str relaxation in mnco3–caco3 solid solution- a mn k -edge exafs study

8/12/2019 Str Relaxation in MnCO3CaCO3 Solid Solution- A Mn K -Edge EXAFS Study

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ORIGINAL PAPER

Y. J. Lee R. J. Reeder R. W. WenskusE. J. Elzinga

Structural relaxation in the MnCO 3 CaCO3 solid solution:a Mn K -edge EXAFS study

Received: 28 January 2002 / Accepted: 18 July 2002

Abstract Mn K -edge EXAFS spectroscopy of solid-solution samples encompassing the complete MnCO 3 CaCO 3 series shows that rst-shell MnO distancesdeviate little from the 2.19-A distance observed in pure

MnCO 3 . Very slight lengthening is observed only in thelimiting case of dilute Mn(II) calcite solid solutions,where the MnO distance is 2.21 A . The observednearly complete structural relaxation and the compo-sition independence of the MnO distance are consis-tent with the Pauling model behavior of solidsolutions, and agree with previous studies showing ahigh degree of relaxation around hetero-sized substit-uents in the calcite structure. Strain occurs throughbond bending, which is facilitated by the exclusivelycorner-sharing topology of calcite. Observed distancesfrom Mn to more distant neighbors show signicantvariation across the solid-solution series that resembles

Vegards law-type behavior but reects averaging. Thehigh degree of relaxation suggests modest enthalpies of mixing in the solution, consistent with calorimetricstudies.

Keywords Calcite Rhodochrosite EXAFS Solid solutions Relaxation Impurities

Introduction

Mixed occupancy of a site by differently sized ions, as ina solid-solution series, is accompanied by local distor-

tions that are absent (or different than) in the pure end-member compounds. The response of the structure toa point expansion or contraction, referred to as therelaxation, is governed by the exibility of the sur-rounding structure. The resultant strain elds may be

isolated in the dilute limit, or they may interact atintermediate compositions, creating buckling on a lengthscale much greater than nearest-neighbor distances. Theextent of structural relaxation is reected in the inter-

atomic distances around the substituent relative to thosein an unsubstituted host. Although the database is stillrather limited, it is evident that the amount of relaxationvaries among different structure types, reecting theirdifferent linkages. These structural relaxations have asignicant effect on the physical, electronic, and chemi-cal properties of solid-solution crystals. The distortionsare accompanied by a positive elastic strain energy, themagnitude of which depends on the elastic constants.This strain is thought to be the primary contribution tothe mixing enthalpy (Martins and Zunger 1984;Carpenter et al. 1999; Geiger 2001). Moreover, phasetransitions and long-range ordering are now largely

understood in terms of long-range correlations in strain(cf. Carpenter and Boffa Ballaran 2001). Structuralrelaxations are known to be responsible for band-gapanomalies in semiconductor alloys and are important forunderstanding optical anomalies. Blundy and Wood(1994) have also argued that the strain associated withsubstitution is a primary factor controlling minor-ele-ment partition coefficients, which carries much petro-logic signicance.

Direct characterization of localized distortionsaround individual ions in solid solutions became possi-ble with the availability of extended X-ray absorptionne-structure (EXAFS) spectroscopy, although the ex-

istence of such distortions was known much earlier fromdiffuse scattering studies. Diffraction techniques, how-ever, provide site-averaged information, and diffusescattering experiments on short-range order have beendifficult to quantify. EXAFS spectroscopy allows directcharacterization of local structure around a specic el-ement, providing bond distances and information aboutcoordinating atoms. Line broadening in infrared spectrafrom solid solutions also demonstrates the presence of local distortions (Carpenter et al. 1999). The majorityof previous studies have considered solid solutions in

Phys Chem Minerals (2002) 29: 585 594 Springer-Verlag 2002DOI 10.1007/s00269-002-0274-2

Y. J. Lee R. J. Reeder ( & ) R. W. Wenskus E. J. ElzingaDepartment of Geosciences,State University of New York at Stony Brook,Stony Brook, NY 11794-2100, USAe-mail: [email protected]


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high-symmetry compounds, particularly semiconductoralloys and alkali halides. Relatively little is known aboutrelaxation in minerals (however, see Galoisy 1996;Bosenick et al. 2001).

