Bernard Henry Grobe ty

The replacement of anthophyllite by jimthompsonite:a model for hydration reactions in biopyriboles

Received: 8 July 1996 /Accepted: 13 December 1996

Abstract Anthophyllite crystals found in ultrama®clenses of the Lepontine Alps (Switzerland) contain co-herent, submicroscopic intergrowths of ordered anddisordered biopyribole polysomes. The chain widthdistributions of disordered polysomes were analyzedusing high resolution transmission electron microscopy(HRTEM). Chains wider than triple were interpreted asintermediate products in the transformation of ant-hophyllite to the triple chain silicate jimthompsonite.The concentration of individual chain types is stronglycorrelated with the reaction progress. Based on observedzipper terminations and the transformation rules givenby Veblen and Buseck (1980) a scheme of possible re-action paths leading from anthophyllite to jimthomp-sonite is proposed. The reaction scheme and a simplekinetic model for elementary reactions allow modelingof the observed chain width distributions. The modelsuggests that the complex reaction paths involving stepswith increasing and decreasing chain width are moreimportant in the formation of jimthompsonite than thedirect transformation from anthophyllite. The widechains (>triple) occurring as intermediate products ofthe multi-step paths are structurally closer to talc thanjimthompsonite. The back-transformation of these widechains to triple chains is, therefore, a strong argumentthat jimthompsonite is a stable phase and not only ametastable intermediate product in the transformationof anthophyllite to talc.

Introduction

Since the early crystal structure determinations of micas,amphiboles, and pyroxenes (Warren and Modell 1930a, b), the close relationship between these structures wasrecognized. Thompson (1978, 1981) introduced a mod-ular description for the amphibole structure based onthe alternate stacking of (010)- pyroxene and mica lay-ers. He pointed out that other combinations of thesemodules are possible and should be found in nature, andhe proposed to revive the term biopyribole (biotite,pyroxenes, amphiboles), introduced by Johannsen(1911), for this polysomatic series. The ®rst non-classicalmembers of this group, the triple chain silicate jim-thompsonite (Jt) and chesterite (Ch), a mixed-chain sil-icate with alternate double and triple chains, werediscovered in ultrama®c rocks from Chester, Vermont(Veblen and Burnham 1978 a, b). The HRTEM inv-estigations of the new phases indicated that they wereformed by hydration of primary anthophyllite (Veblenand Buseck 1980).

The replacement of anthophyllite by wide-chainpolysomes is a solid-state reaction that is stronglycontrolled by the structure of the reactant. Veblen andBuseck (1980) developed a general reaction scheme forthe hydration of amphibole to jimthompsonite andtalc. Their qualitative model, however, does not ad-dress in detail what role the frequently observed widechains (>triple) play in the transformation mecha-nism. Akai (1982) used chain width distributions todevelop a qualitative reaction scheme for the metaso-matic transformation of pyroxene to talc at the Aka-tani ore deposit, Japan. Close to the contact, doublechains were the dominant reaction products, whereasfurther out pyroxene was transformed mainly to triplechains. Both reactions seem to proceed directly with-out intermediates.

Intermediate ordered and disordered polysomes arealso found in products from prograde reactionexperiments involving amphiboles and micas. During

Contrib Mineral Petrol (1997) 127: 237 ± 247 Ó Springer-Verlag 1997

B.H. Grobe tyInstitut fur Mineralogie und Petrographie, ETH-Zentrum,CH-8092 Zurich, Switzerland

Current address:Geologisk Institut, C.F. Mùllersalle 120,AÊ rhus Universitet, DK-8000 AÊ rhus, Denmark

Editorial responsibility: V. Trommsdor�

the dehydration of talc to enstatite and quartz, ant-hophyllite appears as an intermediate, metastable phase(Greenwood 1963, 1971). The HRTEM investigations ofintermediate dehydration products also revealed disor-dered sequences with single, double and triple chains(Konishi and Akai 1991). With increasing experimentduration, these disordered sequences are converted toenstatite. The depolymerization of talc is, therefore, amulti-step process.

The most frequent chain multiplicity faults in hy-drothermally synthesized tremolite are triple chains(Ahn et al. 1991). The faults disappear with increasingannealing time. Chain width reducing reactions mustoccur, and corresponding zipper terminations have beenfound. It is not clear, however, whether the reaction pathstarting with the metastable formation of pyroxene andgoing through the formation and reduction of widechains is important, or if the direct precipitation ofdouble chains is the main amphibole-producing process.

Chain width distributions determined from HRTEMobservations on samples from Alpe Bena, Switzerland(Grobe ty 1996), and a simple kinetic model will be usedto show that the transformation of anthophyllite tojimthompsonite proceeds through a reaction path in-volving several steps with disordered chain sequences asintermediate products.

