Optical Properties of a High Albite (Analbite)-High Sanidine Solid-Solutionseries

American Mineralogist, Volume 71, pages 1393-1398, 1986

Optical properties of a high albite (analbite)-high sanidine solid-solutionseries

Snu-CHuN Su.t Paur. H. Rrssn. F. DoNto Br.oss, Jur,rp K. hnNnn2 Department of Geological Sciences,Virginia Polytechnic Institute and State University, Blacksburg,Virginia 24061, U.S.A.

Ansrrucr In the solid-solution serieshigh albite (analbitelhigh sanidine,it was impossibleto select a set of specimensthat were free from minor constituents(anorthite, celsian,Sr- and Rb- feldspars,and Fe), totally free of evidencesof exsolution, and all of precisely the same structural state. So data were gatheredfor 32 feldsparswhose range of structural stateswas 0.5 = )1, - 0.65 (average0.60), where 2r, = )1, for monoclinic and 2t' : (t'o + t'm) for triclinic feldspars,and t is the Al content of the T,, TrO, and T'm sites. Only specimens determined to be at least 950/ohomogeneous were used, and corrections to the refractive indices were made for nonbinary constituents.The resulting refractive index curves-not labeled conventionally as n., nu, a11dn", according to magnitude, but as nu, no, and n", according to which crystallographic axis the vibration direction is most nearly parallel- were found to change slope at Or-uo. Each was adequately representedby two linear segmentswith different slopes,meeting at Oruo.The segmentsand inflection point corre- spond very closely to those representingthe plot of density versus mole percent Or. As in the case of low microcline-high sanidine, the 2V* versus mole percent Or curves are sigmoidal becausethe no and nc curyes cross; 2V* : 0" at Or-r, for 2tr : 6.69. tn" composition for this crossoverpoint decreasesas )t' decreases.

INrnooucrroN do,oas measuresof the degreeof (Al,Si) order. Hewlett Many attemptshave beenmade to characterizethe vari- combined some of Spencer'sdata with his own to prepare ation of the refractive indices (and2I) of alkali feldspars a semiquantitative picture of the relationshipsamong op- of "high" structural state (seea review of early literature tical properties,composition, and (Al,Si) ordering in alkali by Hewlett, 1959,p. 534). The classicwork of Spencer feldspars.A notable contribution was his recognition that (l 937) producedexcellent sets ofoptical data for naturally structural state is directly related to partial birefringence occurring perthitic specimensand for their heat-treated "b" - n", where "b" is the principal refractive index and presumably homogenized equivalents. Adding six sets whose vibration direction is most nearly parallel to the b of data, only one of which was collectedon a homogeneous crystallographicaxis. specimen,Tuttle (1952, Fig. 2, p. 559; cf. Deer et al., However, as far as the high albite-high sanidine series 1963,Fig. 30, p. 60) drew straightlines through n., nu, is concerned,the relationshipsbetween refractive indices ar,d n,, delineating a "sanidine-anorthoclase" seriesand and composition have remained confusing, at best, and an "orthoclase-lowalbite" series.Smith's Figure 8-9 (1974, the various attempts to summarize and/or simplify them p. 386) is a modified version of Tuttle's drawing with a for determinative purposes(e.g., Bambauer et al., 1979, few additional data points, but it gives limiting curves Fig. 223-232, p. 123; Shelley,1985, Fig. 9.61, p. 182; only for the low series. Phillips and Griffen, 1981, Fig. 7-20, p. 342) are mis- To date, the careful study by Hewlett (1959) of a suite leading. of chemically analyzedsanidines and anorthoclasesis the best documented,because he not only measuredrefractive F.lcrons AFFECTINGREFRACTTvE INDTCES indices and corrected the n. values for effects of minor In addition to minor chemical constituents,a number components,but he also checkedcrystals for homogeneity offactors have combined to obscurethe correct relation- by single-crystalX-ray methods and reported d-spacings ship betweenrefractive indices and Or content in the high determined from powder-diftaction pattems. He used duo' albite (analbitelhigh sanidine series.These include the as an independentmeasure of Ab content (note that strain mixing of specimenswith widely different structural states may affectthis parameter)and was the first to usedoo, and in the data set upon which analysesand conclusionswere based,the way in which the structural statewas quantified, ' Academy Permanent address:Institute of Geology, Chinese and the convention used to label the principal refractive Beijing, People'sRepublic of China. of Sciences, "high" struc- 'zPresent address: Department of Geology, University of New indices. First, let us definewhat is meant by Mexico, Albuquerque,New Mexico 87131,U.S.A. tural state. 0003404x/86/l I l 2-l 393$02.00 I 393 t394 SU ET AL.: OPTICAL PROPERTIES OF HIGH ALBITE-HIGH SANIDINE

