The Anorthoclase Structures: the Effects of Temperature And
American Mineralogist, Volume 67, pages 975-996, 1982
The anorthoclasestructures: the effectsof temperature and composition
GBoncn, E. Henlow
Department of Mineral Sciences American Museum of Natural History New York, New York 10024
Abstract
Cell-parameterand structurerefinements using single-crystal X-ray difraction havebeen carried out on three natural low-Ca anorthoclases(K-analbites)' (Or:z.sAboouAno s, Or223Ab7s.3An6 e, Or133Abs3 7An2 5), at room temperatureand at temperaturesabove the triclinic/monoclinic symmetry inversion (400', 510", and 750"C, respectively). Room temperaturecell parametersare consistentwith monoclinicSi,Al topochemistryand a high degreeof disorder (tr : 0.50 to 0.52 from the b-c plot). A room-temperatureinversion compositionof 0136is extrapolatedfrom cos2a*and T-O-T angleplots. Mean M-O bond lengths and T-O-T angles increasewith potassium content, whereas their variances decrease,indicating a trend to more regular coordination, as in sanidine. A similar relationshipdevelops with thermal expansionand the structuralchanges associated with inversion to monoclinic symmetry, but the individual (M-O) values suggest a non- isotropic, ellipsoidal expansionof Na-rich alkali cavities. Examination of dimensional changein the structuresdue to changein temperatureand alkali compositionindicates that most of the effectis relatedto changein M-O bonding,with the aluminosilicateframework respondingpassively. Anisotropic thermal modelsfor singleM sitesproduce non-positive definiteellipsoids. Modeling with isotropic split-sitesyields four parts for the more sodic structures,essentially identical to the models for high albite or analbite. For the more potassiccrystals, a separateisotropic K site and an anisotropicNa(Ca) site is indicated.
Introduction Wainwright, unpublished,see Smith, 1974:'Ptewitt et al..1976;Winter andGhose, 1977;Winter et al., Thereis much interestin characterizingthe varia- 1979).which are all triclinic (Cl) at room tempera- tion in the feldsparstructures because of the abun- ture, have shownthat they only becomemonoclinic dance and importance of feldspars in petrologic (monalbite, CLlm) upon rapid heating through a processesand becauseof their generalsignificance displacive transformation when the Na-feldspar is in mineralogicalstudies of exsolutionand polymor- very highly to fully disorderedand has monoclinic phism,especially order-disorder. The structuresof Si,Al topochemistry.Disordered Na-feldsparwith disorderedalkali feldsparswith near end-member triclinic Si,Al topochemistryis termed high albite compositionshave been widely studied.Sanidine, a whereasNa-feldspar that has monoclinic Si,Al to- monoclinic (CZlm) hiph-temperature modification pochemistry but a triclinic morphology (i.e., at of K-feldspar, has been examined at 23'C with temperaturesbelow the displacivetransformation) neutrondiffraction (Brown et al., 19'14)and at23", is termed analbite.These studieshave also indicat- 400'and 800' C with X-ray diffraction (Ribbe, 1963; ed the possibilityof positionaldisorder of the alkali Weitz, 1972;Phillips and Ribbe, 1973a;Ohashi and cation(M) site in the collapsedand elongatedcavity Finger, 1974,1975:'Dal Negro et a|.,1978).These at room temperature and have characterized the studieshave shown that sanidinemay have varying nature of the expansionor inflation of the M-site degreesof Si,Al disorderconsistent with the mono- cavity upon rapid heating. clinic symmetry(monoclinic Si,Al topochemistries) Less is known about the structuresof disordered and have elucidated the nature of the irregular alkali feldsparswith intermediatecomposition' An- coordinationof the alkali cation. Similarly, studies orthoclases,one of the most abundant naturally- of disordered Na feldspars (Ribbe et al., 1969; occurring alkali feldspars of this type, are recog- 0003-m4)v82l09I 0-0975$02. 00 975 HARLOW : ANORTHOCLASE STRUCTT]RES
nized by petrographersby their volcanic associa- A structural study has been completedon three tion, rhombic shape and fine polysynthetic, often natural low-Ca (less than Anls) anorthoclase(K- cross-hatched("tartan") twinning. In terms of analbite) samplesat room temperature and at tem- Si,Al order they may occur as topochemicallytri- peraturesat which the crystals are monoclinic (from clinic K,Ca-high albite, topochemicallymonoclinic 400'to 750"C. The resultsof this study are reported K,Ca-analbite or a cryptoperthitic intergrowth of in two parts. This first part treats the features of the Na-sanidine and K,Ca-analbite or K,Ca-high al- crystal structure and cell geometry related to varia- bite. Thoughthere are someproblems with compo- tions in alkali chemistry and temperature. The sitionalcriteria (De Pieri et al.,1977), the composi- secondpart dealswith Si,Al order and the specific tional limits of anorthoclasesare as indicated in nature of apparent thermal motion. Figure I (adaptedfrom Kroll and Bambauer,lggl). Included are cryptoperthites in which the heated Materials and methods phase assemblagesconsist of monoclinic feldspars Specimensof anorthoclasewere provided by W. or a singlehomogenized monoclinic feldspar. Only S. MacKenzieand the National Museumof Natural one published refinement of an anorthoclase is History of the SmithsonianInstitution. Specimens available(De Pieri and Quareni,1973),but as it was from three localities were selected: Grande Cal- refinedfrom film data, the precision is not compara- deira, Azores, Or32.5Ab66.7Anq.s(fragments from ble to that of other refinementson disorderedalkali lavas, #15 of Carmichaeland MacKenzie, 1964); feldspars. Thus we do not have the information Mt. Gibele, Pantelleria Islands, Italy, Orzz-t about disordered Na-rich alkali feldspar structures Ab7s.sAn6.e(loose phenocrysts , #12 of Carmichael neededto make comparisonswith the near end- and MacKenzie,1964); and Kakanui, New Zealand,, member composition structures, or to allow the Or13.sAb33.7An2.5(asxenocrysts in Deborahvolcan- desirablethermodynamic calculations of their equa- ic sequence,NMNH #133868,see Dickey, 1968). tions of state(c/. Thompsonet al., 1974). The most K-rich anorthoclasewas a cryptoperthite
Ab59Or59 Sonidines
Ab5OOr OO
A bTgOr3p Two feldspors
Abgg0r2t Anorthoclose-s
Ab99Or19
logioclos e s
An Ab AbggAn;o AbggAnzo AbToAn3o AbsoAn4o AbroAn5g Fig. l. The phase diagram in the Na-feldspar corner of the feldspar composition triangle: solid lines with temperatures("C) indicate the approximatepoint at which K,Ca-analbites become monoclinic (after Fig. 8, Kroll and Bambauer, lgEl). Samplesexamined in this study are shown by circles. Compositions are in mole percent. HARLOW : ANORTHOCLASE STRUCTURES 977 consistingof a monoclinic K-rich phase (Na-sani- Table 2. Electron microprobe analyses phase (K- dine) and a twinned triclinic Na-rich Grande analbite). Fragmentsof the cryptoperthitic material |,/'r.% Caldeira Mt. Gibele Kakanu i were placedin a platinum capsuleand heatedin an Cao 0.17 1q 0.53 0.79 Ktl 5.9 2.5 2.05 electric furnace at 700"C, within the stability field na20 7,9 8.2 9.9 9.44 of single alkali feldspar (cf. Luth et al., 1974),for Ti02 0.09 Fe203 0.43 0.17 minor approximately24 hours to homogenizethe sample. 51U2 00.O 65.7 65.4 67.4 SubsequentX-ray reexaminationconfirmed the ho- Al2b3 18.6 19.5 20.4 -+20.1 e8.9 99.88' mogenization,and suitable crystals were then se- Total 99.6 98.8 Cationsper lectedfor structureanalysis. 8 oxygen atoms The samplesselected for intensity data collection Ca 0.008 0.069 0.026 0.04 K 0.314 0.224 0.141 0.12 were cleavage fragments, generally bounded by Na 0.686 0.710 0.85n 0.81 (001),(010), and (201) or (100).Approximate dimen- Subtotal 1.028 I .003 7.O230.97 sions of the fragmentsused are given in Table 1. Ti 0.003 (Table Fe 0.014 0.006 The chemicalcomposition of the specimens Si 2.994 t aq2 2.9272.97 2) was determinedwith an ARL-EMXelectron micro- AI 0.987 1.036 7.077 1.05 qq probeusing the datareduction method of Benceand Total 5.023 4.994 ( n?? 4 Albee (1968)with the factors of Albee and Ray Fel dspar component(mol.%) (1970).No inhomogeneitiesor Sr or Ba were detect- 0r r2.5 13.8 72.7 ed in the samples. Ab 66.7 70.8 83.7 84.0 An 0.8 6.9 tq io The furnacesused for the high-temperatureX-ray sj:R* 3.02 3.05 2.77 2.94 1.04 examination(one for the precessioncamera and one RZ0g 1.01 7.O7 1.02 for the diffractometer) are a modification of the r Dickey ( 1968) * n is ii,. totit of Fe+3and Al+3; R203is normalized designof Brown et al. (1973)that allow for easier to the anorthite content to examinepossible non- stoichiometryof the feldsPar
