Triclinic Feldspars: Angular Relations and the Representation of Feldspar

American Mineralogist, Volume 63, pages 98i,-990, 1978

Triclinic feldspars:angular relations and the representationof feldsparseries

Jnuns B. THorvrpsoN,Jn. Department of Geological Sciences,Hqruurd Uniuersity Cambridge, M assachus et t s 02 I 38

nNo Guy L. Hovls Department of Geology, Lafayette College Easton, Pennsyluania I 8042

Abstract

The rhombicsection angles and obliquitiesof triclinicfeldspars are simpletrigonometric functionsof a* and 'y. Alkali-exchangeseries and short-termheating experiments show wide variationin a* but littlevariation in 7. Differingdegrees of Al-Si orderatconstant composition and temperaturecause wide variations in 7 and relativelyminor onesin a*. Graphical methodsare developed by whicha*, ,y,rhombic section angle, and obliquitycan be readeasily from a singleplot. The sameplot alsodifferentiates the varioustypes of feldsparseries at least as well as any other in currentuse. The obliquity,@, is a directmeasure of the departureof a triclinicfeldspar from the dimensionalrequirements for monoclinicsymmetry. The quantity (l - cos@)must vanish for monoclinicfeldspars and is a nearlylinear function of temperaturefor isochemicalfeldspar seriesthat approacha monoclinicstate on heating.A newconvention is proposedfor defining therhombic section of potassicfeldspars in orderto maketheir values consistent with thoseof contiguousK-Na feldspars. Feldsparsof a givencomposition that are in full internalequilibrium should lie along uniquepaths in termsof a* and 7. Sufficientinformation is now at handto showthe general form of suchpaths lor K-Na-Ca feldspars,and to providepreliminary formulations of these pathsfor the end-memberfeldspars.

