ORIGINAL PAPER

A. Mottana á T. Murata á A. Marcelli á Z.Y. WuG. Cibin á E. Paris á G. Giuli

The local structure of Ca-Na pyroxenes.II. XANES studies at the Mg and Al K edges

Received: 24 November 1998 /Revised, accepted: 10 June 1999

Abstract X-ray absorption spectra at the Mg and Al Kedges have been recorded using synchrotron radiationon synthetic end member diopside (Di) and jadeite (Jd)and on a series of natural Fe-poor Ca-Na clinopyrox-enes compositionally straddling the Jd-Di join. Thespectra of C2/c end members and intermediate membersof the solid solution series (C-omphacites) are di�erentfrom those of the intermediate members having P2/nsymmetry (P-omphacites). Di�erences can be interpretedand explained by comparing the experimental spectrawith theoretical spectra calculated via the full multiple-scattering formalism, starting from the atomic positionalparameters determined by single-crystal X-ray di�rac-tion structure re®nement on the same samples. Atomicclusters with at least 89 atoms, extending to more than0.60 nm away from the Mg or Al absorbers, are needed

to reproduce the experimental spectra. This shows thatin the clinopyroxene systems XANES detects medium-rather than short-range order-disorder relationships.Theoretical spectra match the experimental ones well forall features in the regions from 16 to 60 eV abovethreshold. Experimental near-edge features in the ®rst16 eV are also reproduced, albeit less accurately. Certainnear-edge features of C-omphacites re¯ect the octahed-ral arrangement of the back-scattering six O atomsnearest neighbours of the probed atom (Mg or Al) lo-cated at site M1 of the crystal structure, thus being in-dicators of short-range order. Others arise again frommedium-range order. P-omphacites show more compli-cated spectra than C-omphacites. Their additional fea-tures re¯ect the increased complexity of the structureand the greater local disorder around the probed atominduced by the two alternative M1, M11 con®gurationsof the six O atoms forming the ®rst coordination shells.Mg and Al are con®rmed to be preferentially partitionedin the M1 and M11 site of the P-omphacite crystalstructure, however with a certain degree of local disor-der. The relative heights of certain prominent featuresare directly related to sample composition in terms ofDi:Jd ratio in the Al K-edge spectra, whereas they showabrupt variations in the Mg K-edge spectra. Theydemonstrate that XANES is directly related to compo-sition and may be used to distinguish C- fromP-omphacites.

Key words Ca-Na pyroxenes á XANES áMg and Al K-edges á Synchrotron Radiation

Introduction

Ca-Na pyroxenes (Morimoto et al. 1988) have beenstudied extensively because of the peculiar behaviour oftheir solid solutions: end members crystallise in the C2/cspace group, whereas intermediate members have eitherthe same C2/c space group, or the lower-symmetry P2/none.

Phys Chem Minerals (1999) 27: 20±33 Ó Springer-Verlag 1999

A. Mottana (&)Dipartimento di Scienze Geologiche, Universita' di Roma Tre,Largo S. Leonardo Murialdo 1, I-00146 Roma, Italye-mail: mottana@geo.uniroma3.it, Fax: +39-06-5488 8201Also associated with: Laboratori Nazionali di Frascati,Istituto Nazionale di Fisica Nucleare, Via Enrico Fermi 40,I-00044 Frascati RM, Italy

T. MurataDepartment of Physics, Kyoto University of Education,1 Fujinomori-cho, Fukakusa, Fushimi-ku, Kyoto 612, Japan

A. Marcelli á Z.Y. Wu1 á G. CibinLaboratori Nazionali di Frascati,Istituto Nazionale di Fisica Nucleare,Via Enrico Fermi 40, I-00044 Frascati RM, Italy

E. ParisDipartimento di Scienze della Terra, Universita' di Camerino,Via Gentile III da Varano, I-62032 Camerino MC, Italy

G. GiuliDipartimento di Scienze della Terra, Universita' di Firenze,Via Giorgio La Pira 4, I-50121 Florence FI, Italy

Present address:1Laboratoire Pierre SuÈ e,Baà timent 637, CEA-CNRS, CE Saclay,F-91191 Gif-sur-Yvette Cedex, France

Ordering of the cations located in the sixfold (M1)and/or eightfold (M2) coordinated sites of the structurehas been suggested to be the driving force for such abehaviour (Clark and Papike 1968; Clark et al. 1969;Matsumoto et al. 1975; Curtis et al. 1975; Aldridge et al.1978; Fleet et al. 1978; Rossi et al. 1981, 1983; Car-penter et al. 1990a, b; and many others; see Mottanaet al. 1997 for a referenced review). However, consensuson the actual mechanism that drives the ordering processis far from being reached, the more so as the methodchosen to study ordering appears to a�ect the result. Onthe one hand, single-crystal X-ray di�raction structurere®nement (SC-XRef), the preferred method, gives in-formation on long-range order (LRO), but it has a biasdue to its systematic disregard of vacancies (McCormick1986; McCormick et al. 1989). On the other hand,MoÈ ssbauer spectroscopy, which is extensively used toreveal local order in the M1 site, is not e�ective for eitherAl or Mg, i.e., the two predominant cations most likelyto be participating in, if not entirely driving, the orderingmechanism.

X-ray absorption spectroscopy (XAS) is a techniquethat is particularly sensitive to local structure. It is alsoelement-speci®c, in that it can be modulated at will forany element independently of all others. Therefore XAScan provide new insight into order-disorder (O-D) re-lationships and local environments across the entirediopside-(omphacite)-jadeite series by selectively scan-ning Al or Mg (and any other atom involved in theprocess). Information about short-range order (SRO)gathered by XAS complements that about LRO bestobtained by SC-XRef, particularly when the near-edgefeatures are being evaluated. Yet X-ray absorption near-edge structure (XANES) spectroscopy has been rarelyused to the purpose, essentially because the absorptionK edges of light elements lie outside the range of energieswhere standard apparatus can be used and recordinghigh-quality spectra requires monochromator crystalsunavailable until a few years ago.

We carried out well-resolved determinations of theMg and Al K edges in a series of Fe-poor Ca-Na py-roxenes using one of the most reliable apparatusesavailable. Thus we could provide novel experimentalinformation on Mg-Al ordering in these pyroxenes(Mottana et al. 1996a). However, our XANES experi-mental results could be interpreted properly only aftercomparison to and with the support of theoretical cal-culations performed ab initio on the basis of the one-electron multiple-scattering theory (MS), in our casestarting from crystal structure data determined by SC-XRef.

Elsewhere (Part I: Mottana et al. 1997), we have re-ported results obtained at the Na K edge and discussedthem with reference to our previous studies at the Ca Kedge (Davoli et al. 1987; Paris et al. 1995). There wegave complete information on the local structure aroundthe eightfold coordinated M2 site. The aim of this paperis to give similar information on atoms located in thesixfold coordinated M1 site and contribute in this way to

a better understanding of the Ca-Na pyroxene series andits O-D behavior.

State of the art

The state of the art of Ca-Na pyroxenes was given inPart I (Mottana et al. 1997) with emphasis on theeightfold coordinated cation site. We will now enter intodetails about the sixfold coordinated site only.