Table l. Structure refinement information and sample sizes furnacealignment. For a completedescription see Grande Caldeira Mt. Gibele Kakanui Harlow (1977). Crystals selected for high-temperature study RoomTemperature: Reflections col lected 2026 1846 3002 were cementedto silica-glassfibers. Encapsulation Initial unrejected 2003 1822 2460 in silica-glasscapillaries was not deemednecessary Final unrejected I 834 1697 2141 Rwisotropic 0.061 0.090 0.107 becausethere was no iron in the samplesto cause Ru isotropic 0.080 0.097 0.1t8 problems, and becausethe highest tem- Rwanisotropic 0.035 0.041 0.052 oxidation Ru anisotropic 0.046 0.047 0.058 peratures were to be below 800'C, judged low enough not to cause alkali sublimation. For tem- High Temperature(CI): 4000 5t00 7500 peraturesbelow 400"C, Dupont NR-15082polyim- Reflections collected 2030 I 403 2039 ide binder solution(supplied courtesy E. I. Dupont Initial unrejected .167t2016 2002 Final unrejected 1752 de Nemours & Co.) was used. For temperaturesof Rw isotropic 0.1l1 0.096 Ru isotropic 0.138 0.1l9 400' C or greater,the clear cementin Ceramabond Rwanisotropic 0.062 0.063 503 High-TemperatureAdhesive (Aremco Prod- Ru anisotropic 0.074 0.074 ucts. Inc.) was used. No diffraction contribution from the cementswas noticed. High Temperature (C2/n): 4ooo 5100 7500 Initial unrejected I 050 I 044 I 043 The temperature of the displacive monoclinic/ Final unrejected 855 931 899 triclinic inversion for the feldsparswas estimated Rwisotropic 0.077 0.062 0.067 Ru isotropic 0.127 0.089 0.085 by examiningX-ray precessionphotographs taken Rwanisotropic 0.043 0.043 0.022 at temperaturesup to about 50oabove the estimated Ru anisotropic 0.073 0.047 0.'l05 inversion. Precessionphotographs confirmed that the crystals had attained monoclinic symmetry. Crystal dimensions I 50x I 90x I 60x - in microns 70x I 40x 90x Later the twin angleon a-axis nets 2'(90 a*) was 5U on 80 measuredat several elevated temperatures,and * full triclinic data set not collected inversiontemperatures were estimatedby plotting 97E HARLOW : ANORTHOCLASE STRUCTURES
cos2c*vs. temperature(see Fig.2) as suggestedby from Kp X-radiation or from the other twinned Thompsonet al. (1974).All three crystals selected portion of a crystal. For the Kakanui crystal, which for high-temperaturestructure refinement appeared was intimately twinned with nearly equal volumes to be monoclinicat elevatedtemperatures, howev- in the two orientations,a larger number of reflec- er, the most K-rich, GrandeCaldeira, showed some tions were lost due to overlap. Therefore more streakingof diffraction spots in the directions of the reflections were collected (the half-sphereup to 70" old twin displacementsat temperatures100. above 20), and a computer program was developed to that of the estimated transition. This streaking determinewhich reflectionsmight needto be reject- indicatesthat someresidual strain or dislocationsin ed (seeHarlow, 1977,for details). the crystal existed and prevented all parts from A full triclinic data set was collected at high attainingmonoclinic symmetry. However, this ef- temperature for the following reasons: first, to fect was minor and not consideredso seriousas to compare the intensity of the reflections that are precludestructure analysis. equivalent by monoclinic symmetry (hkl versus Intensity data were collected on an automated ftftl); second, to be able to refine a triclinic structure Picker recs-l single-crystaldiffractometer using and compareit with the requirementsof monoclinic unfiltered MoKa radiation at a 3o take-off angle. symmetry,and third, to gain an increasedaccuracy Orientation of a crystal for data collection was by averaging the equivalent reflections before re- provided by a least-squaresrefinement of 12 man- finementof the monoclinic structure.The tempera- ually centeredreflections, which also yielded initial ture of the diffractometer furnace was set at a value unit cell parameters.Data were collectedin one half approximately50" C above the measuredinversion of the limiting sphereof reciprocal spacefrom 5. to temperature.Scans of the 005 reflectionin the b*- 60' or 70' two theta (0.062 < sing/\ < 0.705 or cx plane (normally by meansof a chi rotation) and 0.809)using the 0-20 scan technique with a scan the 12 reflections used for orientation throtgh 0-20 speedof l'lmin and an approximate 2.4oscan range were made to check for splitting. These two steps (extended for KayKa2 dispersion). Background were repeateduntil no peak splitting was found and countswere measuredfor 20 secondson each side to be surethat the crystalswere no longertwinned, of the peak. Two standardreflections were collect- i.e., were monoclinic.After refiningthe orientation ed every 49 reflections.The total numberof collect- matrix obtained from the 12 reflections, the cell ed intensitiesand initially unrejectedones are listed parameterswere checkedto insure that they were in Table 2. Initial rejection of structure data was monoclinicwithin the error of measurement. basedon evidence of interferencedue to overlap After intensity data were collected,the positions of approximately40 to 50 reflections(sinO/), = 0.34) were measuredand the values were entered in a modifiedversion of Burnham's(1962) LCLSe (attice cell least squares)refinement program. The results are given in Table 3. The crystals were reexaminedwith the preces- Kokonui sion techniqueafter data collection at high tempera- tures was completed.In all three casesthe number oo 20 of twin-related orientations and the relative propor- * Mt.Gibele tions of twin orientationsthat had originally existed 6 N changedsignificantly. The changewas most marked
O for the GrandeCaldeira crystal, which showsbeau- tiful M-type twinning that accordingto Laves (1950) can only be causedby Gronde a transformationfrom mono- o clinic to triclinic symmetry. Becausethe highest temperature that any crystal experienced between ,',t." \13' \,.es' the two precessionexaminations was that at which o 200 400 600 800 T"C the intensity data were collected,the crystalsmust Fig. 2. Plot of cos2ax for each anorthoclase (K-analbite) have been monoclinic during data collection. The against temperature. Lines are fit by least squares; inversion intensity data were corrected for background, temperatures(intercept) are shown. scaledto a uniform level relative to standardreflec- HARLOW : AN ORTHOC LA SE STRUCTURES 979
Table 3. Cell parameters
^3 lo r (o) T (oC) a (E) b (fi) c (fl) (o ) B (o) V(A) o* Y* (o) " GrandeCaldeira 0r 32,5 23o Cl 8.290(2) I 2.966(3) 7.r5r(2) er.rB(2) il6.3r(r) e0.14(2) 688.8(3)88.62(2) 8e.26(2) rB3oci B.3to8(B)12.s7zs(s) 7.r578(6)90.007(5)il6.r87(5)eo.o33(6)6e2.s(r) Be.e76(5)Be.e6o(6) 4ooo!2/m 8.3482(7)r2.98oo(7) 7.r582(5)90.0 il6.roe(5)e0.o 6e6.5(r) 90.0 90.0 Mt. Gibele 0r 22.3 23o C] 8.252(2) 12.936(2) 7.13e(r)e2.r1(r) 1r6.32(r) e0.22(1) 682.4(2)87.54(r) BB.7r(r ) 38BocT 8.290(4) 12.954(307 r6n{?\ e0.75(2) il6.r8(2) e0.35(2) 68e.r(6) 89.34(2) Be.eB(2) 51OoCz/n 8.314(r\ 12.973(2) 7.rso(r)90.0 il6.r35(8)eo.o 6e2.4(2)90.0 90.0 Kakanui0r l3.B z3o cT B.zr 68(6) rz.s166(t) 7.1270(5)e2.754(4)r6.357(4)e0.23e(5)676.7(1) 86.808(4)88.367(5) 7000Cz/n B.3ll(l ) 12.972(2)7.r48(r) 90.0 il 6.07r(7 ) e0.0 692.2(2)90.0 90.0 75OoCz/m 8.321(2) 12.969(2) 7.148(r) 90.0 il6.05(r) 90.o 693.0(3)90.0 90.0
