American Mineralogist,Volume 70, pages 455473, 1985

vIMIvTrOo Towardsa structural classificationof minerals: The minerals

F. C. HewrnonNr

Department of Earth Sciences, Uniuersity of Manitoba Winnipeg, Manitoba, Canada R3T 2N2

Abstract Cation bond-valencerequirements are satisfied by their anion coordination polyhedra; anion bond-valencerequirements are satisfiedby the polymerization of thesecoordination polyhedra.When consideredtogether with Pauling'ssecond rule, this suggeststhat structures may be orderedor classifieilacioriling to the polymerizationof thosecoorilination polyhedra with higherbond-oalences. This is the basisof the approachto mineral classificationproposed here, which focuseson the (two) types of coordination polyhedra of higher bond-valence. Minerals are divided into different setsaccording to their cation coordination numbersand cation stoichiometry,with a generalgroup formula M*Ty(D,(M and T are cationsof different coordination number, O : unspecifiedligand). Within a specificset, minerals are classified accordingto their basicheteropolyhedral cluster, or fundamentalbuilding block, and the way in which this clusterpolymerizes to form a three-dimensionalstructure. Thus in eachset are the followingclasses: (l) unconnectedpolyhedra; (2) finite clusters;(3) chains;(4) sheets;(5) frameworks. The presentwork addressesthe classificationof minerals based on tetrahedra and octa- hedra,beginning with the vIMrvT2O, minerals.The 47 structure types of the 102 mineralsof this set are analyredin terms of their basic cluster and modes of polymerization,and orga- nized into a structural hierarchy.The mode of polymerization of the fundamentalbuilding block is related to the Lewis basicity of the simple oxyanions I(MOJ + 2(TO4)l that consti- ture the cluster. The fundamentalbuilding block is repeated(often polymerized)by trans- lational symmetryoperators to form the structuremoilule, a complexanionic polyhedral array whoseexcess charge is balancedby the presenceof (usually)large low-valencecations. The Lewis basicity of the structuremodule may be related,via the valencematching principle, to the Lewis acidity of the extra-module cations. Using simple anion coordination numbers suggestedby the valencesum rule, the coordination number of the extra-modulecation can be calculated.This schemepredicts quite well the extra-modulecation type and coordination number for the structuresexamined here. Mineral solubilitiesin water can also be rational- ized using thesearguments, and qualitative predictions of solubility are in good agreement with the limited amount of data available.

Introduction classesof minerals are recognizedby the common oc- A scientific classificationis a distillation of our knowl- currenceof anions and radicals, and this was greatly ex- edgeconcerning the nature of the objects under consider- tendedby Dana. Although there has beenmuch revisionin ation. This is reflected in the historical developmentof the ensuing period, the schemeof Dana is the only all- mineral classificationfrom ancienttimes to the presentday. encompassingmineral classificationand is still under active Minerals were first classifiedaccording to their physical developmenttoday (Ferraiolo, 1982). the development of crystal- properties.^fmy From the initial work of Theophrastus and Early this century came tte Elder to the detailed work of Agricola and Bir- structure analysis. Chancterization of mineral structures ingucci, the improvementsin mineral classifrcationwere showed that the crystal structure (which encompassesthe based on more accurateobservations of physical proper- chemicalcomposition) controls their physicaland chemical ties. At the beginning of the lgth century, contempor- properties,and probably also certain aspectsof their para- aneouswith tha extensivechemical studies of natural ma- genesis.Many mineralogistshave suggestedthat crystal terials,came the chemicalclassifications of minerals.Initial structure should be the basis of mineral classification. proposal work involved classificationbased on physical and chemi- Except for a few chernicalclasses ofminerals, this cal properties, but with the rapid uduitt.. of chemical has not beenextensively developed; however, it is instruc- (1930) knowledge, completely chemicai classificationssoon re- tive to consider these classificationsbriefly. Bragg placedtliese tryUiid sclemes.Berzelius was flrst to develop classifiedthe silicatesaccording to the ways in which the fur- a system basld on electronegativeelements, in which (SiOo)tetrahedra polymerize; this has beendeveloped 0003-o04x/85/050ffi455S02.00 455 H AW TH ORN E : ST RT]CTU RAL C LASSI F IC AT Io N o F M I N ERALS

Preliminary considerations Hawthorne(1983a) has proposedthe followinghypoth_ esis:structures may be orderedor classifiedaccoritng io the polymerizationof thosecoordination polyheilra with higher bond-ualences.Such a hypothesisis suggestedby pauling,s rules in the following manner. Cation bond_valencere_ quirementsare satisfiedby the formation of anion coordi_ nation polyhedraaround them; thus we can think of the structureas an array of complexanions, that polymerizein order to satisfy their anion bond-valencerequirements. With regard to Pauling's secondrule (pauling, 1960),the most important polymerizationsinvolve those coordi_ nation polyhedra with higher bond-valences,as thesecon_ tribute most to the satisfactionof the anion bond-valence requirements.If the major imperative of a structure is the phosphates based on the polymerization of divalent and satisfactionof its cation and anion bond_valencerequire_ trivalent cation octahedra, a scheme which could also en_ ments,the most important featuresof the structure are the compass some sulphates, arsenates,vanadates. etc. How_ type of cation coordination polyhedra and the way ever, this scheme has the same disadvantage in as the others, which the coordination polyhedra of in that it focuses on just highest or higher one part of the structure. This was bond-valencespolymerize; recognized this suggeststhe abovehypottr_ by Hawthorne (1979)and Moore (19g0),both of esis. whom suggested that a more adequate classification of Hawthorne (1983a)has recentlydeveloped a graph theo- phosphate minerals would be based on the polymerizations retical method to derive all possible polyhedron clusters of octahedral-tetrahedral coordination polyhedra clusters. consonantwith a given stoichiometry.This method is con- All of these schemes have one thing in common; the ceptually of interest when considering the question of basis on which the mineral class is defined is chemical structural classificationof minerals, as it provides a link rather than structural. The classes considered are silicates betweenthe chemicalformula of a mineral and its crystal or borates, that is, chemical divisions rather than structural structure,that is a link betweenthe current chemicalclassi_ divisions. The resulting classifications are thus chemical_ fication of minerals and the analogousstructural arrange_ structural hybrids, in much the same way that the early ments. In principle, it is possible to derive all possible chemical classifications were actually physical-chemical hy_ structuresfor a particular stoichiometry,but this approach brids. A true structural classification should appty to att is obviously not practical for such a general problem as minerals, and should have as its basis structural rather mineral classification.In this case,it is more profitable than chemical considerations. to proceedin an inductive manner and analyzethe structures The development of a structural classification of min_ observed for a specific stoichiometry in terms of poly- erals is part of the more general problem that is the devel_ merizationof homo- or hetero-polyhedralclusters. The fundamental polyhedral cluster or fundamental building block of a mineral structure could be defined as that anay of polyhedrathat is repeatedby the operatorsof the lattice group to form the complete structure. Such a definition might be satisfactory if we were considering every polyhedron in the structure.However, this is not the case; we preferentially select polyhedra of high bond_ valenceand ignore the remaining low bond-valencepoly_ hedra. Sometimes,the polyhedral cluster of interest has higher inherent symmetry (i.e.,pseudo-symmetry) than the structureas a whole, and it is convenientto recognizethis. as the fundamentalcluster of high bond-valencefolyhedra can be smaller than simple structures the asymmetricunit might originally and minerals is not generally considered. suggest. An exception to this is the structural classification of min_ Minerals based on tetrahedral-octahedral clusters The generalmethods adopted here are not restrictedto any particular type or number of different coordination polyhedra.However, the presentpaper will concentrateon minerals in which the higher bond-valencepolyhedra are introduced here. However, Lima-de-Faria (19g3) empha_ tetrahedra and octahedra. All minerals involving tetra_ sizes the layered aspect of structures, and the details of the hedra and octahedrahave beendivided into different sets schemesare interestingly dissimilar. according to the stoichiometry of their octahedral and H AWTHORNE : STRI]CTURAL CLASSIFICATION OF MINERALS 457