Geological settings and petrography

The biopyribole-containing samples were collected from small ul-trama®c bodies located in the surroundings of Alpe Bena and AlpeZotta in the upper Valle Maggia, Southern Switzerland (Stoll1990). The lenses, 20±30 m in diameter, are imbedded in plagio-clase/two-mica gneisses of the northern Maggia transverse zone(Klaper 1982). The Paleozoic basement rocks (KoÈ ppel et al. 1980)were metamorphosed to amphibolite grade during the Alpineorogeny, leading to the formation of kyanite, staurolite, and gar-net. The contact zones of the ultrama®c rocks with the gneissessu�ered strong hydrothermal alteration, and primary peridotiticminerals are rare. Anthophyllite and associated pyriboles can beobserved throughout the lenses, except the outermost ma®c rim.

Anthophyllite formed during the thermal high of the main Al-pine metamorphism by a decrease in pressure and/or by metaso-matic alteration by CO2-containing ¯uids and replaced an earlierenstatite ± olivine ± talc paragenesis (Evans and Trommsdor� 1974;Pfeifer 1978; Berman et al. 1986; Grobe ty 1996). The only mac-roscopic relicts of this previous paragenesis are talc and some rareolivine grains in one of the lenses of Alpe Zotta. Temperature andpressure estimates for the alpine metamorphism in the surroundinggneisses are around 600 � 50 °C (Frey 1974; Klaper 1982) and4±6 kbar (Pfeifer 1987).

The anthophyllite crystals form millimeter-sized ®brous bun-dles. Under crossed nicols, basal cuts show vividly colored striationparallel to (010). Bright-®eld TEM images reveal planar defectsparallel to (010) identi®ed as chain-multiplicity faults (Fig. 1). Theorthoamphiboles form an equilibrium texture with ¯aky talc andferri-chromite. They are overgrown by large magnesite grains,chlorite, and ®brous secondary talc.

Experimental methods and terminology

Chemical analyses were performed with a Cameca SX 50 electronmicroprobe, using an electron acceleration voltage of 15 kV and a

beam current of 20 nA. The standards were natural oxides andsilicates. Data reduction was done using a PAP-enhanced ZAFcorrection method (Pouchon and Pichoir 1984).

The HRTEM samples were prepared from thin sections previ-ously analyzed with the microprobe. The ion-milled and carbon-coated discs were mounted on a double-tilt stage for use in a JEOL200CX microscope operated at 200 kV. Original magni®cationsvaried between 200 and 450kX. Images were recorded nearScherzer defocus values. Image interpretation follows that of Ve-blen and Buseck (1979). The terminology used in this paper is takenfrom Veblen and Buseck (1980). Individual chains are characterizedby their widths given as the number of silicon tetrahedral strips(� subchains) within one chain. Slabs of wide chains parallel to(010) within an amphibole matrix are called ``zippers''. The placewhere the width of a chain or a group of chains changes along [100]or [001] is called ``zipper termination''. Alternatively, biopyribolescan be represented as modular (polysomatic) structures composedof pyroxene- (P) and mica-like (M) (010)-layers stacked along theircommon b-axis. The increase of the chain width by one subchain isequivalent to the addition of one M module.

Mineral chemistry

Electron microprobe analyses of biopyriboles are problematic, dueto the ®ne intergrowth of chains with di�erent widths. To comparedi�erent analyses, all measurements were normalized on the basisof 23 oxygens, as suggested by Schumacher and Czank (1987). Theanalyses for anthophyllite and jimthompsonite in Table 1a weretaken from optically homogeneous regions and are considered tobe representative of the ordered pyriboles at Alpe Bena. The mostevident compositional variation is the negative correlation of tet-rahedrally coordinated cations with octahedral cations. With theincrease of chain width, the ratio of octahedral to tetrahedral sitesdecreases (Fig. 2a) according to:

M tet � ÿ 0:5Moct � 11:5 �1�Iron was assumed to be ferrous (shown as Fe2+ in Table 1) andonly on octahedral sites. Aluminum was distributed among tetra-hedral and octahedral sites in such a way that the analyses plottedclosest to the line given by (1). According to this procedure, most ofthe aluminum is tetrahedrally coordinated and enters the structuremost likely through a glaucophane-like substitution (Schumacherand Czank 1987). The analyses cover the whole composition range

Fig. 1 Bright-®eld transmission electron micrograph of anthophyllitefrom the Alpe Bena sample. The crystal is ®brous, and the image istaken with the beam close to the c-axis, which is parallel to the ®beraxes. The ®ber boundaries are cracked in several places, and di�erentdegrees of rotational mis®t between sectors are visible. The dark lines(star) within the di�erent ®ber sections are chain width errors parallelto (010)

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between anthophyllite and jimthompsonite, indicating the presenceof all stages of the transformation between the two phases. Fewanalyses lie outside this composition range toward the enstatite endmember of the polysomatic series. Enstatite relicts and otherpyriboles with module sequences between amphibole and pyroxenewere found in samples from nearby Val Cramosina (Grobe ty 1996).

