American Mineralogist, Volume 67, pages 975-996, 1982

The anorthoclase structures: the effects of temperature and composition

GBoncn, E. Henlow

Department of Mineral SciencesAmerican Museum of Natural History

New York, New York 10024

Abstract

Cell-parameter and structure refinements using single-crystal X-ray difraction have been

carried out on three natural low-Ca anorthoclases (K-analbites)' (Or:z.sAboo uAno s,Or22 3Ab7s.3An6 e, Or13 3Abs3 7An2 5), at room temperature and at temperatures above the

triclinic/monoclinic symmetry inversion (400', 510", and 750" C, respectively). Room

temperature cell parameters are consistent with monoclinic Si,Al topochemistry and a high

degree of disorder (tr : 0.50 to 0.52 from the b-c plot). A room-temperature inversion

composition of 0136 is extrapolated from cos2a* and T-O-T angle plots. Mean M-O bond

lengths and T-O-T angles increase with potassium content, whereas their variances

decrease, indicating a trend to more regular coordination, as in sanidine. A similar

relationship develops with thermal expansion and the structural changes associated with

inversion to monoclinic symmetry, but the individual (M-O) values suggest a non-

isotropic, ellipsoidal expansion of Na-rich alkali cavities. Examination of dimensionalchange in the structures due to change in temperature and alkali composition indicates that

most of the effect is related to change in M-O bonding, with the aluminosilicate framework

responding passively. Anisotropic thermal models for single M sites produce non-positivedefinite ellipsoids. Modeling with isotropic split-sites yields four parts for the more sodic

structures, essentially identical to the models for high albite or analbite. For the morepotassic crystals, a separate isotropic K site and an anisotropic Na(Ca) site is indicated.

Introduction

There is much interest in characterizing the varia-tion in the feldspar structures because of the abun-dance and importance of feldspars in petrologicprocesses and because of their general significancein mineralogical studies of exsolution and polymor-phism, especially order-disorder. The structures ofdisordered alkali feldspars with near end-membercompositions have been widely studied. Sanidine, amonoclinic (CZlm) hiph-temperature modificationof K-feldspar, has been examined at 23'C withneutron diffraction (Brown et al., 19'14) and at23",400'and 800' C with X-ray diffraction (Ribbe, 1963;Weitz, 1972; Phillips and Ribbe , 1973a; Ohashi andFinger, 1974,1975:' Dal Negro et a|.,1978). Thesestudies have shown that sanidine may have varyingdegrees of Si,Al disorder consistent with the mono-clinic symmetry (monoclinic Si,Al topochemistries)and have elucidated the nature of the irregularcoordination of the alkali cation. Similarly, studiesof disordered Na feldspars (Ribbe et al., 1969;

Wainwright, unpublished, see Smith, 1974:' Ptewittet al..1976; Winter and Ghose, 1977;Winter et al.,1979). which are all triclinic (Cl) at room tempera-ture, have shown that they only become monoclinic(monalbite, CLlm) upon rapid heating through adisplacive transformation when the Na-feldspar isvery highly to fully disordered and has monoclinicSi,Al topochemistry. Disordered Na-feldspar withtriclinic Si,Al topochemistry is termed high albitewhereas Na-feldspar that has monoclinic Si,Al to-pochemistry but a triclinic morphology (i.e., attemperatures below the displacive transformation)is termed analbite. These studies have also indicat-ed the possibility of positional disorder of the alkalication (M) site in the collapsed and elongated cavityat room temperature and have characterized thenature of the expansion or inflation of the M-sitecavity upon rapid heating.

Less is known about the structures of disorderedalkali feldspars with intermediate composition' An-orthoclases, one of the most abundant naturally-occurring alkali feldspars of this type, are recog-

0003-m4)v82l09 I 0-0975$02. 00 975

HARLOW : ANORTHOCLASE STRUCTT]RES

nized by petrographers by their volcanic associa-tion, rhombic shape and fine polysynthetic, oftencross-hatched ("tartan") twinning. In terms ofSi,Al order they may occur as topochemically tri-clinic K,Ca-high albite, topochemically monoclinicK,Ca-analbite or a cryptoperthitic intergrowth ofNa-sanidine and K,Ca-analbite or K,Ca-high al-bite. Though there are some problems with compo-sitional criteria (De Pieri et al.,1977), the composi-tional limits of anorthoclases are as indicated inFigure I (adapted from Kroll and Bambauer, lggl).Included are cryptoperthites in which the heatedphase assemblages consist of monoclinic feldsparsor a single homogenized monoclinic feldspar. Onlyone published refinement of an anorthoclase isavailable (De Pieri and Quareni,1973), but as it wasrefined from film data, the precision is not compara-ble to that of other refinements on disordered alkalifeldspars. Thus we do not have the informationabout disordered Na-rich alkali feldspar structuresneeded to make comparisons with the near end-member composition structures, or to allow thedesirable thermodynamic calculations of their equa-tions of state (c/. Thompson et al., 1974).

A structural study has been completed on threenatural low-Ca (less than Anls) anorthoclase (K-analbite) samples at room temperature and at tem-peratures at which the crystals are monoclinic (from400'to 750" C. The results of this study are reportedin two parts. This first part treats the features of thecrystal structure and cell geometry related to varia-tions in alkali chemistry and temperature. Thesecond part deals with Si,Al order and the specificnature of apparent thermal motion.

Materials and methods

Specimens of anorthoclase were provided by W.S. MacKenzie and the National Museum of NaturalHistory of the Smithsonian Institution. Specimensfrom three localities were selected: Grande Cal-deira, Azores, Or32.5Ab66.7Anq.s (fragments fromlavas, #15 of Carmichael and MacKenzie, 1964);Mt. Gibele, Pantelleria Islands, Italy, Orzz-tAb7s.sAn6.e (loose phenocrysts , #12 of Carmichaeland MacKenzie,1964); and Kakanui, New Zealand,,Or13.sAb33.7An2.5 (as xenocrysts in Deborah volcan-ic sequence, NMNH #133868, see Dickey, 1968).The most K-rich anorthoclase was a cryptoperthite

Ab59Or59 Sonid ines

Ab5OOr OO

A bTgOr 3pTwo feldspors

Abgg0r2t

A b 9 9 O r 1 9

Ab AbggAn;o AbggAnzo AbToAn3o AbsoAn4o AbroAn5gFig. l. The phase diagram in the Na-feldspar corner of the feldspar composition triangle: solid lines with temperatures ("C) indicate

the approximate point at which K,Ca-analbites become monoclinic (after Fig. 8, Kroll and Bambauer, lgEl). Samples examined inthis study are shown by circles. Compositions are in mole percent.

An

Anorthoc lose-s

l o g i o c l o s e s

HARLOW : ANORTHOCLASE STRUCTURES 977

consisting of a monoclinic K-rich phase (Na-sani-dine) and a twinned triclinic Na-rich phase (K-analbite). Fragments of the cryptoperthitic materialwere placed in a platinum capsule and heated in anelectric furnace at 700" C, within the stability fieldof single alkali feldspar (cf. Luth et al., 1974), forapproximately 24 hours to homogenize the sample.Subsequent X-ray reexamination confirmed the ho-mogenization, and suitable crystals were then se-lected for structure analysis.

The samples selected for intensity data collectionwere cleavage fragments, generally bounded by(001), (010), and (201) or (100). Approximate dimen-sions of the fragments used are given in Table 1.The chemical composition of the specimens (Table2) was determined with an ARL-EMX electron micro-probe using the data reduction method of Bence andAlbee (1968) with the factors of Albee and Ray(1970). No inhomogeneities or Sr or Ba were detect-ed in the samples.

The furnaces used for the high-temperature X-rayexamination (one for the precession camera and onefor the diffractometer) are a modification of thedesign of Brown et al. (1973) that allow for easier

Table l. Structure refinement information and sample sizes

GrandeCa lde i r a M t . G ibe le Kakanu i

Table 2. Electron microprobe analyses

|,/'r. %Gr ande

C a l d e i r a M t . G i b e l e Kak anu i

C a o 0 . 1 7Ktl 5. 9n a 2 0 7 , 9T i 0 2Fe203 0 .435 1 U 2 0 0 . O

A l2b3 18 .6

Total 99.6

Ca t i ons pe r8 oxygen atoms

0 . 5 3 0 . 7 92 . 5 2 . 0 59 . 9 9 . 4 4

0 . 1 7 m i n o r65.4 67 .420.4 20.1- +e8. 9 99 . 88 '

0 .026 0 .040 . 1 4 1 0 . 1 20 . 8 5 n 0 . 8 17.O23 0 .97

0 . 0 0 62 . 9 2 7 2 . 9 77 . 0 7 7 1 . 0 5( n ? ? 4 q q

13.8 72 .78 3 . 7 8 4 . 0

t q i o

2 . 7 7 2 . 9 41 . 0 2 1 . 0 4

CaKNa

Subtota l

T iFeS iA I

Total

Fe l d sparcomponen t (mo l .%)

0. 0080. 3140. 6861.028

0 . 0 1 42.9940. 9875 . 0 2 3

1 q

8 . 20 . 09

65.71 9 . 598.8

0 .0690 . 2 2 40 . 7 1 0I .0030. 003

t aq2

1 .0364.994

7 0 . 86 . 93 . 0 57 . O 7

0 r r 2 . 5Ab 66.7An 0 .8s j : R * 3 . 0 2RZ0g 1 .01

r D i ckey ( 1968 )* n i s i i , . t o t i t o f Fe+3 and A l+3 ; R203 i s no rma l i zed

to t he ano r t h i t e con ten t t o exam ine poss ib l e non -s to i ch i ome t r y o f t he f e l dsPa r

furnace alignment. For a complete description seeHarlow (1977).