Introduction suffice,although it may seemaesthetically unappeal- The idealizedstructure of feldsparis topologically ing,at first,to mix directand reciprocal quantities. If consistentwith monoclinicsymmetry, and certain po. a* and 'y or otand 7* arechosen, mathematical and tassiumand bariumfeldspars are indeed monoclinic. trigonometric advantagesare gained (seelater dis- The mostabundant feldspars in rocks,however, are cussion),since angles are determinedby axial ele- triclinic,but even in thesethe departuresof lattice mentsthat lie in two mutually orthogonalplanes. parametersfrom the requirementsfor monoclinic This is not generallytrue if both anglesselected are symmetryare small. Many such feldsparscan be director both reciprocal. transformedcontinuously into monoclinicforms, ei- We shallshow that a* [whichalso may be regarded ther by heattreatment or by alkali exchange. as the dihedralangle between the (001) and (010) Departuresof a triclinic crystal from the dimen- cleavagesland 7 [whichis a measureof the obliquity sionalrequirements of monoclinicsymmetry may be of the (001) face of the unit celll provide unique describedcompletely in terms of two independent advantagesin the treatmentof triclinic feldspars. angularmeasurements. With theb-axis chosen (in the Other anglesof specialinterest are relatedto them by tricliniccrystals) to correspondtopologically to the simple trigonomeftic equations,much more simple D-axisof a possiblemonoclinic variant, a sufficient ones,in fact, than the onesobtaining if wholly direct or pair would be eitherthe a and 7 anglesof the direct wholly reciprocal cell-angles are used. Changes cell, or the a* and 7x anglesof the reciprocalcell. brought about by short-termheating, or by short- Pairssuch as a* and1, or otand 7*, however,will also term alkali exchange,cause wide variationsin a* 0003-004x/ 78 /09 I 0-098l $02.00 981 982 THOMPSON AND HOVIS: TRICLINIC FELDSPARS with but slight variationsin 7 (nearly negligible,in ing Don whichthe traces of the forms(l l0) and(l l0) fact, in many instances).The effectsof long-term form a rhombus.Inasmuch as the diagonalsof a heating, in feldsparsas subsequentlyexamined at rhombusintersect at right angles,an alternativeand room temperature,cause wide variations in 7 and more practical definition is to define the rhombic relativelyminor variationsin a*. Although we are section as the plane definedby b and the line r in concernedprimarily with triclinic feldspars,many of (010)that is perpendicularto b. As a sectionof the the methodsdeveloped are applicableto any mineral unit cell the rhombic section is thus a rectangular group containingtriclinic crystalsthat showcontinu- section,which might indeedbe a bettername for it. If ous variationsabout a monocliniclimit. 0 + 0 thereis a uniquerhombic or rectangularsec- tion, but if : 6, all sectionscontaining D arerhom- Obliquity 6 bic sectionsand the rhombic section,as a unique In a monocliniccrystal, conventionally oriented, it plane,is indeterminate.Even in this last instance, is necessary(but not sufficient)that the b-axisand the however,we may haveinterest in a limiting rhombic pole, b*, to (010) coincide,and that b : l/b* : sectionwhen dealingwith a phasetransformation in d(010).In a tricliniccrystal, on the otherhand, b and which @ - 0 continuously.The orientationof the b* do not, in general,coincide. We shall therefore rhombic section may be specifiedin two alternate follow Donnay (1940) and designatethe angle,e, ways: either as the dihedralangle, which we shall betweenthem as the obliquity.[t follows that designateas d*, betweenthe rhombic section and (001); d(010):r/b*:6cosd (l) or by the angleo, betweenr and a, which is thusan anglein (010).Feldspars have low obliquities Inasmuchas the cell volume,V., of a monoclinic (lessthan 5o), hencethe distinctionbetween o ando* crystalis abc sinB,that for a triclinic crystalis given is of little practicalimportance and doesnot exceeda by few hundredthsof a degreeat most. We V" : abc sinp cos@ (2) shallfind it usefulto designatethe line normal to r in (010)as s, and the poleto therhombic section Similarly for the reciprocalcell volume Z| ass*; r isthus normalto J,J*, b andb*.In additionb is V\ : q*['x.* sinp* cos@ (3) normal to J*, c* or a*, and bx to s, a or c, hence Although it is necessaryfor monoclinicsymmetry sAs*:b6tb*=6 (4) : : that4 0 or cos@ l, it is possible(though we know Also of no examples)that a tricliniccrystal may alsohave zero obliquity, despitethe origin of the word "tri- r lta= o: sA[Iain (010)] (5) clinic". The vanishingof the obliquity thus insures s* A c* = d* : r ltfLb in (001)l (6) only that thegeometric form of the unit cell meetsthe requirementsfor monoclinicsymmetry, and doesnot as shownin Figurel.If A # 0 in a triclinicfeldspar prove that the crystalis indeedmonoclinic. Such a and 7 is 90o,the rhornbic section must coincide with crystal,for example,might have an Al-Si distribution (001);and if a*, whichis alsothe anglebetween the that is inconsistentwith monoclinicsymmetry. (010)and (001) cleavages, is 90o,the rhombic section The obliquityas used here, in thesense of Donnay, must be normal to (001).In eachof thesespecial shouldnot be confusedwith the quantity[d(l3l) - caseso and o* are identical. d(13l)l which has beencalled the "triclinicity" by Goldsmith and Laves (1954) and "obliquity" by Orientation of triclinic feldspars McConnelland McKie (1960;see also Martin, 1969, The crystallographicreference axes for triclinic 1970).Although the quantity td(l3l) - d(l3l)lmust feldsparsare chosenso as to correspondtopologi- vanishwhen @ vanishes, the reverseis not true.The callyto thoseof monoclinicfeldspafs. In centrosym- vanishingof @is thusthe morestringent requirement metric monoclinicfeldspars, because the axesare for monoclinic symmetry,though not in itself suf- non-polar,there are two entirelyequivalent ways of ficient. selectingthe positiveends of theseaxes so asto form a right-handedarray. In centrosymmetrictriclinic Rhombicsection feldspars,though the axesare still non-polar,the The rhombicsection (Rath, 1876)of a triclinic feld- correspondingtwo waysare non-equivalent. An early spar is defined,traditionally, as the sectioncontain- conventionwas to choosethe orientationthat made THOMPSON AND HOVIS: TRICLINIC FELDSPARS 983

