American Mineralogist, Volume 71, pages 869-890, 1986

Behavior of alkali feldspars:Crystallographic properties and characterizutionof compositionand Al-Si distribution

Guv L. Hons Department of Geology, Iafayette College,Easton, Pennsylvania 18042

Ansrnlcr Four new alkali feldspar ion-exchange series have been synthesized, three with topo- chemically monoclinic Al-Si distributions ranging from sanidine to relatively ordered or- thoclase,the other a microcline-low albite series.Parent materials for three serieshave previously been studied by single-crystaltechniques, so Al-Si distributions are well char- acterized.Unit-cell dimensions and volumes have been measuredfor all seriesmembers and, with data for a previously reported fifth series, have been analyzed as a function of both composition and Al-Si distribution. The a unit-cell dimension, cornmonly used as a measureof composition in alkali feld- spars, is affected to a small but significant extent by Al-Si distribution and also apparenfly doesnot vary linearly with composition, as has previously been assumed.Variation of the b and c unit-cell dimensions with composition is best analyzedseparately for triclinic and monoclinic parts of the topochemically monoclinic series.Furthermore, b is not a linear function of c, an assumption that until now has been made in using these dimensions to calculate Al-Si distributions in alkali feldspars. Variation of c with mole fraction KAlSirO8 (N*) is linear in both the triclinic and the monoclinic parts of the topochemically monoclinic alkali feldspar series, as well as in the potassicregion of the low albite-microcline series.In addition, Ac/AN* slopesare virtually constant for all series.This provides an ordering parameter, c*, which for alkali feldspars with No. > 0.32 (feldsparswith No. < 0.32 require other equations given in the text) may be computed from the observed c value of an alkali feldspar (c.J and its composition as cr: cot"+ 0.038(l - N*). For natural feldspars,c* varies from about 7.180 A for high sanidine to approximarely 7.222 A for maximum microcline. The distribution of Al and Si betweenthe T, and T, tetrahedral sitesof an alkali feldspar (measured by the ordering parameter Z, wherc Z vaies from 1.0 for a perfectly ordered feldspar to lower values with disordering) may be calculatedfrom c* as Z : - 138.575 + 19.3153c*. Mole fractionsofAl in T, and T, aregiven by Nrur,r: -34.3939 + 4.82884c" and N^,'r, :34.8939 - 4.82884c". These equations are valid for both topochemically monoclinic and triclinic feldsparsand improve the precision with which Al-Si distributions can be calculated.

INrnooucrroN also seeHovis and Peckins, 1978).only one intermediate Until the present time three types of alkali feldspar series,based on a specimen of orthoclase (Wright and serieshave beenstudied-ion-exchange series,short-term Stewart, 1968), has been investigated until now. crystallization series,and long-term crystallization series Currenfly, information is lacking on topochemically (Hovis, 1980).The short-term crystallization series(Don- monoclinic alkali feldspar serieswith Al-Si distributions nay and Donnay, 1952; Orville,1967; Luth and Querol- more ordered than those of the orthoclase series men- Sfln6, 1970) have highly disordered Al-Si distributions. tionedabove.Furthermore,noserieshasbeensynthesized Even the long-term crystallization series(Kroll, 197l; KroU with an Al-Si distribution possibly corresponding to that et al., 1980) are relatively disordered, owing to the ex- in alkali feldsparfrom a hydrothermal vein deposit, such tremely long annealing times required to achieve Al-Si as the well-known Alpine "adularias," nor are there any redistribution at temperaturesbelow 750.C. Only in ion- seriesbetween orthoclase and the highly disordered san- exchangeseries have relatively ordered alkali feldspars idine-analbite series,e.g., feldspars with Al-Si distribu- been investigated. Most of the work on these has been dons from certain igrreousenvironments. done on highly ordered, topochemically triclinic feldspars Most researchon alkali feldspar serieshas dwelt on unit- (microcline-lowalbiteseriesofOrville, lg6T;Waldbaum cell dimensions and various relations among interaxial and Robie, 197l; and Kroll in Kroll and Ribbe, 1983; angles.Thermodynamic data on these seriesare even more 0003404x/86/0708-0869$02.00 869 870 HOVIS: ALKALI FELDSPARS

Table 1. Chemical analysisfor Madagascarorthoclase, albite no. 7010. Except for the orthoclase,these parent materials USNM B18938 (by electron microprobe, D. Appleman) have been describedpreviously (Hovis, 1974;Waldbaum, I 966; Waldbaum and Robie, 1971).Newchemical dataforthe adularia, l,/eight Cati ons per oxide percent Elment 8 oxygens sanidine, and albite are given in Table 3.' The orthoclase spec- imen, obtained from the Smithsonian Institution (where part of si 02 64 06 si 3.015 remains) was originally a singJecrystal 2.4 cm on A1^0- 17.42 AI 0.966 the specimen Fe0 0.50 Fe 0.020 a side, light yellow, transparent (gemmy), and nonperthitic as l'lg0 n d. 14g n.d. determinedby both microscopicand X-ray examination.Atomic Ca0 n.d. n.d. absorption analysisby Suhr indicates the mole fraction of KAlSirOt Ba0 n.d. Ba n,d. (N*) to be 0.9343. The specimen also has been analyzed by K2o 15.74 0.945 electron rnicroprobe (Table l, Appleman, personal comm.), which NaZ0 0.65 NA 0.059 yielded an No. value of 0.9409. Orthoclasesfrom Madagascar

rn,d. = not detected arewell known for their iron content;however, Appleman's anal- **Ba0analysis by atomic absorption spectroscopy ysis showsthis specimento have a calculatedKFeSirO. content of only 2.0 molo/0. Structuresof the adularia. sanidine. and low albite have been refined using single crystal X-ray and neutron diffraction tech- limited. Apart from molar volumes, thermodynamic da- niques. Tetrahedral site occupancieshave been calculatedfrom ta are available on one very disord€red topochemically the data and are given in Table 13 and discussedlater in the monoclinic series(Hovis and Waldbaum, 1977:,Hovis, paper. 1979b) and one ordered topochemically triclinic series (Waldbaumand Robie, 1971). SvDcrHnsrs TEcHNIeUES It is the purposeofthis paper to report on the synthesis Two techniqueswere employed to synthesizefeldspars of var- and study offour new alkali feldspar series.Three series ious K,/(K + Na) ratios. In the first, parent feldspars were ground have Al-Si distributions betweenthose of microcline and to -325 or -400 mesh size and elutriated. For potassicparent sanidine. and the fourth is a new low albite-microcline materials,a portion of eachpowder was placedwith a largeexcess - series.Structural refinements done previously by single- of Na-rich chloride in a Pt crucible and heated to 8 I 5"C for up ion took place between crystal X-ray diffraction and neutron diffraction tech- to 40 h. At this temperature, exchange the molten salt and feldspar,resulting in a Na-rich equivalent of niques on parent materials used to synthesizethree of the the feldspar. After cooling, the feldspars were separatedfrom the seriesallow precise characteization of the Al-Si distri- solid chloride by dissolving the chloride in water. Several rinses butions of these series. assuredthat all of the chloride wasremoved. A similar procedure Explanations of why the unit-cell dimensions of alkali was followed for the low albite, except that ion exchangewas feldsparsvary the way they do have beenmade by Stewart conducted in molten KCl. and Ribbe (1969), as well as others mentioned in Smith Initial intermediate compositions were createdby mixing the (1974)and Kroll and Ribbe (1983).The emphasesof this ion-exchanged feldspar powder vrith the natural feldspar powder paper are to fill in the gaps in cell-parameter data, to in various proportions to achieve different compositions. A few atl;alyzea large amount of crystallographicdata basedon additional intermediatecompositions were achievedby combin- Mixed pow- an internally consistent set of chemical analyses,and to ing various feldsparsof intermediate compositions. ders were compressedin a cylindrical Pt crucible and annealed discusshow best to calculateAl-Si distributions in alkali at -930t. Under these conditions, K and Na ions exchanged feldsparsusing lattice-parameter data. between grains of the two feldspars. The powders were removed In addition to this investigation, solution calorimetric from the furnace every 24 h and remixed in acetone,optimizing experiments have been conducted on three ofthe series the chancesfor complete homogenization. Relatively homoge- to determine enthalpies of K-Na mixing and their rela- neous feldsparswere produced in -120 h, but some required tionship to Al-Si distribution. This part of the investi- longer heating. gation, as well as volume data, will be discussedin a The secondtechnique used to createfeldspars ofintermediate separatepaper (Hovis, in prep.). K/(K + Na) ratios was to ion-exchange feldspar powders in a mixed (Na,K)Cl molten salt. In this way the parent feldspar ex- DsscRrPTroNS oF PARENTFELDSPARS changedto an intermediatecomposition. It was thought that this techniquemight producebetter homogeneityin the feldsparsthan In order to producean alkali feldsparion-exchange series, one the homogenizationof mixed powders.Two problemsarose with startswith a parentmaterial and makesother feldspars by having this synthesistechnique. First, exchangewas not normally com- theparent material exchange K andNa ionswith anotherK- or plete after the initial run, and in a number ofinstances, achieve- Na-bearingsubstance. In the past, aqueousK-Na chloride so- ment ofthe desiredcomposition required severalruns. Second, lutionshave been used as an exchangemedium (e.g.,Orville, even after the final exchange,the resulting feldspar was generally 1963),as have various K-Nahalide molten salts (e.g., Waldbaum, not of satisfactoryhomogeneity, which necessitatedfurther an- I 966).Because ion-exchange rates are fast and experimental tem- nealing similar to the homogenizationof feldsparpowders men- peraturesare low relative to thoseconditions required for Al-Si tioned above. redistribution,the newly madefeldspars will have the same,or verynearly the sarne,Al-Si distribution(see Hovis, 1980)as the I To receive copies of Tables 2 and 3, order Document AM- parentmaterial. The four alkali feldsparseries studied here were 86-308 from the BusinessOffice, Mineralogical Societyof Amer- basedon samplesof St.Gotthard adularia no. 7007,Madagascar ica, 1625 I Street, N.W., Suite 414, Washington, D.C. 20006. orthoclaseno. BI 8938,Eifel sanidineno. 7002,and Amelia low Pleaseremit $5.00 in advancefor the microfiche. HOVIS: ALKALI FELDSPARS 871

Detailed synthesishistories ofall feldsparsstudied during this Table 4. Compositions of feldsparsfrom intermediate investigation are given in Table 2 (seefootnote 1). members of two alkali feldspar series,based on electron-microprobeanalyses Sr.c.rns oF THE RESULTTNG FELDSpARS Adularia series Chemical composition nenbers NO" NAO