Crystals selected for high-temperature studywere cemented to silica-glass fibers. Encapsulationin silica-glass capillaries was not deemed necessarybecause there was no iron in the samples to causeoxidation problems, and because the highest tem-peratures were to be below 800'C, judged lowenough not to cause alkali sublimation. For tem-peratures below 400" C, Dupont NR-15082 polyim-ide binder solution (supplied courtesy E. I. Dupontde Nemours & Co.) was used. For temperatures of400' C or greater, the clear cement in Ceramabond503 High-Temperature Adhesive (Aremco Prod-ucts. Inc.) was used. No diffraction contributionfrom the cements was noticed.

The temperature of the displacive monoclinic/triclinic inversion for the feldspars was estimatedby examining X-ray precession photographs takenat temperatures up to about 50o above the estimatedinversion. Precession photographs confirmed thatthe crystals had attained monoclinic symmetry.Later the twin angle on a-axis nets 2'(90 - a*) wasmeasured at several elevated temperatures, andinversion temperatures were estimated by plotting

Room Temperature:Re f l ec t i ons co l l e c tedIn i t i a l un re j ec tedFinal unrejectedRw i so t rop i cRu i so t r op i cRw an i so t rop i cRu an i so t rop i c

H igh Tempera tu re (C I ) :Re f l ec t i ons co l l ec tedIn i t i a l un re j ec tedFinal unrejectedRw isotropicRu i so t r op i cRw an i so t rop i cRu an i so t rop i c

Hi gh Temperature (C2/n) :I n i t i a l un re j ec tedFinal unrejectedRw i so t rop i cRu i so t r op i cRw an i so t rop i cRu an i so t rop i c

C rys ta l d imens ionsin m i c rons

20262003I 8340. 0610.0800. 0350. 046

400020302016.167t

0 . 1 l 10 . 1 3 80.0620 . 0 7 4

4oooI 050855

0 . 0 7 70.1270.0430 . 0 7 3

I 50x70x5 U

1 846182216970. 0900. 0970 . 0 4 10.047

5t 00I 403

51 00I 044931

0 . 0 6 20.0890.0430.047

I 90xI 40xon

3002246021410 . 1 0 70 . 1 t 80 . 0520. 058

7 5002039200217520. 0960 . 1 l 90 . 0630. 074

7 500I 043899

0. 0670. 0850.0220 . ' l 0 5

I 60x90x80

* f u l l t r i c l i n i c da ta se t no t co l l ec ted

97E HARLOW : ANORTHOCLASE STRUCTURES

cos2c* vs. temperature (see Fig.2) as suggested byThompson et al. (1974). All three crystals selectedfor high-temperature structure refi nement appearedto be monoclinic at elevated temperatures, howev-er, the most K-rich, Grande Caldeira, showed somestreaking of diffraction spots in the directions of theold twin displacements at temperatures 100. abovethat of the estimated transition. This streakingindicates that some residual strain or dislocations inthe crystal existed and prevented all parts fromattaining monoclinic symmetry. However, this ef-fect was minor and not considered so serious as topreclude structure analysis.

Intensity data were collected on an automatedPicker recs-l single-crystal diffractometer usingunfiltered MoKa radiation at a 3o take-off angle.Orientation of a crystal for data collection wasprovided by a least-squares refinement of 12 man-ually centered reflections, which also yielded initialunit cell parameters. Data were collected in one halfof the limiting sphere of reciprocal space from 5. to60' or 70' two theta (0.062 < sing/\ < 0.705 or0.809) using the 0-20 scan technique with a scanspeed of l'lmin and an approximate 2.4o scan range(extended for KayKa2 dispersion). Backgroundcounts were measured for 20 seconds on each sideof the peak. Two standard reflections were collect-ed every 49 reflections. The total number of collect-ed intensities and initially unrejected ones are listedin Table 2. Initial rejection of structure data wasbased on evidence of interference due to overlap

Kokon u i

Mt . G ibe le

Grondeo

, ' , t . " \13' \ , .es'o 200 400 600 800

T " CFig. 2. Plot of cos2ax for each anorthoclase (K-analbite)

against temperature. Lines are fit by least squares; inversiontemperatures (intercept) are shown.

from Kp X-radiation or from the other twinnedportion of a crystal. For the Kakanui crystal, whichwas intimately twinned with nearly equal volumesin the two orientations, a larger number of reflec-tions were lost due to overlap. Therefore morereflections were collected (the half-sphere up to 70"20), and a computer program was developed todetermine which reflections might need to be reject-ed (see Harlow, 1977, for details).

A full triclinic data set was collected at hightemperature for the following reasons: first, tocompare the intensity of the reflections that areequivalent by monoclinic symmetry (hkl versusftftl); second, to be able to refine a triclinic structureand compare it with the requirements of monoclinicsymmetry, and third, to gain an increased accuracyby averaging the equivalent reflections before re-finement of the monoclinic structure. The tempera-ture of the diffractometer furnace was set at a valueapproximately 50" C above the measured inversiontemperature. Scans of the 005 reflection in the b*-cx plane (normally by means of a chi rotation) andthe 12 reflections used for orientation throtgh 0-20were made to check for splitting. These two stepswere repeated until no peak splitting was found andto be sure that the crystals were no longer twinned,i.e., were monoclinic. After refining the orientationmatrix obtained from the 12 reflections, the cellparameters were checked to insure that they weremonoclinic within the error of measurement.

After intensity data were collected, the positionsof approximately 40 to 50 reflections (sinO/), = 0.34)were measured and the values were entered in amodified version of Burnham's (1962) LCLSe (atticecell least squares) refinement program. The resultsare given in Table 3.

The crystals were reexamined with the preces-sion technique after data collection at high tempera-tures was completed. In all three cases the numberof twin-related orientations and the relative propor-tions of twin orientations that had originally existedchanged significantly. The change was most markedfor the Grande Caldeira crystal, which shows beau-tiful M-type twinning that according to Laves (1950)can only be caused by a transformation from mono-clinic to triclinic symmetry. Because the highesttemperature that any crystal experienced betweenthe two precession examinations was that at whichthe intensity data were collected, the crystals musthave been monoclinic during data collection. Theintensity data were corrected for background,scaled to a uniform level relative to standard reflec-

oo 20

*6

N

O

HARLOW : AN ORTH OC LA S E STRUCTURES

Table 3. Cell parameters

979

T ( o C ) a (E) b (fi) B ( o )c (fl)"

( o )l o r

^ 3V ( A ) o * ( o ) Y * ( o )

G r a n d e C a l d e i r a 0 r 3 2 , 5

23o C l 8 .290(2) I 2 .966( 3 )

rB3o ci B.3to8(B) 12.s7zs(s)4ooo !2/m 8.3482(7) r2.98oo(7)Mt . G ibe le 0 r 22 .323o C] 8.252(2) 12.936(2)38Bo cT 8 .290 (4 ) 12 .954 (3051Oo Cz/n 8.314(r \ 12.973(2)Kakanu i 0 r l 3 .Bz3o cT B. zr 68(6) rz .s166(t )7000 Cz /n B .3 l l ( l ) 12 .972 (2 )75Oo Cz/m 8.321(2) 12.969(2)

7 . r 5 r ( 2 )7 . r 5 7 8 ( 6 )7 . r 5 8 2 ( 5 )

7 . 1 3 e ( r )7 r 6 n { ? \

7 . r so ( r )

7.1270(5)7 . r 4 8 ( r )7 . 1 4 8 ( r )

e r . r B ( 2 )9 0 . 0 0 7 ( 5 )90 . 0

e2 . r1 ( r )e0 .75 (2 )90 . 0

e2 .754 (4 )90 . 090. 0

i l 6 . 3 r ( r )i l 6 . r 8 7 ( 5 )i l 6 . r o e ( 5 )

1 r 6 . 3 2 ( r )i l 6 . r 8 ( 2 )i l 6 . r 3 5 ( 8 )

r 6 . 3 5 7 ( 4 )i l 6 .07 r (7 )i l 6 . 0 5 ( r )

e 0 . 1 4 ( 2 ) 6 8 8 . 8 ( 3 )e o . o 3 3 ( 6 ) 6 e 2 . s ( r )e0 . o 6e6 .5 ( r )

e0 .22 (1 ) 682 .4 (2 )e 0 . 3 5 ( 2 ) 6 8 e . r ( 6 )

e o . o 6 e 2 . 4 ( 2 )

e 0 . 2 3 e ( 5 ) 6 7 6 . 7 ( 1 )e0 .0 692 .2 (2 )9 0 . o 6 9 3 . 0 ( 3 )

88.62(2)B e . e 7 6 ( 5 )90. 0

8 7 . 5 4 ( r )8 9 . 3 4 ( 2 )9 0 . 0

86 .808 (4 )90 . 09 0 . 0

8e .26 (2 )Be . e6o (6 )90. 0

B B . 7 r ( r )B e . e B ( 2 )90 . 0

8 8 . 3 6 7 ( 5 )90 . 09 0 . 0

Est imated s tandard dev ia t ions in paren theses re fe r to the las t d iq i ts

tion intensities, and corrected for Lorentz-polariza-tion effects. No absorption or extinction correctionswere applied as all crystals had maximum dimen-sions less than 0.2 mm and linear absorption coeffi-cients (g.) less than 11 cm-r.