Martins and Zunger (1984) and Boyce and Mikkelsen(1985) outlined the limiting cases for the expected be-havior of the rst-shell bond lengths across a substitu-tional solid solution. The rst case is sometimes referredto as the Pauling model, reecting the view that ionicradii are approximately constant in a given coordinationenvironment. Hence, a particular bond distance (e.g.,A X ) would show essentially no variation across a solidsolution and would be the same as the bond distance inthe pure A end member (Fig. 1). Similarly, the B X distance would be invariant and identical to that in thepure B end member. The other limiting case is an ap-plication of Vegards law to bond distances, sometimescalled the virtual crystal approximation (VCA). Thisview holds that the A X and B X bond distances coin-cide at a value that is a composition-weighted average of the distances in the respective pure end members, re-sulting in a linear variation with composition (Fig. 1).Although diffraction studies are commonly interpretedas lending support to this latter view by showing com-position dependence of interatomic distances, EXAFSstudies reveal that actual rst-shell bond distances insolid solutions show less composition dependence thanconsistent with Vegards law. Martins and Zunger(1984) dened a relaxation parameter, e, such that for Bimpurity substitution in AX , e R BX R 0 AX = R 0 BX R 0 AX , where R BX is the actual B X bond length and R 0 AX and R 0 BX are the A X and B X distances in the pure Aand B end members, respectively. The VCA and Paulingmodel behaviors have relaxation parameter values of 0and 1, respectively, the latter value correspondingto complete relaxation. This relaxation parameter is

essentially identical to the compliance described byDollase (1980), who interpreted a compliance value of 1(or 100%) as the structures ability to adapt completelyto the opposite end member ion size. The relaxation andthe composition dependence of bond distances across asolid solution series vary among different structure typesand should be reected in mixing and other properties.

In a previous study, we used EXAFS to examine therelaxation around several isovalent impurities in calcite(Reeder et al. 1999), both larger (Pb, Ba) and smaller(Co, Zn) than host Ca, near the dilute limit, wheremaximum deviations would be expected. The rst-shellMO distances for the smaller substituents (Co, Zn)were found to be only slightly longer than the MOdistances in the corresponding pure MCO 3 , and forthe larger substituents (Pb, Ba) only slightly shorterthan the distances estimated for the hypothetical MCO 3having the calcite structure, giving relaxation parametervalues in the range 0.80.9. Hence, the calcite structureexhibits a high degree of compliance, which wasexplained by the exclusively corner-sharing linkage of the polyhedra (Reeder et al. 1999). Cheng et al. (2001)used EXAFS to determine the local structure of Mn(II)dopant in calcite, also nding that the rst-shell MnOdistance is similar to that in the end member MnCO 3 .The high degree of relaxation (or high compliance)observed at the dilute limit in the calcite structurecontrasts with the results obtained by Waychunas et al.(1994) for Fe(II) substitution in MgO, where a signi-cant composition dependence was found for the FeOdistance and a relaxation of approximately 50%.Similar behaviors have been found in alkali halides.However, we are not aware of any other studiescovering complete solid-solution series of minerals.

In the present study we use EXAFS spectroscopy todetermine the local structure around Mn(II) over thecomplete MnCO 3 CaCO 3 solid solution series, with aprimary focus on the rst-shell MnO bond distance.With nearly 20% difference in ionic radius, Mn 2+

(0.83 A for sixfold coordination; Shannon 1976) andCa 2+ (1.00 A ) are well suited for evaluating relaxation ina solid solution having the calcite structure. Experi-mental studies of phase relations in the MnCO 3 CaCO 3series have found evidence of immiscibility in the tem-perature range 400700 C (Goldsmith and Graf 1957;deCapitani and Peters 1981; also see the summary byMcBeath et al. 1998). The intermediate ordered com-pound CaMn(CO 3 )2 (kutnahorite), with a structure likethat of dolomite, occurs naturally. However, thisordered phase has not been synthesized at room or ele-vated temperatures (Goldsmith 1983). Studies conduct-ed at or near room temperature have shown that it ispossible to synthesize homogeneous compositions alongthe complete solid-solution series at room temperature(Fubini and Stone 1983; Bo ttcher 1998; McBeath et al.1998). Some question remains as to whether these cal-cite-structured solid solutions are metastable or stable,although the mixing parameters reported by Capobi-anco and Navrotsky (1987) and by McBeath et al.

Fig. 1 Schematic diagram showing possible variations in rst-shell A X and B X bond lengths in the AX BX solid solution series. Thedashed lines showing constant A X and B X bond lengths depictPauling model behavior. The dotted line connecting A X and B X distances of the pure end members depicts Vegards law-type behaviorand is referred to as the virtual crystal approximation (VCA). EXAFSstudies show the actual A X and B X bond lengths ( solid lines ) liewithin these limiting behaviors. (After Martins and Zunger 1984)

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(1998) suggest only a modest positive excess enthalpy of mixing.