Estimatedstandard deviations in parenthesesrefer to the last diqits tion intensities,and correctedfor Lorentz-polariza- final anisotropic refinements were used in most tion effects.No absorptionor extinctioncorrections evaluationsof structural parametersand are listed were applied as all crystals had maximum dimen- in Table 4. Alarge anisotropyfor the M-site tem- sionsless than 0.2 mm and linear absorptioncoeffi- peraturefactor was expected(e.g., Ribbe et al., cients(g.) less than 11cm-r. 1969),but in fact all room-temperaturerefinements The structure factors were entered in L. W. produced M-sites with non-positive-definiteellip- Finger's RFINEII (GeophysicalLaboratory) full- soids(one ellipsoiddisplacement was imaginary)of matrix least-squaresrefinement program. Relativis- apparentvibration. Consequently,and to be con- tic Dirac-Slater X-ray scattering factors (Cromer sistent with refinementsof high albite and monal- andWaber, 1965)for neutralatoms were employed. bite (Ribbeet al.,1969:,Prewitt et al.,1976;Winter Occupanciesof Na, K, and Ca in the alkali cation et al., 1979),the M-site was refined with various (M) site were basedon atomic proportions. Tetra- modelsusing partial atoms on multiple sites.These hedrallycoordinated cation (T) siteswere assumed partial-atomsites will be called subsitesand denot- to be completelydisordered so that the Al and Si ed by subscriptnotation , e.9., M1 andM2. All such occupanciesin each T site were evaluatedas (1 + refinementsuse isotropic partial atoms except the X"")14and (3 - Xu)14, respectively(where X"" is "split-species" models (see discussion)because the mole fraction of CaAl2Si2Osin the crystal). anisotropictreatments of the subsitesusually devel- Each observed structure factor was weighted for op very large correlations among the supposedly refinementas llo where o is the standarddeviation independentparameters and will not converge in of For, basedon counting statistics.For the mono- refinement. For the latter configuration, the se- clinic refinementsthe averageof Fou.was set as the quence of refinement steps was to increase the larger of two estimates of the variance of the number of independentparameters, refining first sampling,one calculatedincluding counting statis- the positionsof the subsites,holding isotropic tem- tics and the other calculatedstrictly from the sam- peraturefactors (B) constant, then a common B, pling. Reflectionsfor which Fo6. was zero or less then independentB's, and finally the constrained than three sigma of the background intensity were occupanciesof the subsites (the amount of the treatedas unobserved. averageM-site atom on each site). These steps in The triclinic least-squaresrefinements were car- the refinementof a model with a given number of ried out in the normal fashion starting with values subsiteswere followed until that model would not from the refinementof a high albite by Wainwright convergein the least-squarestreatment. The num- (unpublished,see Smith, p. 86, 1974);resulting R ber of subsiteswas sequentiallyincreased from two factors are listed in Table 1 The results from the to three to four, etc., for each structure, until an 980 HARLOW : ANORTHOC LASE STRUCTURES
Table 4. Positional and thermal parameters
GrandeCaldeira 230 B x 104 X B1t Bzz Bl: srz Bts Bzl T1o 0.0085( I ) 0.1i53(1) 0.2207(r) s6(2) 17(1) 51(2) -4(1) 28(1) o(1) Tlm 0.0069(1) 0.8180(1) 0.2252(1) s3JJ ( 2Z ),, 15(1) 51(2) 7(L) 26(r) 2(r) t2u 0.69s4(1) 0.1140(1) 0.33s4(1) s1(2) 11(1) 65(2) 0(1) z6(L) 2(1) T2n 0.6941(1) 0.881s(1) 0.3465(1) s4(2) 1r(1) 63(2) 3(1) 27(r) 1(1) M 0.2750(2) 0.0013(1 ) 0.1366(2) -1.4(2) 65(1) 13e(s) 2(r) -7(3) -52(2) on1 0.0016(3) 0.1388(2) 0.9947(3) 124(5) 30(2) s7(6) 612) 61(s) 4(2) onz 0.6056(3) 0.9e72(2) 0.2828(4) 86(5) 18(1 ) 124(6) r(2) 32(4) 2(2) oao 0.8233(3) 0.121e (2) 0.2180(4) 41(2) 158(7) -10(2) 75(5) 5(3) oBm 0.8227(3) 0.8574(2) 0.2329(4) o4rq 3e(2) 151(7) 11(2) 71(5) -2(3) oco 0.0233(3) 0.3012(2) 0.2618(4) 88(4 22(t) 122(6) -3(2) 44(4) -3(2) 0am 0.0241(3) 0.6916(2) 0.2421.(4) 84(4 20(1) 118(6) 3(2) 30(4) 4(2) oDo 0.18e7(3) 0.1204(2) 0.4004(3 ) e0(s) 25(r) 87(6) 6(2) 23(4) 8(2) oDm 0.1883(3) 0.872s(2) 0.4r2s(4) 86(5) 27(1) es(s) -3(2) 22(4) -7(2) GrandeCaldeira 4000 106(3) -8(2) 76(3) -2(2) 124(4) -2(2) i5(3) -1(2) 334(r7) 0 87(e) 0 e8(11) 0 e6(e ) U Le4( 20) 0 8e(14) 0 290(14) -o(/, lse(e) rr(e) 280(16) -12(6) 136(11) -1.4(7) 20s(r2) 15(6) 82(8) L6(7) Mt. Gibele230 Tr0 0.008s(1) 0.1711(1) 0.2185(2) 85(2 ) 1e(1) 69(2 ) 0(1) 47(2) 5(1) T1m 0.0060(1) 0.8r64(i) 0.227 r(2) 82(2) 16(r) 66(2) 11(i) 44(2) 8( I ) Tz0 0.6e33(1) 0.1115(1) 0.328e(2) 80(2) 13(r) 84(2) 5(1) 44(2) 5(1) Tzn 0.6904(l) 0.8ie8(1) 0.3496(i ) 84(2) 13(1) 8r(2) 7(r) 4s(2) 6(i) M 0.2743(2) 0.0033(2 ) 0.13s3(3) 0(3) 74(2) 167(b) 7(2) -3(3) -er(z) Ont 0.0033(4) 0.737 7 (2 0.9e07(4) 150(6) 3s( 2 ) 10s(i) 12(3) i6(6) 12(3) 0nz 0.5ee4(4) 0.994s(2 0.2802(4) rrl(o., re(1) 138(7) 5(2) 52(5) 8(3) 0s0 0.8219(4) 0.1194 (2 0.2092(4) 128(6) 44(2) 177 (8) 1(3) e6(6) 11(3) OBm 0.8212(4) 0.8s3i(2 0.2381(4) 117(6) 44(2) 1i1(8) 14(3 ) 87(6) 4(3) 0c0 0.0207(4) 0.2964(2 0.2688(4) 11s(6) 27(2) r37(7 ) L(2) 63(5) -l(3) Ocm 0.0227(4) 0.6899(2 0.23r2(4) 116(6) 24(2) r28(7) s(2) 44(5) 6(3) 000 0.1e16(4) 0.1171(2 0.3943(4) 126(6) 2s(2) 105(7) e(2) 44(5 ) 11(3 ) ODm 0.1881(4) 0.8701(2 0.4191(4) rro(o,l tol2\ 115(7) 5(2) 38(5) 1(3) Mt. G'ibele 510o T1 0.0081(1) 0.17s2(1) 0.2236(2) e3(2) 28(1) s2(2) -s(i) 4e(2) -2(t) I2 0.6967(1) 0.1164(r) 0.3422(2) 87(2) 21(1) lrr(2) -3(2) 47(2) -2(1) M 0.2780(3) 0.0 0. t372(4) 60(5) 106(3) zer(e ) 0 48(6) 0 ont 0.0 0.13e1(3) 0.0 202(9 ) 12e(e ) 0 s6(8) 0 0az 0.6084(5) 0.0 0.2842(6) 123(8) 28(2) 21e(11) 0 s1(8) 0 0s 0.8230(4) 0.r361(2) 0.2242(5) 14s(6) 70(2) 282(9) -25(3) 13e(6) -6(4) 06 0.0256(4) 0.3044(2) 0.2528(s) 148(6 ) 35(2) 250(8) -1s(3) 86(6) -7(3) 0e 0.i877(4) 0.r24t(2) 0.4063(4) 153(6) 56(2) rs3(7) 1o(3) 35(5) le(3) Kakanui230 Tto 0.0087(1 0.1686(1 0.2168(1) 47(1) 1e(1) 73(2) -5(1) 2s(1) -4(1) Tlm 0.0054(1 0.8153(1 o.227 5 (r) 44(1) 18(1) 68(2) 3(1) 27(r) -2(r) Tzo 0.6923(1 0.109e(1 0.3256(i)0.3256(i 44( i ) 14(1 ) 82(2) -2(r) 25(r) -2(r) rzn 0.6886 (I 0.8789(1 0.3s14(1 4s(1) 15(1) 83(2) 0(1) 28(1) -2(1) M u.zt+J\z 0.0051(2 0.1350(3 -16(3) 11s(3) 227(6) 5(2) -21.(3) -144(3) onl 0.0045(4 0.136s(2 0.9881(4 I I ?/E\ 33(2) 1r7(6) 0(2) 63(s) -3(2) onz 0.5969(3 0.9925(2 0.28r8(4 7s(41 23(2) 118(6) -3(2) 34(4) 4(2) oeo 0 .8220( 4 0.114s(2 0.20s1(4 e0(s) 36(2) 164(7) -10(2) 74(5) -4(3) 0nm 0.8203(4) 0.8499(3 0.2422(4 81(s) 4s(2) 16e(7 ) 6(2) 72(5) -r0(3) o;o 0.0188(3) 0.2e40(2 0.2724(4 77(4) 24(2) 158(7) -6(2) 50(4) -s(2) 0cm 0.022s(3) 0.6882(2 0.2267 (4 t7(4) 27(2) 107(6) 6(2) 2).(4) 3(2) o;o o.re32(3) 0.1146(2 0.3e11(4) 80(4) 2s(2) 102(6) 4(2) 2o(4) 4(2) oDm 0.1882(4) 0.8685(2 0.4232(4) 76(4) 34(2) 10e(b) -4(2) 11(4) 15(2) Kakanui7500 T1 0.0089(3 ) 0.1796(2) 0.2240(3) 144(3) 54( 1) r63(4) -11(2) 88(z) -2(2) 0.6972(2) 0.1170(2) 0.3437(21 r21(2) 45(1) 202(4) -3(2) 81(2) -1(t) M 0.2839(7) 0.0 0.1496(10) 126(8) 247(12) 61s(28) 0 70(r3 ) 0 onl 0.0 0.1378(8) 0.0 327(11) 83( 7) 263(13) U 1s1(10) 0 0M 0.6115(9) 0.0 0.28s8(16) r45,(16) 55(5) 508(34 ) 0 14(18) 0 0g 0.8282(5) 0.1382(7) 0.2288(7) 2',|1/o\ 123(7 ) 407(16) -31( e) 202(10) i8(13) 06 0.0320(5) 0.3030(5) 0.2563(e) 251(11) 64(4) 397(18) -30(7) 150(1r) -6(e) 09 0.1850(s) u,rzf,rIoJ 0.4121(s) 266(12) 84(5) 267(r4) 23(8) 106(8) 1e(10) Estimated standard devjations in parenthesesrefer to last diqits HARLOW : ANORTHOCLAS E STRUCTURES 981 improvementwas seenover the anisotropicmodel Table 5. Ellipsoidsof thermalexpansion strain or until the subsitemodel failed to converge.The i unit strain Angleto resultsfor thesefinal stepsin M-site model refine- (/oc or /Or%) +a +b +C mentsare listed in Table 5. l) r 8.5(l) E-s 8r.2(3) 48.4(6) ss.o(s) Essentiallythe same three steps were followed Grande 2 1.4(2)E-s 8.e(8) e6.s(e) I 21.6(5) -O. Caldeirg J O[ | ,l L-J 88.8(7) 42.5(5) r2e.t(4) for the three high-temperature structure refine- ZJ - IOJ v 3.4(3)E-5 mentsexcept that initially the triclinic Fo6"data sets 2\ r 2.4(r) E-5 22(2) 86(r) e5(2) wererefined in spacegroup Cl to test the consisten- Grande 2 2.5(6) E-6 e8(2) ll (6) 80(60 Caldei ra J u.u(o, r-o lro(2) r00(6) 1r(6) cy of the data with monoclinic symmetry. The I 83o-4ooo v 2.i(r) E-5 starting parameterswere those of the room-tem- 3) r 6.7(l)E-s 82(r) 47.6(7) 5s.8(6) perature refinements for the same crystal and the Mt. Gibele 2 1.2(2)E-5 8(r) e6(r) r21.8(3) 23o -388o 3 -5.2(r) E-5 e0.r (7) 42.s(6) 12e.6(s) resulting triclinic structures were consistent with u 2.7(4)E-s monoclinicsymmetry within the estimatederrors of 4) r 2.6(8)E-5 27(6) e0 89(6) all refined parametersexcept for anisotropicther- Mt. Gibele 2 s.7(3)E-6 90 090 mal parameters.Thus the datawere averagedinto a 388o-51oo 3 -0.3(5)E-5 116(6) 90 r (6) v 3.e(r)E-5 monoclinicset. No attempt was madein any of the ql least-squaresprocedures l 5.r6(3)E-5 78.6(4) c6. | \z ) Jt .6\z ) to refine on the Si,Al Kakanui 2 r.5o(3)E-s lr.7(4) oq R1?