Table 1. Data of homogeneousalkali feldspars with 0.50 < >t, < 0.65

Sample Ab An Cn Srf Rbf Fef 2V, )t, Ref 1 MAB177 0.3(0.3) 99.7(99.7) 0.0 0.0 0.0 0.0 0.0 1.5276(1.5276) 1.5346(1.5346) 1.5364(1.5364) 53.6 0.59 7 2 MABl69 0.3(0.3) 99.7(99.7) 0.0 0.0 0.0 0.0 0.0 1.5279(1.5279\ 1.5344(1.5344) 1.5372(1.5372], 66.1 0.64 7 3 RAMONA(H) 1.1(1.1) 98.7(98.9) 0.2 0 0 0.0 0.0 0.0 1 5273 (1.5272) 1.s344(1.5343) 1.5357(1.53s6) 46.9 0.51. 4 4 DO-1 25.2(27.1) 67I (72.9)6 5 0.4 0.0 0.0 0.0 1.5275 (1.5237) 1 5324(1.5289) 1.s337(1.5303) 56.0 0.54 1 5 HEW-10 27.9(28.7) 69.3(71.3) 1.4 0.5 0 9 0.0 0.0 1.5258(1.5242) 1.5313(1 .s298) 1.5328 (1 .5314) 55.5 0.61 2,3 6 SP-R(H) 39.6(41.0) 56.9(59 0) 3.4 0.1 0.0 0.0 0.0 1.s222 (1.5201) 1.5282(1.5263)1.5293 (1.5274) 49.8 0.62' 5, 6 7 SP-P(H) 43.4(43.41 56.5(56.6) 0.1 0.0 0.0 0.0 0 0 1.5209(1.5208) 1.5265(1.5264) 1.s267(1.5266) 15.0 0.50. 5,6 8 439 438 (46.0)514 (54.0)3.8 0.0 0.1 0.0 0.9 1.s238 (1 .521 0) 1.5292(1.5266) 1.5306 .5281) 53.3 0.59 5, 9 9 SP-N(H) 50.7(51 1) 48.6(48.9) 0.5 0.2 0.0 0.0 0.0 1 5202(1.5198) 1.5255 (1 .5251 ) 1.5258 .52s4) 34.0 0.57. 5,6 10 SP-M(H) 52.2(s3.2)46.0(46.8) 1.8 0.0 0.0 0.0 0.0 1.5206 (1 .5195) 1.5255(1 5245) 1.5263 .5253) 45.0 0.63- 5, 6 11 HEW-15 52.7(55.4) 42.4(44.6) 32 1.2 03 0.2 0.0 1.5223 (1 .51 93) 1s269(1.s242)1.5274 5247) 41.3 0.63 2,3 12 HEW.4 57.6(59.7) 38.9(40.3) 2 0 1.1 0.3 0.1 0.0 1.5226(1.5204) 1.5269(1.s249) 1.5275 52s5) 41.8 0.60 2,3 13 1909-261 s9.7(61.7) 37.1(38.3) 1.7 1.1 0.3 0.0 0.1 1.5221(1.5200) 1.5268(1.s249) 1.5273 .5254) 35.3 0.59 5, I 14 SP-J(H) 61.2(61.8) 37.8(38.2) 0.7 0.0 0.3 0.0 0.0 1.5191(1.5185) 1.5240(1.5234) 1.5240 1.5235) -16.0 0.52- 5,6 15 SP-(H) 640 (64.s) 352 (35.s) 0.8 0.0 0.0 0.0 0.0 1.51 90 (1.51 85) 1.5237(1.5233\ 1.523 1.5233) 0 0 0.55' s, 6 16 SP-K(H) 662 (67.4)32 0 (32.6) 1.6 0.0 0.2 0 0 0.0 1.51 98 (1.5187) 1.5246(1.5236) 1.525 .5241) 20.0 0.58' 5, 6 17 HEW-l3 66.7(68.0) 31.3(32.0) 1.7 0 0 0.0 0.3 0.0 1.s1 94 (1.5184) 1.5239(1.5230) 1 5240 1.s231) 21.8 0.61 2,3 18 HEW.s 67.7 (71.6) 26.9(28.4) 18 1.3 2.2 0.1 0.0 1.5235(1 .5203) 1 5277(1.5247) 1.52831.5253) 42.5 0.62 2,3 19 HEW.3 69.8(72.0) 27.1(28.0) 0.1 2.8 0 2 0.0 0.0 1.5211 (1.5189)1.s253(1 .5232) 1.5258 s237) 35.8 0.65 2,3 20 SP-G(H) 71.1(73.1) 26.2(26.9',)0.1 2.2 0.4 0.0 0.0 1.sl99 (1.s1 80) 1.5247(1.5229) 1.5242 .s224)-29.0 0.53- 5,6 21 SP-H(H) 71.1(73.9) 25.1(26.11 1.9 1.7 0.2 0.0 0 0 1.s203 (1 .51 78) 1.5250(1.5226l- 1.5248 52241 -17.0 0.56- 5,6 22 SP-F(H) 72.8(74.31 25.2(2s.7)1.6 0.2 0.2 0.0 0.0 1.5192 (1 .51 80) 1.5240(1.5229]' 1.5236 .5225}, -28.0 0.54. 5,6 23 HEW.2 740 (74.8)24I (25.2)0.8 0.1 0.1 0 1 0.0 1.5191(1.5185) 1.5237(1.52311 1.5237 .5231) 0 0 0.60 2,3 24 r-1 76.4(77.4) 22.3(22.6)0.8 0.0 0.0 0 0 0.4 1.5201 (1 .51 93) 15252(1.5245) 1.5248 .5241) - 17.0 0.s9. 8 25 HEW.l 77.4(79.8) 19.6(20.2) 1.6 0.9 0.4 0.1 0.0 1.5206 (1 .5187) 1.s248(1 .s230) 1.5248 .5230) 0.0 0.59 2,3 26 HEW-12 79.2(81.9) 17.5(18.1) 2.2 0.6 0.2 0.3 0 0 1.s199 (1 .s1 79) 1.5241(1.5223) 1.s241(1.5223) 10.0 0.57 2,3 27 SP-D(H) 80.9(82.3) 17.4(17 .71 1.2 0.3 0.2 0.0 0.0 1.5189 (1 .51 78) 1.5236(1.5226) 1.5233(1.5223) -33.0 0.56. 5,6 28 HEW-11 79.0(83.8) 15.3(16.2) 1.7 1.2 2.4 0.4 0.0 1.5228 (1 .51 95) 1.5269(1.5239) 1.5270(1.5240) 28.0 0.61 2,3 29 7002H 83.1(85.4) 14.2(14.6) 0.5 1.3 0.0 0.0 0.9 1.51 96 (1.5177) 1.5243(1.5226) 1.5237(1.5220) -42.6 0.54 5, I 30 SP-E(H) 8s 6 (87.s) 12.2(12.5) 0.9 1.1 0.2 0 0 0.0 1.51 90 (1.5175) 1.5235 (1.5221) 1.5232(1.5218) -29.0 0.60. 5,6 31 SP-C(H) 90.s(91.5) 8.4(8.5) 0.7 0.2 0.2 0.0 0.0 1.5187(15180) 1 s233 (1.5227) 1.5227('t 5220) -44.8 0.56" 5, 6 32 SP-A(H) 92.6(92.6) 7.4(7.41 0.0 0.0 0.0 0.0 0.0 1.5192 (1 .5192) 1.5240(1.5240) 1.5230(1 .s230) -53.8 0.52' 5,6 A/ote.For each sample, the adjusted composition, Or/(Or + Ab) and Ab/(Or + Ab), and the corrected refractive indices are given in parentheses beside their respective observed values The negative signs of 2V, values (in degrees) signify that the optic axial plane is parallel to (O1O).The >t1 values were derived either from lattice parameters b and c- or from 2V, and mole percent Or (marked -) using Fig. 2 in Su et al. (1986b).References are as follows:(1) DePieriand Quareni(1973); (2) Emersonand Guidotti(1974); (3) Hewlett(1959); (a) Smitfr(1958);(5) Smith and Ribbe(1966); (6) spencer(1937); (7) Su et at. (1986a);(8) Tutile (1952);(9) warner et at. (1984).