Most of the ion-exchangedfeldspars were analyzed(using atomic 7917 0 2611 .02,] 0.738j .021 7914 0.512i.038 04881.038 absorption spectroscopy)for NarO and KrO by Norman Suhr of 7918 0.707 ! .029 0.293 ! .029 PennsylvaniaState University (Table 3; see footnote l). It has orthoclase seri es beenshown prewiously(Waldbaum, 1966; Hovis, l97l) that the members 7815 0.299t .040 0.7011 .040 exchangeofNa and K ions in alkali feldsparsdoes not afect the 7905 0 467! .021 0.5331 .021 levels ofdivalent or trivalent ions in the feldspars.Spot checks 7908 0.703I .004 0.297* .004 on Ba levelsin various membersof the adularia and Eifel sanidine series,as well as more recent checksfor Fe, Mg, Ca, Ba, and Sr on someion-exchanged plagioclases, confirm this (Hovis, unpub. other series,for example, r;.o.7927 ofthe adularia series(189 h data). total), no. 7906 ofthe orthoclaseseries (240 h for the part ofthe More complete chemical analysesof solid-solution impurities sample having the most complex history), and no. 8201 of the in the parent feldsparsfor the adularia and sanidine seriescan Eifel sanidine series(250 h). befound in Phillipsand Ribbe(1973, p. 264)and in Hovis (1974, To checkthe Al-Si distributions, at least two members of each p. I I 8). The former authorsdid not analyzefor Ba,but the present serieswere back-exchangedin molten KCI to produce a potassic work shows that some Ba exists in both feldspars (Table 3). feldspar whose unit-cell dimensions could be compared with those Completechemical data on Amelia low albite are given in Wald- of the K-exchangedequivalent of the parent feldspar. Because baum and Robie (1971). sodic feldsparsgenerally disorder more readily at a given tem- perature than do potassic feldspars, the members of tire various Homogeneity serieschosen for these experimentswere either the most sodic The synthesis techniquesused here can lead to Na-K inho- intermediate members of the series,or the most sodic interme- mogeneity in the samples.Therefore, feldspars were routinely diate membershaving had the longesthomogenization times. AII checkedfor homogeneity by inspection ofthe X-ray pattern of members of the microcline serieswere checkedbecause of the each feldspar to see if broadened peaks, particularly the com- longer homogenization times. Unit-cell dimensions for the re- position-sensitive(201) peak, could be found. Whenever broad- sulting feldspars are given in Table 5 and may be compared with ened peaks were observed, the feldspar was returned to the fur- data for the appropriate potassicfeldspars ofTable 6. nace for additional annealing. Members of the high sanidine serieshave Al-Si distributions To further check for homogeneity, 8 to' I I points on three which were based on a higher disordering temperature than that specirnenseach from the adularia and orthoclase series were of the homogenization. Since reordering is known to be extremely analyzedby microprobe. The averageanalyses and their standard sluggishunder dry conditions, the high sanidine serieswas not deviations are given in Table 4. Although such small numbers included in this analysis. of data points are not statistically valid for the purpose of de- Comparison of the unit-cell dimensions of feldsparslisted in termining the compositions of the feldspars,the standarddevia- Table 5 with those of their K-rich equivalentsin Table 6 reveals tions do indicate that the compositional rangeswithin the grains little evidence for disordering during the homogenizations of are small. For reasonsexplained previously (Hovis and Wald- intermediate members of topochemically monoclinic series.If baum, 1977, p. 683) these levels of inhomogeneity have little disordering had occurred, feldsparsofTable 5 would have sig- effect on the thermodynamic mixing properties to be reported nificantly larger Ddimensions and smaller c dimensionsthan the later (Hovis, in prep.). comparable feldspars of Table 6. Values of D for feldspars of Table 5 are larger in only three ofeight cases.Although values Check on Al-Si distribution of c are smaller in six of the eight cases,diferences for K-ex- Since it is our aim to deal with serieswhose members are of changed natural versus homogenized feldspars are in the worst a single structural state,it is important to check the state of Al- casesonly about twice the combined uncertaintiesofthe refined Si order in the various feldspar series.It has been established values. that the temperatures(800-825"C) and relatively short times (24 A similar analysisof the data for topochemically triclinic feld- h) of molten-salt ion-exchangeruns do not detectablychange the spars reveals that a small degree of disordering may have taken Al-Si distribution of an alkali feldspar(Waldbaum, 1966; Wald- place at intermediate and sodic compositions, indicated by the baum and Robie, 1971; Hovis, 1977).It also has been noted larger b and smaller c dimensions of K-exchangedfeldspars no. (Hovis, 1979a, 1980) that even the higher temperatures(900- 8414,8410 (and 841 8), and 8415 (synthesizedfrom feldsparsno. 935'C) and longer times (generally 120 h) of the dry homoge- 8047, 8207, and 8205, respectively)relative to no. 71 104. The nizations do not seemto affectAl-Si distributions. In the current effectis especiallypronounced in intermediate feldsparno. 8207, study, however, some of the homogenization times were longer which homogenizedslowly apparentlybecause ofthe closeprox- than those used previously. This was true of all intermediate imity of its composition to the critical composition of the mi- members of the microcline series,which homogenizedmore slowly croclinelow albite solvus and because of the high critical tem- than members of other series and thus were left in the furnace perature of the solvus for these feldspars (Bachinski and Mtiller, for about 240 h. Note that there are two feldsparsofthis series 1971;also Hovis, 1983and in prep.),probably not much below (nos. 8207 and 8429) at essentiallythe same composition but the temperatureof the homogenization.This necessitateda ho- with different homogenizationtimes (316 and 252 h, respective- mogenizationtime of 3 16.0h. A secondseries member, no. 8429, Iy). The reasonfor this will be discussedin greaterdetail below. was synthesizedat the same composition using finer-grained Homogenization times also were longer for certain members of powdersas startingmaterials (- 400 meshinstead of - 325 mesh, 872 HOVIS: ALKALI FELDSPARS

Table 5. Lattice parameters for K-exchanged intermediate members of various ion-exchange series

Potassi c feldspar and refi nenent Parent fel dspar fe'l dspar a(A) b(A) c(A) o (deg) B (deg) v (deg) V{AJ) Scans, I i nes

Eifel Sanidine Series 8419 8201 8.5005(r2) l3.0l9l 07) 7.',t841(l1) 90.0 1r5.997(il ) 90.0 723.02 113) 2, s4 L047Ail 72015 72mlB 8.602s(8) r3.0262(r0) 7.r87t (6) 90.0 115.989(6) 90.0 723.94 l7l 2, 5l 10376M orthoclase Series 7916 7735 8.6012(B) 12.9938t9) 7.1994t7t 90.0 il6.052{6) 90.0 722.8717) 3, 90 L037lt4 79',f5 79c6' 8.6053(8) 12.9964(9) 7.2016 16) 90.0 il6.054 (6) 90.0 723.56(7) 3, iol 10370M AdulariaSeries 't't6.054 7928 7921 8.5995(9) r2.9589n4) 7.2134(9) 90.0 (7) 90.0 722.7219) 3, 92 10304r'l 73023 7301tE 8.s932(9) 12.9686fi4) 7.2091(9) 90.0 il6.029 (8) 90.0 72t.9r (10) 4, 73 1037!14 73025 73013E 8.5955(1s) 12.9719(25] 7.2064(l3) 90.0 1r6.048(',|2) 90.0 721.90n5) 3, 6',1 10378M ',tz.9688 7204 7196C 8.s972fio) il6) 7.2123 19) 90.0 1t5.030(9) 90.0 722.57(111 2, 45 1037iil MicroclineSeries 8415 8205 8.586200) r2.965809) 7.2180(12) 90.57703) ils.932 0r ) 87.8il fi4) 722.10113) 4, 67 104647 8410 8201 8.s896(r2) 12.9691(30) 7.2122(14) 90.509fl6) 1r5.967(l2) 87.98109) 721.85 l-t7) 4,62 104607 8418 8207 8.5893 (8) 12.9687117) 7.210300) 90.5450l) il5.953(8) 87.9830r) 721.71t11) 4, 64 104687 8430 8429 8.5884 (7) 12.9678('t2) 7.21640t) 90.598(8) r'1s.9s8(8) 87.784(8) 722.07110) 4,76 L05l0T 8414 8047 8.5875(9) 12.9676(171 7.z',t6800) 90.5700r) il5.936(9) 87.8400l) 122.18(11) 4,66 104627 8416 8204 8.586500J i2.959109) 7.2173(11) 90.s9702) 115.938(9) 87.740ll?) 721.62 l12l 4, 67 10456I 'n5.9s0 a417 8206 8.5878(8) 12.960705) 7.2197(10) 90.s90fi0) (8) 87.738(l0) 72r.98 ( i0) 4, 74 10457r

Bracketed quantities are uncertainties in the last decimal Dlace(s) of the various Darameters.

but still elutriated) and lower furnace temperatures in the early Burnham's program. Peaks of potassic feldspars and disordered stagesofhomogenization (846'C first 48 h, 901'C next 130 h, analbite were indexed following data in Borg and Smith (1969). 942'C last 74 h). A shorter homogenization time (252 h) and Peaks for crystalline solutions of intermediate composition, for significantly less disordering during homogenization resulted. It ordered sodic feldspars, were indexed as previously described appears that disordering in feldspar no. 8429 was comparable to (Hovis, 1977,p. 674). that which took place in feldsparsno. 8047 and no. 8205. Fur- thermore, a plot of cos ? versus cot a* (Thompson and Hovis, Llrrrcn PARAMETERS 1978) for the K-exchangedequivalents ofthese three feldspars Results indicates that the small degree ofdisordering that did take place parameters for four was apparently between T, and T, tetrahedral sites (Z ordering), Direct and reciprocal lattice the and not between T,O and T,m sites (Y ordering); in no. 8207 seriesoffeldspars describedabove are listed in Table 6. there is evidence for some degreeof T,O-T,m disordering as In addition. data havebeen included for a fifth seriesbased well. on topochemically monoclinic analbite. The lattice pa- It is not known why sodic feldspars of the microcline series rameters for all members of the latter series except one were afected by homogenization temperatures, while composi- (no. 7919) have been published previously (for seven tionally comparable feldspars of the topochemically monoclinic membersin Hovis, 1977, and for nos. 8001, 8008, and series were not. Perhaps the kinetics ofdisordering are increased 8034 in Haselton et al., 1983).However, for internal con- for this series becauseits Al-Si distribution represents a temper- sistency with the new feldspar seriesreported in this paper, ature of equilibration lower than the temperatures represented all seriesmembers have been chemically reanalyzedby by the Al-Si distributions of other series, thereby increasing the errors reported in Hovis potential for disordering at homogenization temperatures that N. Suhr. Furthermore, volume are well above equilibration temperatures for the series. (1977)have been recalculatedaccording to Blasi (1979). All members of the latter series originated from a speci- DnrnnurNlrroN oF LATTTCE pARAMETERS men (no. 7015) made by disordering Amelia low albite at 1052"Cfor 710 h. All feldspars were ground to fine powders and mixed with it will be convenient to refer to the various semiconductor-gradesilicon (ao:5.43054 A; Parrish, 1960) as Henceforth an internal standard. Unit-c€ll parameters were determined by seriesby the name of the endmemberK-feldspars of each, least-squares refinement using the program rcrse of Burnham such as "orthoclase" or "adularia" or "microcline." The (1962).Uncertainties reported in Tables 5 and 6 are least-squares two relatively disordered series will be referred to as the standard errors as calculated using Blasi's (1979) correction to "Eifel sanidine" and "high sanidine" series. HOVIS: ALKALI FELDSPARS 873

CURVES CONNECTUNPLOTTED DATA POINTS

o a (A)

8.26

-:--- oTSoRDERED MONOCLINIC SERIES 8.18 INTERMEOIATE MONOCLINIC SERIES

TOPOCHEMICALLY TRICLINIC SERIES (bollon) 8.10

8.58

6.CU

8.42 aG)o 8.34

8.26

BOIH OISOFDEREOTOPOCHEMICALLY MONOCLINIC SERIES

8.18 BOTH INTERMEDIATETOPOCHEMICALLY MONOCLINIC

ToPocHEMICALLY TRlcLlNlc sERlEs (botlom)

8.10

No, Fig. lA (top). The a unit-cell dimension as a function of mole fraction KAISi3OE(N*) for the high sanidine (top solid curve), Eifel sanidine (short dashes),orthoclase (long dashes),adularia (dots), and microcline (this investigation; bottom solid curve) feldspar series. Curves shown do not represent least-squares fits to the data, but rather connect data points for individual series members. However, to improve clarity, the data points themselves are not shown. Note the extensive overlap between the two sanidine series and also between the orthoclase and adularia series. Fig. lB (bottom). The d unit-cell dimension plotted against composition. Curves represent least-squaresfits to the data for the two sanidine series (top solid curve), the orthoclase and adularia series (dashes),and the microcline series ofboth this investigation and that ofOrville (1967) (bottom solid curve) as expressedby Equations 2,3, and,4.