\ 1)1 Al2\ occupancyof the T sites. At various stagesof the 23o- Tooo 3 -3.30(2)E-5 87.3(r) 42.6(r) r3r.4(r) refinementof the M-site models,difference Fourier v 3.36(5)E-5 sectionswere made of the M-site region parallel to o., r 3.0(6)E-5 22(2) 90 95(2) Kakanui 2 -0.0(4)E-s 112(2) eo 5(2) the b-c plane to evaluate the quality of the fit. Tooo- 7 5oo 3 -0.4(3)E-5 e0 090 Interatomicdistances and anglesand root-mean- v 2.5(8)E-5 square displacementsfor thermal-ellipsoidalaxes 7') r 1.0(3)E-4 7s(2) 4e(r) s8(l) Kakanui- 2 4.s(3)E-4 12(2) l o0(2) 121(2) were calculatedin the RFrNEII program.Estimated Mt. Gibele 3 -5.2(2)E-4 86.6(4) 42.7(6) r3r .8(5) errors for these structural parameterswere calculat- z3o v e.8(5)E-4 ed with Finger's ERRoR. 8) r lr.8(2)E-4 82.0(e) 46.4(8) 30.6(OJ - 1t1 2l r,\ Mt. Gibele 2 4.3(3)E-4 8(t) e6(r) 'l?l Grande 3 -6.e(2 ) E-4 89.5(8) 44.3(7) 1/61 Resultsand discussion Caldei ra v 9.2(s)E-4 ^^O .J Lattice parameters o\ q?r?\ 1 7.4(9)'t.7 E-4 22(3) 90 Mt. Gibele 2 (4) E-4 90 0 90 Cell parametersfor the three anorthoclasespeci- 388o - 3 r.4(7)E-4 il2(3) 90 q/?) Grande v l.r(r) E-3 mens at 23' C and at elevated temperaturesare Caldeira4000 listed in Table 3 and are plotted in Figures 3 and 4. * E-n+xlo-n The room-temperaturecell dimensionsare consist- + 1, 2, 3 are the maximum,intermediate, and minimum ent with alkali feldspars having nearly complere ellipsoid axes and V is the volumetrjccomponent Estinated standard deviations in Darenthesisrefer to Si,Al disorder.The valueslie closeto lines connect- last diqits ing analbite and high sanidineon the a*-y* and b-c plots. The a*-y* relations indicate the difference in Al contentof the Tr sites(t10-t1m; Al in T10minus values of tr0-t1m to approach zero as these feld- Al in Trm), which is a measureof topochemical sparsbecome optically (Grande Caldeira and Mt. triclinicity, whereasthe b-c plot indicatesthe total Gibele by Carmichaeland MacKenzie, 1964)and Al content in the T1 sites (either trO + trm for dimensionallymonoclinic at elevatedtemperatures. triclinic structuresor t1 for monoclinicones). Mac- The results from the least-squarescell parameter Kenzie and Smith (1962) found that in ordered refinementssupport the conclusion of monoclinic albiticplagioclases an increasein An contentcauses symmetry and consequentmonoclinic Si,Al topo- an effect similar to an increasein disorder. On the chemistry. basisof the limited work on ternary feldsparslike It is common for perthitic intergrowths of alkali anorthoclases(Hakli, 1960;Carmichael and Mac- feldspar containing coherent composites of two Kenzie, 1964;Boudette and Ford, 1966;Kroll and phasesto have "anomalous" valuesof a, measured Bambauer,1981), the useof cell-parameterplots for in Aa (: 4obs- 4ss1eS€o Stewart and Wright, 1974; evaluatingSi,Al order appearsvalid for the samples Stewart, 1975).None of the anorthoclasesexam- under investigation. It is natural to expect the ined in this study show Aa values greater than 982 HARLOW : ANORTHOC LASE STRUCTURES
7.22
7.21
7.20 tto + trm
7.t9
7.t8
7.t7 Low olbite
7.r6
7. t5
\Gronde 7.14 a" Coldeiro
7.t3 Kokonui
7.12
7.ll
t2.78 12.80 12.82 |2A4 12.86 12.8 t2.90 t2.92 t2.94 t2.96 12.98 t3.OO t5.o2 t3.O4 b,A Fig. 3. The b-c plot, after Stewartand Wright (1974),for room-and high-temperaturedata (see text); contours from 8. 15to 8.60are for the a cell edge; contours from 0.50 to 0.65 are for trO + I rm (the Al occupanciesof the Tr0 and T1m sites). Heating producesan effect similar to that of an increase in K-feldspar content--{isplacement to the upper right, parallel to lines of constant structural state.
0.014 whereasa minimum value of 0.05 is consid- Brown, 1969)is also included.A linear relationship ered sufficientto indicate strain. is expected for alkali feldspars having the same The overall effect of rapid increasein tempera- degreeof monoclinicdisorder or the sameequilibri- ture on cell dimension (within the limits of the um temperature, as shown by Kroll et al. (1980). experiment,i.e., T < 800) appearsto be the same Such an approximation for these three anortho- as an increasein Or content of a feldsparassuming clasesis reasonablebased on the b-c plot (Fig. 3), Si,Al order is constant. This result is consistent and thus a least squaresline was fit to the points. with the results of Grundy and Brown (1969)and The extrapolation of this line to zero predicts a Kroll er a/. (1980). compositionof 0136for the displaciveinversion at An estimateof the compositionfor the displacive room-temperature.This value compareswell with triclinic/monoclinic inversion (Or disp) at room the valuesof 0136of MacKenzie (1952)and Or3a-36 temperature has been made by plotting cos2a (at of Bambaueret al. (1978),Hovis (1980)and Kroll et room temperature)ys. Or content in Figure 5. A a/. (1980). value for an analbite (F9132 from Grundv and The relationship between alkali chemistry and HARLOW : AN ORTHOCLAS E STRUCTU RES 983
Ioringm m icroclino 92
tro- trm
9l
Lor -(*,o
90 Monoclinic fc ldrpor
Gronde Coldoiro 89
It. Gib.l.
Kolonui
88
86 87 88 l9 90 *: ,( Fig. 4. The a*-7x plot, after Stewartand Wright (1974),used as a measureof triclinic Si,Al order.Room-temperature values for the anorthoclasesexamined in this study are shown by circles and indicate good agreementwith a topochemically monoclinic Si,Al distributionas representedby the line connectinganalbite with monoclinicfeldspar.
cell parameters at the transition temperature has be unique"transition" valuesof cell parametersfor beenestimated by interpolatingbetween the values highly disorderedalkali feldspars.Cooling or high at higherand lower temperaturesin order to evalu- pressureexperiments would yield actualdetermina- ate possiblelimits to the cell parametervalues of tion of theselimits for more potassicfeldspars. The highly disorderedmonoclinic alkali feldspars.The coolingexperiment on a high sanidineby Grove and linear slopes are nearly flat for transition values, Hazen (1974)has not come close to the transition and for a pure K-feldspar estimated values are values. Hazen (1976),on the other hand, did suc- between690 and 69543for the cell volume, 8.30and ceedin reachingthe inversionat high pressures:18 8.354 for a andT.llAfor c. The value of b is nearlv kbar for Ors2and 12 kbar at 0167with values very constantat about l2.g7l with perhapsa slighi closeto thoseindicated by the measurementshere. decreasewith increasingOr content.There seemto Hence, as suggestedby Hazen (1977),there does 984 HARLOW : ANORTHOCLASE STRUCTURES
betweenKakanui and the other two crystals. The ( Anolbiteof GrundyB Brown 1969) results on thermal expansion are virtually identical to those for two synthetic disordered alkali feld- spars(Or1e and Or3s)studied by Henderson(1979). Calculationof the displacementsbetween the Mt. Gibelecell at 388' C and the GrandeCaldeira cell at 400" yield the same result as heating a crystal Kokonu i C oo above the transition temperature, even after taking 20 into account the small difference in temperature.