The accepted model of the Ca-Na pyroxene structure(mostly after Rossi et al. 1983; see also Bo�a Ballaranet al. 1998a and Camara et al. 1998) is as follows.

1. Mg and Al are randomly distributed (disordered)over only one type of site (M1; a very slightly distortedoctahedron with point symmetry 2) in C2/c pyroxenes(Fig. 1a); these are diopside (Di), jadeite (Jd), and theintermediate pyroxenes compositionally closest to endmembers (C-omphacites). By contrast, they tend to bepartitioned (i.e., ordered) over two nonequivalent, dif-ferently distorted octahedral sites (M1 and M11; withpoint symmetry 2) in pyroxenes near the ratioDi:Jd = 1:1. The symmetry lowers to P2/n (P-ompha-cites). In the ideal case (Fig. 1b) Mg would occupy onlyM1 and Al only M11 (full octahedral order), althoughnot completely, because of the possible presence in M1of minor Fe2+ and Mn2+, and in M11 of Fe3+, Mn3+,and Cr3+. In the real case, there is always a certainamount of Mg-Al disorder that increases as the pyrox-ene composition deviates from Di50Jd50.

2. Na and Ca are totally disordered over only onetype of eightfold coordinated site of C-pyroxenes (M2;an irregular polyhedron with point symmetry 2: Fig. 1a).

Fig. 1a, b The sixfold coordinated strip (dark) of a a disordered C2/cpyroxene, and b an ordered P2/n omphacite, projected onto the 100plane, also showing the lateral relationships with the tetrahedral chain(grey) and the eightfold coordinated cation array (white)

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By contrast, in P-omphacites they tend to be locallyordered over two eightfold coordinated sites (M2 andM21) that di�er in shape and size (partial eightfold sitelocal disorder: Fig. 1b).

The model is based purely on SC-XRef measure-ments, and contradicts results of (among others) Clarkand Papike (1968), Matsumoto et al. (1975), Curtis et al.(1975), and Fleet et al. (1978). As a matter of fact, Fleetet al. (1978) had warned against conclusions drawn fromSC-XRef evidence only, but this has been overcome,lately, by an improved method of re®nement (e.g., Car-penter et al. 1990a, b; Bo�a Ballaran 1997; Bo�a Ball-aran et al. 1998a) that strongly relies on experimentallydetermined M-O distances; SC-XRef can determinethese with much greater accuracy than occupancies. It isnow generally assumed that in the P-omphacite idealstructure Ca and Na are intrinsically only partially or-dered, and Mg and Al fully ordered. However, even SC-XRef determines a quanti®able Mg-Al short-range dis-order with increasing deviation of the sample from theideal composition, thus showing the tricritical characterof the C to P transition (Carpenter et al. 1990a, b). Anindependent method of determining Mg-Al O-D is op-portune, since SC-XRef is suited to determine LRO, butit deals with SRO only after circumventing numerousdi�culties (V. Tazzoli, personal communication).

MoÈ ssbauer spectroscopy o�ers such an independentand e�ective way of determining site occupancy and el-ement distribution among sites (SRO as well as LRO),but only for Fe, the amount of which is minor in most Ca-Na pyroxenes. Yet, information on Fe O-D is important,as this cation may proxy for either Mg or Al dependingon its oxidation state. Early studies created problems ofinterpretation, mainly because of the incorrect modelassumed for the P-omphacite crystal structure. Latercomparative work on both natural and synthetic samples(Dollase and Gustafson 1982) established that: (1) thereis no evidence of Fe3+ in any site other than M1 in C-pyroxenes and M11 in P-pyroxenes; (2) the near-neigh-bour environment of Fe2+ is independent on Mg-AlLRO, while size considerations suggest that this cationmostly concentrates in M1 regardless of symmetry; (3)the occurrence of Fe2+ in M2 is not proven. However,Fe2+ in M2 was independently determined by SC-XRef(Rossi et al. 1983; Bo�a Ballaran et al. 1998a).

Recently, an IR method to determine SRO has beendeveloped (Bo�a Ballaran 1997; Bo�a Ballaran et al.1998b) that appears to give information on local struc-tural states down to the unit-cell scale. However, IRvibrations depend upon the atomic repeat in the struc-ture just as SC-XRef does, albeit over a smaller distance;furthermore, IR spectroscopy cannot provide indepen-dent information on the behavior of selected individualatoms as XAS and MoÈ ssbauer spectroscopies do.

Most recently, the e�ect of Fe2+ and Fe3+ replacingMg and Al in the M1 and M11 sites has also been in-vestigated, using a combination of TEM and SC-XReftechniques (Camara et al. 1998). Ordering was found to

decrease signi®cantly with increasing total Fe, up tocomplete disordering for XAe > 20% and XAe+Hd >47% even for compositions close to the Ca:Na = 1:1ideal ratio.

XAS spectroscopy

XAS, a nondestructive technique, is at present the mostpromising element-speci®c method for studying SRO.However, experimental XAS studies on Ca-Na pyrox-enes are still very limited in number. To our knowledge,there are only two spectra at the K edge of Al (McKe-own et al. 1985: jadeite; Li et al. 1995: omphacite).Those at the Mg K edge are just as few (Yoshida et al.1994: diopside; Ildefonse et al. 1995: diopside; Li et al.1997: diopside; Cabaret et al. 1998: ``diopside'', actuallyan augite, since Ca is less than 45% quadrilateral at-oms). Most spectra had been recorded either to show thepotential of the apparatus, or to complete a miscella-neous set on minerals with the example of a pyroxene.Data on other M1-sited atoms concern Fe only (Davoliet al. 1985, 1988): omphacite Fe spectra are broad andunresolved, as they contain contributions from bothFe2+ and Fe3+.

Theoretical studies on Ca-Na pyroxenes are very rareindeed: one for the Al K edge of jadeite (McKeown1989), and one for the Mg K edge of diopside (Cabaretet al. 1998).

Samples

Two synthetic end members, Di and Jd, and nine naturalCa-Na Fe-poor pyroxenes ranging in composition fromDi92Hd4Ae3Jd1 to Jd94Di5Ae1 were studied. Four ofthem had been studied already at the Fe K edge (Davoliet al. 1985, 1988), and seven at the Ca and Na K edges(Davoli et al. 1987; Paris et al. 1995; Mottana et al.1997). The new samples are a C2/c Jd-rich omphacite(C.413f: Smith et al. 1980) and a P2/n omphacite (70-AM-33: Carpenter et al. 1990a, b; Bo�a Ballaran et al.1998a). Composition and crystal data are reported inTable 1 and plotted in Fig. 2.

All natural pyroxenes but four had their structuresre®ned to R < 0.034 by the late Giuseppe Rossi (per-sonal communication 1987). Omphacite 74-AM-33 wassolved by the novel, improved method (Carpenter et al.1990a). Diopside Px-1 is, at Rossi's indication, taken asidentical with the Gouverneur diopside (Rossi et al.1982); by analogy, we consider our natural MZ andKA#3 jadeites to be the same as the Quincinetto jadeite(Rossi et al. 1981). As for our synthetic pyroxenes, weassume that Di has the same atomic positional param-eters as the synthetic diopside re®ned by Cameron et al.(1973). To our knowledge, no SC-XRef was ever madeon a synthetic jadeite (lack of suitable crystals); thereforeour Jd is considered to be identical to the New Idriajadeite (Jd99.6) re®ned by Bo�a Ballaran (1997).