Experimental

Synthesis, samples, and characterization

MnCO 3 CaCO 3 solid solution samples were synthesized at room

temperature and/or 60

C using the method described by Bo ttcher(1998). Briey, 2.5 M (Mn,Ca)Cl 2 and 0.025 M NaHCO 3 solutionswere mixed to create a supersaturated, metastable solution. Purenitrogen gas was allowed to ow over the solutionair surface in asealed vessel, forcing slow degassing of dissolved CO 2 and precipi-tation of an (Mn,Ca)CO 3 phase. Precipitation generally startedwithin 3060 min, and samples were ltered after 48 h, washed re-peatedly in deionized water, and dried at 60 C. In this synthesistechnique the amount of the precipitate is limited by the low con-centration of dissolved carbonate in the system. Because of theirhigh initial concentrations, Mn and Ca concentrations changed verylittle during precipitation, so that precipitates grew from nearlyconstant Mn/Ca ratio. Adjustments of the Mn/Ca ratio in the initialchloride solution allowed synthesis of samplescovering thecompletesolid solution series (0.003 X MnCO 3 0.94). Bo ttcher (1998) pro-vides a more complete description of the method and a discussionof

the Mn partitioning behavior. Additional samples used in the studyincluded a natural rhodochrosite (MnCO 3 mole fractionX MnCO 3 0.996), a pure synthetic MnCO 3 (Alfa-Aesar), and anatural, dilute Mn-containing calcite ( X MnCO 3 0.004), similar incomposition to the most dilute synthetic sample ( X MnCO 3 0.003).

Samples were characterized by powder X-ray diffraction (Scintagwith solid-state detector; Cu K a radiation) with samples mounted inat-plate geometry. The goniometer wascalibratedusing an externalstandard. Positions of the strongest peak, 10 114, and full width athalf-maximum values were determined by tting a pseudo-Voigtfunction to peak proles. Compositions of the (Mn,Ca)CO 3 sampleswere determined by directly coupled plasma (DCP) spectropho-tometry following acid digestion and are reported in Table 1.

EXAFS spectroscopy

Fine powders of the Mn x Ca 1 ) x CO 3 samples ( X 0.05, 0.09, 0.14,0.25, 0.45, 0.55, 0.86, 0.996, 1.0) were mixed with boron nitride andmounted in 1-mm-thick sample holders for EXAFS data collectionat beamline X11A at the National Synchrotron Light Source,Brookhaven National Laboratory. The storage ring was operatedat 2.58 or 2.8 GeV with a current less than 300 mA. Spectra werecollected at the Mn K -edge (6539 eV) in transmission mode using a

pair of Si(111) monochromator crystals, with one crystal detunedby 45% to reduce harmonics. The monochromator was calibratedby assigning an energy value of 6539 eV to the rst inection pointin the absorption edge of a Mn metal reference foil. Samples weremounted in a cryostat cooled by liquid nitrogen ( 77 K) to mini-mize thermal contributions to disorder. Spectra were also collectedfor several samples at room temperature to assess possible effectsassociated with cooling the samples. EXAFS spectra for the dilute,Mn-doped calcite ( X MnCO 3 0.003) and for a natural, diluteMn-containing calcite ( X MnCO 3 0.004) were collected in uo-rescence mode using a 13-element Ge detector, also at room andliquid nitrogen temperatures. Multiple spectra were collected for allsamples; individual spectra were calibrated and averaged foranalysis.

EXAFS tting was performed using the program WinXAS(Ressler 1997) with theoretical phases and amplitudes calculatedwith FEFF7 (Zabinsky et al. 1995). Starting models for these cal-culations included calcite with Mn substituted at the Ca position, acation-disordered Ca 0.5 Mn 0.5 CO 3 phase (Peacor et al. 1987), andrhodochrosite (MnCO 3 ). For normalization, a linear function forthe pre-edge region and a cubic polynomial in the post-edge wereused. The v(k) was extracted using a cubic spline and Fouriertransformed with k3 weighting over the approximate k range1.212.1 A

) 1 with a Bessel function window (beta parameter 2). Asharp feature corresponding in position to the Fe K -edge waspresent in most of the Mn K -edge EXAFS scans, limiting the upperend of the k-space range to 12.1 A

) 1 . Fitting was done in R-spacetypically over a range 0.45.0 A (not corrected for phase shift).Because Mn substitution was expected at the Ca site, the coordi-nation numbers (CN) were xed at their values in calcite (andrhodochrosite). Distances ( R ) and Debye-Waller type parameters(r 2 ) were allowed to vary along with a single E 0 value during tting.The amplitude reduction factor S 20 was xed at 0.75 (cf. Barkyoumband Mansour 1992; Cheng et al. 2001). The total number of parameters allowed to vary was always fewer than the Nyquist limitallowed by the k and R ranges. Estimated errors in the rst-shelldistances are 0.010.02 A and 0.030.05 A for more distantshells. Errors in the Debye-Waller parameters are estimated to be0.002 A 2 .