[ro in(Olo)]

=32.57o

(o) (b)

Fig. l. Angularrelationships in Ameliaalbite (Fl0l of Grundyand Brown, 1969). (a) Axialelements normal to b asviewed in positive directionalong b. (b) Axial elementsnormal to D* as viewedin positivedirection along b*. (c) Axial elementsnormal to r asviewed in positivedirection along r. The crystalis in conventionalorientation (a obtuse).Arrows showpositive ends of axes. d* acute,but Laves(195 l) demonstratedthat this The angularrelations aI 25"C for a typical low orientationplaced microclines out of propercontext albite(Fl0l of Grundy and Brown, 1969)are shown relativeto other closely-relatedtriclinic feldsparsand in Figure I for the crystal in conventionalorienta- proposeda new conventionsuch that a for all tri- tion.The arrowsindicate what we shalltake as posi- clinic feldsparsbe taken as obtuse.We shall refer tive directionsfor r, J, and s*. In a K-Na exchange hereinto the latter orientationas conuentional, andto seriesfrom low albiteto microcline,6 ando* increase the orientationof feldsparsso that a is acuteas anti- continuouslyto betweenl00o and l05o asmeasured conuentionaLThe principaiambiguities that ariseare at 250oC, and a similar effect may be observed with K-rich triclinic feldsparsof very low obliquity throughshort-term, reversible heating of low albite. suchthat the departureof a from 90o lies within the Long-term heating of albite, however,reduces the experimentalerror. If this occurs,the orientationis valuesof o ando* continuouslyto a limitingvalue of consistentwith thosefor relatedfeldspars if y is taken about -3o if measuredat room temperatureafter as acute.Grove and Hazen(1974), for example,give heat treatment.Calcic plagioclaseshave still lower a : 90o and "y : 90.07' for an adulariaat the valuesof o and o*, to between-l5o and -20o for temperatureof liquid nitrogen.This resultsin the pure anorthite.For all of thesefeldspars the appear- anti-conventionalorientation; the conventionalone anceof Figurelc remainsmuch the same, despite the wouldhaveT:89.93'. wide variationsin o ando*. The distinctionbetween conventional and anti- For feldsparsplaced in anti-conventionalorienta- conventionalorientations is useful(see Thompson e/ tions, the positiveand negativeends of the a, a*, c, al., 1974)in dealing with ordering, with twinning, and c* axesare interchanged.The positiveends of D and with domainstructures as related to monoclinic- and b*, however,remain as before.We shall find it triclinictransformations. A changefrom the oneori- convenientto take@ as alwayspositive, and thus to entation to the other may be effectedby inter- permitthe positiveends of r, J, ands* to rotatewith changingthe positiveand negativeends of a, a*, c the crystal during its re-orientation.The o and o* andc*, but not of b or b*. An immediateconsequence values for crystalsin anti-conventionalorientation of sucha re-orientationis that cosinesof a, a*,7, and will then be the supplementsof the valuesfor the 7* all changesign (acute becomesobtuse and uice samecrystal in conventionalorientation, so that o or uersa).Their sines,however, are unaffected.Angles o* anticonventional: (o or o* conventional-180'). -80o such as B and B* and their trigonometricfunctions, This resultsin valuesranging from about in on the other hand,are entirelyunchanged. Properties microclineto about -195o in anorthitewhen placed that changesign on reorientationare odd-symmetric in anti-conventionalorientation. in the senseof Thompsonet al. (1974,p.220-222); The anglesgiven in the abovetwo paragraphsare thosethat areentirely unaffected arc euen-symmetric. at variancewith the tradition that q or o* alwaysbe THOMPSON AND HOVIS: TRICLINIC FELDSPARS reportedas acuteangles, but we shall seethat the and eliminating both cosT