Analysis of the data where n representsthe degreeoffit. Factors that will be In the discussion that follows, lattice-parameter data taken into account in deciding which fits are to be used have been fit by the method ofleast-squaresto equations in a particular situation include (l) the Gauss criterion having the form of simple power series: (Worthing and Geffner, 1943),(2) an overall view of how !:aol atNo,+ a2N2o,+,..* aN"*, (l) all seriesbehave, as opposed to how a single series be- 874 HOVIS: ALKALI FELDSPARS

Table 6. Lattice parametersfor members of alkali feldspar ion-exchangeseries

Fel dspar and * o o_t * o o-r * 01 Scans' Refi nenent No" a,a (A,A ) b,b (A,A-') c,c (A,A') o,o (deg) o,o*{oeg) y,r (deg) v (A') lines

Hjgh Sanidine Series 7015 0099 8,l6t 7 (8) r2.8731(11) 7.|17 (5) 93.479112) il6.450 ili ) 90.2il(12) 667.36(9) 3,53 L0322r .136930(l8) .077871\7) .157435(19) 86.008(ll ) 63 482(lr) 88.030(ll) 7059 1437 8.2267(11) t2.917400) 7.1320(5) 92.60s(1.I) |6.387 (7) 90.t77 (12) 578.0r(9) 5, 100 (61 (1?) (]0) ( 103237 .13573909) 't2.9208.07752t .1s6734 87 003 53.57s 7) 88 508 ill) B00t .1510 8.2315(29) 123) 7.1312fr) 92 555\22) |6 358il7) 90.093(29) 678.74(23) 3, 5s LO27BI . l356tB(41 ) .077494(14) 155599(21) 87.102l'20) 63.60906) 88.629 127) 7919 .2753 8.285204) 12.9602121) 7.-t499(6) 91.40204) 116295 (9) 90.06607) 588.0303) 4, 56 L03241 .134640124) .077189112) r56066l4) 88.404(12) 63 695 (9) 89.234il5) 7057 3508 8.3174 (l5) 12.9839il5) 7.1576(l4) 90 0 |r6.164(l6) 90.0 693.77(l5) 6, 59 (28) 103257 . r339s5 .077018(9) 155661(26) 90 0 '|l6.13063.836n6) 90.0 8008 .4406 8.3669 ( 9) 12.9927112) 7.t509(8) 90.0 (8) 90.0 598.89(9) 3,53 L0279!' .133124(i5) .076966(7) 15554402) 90.0 63.870(8) 90.0 7044 .49| 8.3929(il) r2.9999il3) 7.1653(',to) 90 0 it6.t04 ('10) 90.0 702.04ilo) 3,56 10326M . 132682(tB) .076923(8) . r554r4(rs) 90.0 63.896(r0) 90.0 7058 5993 8.4368(11 ) r3.0r55(r3) 7.1660ilo) 90.0 116.020(10) 90.0 707.13(10) 3,47 t0327M .131897(l8) .076831(7) .155288(t6) 90.0 63.98000) 90.0 8034 .7333 8.499100) 13.0209il4) 7.I 703{B) 90.0 116.004(8) 90.0 713.t7(l0) 3,60 L02B5M .13091307) .076800(9) . rs5r 73 (r6) 90.0 63 996 (B) 90.0 7060 .8074 8.5334(7) 13.0295(9) 7.1752 (7 ) 90.0 r15.992(7) 90.0 717.09(7) 4, 92 103281'1 .130373(]2) .076749\6) .15505102) 900 64.008(7) 90.0 1036 .9600 8.601300) 13.0312il3) 7.I 783 (8) 90.0 il5.992(9) 90.0 723.20110) 3, 78 10329M . r29344n5) .07673917) .154984(15) 900 64.008(9) 90.0 Ei fel Sanidi ne Seri es 71102 .0029 8.1634(l0) 12.8630(1s) 7.il73 (8) 93.33702) |6.447 (9) 90.296(lr) 667.6r(9) 3,58 104437 . 136900(r8) .07792119) .157285(19) 86.r25il0) 63.484(9) 88.006il0) 72003 .1553 8.2288il5) 12.9155il3) 7.t3B9 {B) 92.483fi5) r 16.383n2) 90.2r4(r6) 678.83(13) 3, s8 LOM2I .135698(26) .077525lB) .156561(21 ) 87.122 l'13) 63.580('lt ) 88.528(]4) 820',1 .2898 e 2921 t16) 12.9643\21) 7.r5B4 (9) 90.898(32) 116.266(22) 90.I lB (21) 589.96(23) 6, s9 L04l7T . t34489(43) 07714803) .r55808(34) 88.940(34) 63.729122) 89.4?5 124) 8202 .4346 8.3646(7) 12.9867(8) 7.1678(4) 90.0 116.r29(5) 90.0 599.05(6) 4,8] L04l8T .t33159fit) 077002 15) .1ss393(8) 90.0 63.871(5) 90.0 720018 5557 8.422319) 12.9977llt) 7.17t0(8) 90.0 1r6.049(i) 90.0 705.27(8) 3, 72 L03l9t4 .r32ts8fi4) .076936(6) .155219(12) 90.0 63.951(7) 900 8203 7083 8.4890(8) t3.0lt0 il0) 7 1759(8) 90.0 r5.995(7) 90.0 712.41(8) 4, t07 L04l9l'1 .r3t0s8(10) .076858(6) .155039('l3) 90.0 64.005(7) 90.0 1002 8359 8.5425(8) 13.0195{lt) 7 1829 l7l 90.0 ]l5.994(7) 90.0 7lB 05 (8) 3, 9l L03t8t4 .130237(13) .076808(7) .154889('lt ) 90.0 64 006 (7) 90.0 7052 .9917 8.502417) 13.0202(9) 7.1875(5) 90.0 il5.996{6) 90.0 723.5911) 3,120 L03lTtvl .129332(9) .076804(5) .15479200) 90.0 64.004(6J 90.0 orthoclaseSeries 8431 .0135 8.1435{12) 12.8377(16) 7.1314(7) 93.307i14) |6.516 00) 90.302(t4) 665.51(il) 6, B0 L05t2T .1373t6{23) 078072('tO) .r57062{19) 86 1520l) 63.417(l0) 88 0t0 02) 7735 . I 101 B.1944(t4) 12 8810n0) 7.1486(5) 92.740l12J r6.447 (8) 90.226(12) 674.5s01) 4, 79 103067 . r36352(23) .07775316) .r564770o) 86.8270t) 63.508(7) 88.383ilt) 7818 .2376 8.2470\21) 12.912905) 7.1533(5) 9r.598n4) 116.408t3) 90.14707) 682.83(l6) 4, 56 103077 .'135404(30) .077488{9) . r559s8(l8) 88.03rl2) 63.574{14) 88.99205) 78i5 .3021 8.2780(9) 12.9348(18) 7 1735(8) 90.8s3(26) 116.337il3) 89.931(35) 688.28il5) 7,47 t03087 .r3479609) .07732t{ il ) .15s569(26) 89.083(22) 63.661(l3) 89.655(32) 7906 .3814 8.321719) r2.947600) 7.1761t12) 90.0 |6.278 00) 90.0 693.290t) 4, 54 t0309t4 .1340r7(20) .077234\61 .155412\27) 90.0 63.722 110) 90.0 7905 .4652 8.361802) t2.9548n3) 7.1792(11t 90.0 |5.t73 (ll) 90.0 697.95ilt ) 3, 68 L03ls4 . t33254(21) .077192 {8) .15520505) 90.0 63.827(l1 ) 90.0 7801 .5707 8.4149(9) 12.9710(9) 7.1841(6) 90.0 1r5.r00(7) 90.0 704.t8(7) 3, 83 L03lll'1 .132331(l5) .07709s(5) .r55002(12) 90.0 63.900(7) 90.0 7908 .6981 8.478117) r2.9798(9) 7.t889 (6 ) 90.0 r6.058 (7) 90.0 71068 (7) 3, 62 t03l2tt1 .13i298(il) .077043(5) .154843(l0) 90.0 63 942 t7) 90.0 7903 .7885 B.5174 (8) 12.9879il0) 7.1947 t6) 90.0 1r6.042(6) 90.0 715.09(7) 3,89 L03l3ltl .130673il4) .075995(6) .r54697(12) 90.0 63 958 (5) 90.0 78t4 .8719 B 5558(8) 12.9877(10) 7.1959(6) 90.0 116.032(6) 90.0 718.49(7) 3, 86 L03t4M .130076il2) .076996(6) .1546580t ) 90.0 63.968(6) 90.0 Bl8938 .9343 8.s782 ( 9) 12.9879112) 7.1971(8) 90.0 |6.036 (8) 90.0 720.48(9) 3, 9l L031 5l'1 .12974r(t6) .075995(7) .15463705) 90.0 63.954(8) 90.0 7738 .9649 8.6011(]t) 12.9945'12) 7.2021(7) 90.0 |6.044 (8) 90.0 723.22(l0) 2, 66 L03t6F.t .129404il5) .076956(7) .1545410t) 90.0 63.956(8) 90.0

haves, and (3) not only whether using a higher-order fit ure 1A (compare with Kroll and Ribbe, 1983; Fig. 2). lowers the standard deviation in a particular situation, Three trends are apparent,one for the two sanidine series, but whether the standard deviation of fit is lowered sub- one for the orthoclaseand adularia series,and one for the stantially. Note that feldspar serieswith small numbers microcline series.Both sanidineseries begin at sodic com- of data points, in this casethe microcline and Eifel san- positions with a values that are between0.02 and 0.03 A idine series,may not include enough data points to give greaterthan for any of the other series.Moreover, a dis- a valid reading ofthe best least-squaresfit for a particular tinct differencein q values between these two seriesand pair of parameters.In some casesthe tendency for such the microcline seriesis maintained over the entire com- a series is for the standard deviation of fit to steadily positional range. On the other hand, the difference be- decline until an exact fit is reached(e.g., a sixth-order fit tween the two sanidine seriesand the orthoclaseand ad- for sevendata points). ularia seriesis maintained only betweenNo, values of 0.0 and 0.7. Above the latter composition, the orthoclase- I*nglh of a axis adularia trend merges with that of the sanidines. It is Values of a determined for the five feldspar series of apparent, then, that values ofa are affectedby AVSi dis- this investigation are plotted againstcomposition in Fig- tribution to a small but significant degree. HOVIS: ALKALI FELDSPARS 875

Table 6-Continued

Fel dspar and or Scdils, ') ') * Ref i nenent N0" a.a (A,A b.b (A.A c,c (A,A') o,a (des) 8,8 (deg) ,,) (deg) V (A-) lines

