Crystal Structures and Compositions of Sanidine and High Albite In

American Mineralogist, Volume 63, pages 1264-1273, 1978

Crystalstructures and compositions of sanidineand high albite in cryptoperthiticintergrowth

Krtrs D. Krnrrn eNoGoRpoN E. BnowN Departmentof Geology,Stanford Uniuersity St anford, Cal ifu rnia 9430 5

Abstract

The crystalstructures and compositionsof the phasesin a naturalcryptoperthite from the Rabb Canyon pegmatite,Grant County, New Mexico, have beendetermined using single- crystalX-ray diffraction,transmission electron microscopy, and electron microprobe analysis. The cryptoperthiteconsists of an untwinned,monoclinic sanidine[cell dimensions:d : 8.558(1),b -- 12.997(l),c:7.179(l)A,B: 116.07'(l)landapericline-twinned, triclinic high albite[celldimensions:a:8.AaQ),b:12.989(3),c:7.160(2)A,a:92.10"(2),0: I16.56(2)'and 7 : 90.21(2)"1.The similarity of theb andc celldimensions and precession X- ray photographsindicate that the phasesare partially, but not completely,coherent in the intergrowthplane, -(-601).The bulk compositionof the crystaldetermined by microprobe analysisis Oro.u,AbonrAno.or, and the mole fraction of the sanidinephase in the crystal determinedby X-ray scalefactor refinementis 0.68(l).TEM examinationshowed that the high-albitelamellae are -500,4'wide with -5OA-wide periclinetwin lamellae.The sanidine lamellaeare -1000,4.wide. The compositionof the sanidinephase, as determinedby direct crystallographicsite refinement, is Oro.56111Abo.su.The composition of the high-albitephase, as determinedby mass-balance,is Oro.2212,Abo.rr. Both phasesin this cryptoperthiteare strained, although the natureand amountof strain differ from predictionsof modelsof elasticstrain in perfectlycoherent feldspars. No pre- viously-reportedmethod of predictingthe compositionof the phasesin a cryptoperthitefrom the celldimensions yields correct results for thisspecimen. The observedcompositions lie on an experimentally-determinedcoherent solvus at a temperatureof 465 t 20".

Introduction from the cell volumes (Stewart and Wright, 1974). Cell volumes are, however, affected by elastic strain Cryptoperthitesare submicroscopicintergrowths and thus do not yield a correct estimateof composi- of sodicand potassicalkali feldsparsresulting from tions for coherent cryptoperthite. Robin (1974) and exsolution of a homogeneousfeldspar of inter- Tullis (1975) have developedmethods for correcting mediatecomposition. The unit-celldimensions of the these compositional estimatesby calculating the elas- intergrownphases commonly differ significantly from tic strain of the unit cell caused by coherency. How- those of compositionally-similarnon-intergrown ever, their corrections apply only in the caseof com- phases(Stewart and Wright, 1974).This discrepancy plete coherency of monoclinic phases,and they have is attributedto elasticstrain inducedby preservation not been verified experimentally. Previous attempts of a partially to completelycoherent aluminosilicate to refine the crystal structures of the individual framework acrossthe phase boundary during ex- phasesof a cryptoperthite have not been wholly suc- solution(Owen and McConnell,1974;Yund, 1974). cessful becauseof the difficulties in resolving the dif- Effortsto determinethe amount of strain and how it fraction maxima of the intergrown phases, one or affectsexsolution have been hamperedby the diffi- both of which are usuallytwinned (Ribbe and Gibbs, cultyof determiningthe compositionof the exsolved t97s). lamellae,which are too smallto be chemicallyana- In this study,both intergrownphases of a crypto- lyzedwith an electronmicroprobe. The compositions perthite were examinedby single-crystalX-ray dif- of suchintergrown phases are commonlyestimated fraction and transmissionelectron microscopy with 0003-004x/78l| | | 2-1264$02.00 1264 KEEFER AND BROWN: CRYPTOPERTHITIC SANIDINE AND HIGH ALBITE t265 the following objectives:(l) to developtechniques by which the structuresof the phasesin such an intergrowth may be determined;(2) to determinethe composition of the individual phasesusing X-ray diffraction techniquesand data on the bulk composition;(3) to investigatethe structuralchanges caused by partial coherency;and (4) to use thesedata as a basisupon which to evaluatemethods of determining the composition and amount of strain of the phasesin cryptoperthite from the cell dimensions. br Experimental The material used in this study came from the Rabb Canyon pegmatite,Grant County, New Mex- ico (Kuellmer, 1954).The pegmatite occurs in por- phyry that is the vent facies of a rhyolite dome (J. O'Brient, personal communication, 1976). The cryptoperthite occurs in a matrix of coarselycrystal- line quartz as clear,colorless single-crystal fragments about lcm in diameter, which display perfect cleav- ageparallel to (010)and (001). PrecessionX-ray photographsof a specimen(0.34 X 0.20 x 0.l4mm) taken from a crystal fragment (Molfs, :{E show that the cryptoperthite consists of an untwinned, monoclinic sanidinephase and a pericline- twinned, triclinic high-albitephase'(Fig. l). The ma- jority of diffraction maxima from both phases are distinct and generally well resolved,although slight streakingbetween the maxima is observed.This crystal was later used for integrated intensity measure- tions using Luth and Querol-Sufr6's(1970) regression ments on the intergrown phases.A transmissionelec- equations. tron micrographof the materialis shown in Figure 2. Precessionphotographs show that the spacegroup All measurements of the X-ray diffraction in- of the sanidine phase is C2/m (hkl systematically tensitieswere made on a Picker Fecs-l four-circle absentwhen ft + k : 2n 1- l). The high-albitephase diffractometer with graphite monochromatized was referredto the nonstandardspace group Cl (hkl : MoKa radiation (I 0.71069A). The unit-cell di- systematicallyabsent when i + k : 2n + l) which is mensionsat 23"C of all threelattices were determined conventionally used for triclinic feldsparsto facilitate by least-squaresfit to the angular coordinatesof re- comparisonof the monoclinicand triclinic structures. flectionscentered by the Fecs-1 programs. Eighteen Integrated intensitiesin the range 5-60o 20 wete reflections in the range 12-49" 20 were used for the measured for the sanidine phase with a 0-20 scanat a sanidinephase and l5 reflectionsin the range 12-49" 1"/min scan rate using a l.5o take-off angle and a 20 were used for each of the high-albite twins. The 2.6" 20 scan width compensatedfor ar-a2 splitting. cell dimensionsof the high-albitetwins differ by less Backgroundswere estimatedfrom 20-secondcounts than one standard deviation. The observedcell di- made at eachend of the scan.Intensities in the range mensions are given in Table l, together with cell 30-75o 20 were measuredfor one of the high-albite dimensions calculated from the observedcomposi- twins using a 0.5'/min scan rate, a 2.3" 20 scan width, and l00-second background counts. Other conditions were the same as those usedfor data col- 'The terms sanidineand high albite refer potassic to and sodic lection on the sanidinephase. feldspars, respectively,in which the Al-Si distribution among the from each lattice in the non-equivalent tetrahedral sites is nearly fully disordered. A peri- The diffraction intensities cline twin is a rotation twin with a twin axis oi [010] and a range 40-45' 20 (160 observations for the sanidine composition plane near (001), the so-calledrhombic section. and270 for each of the high-albite twins) were remea- KEEFER AND BROIyN: CRYPTOPERTHITIC SANIDINE AND HIGH ALBITE