be com- tetrahedralcomponents. They are given the generalformu- From a graphical viewpoint, (1) and (2) could la M*Tr@,, where M : octahedrally coordinated cations, bined, but structurally it makes more sense to distinguish five T: tetrahedrallycoordinated cations, and (D: unspecified between them. Detailed classiflcations of each of these ligand.This may also be written as M,(TOo)r@,if the tetra- types can be develoPed. hedra are known to be unpolymerized.It should be empha- The MTrtD" minerals sizedthat this generalformula does not necessarilyrepre- the structuralclassifi- sent the completeformula of a mineral, but just the part The presentpaper will consider part of the more general involving the high bond-valencecation polyhedra' cation of the MTr@" minerals, the funda- It is sometimesnot clear what is the most appropriate M*TyO, minerals. The descriptions will stress of its poly- general formula for a mineral. For example,when both mental polyhedral cluster and the character will also be divalent and trivalent octahedrallycoordinated cations are merization, but the remainder of the structure in presenton distinct sites,should they both be consideredas outlined as this shows systematic trends with variations M cations or should the divalent cationsbe omitted? Here cluster chemistry for a fixed stoichiometry. I have generallyomitted them on principle, unlessthey are Isolated polyhedra disorderedwith the trivalent cations; however, this may 1; the "cluster" not always be the best alternative,and a generalanswer Minerals of this class are given in Table The remaining may require a posteriorianalysis. This is not overly impor- has the general stoichiometry MT2O14' anions are satisfied pre- tant at the presentstage, as the current resultsmay require bond-valence requirements of the the water molecule plays considerablereorganization once the initial classification dominantly by H atoms, and thus With the exception of processis complete. an important role in these structures. the fleischerite group, all of these minerals contain Cluster polYmerization (M(H10)6) octahedra. The progression from the amarillite the alum group is The possiblemodes of cluster polymerizationcan be di- g.oup to the mendozite group to of hydration' The vided into the following classes:(1) unconnectedpoly- characterized by an increasing degree (M(HrO)u) octahedra is the hedra;(2) isolated clusters; (3) chains;(4) sheets;(5) frame- bond-valence structure of the water molecules are works. same throughout, and the additional Ton tetrahedra Table 1. MTr

,0, o) ctl B(o) ,( S.G. Ref Mineral FormuI a a(8t b(R) c(R)

*Amariilite NaIFe3*(S04)2(H20)6] 95.2(l) P?,/a (l) Tamarugite Na[Al(S0O)t(HrO)UJ 7.353(2)25.2?515) 6.091\2)

*Mendozite cZ/c NaIA1(S0O)t(HtO)6]'5H20 2175(3) 9.ll(10) 8.30il) 9?.47\8) Kalinite K[A1(S04)2(H20)6]'5H20 Pa3 *Sodiumalum NalAl(So4)z(H20)61'6H20 12.214(r) Potassiumalum KIAl (S04)Z(H20)6]'6H20 r2.157(r) Tschermigite NH4[Al(S04)Z(H20)6]'6H2012.240(1) 100.28(3) P?,/c (4) Apiohnite MnIAl(S0o)r(Ht0)6]2'10H20 6.198(2)?4.3_41(4) 21.266(41 Bit inite FeZ*tF"3+(io4;2tirolulr:torro 0ietrichite ZnlAl(S0O)t(Ht0)612'l0HZ0 100.99 PZ,lc *Hatotrichite Fe"[Al(S04)2(Hzo)6]2.10H20 6.I 81 24.?97 20.5r9 Pickeringite MSIAI(S0O)r{Ht0)612'10H20 Redingtonite r"2*tc.{doitrlnrotutr'roHro 94.70(3)82.46(3) PI Aubertite cu2+[At(s04)2(H20)6]cl.8H2o6.28213)13.r92(5) 6.260(3)9r.85(3) t07.?2 P2,/c Boussingaultite (NH4)ZIl'19(S04)Z(H20)6] 6.?11 12.597 9.3?4 r04.45(5) P2,/c CyanochroiLeKrICu(500)r(tlr0)UJ 6.r59(5)l2.l3l(7) 9.086(4) r06.8 P2,/c Moh|ite (NH4)2[Fe('(SO4)2(H20)6]6.2? 1257 9.?8 P2,/c *Picromerite KZIMS(S04)Z(H20)6] 6.r2r(3) r2.25(3) 9.09(r) 104.2(l)

Despujolsite ca3[t'4n4+(so4)(oH) .3Hzo 8.56(2) r0.76(4) 2 6] P6?c (8) *Fl Pb3[Ge(s04) (0H)6]'3H20 8.8670) r0.875(1) ei scherite Z (S0O),(0H) 8.s29(r) r0.802(2) P6?c Schauertite CarIGe 6]'3H20 (4) (1969). (2) (1972). (3) Craner et aL. Menchett Ref.: (1) Robinsan and Fang Fang and Robinson di dL SanseuerLno Carapezza and Riua (1976). (5) Ginderau and Cesbron (7979). (6) Carapezaa and Riua SanseuerLno (1970). (B) afta (1975). I the nme r tmE gYouP oJ nLne!'aLst 45E H AW T H ORN E : ST RIJCTU RAL C LASSIF I CAT Io N o F M I N ERALS

Table 2. MTrO. mineralsbased on isolated[(M(TOJrO")-] clusters

Mineral Fomula b(8) o (o) .r(o) "tR) "(8) B(o) s.c. Rer. Anapaire ca2[Fe2+(po4)2(li2o)4] 6.447(r) 6.816(t) s.898(1) 101.64(3) ),04.24(3) 7o.i6(4) pI (r) Bloedite Na2[Mc(so4)2(H2o)4] 11.03 8.14 5,49 100.7 P2,/a (2,3) Leonlre K2[Mc(so4)2(H2o)4] 12.03(3) 9.61(3) 9.98(4) 9s.0(3) c2/n (4) scherrelite (Nil4) 2[Mc(po3oH)2@20) 4] rr.49(2> 23.66(6) 8.62(r) Pbca (5) Roemerire Fe2+[Fe3+(so4)2 :H2o) 412.6H2o 6.463(8)15.309(18) 6.341(8) so.s(2) r01.1(2) 85.7(2) Pl (6) Metavolrine K2Na6Fe2+[Fe3+(so4)60(H2o)3]2.r2H2O 9.575(5) r8.17(1) P3 (7) (1). Ref .: Cqtti et aL, (192-9). lZ). Rmnouq (1960). and MalitskaAq (3). Eukin dnd Nozik ('Lg?s). (4). Syikanta (1968). (5). Khqn and Bqur (1922). et aL, f Ol. rmjil. et at. (197aa). (7). Giaeouazzoet aL. (1926).

added to the coordination polyhedra of the alkali cation to Finite clusters replac€ the oxygen of the (SO4) tetrahedra, which no longer Minerals whose structures are based on finite clusters coordinate the alkali cation. These additional water mole_ of tetrahedra and octahedra are given in Table 2. There cules form hydrogen bonds to the oxygens of the (SOn) are three different kinds of clusters, and these are illustrated in tetrahedra, further linking the structures together. The Figure l. Anapaite, bloedite, leonite and schertelite are alum structure actually forms the end member of this series based on the simple [M(TO4)2O4] cluster with the tetra- at the present time. Increased states of hydration could hedra arranged in a trans configuration relative to the oc- occur, but would entail either an increase in the alkali tahedron (Fig. 1b); this cluster is compatible with a center cation coordination number, or the addition of water held of symmetry at the octahedral cation, and in the first three minerals the cluster has this point symmetry. In these four minerals, the M cation is divalent and all four of the ..un- specified ligands" (@o)of the cluster are (HrO). Roemerite is also based on a simple M(TO4)2O4 cluster, but in this structure the tetrahedra are arranged in M-type cation here. Thus there are five H,O molecules in a cis configuration (Fig. la) relative to the octahedron; the formula unit of these minerals that ire not directly this cluster is not com_ patible with a center of symmetry. The formula bonded to a cation; nonetheless, these water molecules are of roe_ merite (Table 2) has been written to emphasize an essential part of the structure (i.e. non_zeolitic), being the presence of this [M(TOu)r@n] cluster. The charge-balancing held in place by hydrogen bonding. A priori, it is not clear Fe2+ is coordinated by six water molecules, whether or not the minerals of the halotrichite group and thus the roemerite structure consists of an (Fe2+(HrO)u) should be considered as MT2(D. or as M.T.(D" minirals; octahedron and two [Fe3*(SO4)2(HrO)n] clusters linked together however, as shown later, they can be satisfactoriiy interpre_ solely by hy- drogen bonding. The structure ofmetavoltine is based ted as MTr@, minerals. The same situation exists for au_ on a complex but elegant cluster of composition bertite, consisting of discrete (SO.) tetrahedra and [M3OO4)6O4] (Fig. lc) that is also found in a series of synthetic (A(HrO)6) polyhedra, together with a (Cu(HrO).) octa_ com_ pounds investigated by Scordari (1980, lggla). As in hedron, Cl-, and two HrO molecules that aie only in_ all of these "isolated cluster" structures, hydrogen bonding plays volved in hydrogen bonding. Again, it will be shown that an important part in the inter-cluster linkaee. the observed bond connectivity is consistent with its inter_ pretation as an MT2O' structure.