and cos(aA s*) from (7), systemused here leadsto a simplertrigonometric (8), and (9) we obtain treatmentand to a simplergraphical presentation cosd : tano* /tano (t2) thereof.It will alsoprevent the o and o* valuesfor low albite-microclineexchange series from under- By squaringboth sidesof (10) and (12) we may going a l80o discontinuitynear the K-end of the eliminate functions of 4. Becausewe have definedo series!The revisions indicated above are thus entirely and o* so that all their trigonometric functions have consistentwith, and an extensionof, the revisedori- the same sign (and even the same magnitude when entationintroduced by Laves(195 1), and alsomake either a* ory is 90o), and becausea* (and also"y) are useof the obliquityas definedby Donnay(1940). always taken as positive angles less than 180o, we obtain Trigonometricrelations sinax : sino*/sino (13) Eitherr, b, ands* or r, b*,and s may betaken as a which has been derived by Lewis (1899). Squaring setof mutuallyorthogonal reference axes for obtain- both sidesof (ll) and (12) and repeatingthe same ing the desired trigonometricequations relating procedurewe have rhombicsection angles and obliquity to the standard axialangles of crystallography.The resultsusing ei- sinT : coso/coso* (14) therset are identical, hence we shallshow the deriva- The remaining equations of interest may all be ob- tion only for one.In termsof r, b, ands* thedirection tained by simple algebraicmanipulation. From (10), cosinesof otheraxes of interestare givenin TableI (12),and (13)we have (comparewith Fig. l). With the aid of Table I we thenobtain the followins cota* : tan@coso (15) cos(aAb*):0 and from (ll), (12),and (14) : cos@cosT * sin@cos(a A s*) (7) coIT : tan@sino* (16) cos(aAc*):0 and from (12),(13), and (14) : coslrsino* * coso*cos(c A s*) (8) cosd : sina* sinT (17) cos(aAs) : -sino as obtainedby Donnay (1940;see also Gay, 1956). Finally,combining (10) and (ll) with (13) and (14), :-sind cos?+ cos@cos(a A s*) (9) respectively,we obtain And, becausebx A c* : oL*,we alsohave tano*: cos^t/cota* (18) cosa*: sin@coso* (10) and Eliminatingcos(a A s*) from (7) and (9) we obtain tano: cort/cosa* (19) cosT: sin@sino (ll) Equation(18) has also been derived by Tunell(1952) andequation (19) by Story-Maskelyne(1895), Lewis Table l. Direction cosinesreferred to r, 6, and s* as referenceaxes (1899)and Mtigge (1930;correcting an earlier version by Rosenbuschand Miigge, 1927:,see also Tunell, -!- Lrne UOS LAT UOS lAD UOS LAS 1952).Several of the others quite possiblyappear elsewherein the earlycrystallographic literature. r I 0 It is evidentfrom equations(10) through (19) that b 0 I no morethari two of thefive angles d*,nl ,Q, o, ando* independent,and that theseten S 0 0 l may be taken as equations,in fact,relate all possiblesets of threeout b 0 sfn Q of the five.Our choiceof a reciprocalangle a* anda S 0 cos Q directangle 7 ralherthan a and7 or a* andT* may a cos o cos Y cos (aAs ) be disturbingto a purist who prefersto keepdirect and reciprocalthings reciprocal, but it c sln o 0 cos o thingsdirect has many advantages.Not leastof theseis thatfor- THOMPSON AND HOVIS: TRICLINIC FELDSPARS mulasanalogous to ( l0 ) through( l9 ) wholly in termsof a and 7 or of a* and 7* are muchmore cumbersome (o) and requireintroduction of either0 or 0*, respectiuely, whichthe aboue relations auoid. a* and 7 (or e and7* Anticonv€ntionol for that matter) also have the advantageof being o angleslying in two mutuallyorthogonal planes (a* in x the planenormal to a, and 7 in the planenormal to c*). a* mayalso be identifiedwith the angleof inter- sectionof the (001) and (010)cleavages, and thus lendsitself to directmeasurement by severalmeans, providedcrystals are of sufficientsize. ton a'= os z/col a'

