen. BQ3 (Q: O2-, OH-) groups have an average B-Q bond-valence In their crystal-chemical classification of borate approximatelyequal to 1 valenceunit (y.u.), and BQa structures, Christ & Cluk (1977) emphasizedthe groups have an averageB-{ bond-valenceapproxi- importanceof polymerizationof BQ3tiangles and B$, mately equal to t/e,v.u. Hence, both BQ3 and BQo tetahedra to form clusters that are compact,insular groups can polymerize by sharing comers without gtoups, referred to as fundamental building bloclcs violating the valence-sumrule (Brown 1981). Such (FBB). The FBBs forrn the basis of the classification polymerizationis very common in both minerals and scheme of Christ & Clark (1977). Their structural syntheticinorganic compounds,and gives rise to great classificationis basedon threeprincipal criteria: (1) the structural diversify. In general, a borate structure numberof boron atomsin the FBB, (2) the numberof contains clusters of corner-sharingBQ3 and BQa BQ3niangles and BQotetrahedra in the FBB, and (3) polyhedra, which occur as discrete polyanions the mode of polymerizationbetween the FBBs, giving or polymerizeto form larger clusters,chains, sheets or isolated, moffied isolate4 chains, moffied chains, frameworks.The excesscharge of the array of borate sheets and modified sheets.Cbrist & Clark (1977) polyhedrais balancedby the presenceof low-valence proposeda notation (n:iA,+ jT) for eachFBB, which interstitial cations. In the structures of most borate gives the total number of boron atomsin the FBB, as minerals, the B-$ bonds are of much higher bond- well as the number of B$3 triangles (A) and BQa valence(> 0.7 v.u.) ftan ths ls6nining cation-$bonds tetrahedra(Q. For example,the FBB 5:2A+37hasfive (< 0.3 v.u.). Thus, the borate structuresreadily lend boron atomsin the FBB, of which two occur as B0" themselvesto classification on tJre basis of the triangles,and three as BO4tetrahedra. geometryofthe clustersofborate polyhedra. The utility of organizing crystal structures into The occurrenceoflarge FBBs hierarchical sequenceshas long been recognized. Bragg (1930) first classified the silicate structures In developing their classification, Cbrist & Clark accordingto the geometryof the polymerizationof the (1977) consideredthe structuresofthe hydrousborate (Si,Al)O4 tetahedr4 and this schemewas generalized mineralsavailable at that time, as well asthe structures to include sfructuresbased on polymerizedtetrahedra of some anhydrous minerals and hydrous and by Znltai (1960) and Liebau (1985). Suchhierarchical anhydroussynthetic inorganic compounds. They noted classificationsserve to order our knowledge and to that the FBBs of borale structuresare generallysmall, facilitate comparison of crystal structuresowhich is as neruly all sfuctures known at that time were based infrinsically quite diffrcult. Howeveromuch additional upon FBBs with six or less boron atoms. The one insight can be derived from such sftuctural schemeso exceptionwas preobrazhenskite, the structureofwhich particularly regarding the underlying controls on is basedon FBBs containingnine boron atoms.Since bond topology (Hawthorne 1983, 1994) and mineral the work of Cbrist & Clark (1977), however, several paragenesis(Moore L965, L973, Hawthorne 1984). borate structuresthat contain even larger FBBs have There have been several classifications proposed beenreported. Cttice et al. (1994) solvedthe structures specifically for borate structures @dwards & Ross of pringleite{Cae[B2sO2s(oH)ra][BoOo(OID6].13H2O] 1960,Christ 1960,Tennyson L963, Ross & Edwards and ruitenbergite { Car[B2eO2s(OH)rs][B6Oo(OH)o] 1967, Heller 1970, Christ & Clark 1977). Previous .13H2O),both of which containFBBs with 12 boron classifications were reviewed by Christ & Clark atoms.Several synthetic compoundshave 12 or more (1977).Their classificationhas proven very usefirl over boronatoms in the FBB [i.e., Ag6fBpOls(OII)6].3H2O the past fifteen years,and has been widely used.The (Skakibaie-Moehadamet al. 7990),Nax[B,2Oro(OII)n] basisof the Christ & Clark (1977) schemeis the degree (vlenchetti & Sabelli 1979), Na6[Cu2{ B 16024(OtD 10} I .l2H2O of polymerization within the simplest sffuctural unit. @ehm 1983), K6[UO2 { B r6Oz(OID8} ]. I 2H2O They porfayed this with the descriptor n.iA + JT, @ehm I 985), and K5H{CuaO[820O32(OtD8] ].33H2O wheren is the total numberof boron atomswithin this (Heller & Pickardt 1985)1.These more complex unit, which contains i BQ3 and j BQ, polyhedra. structurespresent a problem for the Christ & Clark Although this is usefirl information, it does not give (1977) schemeof classification,which cannotuniquely any indication about the topology of the cluster of distinguishFBBs with its nomenclature.For example, polyhedranor about the degreeto which the cluster is the FBBs v/ith twelve boron atoms in pringleite, translatedthroughout the crystal structure.These two ruitenbergite, Na3[B,rOro(OH)a]and A96[8,rO,, stuctural featuresare the ones we incorporatein the (OI{)61.3H2Oall contain six BQ3triangles and six BQ, presentscheme of classification,as they are essential tetrahedra.and the notation for these FBBs is thus to the understandingof the hierarchy of the borate l2:6L+67. However"examination of theFBBs of these FUNDAMENTAL BTJILDINGBLOCKS IN BORATE MINERALS LL33 b) Frc. l. Examplesof the FBB