fleischerite group are different in that they contain an (M(OH)6) octahedron; this results in very weak hydrogen bonding from this octahedron to the rest of the structure. The water of hydration has the same role in this structure as in the mendozite and alum groups, augmenting the co_ 1: Finite [M(TOo)r@"] clusters found in minerals: (a) cls ordination polyhedron of the large lower-valence cations. _ lt!._ [M(TO)rOn] ; (b) trans [M(TOjrO.] ; (c) [M.(TO)"OJ. HAWTHORNEi STRUCTUR AL CLASSIFICATION OF MINERALS 459

chain is -7.20A' or some multiple of this value, and is normally evident in the cell dimensions (Table 4)' The com- plexity of these structures is much greater than that exhibi- ted by the minerals of Table 3. Perhaps the simplest struc- ture is tancoite (Fig. 4a), in which the [M(TO4)rtD] chains are in a square array (Fig. ab), crosslinked by alkali cat- ions and hydrogen bonds. Scordari (1981b) has proposed that the sideronatrite structure contains this same and unit cell [M(TO4)rO] chain. The general stoichiometry dimensions suggest (Hawthorne, 1983b) that the sideron- atrite structure may be a supercell derivative ol the Acmm ll tl (I) may r1 I I tancoite substructure. Similarly, metasideronatrite '2r 2l also have a tlncoite-derivative structure. The structures of ab d e the minerals of the jahnsite and the segelerite groups con- sist of slabs of tancoite-like structure, intercalated with Fig. 2. Infinite [M(TO4)rO"] and [M2(TO4)4ID.]chains found of (M2*O2(H2O)*) octahedra, as shown in Figure 5' in minerals: (a) [M(TOjrtDz] : krcihnkite-type;(b) IM(TOJTO] slabs (1977) refer to jahnsite and segelerite as : tancoite-type; (c) [M(TOJro] : brackebuschite-tvpe; (d) Moore and Araki and they give an elegant dis- [M(To4)ro] : ransomite-type;(e) [Mr(Ton)n@s] : botryogen- combinatorial polymorphs, ob- type. The fundamental[M(TO4)2O4] and [Mr(TOo)ntD.] clusters cussion of the relationships between both these two are shown unshaded,and the repetitionoperator is shown. served structures and other feasible structural afiange- ments. The basic structural difference between these two minerals depends on the nature of (M2+O2(HrO)n) linking Infinite chains octahedra; in the segelerite structure (Fig. 5)' the linkage A large number of infinite chains of the forms between the tancoite-like slabs is always frans, whereas in structure, the linkage is both rrans (through the [M(TO4)2O"] and [Mr(TOo)n@"] can be built up from thejahnsite octahedron) and cis (through the Mg(2) octahedron)' simple [M(TOn)r@n] clusters. Only a few types have thus Mg(l) based on far been found in minerals (schematically illustrated in Fig. ihe guildite structure is [Fe(SOo)lOH)] by (CuOr(H2O)n) octa- 3), although many more types are found in synthetic inor- chains that are bound together can be considered as a col- ganic compounds. The simplest (least connected) type of hedra (Fig. 6). The structure version of the segelerite structure with no interchain chain is the [M(TO4)rO2] chain (Fig. 2a) that is the basis lapsed (CuO2(H2O)n) octahedra play the of the minerals of the kriihnkite group, the talmessite Ca cations present; the (MgO2(HrO)o) octa- group and the fairfieldite group (Table 3). In each group, same interchain bridging role that the segelerite. The yftisite structure is based on the [M(TO4)r@r] chain is parallel to the c-axis with a hedra do in type' repeat distance of -5.55A. The three structure types (Fig. [T(SiO4)rO] chains (Fig. 6), also of the ta-ncoite Y3+ cations' 3) differ principally in the hydrogen bonding schemes de- bound together by [7]- and [8]-coordinated of the struc- veloped in each. The [M(TO*)2@] chain (Fig. 2c) is the basis minerals, encompassing the Next is the [M(TOu)r

KROHNKITE FAIRFIELDITE T I c sin0 I I

f*.-- b *0.^* ts-- bl2 ----a srn * j

chain shown in Figure Fig. 3. The structures of the krcihnkite, talmessite and fairfieldite groups, all based on the [M(TOo)rOr] type 2a. Different hydrogen-bonding arrangernents between adjacent chains charactetize each structure. HAW T H ORNE : STRU CTU RAL CLASSI FI c AT IoN oF M I N ERALS

Table 3. MTr@n minerals bascd on the infinite [M(TO4)rO2] chain shown in Fig. 3a Mlnerar Fomula b(R) "(R) .(gl ;d) s(5 (") s.c. Rer. Brandrite ca2hrn(Aso4)2(n2o)21 5.89g(2) 72.968(4) ( s. 684 1) 108.0s(2) P2'/" (1) *Kriihnktre Na2lcu(soA)2(H2o)2] 5.807(1) 12.656(2) s.s17(r) r08.32(1) P2,/c (2) Rosellte ca2[(co,Me,)(Asol2cr'20)z] 5.801(1) 12.898(3) (1) 5. 617 rol .42(2) P2,/" (1)

cassrdyite ca2[Ni(po4)2(H2o)2] 5.713(13) (r5) 6.730 s.430(11) 96.7(2) 107.3(3) r04.7(2) Pi (3) colrinsite ca2Lv€eoi2G2o)2f s.734(1) 6.780 (r) s.441(1) 97.29(\) 108.56(r)107.28(1) pr (3,4) Gaitite ca2lzn(Aso4)2(n2o)2] s.915(5) 6.981 (6) 5.s12(6) 96.1o(9) ros.76(6) r07.4o(6) pI (s) Roselire-bera ca2lco(Aso4)2(H2o)2] 5.884(6) 6.963(8) s.581(9) 97.72(8) r09.24(9) 107.5(r) pr- (4) *Talnesstre ca2[Mc(Aso4)2(H2o)2] 5.884(4) 6.99s(4) 5.s64(4) 97.69(9) 109.7(1) 107.9(1) pI (4)

*pairfietdice ca2[Mn(po4)2(H2o)2] 5.79(1) 6.s7(1) 5.5r(1) 102.3(3) 108.7(3) 90.3(3) Pi (6) l'resselite ca2fFe2+ Gol 5.g5(z) 2G2o) 2f 6.52(2) 5.45(2) r02.3(4) 7O7.5(4) 90.8(2) pr (4)

Ref .: (.1) HaDthome and. Fergus,on (792?), (Z) Haathome a/d. Fetgzson (1975), (3) (1922). (s) sturrcn-and. (1s80),-oe;V*;:;1ti".a B?otherton et aL, (1974). (4) qL. ounn r, redueed Catti et ceLL orientotion. (6) Fonfoni et qL. (197Cb).

5). The chain runs parallel to the b-axis in theseminerals, [M(TO4)2O,] chain. Thesestructures are shown in Figure and has a characteristicrepeat -5.29A. distanceof Th' 8, in which it can be seenthat the chains are graphically atomic arrangementsare very similar in all three structure identical to eachother, and have the generalstoichiometry [M(TO4)2O]. The chain can be constructed from a cis M(TO4)2 clusterthat is repeatedby a 2, screwoperaror as shown in Figure 2d. The original cluster links to clusters that are equivalentby virtue of the Zr operation and the t (translation)operation parallel to the length of the chain; structure types; this is discussed in detail by Fanfani and thus the chain is broader than the chains discussedpre_ Zanazzi(1968, 1969) and Shenand Moore (1982). viously. The crystal structuresof ransomite and (Table krausite Although not apparent from the chemical formula the 6) are based on a slightly more complex type of structure of botryogen (Table 6) is based on an

Table 4. MTr

Guildite cuz+[Fe3+(so4)2 (oH)].4H2o 9.786(2) 7.134(l) 7.263(1) 105.38(t) p2,/n (6)

Yftisite Y4[Ti(si04)20] ( F,0H)6 14.949(4) 10.626(2) 7.043(2) cmcn (7)

Referencee: (1) Hadthome (19A3b). (2) (1981b). Seordari (3) Moore md Araki (1924). (4) t4oore ( jgz|). (S) Moore (1922), nd Ito ffid Arqki (6) Wm et al. (1978). (7) Balko and Bakakin (19?s). l etructure not definitiuely establiehed, H AW T H ORNE : STRU CTU RAL C LASSI FI CAT I ON OF M I N ERALS 46r

c

x----tr--- -r,-

Ia til;,fw

+u# b and Fig. 4. The structure of tancoite, showing the constitution of the [M(TOJr@] chains (Fig. 2b), and their relative arrangement binding by interstitial sodium cations and hydrogen bonding; from Hawthorne (1983c). 462 H AW TH ORN E : ST RI]CTU RAL CLASSIF IC AT Io N o F M I N ERALS

