Many mineralogists have suggested that crystal terials, came the chemical classifications of minerals. Initial structure should be the basis of mineral classification ...
American Mineralogist,Volume
70, pages 455473, 1985
vIMIvTrOo minerals Towardsa structural classificationof minerals:The F. C. HewrnonNr Department of Earth Sciences, Uniuersity of Manitoba Winnipeg, Manitoba, Canada R3T 2N2 Abstract Cation bond-valencerequirementsare satisfied by their anion coordination polyhedra; anion bond-valencerequirementsare satisfiedby the polymerization of thesecoordination polyhedra.When consideredtogetherwith Pauling'ssecondrule, this suggeststhat structures may be orderedor classifieilacioriling to the polymerizationof thosecoorilinationpolyhedra This is the basisof the approachto mineral classificationproposed with higherbond-oalences. (two) types of coordination polyhedra of higher bond-valence. the focuses on here, which Minerals are divided into different setsaccordingto 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 basicheteropolyhedralcluster,or fundamentalbuilding block, and the way in which this clusterpolymerizesto form a three-dimensionalstructure.Thus in eachset are (l) unconnectedpolyhedra;(2) finite clusters;(3) chains;(4) sheets;(5) the followingclasses: frameworks. The presentwork addressesthe classificationof minerals based on tetrahedraand octahedra,beginningwith the vIMrvT2O, minerals.The 47 structuretypes of the 102 mineralsof this set are analyredin terms of their basic cluster and modes of polymerization,and organized 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 constiture the cluster. The fundamentalbuilding block is repeated(often polymerized)by translational symmetryoperatorsto form the structuremoilule,a complexanionic polyhedralarray whoseexcesschargeis 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 schemepredictsquite well the extra-modulecation type and coordination number for the structuresexaminedhere. Mineral solubilitiesin water can also be rationalized 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 ocA scientific classificationis a distillation of our knowl- currenceof anions and radicals, and this was greatly exedgeconcerningthe 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 allmineral classificationand is still under active mineral classificationfrom ancienttimesto the presentday. encompassing (Ferraiolo, 1982). physical today their development to according first classified Minerals were came the development of crystalthis century Early and of Theophrastus work the initial From properties. ^fmy of mineral structures Chancterization Biranalysis. and structure tte Elder to the detailed work of Agricola the (which encompasses structure the crystal were that showed mineral classifrcation in improvements the ingucci, based on more accurateobservationsof physical proper- chemicalcomposition)controls their physicaland chemical ties. At the beginning of the lgth century, contempor- properties,and probably also certain aspectsof their paraaneouswith tha extensivechemicalstudiesof natural ma- genesis.Many mineralogistshave suggestedthat crystal terials,came the chemicalclassificationsof minerals.Initial structure should be the basis of mineral classification. proposal work involved classificationbasedon physical and chemi- Except for a few chernicalclassesofminerals, this instrucit is however, developed; extensively not been has chemical of rapid uduitt.. the with cal properties, but (1930) knowledge, completely chemicai classificationssoon re- tive to consider these classificationsbriefly. Bragg the in which ways the to according silicates the placedtliesetryUiid sclemes.Berzeliuswas flrst to develop classified furdeveloped has been polymerize; this (SiOo) tetrahedra which in elements, a system basld on electronegative 455 0003-o04x/85/050ffi455S02.00
H AW T H ORNE : ST RT]CTU RAL C LASSI F IC AT Io N o F M I N ERALS
phosphates based on the polymerization of divalent and trivalent cation octahedra, a scheme which could also en_ compass some sulphates, arsenates,vanadates. etc. How_ ever, this scheme has the same disadvantage as the others, in that it focuses on just one part of the structure. This was recognizedby Hawthorne (1979)and Moore (19g0),both of whom suggested that a more adequate classification of phosphate minerals would be based on the polymerizations of octahedral-tetrahedral coordination polyhedra clusters. All of these schemes have one thing in common; the basis on which the mineral class is defined is chemical rather than structural. The classes considered are silicates or borates, that is, chemical divisions rather than structural divisions. The resulting classifications are thus chemical_ structural hybrids, in much the same way that the early chemical classifications were actually physical-chemical hy_ brids. A true structural classification should appty to att minerals, and should have as its basis structural rather than chemical considerations. The development of a structural classification of min_ erals is part of the more general problem that is the devel_
simple structures and minerals is not generally considered. An exception to this is the structural classification of min_
introduced here. However, Lima-de-Faria (19g3) empha_ sizes the layered aspect of structures, and the details of the schemesare interestingly dissimilar.