Results

XRD and compositional analysis

The XRD diffraction data conrm that only a singlephase having the calcite structure is present in each of the experimental products. The 10 114 peak positionshows a nearly linear variation as a function of com-position across the series (Fig. 2). Previous workers havereported a nearly linear variation in unit-cell parametersand/or volume with composition for the MnCO 3 CaCO 3 binary join (Goldsmith and Graf 1957; deCapi-tani and Peters 1981; Fubini and Stone 1983; McBeathet al. 1998). Broadening is evident in the XRD peakproles for intermediate compositions, which is typicalfor solid solutions. Full width at half-maximum valuesfor the 10 114 diffraction peak are also shown in Fig. 2.Peak width increases from end members toward mid-composition samples. This suggests structural hetero-geneity associated with increasing substitution. It mayalso reect very slight compositional variations and/orshort-range order within a sample. However, there is noindication of splitting of any diffraction peaks, as wouldbe expected for unmixing, and peaks were well tted bysingle pseudo-Voigt prole functions.

Table 1 Compositional data for (Mn,Ca)CO 3 solid-solution sam-ples

Sample X MnCO 3 2h ( ) 10114

Mnfrk3 0.004 29.448Mnbt1 0.003 29.441Mn33 0.05 29.531Mn32 0.09 29.627Mn21 0.14 29.737Mn23 0.25 29.946Mn15 0.45 30.306Mn2a 0.55 30.520Mn5b a 0.78 30.948Mn5a 0.86 31.058Mn2b a 0.90 31.181Mn4a a 0.94 31.228MnCO3 a 1 31.409MnCO3 c 0.996 31.410

a Not used for EXAFS study

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Mn K -edge XANES

X-ray absorption near-edge structure (XANES) spectra

for the dilute Mn-doped calcite (uorescence spectrum),two intermediate composition (Mn,Ca)CO 3 samples,pure MnCO 3 , and the Mn metal reference foil are shownin Fig. 3. Other workers have shown that the Mn(III)edge is typically shifted 4 eV above the Mn(II) edge(Ressler et al. 1999), so the coincidence of edges (ex-cluding the Mn foil) conrms that Mn occurs in the 2+oxidation state in the carbonate samples, as expected.For all Mn(II)-containing carbonate samples, the high-est peak in the rst derivative of the edge spectra wasobserved at 6549 eV, and a very weak pre-edge featurewas consistently observed at 6539 eV (arrow in Fig. 3).

EXAFS ts

EXAFS tting was carried out for the two dilute Mnsamples, seven intermediate composition samples(X MnCO3 0.05, 0.09, 0.14, 0.25, 0.45, 0.55, and 0.86),and the two MnCO 3 reference samples. Best ts for thetwo MnCO 3 samples gave results that were essentiallythe same and generally consistent with distances deter-mined by X-ray diffraction. The largest discrepancy wasfound in the longest MnO distance tted (4.55 A ),which is shorter than the 4.62 A value given byEffenberger et al. (1981). Other distances are in goodagreement, which supports the EXAFS tting approach.

The primary focus of the EXAFS tting was to assessthe variation in the rst-shell MnO distance among thedifferent samples. However, other distances were also of interest, including shells that could be affected becauseof mixed occupancy by Ca and Mn. Initial tting con-sidered only the nearest four shells: MnO(1), MnC(1),MnO(2), and MnCa/Mn(1) (see Table 2). However, itwas found that more distant shells (two or three MnOshells and a further MnCa/Mn shell) also contributesignicantly to the v(k) and to features that overlap withthe MnCa/Mn(1) peak and with one another in the FT

magnitude. Therefore, subsequent ts included shells outto the second metal position at 4.755.00 A . Theexception was the very weak MnC(2) contribution at3.94.1 A , which was found not to inuence t resultsand was excluded. With as many as nine shells, severalof which overlapped, some signicant correlations wereobserved among parameters in the tting procedure(described below). However, no signicant differences in

the t results of the rst four shells were found betweents including or excluding these more distant shells. Nomultiple-scattering paths were found to be important.

Several strategies were used in tting the mixed oc-cupancy Mn/Ca(1) shell at 3.84 A . For Ca-rich andMn-rich compositions, backscattering from this shellshould be dominated by Ca and Mn, respectively, andthe appropriate path (i.e., MnCa or MnMn) was used.For intermediate compositions, this shell is likely tocontain both Ca and Mn, ideally in proportions corre-sponding to bulk composition, in which case we used

Fig. 2 Two-theta position (CuK a) of the 10 114 diffraction peakof samples in the MnCO 3 CaCO 3 solid-solution series(solid circles ). Full width athalf-maximum of the 10 114 dif-fraction peak ( open triangles )

Fig. 3 Near-edge regions of the Mn K -edge absorption spectra of selected samples in the MnCO 3 CaCO 3 solid solution compared withthe absorption edge for Mn metal reference foil. A weak pre-edgefeature is present in all the Mn-containing carbonates ( arrow )