6 N Crystal structure Mt.Gibele o Discussion of the anorthoclase (K-analbite) structure in this section is restricted to structural Gronde features that show correlations with changes in Coldeiro alkali chemistry and/or temperature. These are M- \,'0,"0 O bond lengths, T-O-T interatomic angles, and OL 36 40 overall and M-cation apparent thermal motion. Mol. oer cenl Or Hence, somerelations which appearto be mainly a Fig. 5. Plot of cos2a at room temperature for the three consequenceof a changefrom triclinic to monoclin- anorthoclases(K-analbites) and analbite (F9/32, Grundy and ic crystal symmetry are ignored here. Brown, 1969) against Or content. Least squares linear fit M-O bonding. The alkali cation to oxygen bond- indicatesa transition composition of 0136. ing is the structural feature most correlated with triclinicity and the degree of the expansion of the appear to be a particular structure configuration at framework structure. In triclinic alkali feldspars the displacivetransition which is directly relatedto coordinationabout the M site is very irregular,with unit cell geometry. nine nearestneighbor oxygen atoms within l.SA. The changein cell dimensionsupon heatingdoes However, only five to seven of these are within not necessarilygive an adequate picture of the 0.4A of the shortestM-O distanceand can thus be thermalexpansion in crystalsthat havelow symme- considered the first coordination sphere. Smith try becausethe directions of maximum and mini- (1974)discusses the M-site relationsfor most feld- mum expansion or strain are not symmetrically sparsin detail. constrainedto lie parallel to lattice translations. In spite of the fact that the averagenature of the Ohashiand Burnham(1973) developed a mathemat- measuredstructure obscures the bondingof individ- ical approach for analyzing small lattice deforma- ual sodiumand potassium(and calcium)atoms and tions in terms of a second-orderthermal strain that the single atom M-site model is evidently tensor. A strain analysis was performed on the unrealistic (to be treated in a later section), the anorthoclasecell refinements using the program variation in M-O bond lengths (Table 6 and Figs. 6 srRArN, (Ohashi and Finger, 1973) in order to and 7) does elucidateseveral features in the struc- examinethe changeswith temperatureand compo- tures. First, as expected, the average M-O dis- sition;the resultsare listed in Table 5. The effectsof tancesincrease with increasingOr contentand with temperatureand of increasingOr content on the increasingtemperature. Second, the varianceof the orientation of the thermal strain ellipsoid at tem- average(M-O) value decreaseswith increasingOr peraturesbelow the monoclinic/triclinic transition content and with increasing temperature for any are almost identical, and are consistent with the particular composition, indicating the increasing results of Ohashi and Finger (1973). Above the geometric regularity of the cavity for an effectively transition temperature, the strain ellipsoid must largerM-site occupant.This increasingregularity is havean axis parallelto the b cell edgenormal to the also demonstratedby the decreasingdifference in (010) mirror plane. The major strain axis rotates the pseudosymmetricallyequivalent bond distance slightly, becoming almost parallel lo a*, whereas pairsfor the room-temperaturestructures (i.e., (M- the other two axes apparentlyvary with composi- Oer0)and (M-Oarc) or (M-Os0) and (M-Oem)). tion: the intermediateand minor axes are reversed Third, with the exceptionof (M-Os), all of the M-O HARLOW : ANORTHOC LASE STRUCTURES 985
Table6. M-O distancesfor both room- and high-temperaturestructures including correctionsfor noncorrelatedthermal motion (in A)
GrandeCaldeira Mt. Gibele Kakanu i 230 4000 230 5l 00 caa 7500 raw noncoff raw n0ncorr raw noncorr raw noncorr raw noncorr raw noncorr M-0A10 2.720(3)2.742 2.782(3) 2.818 2.684(4) 2.7r0 2.750(4) 2.786 2.655(4)2.687 2.775(4)2.8s0 -0A1. 2.728(3)2.748 2.722(4) 2.745 2.722(4)2.75? -onz 2.464(3) 2.490 2.524(4) 2.569 2.414(3) 2.446 2.472(4) 2.51e 2.38e(3)2.432 2.454(4)2.s64 -0s0 2.80e(3) 2.831 2.934(4) 2.968 2.679(3) 2.709 2.930(4) 2.963 2.611(4)2.651 2.982(4)3.043 -0Br 3.050(3) 3.063 3.r12(4) 3.125 3.rse(5)3.170 -0c0 3.203(3)3.21e 3.112(3)3.r45 3.274(4) 3.293 3.r40(4)3.171 3.3r5(5)3.336 3.r58(s)3.218 -Ocr 3.072(3)3.088 3.015(4)3.033 2.969(4)2.99r -000 2.740(3) 2.761 2.882(4) ?.919 2.642(3) 2.672 2.8s2(4) 2.884 2.572(4)2.611 2.e12(4)2.e76 -ODr 2.930(3)2.941 3.0r8(4) 3.o29 3.075(4)3.085
M-0Av 2.857 2.876 2.882 2.932 2,840 2.863 2.869 2.903 2.830 2.857 2.901 2.971 o .228 .224 . I 80 .150 .276 .270 .207 .202 .31I .300 .217 .202
Length 5.980 6.004 5.816 5.886 6.130 6.154 5.783 5.847 6.235 6.255 5.898 6.019
lllidth 4.507 4.550 4.574 4.646 4.443 4.494 4.547 4.621 4.408 4.474 4.577 4.745 = + = Length
bond lengths for high-temperature monoclinic atom. The inflation is ellipsoidal.Although there is structuresincrease with respectto monoclinicaver- enough increase in effective volume of the alkali agesof the room-temperatureresults for non-cor- cavity to expand the K-analbite structures to mono- rected distances(Fig. 7). If bond lengths are cor- clinic symmetryat high temperature,each cavity is rected for apparentthermal motion (both room- and progressivelymore elongate(llto b) and narrow (llto high-temperaturestructures) this relationship is [l00]) with increasingNa content. The cavities are true for all of the M-O distances. Fourth, the not a replica of or comparable to that in sanidine. elongatenarrow alkali cavity becomesshorter along Possible constraints on the inflation geometry, [011] and wider along [100] with increasing Or apart from size, may be the charge and mass of the content. This feature can be seen for the room- M-site occupant,as theseproperties influence pos- temperature data with the aid of Figure 8. The siblethermal vibration. Resultsof M-site modeling, length of the cavity can be defined by the Osm- describedin the following discussion,support this Opm distanceor the almostequivalent (M-Osm) + suggestion.A possiblyunique feature of the M-site (M-Oom), both of which decreasewith increasing coordination in the high-temperature monoclinic Or content. Similarly, the width of the cavity is feldspars is the direction of the M-site bonds. related to (M-OA) + (M-OAr)*cos [/z(OarO-M- Stereographicprojections of the M-site coordina- Oarc)1,which increaseswith increasingOr content. tion for the three crystals are indistinguishablefrom These features can be seen graphically in Figure 8 one another at high temperaturesfor either the nine by following the trends of the M-O values with immediateoxygens or the twelve closest T sites, composition. but are markedly different at room temperature. The effect of increasingtemperature is not simply Most of the thermal effect on cell dimensionsof to inflate the sodium (and calcium) filled cavity thesefeldspar structures can be explainedby short- isotropically to approach the shape of the cavity ening of the M-Osm, M-Oprn, and M-O60 bonds when filled with the larger potassium(or rubidium) and lengtheningof the M-O'O, M-OpO, and M- 986 HARLOW : ANORTHOCLASE STRUCTURES
oco
oBm oDm
3.O
ocm 2.9 v o I 2.8 oAv.
2.7 oAlc
2.6 oaro
2.5 oao ooo
2.4 oaz 2.3 60 70 80 90 too Mol.per cenl. Ab*An Fig. 6. The variationof individual M-O distanceswith composition.The dashedlines representreasonable extrapolations for a room-temepraturetransition to monoclinicsymmetry at Or.u.
O6m bonds. A projectionr of the M-site coordina- viewed down the intermediateaxis of the thermal tion for both the room- and high-temperaturestruc- expansion "strain" ellipsoid, shows the obvious tures (superimposed) of the Kakanui sample, correlationbetween the above-mentionedbond dis- gross the feldspar 'This tances and the expansion of projectionof two structuresupon one anotherrequrres structureon heating(Fig. 9). The interlinkageof the the choice of a joint reference frame. This frame should not be theone chosen by Ohashiand Burnham(1973) for calculatingthe framework tetrahedra causes adjustments in the strain tensor from an arbitrary deformation tensor, because it geometrythat accountfor the slightmisalignment of includesa rotationproduced by constrainingthe c and d axesto the inter-structuresite displacementswith respect be parallel for the two lattices. Consequently,the reference to the cell thermal expansion between the struc- frame chosen for the projection is the one for which the tures.These changes are basicallyrotations offixed deformationtensor relating the two lattices is a symmetric tensor (1979)suggests that the describinga pure strainand no rotation.The amountofrotation sizetetrahedra. Henderson is less than 2'for the crystals examinedhere, but it is still M-Ooz extension with rotation of the framework noticeablein the projectionsif it is not taken into account. structure is chiefly responsiblefor the expansion. HARLOW : ANORTHOCLASE STRUCTURES 9E7
3.O
2.9 oBov. 2.8 oDov. o oo, I ?.7
2.6
2.5
?.4
2.3 60 70 80 90 roo Mol.per cent.Ab + An Fig. 7. M-O distancesversrs compositionfor the high-temperaturestructures (circles and solid lines) and for the monoclinic averagesof the room-temperaturestructure values (squares and dashedlines). Note the generalincrease in M-Oa1, and M-Oa2, which reflect the M-site cavitv width.
Inflation of the cavity is a more accurate cause as equivalentfor monoclinic symmetry k.9., T-OB0- other bonds (M-OD0, M-OB0 and M-O6m) show T vs. T-Osm-T). The difference decreaseswith greaterexpansion. increasingOr content, trending to zero on transition T-O-T angles. The T-O-T angles (Table 7) in to monoclinic symmetry. As in the caseof the cell feldspars are extremely variable and manifest in angle, a graphical examination can be helpful in some degree the compliance of the tetrahedral evaluating the composition of the triclinic/mono- framework to the lattice geometry determined by clinic inversion. The value cos2(AT-O-T), where the overall nature of the feldspar structure, the AT-O-T is the differencebetween pseudosymmetri- degreeof "inflation" from bondingeffects ofalkali cally related T-O-T angles, was plotted against Or atomsin the M-site cavity, and the degreeof Si,Al content in Figure 10 in expectationthat it would order. IncreasingOr content and increasingtem- have the same linear relationshipas expectedfor peratureboth decreasethe variance in the angles cos2a(Thompson et al.,1974). The relationshipfor and increase their average value for a single struc- each of the differencesfor Os, Oc and Op is very ture, which indicates inflation of the structure and closeto linear, extrapolatingto valuesclose to 0136 an approach to the ideal monoclinic feldspar struc- (35.8, 35.3 and 35.1, respectively)for a room- ture (c/. Megaw, 1974).This relation also meansa temperatureinversion, which is consistentwith the decreasein triclinicity for the triclinic structures, estimatebased on cosza. which is evident on comparing the angles that are Apparent thermal motion. The magnitudes of 988 HARLOW : ANORTHOCLASE STRUCTURES
+Mt Mtb
'Tro
Fig. 8. The M-site coordinationfor the Mt. Gibelecrystal (23")projected onto the b-c plane(down a*) with split sites.Note the elongationin the Osm-Opm directionand the distributionofthe subsitesin that direction.O-O tetrahedronedge lines taper to show relativeheight of site in the projectiondirection; higher site is at the wide end of the line.
apparentthermal motion (eitherin terms of equiva- this can be partially improved with an extinction lent isotropic B or root-mean-square(RMS) dis- correction, although such a correction was not placements)for the room-temperaturestructures attempted.Finally, of course,variation in a system- (Table8) are comparableto thosefrom other disor- atic error in each data set (such as absorption)can dered feldspars,except perhapsfor the large and causedecreases in "high angle" diffraction intensi- unusual values for the M-site. On the average, ties. However, the anorthite content is the most Grande Caldeira, Or32.5An6.6has the lowest tem- likely controlling factor, and it is significant that the peraturefactors, Kakanui, Or13.6An25, has the in- small variations in An content 6 moleVo)cause such termediate,and Mt. Gibele, Or223An6.e,has the noticeableeffects. largest.There are severalpossible reasons for this Apparent thermal motion models in high tem- relationship.First, greater differencesin the real perature structures are likely to represent an aver- positionsof the atomsrelative to that in the average age of real vibrational motion and inter-M-site mi- structuremay exist within the respectivecrystals. gration as well as positional disorder becausethe The larger temperature factors in crystals with effect of temperature is to increase atomic and higherAn content are causedby large local distor- lattice vibrations and alkali diffusion within a feld- tions from extra aluminum in the T sites (Phillips sparcrystal. Magnitudesof equivalentisotropic B's and Ribbe, 1973b)and by the strongerbonding of for atoms in the high-temperaturerefinements are Ca in the M-site. Second,variation in the perfection 1.4to 3.4 times larger than for their room-tempera- of the crystals can affect the temperaturefactors; ture equivalents. They decrease, in both room- HARLOW : ANORTHOCLASE STRUCTU RES 989
Tro Tzo T2 T1
Ttm
TZ lt!