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Experimental

Information on sample origin, chemical analysis, crystal structurere®nement, and other physical measurements, as well as on theirpreparation, was given in Part I. We include here only a detaileddescription of the improvements to the XAS and MS methodsspeci®cally introduced for this study.

XANES spectroscopy

The experimental spectra were collected at UVSOR, the synch-rotron radiation (SR) source of Institute of Molecular Science(IMS) at Okazaki, Japan, where the 750-MeV electron storage ringusually operates at 200 mA current with a lifetime of about 4 h(Watanabe 1991). The soft X-ray beamline BL7A derives SR by asuper-conducting wiggler under an acceptance angle of 1 mrad inthe horizontal plane and of 0.15 mrad in the vertical plane, yieldingphotons in the energy range 800±4000 eV. The beamline is equip-ped with a double-crystal monochromator of either beryl or quartz,both crystals being cut along the 100 plane (Murata et al. 1992).Beryl was used to scan across the Mg K edge and quartz the Al oneby angle steps of 0.01 °h. Resolutions, as determined from therocking curves, are better than 1.0 eV for beryl, and certainly1.28 eV for quartz (Krause and Oliver 1979): they are estimated tobe in the order of 0.7 eV (Murata et al. 1992). The sample is spreadas a ®lm on a piece of graphite tape, which is adhesive on both

sides. The other side of the tape is attached onto the ®rst photo-catode of an electron multiplier, which measures the total yield ofphotoelectrons (TEY) emitted from the sample under X-ray exci-tation as its output current. TEY is proportional to absorptiontaken in the transmission mode (Gudat and Kunz 1977). The entiremonochromator plus sample system is held in a vacuum chamberat 1 ´ 10)7 torr.

The observed features were carefully located by ®rst ®tting thewhole spectrum with an arctangent to account for the edge jump,and then each feature with a Gaussian function. Derivatives werealso used, especially to better locate the energies of the high-energyregion peaks. Feature energies and intensities are given as mid-point and height of the related Gaussian curves.

MS calculation

Theoretical calculations were carried out at INFN-LNF, by theCONTINUUM code, the formalism developed through the yearsby C.R. Natoli and his coworkers. Our calculation procedure isbased on the one-electron, multiple-scattering (MS) theory (Leeand Pendry 1975) that Natoli implemented computationally andtheoretically by considering multiple-scattering paths for the out-going photoelectrons (Natoli et al. 1980; Natoli and Benfatto 1986;Natoli et al. 1990; Tyson et al. 1992; Wu et al. 1996b; see alsoDurham et al. 1982; Durham 1988). We make use of Mattheiss'(1964) prescription to construct the total potentials of clusters inthe mu�n-tin approximation i.e., by superimposing neutral atomiccharge densities using the Clementi-Roetti (1974) basis set. In orderto simulate the charge relaxation around the core hole we use thewell-screened Z + 1 approximation (Lee and Beni 1977), Z beingthe atomic number of the atom taken as the absorber. Mu�n-tinradii are chosen according the criterion of Norman (1974), and a10% overlap between contiguous spheres is allowed to simulate theatomic bond. The unpolarised photoabsorption cross section forphotons with a given energy is then solved numerically in Rydbergunits of energy and lengths. We routinely performed the calcula-tions using the Hedin and Lundqvist (1971) energy- and position-dependent complex potentials (H-L) and Slater's (1979) energy-independent type of exchange (Xa). Both have been tested re-peatedly and proved successful for insulating materials. Only Xa isgiven, because it showed best in the high-energy region where it notonly reproduces all features at higher energy, but emphasises theirintensities, while H-L tends to ¯atten everything due to its imagi-

Fig. 2 Composition of the studied Ca-Na pyroxenes in terms of Jd(jadeite) ± Ae (aegirine) ± Q (augite) components (Morimoto et al.1988), after partition of total Fe between Fe2+ and Fe3+ accordingto Mottana's (1986) charge balance procedure. Numbers as inTable 1

Table 1 Chemical and crystal data of the investigated Ca-Na clinopyroxenes (cf. Mottana et al. 1997; Fig. 2)

1 2 3 4 5 6 7 8 9 10 11Di Px-1 Ala-1 68MV45 M.1 74AM33 C.413f GR-P1-25 KY#3 MZ Jd

Si 2.000 1.969 1.976 1.963 1.981 1.983 2.011 2.005 1.999 1.994 2.000Al(4) 0.000 0.028 0.022 0.037 0.019 0.017 ± ± 0.001 0.006 0.000Al(6) 0.000 ± ± 0.451 0.519 0.504 0.635 0.705 0.828 0.942 1.000Ti 0.000 0.007 0.000 0.001 0.000 0.003 0.003 0.008 0.000 0.000 0.000Fe3+ 0.000 0.034 0.053 0.024 ± 0.034 0.049 0.029 0.012 0.009 0.000Cr 0.000 0.006 0.001 0.000 0.000 0.002 0.001 0.000 0.000 0.000 0.000Fe2+ 0.000 0.057 0.035 0.130 0.080 0.033 0.060 0.086 0.075 0.002 0.000Mn 0.000 0.002 0.001 0.000 0.000 0.001 0.002 0.002 0.003 0.001 0.000Mg 1.000 0.921 0.916 0.467 0.415 0.414 0.262 0.204 0.113 0.049 0.000Ca 1.000 0.961 0.972 0.484 0.490 0.479 0.263 0.202 0.129 0.051 0.000Na 0.000 0.017 0.027 0.440 0.496 0.530 0.713 0.760 0.835 0.946 1.000K 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.004 0.000 0.000Q 100 98.3 97.3 55.1 49.8 47.7 29.1 24.4 15.9 5.2 0Ae 0 1.7 2.7 2.3 0 0.4 5.2 3.0 1.2 0.9 0Jd 0 0 0 42.5 50.2 51.9 65.7 72.8 82.9 93.9 100a (nm) 0.9748 0.9750 0.9760 0.9612 0.9566 0.9557 0.9526 0.9510 0.9471 0.9439 0.9416b (nm) 0.8927 0.8921 0.8925 0.8794 0.8769 0.8752 0.8692 0.8666 0.8608 0.8585 0.8564c (nm) 0.5250 0.5251 0.5258 0.5248 0.5252 0.5254 0.5246 0.5246 0.5235 0.5226 0.5226b (dg) 105.83 105.81 105.85 106.79 106.93 106.97 107.21 107.31 107.97 107.46 107.58V (nm3) 0.4395 0.4395 0.44046 0.4255 0.4215 0.4203 0.4149 0.4127 0.4049 0.4040 0.4017sp.gr n.d. C2/c C2/c P2/n P2/n P2/n C2/c C2/c C2/c C2/c n.d.

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nary part. Calculations were routinely made at steps of 0.05 Ry(i.e., 0.68 eV), but for the ®rst 10 eV above threshold, where thenumber of steps was increased to be at 0.025 Ry (i.e., 0.34 eV). Thecalculated spectra are plotted without introducing any form ofbroadening or smoothing so as to free the calculated features fromartefacts which may hinder comparison with the experimental ones.