Graphicalrelations between a* and'y Figure 2a and Figure2b aregraphical representa- tions of equations(18) and (19),respectively. They appearmuch the same,and evenwhen superposed canbe distinguishedonly if verycarefully drawn. For a positiveangle,0, near 90o we have, if d is in radians, x cosd( (tr/2-0) < cotO(0 acute) (20a) Anodhil. cosd) (n/2-0)> cot?(d obtuse) (20b)

lon c = col 7/cos o' and all threequantities are very nearlythe same.In feldsparsneither a* nor 7 departsfrom 90oby more than4.25o (0.0742 radians), for whichcosd : 0.0741 Fig. 2. Relationsbetween a*, "y, o, Q, and a* for: authigenic andcotd : 0.0743.For anglescloser to 90" theagree- microcline(M-201-Nd, Kastner, l97l); low albite(Fl0l, Grundy ment is evenbetter, and the three quantitiesbecome and Brown, 1969);analbite (307, Grundy and Brown, 1969); (Cole (a) correspondsto identicalas d approaches90o. Both diagramsalso anorthite et al., l95l): and sanidine. equation(18) and (b) to equation(19). showclearly the distinctionbetween the conventional and anti-conventionalorientation for a given feldspar, as well as further justification for the revision gruent, but the foci of the ellipsefor Figure 2a are suggestedearlier in assigningnumerical values to o closeto the origin on the x-axis,and the foci for the and o*. Figures2a and 2b also correspondvery ellipsein Figure2b areat the samedistance from the closelyto Figuresla and lb, respectively.[n Figures origin on the y-axis. The coordinatesof the foci in 2a and2b a line extendingfrom the origin to a plotted either caseare tsin@ tand. The ellipsesare nearly point may be regardedas a vectorcorresponding to circularbecause @ is a smallpositive angle (4.5o or the axis r in Figure 1a or 1b. Theangle subtended by less).If @is in radianswe have the positiuex-axis is the corresponding this uectorand sin@S6StanQ (23) rhombicsection angle. There is alsoq closerelationship betweenthe magnitudeof the uectorr and that of the and also, from either (21) or (22), By squaringboth sidesof equation(17) we obliquity. sindS rStan6 (24) may obtain either The four quantitiessind, tan@,r, and @(in radians) cot2oL*/tan26* cos'z7lsin24: 1 (21) are thus virtuallyindistinguishable graphically from one another,and wemay take thelength of the uector r,for a plottedfeldsparin eitherFigure 2a or 2b, as the cot2l /tanzQ * cos2a*/sin'A : 1 (22) magnitudeof Q (in radians),uery nearly. BecauseFig- Equations(21) and (22) may be regardedas the ure 2a shows(as doesFig. la) the rhombicsection equationsof curvesof constantobliquity in Figures angle,o*, as measuredin a sectionnormal to b, the 2a and 2b, respectively.Both are the equationsof conventionaland anti-conventionalplots for a given ellipses,centered at the origin, that are nearly circu- feldspar in Figure 2a may be thought of as twins lar. For a givenvalue of d the two ellipsesare con- relatedby the periclinelaw. The correspondingplots 986 THOMPSON AND HOVIS: TRICLINIC FELDSPARS in Figure2b maybe thought of astwins related by the dffirentiate the uariousfeldspar seriesof interest at albitelaw. leqst as clearlyas do the a*-7* plot of MacKenzieand It alsofollows from (20a,b)that a plot of Qr/2-t) Smith (1955)or the a-7 plot of Oruille(1967). The against(tr/2-a*), both in radians,produces a dia- pathsof seriesof feldsparsrelated to one anotherby gram that is intermediatebetween Figure 2a and2b, displacivetransformation or alkali exchangeare, in hencevirtually indistinguishable from either.Equa- fact,nearly orthogonal, in theplots here proposed, to tion (17),rewritten as thoseof seriesof feldsparsrelated to one anotherby the diffusiveredistribution of Al and Si. cosd: cosQr/2-a*) cos(tr/2-t) (25) is the equationof a curveof constantobliquity on End-memberfeldspars this third diagram,and is the equationof a nearly As observedat roomtemperature, the end-member circulartranscendental curve of fourfold(4mm) sym- K- and Na-feldsparsshow wide variationin 7, ac- metry.If the correspondingangles are plottedin de- companiedby relativelyslight variationin a*. Ca- greesrather than radians, the diagramdiffers only by feldspars,on the otherhand, show little or no varia- a scalefactor, and the vectorr is then very nearly tion in eithera* or 7. The K- and Na-feldsparsthat equalin magnitudeto d in degrees. have the most acutevalues of 7 (whenin conven- Other alternativesessentially equivalent to the tional orientation)are thosefrom low-temperature abovewould be polarcoordinate plots in termsof o, geologicenvironments. Prolonged heat treatment of or o*, and Q, in eitherradians or degrees,as the suchfeldspars lowers cosT and convertsthese feld- radiusvector. Whichever representation one chooses sparsinto forms like thosefrom higher-temperature is a matter of aestheticsor whim and makeslittle environments.The results obtained by Baskin(1956) practical difference.We shall seethat plots suchas throughlong-term heating of low-temperaturemicro- thosesuggested here prouide not only a graphicaldis- cline and albite are plottedin Figure 3. Structural play of obliquity and rhombic sectionangle, but also studieshave shown that the low-temperatureforms