The number of large cations such as ferrous iron, calcium,manganese, etc., decreases with increasing chain width (Fig. 2b).This trend can be explained by the decrease with increasing chainwidth in the number of distorted octahedral sites, which accommo-date preferentially those large cations (Veblen and Burnham 1978b).The two talc generations cannot be distinguished based on theirchemistry. The iron concentration of coexisting anthophyllite and

talc lies on the partitioning curve given by Evans and Trommsdor�(1974), suggesting equilibrium conditions. Magnesite (Table 1b) hasan XMg � 0:87, but along grain boundaries and cracks a second,more iron-rich generation with XMg � 0:81 is present. The mainopaque phases are ferri-chromite and magnetite (Table 1b).

The transformation anthophyllite ®® jimthompsonite

Reaction mechanism

Veblen and Buseck (1980) recognized two basic mecha-nisms for polysomatic transformations in biopyriboles.The replacement reactions can proceed through bulkmechanisms along broad, irregular reaction fronts, suchas observed in pyroxene being replaced by amphibole(Veblen and Buseck 1981), or by the growth of (010)slabs of the product phase into the reactant phase. Twomodels were proposed for the nucleation of wide chainsin amphibole. In the polymerization model (Nakajimaand Ribbe 1980, 1981), the silicon atoms have to di�use

Table 1a Selected electron microprobe analyses of silicates. Watercontents and structural formulae were calculated with the programNORM (P. Ulmer, ETH ZuÈ rich) on the basis of 22 O + 2 OH andcharge balance for anthophyllite (Ath), 32 O + 4 OH for jim-thompsonite (Jt), 10 O + 2 OH for talc (Tc) and 10 O + 8 OH forchlorite (Chl) assuming all iron as ferrous iron. (± below detectionlimit)

Ath Jt Tc Chl

SiO2 (wt%) 57.38 58.93 61.97 31.02Cr2O3 ± 0.15 ± 2.09Al2O3 0.10 0.19 ± 16.82FeO 14.32 10.62 3.19 6.92MnO 0.52 0.03 ± 0.03MgO 25.30 26.8 29.21 30.30NiO ± 0.12 ± 0.27CaO 0.40 0.22 ± ±Na2O ± 0.09 ± ±H2O 2.16 2.82 4.64 12.47

Total 100:19 99:88 99:22 99:99

Si 7.98 11.95 4.00 2.98Cr ± 0.04 ± 0.16Al 0.02 0.02 0.01 1.91Fe2+ 1.66 1.78 0.17 0.56Mn 0.06 0.01 ± ±Mg 5.24 8.10 2.81 4.35Ni ± 0.02 ± 0.02Ca 0.06 0.05 ± ±Na ± 0.02 ± ±OH 2.00 4.00 4.00 8.00

Si + Al 8.00 11.97 4.00Roctahedral cations 7.02 10.00 2.99XMg 0.748 0.81 0.939

Fig. 2 a Plot of octahedralcations versus tetrahedralcations (see text for procedureto partition aluminum betweentetrahedral and octahedralsites). b Large cations versustotal cations for Alpe Benabiopyriboles. 2-r error-barsare shown (Jt jimthompsonite,Ath anthophyllite)

Table 1b Selected electron microprobe analyses of non-silicates.Structural formula for magnetite (Mg) and ferri-chromite (F-chr)are calculated on the basis of 4 O and charge balance, the twomagnesite analyses [Ms(I), Ms(II)] were normalized to 1 CO3. (±)(below detection limit)

F-chr Mg Ms (I) Ms (II)

FeO (wt%) 32.42 66.28 MgCO3 82.83 76.00MnO 0.28 ± FeCO3 14.77 21.38MgO 0.95 0.03 CaCO3 0.65 0.55NiO 0.14 0.83 MnCO3 0.33 0.17

Fe2O3 14.67 32.34Cr2O3 43.34 ± 98:58 98:13Al2O3 6.46 ±

Total 100:03 99:55Fe2+ 0.977 0.969 Mg 0.876 0.852Mn 0.009 ± Fe2+ 0.115 0.140Mg 0.051 0.002 Ca 0.005 0.006Ni 0.004 0.029 Mn 0.003 0.002Fe3+ 0.398 1.995Cr 1.235 ±Al 0.274 ±