The structure factors were entered in L. W.Finger's RFINE II (Geophysical Laboratory) full-matrix least-squares refinement program. Relativis-tic Dirac-Slater X-ray scattering factors (Cromerand Waber, 1965) for neutral atoms were employed.Occupancies of Na, K, and Ca in the alkali cation(M) site were based on atomic proportions. Tetra-hedrally coordinated cation (T) sites were assumedto be completely disordered so that the Al and Sioccupancies in each T site were evaluated as (1 +X"")14 and (3 - Xu)14, respectively (where X"" isthe mole fraction of CaAl2Si2Os in the crystal).Each observed structure factor was weighted forrefinement as llo where o is the standard deviationof For, based on counting statistics. For the mono-clinic refinements the average of Fou. was set as thelarger of two estimates of the variance of thesampling, one calculated including counting statis-tics and the other calculated strictly from the sam-pling. Reflections for which Fo6. was zero or lessthan three sigma of the background intensity weretreated as unobserved.

The triclinic least-squares refinements were car-ried out in the normal fashion starting with valuesfrom the refinement of a high albite by Wainwright(unpublished, see Smith, p. 86, 1974); resulting Rfactors are listed in Table 1 The results from the

final anisotropic refinements were used in mostevaluations of structural parameters and are listedin Table 4. Alarge anisotropy for the M-site tem-perature factor was expected (e.g., Ribbe et al.,1969), but in fact all room-temperature refinementsproduced M-sites with non-positive-definite ellip-soids (one ellipsoid displacement was imaginary) ofapparent vibration. Consequently, and to be con-sistent with refinements of high albite and monal-bite (Ribbe et al.,1969:, Prewitt et al.,1976; Winteret al., 1979), the M-site was refined with variousmodels using partial atoms on multiple sites. Thesepartial-atom sites will be called subsites and denot-ed by subscript notation , e.9., M1 and M2. All suchrefinements use isotropic partial atoms except the"split-species" models (see discussion) becauseanisotropic treatments of the subsites usually devel-op very large correlations among the supposedlyindependent parameters and will not converge inrefinement. For the latter configuration, the se-quence of refinement steps was to increase thenumber of independent parameters, refining firstthe positions of the subsites, holding isotropic tem-perature factors (B) constant, then a common B,then independent B's, and finally the constrainedoccupancies of the subsites (the amount of theaverage M-site atom on each site). These steps inthe refinement of a model with a given number ofsubsites were followed until that model would notconverge in the least-squares treatment. The num-ber of subsites was sequentially increased from twoto three to four, etc., for each structure, until an

980 HARLOW : ANORTHOC LASE STRUCTURES

Table 4. Positional and thermal parameters

G r a n d e C a l d e i r a 2 3 0X

B x 1 0 4B l :B 1 t B z z srz B t s B z l

T 1 oT l mt 2 uT2nMon1onzo a oo B moco0amo D ooDm

M t . G i b e l e 2 3 0T r 0 0 . 0 0 8 s ( 1 )T 1 m 0 . 0 0 6 0 ( 1 )T z 0 0 . 6 e 3 3 ( 1 )T z n 0 . 6 9 0 4 ( l )M 0 . 2 7 4 3 ( 2 )O n t 0 . 0 0 3 3 ( 4 )0 n z 0 . 5 e e 4 ( 4 )0 s 0 0 . 8 2 1 9 ( 4 )O B m 0 . 8 2 1 2 ( 4 )0 c 0 0 . 0 2 0 7 ( 4 )O c m 0 . 0 2 2 7 ( 4 )0 0 0 0 . 1 e 1 6 ( 4 )O D m 0 . 1 8 8 1 ( 4 )M t . G ' i b e l e 5 1 0 oT 1 0 . 0 0 8 1 ( 1 )I 2 0 . 6 9 6 7 ( 1 )M 0 . 2 7 8 0 ( 3 )o n t 0 . 00 a z 0 . 6 0 8 4 ( 5 )0 s 0 . 8 2 3 0 ( 4 )0 6 0 . 0 2 5 6 ( 4 )0 e 0 . i 8 7 7 ( 4 )

K a k a n u i 2 3 0

0 . 1 i 5 3 ( 1 )0 . 8 1 8 0 ( 1 )0 . 1 1 4 0 ( 1 )0 . 8 8 1 s ( 1 )0 . 0 0 1 3 ( 1 )0 . 1 3 8 8 ( 2 )0 . 9 e 7 2 ( 2 )0 . 1 2 1 e ( 2 )0 . 8 5 7 4 ( 2 )0 . 3 0 1 2 ( 2 )0 . 6 9 1 6 ( 2 )0 . 1 2 0 4 ( 2 )0 . 8 7 2 s ( 2 )

0 . 7 3 7 7 ( 20 . 9 9 4 s ( 20 . 1 1 9 4 ( 20 . 8 s 3 i ( 20 . 2 9 6 4 ( 20 . 6 8 9 9 ( 20 . 1 1 7 1 ( 20 . 8 7 0 1 ( 2

0 . 1 7 s 2 ( 1 )0 . 1 1 6 4 ( r )0 . 00 . 1 3 e 1 ( 3 )0 . 00 . r 3 6 1 ( 2 )0 . 3 0 4 4 ( 2 )0 . r 2 4 t ( 2 )

0 . 1 6 8 6 ( 10 . 8 1 5 3 ( 10 . 1 0 9 e ( 10 . 8 7 8 9 ( 10 . 0 0 5 1 ( 20 . 1 3 6 s ( 20 . 9 9 2 5 ( 20 . 1 1 4 s ( 20 . 8 4 9 9 ( 30 . 2 e 4 0 ( 20 . 6 8 8 2 ( 20 . 1 1 4 6 ( 20 . 8 6 8 5 ( 2

0 . 1 7 9 6 ( 2 )0 . 1 1 7 0 ( 2 )0 . 00 . 1 3 7 8 ( 8 )0 . 00 . 1 3 8 2 ( 7 )0 . 3 0 3 0 ( 5 )u , r z f , r I o J

0 . 2 2 0 7 ( r )0 . 2 2 5 2 ( 1 )0 . 3 3 s 4 ( 1 )0 . 3 4 6 5 ( 1 )0 . 1 3 6 6 ( 2 )0 . 9 9 4 7 ( 3 )0 . 2 8 2 8 ( 4 )0 . 2 1 8 0 ( 4 )0 . 2 3 2 9 ( 4 )0 . 2 6 1 8 ( 4 )0 . 2 4 2 1 . ( 4 )0 . 4 0 0 4 ( 3 )0 . 4 r 2 s ( 4 )

0 . 2 1 8 5 ( 2 )0 . 2 2 7 r ( 2 )0 . 3 2 8 e ( 2 )0 . 3 4 9 6 ( i )0 . 1 3 s 3 ( 3 )0 . 9 e 0 7 ( 4 )0 . 2 8 0 2 ( 4 )0 . 2 0 9 2 ( 4 )0 . 2 3 8 1 ( 4 )0 . 2 6 8 8 ( 4 )0 . 2 3 r 2 ( 4 )0 . 3 9 4 3 ( 4 )0 . 4 1 9 1 ( 4 )

0 . 2 2 3 6 ( 2 )0 . 3 4 2 2 ( 2 )0 . t 3 7 2 ( 4 )0 . 00 . 2 8 4 2 ( 6 )0 . 2 2 4 2 ( 5 )0 . 2 5 2 8 ( s )0 . 4 0 6 3 ( 4 )

2 8 ( 1 ) o ( 1 )2 6 ( r ) 2 ( r )z 6 ( L ) 2 ( 1 )2 7 ( r ) 1 ( 1 )- 7 ( 3 ) - 5 2 ( 2 )6 1 ( s ) 4 ( 2 )3 2 ( 4 ) 2 ( 2 )7 5 ( 5 ) 5 ( 3 )7 1 ( 5 ) - 2 ( 3 )4 4 ( 4 ) - 3 ( 2 )3 0 ( 4 ) 4 ( 2 )2 3 ( 4 ) 8 ( 2 )2 2 ( 4 ) - 7 ( 2 )

- 4 ( 1 )7 ( L )0 ( 1 )3 ( 1 )2 ( r )6 1 2 )r ( 2 )

- 1 0 ( 2 )1 1 ( 2 )- 3 ( 2 )3 ( 2 )6 ( 2 )

- 3 ( 2 )

-8 (2 )- 2 ( 2 )000

- o ( / ,- 1 2 ( 6 )

1 5 ( 6 )