YFTISITE

CafAl(PO.),(OH)l H:H

b Mg(HrO)oOr a aI :H. CaI Al(PO1),(OH)] I H:H

Mg(HaO).oz h- b -----t Fig. 6. The structuresof guildire (left) and yftisite (righ0, both .*-"- basedon the [M(TOo)r@] tancoite-typ€chain, seenin each struc- ture in cross-section;interchain bonding is by (Cu(HrO)oOr)octa- Fig. 5. The structure of segelerite,after Moore and Araki hedrain guilditeand [7]- and y3+ in yftisite. (1977).The IM(TOJTO] tancoite-typechains (shaded) run parallel f8]-coordinated to c and are cross-linkedinto slabs on (010) by Ca cations; the slabsare linked togetherby layersof (Mg(HrO)oOr)octahedra in which the oxygensare arrangedcis to the centralMg cation. the [M(TOn)r@r] sheet (Fig. 9a) that is the basis of the structure of rhomboclase. The fundamental building block is a cis [M(TOn)r

Mineral Formula .rQr dr/r., "rQo(A) c(R) B(o) s.c, Reference

Arsenbrackebuschite Pbz IFez+(As04)2 (H2o)] 7.763(t) 6.046(l) s.022(t) 112.5(l) pz,ln (t) Arsentsumebite PbrIcu(soo)(As0o) (0H)J 7.84 5.9? 8.85 112.6 PT,/n *Erackebuschite ( Pb,[lvln vOo ), (Hr0)J 7.68 6.18 8.88 |1.8 p7,/n (z) Gamagarite Baz[(Fel+Mn ) ( vo4)2(oH,Hzo)] 7.88(r) 6.t7(l) 9.15(t) 112.7(r) p2,/n Goedkeni te sr2[Ar(po4)2(oH)] 7.?6(2) s.74(21 8.4s(2) 113.7(t) pz,/n (3) Tsumebite Pbrlcu( (s0o)(0H) Poo) 1 7.85 5.80 8.70 t]1.5 pT,/n (4)

*Fornacite PbZIcu(As04) (cr04) (0H)] B.l0l(7) 5.892(tl)17.s47(9) il0.00(3) pz,/c (5) Plolybdofornaci te PbrICu(As0O)(t4o04) ( 0H)] 8.r00(s) 5.e46(3)17.65(t) t0e.17(s)p?,/c Tornebohmi te ( (si RE)2lAl 04)2(0H)l 7.383(3) 5.673(3)16.937(6) 112.04(2) p2,/c (6)

Vauquelinite Pbrlcu( ( Poo) croo)(0H) J 13.754(5) 5.806(6) 9.563(3) 94.56(3)pZ,/n (t)

Referenees: (1) Hofrneister md ?iI.lnmns (1g?B). (2) Donqldaan aa'l Bamas tlg|s). (3) Moore et aL- (1975). (4) Nichols (1966). (S) Coeco et aL. (1962). ( 6 ) Shen. md Moore ( 1982 ) . (7) F@f@i and Zmazzi ( 1968) . H AW T HORNE : STRU CT URAL CLASSIF IC AT IO N OF M I N ERALS 463

constructed from a cis [M(TOo)2@n] cluster linked in one I' direction by M-T corner-sharing and is the other direction by T-T corner linkage. In bafertisite, these sheets of com- position [T(SirO?)O2] are linked alternately by layers of f6]-coordinate Fe2+ and fl0]-coordinate Ba' The next type of sheet to be considered is the [M(TrOs)O] sheet (Fig. 9e) that involves M-M edge- c sinp sharing, M-T corner-sharing and T-T corner-sharing, and is formed from the cis [MTOa)rOn] cluster. This sandwich- like sheet is the basis of several important structures (Table 7). In pyrophyllite, the sheets are held together solely by hydrogen bonding, whereas in the dioctahedral micas, the clay minerals of the illite group, and the dioctahedral brit- tle micas, the sheets are held together by alkali and alkali- earth cations. On the basis of the hypothesis proposed ear- l- lier, several minerals traditionally classed as trioctahedral l._b__l micas are included here; these are zinnwaldite, ephesite and bond-valence is -0.17 v.u., whereas Fig. 7. The structure of tdmebohmite, based on the taeniolite. The Li-O the Al-O bond-valence is -0.50 v.u.; on this basis, LitDu IM(TOJTO] brackebuschite-type chain shown in Figure 2c; after Shen and Moore (1982). The chains run parallel to b and are octahedra are not included in the basic unit which conse- crosslinked by RE cations in tcirnebohmite, and large alkaline- quently is that shown in Figure 9e. earth cations in the brackebuschite- and vauquelinite-group min- The last mineral in this class is goldichite; part of the erals. structure is shown in Figure 11. It is based on an [M2(TO4)4O6] cluster, heavily shaded in Figure 11, that is repeated parallel to a, to form a very thick corrugated sheet The more complex [M(TO4)r] sheet of Figure 9c is the parallel (100). Individual clusters are joined by one M-T basis of the merwinite, brianite and yavapaiite structures, to and the rather open sheets that are two of which are illustrated in Figure 10. The sheet can be corner-sharing linkage, formed are bonded together by f9]-coordinate K and a derived from a cis [M(TOn)r(Dn] cluster that is repeated by translations, such that the polymerization involves M-T network of hydrogen bonds. corner-sharing only. In yavapaiite (Fig. 10), the sheet is graphically identical but symmetrically distinct from the Frqmework structures ideal sheet of Figure 9c. In merwinite, the [Mg(SiOn)z] sheetsare bonded together bV [8]- and [9]-coordinate Ca; The minerals of this class are listed in Table 8, arranged in brianite, the [Mg(POn)r] sheets are similarly bonded in order of increasing complexity of cluster polymerization. together by [8]- and [9]-coordinate Na and Ca. In yava- Perhaps the simplest of the framework structures is keldy- paiite, the sheets are bonded together by f10]-coordinate shite (Fig. 12).The basic cis [M(TO4)2O4] cluster is repeat- K. The observed cell-dimensions are related to those of the ed with M-T corner-sharing in two directions to form a ideal sheet (merwinite, obs. (calc.), b : 5.29(5.57), sheet ll(100).This sheetis repeatedby simple translation lla c :9.33(9.56); brianite, obs. (calc.), b : 5.23(5.45), such that adjacent sheets are linked by sharing tetrahedral c:9.13(9.44); yavapaiite,obs. (calc.),a:8.15(9.M), b: corners to form pyro-groups in the three-dimensional 5.15(5.244), but the departures away from the ideal values structure. The complete inter-cluster linkage is thus M-T are considerable. and T-T corner-sharing. The structure of bafertisite is based on an elegantly The structure ofnenadkevichite (Fig. 13) is also based on simple [M(TrOr)@r] sheet (Fig. 9d); this is most easily a simple cis [M(TOo)2(Dn] cluster. This cluster is repeated

Table 6. MTr@, minerals based on the infinite [M(TOn)rO] and [Mr(TOo)nOo] chains shown in Fi8. 3d and 3e

Mineral Fomula

?+- 1+ 10.403(2) 93.o2(3) P2,lc (1) Ransomite cu- LFe- (So4)2(H2o)l2'4H20 4.811(2) 16.2r7(4)

-1+ P2'la (2) Kraus ite KLFe-(soo),(Hro)J 7.908(10) 5.152(s) 8.988(10) r02.75(8)

P2,/^ *Bo t ryogen lrgr[r.]+tso.),(or1)2(H2o)21'r0H2oro-47 17.83 7 'r7 roo.3 (3) zincborryosen nzlle3r+(soo)o(on)r{uro)rl.rouro 10.526(4) r7.872(7) 7,136(4) 100.13(4) P2,/n

Ref.: (L) wood (19?0), (2) Grqeber et qL, (1965). (3) Susse (1968). 4g H AW T H ORN E : STRU CTU RAL C LASSI F I CAT ION OF M I N ERALS