AdulariaSeries 7190 .0t03 8.1407(l4) 12.8244l1B) 7.14s0(8) 93.14507) 1t6.549{r0) 90.250(i7) 665.92(12J 3, 59 LO2B9T .137392(24) .078135{ti) .156773i'20) 86.359(i3) 63.39200) 88.r47 fi3) 7197 .0753 8.1754(l6) 12.8468il9) 7.r536(r0) 92.825{18) il6.5t7(11) 90.22r(r8) 671.19il3) 2, 45 (15) ('|1) 102907 .136757126) 't2,8832.077968 0 I ) .156479122) 86.732 63.436 88.34205) 7927 .1879 8.2336(11) lI2) 7.1663(9) 9i.920{12) il6.453 (B) 90.13003) 680.07(9) 4, 64 L029lT .135681(20) 077679(7) .r5s977(r6) 87.790(10) 63.526(B) 88.898(l1) 730ilE .2308 8.2441(40) 12.8993(43) 7 1718 l2t) 91.523 \271 116.389(28) 90.llr {32) 682.88{30) 5, 48 L0292r .135425(59) .077560 126) .155727149) 88.24s \25) 63.598(28) 89.120(30) 7917 .2585 8.2619(211 12.908108) 7.1792 (11) 90.935 122) il6.355(25) 90.063(39) 685.92{17) 6,57 (22) (36) (25) 102937 .135083 .077485ilt) .r55477 88.926124) 'i16.21063.640 89.467 141) 73013E .3835 8 3234(l5) 12.9305fi3) 7.1855(21) 90.0 (l6) 90.0 693.84il7) 5, 52 L0294tl .133912(29) .077337(8) .155r7 (40) 90.0 63.79006) 90.0 7914 .4917 8.3716(l4) r2.937904) 7.r948(il) 90.0 1r6.169{12) 90.0 699.40(l3) 3, 50 10296M .r33094(2r) .077293(8) .154863(21) 90.0 63.831(i2) 90.0 7196C .5365 8.3996(9) 12.9494(l2) 7.1970(6) 90.0 il6.116(7) 90.0 702.89(8) 3, 76 10297r4 .132590{15) ,077224\7) .r54746(ll) 90.0 63.884(7) 90.0 7918 .6776 8.4648(il) 12.9548('|5) 7.2003(10) 90.0 116.028(9) 90.0 709.5r(r0) 3, 67 10298M .r31470(r7) .077192(9) .i545s7fl7) 90.o 63,972 t9) 90.0 7007 .8602 8.5509{1r) 12.9656fi5) 7.207519) 90.0 1r6.037{ 10) 90.0 717.98{10) 3,64 10300r4 .r30r55l9) .077t27 (9) .r544r5fi3) 90.0 63.96300) 90.0 71 98 .8602 8.5485(7) 12.9688(9) 7.2057\6) 90.0 il6.009 (6) 90.0 717.95l7) 2, 65 10301M .t30r6t il0) .077108(6) .r54418(lr) 90.0 63.991(6) 90.0 7049 .9682 8.5974(5) 12.9706{8) 7.2118t4) 90.0 116.027\4) 90.0 722.66t5) 4, 124 10303'1 .129441(8) .07709115) .r54311(7) 90.0 63.973(4) 90.0 7045 .9972 8.5963(9) 12.970904) 7.?123 110) 90.0 il6.038(9) 90.0 722.57l11l 3, 92 10302M .129470\t4J .077095(9) .154314fl9) 90.0 63.962 19) 90.0 MicroclineSeries 7010 .0099 8.1397il l ) r2.786703) 7.1592(6) 94.251(12) il6.597 (9) 87.679(9) 664.43(9) 4, 79 (21 (8) (9) (9) t04267 . r37398 ) 'r2.8315.078425 .r565r804) 86.40702) 63.493 90.470 8205 .1695 B.2t88il9) (23) 7.1693(B) 93.52ril5) 1r6.344(r4) 87.79103) 676.22l.12) 6, 85 105ilT . r35783(30) .07808704) .155840(2r) 87.r64 fl3) 63.733{ I 4) 90.72300) 8207 .331I 8.3013il6) 12.8926il6) 7.r857(6) 92.434(11) il6.i92 (35) 87.87003) 689.31(2r ) 6, 68 104407 .134276(4s) .077650(9) 155r57(47) 88.334il9) 63.864(35) 91.17807) 8429 .3337 8.2997t12) 12.8882(14) 7.'t882 (7) 92.630 112) 116.il5(]3) 87.695i?) 689.s2ilo) 4, 62 L050 9T .134218(',t5) .077691(9) 1s500907) 88.200(r3) 63.95t(13) 91.279 113) 8047 .4926 B.3B2silB) 12.934s(r5) 7.2006112) 9r.496 il3) 115.98704) 87.68502) 70r.r7(rs) 4,75 LO429r .132784t27t .07737919) .r54505(24) 89.463(i3) 64.048{14) 91.84602) (l3) (4) (7) 'il (6) (7) 8204 .6553 B 4538't3t615 ilO) 12.9496 7.2102 9r.0s4 s.920 87.585 709.29l7l 4, 68 104307 (14) .077291l8) 1s4206(9) 90.00r (7) 64.r00 (6) 92.172\7) 8206 .8295 8.5262(10) 12.9607il4) 7.2134(9) 90 747 (1't) 115.919(B) 87.6640t) 716.3400) 4, 100 (l5) (l1) (B) L043lT .130502 .077221lgt .154r3709) 90.304 'n64.0B9 92.234 lto) 71104 .9972 8.5861(7) r2.9565il2) 7.2198(8) 90.6rr (8) 5.93r (6) 87.672lB) 721.69(8) 10, 172 104737 .129609(9) .077248l7t 1540r9(16) 90.452(8) 64.072\7) 92.291(8)

Bracketed quantities are uncertainties in the last decimal place(s) of the various pa.aneters.

Best least-squaresfits for a-No. relations in the various a change in the curvature of a-i{o. relations). For the ion-exchangeseries are given in Table 7. determination of No, content where the highest precision Indirect determination of composition.The 4 unit-cell and internal consistency is important, therefore, linear dimension has commonly been used to indirectly deter- equationssuggested in the past should be replacedby the mine the Ab and Or contentsofalkali feldspars.Generally, following: For disordered feldspars, linear equations have been given for the relationship be- No. : - 1362.802+ 486.4938a- 58.11977a2 tween a and No. (including Hovis, 1977). There is no + (2) question that such equations give good approximations 2.324427a'; of composition, but for some applications such as ther- for ordered topochemically monoclinic feldspars (ortho- modynamic and phase-equilibrium calculations, maxi- claseand monoclinic adularia), mum precisionis necessary.New data ofthis investigation -366.3261 + 129.2335a- 15.42053a'? provided the opportunity to test whether a is a linear No": (3) function of No. and to develop equations for feldspars + 0.6232109a3; having different Al-Si distributions. and for topochemically triclinic feldspars, Least-squaresanalysis of data for nine feldspar series -657.3958 - (Table 8), including the five discussedin this paper (coef- No.: + 239.9022a 29.40843a2 g) ficients in Table 7), gives linear fits as the best fits in only + 1.211078a3. two cases.When data of feldspars with similar structures The large number of significant figuresin theseequations are combined (microclines, orthoclase-adularia, and san- is required to avoid round-offerror. Curves representing idines), the best fits are still nonlinear. Although no clear these equations are shown in Figure lB. All equations picture emergesas to which order of fit is generallybest, should be applied only to unstrained feldspars. at leasta cubic fit is required basedon the fits to combined data. This is also consistentwith the pattern seenin eight of the nine individual series,which require upward con- Length of D axis cavity at sodic compositions and downward concavity at The b unit-cell dimension (Fig. 2) is strongly affected potassiccompositions (quadratic equations do not allow by both composition and Al-Si distribution. From mi- 876 HOVIS: ALKALI FELDSPARS

Table 7. kast-squares equations for the a unit-cell dimension as a function of No, for feldspar seriesof this investigation

Fel dspar Least-squares coeff icients serr es u0 al ^z u3 u4

Highsanidine 8.1574(.0017) 0.47758(.0082) -0.015435(.0082) Eifel sanidine 8.1623(.0010) 0.37482(.016) 0.4007s (.073) -0.53518(.il) 0.20295(.057) orthoclase 8.1379(.0015) 0.47922t.0024) Adulari a 8. 1357{ .0029) 0. s388s( .042) -0.31683{.r8) 0.590771.27) -0.34729(.13) Micrccline 8.1345(.0026) 0.48954(.025) 0.066772(.050) -0.10443(.039)

Eauations have the form: a(A) = ao * uiNo" * arNzo. + a,N3o" * aoN4o. Bracketed quantities are uncertainties in the calculated coefficients. The nunber of significant figures stated for the coefficients are high relative to the uncertainties, but this is necessary to avoid roundoff error for those who nay uish to use the equations. crocline through the intermediate series to high sanidine, ries. Displacive transformation compositions were deter- b increasesas Al and Si become more disordered. All mined for each series using the parameter (l - cos d) serieshave concave down trends with composition, but (Hovis, 1980). it is important for later discussionsto note that Dbecomes In the triclinic part of the compositional range, least- nearly constant above N* values ofabout 0.75. squaresanalyses of Dindicated that linear fits were best- Stewart(1975) noted that the plots ofvarious unit-cell or at leastcould not be substantiallyimproved upon-for parameters against composition seem to change slope abruptly at an No, value of -0.4 (see also Stewart and Wright, 1974).We have noted the same phenomenon in a separatephase-equilibrium investigation (Hovis, Del- bove, and Roll, in prep.) involving two seriesof feldspars and a considerablylarger number of data points than for any singleseries reported in this paper. The break in slope is especiallyevident on plots of b versusilo. and c versus 12 9g No. and seemsto occur near the composition (lfo. :0.29 to 0.35, depending on the series)of the triclinic-mono- clinic displacive transformation of topochemically mono- 12 94 clinic feldsparseries. It was appropriate,therefore, to ana- lyze the variation of D separately for monoclinic versus b cil triclinic parts of the four topochemically monoclinic se- 1290

Table8. Bestorders ofleast-squares frts for a asa functionof N* for various feldsparseries 1286

Sequence of standard devjations Fel dspar 0rder of of fit fron first prde. serl es best fit to best order (A) 12S2

High sanidine 2 .0031,.0030 {this investigation) Eifel sanidine 4 .0062,.0044, .0019, .0008 (this investigation) 1278 Conbined hi gh sani di ne 3 .0047,.0039, .0033 and Eifel sanidine series {this investigation) orthocl ase seri es I .0036 No, (this investigation) Adularia series 4 .0058,.0050, .0045, .0040 (this investigation) Fig. 2. The , unit-cell dimension as a function of N6n. Data Combined orthocl ase 4 .0051,.0046, .0040, .0038 for topochemically monoclinic feldspars are shown as circles, and adularia series {this investigation) alternating as solid and open from the high sanidine series to the Microcline series 3 .0107,.0039,.0022 adularia series.Microcline data are shown as solid squares.Equa- (this investigation) tions for lines and curves fit through the data are given in Table Microcline series 2 .0t01, .0046 for {orvi I le, 1967) 9. For topochemically monoclinic series,lines and curves Combinedmicrocline 6 .0097,.0039, .0036, .00314, triclinic (sodic) and monoclinic (potassic) compositional regions series of this .00310,.00309 whereas for the microcline series, the quadratic least- investigation and are shown, orvitle (1967) squares fit for the entire series is shown. When microcline data High sanidine series 1 .0061 from Orville ( I 967) are combined with those of the present study, {orvi I le, 1967) a higher-order fit is appropriate to accommodate concave-up orthoclase series 3 .0052,.0050,.0038 (1./right and Stewart, 1968) relationships at sodic compositions and concave-down relation- llicrocline series 4 .0078,.0077, .004t, .0035 ships at potassic compositions; a fourth-order fit is assumed in (Hovis and Peckins, 1978) Fig. 10. HOVIS: ALKALI FELDSPARS 877