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T a

b l e 3 B e s t - t E X A F S p a r a m e t e r s . A

l l C N v a l u e s x e d ( s e e t e x t ) . U n i t s f o r R a n d

r 2 a r e A a n d A

2 . E

s t i m a t e d e r r o r s g i v e n i n t e x t . R

T = r o o m t e m p e r a t u r e

S a m p l e

S h e l l

0 . 0 0 4

N a t

0 . 0 0 3

S y n

0 . 0 0 3

S y n R T

0 . 0 5

0 . 0 9

0 . 1 4

0 . 2 5 a

0 . 4 5 a

0 . 4 5

0 . 5 5 a

0 . 5 5

0 . 5 5 a

R T 0 . 8 6

0 . 8 6 R T

M n C O

3

S y n

M n C O

3

N a t

M n C O

3

S y n R T

M n O ( 1 )

C N

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

R

2 . 2 1

2 . 2 1

2 . 2 1

2 . 1 9

2 . 1 9

2 . 1 9

2 . 1 9

2 . 1 8

2 . 1 8

2 . 1 8

2 . 1 8

2 . 1 8

2 . 1 8

2 . 1 8

2 . 1 8

2 . 1 8

2 . 1 7

r 2

0 . 0 0 3

0 . 0 0 3

0 . 0 0 9

0 . 0 0 5

0 . 0 0 5

0 . 0 0 5

0 . 0 0 5

0 . 0 0 5

0 . 0 0 5

0 . 0 0 5

0 . 0 0 5

0 . 0 0 8

0 . 0 0 5

0 . 0 0 7

0 . 0 0 3

0 . 0 0 4

0 . 0 0 6

M n C ( 1 )

C N

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

R

3 . 1 9

3 . 1 7

3 . 1 6

3 . 1 2

3 . 1 2

3 . 1 0

3 . 0 9

3 . 0 9

3 . 0 8

3 . 0 7

3 . 0 6

3 . 0 6

3 . 0 5

3 . 0 5

3 . 0 7

3 . 0 9

3 . 0 4

r 2

0 . 0 0 2

0 . 0 0 3

0 . 0 0 6

0 . 0 0 8

0 . 0 0 7

0 . 0 0 5

0 . 0 0 5

0 . 0 0 4

0 . 0 0 6

0 . 0 0 4

0 . 0 0 5

0 . 0 0 9

0 . 0 0 3

0 . 0 0 7

0 . 0 0 2

0 . 0 0 2

0 . 0 0 4

M n O ( 2 )

C N

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

R

3 . 4 0

3 . 3 9

3 . 3 2

3 . 2 5

3 . 2 8

3 . 2 5

3 . 2 6

3 . 2 6

3 . 2 5

3 . 2 4

3 . 2 1

3 . 2 1

3 . 2 2

3 . 2 0

3 . 2 4

3 . 2 8

3 . 2 1

r 2

0 . 0 0 3

0 . 0 0 7

0 . 0 1 8

0 . 0 2 6

0 . 0 2 3

0 . 0 2 2

0 . 0 1 7

0 . 0 1 4

0 . 0 2 1

0 . 0 1 5

0 . 0 1 6

0 . 0 2 5

0 . 0 1 2

0 . 0 1 8

0 . 0 0 7

0 . 0 0 2

0 . 0 1 3

M n M n ( 1 )

C N

1 . 5

3

3

3

3

3

6

6

6

6

6

R

3 . 9 2

b

3 . 8 7

b

3 . 7 8

3 . 8 5

b

3 . 7 9

3 . 8 5

b

3 . 8 1

3 . 8 1

3 . 7 9

3 . 7 9

3 . 7 9

r 2

0 . 0 0 9

0 . 0 0 9

0 . 0 0 5

0 . 0 0 8

0 . 0 0 3

0 . 0 1 1

0 . 0 0 8

0 . 0 1 2

0 . 0 0 6

0 . 0 0 6

0 . 0 1 0

M n C a ( 1 )

C N

6

6

6

6

6

6

4 . 5

3

3

3

3

3

R

3 . 9 8

3 . 9 8

3 . 9 5

3 . 9 4

3 . 9 3

3 . 9 4

3 . 9 2

b

3 . 8 7

b

3 . 9 7

3 . 8 5

b

3 . 9 9

3 . 8 5

b

r 2

0 . 0 0 5

0 . 0 0 6

0 . 0 1 1

0 . 0 0 5

0 . 0 0 6

0 . 0 0 9

0 . 0 0 8

0 . 0 0 9

0 . 0 0 3

0 . 0 0 7

0 . 0 0 3

0 . 0 1 3

M n O ( 3 )

C N

6

6

6

6

6

R

4 . 2 6

4 . 2 9

4 . 0 7

4 . 0 5

4 . 0 4

r 2

0 . 0 0 6

0 . 0 0 3

0 . 0 0 6

0 . 0 0 3

0 . 0 0 6

M n O ( 4 )