\o I n,t oJ.' I 1O o_1)ol a\ \

\ Poiossium old \ Feldspors a2d I I t Sodium I qL2 o7d I Feldspors I I ."-lu Z I x t o4d 6 tl-r!^ o 0 14d tr5d lo2ld J t I I -- no, 1 , MOhOCllolC cog-r t,/ s) ?d

9d t8d o o I -l col cr r lO2

Fig. 3. Angular relations in some end-member alkali feldspars:Open circles are heated authigenic microcline (Baskin, 1956),numbers show number of days heatedat -l 100'C; open squaresare correspondingdata (Baskin, 1956)for a low albite from Switzerland;solid circlesareauthigenicmicroclines(Kastner,l97l); solidsquaresareintermediatemicroclinesofWrightandStewart(1968);solidtriangle is the intermediate microcline of Bailey and Taylor (1955). AII observations at room temperature. THOMPSON AND HOVIS: TRICLINIC FELDSPARS 987 havehighly ordered Al-Si distributionsand that the high-temperatureforms have highly disordered Al-Si distributions.The principal effect of Al-Si orderingis thusto increasethe obliquityof the (001)face of the cosy 7S unit cell- Becauseordering or disorderingof the Al and Si atoms is a slow process,the effectsof short-term heatingexperiments are essentiallyreversible in that the room-temperatureproperties in many instances remainvirtually unaltered.High-temperature X-ray studiesshow that K-feldsparsexperience only negli- giblevariation (Grundy and Brown, 1967)in a* and 7 on heating,but that Na-feldspars(Grundy and Brown, 1969;Stewart and von Limbach,1967) and Fig. 5. Changesin o* and @with temperature for an intermediate albite (219 of Grundy and Brown, 1969).Lengths of the dashed Ca-feldspars(Grundy and Brown, 1967,1974) expe- lines are very nearly equal to the corresponding magnitudes of @ riencea markeddecrease in cota* accompaniedby (in radians), as explained in the text. relativelyminor changesin cos7.The resultsfor Na- and Ca-feldsparsare shown in Figure 4. The se- the effecton o* and @.Because these changes are quencefor one of the feldsparsis also shownsepa- rapid and reversible,the structuralchanges associ- ratelyin Figure5 in orderto demonstrategraphically atedwith themare clearly displacive rather than diffusive,as was first pointedout by Laves(1952). The quantity(l - cos@)must vanishif a feldspar becomesmonoclinic, or dimensionallyso, and it is an even-symmetricproperty in thesense of Thompsonet al. (19'74).It may thus be usedto aid in locating triclinic-monoclinictransformations in variousfeld- spar series.In Figure6 this quantityis plottedas a functionof temperaturefor an analbite(MacKenzie, 1957;Grundy and Brown, 1969)and also for an anorthite(Grundy and Brown, 1967).This albiteis monoclinicat 950oC.The line fittedto the anorthite pointshas the equationr