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through the tetrahedron face parallel to (001) into theadjacent tetrahedral site with its apical oxygen atompointing in the opposite direction. This tetrahedral site isconnected over oxygen bridges to the neighboring chain,so that the width of the latter increases by one subchain.The octahedral cations have to di�use through the tet-rahedral layer to their new positions. The HRTEMobservations of zipper terminations, however, are morein favor of a mechanism by which wide chains areformed by repeated displacements through dissolutionand growth of I-beams or parts of them by approxi-mately 0.5 nm along +a or ) a (Fig. 3 a, b). The zipperterminations are regarded as frozen-in reaction fronts, atwhich the (010) slab of the product chains stoppedpropagating. The detailed mechanism of the displace-ments cannot be determined from HRTEM images. Thenumber and the width of chains that transform simul-taneously are controlled by structural constraints. Forcertain chain combinations, the transformation can bedone without introducing strain into the host matrix.The rules governing such coherent, strain-free transfor-mations were given by Veblen and Buseck (1980):

1. The new chain sequence must have the same num-ber of silicate subchains as the chain sequence it replaces.

2. The reactant and the product chain sequence musthave both odd or both even numbers of chains.

Transformations not ful®lling both of the rules willstrain the host matrix around the zipper termination.Chemically two types of zipper transformations can bedistinguished. Transformations that do not change thenumber of chains are isochemical (e.g., Fig. 3b). Suchtransformations change the positions of the mica andpyroxene modules in a sequence but not their overallratio. If the number of chains changes during a trans-formation, transport of matter from and to the reactionfront is required (e.g. Fig. 3a). During such a reaction,mica modules (M) are transformed into pyroxenemodules (P) (or vice versa):

nP� 2n H� � nM� nM�� or �2a�n�Mg,Fe�4Si4O12 � 2n H � n�Mg,Fe�3Si4O10�OH�2

� n�Mg,Fe� �2b�

The stoichiometric coe�cient n is equal to the di�erencein the number of chains on both sides of the termination.Hydrogen (H+) must di�use to the reaction site,whereas octahedral cations (M��) must be removedfrom it. The large channels parallel to [001] observed atthe terminations of wide-chain zippers were proposed byVeblen and Buseck (1980) as fast di�usion paths forthese exchanges.

The net stoichiometry for the transformation ofanthophyllite to jimthompsonite for coexisting mineralpairs found at Alpe Bena (s. Table 1) is given by:

3Mg5:24Fe1:66�Ca,Mn,Cr,Ni,Al�0:10Si8O22�OH�2 � 2H� 0:48Mg!2Mg8:1Fe1:78�Ca,Mn,Cr,Ni,Al�0:12Si12O32�OH�4 � 1:42 Fe �3�The transformation releases only iron and consumesmagnesium. The iron may go into the iron-rich secondmagnesite generation or form magnetite.

Reaction paths

Within the Veblen and Buseck reaction model, everybiopyribole transformation, leading from one orderedstructure to another, can proceed along a large numberof reaction paths. In the case of the transformation ofanthophyllite to jimthompsonite, two di�erent types ofpaths can be distinguished:

1. Along a direct path, double chains transform di-rectly into triple chains. The simplest, coherent zippertransformation corresponding to such a direct path in-volves six double chains, which have to react simulta-neously to four triple chains (Fig. 4 a, b). If the directtransformation is the only jimthompsonite-forming re-action, all chains wider than triple would represent in-termediate stages, either in the transformation of triplechains to talc or in the direct replacement of ant-hophyllite by talc.

2. Along a multiple-step reaction path, triple chainsare formed through intermediate steps involving chainswider than triple. Zipper transformations leading tosuch wide-chain zippers are encountered far more oftenthan the direct replacement described above (Fig. 5).Theoretically, an in®nite number of transformationsleading from double to triple chains is possible. Only afew types of zipper terminations, however, are observedfrequently, which allows a considerable reduction inpotentially important zipper transformations, and,therefore, of reaction paths. The rules for coherent zip-per transformations and the following assumptions,based on HRTEM observations, were used to deducethe theoretical reaction scheme shown in Fig. 6:

1. A maximum of three chains is involved in trans-formations with chain width reductions.

2. Only chains smaller than octuple can be trans-formed back to chains with smaller widths.

3. Because the overall reaction An! Jt is a hydrationreaction, the product sequences are always equally ormore, but never less hydrated than the reactant se-quences.