1 7 ( 1 ) 5 1 ( 2 )1 5 ( 1 ) 5 1 ( 2 )1 1 ( 1 ) 6 5 ( 2 )1 r ( 1 ) 6 3 ( 2 )6 5 ( 1 ) 1 3 e ( s )3 0 ( 2 ) s 7 ( 6 )1 8 ( 1 ) 1 2 4 ( 6 )4 1 ( 2 ) 1 5 8 ( 7 )3 e ( 2 ) 1 5 1 ( 7 )2 2 ( t ) 1 2 2 ( 6 )2 0 ( 1 ) 1 1 8 ( 6 )2 5 ( r ) 8 7 ( 6 )2 7 ( 1 ) e s ( s )

0 . 0 0 8 5 ( I )0 . 0 0 6 9 ( 1 )0 . 6 9 s 4 ( 1 )0 . 6 9 4 1 ( 1 )0 . 2 7 5 0 ( 2 )0 . 0 0 1 6 ( 3 )0 . 6 0 5 6 ( 3 )0 . 8 2 3 3 ( 3 )0 . 8 2 2 7 ( 3 )0 . 0 2 3 3 ( 3 )0 . 0 2 4 1 ( 3 )0 . 1 8 e 7 ( 3 )0 . 1 8 8 3 ( 3 )

4 7 ( 2 ) 5 ( 1 )4 4 ( 2 ) 8 ( I )4 4 ( 2 ) 5 ( 1 )4 s ( 2 ) 6 ( i )- 3 ( 3 ) - e r ( z )i 6 ( 6 ) 1 2 ( 3 )5 2 ( 5 ) 8 ( 3 )e 6 ( 6 ) 1 1 ( 3 )8 7 ( 6 ) 4 ( 3 )6 3 ( 5 ) - l ( 3 )4 4 ( 5 ) 6 ( 3 )4 4 ( 5 ) 1 1 ( 3 )3 8 ( 5 ) 1 ( 3 )

0 ( 1 )1 1 ( i )

5 ( 1 )7 ( r )7 ( 2 )

1 2 ( 3 )5 ( 2 )1 ( 3 )

1 4 ( 3 )L ( 2 )s ( 2 )e ( 2 )5 ( 2 )

- s ( i )- 3 ( 2 )000

- 2 5 ( 3 )- 1 s ( 3 )

1 o ( 3 )

69 (2 )6 6 ( 2 )8 4 ( 2 )8 r ( 2 )

1 6 7 ( b )1 0 s ( i )1 3 8 ( 7 )1 7 7 ( 8 )1 i 1 ( 8 )r 3 7 ( 7 )r 2 8 ( 7 )1 0 5 ( 7 )1 1 5 ( 7 )

1 e ( 1 )1 6 ( r )1 3 ( r )1 3 ( 1 )7 4 ( 2 )3 s ( 2 )r e ( 1 )4 4 ( 2 )4 4 ( 2 )2 7 ( 2 )2 4 ( 2 )2 s ( 2 )t o l 2 \

2 8 ( 1 )2 1 ( 1 )

1 0 6 ( 3 )

2 8 ( 2 )7 0 ( 2 )3 5 ( 2 )5 6 ( 2 )

8 5 ( 2 )8 2 ( 2 )8 0 ( 2 )8 4 ( 2 )0 ( 3 )

1 5 0 ( 6 )r r l ( o . ,1 2 8 ( 6 )1 1 7 ( 6 )1 1 s ( 6 )1 1 6 ( 6 )1 2 6 ( 6 )r r o ( o , l

2 s ( 1 ) - 4 ( 1 )2 7 ( r ) - 2 ( r )2 5 ( r ) - 2 ( r )2 8 ( 1 ) - 2 ( 1 )

- 2 1 . ( 3 ) - 1 4 4 ( 3 )6 3 ( s ) - 3 ( 2 )3 4 ( 4 ) 4 ( 2 )7 4 ( 5 ) - 4 ( 3 )7 2 ( 5 ) - r 0 ( 3 )5 0 ( 4 ) - s ( 2 )2 ) . ( 4 ) 3 ( 2 )2 o ( 4 ) 4 ( 2 )1 1 ( 4 ) 1 5 ( 2 )

- 5 ( 1 )3 ( 1 )

- 2 ( r )0 ( 1 )5 ( 2 )0 ( 2 )

- 3 ( 2 )- 1 0 ( 2 )

6 ( 2 )- 6 ( 2 )6 ( 2 )4 ( 2 )

- 4 ( 2 )

- 1 1 ( 2 )- 3 ( 2 )0U0

- 3 1 ( e )- 3 0 ( 7 )2 3 ( 8 )

s 3 ( 2 )s 1 ( 2 )s 4 ( 2 )

- 1 . 4 ( 2 )1 2 4 ( 5 )8 6 ( 5 )

s 6 ( 2 )J J ( Z , ,

o 4 r q8 8 ( 48 4 ( 4e 0 ( s )8 6 ( 5 )

G r a n d e C a l d e i r a 4 0 0 07 6 ( 3 )i 5 ( 3 )8 7 ( e )e 6 ( e )8 e ( 1 4 )

l s e ( e )1 3 6 ( 1 1 )

8 2 ( 8 )

4 e ( 2 ) - 2 ( t )4 7 ( 2 ) - 2 ( 1 )4 8 ( 6 ) 0s 6 ( 8 ) 0s 1 ( 8 ) 0

1 3 e ( 6 ) - 6 ( 4 )8 6 ( 6 ) - 7 ( 3 )3 5 ( 5 ) l e ( 3 )

s 2 ( 2 )l r r ( 2 )z e r ( e )12e (e )2 1 e ( 1 1 )2 8 2 ( 9 )2 5 0 ( 8 )r s 3 ( 7 )

e 3 ( 2 )8 7 ( 2 )6 0 ( 5 )

2 0 2 ( 9 )1 2 3 ( 8 )1 4 s ( 6 )1 4 8 ( 6 )1 5 3 ( 6 )

- 2 ( 2 )- 1 ( t )000

i 8 ( 1 3 )- 6 ( e )1 e ( 1 0 )

r 6 3 ( 4 )2 0 2 ( 4 )6 1 s ( 2 8 )2 6 3 ( 1 3 )5 0 8 ( 3 4 )4 0 7 ( 1 6 )3 9 7 ( 1 8 )2 6 7 ( r 4 )

1 0 6 ( 3 )1 2 4 ( 4 )3 3 4 ( r 7 )e 8 ( 1 1 )

Le4 ( 20)2 9 0 ( 1 4 )2 8 0 ( 1 6 )2 0 s ( r 2 )

- 2 ( 2 )- 1 ( 2 )0U0

r r ( e )- 1 . 4 ( 7 )L 6 ( 7 )

0 . 1 7 1 1 ( 1 )0 . 8 r 6 4 ( i )0 . 1 1 1 5 ( 1 )0 . 8 i e 8 ( 1 )0 . 0 0 3 3 ( 2 )

T t oT l mTzorznMonlonzo e o0 n mo;o0 c mo;ooDmK a k a n u iT 1

Mon l0M0 g0 60 9

0 . 0 0 8 7 ( 10 . 0 0 5 4 ( 10 . 6 9 2 3 ( 10 . 6 8 8 6 ( Iu . z t + J \ z0 . 0 0 4 5 ( 40 . 5 9 6 9 ( 30 .8220 ( 40 . 8 2 0 3 ( 4 )0 . 0 1 8 8 ( 3 )0 . 0 2 2 s ( 3 )o . r e 3 2 ( 3 )0 . 1 8 8 2 ( 4 )7 5 0 00 . 0 0 8 9 ( 3 )0 . 6 9 7 2 ( 2 )0 . 2 8 3 9 ( 7 )0 . 00 . 6 1 1 5 ( 9 )0 . 8 2 8 2 ( 5 )0 . 0 3 2 0 ( 5 )0 . 1 8 5 0 ( s )

0 . 2 1 6 8 ( 1 )o . 2 2 7 5 ( r )0 . 3 2 5 6 ( i )

1 e ( 1 ) 7 3 ( 2 )1 8 ( 1 ) 6 8 ( 2 )1 4 ( 1 ) 8 2 ( 2 )1 5 ( 1 ) 8 3 ( 2 )

1 1 s ( 3 ) 2 2 7 ( 6 )3 3 ( 2 ) 1 r 7 ( 6 )2 3 ( 2 ) 1 1 8 ( 6 )3 6 ( 2 ) 1 6 4 ( 7 )4 s ( 2 ) 1 6 e ( 7 )2 4 ( 2 ) 1 5 8 ( 7 )2 7 ( 2 ) 1 0 7 ( 6 )2 s ( 2 ) 1 0 2 ( 6 )3 4 ( 2 ) 1 0 e ( b )

0 . 3 2 5 6 ( i0 . 3 s 1 4 ( 10 . 1 3 5 0 ( 30 . 9 8 8 1 ( 40 . 2 8 r 8 ( 40 . 2 0 s 1 ( 40 . 2 4 2 2 ( 40 . 2 7 2 4 ( 40 . 2 2 6 7 ( 4

4 7 ( 1 )4 4 ( 1 )4 4 ( i )4 s ( 1 )

- 1 6 ( 3 )I I ? / E \

7 s ( 4 1e 0 ( s )8 1 ( s )7 7 ( 4 )t 7 ( 4 )8 0 ( 4 )7 6 ( 4 )