sured using identicalinstrument settings. These observations were used to determine the relative amounts of each phasein the sample,as discussed below. The intensitiesfrom each high-albitetwin werethe sameto within 0. I percent,confirming that both twins havethe samestructure and arepresent in equalamounts. Observed intensities were corrected for background, Lorenlz, and polarizationeffects, the latter assuminga 50 percentmosaic monochromator crystal. The observationswere scaled to normalizedstan- dard observationsto correct for instrument drif| maximum and minimum scalingfactors were 1.03 and 0.96, respectively.Corrections for absorption were made using an analyticalmethodz (p : 8.0 cm-1, calculatedfrom the bulk compositionof the crystal;minimum and maximumtransmissions were 0.91and 0.95, respectively). Standard deviations were estimatedusing the formula of Corfieldet al. (1967), whichemploys an instrumental instability constant of 0.04. The crystalused in the diffractionexperiment was analyzedwithan electronmicroprobe. The bulk composition was: (weight percent)66.81 SiOr, 18.67 Al2Os,8.91 KrO, 5.39Na2O, 0.20 CaO, 0.13 FeO, Fig. 2. Bright-field transmission electron micrograph ofa section corresponding to Or0.51Abs.16Ano.or. from the fragment cut parallel to the (001) cleavage plane. The sanidine lamellae have a maximum width of 1000,4and alternate regularly with high-albite lamellae whose rnaximum width is 5004. '9Using the formulaof De Meulenaerand Tompa(1965) in the The intergrowth plane is approximately parallel to (601) and programAcNosr. Programsused for other cal0ulationswere A. normal to this section. Micrographs were made on a 100 kV Zalkin's Fonolp, a modifiedversion of Finger'sRrrrE, and lo- Philips 200 microscope in the D6partment of Materials Science cally-writtenprograms by K. Keeferfor reducingand correcting and Engineering at the University of California, Berkeley. thedata.

Table l. Comparison of observed and calculated cell parameters for sanidine and high albite in cryptoperthitic intergrowth

SANIDINE HIGH ALBITE

34 Observed Calculated ; Straln(Z) Obsened Calcutated A Stratp(Z) AOBS ACALC I a(E) 8.ss8(1) 8.452(5) 0.106 L.25 8.L44(2) 8.248(8) -0.1.04 -t.26 0.4L4 0.204

b(E) L2.997(!) 13.004(1) -O.OO7 _0.0s 12.989(3) L2.932(6) 0.057 o.44 0.008 0.072 (19) c 7.r79(L) 7.169(1) 0.010 0.14 7.L60<2) 7.L40(3) 0.020 0.28 0.019 0.029

c(') 90.00 90.00 0.00 92.LO(2) 92.05(18) 0,05 -2.LO -2.O5

B(') 116.07(1) 116.07(1) O.OO Lr6.s6(2) 116.37(L) 0.19 -0.48 -0,30

Y(') 9o.oo 90.00 0.00 90.2L(2) 90.20(2) 0.01 -o.2L -0.20

v(tr3) 7L7.2 708.0 9.2 1.30 676.9 681.7 -4.8 -0.70 40.3 26.3

t\wnber in patentheses ue e,s,d..,s (1;) in the Least signifi.eant digite. "L= obsewed - alalated 3\oas= oBs(snwDils) - oBS(Hrcn ALBr?E) aLcnrc= cALc(sANrDrNE) - cALc(HrcH ALBr?E) KEEFER AND BROWN: CRYPTOPERTHITIC SANIDINE AND HIGH ALBITE 1267