I The numberin parenthesesrepresents the estimatedstandard deviationof the leastsignificant figure quoted.

-1 0123456789 COT a* x 19'?

Fig. 4. Results of short-term heating of Na- and Ca-feldspars. Circles (numbered series)are albites of MacKenzie (1957) and 'g, Grundy and Brown (1969); open circles are room-temperature measurementsafter heating, closed circles for all seriesexcept F9 G from right to left represent measurementsat temperatures of 25o, Or 140",300',450o,600o,750o, and 850'C. In addition,series Fl0l (J and 307 have data points at 950", and series329 has a data point at I 900'C Triangles are data for "equilibrated" albites at the temperatures of equilibration. Open squares are corresponding o 0 2@ 400 600 800 10m P@ data from Stewart and von Limbach (1967), temperatures of the (t) measurementsincreasing from right to left. Hexagons are for the r F72 anorthite series of Grundy and Brown (1967), temperatures Fig. 6. Variationsof (l - cosd)with temperature:open circles increasing from lower right to upper left. The open hexagon are analbite(307 of Grundy and Brown, 1969);closed circles are representsa room-temperature measurementafter heating. Dashed "equilibrated"albites at temperatureof equilibration(Grundy and curves through the "equilibrated" albites and through the Brown, 1969);open squaresare anorthite(F72 of Grundy and anorthite series represent relations given by equations (29) and Brown, 1967). Lines through the anorthite and albite points (28), respectively correspondto equations(26) and (30), respectively. 988 THOMPSON AND HOVIS: TRICLINIC FELDSPARS

(l - cos@): 0.002820(10) 8.27(13)x lO-?z("c) (26) henceit is evidentthat this feldsparcould only be- comemonoclinic if superheatedwell aboveits melt- ing point. --\ F36(Anp) Alkali-exchangeseries "Low" Plogiocloses Short-termalkali-exchange experiments (Orville, 1967;Wright and Stewart,1968), like short-term heatingexperiments, leave the Al-Si distributionvir- F50(Anrr) tuallyunaltered, hence are essentially reversible. Sev- N o (An51 eral such seriesfor Ca-freefeldspars are shownin F54 5) Figure 7, as observedat room temperature.Com- n parisonwith Figure4 showsthat the effectof replac- o o ing Na by K on a* and is very muchthe sameas 7 --\ \lf F54}| (4n55.5) that of short-termheating at constantcomposition. Certainhighly disorderedalkali feldsparsmay thus beconverted into monoclinicforms either by heating "High" ffi}F?r(An75) for Na. resultshave been or by exchangeof K Similar Plogiocloses obtainedby Kroll and Bambauer(1971) by ex- F74(An93) changingK for Na in calcicfeldspars. High-temper- -l " F9E(Ane1) atureplagioclases more sodic than Anuo may be converted processfollowed ( into monoclinicforms by this Fl09Anes 5) by short-termheating. If bariumcould be exchanged for calciumit is possiblethat someof thehighly calcic '4 plagioclases to 5 6 i E could also be converted monoclinic cot c*x lO2 forms,inasmuch as their Al-Si distributionsare con- (all sistentwith it (Megawet al., 1962)or verynearly so. Fig. 8. Short-term and long-term heating ofplagioclases data from Grundy and Brown, 1974).Sample F54H was prepared by Plagioclasefeldspars long-term heat treatment (7 days, 1080'C) of sample F54' The resultsof Grundy and Brown (1967,1974), someof which havebeen plotted in Figure8, show termand long-termheating experiments. More calcic that plagioclasesless calcic than Anru behave like Na- plagioclases,however, show only the short-termef- feldsparsin the contrastbetween the effectsof short- fects.