Definitions Methods of determining structural state The symbolstro, trm, t2o,t2m are customarilyused to To determine )1, it is most desirableto have a neutron- designatethe Al contentsof the TrO, T,m, TrO, Trm diffraction refinement of the (Al,Si) distribution among tetrahedralsites oftriclinic alkali feldspars(where t, : the nonequivalent tetrahedral sites or, failing that, an X-ray number of Al atoms in T, sitesdivided by the total number structurerefinement. The latter involves interpretation of of T, sites). Thus, high albite (HA) is highly disordered bond lengths in terms of Al content t, of site T,, and this and definedas tro >> trm > t2o : trm. There is no con- is described at length in a review by Kroll and Ribbe vention to exactly define "high" albite relative to "inter- (1983),who also prescribedmethods of quantitatively es- mediate" albite. However,we havedesignated >tr : (t,o + timating 2t, by using the demonstrated relationship among trm) as a measureof structural stateand in this study used lattice parameters,mean T,-O bond lengths,and Al con- only specimensfor which 0.5 < >tr < 0.65.Analbite (AA) tents of tetrahedral sites or pairs of sites, namely 2t, : is also highly disordered and metrically triclinic, but it (tro + t,m) [note that 2t2: | - >t,]. The Kroll-Ribbe has t,o : t,m and tro : trm and thus can invert displa- equations lOa and lOb have recently been revised using cively to metrically monoclinic monalbite abovethe tran- additional structural data plus a better algorithm for sition temperature (-980t for pure, highly disordered regressionanalysis. Accordingly, to estimate )t, for spec- NaAlSirOr). The distinction between HA and AA is un- imens from lattice parameters,we use important at this stageof our investigation. For the K-rich series, monoclinic high sanidine (HS) 2t, : 2t,: 72.245- 3.tt30b - 200.785c* has been defined traditionally on the basis ofhaving its for monoclinic feldsparsand optic axial plane parallel to (010) [shorthand: O.A.P. : (010)1.Using data from crystals whose averagecompo- b - 2t.5398+ 53.8405c* )t,:t,o+trm: sition was Orno,Su et al. (1984) establishedthe fact that 21.1567- 15.8583c* 0.5 < >tr < 0.67 for K-rich high sanidines.See Kroll et al. (1980) for further discussionof nomenclature. for triclinic feldspars(standard error of estimateis +0.01 SU ET AL.: OPTICAL PROPERTIES OF HIGH ALBITE_HIGH SANIDINE r395 for assumederrors of +0.002 A in D and +0.000 02 A-' Table 2. Refractiveindices of some endmemberfeldspars prep.). in c*; Kroll and Ribbe, in Endmember n. np Ref In the absenceof lattice parameters,we have used the CaAlrSirO. 1.5751 1 5838 1.5886 1.5825 2 optic axial angle2V, to estimate21,, as discussedin detail BaAlrsiroo 1.589 1.593 1.599 1.594 4 by Su et al. (1986b).Fortunately, it is not extremelyim- SrAl,SirO. 1.574 1.582 1.586 1.581 3 portant for the present study that structural state be pre- RbAlsi"oo 1.520 1.529 1.525 1 KFeSi3Os 1.554 1.595 1.605 1.585 5 ciselyknown, becauserefractive indices are not extremely sensitive to variation in )1,, varying from as little as Note; The average structures of the alkaline-earthfeldspars are disordered (Ribbe, 1984),the structural state ot the Rb-feldsparis not known' 0.00001 to a maximum 0.00006 per 0.01 >t, in any and the Fe-feldsparis an "iron sanidine"'References are as follows:(1) isocompositional alkali feldspar series. Boratskayaand Vlasova(1975) quoted by W. L. Brown (pers.comm.); (2) Burri ;t al. (1967);(3) Eskola(19221; ($ Rov (1965);(5) wones and Labeling principal refractive indices Appleman(1961). Probably the factor that has most obscured the true relationshipsbetween optical properties and composition in the HA(AAIHS series is the same one that plagued stituentscommonly found in minor amounts in high-tem- the relationshipsbetween refractive indices and structural peraturealkali feldspars.Hewlett (1959,p. 520f.)devised statefor the K-rich alkali feldspar series,low microcline- a simple linear method to correct his n" indices (only) for high sanidine.The principal refractive index ofa feldspar the effects of iron content