Structurerefinement and Prince, 1975)was modifiedto calculatethese Strip-chartrecording of diffractionmaxima during derivativesfor combinedintensities. the intensitymeasurements did not permit unequivo- The initial model usedin the least-squaresrefine- cal determinationof interferenceamong diffraction ment of the sanidinestructure was the feldsparstruc- maxima from the threelattices. Therefore. the differ- ture reportedby Fenn and Brown (1977).The neutral Mann (1968)were encesin the 1, <,r,and 2d instrument-settingangles atom form factorsof Cromerand betweenany reciprocallattice point under observa- employed,and completedisorder of the AllSi distri- tion and the nearestone of each of the other two bution (Sio.?6Alo.2u)in the tetrahedralsites was as- latticeswere calculated. An observationwas excluded sumed. Refinementconverged after l0 cycleswith from the refinementif all three angular differences anisotropicthermal parametersand an alkali-siteoc- wereless than the instrumentalresolution (1.2" in y, cupancy of Ko.aNao.z[estimated from the Tullis 0.5" in ar,and l" in 20\.ln theh0l, h + ll, andh I 2l (1975)modell. The alkali-siteoccupancy was then zones,many points in the high-albitereciprocal lat- refinedfor 7 morecycles to yield Ko.uu*o.orNao.ruawith tice werevery narrowly separatedfrom points in the the constraintthat the total siteoccupancy be 1.00. twin lattice. If the angular separationof points was Refinementwas performedon F usingweights of l/ sufficientlysmall to assurethat both diffracted in- o3. 140observations were excludedfrom the refine- tensitieswere measured completely in a singleobser- menton the basisof the resolutioncalculation, and vation,such an observationwas included in the re- l3 other observationswere rejected because F/or ) finementand treatedas follows. 8, leaving a total of 924 observationsin the final Becauseboth high-albite twins have the same sanidinerefinement (Table 2a)o.The final conven- : : structure,a singleobservation which includesmore tional R 0.029(R 0.033including observations : than oneintensity from differenttwins may be treated rejectedbecause of poor fit), weightedR* 0.039 as a combination of different intensitiesfrom the {R*: Pw(lF.l lF"l)'z/2wlF,l'1"'},and the sametwin. If the individualdiffracted rays do not standarddeviation of a unit weightobservation was interfere,the intensityof the combinationis givenby 1.56.Because of the importanceof the refinedsani- the equation: dine K/Na occupancyin our calculationof the compositionof the albitephase, an analysisof weights I:K>F? was performed.Weights of l/o3 gave essentially whereI is the combined,unresolved intensity, F1 or€ equalvalues of (A,F/o) for equal-sizedgroups of Fo5" the structurefactors of the contributing diffraction and henceare preferableto a non-statisticalweight- maximaand k is a constantwhich includesthe Lp ing scheme.Positional parameters are givenin Table factors,absorption corrections, and a scalingfactor. 3a. (The differencesamong the Lp and absorptionfac- The initial model usedin the high-albiterefinement tors that would havethen applied to the Fr individ- was the structure reported by Ribbe et al. (1969), ually are negligible.)For the casein which the in- with the sameform factorsand tetrahedralsite occu- tensityis due to a singlediffraction maximum, least- panciesthat were usedin the sanidinerefinement. A squaresrefinement requires evaluation of derivatives singlealkali site with an occupancyof Nao.rKo.,was of the form: assumed.After convergenceof refinementwith anisotropic temperaturefactors, the much poorer fit of a\/k)'/':- alFl _ r_, (gL_,-aB \ observationsat larger valuesof sind/trcoupled with aPt aPt:'.-\aPr-av,) residualelectron density in a differenceFourier syn- whereA and B arethe real andimaginary parts of the thesissuggested that a modelwith a disorderedalkali structurefactor and Pyare the parametersbeing var- site might be more appropriatethan a model with a ied. For refinementon combined intensities,these singlealkali atom position.Both the two-site,half- derivativesmay be computedfrom the equation: atom model of Ribbe et al. (1969)and the four-site, a(I/k)'rz A(> F")''' 3 - : / y ''lor\-"' The quoted error is 12a, a conventionused throughout the oPi oPt \? paper. a Structurefactor tablesfor both refinementshave been placed - / AL. rp\ on deposit.To receivea copy of Table2 orderdocument AM-78- 079 from the BusinessOffice, Mineralogical Society of America, 1909K StreetN.W., Washington,D.C. 20006.Please remit $1.00 r heru lr- m at,i * r,u,t-,?u*lt;- -'5* (Finger in advancefor the microfiche. l 268 KEEFER AND BROWN: CRYPTOPERTHITIC SANIDINE AND HIGH ALBITE

Table 3a. Sanidinefractional coordinatesand thermal parameters

a2 A R R Atom P1r- '22 "33 '12 -t-3 -23 M 0.2844(1)1 0. 0000 0. 1383(1) s1(1) 4s(1) 1r-8(2) 0 23(r) 0