KRAUSITE RANSOMITE the Ti analogue of nenadkevichite, is monoclinic, but the structure is virtually the same as that ofnenadkevichite. The structure of batisite and shcherbakovite is shown in Figure 14. Again the basic element is the cis [M(TO4)rO4] cluster; this is repeated to form the sheet shown in Figure l4a, with M-T cornerlinkage lla and T-T cornerJinkage I llb. This sheet is repeated llc with M-M and T-T corner- b sharing linkages to form the framework structure of Figure 14b. The large alkali and alkaline-earth cations occupy the I large voids apparent in Figure 14. I Next is a more familiar structure. that of the alkali and calcic pyroxenes. The basic cis [M(TO4)rA4] cluster (Fig. I 15) is repeated llc, such that there is edge-sharing between octahedra, corner-sharing between tetrahedra, and corner- sharing between octahedra and tetrahedra; this forms the F-c--{ b-----*l familiar chainJike fragment of the pyroxene structure. This is repeated and b, with corner-sharing Fig. 8. The structures of krausite (left) and ransomite (righQ, lla between octa- based on the [M(TOjr@] chain shown in Figure 2d. hedra and tetrahedra, to give the resulting pyroxene frame- work. The last three structures, livenite, wcihlerite and ro- senbuschite, show an interesting progression in the com- by M-M and M-T corner-sharinglinkages llc to form a plexity of the fundamental cluster, Liivenite is formed from (tancoite-like)chain of the kind shown in Figure 2b. This the basic cis [M(TOo)rOo] cluster that is repeated in two chain is repeated by T-T corner-sharinglinkage lla and b dimensions with corner-sharing between octahedra and (Fig. l3a) to form the basicframework (Fig. 13b);note the tetrahedra; this sheet is then repeated with corner-sharing four-memberedtetrahedral rings. The alkali cations pro- between tetrahedra of adjacent sheets. W6hlerite is formed vide additional linkage within the framework,together from a more complex [M2(TO4)4O6] cluster, in which the with a small amount of hydrogenbonding. Labuntsovite, two octahedra are graphically distinct; this cluster is re-

Table 7. MTr

Minerals Formula atflt utRl Rhomboclase H502[Fe3+(S04)2(H20)2] 9.7?414\ 18.333(9) 5.4?\4) Pnma (l) 0lmsteadite KFet+tNb(p04)2021.2H20 7.sr2o) 10.000(3) 6.49212], PbZ,m l?')

Brianite NarCaIMS(pOO)rJ 13.35(s) 5.2312) 9.13(3) 91.zQl pZ,/a (3) *Merwinite CarIMg(Si0O)rJ 13.25(2) 5.293(9) 9.33(2) 91.9(Z) pZ,/a (4)

Yavapaiite KtFe3+(S04)21 8.152(5) 5.153(4) 7.877(5194.90171 CZ/n (5)

Bafertisite BaFe2+[Tisi20702] 10.60 13.64 12.47 119.5 Cz/n (6)

Pyrophyllite IAtSi205(0H)]Z 5.r61 (2) 8.958(2) 9.35t(2) t00.37(2)CT+ 17)

(M*,M2*)[(l43*,M2*)(si,nr)205(0H)]2 fll:::tn"ottt -s.z -9.0 -r0.0 -r00.0 cz/n (8)

Ephesite NaLi[At (Si,At )205(0H) ]2 5.27 9.13 10.25 100.0 C2/n Taeniolite KLitt'tSsirOU(0H)J, 5.231(l) 9.06s(2) 10.140(ll99.86(2) c7ln (9)

(M*,H20)[(M3',M2*)(sr,nr)205(0H)]z 3;::lii::"t -5.2 -e.0 variabre

Bramallite (Mr,H20)x[Al,!t9,Fe) (Si,At )205(0H) ]2 Hydromica (t4-,H20)x[A](si,A1 )205(0H) _ ] 2 *iltite (r4-,H20)xlAt,Mg,Fe)(sj,A1)205(0H)125.2 9.0 9.95 95.5 Czlc

Goldichite K2tFer+(s04)4(H 20)4l.4H20 r0.387(6)10.486(6) 9.086(5)101.68(7)P2, /c (5) (t) (L974). Ref.: Mereiter (2) Moore et qL. (19?6). (3) Moore (1975). (4) Moore and Ataki (19?z). (5) Qraeber and Rosenzaeig (197L). (6) fq-hsien et qL. (1963) (7) Wardle and Brindleg (1972) (8) Bail.eu (1980). (9) Cuqgenhein and Baileu (197s), t= 91.a3(2), : = 89.75(2)a H AW T H ORNE : STRU CTU RAL CLASSIF IC AT ION OF M I N ERALS 465

(a) (b) (c)

t+ L tr 21 (d) (e)

t I

I I I t...... '..'* ot : Fig. 9. Infinite [M(TOJrO"] sheetsfound in minerals:(a) [M(TOjrOz] : rhomboclase-type;(b) IM(TOJrOz] olmsteadite-type; : (c) [M(TOJr] : merwinite-type; (d) [M(TrO?)Or] : bafertisite-type; (e) [M(TrOJ@] muscovite-type. The fundamental [M(TO4)rO4] clusteris unshaded,and the repetitionoperators are shown.

peated with corner-sharing between octahedra, and the re- sultant sheet is repeated with corner-sharing between tetra- hedra. In rosenbuschite, the basic cluster is the [M4GO4)BO8] cluster that is repeated by simple trans-

MERWINITE YAVAPAIITE

I aT b b __*l

I t I Ir I I

______--i r__ c r-b + Fig. ll. The structure of goldichite, a very thick corner-linked Fig. 10. The structuresof merwinite(left) and yavapaiite(right), sheet of [Mr(TOJ4O6] clusters, one of which is unshaded in this basedon the [M(TOjr] sheet(Fig. 9c); adjacentchains are linked diagram; adjacent layers are linked by f9]-coordinated K and a by [S]-and flO]-coordinatedCa and K respectively. network of hydrogen-bonds. 466 HAW T H ORN E : STRU CTTJ RAL C LASSIF I CAT ION OF M I N ERALS

Table 8. MTrOn minerals based on infinite frameworks -s.G:-;;:- lvlineral Formuta a(8) b(8) c(8) o(o) B(o) "(o) Keldyshite (Na,Hr0)[ZrSir0rJ 9.0(1) 5.34(2) 6.96(3) 9211) 116(t ) 88(l) pi 0 ) Parakeldyshite Na ZrSl I ,0, J 5.42 6.66 94.3 I 15.3 89.6 Pr fi ) Nenadkevichite NarINbSirOU(0H)l.2Hr0 7.408(2)14. r98(3) 7.148(2) Pbam 12) '14.f8 Labuntsovite K2[T i Si (0H .2H?0 206 ) ] 13.70 7.74 I|7 C?/n (3) Batisite NarBaITiSi ,0U01, 10.40 13.85 8.10 Ima2 (4) 'f Shcherbakovite KrBa[(Ti,tib)Si2060]2 0.55 13.92 8. t 0 ImaZ

Alkali pyroxenes t'4+[M3*Si206] N9.7 a8.8 tu5.25 1107,5 C?/c (5) calcic pyroxenes catw2*siroui ! 9.8 18.9 N5.24 !']05.5 Cz/c (5)

Ltveni te (Na,Ca) 3[ZrSi2070]F r0.83n) 9.98(l) 7.174(5) 108.1il) P2,/a (6)

Wohlerite NarCaOIZrNb ( Si ,07) ZoiF 10.823(3)r0.244(3) 7.290(2) 109.00(4) P2, (7) Rosenbuschite (Ca,Na)rtZrrTir(SiZOt) 40?FZ)F4 t0. lZ(5) il .29(5) 7.?t(3J 9r.3(s) 99.7(5) nt.8(s) Pi (8)

Referen.ces: (1) Khdlilou et (1922). (Z) perrault al, et aL. (1gZJ), (3) GoLoDastikoD(1974). (4) Nikitin and BeLou (1962). (S) Cmeron and pwike (1981). (6) (198L). MeLLi.ni (7) MeLLini qnd f,lerlino (1979) - (B) Shibaeua et al.. (196'i ) .

lation in all three dimensions, with M-T and T-T corner_ strength of an anion is analogously defined as the charac- sharing. Thus the progressive increasein complexity of the teristic valence of a bond formed by the anion. Simple basic clusters in these three structures is accompanied by anions can show a considerablerange ofbond-valence, but increasing condensation of the component polyhedra. this is generally greatly reduced for complex anions. As an example, consider thenardite, NarSOo. The bond-valences Structural trends to the oxygen anion vary from -0.16 v.u. for Na-O to Brown (1981) has introduced a structure-based scale of -1.5 v.u. for S-O. Now consider the oxyanion (SOn)2-; the S-O bond has a bond-valence of - 1.5 v.u., leaving -0.5 v.u. per oxygen to be satisfied by 3 additional bonds (assuming an average coordination number of [4] for oxygen).Thus the Lewis basestrength ofthe (SOn)2- oxya- nion is 0.513:0.17 v.u. Obviously this value is to some of a characteristic bond formed by that cation, and Brown (1981) lists values for numerous cations. The Lewis base

Table 9. Definitionofstructural units

Complex anion: a cation surrounded by a coordinatjon polyhedron of anions such that the aggregate formal change is negative; e.g. (so4)2-,(si04)4-.

Homopolyhedralcluster: a cluster of similar coordination polyneora

bonded together. csinPI Heteropolyhedral cluster: a cluster of nore than one type of coordtna_

tion polyhedra bonded together.