Qaz
T2 Tzo
oato
Ttm
Y X t.o A Fig. 9. Projection of the M-site region down the intermediate,y, axis of the strain ellipsoid of thermal deformation for the Kakanui crystal.The positionsare correctedfor rotation as evaluatedin the strainanalysis (see text). The closestunit cell axis is projected onto the plane of the projection for a reference. Note that the major atomic displacementsrelative to M are in agreementwith the major (x) and minor (3) axes of strain suggestingthe importance of M-O bonding on thermal deformation. O-O lines taper to show the highersite at wide end of the line.
temperatureand high-temperaturestructures, in the Prewittet al.,1976,Winter et al.,1979)except that followingorder: M, Os, Oez,Orz, Oc, Oo, Tr, Tz. the minor axis is always negative, causing the This similarity in ranking indicateseither that the thermal models to be unreal. The thermal parame- relativeeffects of disorder and real thermal motion ters of the M-site cations are highly correlated with are about the same or that real thermal motion alkali chemistry and temperature.Both equivalent dominatesthe effects observed at both room and B and the major axis displacementof the thermal high temperatures.However, this may not be a ellipsoid increasewith decreasingOr content and valid conclusion for the M site with its possible increasingtemperature. Ellipsoid orientations for splitting. The magnitude of apparent motion for the room-temperaturestructures have a consistent each atom increaseswith temperatureexcept for orientationwith the unreal (negative)axis parallel Grande Caldeira the most potassic composition. to a* and the short M-Oez bond and with the major The difference for Grande Caldeira may be related axis orientedsubparallel to the cavity elongationin eithepto the higher Or content or to the crystal the b-c plane (Fig. 8, compare with Fig. 9a of perfection of the sample. Winter et al., 1979).These orientations are con- The very large thermal ellipsoidfor the M site in trolled by the shorter M-O bonds (M-Oer and M- the room-temperatureanorthoclase structures is Oez) and the general triclinic distortion of the comparableto that in high albite (Ribbeet al., 1969, cavity. In the monoclinic structures the cavity is and Wainwright, unpublished, see Smith, 1974, symmetricallyconstrained to be elongatedparallel 990 HARLOW : ANORTHOCLASE STRUCTURES
Table 7. T-O-T aneles
GrandeCaldeira Mt. Gibele Kakanu i 23ocz/n 25o Cz/n qrno 23o czln 230 4000 >ao LJ 7500 Average Average Average oRr r43.5(2) 143.5 r44.4(5) r43.8 (2 ) r43.8 143.3(3) r43.6(2) r43.6 r4r.e(7) onz t'0 2lt\ 132.2 r35.r(5) 130.8(2) 130.8 r32.5(3) r30.5(2) 130.5 r33.7(5)
oso i48.8(2) l5l.6 i 50.7(4 ) 145.2(2) I 50.7 rso.e(2) 143.5(2) 150.6 1s3.2(4) oBt 154 .4(2) 156.2(2) r57.8(2) 'l2t oco 132.1(2) 7 131.9(3) 13r.8(2) i32.8 133.2(2) 131.2(2) 132.7 r36.r(4)
oct r33.3(2) r33.8(2) 134.2(2) ooo r3e.8(2) 142.0 r42.6(3) 137.9(2) 142.3 142.1(2) r36.5(2) r4r.5 i45.4(4)
oDt 144.2(2) 146 .7 (2) 148.4(2) Average 141.32 141.57 I4t.lt 141.29 140.81 142.99 o of Av. 7.76 7.19 8.27 7.09 9.03 Estimatedstandard deviations in parentheserefer to the last diqits to the b axis; the major axis for the M-site also lies distributions as a function of distance from the in this direction, about 37' from that at room- centroid.The electrondensity distributionin the a* temperature(see also Fig. 9b of Winter et al., 1979). direction is apparentlymore peakedthan the com- M-site modeling.Fourier sectionsthrough the M binedX-ray scatteringform-factors (when elliptical- site show a very compactelectron density distribu- ly displacedfrom the centroidin the planenormal to tion in the a* directionand a very elongatedistribu- a*) for the averaged M-site occupants. Use of tion in the b-c plane. Though the distributions extended cumulant approximations (higher order appearellipsoidal in shape,they are evidently not real-spacetensors) to allow for the skewnessand statisticallynormal with respectto electrondensity kurtosisof the scatteringpower distribution (John- son, 1969)do not adequatelyimprove the refine- mentsnor eliminatethe negativeellipsoid axis. 93 The large magnitudesof apparent thermal vibra- tion for the M-sitecation, 0.27 lo 0.404 maximum 94 RMS amplitude, are considered too large to be N Os 9gs purely vibrationalin nature and may be in part due to displacementof individual alkali atoms into one F| ^^ of severalsubsites. In the caseof high albite, Ribbe O :rb et al. (1969)developed a model basedon a split M- I .oo F site, with the site being divided into four separate 3s7 quarter-atomsites, based on an analogywith anor- N v, thite which has a similar structure. Winter et al. 3ge (1979)looked at other possibilitiesof multiple sub- sitesfor high albite and monalbitein relation to low 99 oc albite. The three room-temperaturedata sets de- scribedin this paper were refined with various M roo the applicability of such mod- ro 20 30 40 subsitesto examine els. The following modelsproved to be the best of Mol.per cent Or the many ones attempted, based on Hamilton's Fig. 10. Plot of cos2(AT-O-T) angle (difference in (1965)crystallographic R factor comparison; the pseudosymmetricallyequivalent angles, e.g. for OsOand Osm) vs. compositionof the 23'C anorthoclasestructures. Best fit unreal anisotropic solution is used as a reference lines determined by least squares extrapolate to transition (seeTable 9). For the two most Na-rich anortho- compositionnear Orj6. clases,the best model consistsof four positionally HARLOW : ANORTHOCLASE STRUCTURES 9r
Table 8. Thermalellipsoids-RMS displacementsand anglesto cell axes
GrandeCaldeira 230 Anglesto Cell Axes(o) (R) RMSDisplacements Axis I Axis 2 Axis 3 B equiv. 1.3 b 40(4 42(3 14( 30) 23(10) 1) 6l 142(7) 67(5) 50(5) Lo7(7) 8i(16) 1,37(7) 112(6) i58(s) 76(1,4)2.28(5) 81(8) 146(54) 7s(r2) e4(5s) 123(s5) e9(17) 10(2s)1.83(4) 82(6) 124(7) 105(8) 11,7(7) 144(7) sl(6) 28(7) 1.81(4) 4e(6) e1(10) 14s(7) 116(8) 167(s) e6(s) 52(6) 1.81(4) 50(s) 11i(13) 30(s) 100(10)154(10) 103(12) 42(s) 1.e0(4) GrandeCaldeira 400o e(3) 100(4) 161(3) y8(3) 34(2) 106(J) 86(2) 2.13(r) 1.7(73) 83(21) i61(i3) 108(6e) 33(2) e4(3) 83(2) 2.11(3) 103(3) 77(3) e0 i67(3) e0 0 e0 4.96(16) 8(2) e0 0 e0 18(2) e0 e8(2) 3.32(11) e0 73(10) e0 170(10) 17(i0) e0 e9(r0) 3.18(12) 41(3) 108(8) 18(5) 8s(12) 68(5) 80(18) 4e(4) 3.e8(i0) 86(e) 26(7) e5(10) 141(5) 66(s) 102(5) 52(5) 3.s3(10) 66(8) 71(10) 11.7(el 1s2(e) 21(10) 73(8) 103(8) 3.04(e) Mt. Gibele23o 87(3) 1.33(2) 88(2) r.2s(2) 83(4) L.28(2) 86(4) 1.2e(2) 50(1) 2.8e(5) 89(4) 2.53(s) 10(20) 2.06(s) 2.64(6) 84(r2) 2.59(6) 78(13) z.r3(31 5e(10) 2.14(5) 13(7) 2.17(5) se(6) 2.23(5) Mt. Gibele 5l0o T1 0.r30( 2 ) s2(2) t.76(2) T2 0.132(4) 78(12) 1.70(2) M 0.128(6) 90 4.se(]) 9nt 9.112{q1 e3(5) 3.33(8) uA2 u../.5btbJ 10(e) 2.sr(7) 0s 0.r49(4) 6e(i1 ) 3.86(n) 06 0.162(5) r8(8) 3.24(6) 0j 0.165(4) 45(32\ 3.45(6) Kakanui230 101( e)
87(4) 10e(22) 86(3) 1e(e) e4(e) 57(6) 55(4) 87(7) os(6) 5e(3) Kakanui750o 22(4) 123(4) r20(4) rr2(4) 63(4) 148(4) 88(4) 3.04(5) se(s) 83(10) 167(8) 102(e) 83(4) oot 1, l 34(6) 2.93(s) e1(2) o3(zi 90 179(2) 90 0 90 10.4(4) 6(4) 90 180 90 20(4) 90 e6(4) s.6(2) 81(3) 90 180 90 12s(3) 90 e(3) s.e( 3) s0(3) 107(5) 88(10) 136(s) 10s(4) 17lE\ 76(e) 6.1(2) 100(6) ?4/ 1 ?\ 120(8) r25(30) 80(26)1oo(17) 37(30) 5.4(2) 39(10) s1(12)133(10) 127(r0) 3e(11 ) 53(10) ee(e) 5.4(2)
I t.= Eigr this inaginarydisplacement of the non-posit.ivedef inite ellipsoid Estimatedstandard deviations in parenthesesrefer to the'last diqits 992 HARLOW: ANORTHOCLASE STRUCTURES
Table 9. Results of refinementsof multi-site models for the M site