Fig. 3 a I-beam representation of the formation of a sextuple chainby the net displacement of a double chain I-beam. The reactants, threedouble chains, have 3P and threeMmodules. The product, a sextuplechain, has only one P module and 5 M modules. The chemicalchanges are, therefore, given by 2 P� 4H� ! 2 M� 2M��: b I-beam representation of the formation of two triple chains by the netdisplacement of a part of a quadruple chain. Because both reactantsand products have the same module ratio (M6P2) and only the localstructural con®guration changes, but not the local chemistry

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4. Triple chains are never reactants in chain widthreducing transformations.

5. Double chains are never products of a zippertransformation.

All transformations included in Fig. 6 have beenobserved in HRTEM images of the Alpe Bena samplesand/or the Chester samples (see, for example, Figs. 1,2,3in Veblen and Buseck 1980). A remarkable detail of thisreaction scheme is that all paths, except for the directpath and the two paths containing the reaction522!333, have the reaction 42!33 as ®nal step.

The concentrations of the di�erent zipper termina-tions and the distribution of chain widths in intermedi-ate disordered polysomes should be indicative ofwhether the direct or the multi-step reaction path is themore important mechanism in the formation of jim-thompsonite. The most common chain width transfor-mations in the Alpe Bena samples are 222! 6, 62! 44and 42 ! 33, but the observed number of zippertransformations is too low to make a statisticallymeaningful interpretation. The evolution of the chainwidth distribution with reaction progress should also becharacteristic for a certain reaction path and is easy toobtain from HRTEM images. Zones with di�erent re-action progress (� hydration degree) can already bedistinguished in optical micrographs of basal cuts of theAlpe Bena biopyriboles. The interference colors showconsiderable variation along [010] traverses, but fairlyconstant colors along [100] traverses. Bands with ho-mogeneous interference colors are considered to havethe same hydration degree and range from less than amicron up to several tens of microns. To model the chainwidth distribution for a certain degree of reaction pro-gress along a given reaction path, the rates of the indi-vidual reaction steps must be known. For this purpose, asimple kinetic model based on elementary reaction stepswas developed.

Fig. 4 a [001] HRTEM image showing two zipper terminations,which combined together result in the replacement of six double chainsby four triple chains. Both replacements are, however, not coherent.The group of three triple chains on the right and the isolated triplechain on the left are replaced incoherently (violating the second rule,see text). The strain arising from the incoherence is relieved by astacking fault (arrow) connecting both terminations. b I-beamrepresentation of the transformation. The number of double chainsbetween the triple chain on the left and the group of three triple chainson the right is smaller than in Fig. 4a. In all the following HRTEMimages the crystallographic axes are oriented the sameway as in Fig. 4a

Fig. 5 a Formation of asextuple chain from threedouble chains (see also Fig. 3a).This transformation requirestransport of hydrogen andoctahedral cations to and fromthe reaction site. The widths ofselected zippers are indicated.b Coherent, isochemical zippertransformation. . . 25 . . .! . . . 43 . . .

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Kinetic model

In the following it will be shown that the individual stepsof the overall reaction anthophyllite ! jimthompsonite(�magnetite, �magnesite) can be modeled as elemen-tary reactions. The rate for an elementary reaction isproportional to and only to the concentrations of thereactants (Lasaga 1981). The change of the concentra-tion C of a species i in a system of r elementary reactionsimplying s di�erent reacting species is given by:

dCi

dt�X

r

kr

Ys

�Cs�ns;r �4�

where n is the stoichiometric coe�cient of the species i inthe rth elementary reaction, and kr is the kinetic constant.The ``order of reaction'' rate law describes reactions ingaseous and liquid mediums and is based on the prob-ability that the R activated molecules necessary to pro-duce a molecule i collide simultaneously and in the rightway. It is also widely used to describe the kinetics ofsolid-solid reactions (see Rubie and Thompson 1985),but in most cases the equations are empirical and are notfounded on the actual reaction mechanisms. Molecu-larity and molecular collision probabilities have gener-ally little signi®cance in solid-state reactions (Gomes1961). For reactions between zippers in biopyriboles,however, it is possible to de®ne a ``speciation'' (molec-ularity) and to consider collision probabilities. All (010)slabs (� zippers) with equal width (double, triple) in abiopyribole sequence de®ne one ``species.'' In the modelcrystal, all slabs have the same dimensions along the aand c axes, and no zipper terminations are present. Themodel can, therefore, be represented as a ``one-dimen-sional'' mixture of slabs along b. The concentration Cwof Nw slabs with width w in a sequence of unit length L isgiven by:

Cw � Nw

L�5�

This concentration is not equivalent to the value A0�i�used by Ahn et al. (1991), where the number of zippersof a certain type is weighted by their width. Theweighting within the kinetic model is done by the sto-ichiometric coe�cients of each reaction.