Results

Mg K edge

The experimental XANES spectra of our synthetic Diand natural diopside Px-1 compare well with those oftwo synthetic diopsides recorded at UVSOR (Yoshidaet al. 1994; Li et al. 1997); moreover, they comparereasonably well with those of synthetic diopside re-corded at LURE (Ildefonse et al. 1995) and also ofnatural ``diopside'' recorded at Super-ACO (Cabaretet al. 1998) despite the signi®cant di�erence in compo-sition.

The spectra of Di and Px-1 are identical in spite of thelatter deviating from pure composition (0.921 Mg at.p-fu), thus giving an indication of the detection limits atthe Mg K edge of our technique using this experimentalsetup. The typical spectrum (Fig. 3, top) shows threemajor features (A, at 1309.9 eV; B, at 1314.2 eV; and C,1318.8 eV) in the energy range 1306�1323 eV, peak Bbeing the mainedge. This low-energy section of thespectrum, that is located at and immediately follows theabsorption edge, is de®ned as the full-multiple-scattering(FMS) region (Natoli and Benfatto 1986). A shoulder isalso noticeable on the high-energy limb of C, but it

could be located properly only in the derivative spectra(C¢, at 1320.7 eV). At higher energies (i.e., in the inter-mediate-multiple-scattering region, IMS, of Natoli andBenfatto 1986), there are four broad bumps (D, at1326.2 eV; E, at 1330.9 eV; F, at 1345.9 eV; and G, at1353.7 eV). The upper end of XANES (Bianconi 1988) islocated at 1370 eV in this system.

The Ala-1 spectrum is weaker, broader and noisierbecause the sample is compositionally inhomogeneous(the Table 1 value 0.916 Mg at.pfu averages several datapoints on many grains).

At the Jd-rich end of the compositional join,C-omphacites C.413f and P1-25 display fairly goodspectra (Fig. 3, bottom), albeit with understandablyhigher degrees of noise owing to their fairly low Mgcontents (0.262 and 0.204 at.pfu, respectively). This alsois why the spectrum of KA#3 jadeite (0.113 Mg at.pfu)is poor despite being qualitatively identical to all others.This spectrum is not shown, as also the spectrum of MZjadeite (0.067 Mg at.pfu) which is totally ¯at. KA#3 andMZ bracket compositionally the Mg detection limit forthe X-rays ¯ux delivered by the monochromator of ourapparatus.

The Mg K absorption energies of all C-pyroxenes arethe same (within 1r). This indicates that the arrange-ment of the six backscattering O atoms surrounding theMg absorber (Fig. 1) does not change substantiallywhen moving from one end to the opposite end of theDi-Jd join. However, although not easy to be seen be-cause of the greater noise, P1-25 appears to have aspectrum less de®ned than Px-1. This is to be related tothe high dilution of Mg with respect to Al, the otheratom present in the M1 strip.

The energy values of the main absorption features donot change appreciably (maximum 2r) even whenmoving across the change in the space group, to P-omphacites (cf. Fig. 3 with Fig. 4), again indicating thatno substantial change occurs in the octahedral strip(Fleet et al. 1978). Indeed, the major change we note isin the noise of the entire spectrum owing to the de-creased Mg total content, a greater noise going hand inhand with lower de®nition (e.g., shoulder C¢ disappears).As for the IMS region, the P-omphacite spectra showthe same number of features as the C-omphacite ones;actually, D and E are even better resolved despite theinevitably increase in noise.

However, in the FMS region there is a signi®cantchange in the height of main edge B relative to those offeatures A and C when moving across the entire Di-Jdjoin. Moreover, feature C seems to change indepen-dently in height also with respect to A: in particular, theC/A height ratio ®rst increases slowly with increasing Jdcontent, then drops suddenly in P-omphacites, and ®-nally increases again in the C-omphacites P1-25 closestto the Jd apex (Fig. 5a). According to the MS theory,peak intensity is related to the number of MS pathwaysinvolving the probed atom and its ®rst- and higher-orderneighbours. Thus, we can anticipate that the presence ofeither Al or Mg in the neighbouring octahedra of the

Fig. 3 Experimental (dotted curve) and MS calculated (continuouscurve) XANES spectra at the Mg K-edge of C2/c Ca-Na pyroxenesof extreme and intermediate composition (cf. Fig. 2). Individualspectra have been normalised at the high-energy side (1370 eV)after correcting the base line. See text for explanations

24

M1, M11 strip of P-omphacites does not appreciablya�ect the energy of the Mg K-edge spectra, but it cer-tainly a�ects their peak intensity and de®nition. Thisimplies a structural reordering depending on composi-tion, with segregation of a part, but not all Mg in onesite of the octahedral strip.

Al K edge

The experimental Al K-edge spectrum of syntheticjadeite Jd (Fig. 6, top) shows two major features overthe FMS region, which in this case extends from 1564 to1580 eV. The main edge A is at 1568.3 eV and is fol-lowed at 1571.7 eV by a B peak almost as strong. Fur-thermore, there are at least three other features, albeit

poorly resolved: two shoulders, the energy positions ofwhich could be located properly only in the derivativespectra (A¢ at 1566.4 eV, on the lower-energy limb of A,and B¢ at 1573.8 eV, on the higher energy of B) and theweak, but clearly recognisable C peak at 1576.4 eV. TheIMS region, that extends from 1580 to 1615 eV, showsthree additional, albeit weak and broad peaks: D at1584.2 eV, E at 1588.9 eV, and G at 1612.6 eV. Anotherweak, but recognisable shoulder (A¢¢) precedes the mainedge A at 1565.1 eV. It may be interpreted as the pre-peak, and related to violation of the forbidden transi-tions from 1s to empty antibonding s-like shells owing to

Fig. 4 Experimental and MS calculated XANES spectra at the MgK-edge of P2/n omphacites. Same conditions as in Fig. 3; see text forexplanations

Fig. 5 a Plot of various featureheight ratios as a function ofcomposition (Jd mol.%) in theexperimental Mg K-edge spec-tra of Ca-Na pyroxenes (cf.Figs. 3 and 4). b Same plot forB/A in the Al K-edge spectra(cf. Figs. 6 and 7)

Fig. 6 Experimental and MS calculated XANES spectra at the AlK-edge of C2/c pyroxenes close in composition to the Jd apex (cf.Fig. 2.) Individual spectra normalised at the high-energy side(1615 eV) after correcting the base line. See text for explanations

25

octahedral distortion (Waychunas et al. 1983). Alterna-tively, it is related to transitions towards Al 3p emptystates mixed with the empty states of Ca, Na atoms inthe nearby M2 site (Wu et al. 1996a).

The MZ and KA#3 jadeite spectra (Fig. 6) matchclosely that of synthetic Jd: the only di�erence lies in thesharpness of all features, which is lower than in syntheticJd. By contrast, feature A¢¢ is sharp and strong, and alsoin MZ shoulder A¢ too becomes distinct: de®nitively, A¢is not the prepeak, but an independent feature generatedby structural reasons. It may re¯ect either the high totalamount of impurities substituting for Al in these jadeitesor rather their ordering, because MZ (0.942 Al at.pfu) infact contains less impurities than KA#3 (0.828 Al at.p-fu). Both natural jadeites have their IMS regions lessresolved than synthetic Jd.