1 4 4 ( 3 )r 2 1 ( 2 )1 2 6 ( 8 )3 2 7 ( 1 1 )r 4 5 , ( 1 6 )2 ' , | 1 / o \2 5 1 ( 1 1 )2 6 6 ( 1 2 )

0 . 3 e 1 1 ( 4 )0 . 4 2 3 2 ( 4 )

0 . 2 2 4 0 ( 3 )0 . 3 4 3 7 ( 2 10 . 1 4 9 6 ( 1 0 )0 . 00 . 2 8 s 8 ( 1 6 )0 . 2 2 8 8 ( 7 )0 . 2 5 6 3 ( e )0 . 4 1 2 1 ( s )

5 4 ( 1 )4 5 ( 1 )

2 4 7 ( 1 2 )8 3 ( 7 )5 5 ( 5 )

1 2 3 ( 7 )6 4 ( 4 )8 4 ( 5 )

8 8 ( z )8 1 ( 2 )7 0 ( r 3 )

1 s 1 ( 1 0 )1 4 ( 1 8 )

2 0 2 ( 1 0 )1 5 0 ( 1 r )1 0 6 ( 8 )

E s t i m a t e d s t a n d a r d d e v j a t i o n s i n p a r e n t h e s e s r e f e r t o l a s t d i q i t s

HARLOW : ANORTHOCLAS E STRUCTURES 981

improvement was seen over the anisotropic modelor until the subsite model failed to converge. Theresults for these final steps in M-site model refine-ments are listed in Table 5.

Essentially the same three steps were followedfor the three high-temperature structure refine-ments except that initially the triclinic Fo6" data setswere refined in space group Cl to test the consisten-cy of the data with monoclinic symmetry. Thestarting parameters were those of the room-tem-perature refinements for the same crystal and theresulting triclinic structures were consistent withmonoclinic symmetry within the estimated errors ofall refined parameters except for anisotropic ther-mal parameters. Thus the data were averaged into amonoclinic set. No attempt was made in any of theleast-squares procedures to refine on the Si,Aloccupancy of the T sites. At various stages of therefinement of the M-site models, difference Fouriersections were made of the M-site region parallel tothe b-c plane to evaluate the quality of the fit.

Interatomic distances and angles and root-mean-square displacements for thermal-ellipsoidal axeswere calculated in the RFrNE II program. Estimatederrors for these structural parameters were calculat-ed with Finger's ERRoR.

Results and discussion

Lattice parameters

Cell parameters for the three anorthoclase speci-mens at 23' C and at elevated temperatures arelisted in Table 3 and are plotted in Figures 3 and 4.The room-temperature cell dimensions are consist-ent with alkali feldspars having nearly complereSi,Al disorder. The values lie close to lines connect-ing analbite and high sanidine on the a*-y* and b-cplots. The a*-y* relations indicate the difference inAl content of the Tr sites (t10-t1m; Al in T10 minusAl in Trm), which is a measure of topochemicaltriclinicity, whereas the b-c plot indicates the totalAl content in the T1 sites (either trO + trm fortriclinic structures or t1 for monoclinic ones). Mac-Kenzie and Smith (1962) found that in orderedalbitic plagioclases an increase in An content causesan effect similar to an increase in disorder. On thebasis of the limited work on ternary feldspars likeanorthoclases (Hakli, 1960; Carmichael and Mac-Kenzie, 1964; Boudette and Ford, 1966; Kroll andBambauer, 1981), the use of cell-parameter plots forevaluating Si,Al order appears valid for the samplesunder investigation. It is natural to expect the

Table 5. Ellipsoids of thermal expansion strain

i un i t s t ra in( /oc o r /Or%)

Ang le t o+a +b +C

l )GrandeCaldei rgZ J - I O J

2 \GrandeCal dei raI 83o-4ooo

3 )Mt . G ibe le2 3o -388o

4 )M t . G i b e l e388o-51 oo

q l

Kakanui23o- Tooo

o.,Kakanu iTooo - 7 5oo

7')Kakanui -M t . G ibe le

z3o

8 )Mt . G ibe le -Gran deCal dei ra

^ ^ O. J

o \M t . G ibe le388o -GrandeCa lde i r a 4000

8 2 . 0 ( e )8 ( t )

8 9 . 5 ( 8 )

2 2 ( 3 )90

i l 2 ( 3 )

3 0 . 6 ( O J1 t 1 2 l r , \' l ? l 1 / 6 1

q ? r ? \

90q / ? )

r 8 . 5 ( l ) E - s2 1 . 4 ( 2 ) E - sJ - O . O [ | , l L - J

v 3 .4 (3 ) E -5

r 2 . 4 ( r ) E - 52 2 . 5 ( 6 ) E - 6J u . u ( o , r - ov 2 . i ( r ) E - 5

8 r . 2 ( 3 ) 4 8 . 4 ( 6 ) s s . o ( s )8 . e ( 8 ) e 6 . s ( e ) I 2 1 . 6 ( 5 )8 8 . 8 ( 7 ) 4 2 . 5 ( 5 ) r 2 e . t ( 4 )

2 2 ( 2 ) 8 6 ( r ) e 5 ( 2 )e 8 ( 2 ) l l ( 6 ) 8 0 ( 6 0

l r o ( 2 ) r 0 0 ( 6 ) 1 r ( 6 )

4 7 . 6 ( 7 ) 5 s . 8 ( 6 )e 6 ( r ) r 2 1 . 8 ( 3 )4 2 . s ( 6 ) 1 2 e . 6 ( s )

e 0 8 9 ( 6 )0 9 0

9 0 r ( 6 )

90 95(2)e o 5 ( 2 )0 9 0

r 6 . 7 ( l ) E - s 8 2 ( r )2 1 . 2 ( 2 ) E - 5 8 ( r )3 - 5 . 2 ( r ) E - 5 e 0 . r ( 7 )u 2 . 7 ( 4 ) E - s

r 2 . 6 ( 8 ) E - 5 2 7 ( 6 )2 s . 7 ( 3 ) E - 6 9 03 - 0 . 3 ( 5 ) E - 5 1 1 6 ( 6 )v 3 . e ( r ) E - 5

l 5 . r 6 ( 3 ) E - 5 7 8 . 6 ( 4 )2 r . 5 o ( 3 ) E - s l r . 7 ( 4 )3 - 3 . 3 0 ( 2 ) E - 5 8 7 . 3 ( r )v 3 . 3 6 ( 5 ) E - 5

r 3 . 0 ( 6 ) E - 5 2 2 ( 2 )2 -0 .0 (4) E-s 112(2)3 - 0 . 4 ( 3 ) E - 5 e 0v 2 . 5 ( 8 ) E - 5

r 1 . 0 ( 3 ) E - 42 4 . s ( 3 ) E - 43 -5 .2 (2) E-4v e . 8 ( 5 ) E - 4

r l r . 8 ( 2 ) E - 42 4 . 3 ( 3 ) E - 43 -6 . e (2 ) E-4v 9 . 2 ( s ) E - 4

1 7 . 4 ( 9 ) E - 42 ' t .7 (4 ) E-43 r . 4 ( 7 ) E - 4v l . r ( r ) E - 3

7s (2 ) 4e ( r ) s8 ( l )12(2) l o0(2 ) 121 (2)86 .6 (4 ) 42 .7 (6 ) r 3 r . 8 (5 )

4 6 . 4 ( 8 )e 6 ( r )4 4 . 3 ( 7 )

c 6 . | \ z ) J t . 6 \ z )o q R 1 ? \ 1 ) 1 A l 2 \

4 2 . 6 ( r ) r 3 r . 4 ( r )

900

90

* E - n + x l o - n+ 1 , 2 , 3 a re t he max imum, i n t e rmed ia te , and m in imum

e l l i pso id axes and V i s t he vo lume t r j c componen tEst inated standard deviat ions in Darenthesis refer tol a s t d i q i t s

values of tr0-t1m to approach zero as these feld-spars become optically (Grande Caldeira and Mt.Gibele by Carmichael and MacKenzie, 1964) anddimensionally monoclinic at elevated temperatures.The results from the least-squares cell parameterrefinements support the conclusion of monoclinicsymmetry and consequent monoclinic Si,Al topo-chemistry.

It is common for perthitic intergrowths of alkalifeldspar containing coherent composites of twophases to have "anomalous" values of a, measuredin Aa (: 4obs - 4ss1e S€o Stewart and Wright, 1974;Stewart, 1975). None of the anorthoclases exam-ined in this study show Aa values greater than

982 HARLOW : ANORTHOC LASE STRUCTURES

7 . 2 2

7 . 2 1

7 . 2 0

7 . t 9

7 . t 8

7 . t 7

7 . r 6

7 . t 5

7 . 1 4

7 . t 3

7 . 1 2

7 . l l

t2.78 12.80 12.82 |2A4 12.86 12.8 t2.90 t2.92 t2.94 t2.96 12.98 t3.OO t5.o2 t3.O4

b,AFig. 3. The b-c plot, after Stewart and Wright (1974), for room- and high-temperature data (see text); contours from 8. 15 to 8.60 are

for the a cell edge; contours from 0.50 to 0.65 are for trO + I rm (the Al occupancies of the Tr0 and T1m sites). Heating produces aneffect similar to that of an increase in K-feldspar content--{isplacement to the upper right, parallel to lines of constant structuralstate.