Table 9. Least-squaresequations for D and c unit-cell dimensions as a function of N* for feldspar series of this investigation

Series and conpositional-:;&i;"- - unit-cell^ Least-squares coefficients standard deviation (A) pu.i.etei i[) ao ul .2 of fit

High sanidine, b 12.8703(.0010) 0.3284(.0061 ) 0.0008 triclinic c 7.1104(.0012) 0.l43B t .0070) 0.0009 High sanidine, b 12.9153(.0,]1) 0.2312(.037) -0.I 143(.028) 0.0026 rcnoc I in ic c 7.1466 ( .0015) 0.0336(.0023) 0.0014 Eifel sanidine, b r2.86t5(.00r9) 0.3533( .010) 0.0010 tricl in ic c 7.|68 (.0003) 0.r434(.00r7) 0.0002 Eifel sanidine, b 12.9123(.0r7) 0.2157(.050) -0.r07l (.035) 0.00t8 rcnocl inic c 7.t5il (.0021) 0.0368(.0028) 0.001I 0rthocl ase, b r2.8379{.0080) 0.324r(.040) 0.0064 c 7.1308(.0025) 0.14t3(.0r3) 0.0020 triclinic -0.il0r orthocl ase, b 12.87641.012) 0.2255(.03B) (.028) 0.0027 rcnocl inic c 7.r600(.0014) 0.04r9(.0019) 0.00]3 AduI ari a, b 12.8210(.0007) 0.3355( .004r) 0.0008 triclinic c i.1434(.00r8) 0.1296(.0099) 0.00l8 -0.07r4 Adulari a, b 12.8770\.012) 0.1657(.036) (.026) 0.0027 rcnoc I in ic c 7.1737(.0019) 0.0390(.0025) 0 00'19 Microcl i ne, b 12.7818(.0080) 0.3134t.037) 0.0004 sodic c 7.i569 ( .0065) 0.0896(.030) 0.0034 Microcl ine, b 12.8257(,0431 0.30s7{ . l2) -0.1746(.080) 0.0022 c 7.1843(.0058) 0.0359(.0075) 0.0020 Microcl ine, b 12.7765(.0065) 0.4239(.030) -0.2429l.O29l 0.0072 whole series c 7.1559(.0025) 0.il15 (.012) -0.0479(.0il) 0.0028

Eauations have the form: b (or c) = aO + a]No. + arNzo" Bracketed quantities are uncertainties in the calculated coefficients. The numberof sign'ificant figures stated for the coefficients are high relative to the uncertainties, but this is necessary to avoid .oundoff error for those who may wish to use the equations.

all three ofthe topochemically monoclinic seriesin which calculate the compositions at which they intersect, thus a quadratic fit did not represent an exact fit to the data. predicting the No. values at which the triclinic/monoclinic Furthermore, the Ab/AN* slopesof the lines for various transformations take place. The transformation N* val- series were quite similar and nearly within the statistical ues so calculatedare within 0.02 ofthose predicted from uncertaintiesof eachother (Table 9). Even the microcline the earlier-used(l - cos @)parameter (Hovis, 1980). series(which cannot undergoa monoclinic-triclinic trans- formation), with its three most sodic members fit sepa- Length of c axis rately, yielded a slopealmost identical to thoseof the other The c unit-cell dimension (Fig. 3) is also strongly af- four series. fected by both composition and ordering. As a feldspar Monoclinic parts of the four topochemicallymonoclinic becomesdisordered its c parameter decreases.The vari- seriesall require at least a quadratic least-squaresfit of D ation ofc acrossany one ofthe seriesproduces a concave- as a function of No.. In no casewould a cubic equation down c-No. trend. Unlike D, however, c continues to in- significantly improve the standard deviation of the least- creaseto the K end of each series.This, combined with squares fit. Curvature of the two sanidine series and the the tendency of D to become constant for potassic feld- orthoclase series are similar. while the curve for the ad- spars, means that a plot of D against c, commonly used ularia series is somewhat flatter. to determine Al-Si distributions, will produce a nearly The potassicpart ofourmicrocline seriesis more strongly vertical tail at the potassicends of ion exchangeseries. curved than that of the other series,and there is some Just as for b, the variation ofc was analyzed separately suggestion for this series that D may go through a maxi- for the triclinic and monoclinic segmentsof all topochem- mum and then decrease slightly at the K end, although ically monoclinic series.In the triclinic part of the com- this is not substantiatedby the data of Orville (1967), or positional range, linear least-squares fits were generally the unpublished data of Kroll (in Kroll and Ribbe, 1983; best (Table 9) as an expressionof c-No, relations. The Acl also seeKroll et al., 1986).At the very least, b does level ANo. slopes of these lines all are within the combined of at K-rich compositions. There are small differencesin uncertainties of each other (see coefficiencies in Table 9). b between the microcline series reported here and Or- Unlike b, c also behaveslinearly in the monoclinic regions ville's. Thesecannot be due to small degreesof disordering of these series. Only in the case of the adularia series did during homogenization, becausethey occur mainly in the a quadratic equation lower the standard deviation offit, potassic part of the compositional range where such effects and in that case improvement was minimal. Here, too, are clearlyeither nonexistentor at leastminimal, but must Ac/LN* slopes(coefrcient a, of Table 9) are within the be due to other factors such as data selection for the re- combined uncertainties of each other (except if comparing finements. the high sanidine and orthoclase series) and have an av- Becauseseparate relationships of b vs. N* have been eragevalue of 0.038 + 0.003 A. ttre linear behavior of calculated for triclinic and monoclinic parts of each topo- c in both the triclinic and monoclinic compositional re- chemically monoclinic feldspar series, it is possible to gions ofthese series,as well asthe constantAclAN* slopes 878 HOVIS: ALKALI FELDSPARS

1 miclo:ctDs- 7.20

718 c (A) high 7.16

7.14

7.12

7.10

t.0 No, Fig. 3. The c unit-cell dimension as a function of N*. Data for topochemically monoclinic feldspars are shown as circles, alternating as solid and open from the high sanidine series to the adularia series. Microcline data are shown as solid squares. For topochemically monoclinic series,linear least-squaresfits are shown for both triclinic and monoclinic segmentsof the series(see equationsof Table 9). Note the similarity in slopesamong all series.For the microcline series,only a linear fit of the data for No" > 0.4 is shown, to emphasizeits similarity to the other series. from seriesto series,makes the c dimension a primary published data of Kroll (seec-N6, plot of Fig. 2, p.72, in candidate as an ordering parameter in alkali feldspars. Kroll and Ribbe, 1983) agreewith this. Again, .l[* values for the triclinic-monoclinic transition Becausethe microcline seriesdoes not undergo a tri- determinedby the intersectionof monoclinic and triclinic clinic-monoclinic transformation, it is also reasonableto c-N* lines agreewell with those using the (l - cos @) treat both Dand c ascontinuous functions acrossthe entire parameter. compositional region.Coefficients for theseequations also Even though the microcline seriesdoes not undergo a are includedin Table 9. triclinic-monoclinic transformation, parallels can be drawn between its behavior and that of the topochemically monoclinic series,particularly at K-rich compositions. If Interaxial angles one fits by least squaresthe four most potassicdata points The four topochemically monoclinic alkali feldspar se- (No. > 0.49) only, c-No, relations are linear, and AclN* ries have non-90oa and 7 values only in the sodic third is 0.036 + 0.008 A, virtually identical to that ofthe other of their compositional ranges (Fig. a) owing to the tri- series.A similar approach to Orville's (196j) microcline clinic-monoclinic displacive transformation in these se- seriesfor data at No" > 0.48 yields a linear fit and a slope ries. Over this range,a is sensitive to ordering within the of 0.039 + 0.003 A (or for l/o. > 0.38 a linear fit and topochemically monoclinic seriesto a very small degree, slopeof 0.040 + 0.003 A). Thus, the usefulnessof c as with the high sanidine serieshaving slightly higher and an ordering parameter is extendedto topochemically tri- the adularia seriesslightly lower valuesof a than the other clinic series. two series.In the microcline series,a has distinctly higher With only three data points at the sodic end (No, < values than in the other series and varies as indicated 0.034) of the microcline series,no test could be made for previously(e.g., Orville, 1967;Hovis and Peckins,1978; nonlinearity of the data. The AclANo. slope of the linear Thompson and Hovis, 1978). The 7 value is relatively fit yielded a slope of 0.090 + 0.030 A, shallower than insensitive to both composition and ordering vrithin the those of the topochemically monoclinic series.A similar topochemicallymonoclinic series;in the microcline series, treatment to sodic membersof Orville's (1967) microcline 7 has distinctly lower values that hardly vary with com- seriesalso yielded shallower slopesthan for topochemi- position. Becauseofthe behavior ofa and 7, the plot of cally monoclinic series.It is likely, however, that nonlin- cosT vs. cot a* devisedby Thompsonand Hovis (1978) ear fits are a better choice for c-try'* relations in the sodic shows the four topochemically monoclinic series to be regionsof microcline series.Ifindividually fit to quadratic virtually inseparable,whereas the microcline serieshas a equations,the data ofboth Orville (1967) and the present distinct trend of its own, very similar to Figure 7 of the seriesyield concave-up relations in this region. The un- aforementionedpaper. HOVIS: ALKALI FELDSPARS 879

microclingsorios .\ topoch€mically monoclinic sgries rs=EEo=+=! - 90

(des) I sg

microclingseries

1.0 No,

Fig. 4. Variation of the o and 7 interaxial angles as functions of N*. Curves are not least-squares fits to the data, but rather connect data points for individual seriesmembers. For clarity, individual data points are not shown, and only three ofthe topo- chemically monoclinic feldspars are represented, the high sanidine series (solid curve), the orthoclase series (dashes),and the adularia series(dots).

The B interaxial angle has a concave-up relationship most of the compositional range. Within the topochem- with composition for all five feldspar series(Fig. 5). This ically monoclinic series,B is somewhat sensitive to or- parameterhas a higher value at the sodic (low albite) end dering, the adularia and orthoclase seriesgenerally having of the microcline series than that for any of the topo- higher values of B than those for members of the two chemically monoclinic series. However, it rapidly de- sanidineseries. Fourth-order B-No,relationships are given creaseswith K content and haslower valuesfor low albite- in Table 10 since theserepresent the lowest standard de- microcline membersthan for membersofother seriesover viations offit for four ofthe five series.

I to"gl

116.1

r 16.0

115.9 0.8 t.0 No.

Fig. 5. The B interaxial angle as a function ofN",. Solid circles and the solid curve at the top are for the orthoclase series, open circles and dashesare for adularia. Lower solid circles and solid curve are for the high sanidine series, and overlapping open circles and dashes are for Eifel sanidine. Open squares and the dotted curve represent data from the microcline series. 880 HOVIS: ALKALI FELDSPARS

Table 10. Ireast-squaresequttions for 6 as a function of N- for feldsparseries of this investigation

Fel dspar Least-squares coeff i cients Standard deviation serles a0 ul a2 a3 a4 of fit (deg)

High sanidine r16.450(.019) -0.1366(.28) -3.150 0.2) 4.9950.9) -2.r70(r.0) 0.021 Eifel sanidi ne 116.446(.003) 0.0979(.048) -4.079 1.22) 6.r65 (.34) -2.6351.17) 0.002 0rthocl ase 1',|6.504(.0r5) 0.07461.24) -3,268 0.r) 4.275l't.7) -r.533(.84) 0.018 Adularia I 16.552(.013) -0.r929(.19) -3.r87 (.80) 4.779(1.2) -r.9r6(.60) 0.018 Microcl ine ll6.6l4 (.009) -1.646 (.r6) -0.2313(.70) 2.724l't.1) -1.530(.54) 0.006

Equations have the forn: B (deg) = u0 * ulNo" t arNzo. + a,N3o" * aoN4o. Bracketed quantities are uncertainties in the calculated coefficients. The numberof significant figures stated for the coefficients are high relative to the uncertainties, but this is necessary to avoid roundoff error for those who may wish to use the equations.