plus Ca-, Ba-, Sr-, and Rb- should be labeled, not a, p, and ,y or n., nB,and n, in the feldspar components. Our sourcesof mean refractive in- traditional manner, but nu,no, and n" accordingto which dices fl, were the same as his for SrAlrSirO' (Srf), but crystallographicaxis a, b, or c the vibration direction is differed for anorthite (An), celsian(Cn), RbAlSi.O' (Rbfl, parallel or most nearly parallel. Hewlett's (1959) "b" cor- and KFeSi.O, (Fe|; seeTable 2. We used the following respondsto no, and in all alkali feldsparsn^: n,. For approach to calculate the corrected indices: monoclinic high sanidineswith O.A.P. : (010), /h,: ns n|.T".: nlH..- - n2b;,.)M,/1001, and n. : n,, b:ur these are reversed for all other alkali l(n, feldspars,i.e., those with O.A.P. I (010)or approximately whereM, is mole percent of the lth component and u3$". I (010)(Su et al., 1984;Bloss, 1985). is the value of n^, no,or n" appropriate to the mole percent feldsparas determined from regressionlines fitted Trm n.l.:ra n.q,sp Or of a to the observedindices (plotted in the upper portions of Choice of specimens Figs. la, lb, and lc; lines not shown). The 32 chemicallyanalyzed alkali feldsparswith 0.50 s More refined values for fi33'.could have been attained >tr < 0.65 selectedfor this study are listed in Table 1. by iterative methods, and we testedtwo of the more "im- They include a heatedhigh albite from Ramona, Califor- pure" specimens(Hew-l I and Hew-I5) only to find that nia (J. R. Smith, 1958), two high albite single crystals the final values of n;"4" changed insignificantly (by prepared by heating a Clear Creek, California, specimen + 0.000 I 5 or less).Corrected indices are listed besidetheir at high pressures(Su et al., 1986a), a highly disordered respectiveobserved values in Table l. Corrected indices anorthoclase,whose structure was determined by DePieri are plotted in the lower portions of Figures |a, lb, and and Quareni (1973), a homogeneousEifel sanidine (Tut- lc as a function of Or/(Or + Ab), whereasthe observed tIe, 1952), the fourteen homogenizedand "sanidinized" values are plotted in the upper portions as a function of specimensof Spencer( I 93 7) that had beenheated for I 00 Or/(Or + Ab + An + Cn + Srf + Rb|. to 300 h at 1075'C, and nine sanidinesand one anorthoclase from Hewlett (1959). New data were added for a Y.lnrlrrox oF REFRACTIvEINDICES wrrH heatedEifel sanidine(7002H) and for two natural volcanic COMPOSITION specimens (439 and 1909-261;' Carmichael, 1965) by Warner et al. (1984) attempted to correlate no, nb, and Warner et al. (1984), who determined optical properties n" with Or content for a few analyzedsingle crystals whose and lattice parameterson the samesingle crystal. Because lattice parametershad been determined. In that prelim- submicroscopicintergrowths have some small effectson inary study, effects of minor constituents were ignored, refractive indices,we have attemptedto usehomogeneous and linear regressionlines showed that no and n. crossed feldsparsfor our investigation. To our knowledgewe have betweenOrro and Orro.However, it was observedthat the allowed only two exceptions to this, namely Hewlett's n" data were fit using a quadratic equation significantly specimens4 and 15, which are described as having less better than with a linear one. Numerous unresolvedques- than 5oloexsolved Na-feldspar component (his Table 8, tions led to this broader investigation using the 32 data p. 527; seealso powder-difraction studies of the Hewlett setsdescribed above. Indices,composition, and structural specimensby Emersonand Guidotti,1974). state were all measured on the same crystal for five of these,so it is obvious that somescatter in the relationships Correctionsfor minor constituents is to be expected.Moreover, scatteris inevitable because Chemical factors that obscurethe relationship between a rather wide rangeof structural states(0.50 = >tr < 0.65) refractive indices and Or content are the nonbinarv con- was intentionally allowed, and some chemical zoning and r396 SU ET AL.: OPTICAL PROPERTIES OF HIGH ALBITE-HIGH SANIDINE