11 0.0091(1) 0.1834(1) 0.2236(L) 4e(L) le(r-) 3s(1) -4 (1) 22(L) -2(1)

12 0.7069(1) 0. 1177(1) o. 3431(1) 46(1) 14(1) 4s(1) -1 (1) 2o(1) o(1)

oet 0.0000 0.t443(2) 0. 0000 r-04(3) 31(1) 76(4) 0 s0(3) 0

ot2 0.6308(3) 0.0000 0.2832(3) 87(3) 19(1) r-r-3(5) 0 21(3) 0

ot o.827O(2) o. 1448(r) 0.225s(2) 78(2) 44(L) 120(3) -e (1) s8(2) s(1)

oc 0.0327(2) 0. 3092(r-) 0.2568(2) 71(2) 25(1) 98(3) -s(1) 30(2) -6(1)

oo 0.1814(2) 0.12s6(1) o.4049(2) 80(2) 28(1) 63(3) 2(1) r.3(2) 2(L)

rNunbers in pa.rentheses are e,s.d,'s (1&) Ln the Least significant digits. zTlpnnaL paroneters (s10a) ate of tVrc forn T=erp(-tznrhrBr,). quarter-atom model of Prewitt et al. (1976) were experimental source of error could be found, the tried; neither gaveany significantimprovement in the high-albitetwin studiedcomprised only l6 percentof refinement. On the basis of simplicity and easeof the total volume of the crystal; thus the effectsof any interpretation,the singlealkali site model was chosen interferenceof the sanidine intensitieswith the in- for the final refinement. Several cycles of refinement tensities of the high albite were exacerbated.One in which the Na fraction of the alkali site occupancy likely, although unproven, explanation for this poor was varied (the K fraction was constrainedso that the agreement is that the structure within each albite total site occupancy was 1.00) failed to produce a lamella may vary in distortion from the intergrowth chemically reasonable Na fraction. Therefore the boundary to the center, resulting in the high thermal alkali site occupancywas fixed at Na".rKo.r,based on parameters reported below. Such a structure would tentative results of the calculation of the analbite not diffract as well as an undistorted one, and the composition describedbelow. Refinement was per- anisotropic thermal model used does not adequately formed on F with weightsof l/o3, which were found account for this effect. to be satisfactoryafter making the same analysisas was made of the sanidine weights. Becauseof the Results large number of observations,many of which were The mole fraction of each phase in the crystal was extremelyweak, only observationsfor which F ) 3op calculated from the relative diffraction intensities of were usedin the refinement.Of the 2306observations each phase.The observedX-ray diffraction intensity which met this criterion, 479 were excluded on the may be expressedas: basis of the resolution calculation and 129 were re- Iou. : eNkF2 jected because AF/or ) 8, leaving a total of 1698 observationsin the final cycle of refinement (Table where N is the number of unit cellsdiffracting, k is 2b). The final conventionalR : 0.083(R : 0.107 the combined Lp and absorption correction, F is the including observationsrejected due to poor fit), R* : structure factor. and e is an instrumental constant 0.096, and the standard deviation of a unit weight which is the same for setsof observationsmeasured observationwas 2.87.Positional parameters are given under identicalexperimental conditions. The product in Table 3b. eN is then the scaling factor used as a parameter in Theselarge residuals and large number of observa- least-squaresrefinement. These values for each phase tions rejected due to poor agreementreflect the exper- were determined by least-squaresrefinement of the imental difficulties encountered in measuring the scaling factor of each of the fully refined structures, high-albite intensities. Ninety percent of the Fou"re- using observations of each phase measured under jected were much smaller than F""t". Although no identical experimental conditions. The fraction of KEEFER AND BROWN: CRYPTOPERTHITIC SANIDINE AND HIGH ALBITE 1269 unit cellswhich constitutethe sanidinephase may percentbulk FeO is evenless; thus the error due to then be calculatedfrom the equation: the neglectof thesecomponents is within the esti- matederrors noted above. The calculateddensity of Fractionof sanidinecells : eNsanidine/(eNsanidine the crystalis 2.55g/cms and the densitydetermined * 2eNhighalbite) by flotationis 2.57E/cms. (the factor 2 appearsin the denominatorbecause thereare two high albitetwins). Because Z : 4 for The sanidinestructure both structures,the resultis the molefraction of the The structureof the intergrownsanidine phase is sanidine,found to be 0.68t0.02 for this specimen. virtually identicalto the structureof a non-inter- This figureis in excellentagreement with an estimate grownsanidine of compositionKo.ruNao.tuAlSirOr re- (0.67)derived from the electronmicrographs of this portedby Phillipsand Ribbe(1973). This similarity, material. reflectedby the small differencesof the cell dimen- As notedabove, the composition of the high-albite sions()0.02A), is probablycoincidental, considering phasecould not be determinedby site refinement. the large difference in composition between the However,because the sanidine composition, the mole phases.Because no structurehas been reported for a fractionsof sanidineand high albite,and the bulk non-intergrownsanidine closer in compositionto the compositionof the crystalare known,the composi- sanidineexamined in this study,there is no reference tion of the high-albitephase may be determinedby structureavailable for readycomparison. Fenn and mass-balance.The resultobtained is Naorr*o.ouKo.r, Brown (1977) found that the mean alkali-oxygen AlSisO..The Ca and Fe contentof the crystalis neg- distance,(M-O), variesalmost linearlywith the K lected,because there is no practicalway of estimat- contentof alkali feldsparscontaining little or no Ca. ing the Ca or Fe contentof eitherphase. The bulk For the compositionof the sanidinein this study, CaAlrSirO.component determined by microprobe their resultspredict an (M-O) 0.024 shorterthan that analysisis only I percentof totalcomponents and the observed.This differenceis consistentwith the elon-