Reciprocalcell dimensions No,: -712.924 + 3.16601V- (4.70247x lO-')W The behavior of reciprocal cell dimensions is largely + (2.33648x lQ-a)fi. (7) analogousto that ofthe direct cell dimensions.Their vari- The three curves representing these equations are shown ations with composition are in shown Figures 6 and 7. in Figure 8B (comparewith Kroll and Ribbe, 1983,p.72 generally Unit-cell volumesas indicators of composition and74). Theseequations reproducedinput com- positions to within 0.02 in N*, or better. Unit-cell volumes for seriesmembers included are in A K/K + Na) ratio grven by any equation based on a Table 6 and plotted in Figure 8A. A detailed analysis of or on volume will be in error if significant amounts of volumes as thermodynamic parameterswill be made in solid-solution impurities are incorporated into the feld- a secondpaper (Hovis, in prep.). However, inspection of spar in question. And for a strained feldspar, even Equa- Figure 8A indicates that they are functions of both com- tions 5, 6, andT are certain to produce slightly erroneous position and At-Si distribution. The two sanidine series results.GriffenandJohnson (1984) have shown that strain have volumes that are generallyhigher than those of any afects all the cell dimensions of an alkali feldspar, so it of the other series.Volumes of the orthoclaseand adularia is certain to affect cell volume to at least a small degree. seriesrepeatedly cross each other and, at most composi- There is no substitutefor a direct chemical anabsls, even tions, are between those of the other Volumes series. of if it is a partial analysis for the major A-site cations. the microcline series are lower than any of the other four seriesat values of No. < 0.4 and No. > 0.75 but, in the X-ray data middle part of the compositional range, become inter- One of the important results of a study such as the mediate betweenthose of the two sanidine seriesand the presentone is a knowledge of how the individual X-ray two more-ordered, topochemically monoclinic feldspar peaks of alkali feldspars vary with composition, sym- series. metry, and Al-Si order. Diagrams that are useful for in- It has been suggestedthat unit-cell volume good is a dexing peakson X-ray chartsfor feldsparslike those stud- measrue of composition in alkali feldspars because of its ied in this investigation have been constructed and will insensitivity to Al-Si distribution, particularly for strained be presentedin a separatepaper (Hovis, in prep.). feldspars(Smith, 196l) in which the a dimension is af- fected by the strain and is not useful for composition determination. Basedon the two sanidine series,the ap- DprnrurrN,trroN oF THE srATE or Ar,-Sr oRDER rN propriate equation for compositional determination in ALKALI FELDSPARS disordered feldsparsis The D-c plot Perhaps the most important use of unit-cell dimension No.: -238.102 + t.09469v - (1.6925Jx lQ-)p data for alkali feldspars is for characterization of their (8.79388x + rQ-t)ft. (5) chemical compositions and structural states,both in terms of symmetry and Al-Si distribution. Wright and Stewart Based on data for the orthoclase and adularia series, the (1968, p. 46) were the first to suggestthat a plot ofthe b equation for relatively orderedtopochemically monoclin- against the c unit-cell dimensions of an alkali feldspar ic feldsparsis would give a good estimate of both its I(,/(K + Na) ratio and its state of Al-Si order. Later, Stewart and Ribbe -129.248 - No,: + 0.610959V (9.76800 x l}-o)W (1969) made formal use of the b-c plot to estimate the + (5.26832 x lO-,)W. (6) mole fraction of Al in T, and T2 tetrahedral positions for both topochemically monoclinic and triclinic feldspars And based on data for the microcline seriesreported here, using the ordering parameter A(Dc). Endmember unit-cell plus the data of Orville (1967), the equation for topo- dimensionson which the A(Dc)parameter was basedhave chemically triclinic seriesis since been revised by Stewart and Wright (1974) and by HOVIS: ALKALI FELDSPARS 881

0.1380

- microcline series (top) 0.1360 --- orthoclase series a* (4") - high sanidine series (bottom) 0.1340

0.1320

0.1300

0.0784

0.0780 b* rA"t microclineaeries o.0776

o.o772

high sanidine series 0.0768

0.1580

0.1570 \\ c* (A-'l 0.1560

0.1550

0.1540

0.6 No,

Fig. 6. Reciprocal unit-cell dimensions as functions ofN*. Curves shown are not least-squaresfits, but rather connect data points for individual series members. However, for clarity, the data points themselves are not shown. For a*, becauseof the close spacing ofthe curves, data are shown only for the microcline series (top solid curve), the orthoclase series (dashes), and the high sanidine series (bottom solid curve). For D*, the sequencefrom top to bottom is microcline (solid curve), adularia (dots), orthoclase (Iong dashes), Eifel sanidine (short dashes), and high sanidine (solid curve). Symbols for C are the same as for D*, but note that the sequenceis reversed with high sanidine on the top and microcline on the bottom.

Kroll and Ribbe (1983). The latter authors also have sug- mensions of an alkali feldspar, a method originally sug- gestedthat separateplots be used to estimate T, and T, gestedand used by Hovis (1974, Eqs. 3, 4a, and 4b). contents for topochemically monoclinic vs. topochemi- Since the precise and accurate determination of Al-Si cally triclinic alkali feldspars. Furthermore, instead of us- distributions in alkali feldspars can be ofgteat importance, ing the A(Dc) parameter to estimate Al-Si distributions, especially in the calculation of thermodynamic data, it is Kroll and Ribbe (1983) have given equationsto estimate worthwhile to examine precisely how D and c behave as site occupancies directly from the b and c unit-cell di- functions of one another. The following discussion will 882 HOVIS: ALKALI FELDSPARS

91.0

90.0 f(o"sl 89.0

88.0

E7.0 q*(oeg)

86.0

64.1

sanidine series 64,0 *:

63.9 orthoclase & adularia series

63.8 9*toesl 63.7

63.6

63.5

63.4

0.8 1.0 No.

Fig. 7. Reciprocalunit-cell interaxial angles. Curves simply connect data points for individualseries members. For o* and 7*, thecontinuous solid curve over the whole compositional range is for thernicrocline series. For clarity only threeofthe topochemically monoclinicseries are shown, the adulariaseries (dotted), the orthoclaseseries (dashed), and the high sanidineseries (solid). For B*, all seriesare shown,microcline (opensquares, dotted curve) at the top, high sanidine(solid curve)and Eifel sanidine(dashes) in the middle,and orthoclase(solid curve) and adularia(dashes) at the bottom. necessarilydwell on the distribution ofAl and Si between was that the AclAb slopes of the various series system- T' and T, tetrahedralsites, and not between atically decreasefrom microcline-low albite to sanidine- sites, since most of the new data are for topochemically analbite series.In the more recent use of the b-c plot by monoclinic feldspars. Kroll and Ribbe (1983) this haschanged; one slopeis used The main assumption made in the use of the 6-c plot for microcline series,while all topochemically monoclinic to estimateAl-Si distributions has been that Dbehaves as seriesare assumedto have a different, but constant, Acl alinearfunctionofcacrossallalkalifeldsparion-exchange Abslope of0.434.Thenewbodyofunit-celldatainTable series(see Figs. 4a and 4b of Kroll and Ribbe, 1983).An 6 has allowed the testing of these assumptions. additional assumptionmade in using the A(Dc)parameter Least-squaresanalyses of b-c data were performed for HOVIS: ALKALI FELDSPARS 883

CURVES CONNECT UNPLOTTEDDATA POINTS

V cA.l

DISOROEREOTOPOCHEMICALLY MONOCLINIC SERIES

INTERMEOIATE MONOCLINIC SERIES

ToPocHEMICALLY TRlCLlNlc sERlEs (bottom)

LEAST-SQUARE S

V ri.l

BOTH OISOROEREDTOPOCHEMICALLY MONOCLINIC SERIES

SOTB INTERMEDIATETOPOCHEMICALLY MONOCLINIC SERIES

TOPOCHEMICALLYTRTCLINIC SERTES (bOItOM)

1.0 No,

Fig. 8A (top). Unit-cell volumes as functions of N*. Curves shown connect data points for the high sanidine series(top solid curve), the Eifel sanidine series (short dashes),the orthoclase series (long dashes),the adularia series (dots), and the microcline series (bottom solid curve). Note the overlap between data for the two sanidine series, as well as for the orthoclase and adularia series, over most of the compositional range. Fig. 88 Oottom). Unit-cell volumes as functions of No,. Curves representleast-squares fits to data for the sanidine series(top solid curve), the orthoclase and adularia series (dashes), and the microcline series of both this investigation and that of Orville (l 967) (bottom solid curve) as expressedby Equations 5, 6, and 7. entire feldsparseries as well asfor triclinic and monoclinic for seriesthat are extremely disordered).First, when best segmentsof topochemically monoclinic series(and sodic lines are fit for each series,the resulting distribution of and potassicsegments of the microcline series).There are data points about eachline is systematic,with data points several indications that b and c are not linear functions near endmembercompositions falling above the lines and ofone another over entire feldspar series(except possibly for intermediate compositions below the lines (Fig. 9), 884 HOVIS: ALKALI FELDSPARS

mlcrocline

7.18 c (il low albits la

7.14

12.78 12.92 t2.90 b (A) Fig. 9. Plot of the D and c unit-cell dimensions of all alkali feldspars of this investigation. Solid lines represent linear least- squares frts of b as a function of c for all members ofeach series. Dotted lines represent separate least-squaresfits for triclinic vs. monoclinic segments of topochemically monoclinic series, or for sodic vs. potassic segments of the microcline series. Light dashes connect D-c values for alkali feldspar endmembersas suggestedby Kroll and Ribbe (1983).