A second requirement for the application of the ratelaw for elementary reactions is that the species are mo-bile, giving them the possibility to ``collide.'' The zippersin biopyribole sequences can move along the b-axis, theonly direction in the one-dimensional mixture, by ``side-stepping'', that means changing positions with a neigh-boring zipper (Fig. 7; Whittaker et al. 1982). Theformation of a sextuple chain zipper, for example, can bevisualized as the simultaneous ``collision'' of three dou-ble chain zippers. The relatively low concentration ofzipper terminations within anthophyllite suggests thatthe time the new zipper requires to propagate throughthe entire crystal is short. In the model, the transfor-mation of the entire zipper(s) occurs instantaneously.

This kinetic model based on elementary reactions wasapplied to a simpli®ed reaction scheme, which containsonly the most frequently observed transformations in-volving sextuple (S ), quadruple (Q), triple (T ), anddouble (D) chains. The following reactions were takeninto account:

a) 3 D� 4 H� ! S � 2 M��b) S � D! 2 Qc) S � 2 D! Q� 2 Td) Q� D! 2 Te) 4 D� 4 H� ! 2 Q� 2 M��f) 6 D� 4 H� ! 4 T � 2 M��

Two types of reactions can be distinguished: reactions(a), (e), and (f) increase the average chain width of thereacting zipper and require an exchange of matter(H� �protons, M�� � octahedral cations) with the ex-terior of the crystal. Octahedral cations have to be re-moved from the reaction site, and protons have to be

Fig. 6 Reaction scheme for biopyriboles. The small numbers indicatethe widths of the reacting chains, large numbers the widths of theproduct chains. Isochemical reactions are shown by dashed arrows,transformations involving exchange of octahedral cations andhydrogen are shown by full arrows. The ®ne lines connect the productsequences with the next possible reactions

Fig. 7 [001]-HRTEM image showing the three-fold side stepping of atriple chain (arrows)

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added. The concentration of the reactant exchangespecies (e.g., hydrogen) at the reaction site must be ac-counted for in the rate equations. For example, the rateequation for reaction (a) is:

d�S�dt� k01�D�3�H��4 �6�

Transport to and from the reaction site, i.e., the zipperterminations, is greatly facilitated by the channels at thetermination of each zipper (Veblen and Buseck 1981).Di�usion through such channels (``pipe di�usion'') isconsidered to be many orders of magnitude faster thanbulk di�usion and, therefore, not rate-limiting. Assum-ing that the pH within the rock does not change duringthe reaction, the proton concentration can be taken asconstant at the reaction site. The pH can, therefore, beincluded in the kinetic constant:

k1 � k01�H�4 �7�

The same procedure is applied to reactions (e) and (f).The resulting rate equations for the four zipper speciesinvolved in the six reactions of the simpli®ed reactionscheme are:

d�S�dt� k1�D�3 ÿ k2�S��D� ÿ k3�S��D�2 �8�

d�Q�dt� 2k2�S��D� � k3�S��D�2 � k5�D�4 ÿ k4�Q��D� �9�

d�T �dt� 2k2�S��D� � k3�S��D�2 � k5�D�4 ÿ k4�Q��D� �10�

d�D�dt�ÿ 3k1�D�3 ÿ 2k2�S��D� ÿ 2k3�S��D�2

ÿ 4k5�D�4 ÿ 6k6�D�6 �11�The absolute rate of the zipper reactions is not known.Therefore, the behavior of the model system was ex-plored using di�erent ratios among the kinetic constants(Fig. 8a±d). The resulting distributions were then com-pared with the chain width distribution found in nature.

The concentrations of double, triple, quadruple, andsextuple chains were determined from (001) HRTEMimages such as that in Fig. 9. Chains with other widths(e.g., quintuple and >sextuple) were included in theconcentration for sextuple chains, because they occur inthe same position in the reaction scheme as sextuplechains. The sample volume, used to determine the spe-cies concentration in gaseous mixtures, is generally sev-eral orders of magnitude bigger than the size of theanalyzed species. The analyzed concentrations aretherefore independent of sample size, sample location,and sampling time. Suitable sampling sizes to determinezipper concentrations by HRTEM are only one to twoorders of magnitude larger than the zipper dimensions.To examine the dependence of the concentration on thesampling volume, the zipper concentrations in 1.1 lm-wide regions of two slabs with homogenous interferencecolor, but di�erent hydration degree, were analyzed atdi�erent scales and compared with the mean concen-trations for the entire area (Fig. 10a±d). To obtainconcentrations that are within 10% of the mean con-centration in a certain slab, the width of the overall