Table 3b. High-albite fractional coordinates and thermal parameters

Atom K- R R R, R R "11 -22 "33 'L2 "'13 -23

M o.2690G)2 0. 0048(5) 0. 1319(8) 10r.(4) 143(4) 3s7(r2) e(3) 26(5) -113(6)

T 0.0078(2) 0. r.594(1) o.2182(2) 63(2) -2(t) IO 30(1) 36(3) 23(2) 0(1) T. 0.0057(2) 0. 817s(1) o.226L(2) (2) (r") (3) (1) (2) IM se 30 36 6 17 5(1)

Tzo 0.6893(2) 0.1104(1) o.3287(2) s0(2) 29(r) so(3) 0(1) r2(2) 3(1) T^ 0.68s7(2) 0. 8802(l_) zm o,3484(2) s1(2) 2e(1) 4s(3) 3(1) 73(2) 3(1) oat o. 0035(7 ) 0.13s9(3) 0.9914(8) 125(6) 42(2) 88(8) -1 (3) 5e(s) -3(3)

ot2 0. s913(s) 0. ee43(3) o.282t(6) 7r(5) 35(2) 9L(7) -2(2) 26(4) 1(3)

oBo 0.8216 (6 ) 0. 114s(4) 0.2108(8) 81(6) s4(3) 154(11)-11 (3) 74(7) -3 (4)

oBt 0.8184(6) 0. 8s52(4 ) 0. 2378(8 ) 8e(6) 61(3) 722(ro) 13(3) 48(6) -1(4)

oco 0.or-s2(6) 0.29s9 (3) 0.26s8(7) 90(6) 4o(2) 97(s) -10 (3) 32(6) -4(3)

oct o.0202(6) 0. 68e3(3) o.2329(7) 8e(6) 34(2) e6(e) 10(3) ls(s) 6(3)

oDo 0.1e6s(6) 0. r_168(3) 0.39s0(7) e1(6) 4o(2) 77(e) e(3) 18(s) 8(3)

out 0.1918 (6) 0.8710(3) 0.4190 (7 ) 100(6) 39(2) 69(8) -4 (3) -r.0(s) -6 (3)

rVrtnbers in parentheses are e.e.d..rs (1A) in the Least significant digits. 2L'hevmaL paruneters (c10a) az,e of tVue r:erp(-rDh,h,g,,). forn ' 1l rJ T27O KEEFER AND BROIYN: CRYPTOPERTHITIC SANIDINE AND HIGH ALBITE

gation of the intergrown sanidinealong a (seeTable Table 4. T-O and M-O interatomic distances (in A) in the l). The Ribbe and Gibbs (1969)equation estimatesa intergrown phases slight ordering of Al into the T, site(t, : 0.2841)and estimatesa total Al content (tl + tr) of l 03. T-O and Sanldlne High Albite K-O interatomic distancesin this structureare siven T. - ol1 1. 653(1) t 1.651 (s) 10 in Table 4. oBo 1.643(2) 1.6s1 (4) (1) (s) The high-albite structure oco r. 6s1 1. 660 r..6s7 (1) 1.663(4) The structureof the intergrown high-albitephase is 1. 651, L.656 significantly different from that of a synthetic, non- ,l:: intergrown albite (composition Nao.rrKo.orCao.orAlSi, T- -Al 1. 653(1) r.662(5) OB,24"C) reported by Prewitt et al. (1976).This dif- IM (5 ference manifests itself as a lesser deviation from oBt L.643(2) 1.640 ) monoclinic symmetryin the intergrown phase.This is oct 1. 651(1) L,67L(4) in large part accountedfor by the higher K content oot 1. 6s7(1) 1.6s4(4) of the high albite in this study, although partial co- L. 651 L.657 herency of the high albite with the monoclinic sanidine is expectedto have a similar effect. T2o - olt2 r.644(r) L.6s6(4) As in the caseof the sanidine,no study of a non- oBo L.629(2) 1.641(4) intergrown high-albite structure similar in composi- 0^ r.. 642(1) !.623(4) UM tion to the albite in this study has been reported to 1. 636(1) 1.631(4) date, which restrictsdiscussion of the effectof inter- ,ln 1. 638 1.638 growth to generalfeatures. The mean alkali-oxygen distanceof the nine nearestoxygen atoms is within '2m -Az 1. 644(1) 1.6s6 (4) 0.0024 of that reported (1976), by Prewitt et al. al- oB. r.629(2) 1.628 (s) though individual M-O distancesdiffer by as much oco L.642(L) 1.638(4) as 0.1254 (for M-Op-, Table 4). The mean M-O 1. 636(1) 1.648(4) distancepredicted by Fenn and Brown's work for the 1. 538 L.543 observedhigh-albite composition is 0.034 largerthan ,l:: that observed. M - ol(rooo) 2.882(L) 2.607(7) The Tro-Osoand Tr^-Og- bonds in the intergrown phaseare 0.022 and 0.027A longer, respectively,than oeltoo"y 2.882(1) 2.671(7) in the non-intergrown phase. These differencesare or,(zooo) 2.676(2) 2.3s7(4) significantlylarger than would be expectedsolely due on(ooo") 3.OL4(2) 2.6s9(7 ) to the effect of the different Na/K ratio on these os(roo.) 3. 014(2) 3.083(9) bondsu.This elongationof the Tro-Osoand T,--Os* oe(ozio) 3. 131(1) 3.289(7) bonds, which are essentiallyparallel to the b axis, oc(.zio) 3. 131(1) 2.e96(7) contributes roughly 80 percent of the elongation of oo(oooo) 2.93r(2) 2.6LO(7) the D axis indicatedin Table l. A further consequence %'T::] 2.937(2) 3.008 (e) of this elongation is an averageT-O distancewhich 2.955 2.809 yields a total Al content (as predictedby the Ribbe and Gibbs equation) of 1.13,thereby invalidating rMutnbers 'Ln peentheses are e.s.d. ts (L6) in the estimatesof the degreeof Al-Si ordering in the inter- Least significurt digits. grown high albite. Discussion