Equilibratedfeldspars For feldsparsthat arefully equilibratedinternally, low olbrte thereshould be a uniquevalue of a* and7 for each pressure,temperature, and composition.It thus fol- lowsthat for eachfeldspar composition there should r2 be a unique path in terms of a* and 7 or their I trigonometricfunctions. For pureK-feldspars, which show only the diffusivechanges, and for pure Ca- feldspars,which show only the displaciveones, these pathsmust be essentiallythe onesshown by dashed -1 linesin Figures3 and4. For the K-feldsparsthe path -1 0123456789 coT ar x lo' may be formulated,tentatively, as Fig. 7. Alkali-exchangeseries: circles (solid, analbite-sanidine; cota* : -0.095(7)cos7 - 56(7)cossf Q7) open, low albite-microcline)from Orville (1967);open squares (analbite-orthoclase),solid triangles(Albite III), open triangles and for the Ca-feldsparsas (SpencerU), and solid squares(562-34) from Wright and Stewart ( r968). cosy : 0.046(17)cota* - 66(4)cotsa* (28) THOMPSON AND HOVIS: TRICLINIC FELDSPARS 989

K - No Feldspors rl l/ l/ 'l1t Ir o .d/E o !, P zo N ./L o o ;r K x Feldspors o (,o \ =- // /-=-_- - Monoclinic Feldspors -l

-2

-l 34 colo*x lO2

Fig. 9. a+-7 paths for equilibrated K-Na-Ca feldspars. Solid curves correspond to equations (21), (28) and (29), dashed ones are schematic for K-Na and Na-Ca feldsoars

PureNa-feldspars, however, are more complex be- (l -cosd):0.00376(6) causethey show both the displaciveand diffusive 3.82(8)x 10-6('C) (30) effects,hence cover a widearea in a plot suchas that indicatingthat thetemperature of thetriclinic-mono- of Figure4, ralher than havinga distributionthat clinic transformationfor fully equilibratedalbites is may be approximatedby a simpleplane curve. Cer- to 983"C(compare with Thompsonet al., 1974, tain of the feldsparsin Figure4, however,were syn- close thesizedoriginally by MacKenzie(1957) and heldat Fig.9). Equations(26) and (28)thus constitutea prelimi- temperatureuntil any observablevariation in their nary formulationof the angularproperties of equili- crystallographicproperties became negligible. They brated Ca-feldsparsas functions of each other and are, therefore,probably near the true equilibrium temperature,and equations (29) and (30) do thesame albitesfor their temperaturesof synthesis.The ob- for equilibratedNa-feldspars. For K-feldsparswe served(solid triangles)or interpolated(open tri- (27), owingto the lack of known angles)values of cota* and cos7for thesefeldspars haveonly equation temperaturesfor thevarious triclinic K- areshown in Figure4, andthe curve passing through equilibration them hasthe equation feldspars. The generalform of the probablepaths for equili- cos7: -0.10(6)cotax * 166(26)cotsa* (29) bratedK-Na-Ca feldsparsis shownin Figure9. The solid curves are for the end-memberfeldspars as The solid circlesin Figure 6 correspondto the basedon equations(27), (28), and (29).The dashed trianglesin Figure 4, and the dashedline passing curvesare schematicand are presentedto encourage throughthem hasthe equation othersto obtain a better set. 990 THOMPSON AND HOVIS: TRICLINIC FELDSPARS

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