Preliminary considerations Hawthorne(1983a)has proposedthe followinghypoth_ esis:structuresmay be orderedor classifiedaccoritng io the polymerizationof thosecoordinationpolyheilra 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 imperativeof a structure is the satisfactionof its cation and anion bond_valencerequire_ ments,the most important featuresof the structureare the type of cation coordination polyhedra and the way in which the coordination polyhedra of highest or higher bond-valencespolymerize;this suggeststhe abovehypottr_ esis. Hawthorne (1983a)has recentlydevelopeda graph theoretical method to derive all possible polyhedron clusters consonantwith a given stoichiometry.This method is conceptually of interest when considering the question of structural classificationof minerals, as it provides a link betweenthe chemicalformula of a mineral and its crystal structure,that is a link betweenthe current chemicalclassi_ fication of minerals and the analogousstructural arrange_ ments. In principle, it is possible to derive all possible structuresfor a particular stoichiometry,but this approach is obviously not practical for such a general problem as mineral classification.In this case,it is more profitable to proceedin an inductive manner and analyzethe structures observed for a specific stoichiometry in terms of polymerizationof 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 the asymmetricunit might originally suggest. 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 tetrahedra and octahedra. All minerals involving tetra_ hedra and octahedrahave beendivided into different sets according to the stoichiometry of their octahedral and
457
H AWTHORN E : STRI]CTURAL CLASSIFICATION OF MINERALS
tetrahedralcomponents.They are given the generalformula M*Tr@,, where M : octahedrally coordinated cations, T: tetrahedrallycoordinatedcations,and (D: unspecified ligand.This may also be written as M,(TOo)r@,if the tetrahedraare known to be unpolymerized.It should be emphasizedthat this generalformula does not necessarilyrepresent the completeformula of a mineral, but just the part involving the high bond-valencecation polyhedra' It is sometimesnot clear what is the most appropriate general formula for a mineral. For example,when both divalent and trivalent octahedrallycoordinatedcations are presenton distinct sites,should they both be consideredas M cations or should the divalent cationsbe omitted? Here I have generallyomitted them on principle, unlessthey are disorderedwith the trivalent cations; however, this may not always be the best alternative,and a generalanswer may require a posteriorianalysis.This is not overly important at the presentstage,as the current resultsmay require considerablereorganization once the initial classification processis complete. Cluster polYmerization The possiblemodesof cluster polymerizationcan be divided into the following classes:(1) unconnectedpolyhedra;(2) isolatedclusters;(3) chains;(4) sheets;(5) frameworks.
From a graphical viewpoint, (1) and (2) could be combined, but structurally it makes more sense to distinguish between them. Detailed classiflcations of each of these five types can be develoPed.
The MTrtD" minerals The presentpaperwill considerthe structuralclassifi-
cation of the MTr@" minerals, part of the more general M*TyO, minerals. The descriptions will stress the fundamental polyhedral cluster and the character of its polymerization, but the remainder of the structure will also be outlined as this shows systematic trends with variations in cluster chemistry for a fixed stoichiometry. Isolated polyhedra
Minerals of this class are given in Table 1; the "cluster" has the general stoichiometry MT2O14' The remaining bond-valence requirements of the anions are satisfied predominantly by H atoms, and thus the water molecule plays an important role in these structures. With the exception of the fleischerite group, all of these minerals contain (M(H10)6) octahedra. The progression from the amarillite g.oup to the mendozite group to the alum group is characterized by an increasing degree of hydration' The bond-valence structure of the (M(HrO)u) octahedra is the same throughout, and the additional water molecules are
Ton tetrahedra Table 1. MTr
Roemerire
Fe2+[Fe3+(so4)2 :H2o)
Metavolrine
K 2 N a 6 F e 2 + [ F e 3 + ( s o 4 ) 6 0 ( H 2 o ) 3 ] r22. H 2 O 9 . 5 7 5 ( 5 )
Ref.:
412.6H2o
6.447(r)
23.66(6)
1 0 0 .7 9s.0(3)
8.62(r)
6.463(8)15.309(18) 6.341(8) so.s(2)
r 8 . 1 7( 1 )
s.c.