5 strain For example, the Tro-O"o distance in the non-intergrown sani- Coherency dine structureof Phillips and Ribbe (1973)is 0.0204 longer than Robin (1974)and Tullis (1975) havecalculated the that of the non-intergrown high albite, which contains 84 mole elastic strain induced by perfect coherency between percent more Na than the sanidine. The Tro-O.o distance in the feldspars different intergrown high albite is 0.0274 longer than that of the non- intergrown monoclinic alkali of intergrown high albite, which has only 2l mole percentmore Na compositions.Knowledge of this strain is important than the intergrown phase. becausethe compositions of submicroscopicallyin- KEEFER AND BROWN: CRYPTOPERTHITIC SANIDINE AND HIGH ALBITE l27l tergrown alkali feldspars are often estimated from than the high-albitephase, although comparisonof Z observed a and d2orvalues and nomograms derived suggeststhe reverse to be true. The a axes of both from cell parameters of unstrained phases (cl Stew- phasesare highly strained.The strain in the a direc- art and Wright, 1974). lntergrown phases are com- tion predicted by the models of Robin (1974) and monly strained,so compositionalestimates based on Tullis (1975) for both phasesis lessthan half of that such nomograms are incorrect. actually observed.The observedvolumetric strain is The compositional and structural data from our positive in the sanidine phase and negative in the study provide the first test of thesetheoretical models high-albite phase, exactly the reverseof theoretical used to predict strain and the effectsof strain on the predictions. Furthermore, both models predict a compositional estimatesof intergrown alkali feldspar lesser magnitude of volumetric strain in the vol- lamellae. Becauseexperimentally-determined cell di- umetrically-dominantphase, in this casethe sanidine, mensionsfor unstrained feldsparswith the samecom- and again the opposite is observed. positions as our intergrown phasesare not available, The most probable reasonfor the discrepancybe- we have used as a reference state for strain analysis tween our observationsof the strain of the phasesof cell dimensions calculated from the regression equa- cryptoperthite and the predictions of the models of tions of Luth and Querol-Sufr6(1970) for the Orville Robin (1974) and Tullis (1975) is that our natural (1967) syntheticsanidine-high albite series(Table 1). systemconsists of a monoclinic phaseand a twinned The major and minor axesof the strain tensor calcu- triclinic phase,whereas both models are derivedfor a lated with Ohashi and Finger's (1973) SrnnrN pro- system of two untwinned monoclinic phases.The gram are essentiallyparallel to the a and D cell axes, inversion of the high-albitephase from a monoclinic respectively. Further referencesto strain will there- to a triclinic structure(cl Smith, 1974,pp.301-305) fore be made in terms of the components along the probably allows some relaxation of the strain in that direct cell axes rather than the axes of the strain phase,and also producesa differentset ofstresses on ellipsoid. the sanidinethan exist when both phasesare moho- The cell dimensionsand crystal structures of the clinic. Our resultsdemonstrate that models of strain intergrown phases reported in this study represent derived for coherent monoclinic feldspars are not average structures of the phases. If strain due to generallyvalid, even as approximations,for strain in partial coherency decreases away from the phase intergrowthsof a monoclinic and a triclinic feldspar, boundary, the structures at the boundary may be and that predictedcompositions based on cell dimen- quite different from those at the center of the la- sions corrected for these strain effectsare also invalid mellae. Robin (1974) has shown that if the lamellae (Table5). are elastic, perfectly coherent, and have large aspect ratios, strain is uniform throughout the lamellae. Table 5. Estimates of the compositions of the phases in the However, the very large r.m.s. amplitudesof atomic cryptoperthite of this study vibration found in the refinementsof the intergrown Cments structures suggest that structural distortion varies Sanidioe ELsh Alblte within the lamellae.These amplitudesare almost an o. 65(r) I 0.22(2)2 CodpositioD detemined in thls study. order of magnitude larger than the dimensionalmis- 0.85 -0.242 Estimted3 fld ganLditre cell voluue. match of the average lattices of the intergrown -0.312 ceII edge. phases,and are more likely due to a space-averaged 0.88 Estfuated3 fEoE saoldine 4 disorder causedby a variation in strain than to true 0.682 0.16 Estioated3 frm high albite cell volue. thermal motion. This interpretation implies that 0.75' -0.01 Esti@ted3 fron high alblte 4 cell edBe. strain is not uniform throughout the lamellae. o.92 o.L4 E6ti@ted uslng Dethod of Robin (1974).