C N

6

6

6

6

6

1 2 c

1 2 c

1 2 c

1 2 c

1 2 c

1 2 c

1 2 c

1 2 c

1 2 c

1 2 c

1 2 c

1 2 c

R

4 . 3 2

4 . 3 0

4 . 3 0

4 . 2 6

4 . 2 7

4 . 2 1

4 . 1 8

4 . 1 1

4 . 0 8

4 . 0 6

4 . 1 0

4 . 0 2

4 . 0 4

4 . 0 2

4 . 0 8

4 . 1 0

4 . 0 4

r 2

0 . 0 0 3

0 . 0 0 3

0 . 0 0 3

0 . 0 0 3

0 . 0 0 3

0 . 0 1 1

0 . 0 1 3

0 . 0 1 9

0 . 0 1 7

0 . 0 2 2

0 . 0 1 0

0 . 0 3 1

0 . 0 2 1

0 . 0 2 4

0 . 0 1 5

0 . 0 1 1

0 . 0 2 4

M n O ( 5 )

C N

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

R

4 . 7 8

4 . 8 1

4 . 7 5

4 . 7 2

4 . 7 2

4 . 6 8

4 . 6 6

4 . 6 5

4 . 6 6

4 . 6 1

4 . 6 3

4 . 6 4

4 . 5 8

4 . 5 9

4 . 5 5

4 . 5 5

4 . 5 6

r 2

0 . 0 0 2

0 . 0 0 3

0 . 0 0 3

0 . 0 0 3

0 . 0 0 2

0 . 0 0 2

0 . 0 0 3

0 . 0 0 4

0 . 0 0 3

0 . 0 0 3

0 . 0 0 3

0 . 0 0 8

0 . 0 0 3

0 . 0 0 4

0 . 0 0 3

0 . 0 0 2

0 . 0 0 4

M n C a / M n ( 2 )

C N

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

R

5 . 0 0

4 . 9 8

4 . 9 9

4 . 9 4

4 . 9 5

4 . 9 2

4 . 9 2

4 . 8 8

4 . 8 9

4 . 8 8

4 . 8 8

4 . 8 7

4 . 7 9

4 . 7 9

4 . 7 5

4 . 7 5

4 . 7 5

r 2

0 . 0 0 3

0 . 0 0 3

0 . 0 0 8

0 . 0 0 6

0 . 0 0 4

0 . 0 0 5

0 . 0 0 5

0 . 0 0 8

0 . 0 0 8

0 . 0 0 5

0 . 0 0 6

0 . 0 1 3

0 . 0 0 7

0 . 0 1 2

0 . 0 0 4

0 . 0 0 3

0 . 0 0 9

a

F i t s u s i n g c o r r e l a t e d M n M n ( 1 ) a n d M n C a ( 1 ) s h e l l s ( s e e t e x t )

b

D i s t a n c e s c o r r e l a t e d f o r M n M

n ( 1 ) a n d M n C a ( 1 ) s h e l l s t o g i v e a v e r a g e M n M n / C a ( 1 ) s h e l l

c

M n O ( 3 ) a n d M n O ( 4 ) s h e l l s c o m b i n e d i n s i n g l e s h e l l

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dra, respectively (see Fig. 7), the magnitude of thevariation is greater (0.2 and 0.25 A ). For the ts usingcorrelated MnMn(1) and MnCa(1) shells, the Debye-Waller-type factors of these shells are larger forintermediate compositions than for the dilute Mn andthe MnCO 3 samples. Because coordination numberswere xed, this indicates a range of distances, which isconsistent with mixed Mn/Ca occupancy of the neigh-boring octahedra.

We noted discrepancies in the ts of the Fouriertransform magnitudes in the region from 3.5 to 4.5 A (not corrected for phase shifts) in the dilute and low Mnsamples using the single-scattering paths from the calcite

structure model. Debye-Waller-type factors for theMnO(3) and MnO(4) shells were observed to be cor-related with one another. In addition the Debye-Wallertype factor for the MnO(5) shell in these ts sometimesrequired constraints to maintain values above 0.002 A 2 .Multiple-scattering paths were not found to improve thets in this region.

Fit results for room-temperature spectra of the dilutesample, the intermediate samples X MnCO 3 = 0.55 and0.86, and a MnCO 3 reference sample are also reported inTable 3. The tted distances are generally consistentwith those from the spectra collected at liquid nitro-gen temperatures; the Debye-Waller-type factors wereconsistently larger than those for the cold samples. Wenote, however, that the distances for the second MnOshell are shorter in the room-temperature t comparedto the low-temperature t, but the large Debye-Wallertype factors make it difficult to evaluate the signicance

Fig. 4 Fourier transform magnitudes ( solid lines ) and ts ( dotted lines )from EXAFS analysis of the Mn x Ca 1 ) x CO 3 samples. Samples aredesignated by MnCO 3 mole fraction. RT Room temperature. See textfor further description

Fig. 5 The k3 -weighted EXAFS ( solid lines ) and ts ( dotted lines ) forthe Mn x Ca 1 ) x CO 3 samples as shown in Fig. 4

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of this observation. In general, the results suggest thatcooling the samples to liquid nitrogen temperature did

not introduce any additional distortions.