Fundamentalbui lding block (FBB): the horno-or heteropolyhedral 1 q-i cluster that is repeated by the (translational) 51ryeg1y operators Fb sin of the t-+ structure to form the strongly bonded part of the sf,rucrure I 21 Structure Module: the strongly bonded part of the structure that is Fig. 12. The structure of keldyshite, based on a lZrSirOrf forned by repetition/polynerization of the polyhedral cluster that framework; the fundamental [M(TOjrrDo] is shown unshaded, forms the FB8 of the structure. and the repetition operators are shown; the repetition operaror (not shown) orthogonal to the diagram is a simple translation. H AWT H ORN E : ST RT]CTU RAL CLASSIF IC AT I ON OF M I N ERALS 467

I I I t l+-b------t t<_b______l

Fig. 13. The structure of nenadkevichite: (a) shows tancoite- 2r t- type chains llc, crossJinked by corner-sharing between tetrahedra to form pyro-groups; (b) shows linkage of tancoite-type chains in the two directions orthogonal to their length, with the 4- membered SioO, rings cross-linking chains. 9v Fig. 15. The pyroxenestructure as a framework structure; the extent sensitiveto the averagecoordination number as- basic [M(TOn)r(Do] cluster is unshaded,and is repeatedby 2t screwand verticalglide operatorsin the plane of the diagram,and sumedfor oxygen;the value [4] is usually adequate,and it by a translationoperator orthogonal to the planeof the diagram. is generallyobvious when another value is more appropri- ate. Brown (1981)also lists Lewis basicity values for nu- merousoxyanions; these values can easily be calculatedas couraging; it will be interesting to see if this type of re- indicatedabove. lationship holds for other M,T'(D" stoichiometries. Considernow the hypothesisof Hawthorne(1983a). In terms of Lewis acid and base strengths,it considersthe Inter-module linkage polymerization of the most tightly-bonded oxyanions in Translational symmetry operators repeat the fundamen- Increasingpolymerization of theseoxyanions the structure. tal building block to form a three-dimensional array that resultant Lewis basestrength. This sug- will decreasetheir may be connected in 0, 1,2 or 3 dimensions. Let us define gests of polymerizationin thesestructures that the degree this array as the structure module. So far, this scheme has be related to the averageLewis base strength of should exploited the strong intra-module linkage and has focussed their componentoxyanions, i.e. the Lewis basestrength of solely on this aspect of structures. However, by going one 2{TOi-)l in the structuresconsidered here. t(MO3-) + step further, we can get insight into the extra-module link- This premiseis examinedin Figure 16; there is a general age, that is the weak bonding between the structure module trend of increasingpolymerization (condensation) with in- and the low-valence charge-balancing cations. creasingLewis basestrength of the componentoxyanions. The definitions of Lewis acid and base strength outlined Furthermore,minerals lying closeto the averagetrend line tend to be more common (alum and halotrichite groups, kr

(a) (b) I I c s"-t a i

sYl o.30 0.35 o 40 21 cluaTER BASlclTY (v.u-) + Fig. 14. The structure of batisite: (a) the basic [M(TO4),O4] Fig. 16. Structuretype as a function ofthe Lewis basicityofthe cluster (unshaded) is repeated by glide and screw operators to componentoxyanions KMO?-) + {TO.2-)l:the sizeof the circles form a sheet; (b) this sheet is repeated by a 2, screw op€rator to is proportional to the number of specieswith that particular ba- form a framework. sicity and structuretype. 46E HAW T HORN E : STRU CT U RAL CLASSI F I CAT ION OF M I N ERALS

earlier lead to the valence matching principle (Brown, 1981),which states that vry3+e--o.ro-- the most stable structures will be *"dn vrM2+o formed when the Lewis acid strength of the cation is most \'e,1.* nearly equal to the Lewis base strength of the anion. This principle may be exploited in this instance by considering Fig. 17. Bond-valence structure of HrO bonded to [6]- the principal module of a structure as a (very complex) coordinatedivalent and trivalentcations. oxyanion. The Lewis basicity of the module may be calcu_ lated, and through the valence matching principle, may be bond-valence requirements around each hydrogen atom, related to the Lewis acidity of the weakly-bonding cations each hydrogen forms at least one hydrogen bond with in the structure. This provides an insight and even some neighboring anions. Thus the HrO molecule is acting as a predictive capability with regard to the identity and coordi_ bond-valence transformer, causing one stronger bond to be nation number of theseweakly-bonding cations. split into (at least) two weaker bonds. The presence of non- Graphical isomers (Hawthorne, 1984) have the same module HrO in the structure increases the number of Lewis basicity (assuming the same type of cations); inspec- bonds from the charge-balancing cation(s) to the module, tion of actual structures indicates that this is not chemi_ and decreasesthe valence of these bonds: this increases the cally realistic. This difference can be traced to variation in effective coordination number of the charge-balancing anion type, and can be naturally handled by including hy- cation (defined as the number of bonds formed to the struc- drogen (as OH or HrO) as a component of the structure ture module), and decreasesits effective Lewis acidity. Note module in the following way. If the bond-valence contrib_ that all of the HrO molecules need not be bonded directly uted to the anion is less than 0.67 v.u., the anion is con_ to the cations, so this transformer action can also function sidered to be HrO; it is bonded to no more cations, and entirely through hydrogen bonds (e.g., halotrichite group forms two hydrogen-bonds. If the bond-valence contrib- minerals). uted to the anion falls between 0.62 and 1.00 v.u. (and the As an example, consider the structure of botryogen anion is not bonded to a tetrahedrally coordinated cation), (Table 6 and Fie. 2e). The module formula is the anion is consideredto be OH; it is assumedto form no [Fe]+(SOn)n(OH)r(HrO)2la-; the oxygen atoms bonded additional bonds to other cations (this is not always valid to Fe3* and S have an assigned (and observed) coordi- of course). It should be noted that this scheme invariably nation number [3], the hydroxyl and water oxygens are reproduces the anion type of the structure module; the assumed to be satisfied, with two hydrogen bonds emanat- validity of this procedure stems from the valence-sumrule ing from each HrO anion; the remaining oxygens have an (Brown, 1981),which is closely related to pauling's second assigned coordination number [4]. The number of bonds rule (Pauling, 1960). needed to satisfy these anion coordination number require- Calculation of module basicity hinges on the use of the ments is 2x l0+ 6 x 1- 4:22: the -4 term refersto most appropriate anion coordination numbers. In the ab_ the four hydrogen bonds emanating from the HrO anions. senceof a systematic study of anion coordination numbers The total bond-valence needed to satisfy the valence-sum in these structures, the following approximation is used: rule in the module is (2 - 010 + (2 * t - o)6 - 4h when 02- is bonded to M3+ and T6*, the assignedCN is : 32 - 16t - 6o - 4h, where t, o and h are the 3; at all other times it is 4, except when H is involved (see tetrahedral (1.5),octahedral (0.5)and hydrogen (0.25)bond- above). valencesrespectively. The module basicity is (32 - l6t - According to the valence matching principle, the module 6o - 4h)122: 0.18 v.u. and the module charge is 4-. The basicity should approximately match the linking cation number of bonds to the module from the linking cations is acidity; thus the linking cation may be predicted on this 22 and the charge of the linking cations is 4+; this indi basis. The cation coordination number may be predicted cates a monovalent cation coordination number of from the number of bonds required for the simple anions of 2214 - 16l and a divalent cation coordination number of the module to attain their ideal coordination numbers (of 2212 : Ulf. Thus we predict a cation acidity of 0.18 v.u. [3] or [a]), divided by the number of linking non-module and cation coordination numbers of [6]+ and [11]2+. In cations. The actual acidity of the linking cation can (and botryogen, the module charge of 4- is balanced by the frequently does) depart from its ideal (average) value. The presence of 2Mg, with an ideal Lewis acidity of 0.36 v.u. value of a cation's acidity in an actual structure is equal to (Brown, 1981).However, there are five waters of hydration its formal charge divided by the number of bonds it forms for each Mg, and thus the anion coordination of Mg is to the module. This number of bonds is equal to the con- (HrO)rO; each water anion functions as a bond-valence ventional coordination number, except for structures in transformer, giving the Mg an effective coordination which there are non-module nonzeolitic HrO molecules. number (i.e. number of bonds to the structure module) of To appreciate the effect of such HrO molecules, consider 5x2+ l:[11], and a (modified) actual acidity of the bond-valence structure around the oxygen atom (Fig. 2lll : 0.18 v.u., both values in agreementwith predictions. 17).The bond-valencerequirements of the oxygen are satis- This scheme thus provides an explanation as to why botry- fied by a cation-anion bond of valence less than or equal ogen is hydrated, and in fact would predict that botryogen -0.5 to v.u., together with two short O-H bonds of val- would be hydrated, given the module part of the structure ence greater than or equal to -0.75 v.u. To satisfv the and the identity of the charge-balancing cation. HAWTHORN E: STRUCTURAL CLASSIFICATION OF MIN ERALS 469