The 6 and c cell dimensionsof the intergrown high o.79 0.07 EstiMred usiog merhod of Tullts (1975). albite are more nearly equal to those of the inter- lcornpoeitims grown sanidine than would be the casefor the two ue giuen as nole firctim of the fmLa wit non-intergrown phases.Therefore, the sanidineand MLSi -O^. zThese ualuee coftputed by ws balmce, baeed n bulk carpo- high-albite phases are inferred to be strained and sitim of Ko.stNo\.laCoo.o/Lsi|o|, a nol'e fractin of the partially coherent in the intergrowth plane, -(601). emidine phase in the crABtaL of 0.68, iltd the cqrposi'ti& eatircted for the othe! p|nee. Comparison of the observedand calculatedvalues of 3cornpositi,on estinates frm ceLL direrei'ons calruLated fm b and c shown in Table I suggests that the vol- the regreseion equations of Luth md querol-Sw (7970) fq the (1967) ql.bi'te umetrically-dominant sanidinephase is lessstrained 1tuille emidine-high e%iee. t272 KEEFER AND BROWN: CRYPTOPERTHIT,IC SANIDINE AND HIGH ALBITE

Another possiblecontribution to the discrepancy betweenthe theoreticalcalculations and the observed I resultsis that neithermodel treatsthermal strain TIM effects.Thermal expansionof feldsparsdoes vary I significantlywith composition(Stewart and von Lim- I bach, 1967;Brown and Fenn, 1975;Prewitt et al., I 1976).The intergrowthboundary between the phases is establishedat temperatureson the order of 400- 600 550o higher than room temperatureat which cell dimensionsare usuallymeasured. Hence, differential thermalcontraction might contributean additional strainto systemsstudied at room temperature. r ec) Soluiand exsolution Solvi for coherent alkali feldspar systemshave 500 beencalculated by Robin (1974)for a pressureof I kbar and measuredby Siplingand Yund (1976)at a pressureof I bar6.These solvi and the equilibrium solvuscalculated from the Margulesparameters determinedby Luth et al. (1974)are shown in Figure3. Both calculatedsolvi have beenextrapolated to 200 bars,the estimatedpressure at which the cryptoperthite in the presentstudy cooled (J. O'Brient,per- 400 sonal communication).Within experimentalerror, o.o o.2 0.4 0.6 0.8 l.o thecompositions of thephases in thepresent study lie Ab Mole FroclionKAIS|3OB Or on the experimentalcoherent solvus of Siplingand Yund (1976)at a temperatureof 465i20"C and do Fig. 3. Curvea is the equilibriumsolvus at 200bar, curve b is the Robin (1974)'curve c is not, at any temperature,lie on the other two solvi coherentsolvus at 200 bar calculatedby the coherentsolvus at I bar experimentallydetermined by Sipling (Fig.3). and Yund (1976).The dashedline is the monoclinic-triclinic Smith (1974,p. 305) has used Kroll and Bam- inversionboundary basedon the data of Kroll and Bambauer bauer's(1971) data to constructthe phaseboundary (1971).The compositionsof the phasesin this studyare shown betweenmonoclinic and triclinic sodic feldspars, plottedon curvec with 2,i error bars. whichis alsoshown in Figure3. This phase boundary intersectsthe coherentsolvus of Siplingand Yund in tion of coherency, metastable equilibrium as defined the temperaturerange 465+20"C, the sametemper- by the coherent solvus can no longer exist, and the atureat whichour observedcompositions lie on that only equilibriumwhich doesexist is betweenphases solvus.The compositionsobserved in our studymay whosecompositions lie on the equilibriumsolvus. be explainedby the followingexsolution path, illus- Becausethe systemis presumablyclosed and the tratedin Figure3. compositionof the potassicphase lies outsidethe As the crystal of bulk composition chemicalspinodal at 465"C, furtherphase separation Oro.urAno.orAbo.nscooled from -570o to -465oC,co- will not, in theory, occur without nucleationand herentmonoclinic phases with compositionslying on growthof phaseswhose compositions lie on the equi- the coherentsolvus exsolved. At -465'C the sodic librium solvus.At theserelatively low temperatures phase inverted to triclinic symmetry and pericline nucleationand growth is kineticallyinhibited. Thus twinned.Consequently coherency with the mono- phaseswhose compositions lie on the coherentsolvus clinic potassicphase was reduced.After this reduc- at 465"Cwill tendto persistmetastably when cooling is complete,accounting for the compositionsob- 6 The compositions for the Sipling-Yund solvus were determined servedin this study. using cell dimensions corrected for strain effectsby Tullis's (1975) strain model. Although we questionthe validity of this model for Acknowledgments an intergrowth of a triclinic sodic and a monoclinic potassic feld- We thank Dr. C. M. Taylor (Stanford University) for per- spar, we have no reason to doubt its validity for an intergrowth of formingthe microprobeanalysis of thecryptoperthite crystal used two monoclinic feldspars. in this study,Dr. H.