GrandeCaldeira 230 Ru R Si9n i f. occup. x B Equiv, Major Level% Splitting Anisotropi c 0.0351 0.0488 r.0 0.2750(2\ 0.0013(2) 0.1366(2) 2.36(6) Two Subsites 0.0406 0.0546 0.457(29) 0.2749(6) 0.9861(9) 0.1s65(12) 0.99(13) 0.43(2) 0.543 0.2749(5) 0.0130(7) 0.1214(10) 0.67(11) 0.0327 0.0412 1.076 >99.5 0.675(Na-Ca)0.2750(?) 0.0013(1) 0.1365(2) 't.46(8)7.20(16) 0.325(K) 0.2750 0.0013 0.1365 0.0318 0.0400 i.106 >99.5 0.675(Na-Ca)0.2815(7) 0.0005(5) 0.1410(10)7.15(16) 0.10(1) ^ 0.325 0.2681(8) 0.0018(3) 0.1324(8) 2.39(71 RMS0isplacements (A) of Na-CaSite 1: 0.089(8) ?: 0.248(8) 3: 0.a50(5) C = 0.56+ General Mt, Gibele 23o Anisotropic 0.0406 0.0469 1.0 0.2743(?) 0.0033(2) 0.1353(3) 2.8e(5) Two Subsites 0.0439 0.0536 0.518( 18 ) 0.273L(5) 0.e890(5) 0.15s9(8) 0.63(11)0.51(1) 0.482 0.2757(5) 0.0191(6) 0.i126(e) 0.66(11) Four Subsites 0.0400 0.0460 1.014 >99.5 0.25 0.2734(24) 0.0056(23) 0.1437(26) 0.0 0.25 0.2770(ro) 0.e773(5) 0.1715(16)0.76(11) 0.86(2) 0.25 0.2808(10) 0.0286(5) 0.1001(15) 0.76 0.25 0.?697(24) 0.0018(23) 0.1261(25) 0.0 0.0404 0.0466 i.005 >99.5 0.777(Na-Ca)o.?743(2) 0.0033(2) 0.1353(3) 4.27(13) 0.223(K ) 0.2743 0.0033 0.i353 7.26(55) (n1 if (no.iac 2 0.0402 0.0467 1.008 >99.s 0.777(Na-ca)0.2733(s) 0.0033(5) 0.i360(8) 3.96(11)0.07(3) ^ 0.223(K) 0.280s(23) 0.0028(16) 0.1326(30) 8.46(53) Rl4SDisplacements (X) of Na-CaSite 1: 0.085(7) 2: 0.I29(I0\ 3: 0.356(4) C = 0'84+ Prolate Kakanui230 Anisotropic 0.0516 0.0579 1.0 0.2743(2) 0.0051(2) 0. r350(3) 4.27(8) Two Subsites 0.0599 0.0709 0.s01(12) 0.2731(5) 0.9883(5) 0.1604(7) 0.76(10)0.se(i) 0.499 0.2752(5) 0.0221(s) o.1oe4(7) 0.73(10) Three Subsi tes 0.0519 0.0586 0.218(7) 0.2783(10) 0.9711(e) 0.i816( 14) 0.22(4) 0.481(7 ) 0.27r0(s) 0.0026(6) 0.13e1(lo) 0.22 1.00(2) 0.301 o.27et(j) 0.0308(6) 0.0977(10) 0.22 Four Subsites 0.0512 0.0572 1.007 >99,5 0.25 0.26e7(r3\ 0.0059(9) 0.r5o4 (12 ) 0.0 0.25 0.2777(8) 0.9734(5) 0.i763( 10) 0.22(8) 1.oo(2) 0.25 0.2802(8) 0.0347(5) 0.0e72(L0l 0.22 0.25 0.2725(13) 0.0047(10) 0.1185(12)o.o GrandeCaldeira 4000 Anisotropic 0.0430 0.0728 1.0 0.2796(5) 0.0 0.1366(7) 4.s6(16) Two Subsites 0.0460 0.0758 0.5 0.2i9r(6) 0.0148(6) 0.13s6(7) 3.5e(13)0.38(1) Three Subsites 0.0439 0.0748 0.644(53 ) 0.2812(r1) 0.0 o.15oo(26) 2.54(22) 0.178 0.2755(22) 0.03i0(2e) 0.r017(38) 2.77 0.81(3) (nlif qnorio< l 0.0423 0.0686 1.01 7 >99. 5 0.675(Na-Ca ) o.27s7(5) 0.0 0.1368(7) 10.1(1) 0.325(K) 0.2797 0.0 0.1368 4.6(3) 0.0415 0.0674 1.035 >99.5 0.675(Na-Ca)0.2889(20) 0.0 0.1352(30)10.3(6) ^ 0.32s(K) 0.2688(24) o.o 0.1365(26)4.?5(22\ o.r7(3) Rl'lS0isplacements (X) of Na-CaSite l: 0.18(1) 2: 0'38(1) 3: 0.46(2) c = 0.29+ oblate
t'lt. Gibele 5100 Anisotropi c 0.0343 0.0467 1.0 0.2780(3) 0.0 0.r372(4) 4.5e(71 Two Subsites 0.04i3 0.0592 0.5 0.2780(4) 0.0156(4) 0.1370(5) 3.38(10)0.40(2) Three Subsites 0.0373 0.0544 0.327(32, 0.2806(14) 0.0 o.r73s(35) 2.r7(Lt) 0.336 0.2767(8) 0.0204(7) 0.1190(18)2.r7 0.53(3) Four Subsites 0.0354 0.0505 0.25 0.2707(I9l 0.0 0.0e44(20)r.71(11) 0.25 0.2774(21) 0.0 0.1732(22)r.7L 0.25 0.28Le(17) 0.025e(5) o.r4o1(14) 1.71. 0.67(2\ q^lii qna.icc l 0.0336 0.0454 1.020 >99.5 0.777(Na-ca)0.2780(3) 0'0 0.1371(4) 7.90(27) 0.223(K) 0.2780 0.0 0.13i1 4.62(39) qnl ii Sna.ia( 2 0.0326 0.0437 I.051 >99.5 0.777(Na-Ca)0.2862(8) 0.0 0.1418(14)7.84(23) 0.20(3) ^ 0.223(K) 0.259r(?1.) o.o 0.L267(24)4.18(25) RIYSDisp'lacements (A) of Na-CaSite 1: 0.154(9) 2: 0.338(9) 3: 0'400(7) C=0.25+0blate Kakanui750o Anisotropic a.0221 0.1047 1.0 0.2839(7) 0.0 0.1406(10)10.4(4) Four Subsites 0.0221 0.1094 1.0002 >50. 0.285(22) 0.2776120) o.o 0.0792(37) 3.32(18) 0.370(2s) 0.2804(1e) 0.0 0.1664(37)3.32 0.172 0.2944(23) 0.0544(21) 0.14e5(30)3.32 1.41(4) Five Subsites 0.0210 0.1082 1.055 >99.5 0.193(24) 0.2837(30) o.o 0.0601(70) 3.93(26) 0.194(26) 0.2840(34) 0.0 0.2082(86) 3.e3 0.1e8(1e) 0.295?(2r') 0.0516(21) 0.147e(31)3.e3 1.34(s) 0.2r8 0.2732(r9) 0.0 0.131.2(47)0.5
Estimatedstandard deviations in parenthesesrefer to last digits HARLOW: ANORTHOCLASE STRUCTURES 993 independentquarter-atom subsites with partially fact, consideringthe 12 nearestT atoms bonded to constrained(two fixed and two refined, but equal) the 9 nearestoxygens around the M site of an alkali isotropicthermal parameters(B's) and each with a feldspar, there are 110 configurationswhich have Na/K ratio equal to the overall value. The geometry no Al-O-Al bonds (the aluminum avoidanceprinci- of subsitepositions is essentiallythe same as that ple) and have neutral charge (Al:Si : 1.3). This for the high-albitemodel (Ribbe et al., 1969).with number increases by 390 if + I electron/M-site two inner sitesclose to the centroidfor the anisotro- charge is allowed. These possibilities obviously pic model and two outer sites aligned with the suggestthat four discretedomains are unlikely and cavity elongation(Fie. 9). The value of B for the that local configurationstend to smearout the locus inner sites, M12 and M26, w€ls optimized at 0.0, of M sites. Further studies of polarized single- obviouslyan unrealisticapproximation, but roughly crystal vibrational spectra or a low-temperature equivalentto a singlecentral site with a cylindrical structure refinement would be useful in evaluating ellipsoidof electrondensity distribution.The maxi- the nature of the M-site. The data presentedhere mum distance between subsites, M16-M2u, de- showthat the electrondistribution is not normal for creasesand unconstrainedB's increase with in- a single-sitemodel. If thermalvibration is the cause, creasingOr content. Models for the most K-rich there is either more than one node to the vibration, anorthoclasedo not convergein least-squaresre- i.e., there is some type of positional disorder that finement with more than three M-subsites, and may changewith time, or the motion is anharmonic. none of thesemodels are an improvementover the Introduction of potassium into the Na-feldspar anisotropicmodel. structure causes expansion of the average alkali Consideringthe difference in the relative mass atom cavity so that the sodium may reach greater and ionic radius of potassium and sodium, it is displacements(either thermal or positional) from likely that the two cations will behavedissimilarly the M-site centroid.Also the presenceof potassium in intermediatealkali feldspar structures as was changesthe distribution of electron density such found by De Pieri and Quareni(1973) and Fenn and that it is not modelled well by a single averaged Brown (1977).The smaller sodium should be more atom. Consequently,even more than for the feld- free to vibrateor rattle in the expandedcavity of an spars studied by De Pieri and Quareni (1973),the alkali feldsparof intermediatecomposition, where- use of modelswith separateK and Na(Ca) sites is as potassium, with its greater mass and radius, necessaryto achievea reasonabledescription of the shouldbe relatively fixed in the center of the alkali structures.Splitting of the M-site into many sub- cavity. Thus a model similar to that of De Pieri and sitesis not demandedbut is perhapsreasonable. Quareni (1973),here called a split-speciesmodel, In the high-temperaturestructures the magnitude consistingof an isotropic potassium site and an of apparentthermal motion for the M-site occupant anisotropicsodium (and calcium) site, with occu- is greaterthan for the room-temperaturestructures. panicesdetermined by bulk composition,was test- The apparentmotion is constrainedto be symmetric ed and yielded both a significantly improved R- acrossthe (010)mirror plane on which the M site factor and realistic temperature factors (see Table lies, and the delocalizationcan be adequatelyde- 9). The resultingRMS displacementsfor the sodium scribedby a real anisotropicmodel. Thus, there is portion of the model are even larger than those for lessreason to attempt modelswith mutliple partial modelsusing a singleanisotropic atom and a multi- atoms.However, such modelingwas performedto ple subsite solution of the sodium site may be be consistent with the room-temperatureresults indicated. However, no further modeling was at- and with the four-site model proposed by Okamura tempted. Small differencesin the positions of the and Ghose(1975) and Prewitt et al. (1976)for high Na and K subsitesare not consideredto be signifi- albiteand the two-site model of Winter et al. (1979) cant. for monalbite. The uniquenessof these multiple partial-atom Results of these subsite (averagedalkali atom) models is open to debate. Generally the results models are given in Table 9 and show no measur- presentedhere are comparableto thoseof Winter et able improvement over the anisotropic approach. al. (1979)for high albite,particularly with respectto However, the subsitemodeling does suggestthere sodiumanisotropy. They found no compellingrea- is less delocalizationof electrons (fewer subsites) son to accepta static subsitemodel basedon four