I solated polyhedra structures Table 11. Basicities, acidities (v.u.) and cation coordination numbers (CN) in the finite cluster structures The [M3*(Tu*On)r(HrO)u]- cluster has a basicity of -rcaur - - - 0.08 v.u. and a predictedmonovalent cation coordination e f iiai cteri---frotiu-re iioniTnal actual- ii-ulGiilid basicity CN charge acidity acidity CN number of For amarillite,both the ideal and observed [12]. 0.29 7 cation aciditiesare 0.16 v.u. and the observedcation coor- Anapaite 0.29 7 4 0.29 dination number is [6]. Thesevalues are significantlydif- Bl oedi te 0.14 7 2 0.16 0.14 B ferent from the calculated values, suggestingthat higher Leoni te 0.l4 7 2 0.13 0.l4 8 hydratesshould be quite stable,and indeedthis is the case, i te 0.25 6 2 0.25 0.20 5 with membersof the mendoziteand alum groups showing Schertel good agreementwith predictedvalues (Table 10).This clus- Roemerite 0.08 t8 2 0.36 0.t8 12 ter has a predicted divalent cation coordination of [24] lvletavol ti ne 0.12 9 t0 0.l8 0.t4 8 and a predicted cation acidity of 0.08 v.u. No individual cation has thesecharacteristics, but they may be attained by high degreesof hydration through the transformer numbers are in good agreement with these values, although action of the HrO anion. In the membersof the halotri- highly hydrated divalent cation equivalents should also be chite group (Tables I and 10), the divalent cations have possible. nominal acidities of 0.3GO.40v.u. and nominal coordi- The [M4+(T6*O4)2(OH)6]6- module is the basis of the nation numbers of [6]. However, the divalent cation is minerals of the fleischerite group, with a basisity of 0.17 coordinated by six (HrO) anions, and thus twelve v.u. and predicted coordination numbers of [5] and [10] hydrogen-bondsemanate from this group. These are fur- for monovalent and divalent cations respectively. Brown ther split by the hydrogen-bondingnetwork of the ad- (1981) does not give a Lewis basicity for Pb2*, but the ditional four HrO anions to form twenty bonds to the value will be -0.2 v.u. (Table 10). Again the observed module. Thus the divalent cation has an effectivecoordi- values are in reasonably good agreement with the predicted nation number of [20] and an actual acidity of 2120:0.1O values. v.u., in good agreementwith the predicted values. This provides an adequateexplanation for the high degreesof Finite cluster structures hydration in someof theseminerals, the hydrogen-bonding Anapaite, bloedite and leonite show good agreement network reducing the effectiveLewis acidity of the cation with the predicted values of cation acidity and coordi- and bringing it into a reasonablematch with the Lewis nation number (Table 1l). Schertelite is an interesting ex- basicity of the structuremodule. The situation is similar in ample: the presence of acid phosphate groups modifies the aubertite,except for the additional Cl that balancesone of bond-valences in the phosphate group to 1.0 to the OH the chargesofthe Cu2+cations. anion and 1.33 v.u. to each of the remaining three oxygens. The minerals of the picromeritegroup are basedon the The resultant module basicity is 0.25 v.u. with a predicted [M2*(T6*O4)r(HrO)u]'- module,with a basicityof 0.13 cation coordination of [6]. Ammonium (NHo)* is a com- v.u. (Table 10) and predictedcation coordination numbers plex cation with an ideal acidity of $a)la:0.25 v.u.; in thus of [10] and [20] for monovalent and divalent cations re- schertelite, there is one bifurcated hydrogen-bond, and spectively.The observedcation aciditiesand coordination the actual cation acidity is 0.20 v.u. with an observed coor- dination number of [5], in reasonable agreement with the predicted values (Table 11). The agreement for roemerite is good; basicity and predicted Table 10. Basicities, acidities (v.u.) and cation coordination not the calculated module numbers (CN) in the isolated polyhedra structures cation coordination number suggests that a more hydrated form (with - l0H2O) would occur. The agreement for me- module predicted module nominalt actual, obser{ed basicitv CN charoe aciditv'aciditv- CN' tavoltine is good, particularly so in view of the complexity of the structure; although only average values can be pre- Amarillite 0.08 t? I 0.l6 6 dicted, these agree well with the average values of cation l4endozite 0.08 12 I 0.16 0.09 ]l acidity and coordination number observed in the actual Kalinite 0.08 12 I 0.13 0.09 ll structure.

Sodium alum 0.08 12 I 0.16 0.08 12 '12 Potassium alum 0.08 12 l 0.13 0.08 Chain structures Minerals of the kr

Table 12. (v.u.) Basicities, acidities and cation coordination Table 13. Basicities, acidities (v.u.) and cation coordination (CN) numbers in the chain structures numbers (CN) in the sheet structures

module predicted moduT6--n-oiJi-iT--- ooserveo module predicted nodule nominal actual observed basicity CN charqe acidjty acidjty CN basicity CN charqe acidity aciditv CN

Krohnkite 0.13 B 2 0.16 0.14 7 Rhomboclase 0.r3 8 r 0.25 0.20 5 Brandti te 025 8 4 0.29 0.29 7 0l msteadite 0.23 9 5 0.28 0.23 7 Tancoi te 0.17 7 3 0.18 0.15 7 Merwini te 0.33 6 6 0.29 0.25 8 Sideronatrite 0.17 6 2 0.t6 Bri ani te 0.22 8 4 0.20

Jahnsite 0.20 t0 4 0.34 0.25 9 Yavapaite 0.08 12 I 0.13 0.10 t0

GuiI di te 0.13 t5 2 0.45 0.20 t0 Baferti site o,27 7 s 0.31 0.29 7

Yfti si te 0.30 10 6 0.38 8 Itluscov i te 0.15 7 r 0.13 0.13 8 '| Brackebuschite 0,24 9 4 \0.2 o.25 8 Gol di chi te 0.08 t2 0.r3 0.09 ll Goedkenite 0.22 l0 4 0.?4

Fornacite 0.rB il 4 t0.2 0.20 l0 Tornebohmite 0.30 l0 6 0.30 l0 valuesfor the remainingstructures (Table 13),including the Ransomite 0.08 24 2 0.45 0.20 t0 dioctahedralmicas, are good; this is particularly notable Krausite 0.08 12 I 0.13 0.t0 l0 for bafertisite,in which the low observedmean cation coor- dination number of Botryogen 0.18 tl 4 0.36 0.l8 tl [7] is successfullyforecast. Framework structures hydration states in these minerals are necessary to reduce Predictedand observedvalues for the framework struc- the ideal cation acidities and bring them more into line tures are given in Table 14. There is good agreementbe- with the predicted values. There is some discrepancy for tween predicted and actual values,a fact that is particu- guildite, in which the actual cation acidity is larger than the larly encouragingconsidering the complexity of such min- module basicity; the same situation occurs for ransomite eralsas livenite, wtihleriteand rosenbuschite. (Table 12), as well as roemerite and amarillite, and suggests Mineral solubility that the method of handling anion coordination number is In water, the intermolecularbonds not yet quite adequate for the [M.*(Tu*On)@"] modules will have the valence linked by divalent cations. structure illustrated in Figure 18 (Brown, 1981).The hy- drogen For the brackebuschite, fornacite and vauquelinite atomshave a Lewis acid strengthof 0.2 v.u. and the oxygen groups (Table 5), the calculations are in good agreement atoms have a Lewis base strength of 0.2 v.u., as- suming : with the observed data, correctly predicting the identities of a CN [4] for oxygen. Hence water forms an the linking cations (Pb2+, Sr2+) and their high (t9l-tlll) acid-basenetwork that can react with other acid-basecom- pounds coordination numbers, as compared for example with the of suitable strength. Minerals in which the base talmessite and fairfieldite groups, with Ca as the linking strengthof the structure module matchesthe acid strength of water and the base strength of water cation and observedcoordination numbers of [7]. Krausite matchesthe acid and botryogen show good agreement(Table l2). It is curi- strength of the extra-modulecation are generallysoluble, ous that the very complex botryogen and metavoltine structures show good agreement with these calculations. (v.u.) whereas the simpler M3+T6+ structures (ransomite, guil- Table 14. Basicities, acidities and cation coordination numbers (CN) in the framework structures dite, etc.) do not; perhaps it is of significance that the reasonably common minerals, wheras the latter module predicted module noninal actual ooserveq l.rtff;J* basjclty CN charge acidity acidity CN