The experimental Al K-edge spectra of C-omphacitesP1-25 and C.413f (Fig. 6, bottom) are almost as strongand well resolved as those of the jadeites in the FMSregion, but de®nitively poorer in the IMS region. Theyshow shoulder A¢ as strong as MZ does. This supportsthe inference that A¢ derives from ordering of thechemical impurities substituting for Al (mainly Mg andFe3+). In C.413f (0.705 Al at.pfu), and also in P1-25(0.635 Al at.pfu) but to a much lesser extent, feature Cbecomes a distinct peak. In the IMS region, both spectraconsist of two very broad features roughly at the sameenergies where Jd has D and E.

The experimental spectra of P-omphacites (Fig. 7)are noisy but resolved well enough to show a number offeatures other than those of C-pyroxenes: note, in par-ticular, the skewed low-energy limb of peak B, whichindicates the presence of a feature (B¢¢, at 1570.5 eV)that is adequately resolved only in 74-AM-33.

Moreover, on the high-energy limb of B, feature C is nolonger a shoulder, but always a well-resolved weak peak,such as in C.413 f. Other signi®cant changes are:(1) A and B have heights which are almost as strong; (2)A¢, albeit undoubtedly present (e.g., in M.1), changes inheight to the point of becoming only a vague shoulderon the low-energy limb of main edge A; (3) nowhere isprepeak A¢¢ present. The IMS region consists of a wideband that encompasses D and E, and is considerablystronger than any one of these in C-pyroxenes.

The height ratio of the two main features A/B is astrict linear function of composition (Fig. 5b), irrespec-tive of C- or P-symmetry, suggesting an original way ofdetermining the octahedral M1 strip composition. It alsosuggests that the contribution of Al to Mg-Al O-D ofthese pyroxenes is minor.

All our experimental XANES spectra of P-ompha-cites appear to be much better resolved than the spec-trum of an omphacite of composition Jd53Di44Hd3recorded by Li et al. (1995). The reason lies in thecomposition of that omphacite, which Li et al. them-selves point out to be anomalous (p. 439).

Discussion

Mg K edge

Our Ca-Na pyroxene Mg K-edge XANES spectra areessentially identical to the published spectra of otherminerals where Mg is in sixfold coordination with O orOH (see above, and in addition Wong et al. 1994, Fig. 5:talc and brucite; Wu et al. 1996b Fig. 5: forsterite;Mottana et al. 1996b: olivines). However, all spectra arecompletely di�erent and contain much fewer featuresthan the spectrum of periclase (Rowen et al. 1993; Wonget al. 1994; Ildefonse et al. 1995; Wu et al. 1996b), themodel compound where Mg is in regular octahedralcoordination.

XANES displays here one of its best properties: it isable to show how a polyhedron deforms i.e., changes itscentral angles, even when coordination number andbondlengths remain the same (Bianconi 1988). As amatter of fact, while all compounds listed above havetheir six octahedral Mg-O bonds essentially constant inthe range 0.2071�0.2105 nm, their octahedral quadraticelongation (OQE: Robinson et al. 1971) increases from1.0000 for periclase to 1.0269 for forsterite, the mostirregular polyhedron, being 1.0050 for diopside.

In order to understand the implication properly, wecomputed the Mg K-edge spectrum of diopside ac-cording to the MS formalism via atomic clusters of in-creasing size up to convergence. Interatomic distancesand monoclinic two-point symmetry were those of theM1 site for all clusters, since Mg is located only there(Cameron et al. 1973). The calculated spectra convergefor clusters containing at least 89 atoms [7 Mg +10 Ca + 20 Si + 52 O] extending to 0.619 nm awayfrom the Mg atom taken as the absorber.

Fig. 7 Experimental and MS calculated XANES spectra at the AlK-edge of P2/n omphacites (cf. Fig. 2). Same conditions as in Fig. 6;see text for explanations

26

Our calculated spectrum (Fig. 3, top) broadly agreeswith the diopside spectrum calculated by Cabaret et al.(1998, Fig. 1), and represents an improvement over it forthe IMS region. By contrast, in the FMS region it doesnot look as good because we neither convoluted ourcalculated features with a Lorentzian function nor madeuse of the Dirac-Hara (D-H) exchange potentials as theydid. In MS calculations, the choice of the potentials iscrucial also to determine the type of convolution(smoothing) of the spectra. We decided to keep on usingSlater's Xa method after computing the Di spectrumalso with the H-L and D-H methods, because the Xaenergy-independent potentials permit a better compari-son of the calculated spectra among all C- and P-py-roxenes. As a matter of fact, the Xa method emphasisesthe heights of the D, E, F, and G peaks, while the H-Lmethod exhibits a damping e�ect after about 10�15 eVfrom threshold that makes the calculated IMS spectrumde®nitively poorer than the experimental one. As for theD-H potentials, apparently they are better suited for theFMS region, but fail to reproduce the IMS region, thatis crucial to our purpose because it re¯ects medium-range order (MRO).

In detail (Fig. 8, left panel), peaks B and G (and,possibly, also D) already appear in the calculation for acluster containing only seven atoms. Therefore, theyarise from interaction of the photoelectron emitted byMg with the six O nearest-neighbours in the ®rst coor-dination shell. These peaks do indeed re¯ect funda-mental atomic properties of the Mg-O interaction andgive an indication of SRO around Mg at the M1 site ofpyroxene. All other features, in particular A and C, arise

when the cluster attains a considerable size (0.497 nmi.e., 50 atoms), and match the experimental data when asmany as 89 atoms are taken into account over a sphere0.619 nm in diameter (see above). Thus, they are indi-cators of MRO, i.e., they give information about samplecrystallinity on a spatial resolution that cannot yet beattained by SC-XRef. Moreover, they indicate Mg-atomdistribution between the M1, M11 in P-omphacites.

The Mg K-edge calculated spectrum of P1-25 C-omphacite (Fig. 3, bottom) is the example for an inter-mediate Ca-Na clinopyroxene where Mg is diluted anddisordered over an M1 octahedral chain occupiedmostly by Al. The convergent cluster again contains 89atoms [1 Mg+ 6 Al + 2 Ca+ 8 Na+ 20 Si + 52 O] to0.606 nm away from the Mg absorber. The spectrumessential features are in good agreement with those justgiven for Di. However, certain characteristics that madethe experimental spectrum of P1-25 remarkable whencompared with those of the Di-rich Px-1 and Ala-1pyroxenes are faithfully reproduced, such as peak Cincrease in intensity and A drastic decrease. This ispossibly related to disordered variations in the shells faraway from the absorber, although calculations per-formed by changing number and/or location of the Caand Na atoms did not result in spectra with detectablechanges. Note how the energy separations between Dand E, and between F and G, are easy to be seen in thecalculated spectrum whereas they could not be resolvedin the experimental one. From this point of view, an MScalculation that starts from the atomic coordinates de-termined by SC-XRef on the sample under study com-plements and obviates the poor resolution of its

Fig. 8 MS calculated spectra atthe Mg (left) and Al (right) Kedges in endmember C-pyrox-enes Di (synthetic diopside) andJd (New Idria jadeite) for clus-ters with increasing number ofatoms (indicated on each curve)

27

experimental spectrum due the dilution of the probedatom in the structure. Furthermore, calculation makesone aware of the di�erence in the degree of order ex-isting in the actual sample with respect to the LRO-determined via SC-XRef by pointing out the di�erencesbetween the calculated spectrum and the actual one. Asa matter of fact, a disordered distribution of the Mgatom among its Al near-neighbours (i.e., SRO) mayexplain the discrepancies observed between the P1-25experimental and calculated spectra (Fig. 3).