with decreasing temperature and/or increasing Or discrete Si,Al ordering schemesfor subsites. In content (consistentwith the room-temperaturere- 994 HARLOW : ANORTHOCLASE STRUCTURES finements).Also the fact that these multiple partial- perature (K-monalbites) reveal the following atom models do not result in better refinements points: indicates that the use of displacive disorder is (1) Room-temperaturecell parametersindicate a probably not an adequate model in these high- largedegree of Si,Al disorderconsistent with mono- temperaturestructures. clinic topochemistry. High temperature measure- A large central positive residual on several differ- mentsshow that thesesamples do becomemetrical- ence Fourier maps suggesteda "split-species" ly monoclinic. model as used for two room-temperaturestruc- (2) Extrapolationsof cos2avalues predicts 0136 tures. Thus, a model using an isotropic potassium as the composition for the displacive transformation and an anisotropic sodium (calcium) site was at- to monoclinic symmetry at room temperature, tempted. The refinements produced a significantly which is comparableto estimatesof Bambaueret better R factor than any other model (Table 9). The al. (1978), Hovis (1980) and Kroll et al. (1980). resultinganisotropic site for the Na,Ca contribution Extrapolations for cos2(AT-O-T) yield an equiva- is slightly less oblate and has a slightly larger lent result. anisotropythan the totally-averagedsite, with the (3) T-O-T anglesand M-O distancesincrease in residualson the difference Fourier section being average value and the variance for the averages noticeablysmaller. Consequently,a model involv- decreaseswith increasingOr content at room tem- ing distinct M-site specieswith different thermal perature. This shows a trend to a more regularly parametersis reasonableand consistent with the coordinatedM-site as in the sanidinestructure. At data. M-O bond distancesfor the split sites in the high temperature in K-monalbites, increase in Or monoclinic high-temperaturestructures suggesta content and temperature have similar effects upon distortedfive- or six-fold coordination,with the M the alkali feldspar structure, except that K-rich K- atomsbeing displaced towards the endsand sidesof monalbitesalways have a wider and shorter M-site the alkali cavity (Table 10). cavity than Na-rich ones. This feature is due to the strong capacity of K to expand the average alkali Conclusions cation cavity. Refinement of three anorthoclase structures at (4) An increasein apparent-thermal-motionmag- room-temperature (K-analbites) and at high-tem- nitudesis correlatedwith the additionof An content and is probably a result of increasedlocal displace- ment of atoms from the average sites due to the influenceof addedCa and Al in the feldsparstruc- Table 10.M-O distancesfor modelswith split M subsites(in A) ture. t'l Subsites ont OnZ 0g 0g 0p Average (5) Anisotropic thermal modelsof the M site are Monalbite9800 (llinter et al., 1979) unreal at room temperature but, similar to the case Na1- 2.5s(2) 2.44(Il 2.7s(2) 2.e1(2\ 2.68(?\ 2.867 2.95(2\ 3.11(2) 3.3s(2) 2.ss(2) of high albite (Ribbe et al., 1969,Wainwright in (0kamura lilona'lbite9800 and Ghose,1975) Smith, 1974) and analbite (Winter et al., 1979), Ha1(m) 2.73(8) 2.51(9) ?.68(9\ Naz(m) 2.74(5\ 2.51(7) maximum apparent motion is parallel to the cavity Na3 2.s4(5) 2.40(4) 2.71(10) 2.70 2.60(10 ) length and minimum motion is parallel to a*, the Mt. Gibele 5100 highly constraineddirection of M-Oa2 and M-Oa1 2.876 tr1(m) 2.73(2\ 2.s2(2) 2.7112) 3.18(1) 3.07(2) multiple isotropic partial r'42(m) 2.75(2) 2.51.(2) 3.13(2) 3.i6(2) 2.65(?) 2.878 bonding. Modeling with M3 2.57(2) 2.47(?\ 2.ss(2) 2.87(1) 2.68(2.t 2.881 atoms suggestsstructures equivalent to that of 3.00{2) 3.r6(2) 3.40(1) 3.06(2) Ribbe el al. (1969)for high albite or Winter et al. Kakanui750o lulr(m) 2.84(3) 2.48(3) 2.58(4) 3.1s(2) 3.38(5) 2,s41 (1979)for analbite-four M subsitesof which two t't2(m) 2.81(3) 2.s2(4\ 3.36(5) 3.21(3) 2.54(5\ 2.e30 are greatly displaced from the average centroid rif3 2.47(3) 2.46(3) 2.67(3) 2.se(3) 2.61(3) 2.863 are 3.30(3) 3.46(4) 3.34(4) parallelto the cavity elongation.These models increasesand proba- Split Species less applicableas Or content Grandecaldeira 4000 bly represent an average of many local geometric Na(ca) 2.84(l) 2.4512| 2.92(2) 3.07(1) 2.e3(1) 2.899 configurations rather than a domain texture. How- K 2.73(2) 2.6r(2) 2.s4(2) 3.16(1) 2.83(1) 2.882 ever a "split-species" model, using a separate llt. Gibele 510o Na(Ca) 2.80(1) 2.41(1) 2.es(1) 3.10(1) 2.87(r\ 2.871 isotropic site for K and an anisotropic site for K 2.6s(2) 2.6r(2) 2.8s(2\ 3.23(2) 2.83(2) 2.865 Na(Ca),yields real thermal parameterswith signifi- Estimatedstandard deviations in parenthesesrefer to the last digits cantly improved weighted R factors, further sup- HARLOW : ANORTHOCLASE STRTICTL]RES 99s porting the conclusionsof De Pieri and Quareni De Pieri, R., Molin, G. and Zollet, R. (1977)Anorthoclases or (1973)and Fenn and Brown (1977\on the different plagioclases?A problem ofnomenclature. NeuesJahrbuch fiir nature of K and Na in intermediate alkali feldspars. Mineralogie, Monatshefte, 413-420. De Pieri, R. and Quareni, S. (1973)The crystal structure of an Nonetheless,the largeanisotropy and displacement anorthoclase:an intermediate alkali feldspar. Acta Crystallo- magnitudesof the Na(Ca)portion of the site suggest graphica, 829, 1483-1487. positionaldisorder as in high albite or analbitefor Dickey,J. S. (1968)Eclogitic and other inclusionsin the mineral theserefinements. For the high-temperaturestruc- breccia member of the Deborah volcanic formation at Ka- tures multiple partial-atom sites do not provide kanui, New Zealand. American Mineralogist, 53, lt04-1319. Fenn, P. M. and Brown, G. E. (1977)Crystal structure of a improvement in modeling of the M-site over an synthetic, compositionally intermediate, hypersolvus alkali anisotropicapparent thermal motion model. "Split- feldspar: evidence for Na, K site ordering, Zeitschrift fiir species"models for the more potassiccrystals yield Kristallographie,145, 124-145. a better match to the data than the other approach, Grove, T. L. and Hazen, R. M. (1974)Alkali feldsparunit-cell parameters but do not yield the samedegree of improvementas at liquid-nitrogen temperatures:Low-temperature limits of the displacive transformation. American Mineral- found in the room-temperaturestructures. ogist,59, 1127-1329. Acknowledgments Grundy,H. D. and Brown, W. L. (1969)A high temperatureX- ray study of the equilibrium forms of albite. Mineralogical I want to thank Gordon E. Brown, JamesB. Thompson,Jr. Magazine,37, 156-172. and the late David R. Waldbaum for stimulating my interest in Hakli, A. (1960)On high temperaturealkali feldsparsof some the feldsparsin generaland this topic in particular. I am indebted volcanic rocks ofKenya and northern Tanganyika. Bulletin of to Eric Dowty and Dan Appleman who offered support and the GeologicalSociety ofFinland, 188,99-108. criticism throughout the project. This paper was benefittedfrom Hamilton,W. C. (1965)Significance tests on the crystallographic the thoughtful reviews and suggestionsof Drs. Hans-Ulrich R factor. Acta Crystallographica, 18, 502-510. Bambauer,Maryellen Cameron, Phillip Fenn and Herbert Kroll. Harlow, G. E. (1977)The anorthoclasestructures: A room- and This researchwas supportedby National ScienceFoundation high-temperaturestudy. Ph.D. Thesis,Princeton University, Grant NSF-DES-00527(Eric Dowty, PrincipalInvestigator). Princeton,New Jersey. (1976) References Hazen, R. M. Sanidine:Predicted and observedmono- clinic-to-triclinic reversible phasetransformation at high pres- Albee, A. L. and Ray, L. (1970)Correction factors for electron sure.Science. 194. 105-107. microanalysisof silicates,oxides, carbonates, phosphates and Hazen, R. M. (1977)Temperature, pressure and composition: sulphates.Analytical Chemistry,42, 1408-1414. Structurallyanalogous variables. Physics and Chemistry of Bambauer,H. U., Kroll, H. and Schirmer,U. (1978)Phase Minerals,l,83-94. transformationsand thermalexpansion of synthetic,sodium- Henderson,C. M. B. 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