Keldyshite 0.14 1 1- 0.13 0.13 8 Sheet structures Nenadkevichite 0.06 13 2- 0.13 O.O9 ll Rhomboclase is another M3+T6+ structure which shows some discrepancy between observed and predicted values. Batisite 0.ll l0 4 0.17 0.13 l0 The assignment of this disagreement to inadequate anion Calcicpyroxene 0.22 lO 2- O-29 0.25 8 coordination assignment is also suggested by the fact that Sodicpyroxene 0.17 8 l- O 16 0.17 8 the agreement for olmsteadite (Table 13), whose structure module is a geometrical isomer of that of rhomboclase, is Lrvenite 0.23 8 5- 0.27 0.24 8 very good. The values for merwinite are not well-predicted, llcihlerite 0.23 7 l0- 0.25 0.24 7 but it should be noted that the Ca coordinations in the Rosenbuschite 0-23 7 l0- 0.23 O.Z4 observed structure do have strong octahedral aflinities. The 6 HAWTHORN E: STRUCTURAL CLASSIFICATION OF MINERALS 471

ted) whose excesscharge is balanced by the presenceof (linking) large low-valencecations. 4. The Lewis basicity of the structure module should approximately match the Lewis acidity of the charge- balancingcations for the structureto be stable. Thesefour points form the basisof a method of structur- \, al classificationof minerals,which has been applied to a ,f ': /' o.2 0.2 broad group of sulphates,chromates, phosphates,arse- Fig. 18.The bond-valencestructure of liquid water (from nates,vanadates and silicateswith the generalstoichiome- Brown,l98l). try MT2O' (M : octahedrally coordinated cations, T: tetrahedrally coordinated cations, @: unspecificd anions).In addition to its applicability to a wide variety of provided that the module is not infinite in three- minerals,this schemehas the additional advantagethat the dimensions.This is becausethe acid and basecomponents nature of its formulation allows rationalization and predic- will, accordingto the valencematching principle, form an tion of such featuresas large low valencecation type, large equally good or evenbetter match with the water than they cation coordination, the degreeof hydration of minerals, do with each other. Minerals whosemodule basicitiesand and their relativesolubilities in water. cation aciditiesare much greaterthan 0.2 v.u. will be inso- luble, as they can form a better match with eachother than Acknowledgrnents they can with water. A qualitative survey of the minerals Financialsupport during this work wasprovided by the Natu- discussedhere showsthis to be the case.All ofthe isolated ral Sciencesand EngineeringResearch Council of Canadain the grant would polyhedraminerals of Table I are soluble,with the possible form of a fellowshipand a to the author.I like to thankRobert M. Hazen,Paul B. Mooreand MalcolmRoss for exception of those of the fleischeritegroup. Of the finite theirreviews. cluster minerals (Table 2), anapute is insoluble (relatively) while the rest are soluble.In the chain structures(Tables 3, References 4 and 5), predictions work particularly well. In the Andersen,S. (1981) The description of complexalloy structures. In kriihnkite (module :0.13, basicity observed cation aci- M. O'Keefe and A. Navrotsky, Eds., Structure and Bonding in : tity 9.16 v.u.) is soluble where the isostructuralminerals Crystals,ll, p. 233-258.Academic Press, New York. roselite and brandtite (module basicity:0.25, observed Andersen,S. and Hyde, B. G. (1982)An attemptedexact, system- cation acidity : 0.29 v.u.) are insoluble; the talmessiteand atic, geometricaldescription of crystal structures.Zeitschrift ftir fairfieldite group minerals are likewise insoluble. In the Kristallographie,158, I 19-131. tancoite-typechain minerals,sideronatrite is soluble; data Bailey,S. W. (1980)Structures of layer silicates.In G. W. Brindley are not available for most of the other minerals,but tan- and G. Brown, Eds., Crystal Structuresof Clay Minerals and their X-ray ldentification, p. l-123. Mineralogical Society, coite and guildite are predictedto be soluble,with the rest London. insoluble.The brackebuschiteminerals of Table 5 are ex- Balko, V. P. and Bakakin, V. V. (1975)The crystal structureofthe pectedto be insoluble,and the complex chain minerals of naturel yttrium and rare-earth fluortitano-silicate Table 6 are expectedto be soluble;available data bear out (Y,Tr)of,OH)uTiO(SiOr, (Yftisite). Zhurnal Strukturnoi thesepredictions. Khimii, 16,837-842. It would be of interest to put these qualitative predic- Bragg W. L. (1930)The structure of silicates.Zeitschrift fiir Kri- tions on to a more quantitative basis. For example,one stallographic,7 4, 237-305. might expectthe solubility of a mineral to dependquanti- Brotherton, P. D., Maslen, E. N., Pryce,M. W. and White, A. H. tatively on both its module basicity and the degreeof mis- (1974) Crystal structure of collinsite. Australian Journal of match betweenthe module basicityand the nominal cation Chemistry,27,653456. acidity. Unfortunately there is very little quantitative solu- Brown, I. D. (1981)The bond-valencemethod: an ernpirical ap- bility data for the minerals discussedhere, and so general proach to chemicalstructure and bonding. In M. O'Keeffe and trends betweendifferent structure types cannot be exam- A. Navrotsky, Eds., Structure and Bonding in Crystals, II, p. ined in detail. 1-30.Academic Press. New York. Bukin, V. I. and Nozik, Yu. Z. (1975)Neutron-diffraction study of the crystal structure of cobalt astrakhanite NarCo(SOn)r' Summary 4HrO. SovietPhysics Crystallography, 20, 180-182. 1. It is proposed that mineral structuresmay be orilereil Cameron, M. and Papike, J. J. (1981) Structural and chemical or classifieilaccording to the polymerizationof thosecation variationsin pyroxenes.American Mineralogist, 66, 1-50. coordinationpolyhedra of higherbond-oalences. Carapezza,M. and Riva di Sanseverino,L. (196E)Crystallography 2. Higher bond-valence polyhedra bond together to and genesisof double sulfatesand their hydrates.II. Structure, powder pattern and thermoanalysis of cyanochoite, form homo-or heteropolyheilralclusters that constitute the K 6H MineralogiaPetrologia Acta"14, 23-37. (FBB) rCu(SOa)2' rO. fundamentalbuikling blocft of the structure. Canpezza,M. and Riva di Sanseverino,L. (1970)Crystallography 3. The FBB is repeated(often polymerized)by trans- and genesisof double sulfates and their hydrates. III. Pic- lational symmetryoperators to form the structuremodule, a romerite, KrMg(SO)r' 6HrO: a methodologicalcheck. Miner- complex anionic polyhedral array (not necessarilyconnec- alogiaPetrologia Acta, 16,5-ll. 472 H AW THO RN E : STRU CTU RAL CLASSIF I CAT ION OF M I N ERALS

Catti, M., Ferraris,G. and lvaldi, G. (1977)Hydrogen bonding in TschermaksMineralogische und PetrographischeMitteilungen, the crystallinestate. Structure of talmessite,Car(Mg,Co[AsO), 3r, l2t-135. 'zHzO, and crystal chemistryof relatedminerals. Bulletin de la Hawthorne,F C. (1984)The crystal structureofstenonite, and the Sosi6t6 francaisede Min6ralogie et de Cristallographie, 100, classificationof the aluminofluorideminerals. Canadian Miner- 230-236. alogjst,22,245-251. Catti, M., Ferraris, G. and lvaldi, G. (1979) Refinementof the Hawthorne, F. C. and Ferguson,R. B. (1975)Refinement of the crystal structure of anapaite, CarFe(PO*)r. 4HrO: hydrogen crystal structure of krcihnkite. Acta Crystallographica,B31, bonding and relationshipswith the bihydrated phase.Bulletin 1753-1755. de la Soci6t6francaise de Min6ralogie et de Cristallogxaphie, Hawthorne,F. C. and Ferguson,R. B. (1977)The crystal strudure 102.31,1-318. of roselite.Canadian Mineralogist, 15,3H2. Christ, C. L. 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The crystal struc- tation and ordering on a table of inorganic structure types. ture of mendozite,NaAl(SOn)2 . 11H2O.American Mineralogist, Journal of Solid StateChemistry , 16,7-20. 57,1081-1088. Loeb, A. L. (1970)A systematicsurvey of cubic crystal structures. Ferraiolo, J. A. (1982) A systematicclassification of nonsilicate Journal of Solid StateChemistry, 1,237-267. minerals.Bulletin of the American Museum of Natural History, Makovicky, E. (1981)The building principlesand classificationof t72, t-237. bismuth-leadsulphosalts and related compounds.Fortschritte Giacovazzo,G., Scordari,F., Todisco,A. and Menchetti,S. (1976) der Mineralogie,59, 137-190. Crystal structure model for metavoltine from Sierra Gorda. Mellini, M. (1981)Refinernent of the crystal structure of Hvenite. TschermaksMineralogische und PetrographischeMitteilungen, TschermaksMineralogische und PetrographischeMitteilungen, 23.15s-165. 28.99-112. Ginderow, D. and Cesbron,F. 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