Rer.
pI
(r)
P2,/a (2,3) c2/n Pbca
r01.1(2) 85.7(2)
(4) (5)
Pl
(6)
P3
(7)
(1). Cqtti et aL, (192-9). lZ). Rmnouq and MalitskaAq ( 1 9 6 0 ) . (3). Eukin dnd Nozik ('Lg?s). (4). Syikanta et aL, (1968). (5). Khqn and Bqur (1922). f Ol. rmjil. e t a t . ( 1 9 7 a a ) . ( 7 ) . G i a e o u a z z oe t a L . ( 1 9 2 6 ) .
added to the coordination polyhedra of the alkali cation to replac€ the oxygen of the (SO4) tetrahedra, which no longer coordinate the alkali cation. These additional water mole_ cules form hydrogen bonds to the oxygens of the (SOn) tetrahedra, further linking the structures together. The alum structure actually forms the end member of this series at the present time. Increased states of hydration could occur, but would entail either an increase in the alkali cation coordination number, or the addition of water held
M-type cation here. Thus there are five H,O molecules in the formula unit of these minerals that ire not directly bonded to a cation; nonetheless, these water molecules are an essential part of the structure (i.e. non_zeolitic), being held in place by hydrogen bonding. A priori, it is not clear whether or not the minerals of the halotrichite group should be considered as MT2(D. or as M.T.(D" minirals; however, as shown later, they can be satisfactoriiy interpre_ ted as MTr@, minerals. The same situation exists for au_ bertite, consisting of discrete (SO.) tetrahedra and (A(HrO)6) polyhedra, together with a (Cu(HrO).) octa_ hedron, Cl-, and two HrO molecules that aie only in_ volved in hydrogen bonding. Again, it will be shown that 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_ ordination polyhedron of the large lower-valence cations.
Finite clusters Minerals whose structures are based on finite clusters of tetrahedra and octahedra are given in Table 2. There are three different kinds of clusters, and these are illustrated in Figure l. Anapaite, bloedite, leonite and schertelite are based on the simple [M(TO4)2O4] cluster with the tetrahedra arranged in a trans configuration relative to the octahedron (Fig. 1b); this cluster is compatible with a center 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 ..unspecified 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 a cis configuration (Fig. la) relative to the octahedron; this cluster is not com_ patible with a center of symmetry. The formula of roe_ merite (Table 2) has been written to emphasize the presence of this [M(TOu)r@n] cluster. The charge-balancing Fe2+ is coordinated by six water molecules, and thus the roemerite structure consists of an (Fe2+(HrO)u) octahedron and two [Fe3*(SO4)2(HrO)n] clusters linked together solely by hydrogen bonding. The structure ofmetavoltine is based on a complex but elegant cluster of composition [M3OO4)6O4] (Fig. lc) that is also found in a series of synthetic com_ pounds investigated by Scordari (1980, lggla). As in all of these "isolated cluster" structures, hydrogen bonding plays an important part in the inter-cluster linkaee.
1: Finite [M(TOo)r@"] clusters found in minerals: (a) cls _ lt!._ [M(TO)rOn] ; (b) trans [M(TOjrO.] ; (c) [M.(TO)"OJ.
STRUCTUR AL CLASSIFICATION
HAWTHORNEi
I
lt ll
r1 '2r
ab
I 2l
e
d
Fig. 2. Infinite [M(TO4)rO"] and [M2(TO4)4ID.]chains found in minerals: (a) [M(TOjrtDz] : krcihnkite-type;(b) IM(TOJTO] : tancoite-type; (c) [M(TOJro] : brackebuschite-tvpe; (d) (e) [Mr(Ton)n@s]: botryogen[M(To4)ro] : ransomite-type; type. The fundamental[M(TO4)2O4] and [Mr(TOo)ntD.] clusters are shown unshaded,and the repetitionoperatoris shown.
Infinite chains A large number of infinite chains of the forms [M(TO4)2O"] and [Mr(TOo)n@"] can be built up from simple [M(TOn)r@n] clusters. Only a few types have thus far been found in minerals (schematically illustrated in Fig. 3), although many more types are found in synthetic inorganic compounds. The simplest (least connected) type of chain is the [M(TO4)rO2] chain (Fig. 2a) that is the basis of the minerals of the kriihnkite group, the talmessite group and the fairfieldite group (Table 3). In each group, the [M(TO4)r@r] chain is parallel to the c-axis with a repeat distance of -5.55A. The three structure types (Fig. 3) differ principally in the hydrogen bonding schemes developed in each. Next is the [M(TOu)r