no observed

ooa - x o . . t. o !t !, .9r t- tt'.' s2o .9 3.a o o ': o I Ol 52 o o o t a

nO COtreclcd

mol % Or mol % Or

N 50. o E .-c o .= x 0 o o t, .g o o G. o o o G,

mol% Or mol% Or

Fig. 1. Principal refractive indices as a function ofcomposition for specirnens\nith 0.5 = )t, = 0.65: (a) n", (b) no, and (c) n". The upper portion ofeach figure displays the observedrefractive indices plotted againstOr/(Or + Ab + An + Cn + Srf + Rb|; the lower portions have indices correctedfor minor constituentsand are plotted againstOr/(Or + Ab). Regressionlines are drawn through the correcteddata sets,segmented at Oruo.(d) The regressionlines for HA-HS seriesfrom the three separate(a), (b), and (c) plots on the same scale,together with the observed 2V, data points and the 2V, curve calculatedfrom the regressionlines for refractive indices. Data in Tables I and 3. Solid symbolsare for homogeneousspecimens; open symbols are for unmixed specimens. variation in structural state are expected from grain to but much less steep from Oruoto Or,oo.If a single curve grain within any bulk-analyzedsample (seeespecially Ta- were fitted to each full data set (Oro to Ornr), each would ble 5 of Hewlett, 1959). be concave upward and resemble Hewlett's plot of the Plots of both the observedand the correctedn^, no, and index n. versus Or content for (l) alkali feldspars from n. indices versusOr content (Figs. la, lb, and lc) disclose Or' to Or' that he had heatedand homogenizedto high negative slopesthat are relatively steepfrom Oro to Oruo structural states(see Hewlett's Fig. 2a) and (2) Spencer's

Table3. Statisticsfor equationsrelating principal refractive indices to molefraction of KAlSi.O,(: Xj for the samplesin Table1

Predictedn Eq Or range no (mol%) Dep var. ao aj s Oro Or* Or,oo 1 0-60 n" (n) 1.5276(5) -0.0146(11) 0.951 0.0008 1.5276 1.5188 2 0-60 n" (ne) 1 5345(3) -0.0180(8) 0.984 0.0006 1.5345 1.5237 J 0-60 no(n) 1.536s(5) -0.0205(11) 0.973 0.0008 1.5365 1.5242 4 60-100 n, (n"l 1.s205(1 5) - 0.0026(19) 0.091 0.0008 1.5189 1.51 79 60-100 n. (np) 1.5257(14) -0.0032(19) 0.137 0.0008 1.5238 1.5225 o 60-100 n, (n,) 1.5280(1 7) -0.0063(22) 0.319 0.0009 1.5242 1.5217 Note; The statistics were derived by linear least-squaresregression methods (n,: ao + a,Xo). The numbers in parenthesesare standard errors referringto last digit(s).Coefficient of determination,2, square root of mean errors s, and predicted values for Oro,Or* and Or,ooare also listed. The very small I values for the range Oro-Or@are due to the very limited range of the independentvariable X@. SU ET AL.: OPTICAL PROPERTIES OF HIGH ALBITE-HIGH SANIDINE 1397

(1937) data (seeHewlett's Fig. 2b) that cover a slightly 26 (Oroo a LA-LM series broader range to Ornr). A o AA-HS series