Fig. 8a±d Evolution of thezipper concentrations with timefor di�erent values of thekinetic constants in Eqs. (8)±(11):a k1 � k2 � k3 �k4 � k5 � k6 � 0:05;b k1 � 0:0045; k2 � 0:05; k3 �0:03; k4 � 0:055; k5 � 0:002;k6 � 0:1;c k1 � 0:0045; k2 � 0:05;k3 � 0:03; k4 � 0:055;k5 � 0:002; k6 � 0:001;d k1 � 0:0045;k2 � 0:05; k3 � 0:03;k4 � 0:055; k5 � 0:0; k6 � 0:0

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sequence (L in Eq. (5)) must be at least 500 nm. Imagescovering 500 nm were taken at a magni®cation of200000´. The zippers were counted along b. If the imagecontained zipper transformations, the zippers along themost hydrated traverse were taken into account. Re-gions with more than 50% ordered chesterite sequencesand regions close to grain boundaries were excluded.Counting errors due to misinterpretation of the contrastare considered to be small (<1%). The error due tocounting statistics (1r) is on the order of �15% andexplains to some extent the large scatter in the datapoints.

The absolute reaction duration in a certain region ofthe natural sample is not known. To compare the nat-ural zipper distribution with the model distributions, anindirect measure for the reaction progress in the naturalsamples is needed. Because double chains appear only asreactants, their concentration is, although not linearly,proportional to the reaction progress. The concentra-tions of the other zipper species were, therefore, plottedagainst the double chain zipper concentration. Unre-acted anthophyllite (�100% double chains) has 0% re-action progress, pyriboles without any double chainshave reacted to 100% (Fig. 11a±d).

Fig. 9 Typical disordered chainsequence in the Alpe Benasample. The sequence contains88 double, 28 triple, 7quadruple, 4 quintuple and onesextuple chain. The meancomposition is M93P64. Thereaction progress for thissequence is 44%

Fig. 10 Comparison of thehomogeneity of the triple andquadruple chain concentrationsat di�erent scales for two1.1 lm-wide areas, one withmedium (a, c) and the otherwith small (b, d) reactionprogress. Two sampling sizeswere used: 250 nm (grey lines)and 500 nm (black lines). Afterthe chain concentrations weredetermined in the ®rst250/500 nm of the 1.1 lm-widetest areas, the starting point ofthe 250/500 nm-wide samplegrid was displaced by 20 nmand the chain concentrationswere determined again. Thisprocedure was repeated 30times. The straight lines indicatethe average concentrationswithin the full 1.1 lm-wideareas

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Discussion

Although an in®nite number of combinations of kineticconstants is possible, only certain ratios among the in-dividual kinetic constants (1) reproduce the chain dis-tribution found in the natural samples and, (2) give purejimthompsonite as the end product. If all the reactions ofthe reduced scheme had the same rate, pure jim-thompsonite could never be formed because the con-centration of double chains, needed to reduce the widerchains, decreases too fast (see Fig. 8a). In a systemwhere the direct formation of jimthompsonite fromdouble chains dominates, the concentration of widechains would never exceed a few volume percent (seeFig. 8b). The magnitude of the kinetic constants givingthe best match with the observed concentrations is re-lated to the complexity and the type of the transforma-tions (see Figs. 8c, 11a±d). The isochemical zippertransformations (b), (c), and (e) (see above) must be atleast one order of magnitude faster than the reactions(a), (d), and (f), which require exchange of matter.Within these two groups, the rates decrease with in-creasing complexity of the reactions. Reaction (a), withthree double chains reacting simultaneously, must befaster than reaction (d), with four double chains reactingsimultaneously. The direct transformation, where sixdouble chains react simultaneously, is consequently theslowest reaction. The same criteria hold also for the

second group: reactions (b) and (e) have almost the samerate, whereas the more complex reaction (c) is slower. Ina model with no contribution from the direct replace-ment reaction, the rate of increase of the triple chains istoo slow and the concentration of zippers wider thanfour are too high during the initial stages of the reaction(see Fig. 8d). In the best-®tting model, 15% of all triplechains are formed through the direct transformation ofdouble chains.

Direct evidence for the multiple-step paths can befound in rare places, where zipper transformations cor-responding to steps that follow each other along thereaction path are close together along [100] (Fig. 12). Aspredicted by the model, the most frequent chain-multi-plicity errors found in regions converted almost com-pletely to jimthompsonite are ``lonely'' double andquadruple chains (Fig. 13).