-R. Wenk (U.C. Berkeley)for ion-thinningan KEEFER AND BROWN: CRYPTOPERTHITIC SANIDINE AND HIGH ALBITE 1273 oriented section of our cryptoperthite for TEM work, and Ms. C. Orville, P. M. (1967) Unit-cell parameters of the microcline-low Gosnell (U.C. Berkeley) for helping us obtain the TEM micro- albite and the sanidine-high albite solid solution series. Am. graph. Dr. V. C. Kelley (University of New Mexico) kindly pro- Mineral.. 52. 55-86. vided the cryptoperthite specimen. We gratefully acknowledge Owen, D. C. and J. D. C. McConnell(1974) Spinodalunmixing in Drs. P. M. Fenn and M. P. Taylor (Stanford University)and Dr. J. an alkali feldspar.In W. S. MacKenzie and J. Zussman,Eds., Tullis (Brown University) for helpful discussionsand for critical The Feldspars, p. 424-439. Manchester University Press, Man- readings of an early version of the manuscript. Standard Oil of chester, England. California generouslyallowed us to use their IBM 370,/168com- Phillips, M. W. and P. H. Ribbe (1973) The structuresof mono- puter for many of the calculations. This study was supported by clinic potassium-rich feldspars.Am. Mineral., 58, 263-270. NSF grant EAR-74-03056-A01. One of us (KDK) received sup- Prewitt, C. T., S. Sueno and J. J. Papike (1976) The crystal struc- port as a National ScienceFoundation Graduate Fellow. tures of high albite and monalbite at high temperatures. Am. Mineral.. 6l. 1213-1225. References Ribbe, P. H. and G. V. Gibbs (1969)Statistical analysis of mean Al-Si-O bond distancesand the aluminum content oftetrahedra Brown,G. E.and P. M. Fenn(1975) High temperature structural in feldspars.Am. Mineral., 54, 85-94. study of an homogeneous,intermediate composition alkali feld- - and - (1975) The crystal structure of a strained inter- spar (abstr.). Geol. Soc. Am. Abslracts with Progrums,7, 1012. mediate microcline in cryptoperthitic association with low al- Corfield, R., R. J. Dodens and J. A. lbers (1967)The crystaland bite (abstr.). Geol. Soc. Am. Abstracts with Programs, 7, 1245. molecular structure of nitridodichlorobis(triphenylphosphine) -, H. D. Megaw, W. H. Taylor, R. B. Fergusonand R. J. rhenium(V ReNCldP(C"H Ino rg. Chem., 6, 197-204. ), u)s)2. Traill (1969) The albite structures.Acta Crystallogr., 825, 1503- Cromer, D. T. and J. B. Mann (1968) X-ray scatteringfactors l5 18. computed from numerical Hartree-Fock wave functions. lcra Robin, P.-Y. F. (1974) Stressand strain in cryptoperthite lamellae Crystallogr., A24, 321-124. and the coherent solvus of alkali feldspars. Am. Mineral., 59, De Meulenaer,J. and H. Tompa (1965)The absorptioncorrection 1299-13r8. in crystal structure analysis. Acta Crystallogr., 19, l0l4-1018. Sipling, P. J. and R. A. Yund (1976)Experimental determination Fenn, P. M. and G. E. Brown (1977) Crystal structureof a syn- of the coherent solvus for sanidine-high albite. Am. Mineral., 6I , thetic, compositionally intermediate, hypersolvus alkali feld- 897-906. spar. Z, Kristallogr., 145, 124-145. Smith, J. V. (1974) Feldspar Minerals, Vol. I, Crystal Structure and Finger, L. W. and E. Prince (1975) A system of FoRTRANlV Physical Properties. Springer-Verlag, New York. computer programs for crystal structure computations. NB^S Stewart,D. B. and D. von Limbach (1967)Thermal expansionof Technical Note 854, U.S. Department of Commerce, Washing- low and high albite. Am. Mineral , 52, 389-413. ton. - and T. L. Wright (1974) Allsi order and symmerry of Kroll, H. and H. U. Bambauer(1971) The displacivetransforma- natural alkali feldspars, and the relationship of strained cell tion of (K,Na,Ca) feldspars. Neues Jahrb. Mineral,, Monatsh., parameters to bulk composition. Bull. Soc. fr. Mineral. Cristal- 413-416. logr., 97, 356-377 . Kuellmer, F. J. (1954) Ceologic Section of the Black Range at Tullis, J. ( 1975) Elastic strain effectsin coherent perthitic feldspars Kingston, New Mexico. New Mexico Bur. Mines Bull. 33. Contrib. Mineral. Petrol., 49, 83-91. Luth, W. C., R. F. Martin and P. M. Fenn (1974) Peralkaline Yund, R. A. (1974)Coherent exsolution in the alkali feldspars.In alkafi feldsparsolvi. In W. S. MacKenzie and J. Zussman,Eds., A. W. Hoffmann, B. J. Giletti, H. S. Yoder, Jr. and R. A. Yund, The Feldspars,p. 297-312. Manchester University Press, Man- Eds., GeochemicalTransport and Kinetics, p. 173-183.Academic chester, England. Press.New York. - and F. Querol-Sufr6 (1970) An alkali feldspar series.Coz- trib. Mineral. Petol., 25,254O. Ohashi, Y. and L. W. Finger (1973)Lattice deformationsin feld- Manuscript receiued, Nouember 28, 1977; accepted spars. Carnegie Inst. Wash. Year Book,72, 569-573. for publication, April ll,1978.