0.014 whereas a minimum value of 0.05 is consid-ered sufficient to indicate strain.

The overall effect of rapid increase in tempera-ture on cell dimension (within the limits of theexperiment, i.e., T < 800) appears to be the sameas an increase in Or content of a feldspar assumingSi,Al order is constant. This result is consistentwith the results of Grundy and Brown (1969) andKroll er a/. (1980).

An estimate of the composition for the displacivetriclinic/monoclinic inversion (Or disp) at roomtemperature has been made by plotting cos2a (atroom temperature) ys. Or content in Figure 5. Avalue for an analbite (F9132 from Grundv and

Brown, 1969) is also included. A linear relationshipis expected for alkali feldspars having the samedegree of monoclinic disorder or the same equilibri-um temperature, as shown by Kroll et al. (1980).Such an approximation for these three anortho-clases is reasonable based on the b-c plot (Fig. 3),and thus a least squares line was fit to the points.The extrapolation of this line to zero predicts acomposition of 0136 for the displacive inversion atroom-temperature. This value compares well withthe values of 0136 of MacKenzie (1952) and Or3a-36of Bambauer et al. (1978), Hovis (1980) and Kroll eta/. (1980).

The relationship between alkali chemistry and

t to + trm

Low olb i te

Koko nu i

a" \Gronde Coldeiro

- ( * , o

9 0

92

9 l

89

88

I o r i n g m m i c r o c l i n o

tro- trm

Lor

Monoclinicfc ldrpor

Gronde Co ldo i ro

I t . G i b . l .

K o l o n u i

HARLOW : AN ORTHOC LAS E STRUCTU RES 983

be unique "transition" values of cell parameters forhighly disordered alkali feldspars. Cooling or highpressure experiments would yield actual determina-tion of these limits for more potassic feldspars. Thecooling experiment on a high sanidine by Grove andHazen (1974) has not come close to the transitionvalues. Hazen (1976), on the other hand, did suc-ceed in reaching the inversion at high pressures: 18kbar for Ors2 and 12 kbar at 0167 with values veryclose to those indicated by the measurements here.Hence, as suggested by Hazen (1977), there does

90l 98 88 78 6

,( *:

Fig. 4. The a*-7x plot, after Stewart and Wright (1974), used as a measure of triclinic Si,Al order. Room-temperature values for theanorthoclases examined in this study are shown by circles and indicate good agreement with a topochemically monoclinic Si,Aldistribution as represented by the line connecting analbite with monoclinic feldspar.

cell parameters at the transition temperature hasbeen estimated by interpolating between the valuesat higher and lower temperatures in order to evalu-ate possible limits to the cell parameter values ofhighly disordered monoclinic alkali feldspars. Thelinear slopes are nearly flat for transition values,and for a pure K-feldspar estimated values arebetween 690 and 69543 for the cell volume, 8.30 and8.354 for a andT .llAfor c. The value of b is nearlvconstant at about l2.g7l with perhaps a slighidecrease with increasing Or content. There seem to

984 HARLOW : ANORTHOCLASE STRUCTURES

oo 20

6N

o

Anolbite of Grundy B Brown ( 1969)

Koko nu i

M t . G i b e l e

GrondeColde i ro

\,'0,"0O L

36 40Mol . oer cen l Or

Fig. 5. Plot of cos2a at room temperature for the threeanorthoclases (K-analbites) and analbite (F9/32, Grundy andBrown, 1969) against Or content. Least squares linear fitindicates a transition composition of 0136.

appear to be a particular structure configuration atthe displacive transition which is directly related tounit cell geometry.

The change in cell dimensions upon heating doesnot necessarily give an adequate picture of thethermal expansion in crystals that have low symme-try because the directions of maximum and mini-mum expansion or strain are not symmetricallyconstrained to lie parallel to lattice translations.Ohashi and Burnham (1973) developed a mathemat-ical approach for analyzing small lattice deforma-tions in terms of a second-order thermal straintensor. A strain analysis was performed on theanorthoclase cell refinements using the programsrRArN, (Ohashi and Finger, 1973) in order toexamine the changes with temperature and compo-sition; the results are listed in Table 5. The effects oftemperature and of increasing Or content on theorientation of the thermal strain ellipsoid at tem-peratures below the monoclinic/triclinic transitionare almost identical, and are consistent with theresults of Ohashi and Finger (1973). Above thetransition temperature, the strain ellipsoid musthave an axis parallel to the b cell edge normal to the(010) mirror plane. The major strain axis rotatesslightly, becoming almost parallel lo a*, whereasthe other two axes apparently vary with composi-tion: the intermediate and minor axes are reversed

between Kakanui and the other two crystals. Theresults on thermal expansion are virtually identicalto those for two synthetic disordered alkali feld-spars (Or1e and Or3s) studied by Henderson (1979).Calculation of the displacements between the Mt.Gibele cell at 388' C and the Grande Caldeira cell at400" C yield the same result as heating a crystalabove the transition temperature, even after takinginto account the small difference in temperature.

Crystal structure

Discussion of the anorthoclase (K-analbite)structure in this section is restricted to structuralfeatures that show correlations with changes inalkali chemistry and/or temperature. These are M-O bond lengths, T-O-T interatomic angles, andoverall and M-cation apparent thermal motion.Hence, some relations which appear to be mainly aconsequence of a change from triclinic to monoclin-ic crystal symmetry are ignored here.

M-O bonding. The alkali cation to oxygen bond-ing is the structural feature most correlated withtriclinicity and the degree of the expansion of theframework structure. In triclinic alkali feldsparscoordination about the M site is very irregular, withnine nearest neighbor oxygen atoms within l.SA.However, only five to seven of these are within0.4A of the shortest M-O distance and can thus beconsidered the first coordination sphere. Smith(1974) discusses the M-site relations for most feld-spars in detail.

In spite of the fact that the average nature of themeasured structure obscures the bonding of individ-ual sodium and potassium (and calcium) atoms andthat the single atom M-site model is evidentlyunrealistic (to be treated in a later section), thevariation in M-O bond lengths (Table 6 and Figs. 6and 7) does elucidate several features in the struc-tures. First, as expected, the average M-O dis-tances increase with increasing Or content and withincreasing temperature. Second, the variance of theaverage (M-O) value decreases with increasing Orcontent and with increasing temperature for anyparticular composition, indicating the increasinggeometric regularity of the cavity for an effectivelylarger M-site occupant. This increasing regularity isalso demonstrated by the decreasing difference inthe pseudosymmetrically equivalent bond distancepairs for the room-temperature structures (i.e., (M-Oer0) and (M-Oarc) or (M-Os0) and (M-Oem)).Third, with the exception of (M-Os), all of the M-O

HARLOW : ANORTHOC LASE STRUCTURES

Table 6. M-O distances for both room- and high-temperature structures including corrections for noncorrelated thermal motion (in A)

985

Grande Ca lde i r a

230raw noncoff raw

4000n0ncorr raw

M t . G i b e l e

230noncorr raw

Ka kanu icaa

raw noncorr7500

raw noncorr5l 00

noncorrM - 0 A 1 0 2 . 7 2 0 ( 3 )

- 0 A 1 . 2 . 7 2 8 ( 3 )

-onz 2 .464(3)

-0s0 2 .80e(3)

-0Br 3 .050(3)

- 0 c 0 3 . 2 0 3 ( 3 )

- O c r 3 . 0 7 2 ( 3 )

-000 2 .740(3)

- O D r 2 . 9 3 0 ( 3 )

M-0 Av 2.857

o . 2 2 8

2.742 2 .782(3)

2 . 7 4 8

2.490 2 .524(4)

2 .831 2 .934(4)

3 . 063

3 . 2 1 e 3 . 1 1 2 ( 3 )

3. 088

2.761 2 .882(4)

2 .941

2.876 2 .882

.224 . I 80

2 . 8 1 8 2 . 6 8 4 ( 4 ) 2 . 7 r 0

2 . 7 2 2 ( 4 ) 2 . 7 4 5

2.569 2 .414(3) 2 .446

2.968 2 .679(3) 2 .709

3 . r 1 2 ( 4 ) 3 . 1 2 5

3 . r 4 5 3 . 2 7 4 ( 4 ) 3 . 2 9 3

3 . 0 1 5 ( 4 ) 3 . 0 3 3

?.919 2 .642(3) 2 .672

3 . 0 r 8 ( 4 ) 3 . o 2 9

2.932 2 ,840 2 .863

. 1 5 0 . 2 7 6 . 2 7 0

2.750(4) 2 .786

2 . 4 7 2 ( 4 ) 2 . 5 1 e

2 . 9 3 0 ( 4 ) 2 . 9 6 3

3 . r 4 0 ( 4 ) 3 . 1 7 1

2 . 8 s 2 ( 4 ) 2 . 8 8 4

2 . 8 6 9 2 . 9 0 3

.207 .202

2.655(4) 2 .687

2 . 7 2 2 ( 4 ) 2 . 7 5 ?