Discussion

Our EXAFS t results reveal a complex but systematicresponse of the calcite structure type to MnCa substi-tution on the octahedral site. The near absence of composition dependence of the rst-shell MnO dis-tances matches the Pauling model behavior describedearlier and is inconsistent with the VCA model. It would

be valuable to determine if rst-shell CaO distances arealso largely invariant with composition in this same se-ries. The slight increase in the MnO distance observedfor the dilute limit samples is similar to the behavior forCo(II) and Zn(II) impurities in calcite (Reeder et al.1999). Based on the observed EXAFS distances and theCaO distance of 2.36 A in pure calcite, the relaxationparameter e for dilute Mn(II) in calcite is 0.9 (or 90%),indicating a high degree of relaxation, or compliance.This compares well with the 8090% compliance foundfor divalent Co, Zn, Pb, and Ba substitution in calcite(Reeder et al. 1999).

We note that the lack of composition dependence inthe rst-shell MnO distances could also be explained if the Mn were clustered in the solid, forming Mn-richdomains much like pure MnCO 3 . There are two reasonsthat we do not consider this likely in our samples. The10114 peak positions from X-ray diffraction show a nearlinear increase with Mn content across the entire series(Fig. 2), which would not be expected if signicantclustering existed, and the absence of peak splittingprecludes separate Mn-rich and Ca-rich phases in theintermediate bulk composition range. Furthermore, if MnCO 3 -like domains were present in the samples, thendistances to further shells, not just the rst shell, shouldalso be the same as in MnCO 3 . Clearly this is not thecase. For example, we noted that the EXAFS averagedMnCa/Mn(1) and MnCa/Mn(2) distances varysystematically across the series, almost resembling VCA-like behavior. Fits using separate MnMn(1) and Mn Ca(1) shells also resulted in distances that differed fromthose in MnCO 3 . These longer radial distances representcomplex linkages through several bonds and thereforereect averaged dimensions on the scale like that of theunit cell, which shows VCA-like behavior.

Previous studies of dilute, divalent metal substitutionin calcite have shown that the strain is highly localizedaround the substituent. Reeder et al. (1999) observedthat the radial strain ( R R 0 , where R 0 is the distance inideal calcite) decreases rapidly as a function of distancefrom the central impurity and approaches zero over thedistance to neighboring octahedra. For the dilute Mnsamples in this study we also see that the radial straindecreases away from the Mn but not in a regular andprogressive manner. The radial strains ( R R 0 ) for theMnO(1), MnC(1), MnO(2), and MnCa(1) shells inthe synthetic dilute Mn sample are ) 0.15, ) 0.04, ) 0.07,and ) 0.07 A , indicating that most of the distortion oc-curs within the rst few shells. The MnO(1), MnC(1),MnO(2), and MnCa(1) distances in the dilute Mnsamples are all shorter than the corresponding distancesaround Ca in calcite, which is consistent with the smallerionic radius of Mn(II) (0.83 vs. 1.00 A ). For the Mn Ca(2) shell at 5 A the radial strain is ) 0.01 A , sug-gesting that the structure is minimally affected at thisdistance.

We note that our MnC(1) and MnO(2) distances( 3.18 and 3.40 A ) in both the natural and syntheticdilute Mn samples differ signicantly from the distances

Fig. 6 Selected radial distances from Mn determined from EXAFStting of the Mn x Ca 1 ) x CO 3 samples. In the MnMn/Ca(1) plot, thecircles (squares ) represent t results using a single Ca(Mn) shell; thetriangles represent t results using an averaged Ca/Mn shell (seeTable 3)

Fig. 7 Portion of the ideal calcite structure showing the rst-shellcoordination of metal positions ( black spheres ) and the relationship of corner-sharing ( top and bottom ) and noncorner-sharing ( left and right )Ca octahedra

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reported by Cheng et al. (2001). In the latter study, thesedistances were found to be 3.46 and 3.63 A , which arelonger than the corresponding CaC(1) and CaO(2)distances in pure calcite (3.21 and 3.45 A ; Table 2), re-sulting in positive radial strains of 0.25 and 0.18 A andsuggesting an expansion around the smaller Mn(II). Toaccount for these expanded distances, the authors pro-posed MnOC bond-bending by 20 relative to that incalcite as well as OCO bond-bending within the CO 3unit. A change in the MnOC bond angle of 20 wouldintroduce signicant distortions in adjacent octahedra(see Fig. 7). Furthermore, deviations in the OCO an-gle of more than 12 from the ideal value of 120 arenot likely, since the CO 3 unit behaves largely as a rigidbody (Reeder 1983). Using our EXAFS-determineddistances for the rst four shells, we nd that MnOCbond-bending of less than 5 is required for Mn substi-tution; this is similar in magnitude to the rotation of CO 3 units necessary to accommodate CaMn orderingin kutnahorite [CaMn(CO 3 )2 ] (Peacor et al. 1987). Nochanges within the CO 3 unit itself are required. Hence,our results indicate that the strain associated with sub-stitution of Mn in the Ca site involves only slight rota-tion and twisting of the CO 3 units sharing corners withthe MnO 6 octahedra. This results in minor distortions of the adjacent octahedra.