The preceding trends relating refractive indices to Or OA content find corroboration in terms of the variation of o density with Or content. Densities of the high albite (an- ? o albitefhigh sanidine serieshave been studied by Spencer 3, (1937),Barth (1969), and Smith(l974,Fig.l2-15). Using oA OA unit-cell volumes and compositionsfor well-characterized oo LA-LM (low albite-low microcline) and AA-HS ex- "od6l4|crodo^ change series from Kroll et al. (1986, Tables 4 and 5), theoretical densitieswere calculatedand plotted in Figure 254 mol 7" Ot 2 versusmole percentOr for both the low- (LA-LM) and percent high-temperature(AA-HS) series.The trends in Figure 2, Fig. 2. Variations of density with mole Or for the LA-LM and the AA-HS alkali-exchangeseries. Densities were which resemblethose in Smith's Figure 12-15, mimic calculatedfrom unit-cell volumes and compositions reported by those in Figures la, lb, and lc. This is not surprising Kroll et al. (1986,Tables 4 and 5). becauseit is well known that, in general,refractive index and density vary sympathetically. Although polynomial curves best fit the density versus proximation, it is probably all that the data can substan- composition data, we arbitrarily chose Oruoas a flexure tiate. More sophisticated treatment would require a series point in Figure 2 and assumedthat Oruoalso marked a ofdata sets for which indices, 2Z structural state, and flexure point in the index versus composition data (Figs. bulk composition had each been measured on the same la, lb, and lc). Accordingly,least-squares regtessions were crystal. The work involved in such an undertaking would performed on the refractive-index data between Oro and seem unjustified in the light of the present results. Even Oruoand between Oruoand Or,oo.The six lines shown in if better curyes for nu, no, and r. versus mole percent Or Figures la, lb, and lc, whose intercepts (ao) and slopes were to be produced, they would have no practical ap- (a,) are listed in Table 3, were thus obtained. Whether plication. thesesix linear relationships truly prevail remains moot. The curve plotted in Figure ld represents the variation On the other hand, lf nu, no, or n" is predicted for the of optic axial angle 2V* with Or/(Or + Ab) as calculated composition Oruousing the line from Oro to Oruoline and, from the equations of no, no, and n,, summarized in Table again, using the line from Oruoto Or,oo,the values agree 3. If the observed 2V*values for the 32 specimens (Table to within +0.0001 (Table 3). l) are plotted in Figure ld, the scatter is great and is due The mean refractive index (n) of our correcled nu, no, almost exclusively to differences in the structural states and n" refractive indicesequals I .53 29 for high albite (Oro) of the specimens used for determining the refractive-index and 1.5207 for high sanidine (Or,oo),whereas their den- curves. This is discussed in detail by Su et al. (1986b). sities (p),as calculatedfrom the data ofKroll et al. (1986), g/cm3(Oro) g,/cm3(Or,oo). are 2.615 and 2.555 Inserting AcrNowr,BncMENTS these values into the left side of the Gladstone-Dale re- part lationship This work was supported in by National ScienceFoun- dation Grant EAR-83-08308to F.D.B. and P.H.R. S.C.S.grate- fully acknowledgesfinancial support from N.S.F. and a Cun- ningham Fellowship awarded by Virginia Polytechnic Institute T:,0,r,, and State University. We are grateful to H. Wondratschek of Universitiit Karlsruhe, West Germany, and especiallyto D. B. Reston,Virginia, for com- where k, is the Gladstone-Dale "constant" and is the Stewartof the U.S. GeologicalSurvey, {, ments and constructive criticism. We appreciatethe helpful re- weight fraction of the ith oxide (see Larsen, l92l), the views of this manuscript by G. L. Hovis and P. Cern!. quotient (n - l)/ p equals0.2038 in both cases.The precise equality trends to corroboratethe correctedvalues for n", no, andn., as well as the calculateddensities. RrrnnBNcBs Note that in Figure ld the no and n. curves cross at Bambauer,H.U., Taborszky, F., and Trochim, H.D. (1979) Op- about Orrr, where 2V*: 0o and the optic axial plane tical determination of rock-forming minerals. Part 1. Deter- changesfrom O.A.P. approximatelyf (010)to O.A.P. : minative tables. Schweizerbart'sche Verlagsbuchhandlung, 188 p. (010). Stuttgart, This intersection will vary, depending on the av- Barth, T.F.W. (1969)Feldspars,26l p. 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