Turning now to P-omphacites, in Fig. 4 we haveplotted the calculated spectra for the two compositionalextremes, 68-MV-45 and 74-AM-33. In these calcula-tions we considered Mg to be fully partitioned in M1,and obtained convergence for clusters containing at least89 atoms [5 Mg+ 2 Al + 6 Ca+ 4 Na+ 20 Si + 52 O]extending 0.614�0.617 nm in radius away from theabsorber. The P-omphacite calculated spectra are verysimilar to those of C-pyroxenes in the IMS regions (cf.Fig. 4 with Fig. 3), which is the one that best re¯ects thesimilarity of the overall structures (Fleet et al. 1978).However, most, if not all, features appear to be doubled(e.g., D and D¢, E and E¢) as a result of the order of theP2/n structure. Thus, calculations hint at the possiblepresence of Mg in both M1 and M11, but in the re-corded spectra either a local disorder or the experi-mental broadening smoothes all these features andmakes them broad, so that only rarely can unequivocaldi�erences be detected.

Consequently, where di�erences can best be seen is inthe calculated FMS regions (cf. Fig. 4 with Fig. 3). HereP-pyroxenes are always richer in features than C-py-roxenes: they show at least four main calculated features(A, B, B¢, C), plus one shoulder (A¢) on the raising limbof feature A, located between A¢¢ and A. It is reasonableto surmise that each FMS feature would turn out to bedoubled, had calculation been brought to higher accu-racy. Furthermore, feature C at +11 eV, which in C-pyroxenes was only a shoulder, is now a resolvedalthough weak peak; unfortunately, this feature couldnot yet be resolved in any experimental spectrum.

An increase in the number of calculated FMS fea-tures is related to a greater complexity of the electronictransitions around Mg. In experimental spectra, broad-ening may obliterate such a complexity and force manyindividual features to merge into a few. Indeed, this isthe case with our P-omphacites, where we note onlythree major peaks similar to those occurring in C-py-roxenes, although they are a little broader and smootherthan these. Such calculated features as B¢ and C mergeinto a sort of plateau, being resolved enough (thus de-tectable) only in the M.1 P-omphacite experimentalspectrum (Fig. 4).

The M1 site of a P-omphacite di�ers from that of aC-omphacite in two fundamental points at the sametime: (1) much greater average size, and (2) greater dis-tortion (cf. Fig. 1a, b). For example, in the natural74-AM-33 P-omphacite hM1-Oi is 0.2068 nm andOQE = 1.0138 (Bo�a Ballaran et al. 1998a, Table 5b);

they drop to 0.1999 nm and 1.0096, respectively, after itsannealing at 950 °C, when symmetry turns to C2/c(Bo�a Ballaran et al. 1998a, Table 5a). Consequently,we assume that the greater complexity of the calculatedFMS regions of our P-omphacites re¯ects the activationof a number of additional MS pathways in their un-usually large M1 octahedra; these pathways wouldoverlap with others when activated in a smaller envi-ronment such as the M1 octahedron of C-pyroxenes. Ifthis were indeed the case, then any Mg located in theeven smaller M11 octahedron of a P-omphacite (seebelow) would produce a spectrum that does not coincideat all with the M1 spectrum. Such a spectrum may beexperimentally detected by subtracting from the totalMg K-edge spectrum the spectrum for Mg in the M1octahedron of a reference sample, e.g., diopside. Nev-ertheless, to discriminate two superimposed spectra, thecombination of a careful calculation of both contribu-tions with a high-resolution experimental spectrum isneeded. Only then can a quantitative evaluation beachieved (Mottana et al. Part III in preparation).

Al K edge

The calculated Al K-edge spectra of C- and P-pyroxenesdisplay the same major doublet as the experimentalones, but they contain information useful to deconvoluteit into a considerably greater number of features.

Indeed, in Jd, our reference disordered C-pyroxene,the calculated spectrum (Fig. 6) consists of at least tenfeatures, including four in the IMS region which areessentially the same as those occurring in the IMS regionof the calculated Mg spectrum; however, they are muchcloser in energy one to the other. Therefrom, we infer theXAS con®rmation of what is already well known fromSC-XRef: in jadeite the Al atom distributes over thecrystal structure according to the same symmetry rulesas Mg in diopside or, in other words, Al occupies in Jdthe same M1 sites as Mg in Di, but within a smallervolume (owing to Al smaller ionic radius). In turn, this®nding con®rms, once more, that the features in the IMSregion of a spectrum arise from contributions of higherorder related to the crystallinity of the sample, i.e., re-¯ect medium- to long-range ordering rules that are beingrevealed by SC-XRef.

By contrast, features in the FMS region are associ-ated with fundamental electronic properties of the pro-bed atom as well as to its organisation in the structure;there the photoelectron mean free path is signi®cantlylonger than in the IMS region, where it does not evenreach 1.0 nm (Muller et al. 1982; Bianconi et al. 1987).The entire FMS region of the Al spectrum is also af-fected by the general contraction due to the small radiusof this cation; that is why certain calculated features areso close in energy as to overlap. They may even escapedetection in the experimental spectrum, where they arefurther convoluted owing to resolution. Nevertheless,FMS features are always worth a detailed analysis, being

28

the most signi®cant piece of evidence to demonstrateXANES unique capability at determining local envi-ronment around a speci®ed atom.

In order to achieve this goal, in Fig. 8 (right panel)we report the sequence of calculated Al K-edge spectrafor Jd obtained with increasing clusters till convergence(i.e., for a cluster of 89 atoms [7 Al + 10 Na + 20 Si +52 O] extending to 0.605 nm from the absorber). Mainedge A and feature G arise even from the 7-atomsmallest cluster: they represent interaction between Aland surrounding shell of 6 O neighbours in the M1 oc-tahedron, as previously described. All other featuresarise only when next-nearest atom shells are beingadded, up to 50 atoms [3 Al + 5 Na + 8 Si + 34 O] to0.492 nm from the central Al atom, and agreement be-tween calculation and experiment is never reached forthe FMS region, not even when it is attained for the IMSregion with the 89-atom cluster. However, the quality ofMS calculations is constantly improving and our matchwith the experimental spectrum is certainly much betterthan McKeown's was (1989 Fig. 5b). He had tried toreproduce the jadeite Al K edge with a cluster containingonly nine atoms i.e., three additional atoms beyond theoctahedral core shell, but his simple calculation did notsucceed, as he himself correctly pointed out (McKeown1989, p. 682).