2.38e(3) 2 .432

2.611(4) 2 .651

3 . r s e ( 5 ) 3 . 1 7 0

3 . 3 r 5 ( 5 ) 3 . 3 3 6

2.969(4) 2 .99r

2 . 5 7 2 ( 4 ) 2 . 6 1 1

3 . 0 7 5 ( 4 ) 3 . 0 8 5

2.830 2 .857

. 3 1 I . 3 0 0

2.775(4) 2 .8s0

2.454(4) 2 .s64

2 . 9 8 2 ( 4 ) 3 . 0 4 3

3 . r 5 8 ( s ) 3 . 2 1 8

2 . e 1 2 ( 4 ) 2 . e 7 6

2.901 2 .971

.217 .202

L e n g t h 5 . 9 8 0 6 . 0 0 4 5 . 8 1 6 5 . 8 8 6 6 . 1 3 0

l l l i d t h 4 . 5 0 7 4 . 5 5 0 4 . 5 7 4 4 . 6 4 6 4 . 4 4 3

6 . 1 5 4 5 . 7 8 3 5 . 8 4 7 6 . 2 3 5

4.494 4 .547 4 .621 4 .408

6 . 2 5 5 5 . 8 9 8 6 . 0 1 9

4 . 4 7 4 4 . 5 7 7 4 . 7 4 5

Length = <M-orm + <M-0DID Width = <M-00r, +

Estimated standard deviat ions in parenthese refer

<M-00., > [cosr-"(0Al -M-0Al ) ]

t o t he l as t d i g i t s

bond lengths for high-temperature monoclinicstructures increase with respect to monoclinic aver-ages of the room-temperature results for non-cor-rected distances (Fig. 7). If bond lengths are cor-rected for apparent thermal motion (both room- andhigh-temperature structures) this relationship istrue for all of the M-O distances. Fourth, theelongate narrow alkali cavity becomes shorter along[011] and wider along [100] with increasing Orcontent. This feature can be seen for the room-temperature data with the aid of Figure 8. Thelength of the cavity can be defined by the Osm-Opm distance or the almost equivalent (M-Osm) +(M-Oom), both of which decrease with increasingOr content. Similarly, the width of the cavity isrelated to (M-OA) + (M-OAr)*cos [/z(OarO-M-Oarc)1, which increases with increasing Or content.These features can be seen graphically in Figure 8by following the trends of the M-O values withcomposition.

The effect of increasing temperature is not simplyto inflate the sodium (and calcium) filled cavityisotropically to approach the shape of the cavitywhen filled with the larger potassium (or rubidium)

atom. The inflation is ellipsoidal. Although there isenough increase in effective volume of the alkalicavity to expand the K-analbite structures to mono-clinic symmetry at high temperature, each cavity isprogressively more elongate (llto b) and narrow (llto[l00]) with increasing Na content. The cavities arenot a replica of or comparable to that in sanidine.Possible constraints on the inflation geometry,apart from size, may be the charge and mass of theM-site occupant, as these properties influence pos-sible thermal vibration. Results of M-site modeling,described in the following discussion, support thissuggestion. A possibly unique feature of the M-sitecoordination in the high-temperature monoclinicfeldspars is the direction of the M-site bonds.Stereographic projections of the M-site coordina-tion for the three crystals are indistinguishable fromone another at high temperatures for either the nineimmediate oxygens or the twelve closest T sites,but are markedly different at room temperature.

Most of the thermal effect on cell dimensions ofthese feldspar structures can be explained by short-ening of the M-Osm, M-Oprn, and M-O60 bondsand lengthening of the M-O'O, M-OpO, and M-

986 HARLOW : ANORTHOCLASE STRUCTURES

3.O

2 . 9

2 . 8

2 . 7

2 . 6

2 . 5

2 . 4

2 . 3

O6m bonds. A projectionr of the M-site coordina-tion for both the room- and high-temperature struc-tures (superimposed) of the Kakanui sample,

'This projection of two structures upon one another requrresthe choice of a joint reference frame. This frame should not bethe one chosen by Ohashi and Burnham (1973) for calculating thestrain tensor from an arbitrary deformation tensor, because itincludes a rotation produced by constraining the c and d axes tobe parallel for the two lattices. Consequently, the referenceframe chosen for the projection is the one for which thedeformation tensor relating the two lattices is a symmetric tensordescribing a pure strain and no rotation. The amount ofrotationis less than 2'for the crystals examined here, but it is stillnoticeable in the projections if it is not taken into account.

oco

oBm

o D m

o c m

oAv.

oAl c

oaro

oaoooo

oaz

viewed down the intermediate axis of the thermalexpansion "strain" ellipsoid, shows the obviouscorrelation between the above-mentioned bond dis-tances and the gross expansion of the feldsparstructure on heating (Fig. 9). The interlinkage of theframework tetrahedra causes adjustments in thegeometry that account for the slight misalignment ofthe inter-structure site displacements with respectto the cell thermal expansion between the struc-tures. These changes are basically rotations offixedsize tetrahedra. Henderson (1979) suggests that theM-Ooz extension with rotation of the frameworkstructure is chiefly responsible for the expansion.

oI

too90807060

Mol . pe r cen l . Ab*AnFig. 6. The variation of individual M-O distances with composition. The dashed lines represent reasonable extrapolations for a

room-temeprature transition to monoclinic symmetry at Or.u.

v

HARLOW : ANORTHOCLASE STRUCTURES

3.O

2 . 9

2 . 8

? .7

2 . 6

2 . 5

? .4

2 . 3roo

Mol. per cent . Ab + AnFig. 7. M-O distances versrs composition for the high-temperature structures (circles and solid lines) and for the monoclinic

averages of the room-temperature structure values (squares and dashed lines). Note the general increase in M-Oa1, and M-Oa2,which reflect the M-site cavitv width.

9E7

Inflation of the cavity is a more accurate cause asother bonds (M-OD0, M-OB0 and M-O6m) showgreater expansion.

T-O-T angles. The T-O-T angles (Table 7) infeldspars are extremely variable and manifest insome degree the compliance of the tetrahedralframework to the lattice geometry determined bythe overall nature of the feldspar structure, thedegree of "inflation" from bonding effects ofalkaliatoms in the M-site cavity, and the degree of Si,Alorder. Increasing Or content and increasing tem-perature both decrease the variance in the anglesand increase their average value for a single struc-ture, which indicates inflation of the structure andan approach to the ideal monoclinic feldspar struc-ture (c/. Megaw, 1974). This relation also means adecrease in triclinicity for the triclinic structures,which is evident on comparing the angles that are

oBov.

oDov.

equivalent for monoclinic symmetry k.9., T-OB0-T vs. T-Osm-T). The difference decreases withincreasing Or content, trending to zero on transitionto monoclinic symmetry. As in the case of the cellangle, a graphical examination can be helpful inevaluating the composition of the triclinic/mono-clinic inversion. The value cos2(AT-O-T), whereAT-O-T is the difference between pseudosymmetri-cally related T-O-T angles, was plotted against Orcontent in Figure 10 in expectation that it wouldhave the same linear relationship as expected forcos2a (Thompson et al.,1974). The relationship foreach of the differences for Os, Oc and Op is veryclose to linear, extrapolating to values close to 0136(35.8, 35.3 and 35.1, respectively) for a room-temperature inversion, which is consistent with theestimate based on cosza.

Apparent thermal motion. The magnitudes of

oI

9 0807060

oo,

988 HARLOW : ANORTHOCLASE STRUCTURES

Fig. 8. The M-site coordination for the Mt. Gibele crystal (23") projected onto the b-c plane (down a*) with split sites. Note theelongation in the Osm-Opm direction and the distribution ofthe subsites in that direction. O-O tetrahedron edge lines taper to showrelative height of site in the projection direction; higher site is at the wide end of the line.

apparent thermal motion (either in terms of equiva-lent isotropic B or root-mean-square (RMS) dis-placements) for the room-temperature structures(Table 8) are comparable to those from other disor-dered feldspars, except perhaps for the large andunusual values for the M-site. On the average,Grande Caldeira, Or32.5An6.6 has the lowest tem-perature factors, Kakanui, Or13.6An2 5, has the in-termediate, and Mt. Gibele, Or223An6.e, has thelargest. There are several possible reasons for thisrelationship. First, greater differences in the realpositions of the atoms relative to that in the averagestructure may exist within the respective crystals.The larger temperature factors in crystals withhigher An content are caused by large local distor-tions from extra aluminum in the T sites (Phillipsand Ribbe, 1973b) and by the stronger bonding ofCa in the M-site. Second, variation in the perfectionof the crystals can affect the temperature factors;

this can be partially improved with an extinctioncorrection, although such a correction was notattempted. Finally, of course, variation in a system-atic error in each data set (such as absorption) cancause decreases in "high angle" diffraction intensi-ties. However, the anorthite content is the mostlikely controlling factor, and it is significant that thesmall variations in An content 6 moleVo) cause suchnoticeable effects.