The highly localized extent of the strain elds hasimportant implications for understanding minor elementincorporation in calcite. For dilute samples, strain eldsof substituents are unlikely to interact. For intermediatecompositions, overlapping strain elds from adjacentoctahedra create a buckling of the structure, possiblyresembling that described by Frenkel et al. (1996) foralkali halides. However, unit-cell parameters are re-ported to show a linear behavior across the series(Goldsmith and Graf 1957; deCapitani and Peters 1981;Fubini and Stone 1983; McBeath et al. 1998), so anysuch distortion is presumably weak. Because corner-sharing octahedra (i.e., those in adjacent cation layers)are more affected by substitution than noncorner-shar-ing octahedra (i.e., adjacent octahedra in the same ca-tion layer), any tendency for metalmetal interactions(e.g., cosubstitution of smaller and larger impurities)should occur between corner-shared octahedra. This isprecisely the pattern of cation order attained in the in-termediate ordered compounds dolomite and kutnah-orite.

The lack of composition dependence of MnO dis-tances in the MnCO 3 CaCO 3 solid solution (Paulingmodel behavior) contrasts with the behavior observed byWaychunas et al. (1994) for FeO distances in the MgO FeO solid solution. Their EXAFS results showed rst-shell FeO distances forming a roughly linear trend withFe content midway between the VCA and the Paulinglimiting behaviors, corresponding to a relaxation pa-rameter of roughly 0.5. EXAFS studies of alkali halidesolid solutions also show a signicant compositiondependence of rst-shell distances, typically yieldingrelaxation parameter values of 0.40.6 (Boyce and

Mikkelsen 1985; Yokoyama et al. 1990; Sato et al. 1992;Frenkel et al. 1996). Less composition dependence of rst-shell distances has been reported in semiconductoralloys, e.g., GeSi, (Ga,In)As, where bonding is domi-nantly covalent (Mikkelsen and Boyce 1983; Woiciket al. 1998; Aubry et al. 1999). However, distance-least-squares modeling by Dollase (1980) suggests that thetopology of the bonding network should play animportant role in determining the extent of compositiondependence of bond lengths in a solid solution. In thisregard, it is worth recalling that the calcite structurediffers signicantly from the rock salt structures of MgOand the alkali halides. In calcite, the polyhedral units areexclusively corner-sharing, whereas in the rock saltstructure the octahedra are exclusively edge-sharing. Thelatter topology allows less exibility so that the strain isaccommodated over a greater radial distance thanwithin calcite.

In view of the high degree of relaxation in theMnCO 3 CaCO 3 system, it follows that the elastic energyassociated with substitution, and hence the excessenthalpy of mixing, should be relatively small. This isconsistent with the results reported by McBeath et al.(1998), which suggest stable solid solutions over a broadrange in this series.

Conclusions

The EXAFS results demonstrate that the rst-shell Mn O bond length is conservative in the CaCO 3 MnCO 3solid solution, supporting Pauling model behavior. Ourndings also attest that Mn(II) is readily accommodatedin the calcite structure with minor local strain, consistinglargely of bond bending. Previous EXAFS results forsubstitution of other divalent metals in calcite lead tosimilar conclusions. We have noted that the topology of the calcite structure is based on corner-shared polyhedra(CaO 6 octahedra and planar CO 3 triangles), with noshared edges. This allows ready distortion through bondbending, which costs less in energy than bond com-pression or expansion in this structure. The exibility of the calcite structure is surely the main reason why it iscapable of accommodating such a wide range of impu-rities and is host to such extensive substitutional solidsolution, much of it metastable. Recent EXAFS resultsalso indicate a high degree of compliance associated withtrivalent rare-earth element substitution in calcite(Elzinga et al. 2002). However, larger rare earths Nd andSm have sevenfold coordination by oxygen, whereassmaller rare earths Dy and Yb retain sixfold coordina-tion in calcite. This suggests that distortions accompa-nying heterovalent substitution in calcite may be moresignicant than those associated with size differencesalone. The high degree of structural compliance incalcite makes it potentially useful for scavenging andsequestering a wide range of toxic metals and radio-nuclides. Further study is needed to address the stabilityof substitutional solid solutions with the calcite structure

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and to relate the observed strain with thermodynamicmixing properties.

Acknowledgements Funding for this work was provided by NSFgrants EAR9706012 and EAR027756 and by DOE grantDE-FG07-99ER15013. We thank K. Pandya (X11A, NSLS) forassistance with data collection. Comments from two anonymousreviewers improved the nal manuscript.

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