The Al K-edge calculated spectrum of P1-25omphacite (Fig. 6) is the example for an intermediateCa-Na C-pyroxene where Al is indeed the predominantcation (0.705 at.pfu), but Mg is also signi®cant(0.204 at.pfu) although diluted over the M1 octahedralchain. This calculation reached convergence for a clustercontaining 89 atoms [6 Al + 1 Mg + 8 Na + 2 Ca +20 Si + 52 O] extending 0.605 nm from the Al absorber.The essential features are in good agreement with thosegiven for Jd. However, some more features become ap-parent that were not so evident in the Jd spectrum. Inparticular, after features D and E, the IMS region clearlyshows the additional feature E¢. The presence of thisfairly intense E¢ at a small energy distance from D and Eexplains well the broad plateau to be seen in this part ofthe experimental spectrum. Similarly, in the FMS re-gion, the small, but clearly resolved calculated feature A¢attracts attention on the weak, barely detectable shoul-der on the raising slope of the experimental main edgethat could otherwise be mistaken for the prepeak. Giventhe composition of P1-25 C-omphacite, we considerthese additional features to be due to the interaction ofthe photoelectron emitted by Al with the Mg next-nearest neighbours, and explain their weakness by itsdilution.

Turning now to P-omphacites, in Fig. 7 we plot thecalculated Al spectra for the two compositional ex-tremes, 68-MV-45 (0.451 Al at.pfu) and 74-AM-33(0.256 Al at.pfu). In these calculations, we consideredAl to be fully partitioned in M11, and we obtainedconvergence for 89-atom clusters extending to0.617�0.619 nm, as for C-pyroxenes [5 Al + 2 Mg + 6Na + 4 Ca + 20 Si + 52 O]. The IMS regions of all

pyroxenes (cf. Fig. 6 with Fig. 7) are identical, thuscon®rming their structural similarity on the mediumrange. By contrast, P-omphacites di�er from C-pyrox-enes in the calculated FMS regions, particularly for therelative width and height of the two major features.These di�erences are much more emphasised in thecalculated spectra than they were in the experimentalspectra, where experimental broadening and, possibly,also some local disorder force certain features to merge.

The site where Al preferentially partitions in a P-omphacite is M11, which di�ers from M1 (i.e., the sitewhere Al is in a C-omphacite of identical composition),for its: (1) much smaller average size, and (2) smallerdistortion. For example in natural 74-AM-33 P-omphacite, hM11-Oi is 0.1932 nm and OQE 1.0067(Bo�a Ballaran et al. 1998a, Table 5b), as against0.1999 nm and 1.0096, respectively, for hM1-Oi whenthe same grain turned to C-symmetry after 458 h ofannealing at 950 °C (see above). Consequently, the in-creased complexity of the Al-calculated spectra may berelated either to the superimposition of contributionsfrom two di�erent environments or to the properties ofthe Al-O bond, and possibly to both.

Comparison between K edges

A direct comparison between the calculated K edges ofMg in diopside and Al in jadeite (Fig. 8) is the bestpossible evidence supporting their close similarity instructural environment as revealed by their similarspectroscopic behaviours.

Indeed, the IMS regions of the two convergent clus-ters display the same sequence of four features withidentical shape. Moreover E¢, although very weak, ispresent in both spectra. We already recognised theseIMS features to be due to MRO, since they developwhen the clusters attain considerable sizes (>0.6 nm).We conclude that the IMS region of a XANES spectrumis indeed sensitive to the overall symmetry induced bythe crystalline state onto the examined material, but overa linear range at least one order of magnitude shorterthan XRD, which, to be e�ective, requires an LRO ex-tending over a 20�30 nm width. Conversely, IMS alsocontains indications of local disorder that SC-XRef willnever have. Note, however, that lack of visible di�erencebetween our experimental and calculated spectra may bedue to our calculation method. Atomic positional datadetermined by SC-XRef that are used as input for ourMS calculations have errors at the fourth decimal ®gureof an nm. By contrast, our calculations show distinctdi�erences only when atomic displacements are appliedto systems are of the order of several thousandths of annm, so that some ®ne details contained in the XRDinformation may become lost. However, XRD dataaverage a large volume, whereas XAS directly probes ona much smaller one. The two methods have intrinsicproperties that make them complementary rather thansuperimposable, and this should be always be considered

29

when performing MS calculation addressed to comparethe two.

As for the calculated FMS regions at the Al and MgK edges, they are clearly di�erent even when the IMSregions are identical (Fig. 8) in pyroxenes having thesame MRO. However, this discrepancy is more visualthan real. Indeed, our calculated FMS region for Jdcontains the same four features (and prepeak A¢¢) as thecorresponding Mg region for Di. They di�er only in theenergy spacing and relative height of the three majorfeatures: in the Al calculation, the ®rst feature (labelledA¢) appears as a vague shoulder below the second one(labelled A), whereas in the Mg K-edge calculation ofdiopside all three major peaks are well resolved (Fig. 8,left). Features are labelled di�erently in the two spectrabecause the present assignments coincide with those thatwere obvious when inspecting visually the experimentalspectra, but such a mismatch actually does not exist:calculations con®rm the expected close similarities of thelocal arrangements around the probed Mg and Al at-oms, and consequently support the validity of the ``®n-gerprinting'' method of XANES evaluation. At the sametime, they clarify that all di�erences to be seen betweenthe Mg and Al experimental spectra arise from di�er-ences in the site average sizes, these, in turn, re¯ectingthe atom sizes, in spite of having identical symmetry.Thus, in this way the problem is brought back to itsstereometric essentials.

In diopside, the M1 site centred by Mg is a fairlyregular octahedron (OQE = 1.0050) having three pairsof Mg-O bonds that are 0.2050 (1), 0.2065 (3) and0.2115 (1) nm long, respectively (Cameron et al. 1973,Table A-7): in other words, four nearly equal shortbonds and two long ones. In jadeite, the M1 octahedroncentred by Al is less regular (OQE = 1.0152) since allthree Al-O bond pairs are substantially di�erent inlength, being 0.1995 (2), 0.1940 (1), and 0.1852 (2) nm(Cameron et al. 1973, Table A-7; cf. Bo�a Ballaran1997). The local environments being similar, then boththe Mg and Al FMS regions should be intrinsicallystructured to show the same number of features, al-though changing in shape because of the individualproperties of the atom involved. However, the experi-mental Al K-edge has only two evident features, and theMg K-edge three features that are neatly separated. Thisunexpected XANES shape is generally determined bythe crystal-structure e�ect in the medium range, becausein all our calculations it shows up only when clusterscontain at least three shells of atoms.

Furthermore, we argue that the observed XANESdi�erence has something to do with the electrostaticcharacter of the bonds involved that, in turn, depends onthe atom electronic con®guration. Mg, [Ne] 3s2, and Al,[Ne] 3s23p1, di�er only for one free electron, and yet theMg-O bond is de®nitively ionic, while Al-O has a rathersigni®cant covalent component. This is long sinceknown from multiple-scattering self-consistent-®eld Xacluster calculations (Tossel 1975), and has also recentlybeen con®rmed via improved theoretical methods

(Causa' et al. 1986; Sousa et al. 1993). Things do notchange when using the well-screened Z+1 approxima-tion as it is routinely applied with the CONTINUUMcode. Consequently, in the pyroxene system the Mg K-edge can be easily reproduced by MS calculations, sinceCONTINUUM works well for ionic crystals although ithad been ®rst designed for molecular substances (Natoliet al. 1980; Tyson et al. 1992); the Al K-edge can also bereproduced, and satisfactorily, but with a greateramount of di�culty.