7.18 c (i) fow afbite

7 11

12.78 12.82 12.86 12.90 12.94 t2.98 13.02 b ril Fig. 10. Plot of D-c relations for alkali feldsparsof the present investigation. Behavior in topochemically monoclinic seriesis shown by the solid curves, which represent changes in D-c values along each ion-exchange series, determined by solving equations in Table 9 as a function of N*. The heavy dashed line represents the position of the triclinic-monoclinic displacive transformation at room temperatureand pressure.Dotted lines are isochemicaland drawn at intervals of 0.1 from an N", of 0.0 at the left to 1.0 at the right. For microcline series, open squares represent solutions to fourth-order equations for D and c for the combined data of the presentinvestigation and those ofOrville (1967), also at intervals ofO.l in N*. The spacingofpoints at the K-rich end ofthe microcline series is due to the leveling off of D with composition. Light dashed lines on this diagram connect D-c values suggested by Kroll and tubbe (1983) for alkali feldspar end members. HOVIS: ALKALI FELDSPARS 885

Table I l. Successivelinear least-squaresfits of c as a Table 12. Equations for isochemicallines for topochemically function of b starting from sodic and potassic ends of monoclinic feldsparson a plot of c vs. D the feldspar seriesof this investigation

Cornposition, Least-squares coefficients No" ao ar Fron From sodic ends potassic ends of series of series 0.0 t5.552 -.6559 Number STenfi(- Sta-ndanI- 0.1 15.r64 -.6229 -.5822 of data deviation deviation 0.2 't4.2M14.672 points of fjt (A) Slope of fit (A) Slope 0.3 -.5434 0.4 I3.258 -.4694 High sanidine .0016 .430 .0014 .710 0.5 I 3.236 - .4670 .00i2 .437 .0010 .726 0.6 13.260 -.4682 .0013 .4t9 .0029 404 0.1 13.351 - .4746 .0013 .412 .0025 392 0.8 t3.487 - .4846 't3.694 -. .0012 .415 .0022 .386 ,l.00.9 5000 .0021 .397 .002I .369 13.998 -.5231 .0020 .393 .0021 .393 .0019 .394 .0020 .390 Equations have the form .00t 9 .399 .0019 .399 c(E)=ao*ur! Ei fel sani di ne .0002 406 .0027 1.077 .0002 .407 .0030 .658 .0005 .402 .0030 .0007 . 398 .0028 .471 .0012 .406 .0027 .430 as more data are added. The changesare not as dramatic .co25 420 .0025 420 starting from the sodic ends ofthe series,pointing to the 0rthocl ase .0010 423 .0007 .839 .0009 .434 .0012 929 disproportionate influence of sodic members on Lc/Ab .0013 420 .0010 986 .0012 .415 .0012 .765 slopes.In fact, it is the large changesofboth D and c with .0014 .405 .0022 .571 that control the A,c/ 8 .0013 .403 .00?2 .527 composition at sodic compositions 9 .0014 .409 0025 .469 Ab slopes, yet it is mainly for the characteization of nat- t0 .00,]6 .416 .0025 .445 il .0018 .422 0023 .440 ural potassic feldspars that the b-c plot is useful. t2 .0023 .431 .0023 .431 When triclinic and monoclinic segmentsof topochem- Adul ari a 3* .0004 .361 .0003 .356 .0028 .931 ically monoclinic seriesare treated separately,it is only .0018 .385 .0024 .666 .0015 385 .002t 645 in the triclinic segment of each series that b and c are .0027 .414 .0024 .522 a fact not surprisingin that .0025 .420 .0024 .573 linear functions ofeach other, .0024 .426 .0025 .519 individually theseparameters behave linearly with com- t0* .n24 .525 tl .0024 .437 .0023 .511 position in this region. In monoclinic segmentsof series, 12 .0027 .447 .0027 .475 l3 .0029 .0029 .455 at least quadratic fits to D-c data are required, since for

Microcline 3 .0022 .288 .0062 .397 linear fits. data near the endmembersfall above and data 4 .0016 .281 .0046 .616 5 .0025 .307 .0046 .395 in between fall below the lines (Fig. 9). This too is not 6 .0024 .314 .004t .362 in view ofthe nonlinear behavior ofb but the 1 .0042 .332 .0042 .332 unexpected linear behavior of c in the monoclinic compositional range. *ltlembersof #7007 and 7198 of the adularia series have identical con positions, thus the dbsence of a 3-point fit fron the potassium end Although nonlinear D-c relationships are clearly re- and a lo-point fit fr@ the sodium end of that series. quired, simple quadratic fits of c as a function of D do not representthe data well, sincethe curvature in each series is not spreadevenly acrossthe monoclinic compositional indicating a concave-up b-c relationship in the general range,but occursrather abruptly at No. values above ap- case.This is due mainly to the tendency of b to level off proximately 0.75. The most satisfactoryrepresentation of with increasingK content while c continues to increase. c as a function of b was found by employing the relation- Even if D were a linear function of c, the AclAD slopes ships for each of these parameters(Table 9) in terms of would not be constant,varying from 0.40 for the sanidine No, to determine b-c pairs at specificvalues of N*. It was seriesto 0.46 for the adularia series(Fig. 9). Second,when in this way that the curyes in Figure 10, representingb-c lines are fit separatelyto triclinic and monoclinic segments behavior for the various ion-exchangeseries reported in of each seriss, the diferences in the two slopes system- this paper. were determined. It also was this method that atically decreasefrom adularia to orthoclaseto sanidine, allowed the calculation of isochemical lines on the D-c to the point where they are virtually identical in the most quadrilateral. For eachof the four topochemically mono- disorderedseries (Fig. 9). (Ifpotassic and sodic segments clinic series, b-c pairs were determined for particular val- of the microcline series are fit separately, the difference uesof No.. The four points at eachcomposition then were in slope is even greater than in adularia, suggestingthat linearly fit by least-squaresto obtain the isochemical lines this pattern extendsto triclinic series.)Finally, when linear shown. Equations for these lines are given in Table 12. least-squaresfits are performed on successivelylarger Note that theseare based on an internally consistent set groups of data points starting from either the Na-rich or of chemical data (Table 3). the K-rich end of eachseries, slopes systematically change Severalfeatures ofthe D-c plot ofFigure l0 are worth (Table I l). The effectis particularly dramatic when start- noting. First, in addition to the fact that c is not a linear ing from the potassicend of a serieswhere initial slopes function ofD, neither are the various seriesperfectly par- of 0.6 to 1.0 (as opposed to the generalizedslopes of 0.4 allel to each other. Second, isochemical lines for topo- that are currently used for entire series) rapidly decrease chemically monoclinic seriesat N* values of 0.0 and 1.0 886 HOVIS: ALKALI FELDSPARS

Table 13. Data used to determine the Z-c* relationships of Figure 1I and Equations 13, 14, and 15

Grand NAn no" mean calculatedcalculated'"{ttrit" Monoclinic ,AN ,0r,' T-0 fel dspar Reference(s)' or+Ab+An' or+Ab' di stance MeanT-0 distances (i) 5ortgt rr 12

AnnealedEifel I 0.0002 0.888 1.64215 I .64500 1.64050 7.178 0.072 7 1823 Sanidine Annealed 0.0050 0.9179 1.64213 I .64450 I .639/5 t . t749 0.076 7.1780

Eifel Sanidine 0.0005 0.8542 1.64313 1.64925 1.63700 7.179 0 196 7 1845 70@. Eifel Sanidine 0.0002** 0.8359** 1.64225 1.54975 I .63475 7.179 0 240 7.1852 704. Eifel Sanidine 0.0002** 0.8359** 1.64138 l 65100 1.53175 7.t83 0.308 7.1892 704 Ei fel Sanidi ne 0.0002 0.8359 0.248* 7.1879* 1002 Eifel Sanidine 0.0002 0.900 1.64375 I .64250 | .63500 7.t88 0.280 7.t9t8 (not 7002) 0.0050 0.9179 1.64188 I .65550 1.62825 7.1934 0.436 7.1965 0.0005 0.9003 1.64275 1.66350 1.62200 7.207 0.664 7.2108 Adul ari a 7007 0.0020 0.8808 1.64325 1.66525 1.65125 7 -201 0.704 7.2055 Adularia 7007 0.0009 0.8602 - 0.704* 7.2128* Hi maI ayan 0.0025 0.8933. 1.64188 I 66750 1.6-t625 7.2099 0.820 7.2140, 0rthocl ase 0.8999 7.2137

Tricl inic T,0 T.n IZO IZ^ 'i 'l P28 10,1t 0.009 0.944 1.64425 I .65950 I .65700 .63075 -62975 7.197 0.448 0.020 7.1991 P2A 10,il 0 009 0.944 t.54306 1.66500 1.65550 1.62550 1.62625 7.202 0.550 0.076 7.2041 Pt 7C 10,ll 0.001 0.880 1.54188 1.66900 1.65375 1.62300 1.62175 7 200 0.624 0.122 1.2046 0.636 0.182 1 2043 AID ,10,tl10,il 0.005 0.914 1.64225 '|I .67350 I .65075 'tI .62350 1.62125 7.201 CAIA 0.003 0.899 1. 64406 .67225 I .65875 -62275 1.62250 7 .210 0.686 0.108 7.2138 Ptc 10,ll 0.005 0.9il 1.64250 1.700/5 I 63050 1.61975 I 51900 7.210 0.140 0.562 7.2134 950 l 61875 7.209 0 790 0.412 7.?128 CAIB t0, il--' 0.003 0.899 I .64381 1 -69425 1.64275 I 6t Spencer U 12,l3 0.014 0.937 I 6428t 1.69425 1.64250 I 6t850 I .61600 7.213 0 Bt8 0.4,]4 7.2154 RC20C l0,lt 0 009 0.865 1.64431 1.71700 1.62950 1.61525 1.61550 7.221 0.926 0.700 7.2261 CAIE 10,11 0.003 0.899 1.64544 1.73125 I .6t800 I .51525 1.61 625 7.223 0.934 0 906 7.2238 Pontiskalk t4 0 0.948 I .64406 1.73475 I .61325 1.61900 1.60925 7.2188 0.958 0.972 7.2208 l,4icrocline P.i lep l5 0 0.965 1.64500 1.738 1.613 1.6f4 1.615 1.2211 0.976 l 000 7.2224 l4icrccli ne

References: 13. ltlright and Stewart, 1968 1. Heitz,1972 5. Erownet al., 1977 'l0.9. Prince et al., 1973 2. Cole et al., ]949 6, 0hashi and Finger, 1974 Dal Negro et al., ]978 14. Finney and Bailey, 1964 Dal Negro et al., ]980 15. strob (19B3), as reported in 3. Ribbe, ]953 7. Hovis, 1974 and this investigation ']2.ll. ,]983 4. Phillips and Ribbe, 1973 8. Colville and Ribbe, 1968 Bailey, 1969 K.oll and Ribbe, *Z for Eifel Sanidine is an average value based on references #4, 5, and 6; for adularia it is that of reference #4 g{ values are based on c-values for all mnoclinic membe.sof the two ion-exchangeseries. **Che[ical data of the present investigation and c-va]ues of the invest'igators listed were used to determine E, -First value from vet chemical analysis, secondfrom elect.on microprobe. --Chemical and cell dimension data from reference #13. and distances from reference #12.

do not coincide with any ofthe previously proposedsides 0.140 + 0.007 A in the triclinic range(Fig. 3, Table 9). for the alkali feldspar quadrilateral (Wright and Stewart, Linearity with composition even extends to the potassic 1968;Stewart and Wright, 1974;Kroll and Ribbe, 1983). region of microcline series.Thus, at any one composition, The line representingpure-K feldspars has a shallower the observedc value of an alkali feldspar is unique and a slope and that representingpure-Na analbites a steeper measureof its Al-Si distribution. If the c valuesof a group slope than those which have been previously srrggested. of alkali feldsparshaving various compositions and Al- Furthermore, the slopesof the isochemical lines system- Si distributions were colTectedto a common composition, atically changeas they sweepacross the diagram. the feldsparscould easily be ranked from most ordered Although the b-c plot remains an excellent means for (highest corrected c value) to least ordered (lowest cor- determining approximate compositions and T,-T, site rected c value). populations in alkali feldspars,a more precisemethod is Although the correction of observed c values of alkali needed for quantitative determination of Al-Si distribu- feldspars (c.o) to any composition would work equally tion. well. let us correct these values to those of pure-K end- members (thus the designation of this parameter as cf A new ordering parameter, cK since it is mostly for natural potassicfeldspars that Al-Si distributions are calculated.For any monoclinic feldspar, The c unit-cell dimension not only behaveslinearly with or for a microcline seriesmember with an No. value be- composition in both triclinic and monoclinic parts of tween 0.4 and 1.0, the equation that makes this correc- topochemically monoclinic alkali feldspar series,but slopes tion is for all series are virtually identical, averaging 0.038 + 0.003 A in the monoclinic compositional range and cr : cor.+ 0.038(l - N"J. (8) HOVIS: ALKALI FELDSPARS 887