The above model does not include the formation ofchesterite as an intermediate phase. It is di�cult to as-sess the role of chesterite in the formation of jim-thompsonite. Only a few areas with more than 50%ordered (32) sequences were found in the Alpe Benasamples. Based on the observation that jimthompsoniteis always separated from anthophyllite by chesterite inthe Chester samples, with the exception of one iron-poorsample in which anthophyllite is in direct contact withjimthompsonite, Veblen and Buseck (1980) proposedthat the formation of chesterite requires high iron ac-tivities. The biopyriboles from the Lepontine Alps havelower iron contents than any of the Chester pyriboles,which might explain the scarcity of chesterite in theserocks. The distributions of chain-multiplicity faults inhydrothermally synthesized tremolite (Ahn et al. 1991)indicate that the wide chains are also transformed by a

Fig. 11a±d Comparison of the zipper distributions calculated usingthe rate constants from Fig. 8c with chain distributions found in theAlpe Bena samples. Reaction progress is increasing from right to leftand is given as remaining double chain concentration

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multi-step process. Additional short-duration experi-ments together with the existing results should allowquantitative determination of the rates of zipper trans-formation reactions.

The above results, establishing the multi-step path asthe probable dominant formation mechanism for jim-thompsonite, also give some indications about thethermodynamic stability of jimthompsonite. Structureenergy minimization calculations (Abbott and Burnham1991) and the application of an Ising model to biopyri-boles (Price and Yeomans 1986) suggested that jim-thompsonite and some other ordered polysomes have

possible stability ®elds. The multi-step reaction path forthe transformation anthophyllite ! jimthompsonitequalitatively supports the results of the previous inv-estigations. The important observation in this study isthe presence of chain width reducing reactions in theformation of jimthompsonite. The wide-chain zippersare structurally closer to talc than jimthompsonite. Ifjimthompsonite were only a metastable intermediate inthe formation of talc, it is hard to understand why itshould be energetically more favorable to depolymerizethe wide chains and then later repolymerize them to ®naltalc. If jimthompsonite, however, is stable, then themulti-step reaction path can be interpreted as a sequenceof Ostwald steps. In this case, the metastable wide-chainintermediates are formed because they require a loweractivation energy than the direct replacement of ant-hophyllite by triple chains. Talc usually forms large re-action fronts and progresses into anthophyllite by aledge mechanism, in which wide chains increase theirwidths by two amphibole chains at a time (Fig. 14).

Concluding remarks

The retrograde formation of jimthompsonite from ant-hophyllite found in ultrama®c lenses of the LepontineAlps occurs through solid-state reactions. The analysisof the chain width distributions of intermediate, disor-dered polysomes strongly suggests that the wide chainsare intermediate, metastable products of these reactions.Most of the jimthompsonite is formed by a multi-stepreaction, and only a small amount is formed throughdirect, one-step replacement of anthophyllite. The evo-lution of the chain width distribution with the reactionprogress can be modeled using a kinetic model basedon the rate law for elementary reactions. The zipper

Fig. 12 [001]-HRTEM image showing two zipper terminationsfollowing each other. First, 4 double chains transform into 2quadruple chains, then the left quadruple chain reacts with a doublechain to form 2 triple chains. The left triple chain immediately side-steps to the left

Fig. 13 Coherent zipper transformation, which corresponds to thelast step in the reaction scheme shown in Fig. 6. Only a ``lonely''double chain ``survives'' the transformation. A complete eliminationof the chain width errors is only possible through extensive side-stepping. The double chain must side-step to left to meet with the``lonely'' quadruple chain on the left of the image or vice versa

Fig. 14 Edge of an anthophyllite (anth) crystal, which has beenpartially consumed by talc (tc). The wide chains penetrate into theanthophyllite crystal by incorporating two double chains at the time(arrows)

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transformations requiring chemical di�usion are therate-limiting steps of the overall reaction. The same typeof kinetic model may be applied to other biopyribolereactions, such as the replacement of pyroxenes by am-phiboles. The multi-step reaction path is a strong argu-ment for jimthompsonite to be a stable phase.

Acknowledgements This work was part of the Ph.D. thesis of theauthor at ETH, ZuÈ rich. I would like to thank U. Nissen, R. Wes-sicken and P. WaÈ gli at the Labor fuÈ r Elektronenmikroskopie andE. Reusser at the Electron Microprobe Laboratory of the Instut furMineralogie und Petrographie for providing access to their labo-ratories and invaluable assistance. I am grateful to Lissie Jans, whohelped with the preparation of the ®gures. Constructive discussionswith J. Conolly, K.J. Livi and K. Bozhilov, and careful reviews byM. Mellini and D.R. Veblen greatly improved the manuscript.

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