A ®nal note: both calculated spectra for the 89-atomcluster have distinct pre-edges (A¢¢) that do not show upin the experimental spectra. Additions of farther-up,higher-shell atoms would result in calculated spectrawith a number of features that do not occur in the ex-perimental spectra, at least for the pyroxenes studiedhere. This does not mean that they may be detected inother pyroxene spectra, where these potential pathwaysmigth become activated through contributions of minorcations (chemical impurities), or by some form of clus-tering. Peaks such as A¢ in MZ (Fig. 4) and C¢ in Px-1(Fig. 2) warn about this possibility.

The now clari®ed close similarity of the Mg and AlK-edges of Ca-Na pyroxenes bears conclusive evidenceto the belief that a XAS spectrum up to about 60 eVfrom threshold mainly depends on the geometricalcon®guration of the ®nite cluster of atoms that sur-rounds the absorber atom i.e., upon the interactions ofthe photoelectron with the near- and next-nearestneighbours of the absorber in the structure. Conversely,and in spite of some remaining problems, it furthervalidates the reliability of CONTINUUM as a tool tointerpret the XANES spectrum in terms of full multiplescattering resonances within a cluster of ®nite size in thereal space (cf. Wu et al. 1996a, b; Cabaret et al. 1998).

Conclusions

The UVSOR wiggler is an intense source and yet, be-cause of the low energy of the ring, it does not inducesigni®cant thermal stress into the monochromatorcrystals and is exceptionally stable. These intrinsicqualities allow recording at UVSOR soft X-ray spectraat the Mg and Al K-edges with a high degree of accu-racy. Consequently, experimental spectra can be evalu-ated in great detail in spite of their intrinsic experimentalbroadening. However, successful interpretation isachieved only after theoretical spectra are calculated forthe same samples starting from their atomic positionalparameters determined by single-crystal X-ray di�rac-tion re®nement. These calculated spectra are used forcomparison under the assumption that they representthe XANES spectrum of the studied material in thecondition of LRO. Then, di�erences can be interpretedas indicating local deviations from LRO towards MROand SRO, the evaluation being limited only by experi-mental broadening and by the resolution of the appa-ratus, and lead to the following conclusions:

30

1. In all C2/n Ca-Na pyroxenes the Mg and Al atomsoccupy sixfold sites that are essentially identical inshape. This experimental ®nding is also supported byMS calculations.

2. In the UVSOR setup, the photoelectrons emitted atthe Mg and Al K-edge energies probe a volume over0.6 nm in radius in the real space. Thus, information onpyroxene structure gathered by XAS concerns theirmedium-range order (MRO), with a spatial resolution atleast three orders of magnitude better than that providedby SC-XRef.

3. C-pyroxenes have the FMS regions of their Mgand Al K-edge spectra that are not as di�erent as theywould appear at ®rst glance. They contain the samenumber of features, however di�erently spaced in energyand with di�erent heights so as to show up as threemajor separated peaks for Mg, and only two majorpeaks for Al; as a matter of fact, the ®rst peak of the AlK-edge spectrum contains two overlapping contribu-tions. The reason for this di�erent behaviour lies in theelectronic con®gurations of the two atoms that re¯ectsinto di�erent degrees of ionic vs. covalent character ofthe Mg-O and Al-O bonds.

4. The IMS regions of C-pyroxenes are identical forboth the Mg and Al K-edges, thus implying that the twoatoms occupy the same site of the structure (M1) or,conversely, that they are constrained there by the sametype of symmetry rules. Since the IMS features arisefrom interaction of photoelectrons with the higher-ordershells of large atomic clusters (at least 89 atoms), thisregion of the spectrum gives information on medium-range order (MRO) only.

5. Features in the FMS region mostly arise fromcontributions of higher-order shells. Even the white linecontains contributions from these, although it initiallyarises from the contributions of the nearest six O atomsforming the ®rst coordination shell of the absorber.

6. The IMS regions of P-pyroxenes are essentially thesame as those of C-pyroxenes, for their shape, butcontain twice as many peaks, suggesting duplication ofthe periodicity of the atomic array i.e., interaction over alarger volume of the ordered structure. Alternatively,they may taken as the evidence indicating that the pro-bed atom is present in two nonequivalent, but similarsites.

7. Calculated features in the FMS region are twiceas many in P-pyroxenes as they are in the C-ones. Theyre¯ect again the greater complexity of the P-structureeven at the local scale, the sixfold coordinated sitesbeing split into two nonequivalent alternating M1 andM11 sites. However, the medium-range well-orderedarrays of the Mg and Al atoms remain essentially thesame across the C- to P-structure transition. Experi-mentally, this is better seen in the Al K-edge spectrathan in the Mg ones.

8. XAS spectra indicate that the Al atoms distributeregularly over the octahedral strip on changing compo-sition from Di to Jd, whereas the Mg atoms do not: theytend to be partitioned between the M1 and M11 sites of

the ordered P-structure. Thus, XAS hints for an element-selective physical method totally independent uponX-raydi�raction to estimate in P-omphacites the extent of localMg-Al disorder on a short-range scale (Mottana et al.Part III in preparation).

Acknowledgements Most crystal structure re®nements were carriedout by the late Giuseppe Rossi ( 1987) as a part of a project onalpine omphacites carried out jointly with A.M. that was initiatedin 1976 and continued till his premature death. M.C. Dome-neghetti and T. Bo�a Ballaran kindly provided additional infor-mation by courtesy of V. Tazzoli. M. Bondi, L. Morten, and D.C.Rubie donated synthetic samples. Natural samples are either ourown, or from the Museo di Mineralogia della Universita' di Roma(MMUR) and the US National Museum (USNM) of WashingtonDC, and were received as gifts by those who had studied them.Financial support was granted by MURST, Italy, under Project1996 Aspetti cristallochimici cinetici e termodinamici, and by theEU Grant HC&M Access to Large Facilities. Z.Y.W. acknowl-edges a temporary contract by the Dipartimento Scienze Geolog-iche of Universita' Roma Tre during which calculations werecarried out. Experimental work at UVSOR was performed withsupport from I.M.S. through proposal No. 6-D-567. Discussionsand preliminary readings by Rino Natoli, Fritz Seifert, andVittorio Tazzoli are gratefully acknowledged because they signi®-cantly improved the manuscript. Antonio Grilli provided technicalhelp. The unrevised paper appeared on 14 January 1999, as in-ternal report LNF-99/002(P) of the Laboratori Nazionali di Fra-scati. Other very valuable suggestions came from referees MichaelE. Fleet and Delphine Cabaret and from Editor Klaus Langer. Wethank them warmly for pointing out to us shortcomings andpossible misunderstandings. Obviously, all remaining errors areentirely our own.

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