For a triclinic feldspar in a topochemically monoclinic 7007 and Eifel sanidine no.7002 (Hovis, 1974; also, ad- feldspar series,the pertinent equation is ditional data in this paper). Becauseof theseproblems the Al-Si distributions based cr: cob"- 0.l40No, + 0.0706. (9) on the ten studies listed in Table 2 of Kroll and Ribbe For microcline seriesmembers with 1V".values between (1983) were reformulated (using Eq. 5 of the same au- 0.0 and 0.4, c* is calculated according to the nonlinear thors). Thesedistributions are presentedin Table l3 and relationship are expressedin terms of Z (Thompson,1969, 1970)as cx: cous+ 0.0658079- 0.0574870No,- 0.280817N4. Z = Nonrro,* N^

diate microcline K235 becauseit was a strained feldspar and plotted away from the other data and Pellotsalo mi- crocline (Brown and Bailey, I 964) becausedata from the latter publication gave a very large and physically unat- tainable value of Z (1.07). The data points for topochem- ically triclinic feldspars are shown as open symbols in Figure I l, and the relationship given by Equation 14 is shown as a dot-dash line toward the bottom of the dia- gram. Note the near-coincidenceofthis line with the dashed line representingrelations for monoclinic feldspars,even though the two are basedon entirely different setsofdata. Furthermore, feldsparswith vastly different values of I (seeTable 13) plot near the calculated line and are scat- tered only slightly more than monoclinic data points of the same figure. Thus, Z-c* relations are afected sub- stantially neither by the displacive transformation nor by Iordering. It appeared,then, that a singleequation could be employed to determine T'-T, site occupanciesfor all alkali feldspars. Least-squaresanalysis of data for both monoclinic and triclinic feldspars resulted in the following relationship: Z: -138.575* 19.3153c", (15) which is representedby the prominent solid line on Figure 1I . On the basisofEquation I 5, one can calculatefractions of Al and Si in the T' and T, tetrahedral sitesas follows: NerrrD:$ + Z)/4 (l 6) 7.16 7.17 7.14 719 7 21 7.22 723 : -34.3939+ 4.82884c". (l7) cK Nerrrur:0 - 4/4 (18) Fig. I l. Plot of Z (for definition,see Eqs. I I and I 2) against :34.8939 - 4.82884c". (le) c*. Solidcircles represent data for monoclinicfeldspars, and open : - : - (20) circlesare for triclinic feldspars(see Table I 3). Heavy solid line N.ir.,r I Nera,l Q Z)/4 is thelinear least-squares fit to all data(Eq. I 5),the upper dashed :35.3939 - 4.82884c". (2r) line is the fit to monoclinicdata only (Eq. 13),and the lower Ns,rta: I - -lfAr(T2):Q + 4/4 (22) dash-dotline is the fit to triclinic data only (Eq. 1a).Note the : -33.8939+ 4.82884c". (23) very closeproximity of the latter two lines to the fit for all data. Upward extensionof the diagam emphasizesthat orderingbe- Values of Zhave been calculatedfor all feldsparsof the tweenthe T, and T, sitesin alkali feldsparsis nonconvergent presentinvestigation. The standard deviation in Z fot all (Thompson,1969 and 1970). seriesis about 0.03. Since Z is twice the diference in the mole fractions of Al in the T, and T, sites,an uncertainty Table I 3 (alsosee Table 3 in Kroll and Ribbe, I 983). Note of 0.03 in Z correlateswith an uncertainty of +0.008 for that Z valuescalculated for thesefeldspars are defined by the mole fraction of Al in either of the tetrahedral sites. Equation I I . Original sourceswere checked for No. values; Thus, for most alkali feldspars,use of Equation 15 will only the unpublished data of Strob (1983) were taken result in knowing the amount of Al in the T' and T, directly from Table 3 of Kroll and Ribbe ( I 983). Corrected tetrahedral sites to within less than I molo/oAl of those unit-cell dimension data (for cob")as given by Dal Negro amounts that would have been derived from a direct sin- et al. (1980) were used for the intermediate microclines gle-crystalanalysis on the specimen.(For topochemically reported previously (1978) by those authors. Again, the triclinic feldspars, note that additional characterizationis averageT-O distancesgiven are statedto a larger number neededto determine "O" versus "m" site occupancies.) ofsignificant figuresthan can bejustified in order to avoid precision round-offerror in the calculation of the ordering param- Accuracy versus etersZ and Y[= No,t'or - N"tminerals. Geological Society of America fully disordered parent material no. 7002). Further- Memoir 122,896 p. Qike Brown, B.E., and Bailey, S.W. (1964) The structureof maximum more, three of the five ion-exchangeseries reported in this microcline. Acta Crystallographica,I 7, I 39l-l 400. paper are based on parent materials on which extensive Brown, G.E., Hamilton, w.C., and Prewitt,C.T. (1974) Neutron single-crystalworkhas previously beendone and therefore diffraction study ofAl/Si ordering in a sanidine:A comparison on which Al-Si distributions are well characterized.In with X-ray diffraction data. In W.S. MacKenzie and J. Zuss- man, Eds. The feldspars,68-80. ManchesterUniversity Press, addition to the structural control on the series, compar- Manchester,England. isons of the variation of unit-cell dimensions from series Burnham, C.W. (1962) Lattice constantrefinement. Carnegie In- to serieshave been based on an internally consistent set stitution of Washington Year Book 61,132-135. of chemical analysesfor all feldspars. Cole, W.F., Siirum, H., and Kennard, O. (1949) Thecrystal struc- One of the most important resultsof this work has been tures of orthoclaseand sanidinized orthoclase.Acta Crystal- lographica, 2, 280-287 . the conclusionthat the c unit-cell dimension behaveslin- Colville, A.A., and Ribbe, P.H. (1968) The crystal structure of early with composition in both the triclinic and mono- an adularia and a refinement of the structure of orthoclase. clinic parts of all topochemicallymonoclinic series,as well American Mineralogist, 53, 25-37. as in the potassicpart of microcline series.The constancy DalNegro, A., De Pieri, R., Quareni, S.,and Taylor, W.H. (1978) The crystal structures of nine K-feldspars from the Adamello of the AclAN* slopeshas allowed the use of these rela- massif (northern Italy). Acta Crystallographica, B.34, 2699- tionships to develop a new ordering parameter c*, which 2707. in turn has been used to give highly precise estimatesof Dal Negro, A., De Pieri, R., and Quareni, S. (1980) The crystal 890 HOVIS: ALKALI FELDSPARS

structureof nine K-feldsparsfrom the Adamello massif (north- Ohashi, Y., and Finger, L.W. (1975) An etrectof temperatureon ern Italy): Erratum. Acta Crystallographica,836,3211. feldsparstructure: Crystal structure of sanidine at 800qC.Car- De Pieri, R. (1979) Cell dimensions,optic axial angleand struc- negie Institution of Washington Year Book 74,569-572. tural state in triclinic K-feldspars of the Adamello massif Orville, P.M. (1963) Alkali ion exchangebetween vapor and (northern Italy). Memorie di ScienzeGeologiche, Padova,32, feldspar phases.American Journal of Science,261, 20 l-237 . l7 p. - (1967\ Unit-cell parametersof the microcline-low albite Donnay, G., and Donnay, J.D.H. (1952) The symmetry change and sanidine-high albite solid solution series. American Min- in the high-temperature alkali feldspar series. American Jour- eralogist,52,55-86. nal ofScience, 250A, I 15-132. Parrish, W. (1960)Results of the I.U.Cr. precisionlattice param- Finney, J.J., and Bailey, S.W. (1964) Crystal structure of an au- eter project. Acta Crystallographica,13, 838-850. thigenic maximum microcline. Zeitschrift liir Kristallographie, Phillips, M.W., and Ribbe, P.H. (1973) The structuresof mono- t45, t24-145. clinic potassium-rich feldspars.American Mineralogist, 58, 263- Griffen, D.T., and Johnson,B.T. (1984) Strain in triclinic alkali 270. feldspars: A crystal structure study. American Mineralogist, Prince, E., Donnay, G., and Martin, R.F. (1973) Neutron dif- 69, 1072-10'77. fraction refinement of an ordered orthoclasestructure. Amer- Harlow, G.E., and Brown, G.E., Jr. (1980) Low albite: An X-r4y ican Mineralogist, 58, 500-507. and neutron diftaction study. American Mineralogist, 65, 986- Ribbe, P.H. (1963) A refinement of the crystal structure of san- 99s. idinized orthoclase.Acta Crystallographica,I 6, 426-427 . Haselton, H.T., Jr., Hovis, G.L., Hemingway, B.S., and Robie, Smith, J.v. (1961) Explanation of strain and orientation effects R.A. (1983) Calorimetric investigation of the excessentropy in perthites. American Mineralogist, 46, 1489-1493. of mixing in analbite-sanidinesolutions: Implications for Na,K -(1974) Feldsparminerals, volume 1. Springer-Verlag,New short range order and two-feldspar thermometry. American York. Mineralogist,68, 398-413. Smith, J.V., Artioli, G., and Kvick, A. (1986) Low albite, Hovis, G.L. (1971) Thermodynamic properties of monoclinic NaAlSiOr: Neutron difraction study of crystal structue at 13 potassium feldspars.Ph.D. thesis, Harvard University, Cam- K. American Mineralogist, 7 1, 727-7 33. bridge, Massachusetts. Stewart, D.B. (1975) Lattice parameters,composition, and AV - ( I 974) A solution calorimetric and X-ray investigation of Si order in alkali feldspars.In P.H. fubbe, Ed. Feldspar min- Al-Si distribution in monoclinic potassium feldspars.In W.S. eralogy,St. l-22. Mineralogical Society ofAmerica Short Course MacKenzie and J. Zussman, Eds. The feldspars, lI4-144. Notes, 2 (lst edition). ManchesterUniversity Press,Manchester, England. Stewart,D.B., and fubbe, P.H. (1969) Structural explanation for -(1977) Unit-cell dimensions and molar volumes for a variations in cell parameters of alkali feldspar with AVSi or- sanidine-analbiteion-exchange series. American Mineralogist, dering. American Journal of Science,267 - 4, 444-462. 62,672-679. Stewart,D.B., andWright, T.L. (1974)AVSi orderand symmetry - (1979a) Thermodynamic and crystallographicproperties ofnatural alkali feldspars,and the relationship ofstrained cell of an orthoclase ion-exchangeseries. Geological Society of parametersto bulk composition. Bulletin de la Soci6t6Fran- America Abstracts with Programs, ll, 446. gaisede Min6ralogie et de Cristallographie,97, 356-377. -(1979b) A solution calorimetric investigation of K-Na Strob, W. (1983) Strukturverfeinerungeines tief-mikroklins, zus- mixing in a sanidine-analbiteion-exchange series: Corrections. samenhangezwischen < T-O > tief-albit/tief-mikroklin- American Mineralogist, 64, 925. mischkristallreihe. Diplomarbeit, Institut fiir Mineralogie, -(1980) Angular relations of alkali feldspar seriesand the Westfalischen Wilhelms-Universitiit, Miinster, Federal Re- triclinic-monoclinic displacive transformation. American public of Germany. Mineralogist, 65,'l 7 0-7 78. Thompson, J.B., Jr. (1969) Chemical reactionsin crystals.Amer- -(1983) Thermodynamic mixing properties and a calcu- ican Mineralogist, 54, 341-375. lated solvus for low albite-microcline crystalline solutions. -(1970) Chemical reactions in crystals: Corrections and Geological Society of America Abstracts with Programs, 15, clarification. American Mineralogist, 55, 528-532. 519. Thompson, J.B., Jr., and Hovis, G.L. (1978) Triclinic feldspars: Hovis, G.L., and Peckins, E. 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