Apparent thermal motion models in high tem-perature structures are likely to represent an aver-age of real vibrational motion and inter-M-site mi-gration as well as positional disorder because theeffect of temperature is to increase atomic andlattice vibrations and alkali diffusion within a feld-spar crystal. Magnitudes of equivalent isotropic B'sfor atoms in the high-temperature refinements are1.4 to 3.4 times larger than for their room-tempera-ture equivalents. They decrease, in both room-

+ M t

M t b

' T r o

HARLOW : ANORTHOCLASE STRUCTU RES 989

Tro

T t m

T2 Tzo

oato

temperature and high-temperature structures, in thefollowing order: M, Os, Oez, Orz, Oc, Oo, Tr, Tz.This similarity in ranking indicates either that therelative effects of disorder and real thermal motionare about the same or that real thermal motiondominates the effects observed at both room andhigh temperatures. However, this may not be avalid conclusion for the M site with its possiblesplitting. The magnitude of apparent motion foreach atom increases with temperature except forGrande Caldeira the most potassic composition.The difference for Grande Caldeira may be relatedeithep to the higher Or content or to the crystalperfection of the sample.

The very large thermal ellipsoid for the M site inthe room-temperature anorthoclase structures iscomparable to that in high albite (Ribbe et al., 1969,and Wainwright, unpublished, see Smith, 1974,

Prewitt et al.,1976, Winter et al.,1979) except thatthe minor axis is always negative, causing thethermal models to be unreal. The thermal parame-ters of the M-site cations are highly correlated withalkali chemistry and temperature. Both equivalentB and the major axis displacement of the thermalellipsoid increase with decreasing Or content andincreasing temperature. Ellipsoid orientations forthe room-temperature structures have a consistentorientation with the unreal (negative) axis parallelto a* and the short M-Oez bond and with the majoraxis oriented subparallel to the cavity elongation inthe b-c plane (Fig. 8, compare with Fig. 9a ofWinter et al., 1979). These orientations are con-trolled by the shorter M-O bonds (M-Oer and M-Oez) and the general triclinic distortion of thecavity. In the monoclinic structures the cavity issymmetrically constrained to be elongated parallel

T1

TzoT 2

Qaz

TZ lt!

T t m

XYt .o A

Fig. 9. Projection of the M-site region down the intermediate, y, axis of the strain ellipsoid of thermal deformation for the Kakanuicrystal. The positions are corrected for rotation as evaluated in the strain analysis (see text). The closest unit cell axis is projectedonto the plane of the projection for a reference. Note that the major atomic displacements relative to M are in agreement with themajor (x) and minor (3) axes of strain suggesting the importance of M-O bonding on thermal deformation. O-O lines taper to show thehigher site at wide end of the line.

990 HARLOW : ANORTHOCLASE STRUCTURES

Table 7. T-O-T aneles

7500L J230

Grande Ca lde i r a

23o cz/nAverage

Mt . G ibe le

>ao 25o Cz/n qrnoAverage

4000

Ka kanu i

23o czlnAverage

oRr

onz

oso

oBt

oco

oct

ooo

oDt

1 4 3 . 5

132.2

l 5 l . 6

' l2t 7

142.0

r 4 3 . 8 ( 2 ) r 4 3 . 8

1 3 0 . 8 ( 2 ) 1 3 0 . 8

1 4 5 . 2 ( 2 ) I 5 0 . 7

156.2(2)

1 3 r . 8 ( 2 ) i 3 2 . 8

r 3 3 . 8 ( 2 )

1 3 7 . 9 ( 2 ) 1 4 2 . 3

1 4 6 . 7 ( 2 )

I 4 t . l t

8 . 2 7

r 4 3 . 6 ( 2 ) r 4 3 . 6 r 4 r . e ( 7 )r 3 0 . 5 ( 2 ) 1 3 0 . 5 r 3 3 . 7 ( 5 )

1 4 3 . 5 ( 2 ) 1 5 0 . 6 1 s 3 . 2 ( 4 )

r 5 7 . 8 ( 2 )

131 .2 (2 ) 132 .7 r36 . r (4 )

134 .2 (2 )

r 3 6 . 5 ( 2 ) r 4 r . 5 i 4 5 . 4 ( 4 )

148 .4 (2 )

140.81 142.99Average 141.32

o o f A v . 7 . 7 6

r 4 3 . 5 ( 2 )t ' 0 2 l t \

i 4 8 . 8 ( 2 )

1 5 4 . 4 ( 2 )

1 3 2 . 1 ( 2 )

r 3 3 . 3 ( 2 )

r 3 e . 8 ( 2 )

1 4 4 . 2 ( 2 )

r 4 4 . 4 ( 5 )r 3 5 . r ( 5 )

i 5 0 . 7 ( 4 )

1 3 1 . 9 ( 3 )

r 4 2 . 6 ( 3 )

1 4 1 . 5 7

7 . 1 9

1 4 3 . 3 ( 3 )

r 3 2 . 5 ( 3 )

r s o . e ( 2 )

1 3 3 . 2 ( 2 )

142.1 (2 )

1 4 1 . 2 9

7 . 0 9 9 . 0 3Est imated s tandard dev ia t ions in paren these re fe r to the las t d iq i ts

to the b axis; the major axis for the M-site also liesin this direction, about 37' from that at room-temperature (see also Fig. 9b of Winter et al., 1979).

M-site modeling. Fourier sections through the Msite show a very compact electron density distribu-tion in the a* direction and a very elongate distribu-tion in the b-c plane. Though the distributionsappear ellipsoidal in shape, they are evidently notstatistically normal with respect to electron density

ro 20 30 40

Mol . per cent OrFig. 10. Plot of cos2(AT-O-T) angle (difference in

pseudosymmetrically equivalent angles, e.g. for OsO and Osm)vs. composition of the 23'C anorthoclase structures. Best fitlines determined by least squares extrapolate to transitioncomposition near Orj6.

distributions as a function of distance from thecentroid. The electron density distribution in the a*direction is apparently more peaked than the com-bined X-ray scattering form-factors (when elliptical-ly displaced from the centroid in the plane normal toa*) for the averaged M-site occupants. Use ofextended cumulant approximations (higher orderreal-space tensors) to allow for the skewness andkurtosis of the scattering power distribution (John-son, 1969) do not adequately improve the refine-ments nor eliminate the negative ellipsoid axis.

The large magnitudes of apparent thermal vibra-tion for the M-site cation, 0.27 lo 0.404 maximumRMS amplitude, are considered too large to bepurely vibrational in nature and may be in part dueto displacement of individual alkali atoms into oneof several subsites. In the case of high albite, Ribbeet al. (1969) developed a model based on a split M-site, with the site being divided into four separatequarter-atom sites, based on an analogy with anor-thite which has a similar structure. Winter et al.(1979) looked at other possibilities of multiple sub-sites for high albite and monalbite in relation to lowalbite. The three room-temperature data sets de-scribed in this paper were refined with various Msubsites to examine the applicability of such mod-els. The following models proved to be the best ofthe many ones attempted, based on Hamilton's(1965) crystallographic R factor comparison; theunreal anisotropic solution is used as a reference(see Table 9). For the two most Na-rich anortho-clases, the best model consists of four positionally

9 3

94N

9gs

F| ^ ^O :rb

I

F

3s7N

v,

3ge

99

roo

Os

.oo

oc

HARLOW : ANORTHOCLASE STRUCTURES

Table 8. Thermal ellipsoids-RMS displacements and angles to cell axes

9r

Ang les t o Ce l l Axes (o )

A x i s 2

b

Ax i s 3 B e q u i v .

106(J) 86(2) 2 .13( r )e 4 ( 3 ) 8 3 ( 2 ) 2 . 1 1 ( 3 )0 e0 4 .96(16)

e 0 e 8 ( 2 ) 3 . 3 2 ( 1 1 )e 0 e 9 ( r 0 ) 3 . 1 8 ( 1 2 )80(18) 4e(4) 3 .e8( i0 )

102(5) 52(5) 3 .s3(10)7 3 ( 8 ) 1 0 3 ( 8 ) 3 . 0 4 ( e )

Ax i s I

Grande Caldeira 230

RMS D i sp lacemen ts (R )

1 . 3

i58(s) 76(1,4) 2.28(5)e 9 ( 1 7 ) 1 0 ( 2 s ) 1 . 8 3 ( 4 )s l (6 ) 28(7) 1 .81(4)e 6 ( s ) 5 2 ( 6 ) 1 . 8 1 ( 4 )

103(12) 42(s ) 1 .e0(4)

50(5) Lo7(7) 8 i (16) 1 ,37(7)81(8) 146(54) 7s( r2 ) e4(5s)82(6) 124(7) 105(8) 11,7(7)4e(6) e1(10) 14s(7) 116(8)5 0 ( s ) 1 1 i ( 1 3 ) 3 0 ( s ) 1 0 0 ( 1 0 )

e (3 ) 100 (4 ) 161 (3 ) y8 (3 ) 34 (2 )1 .7 (73 ) 83 (21 ) i 61 ( i 3 ) 108 (6e ) 33 (2 )

1 0 3 ( 3 ) 7 7 ( 3 ) e 0 i 6 7 ( 3 ) e 08 (2 ) e0 0 e0 18 (2 )

e 0 7 3 ( 1 0 ) e 0 1 7 0 ( 1 0 ) 1 7 ( i 0 )4 1 ( 3 ) 1 0 8 ( 8 ) 1 8 ( 5 ) 8 s ( 1 2 ) 6 8 ( 5 )8 6 ( e ) 2 6 ( 7 ) e 5 ( 1 0 ) 1 4 1 ( 5 ) 6 6 ( s )66 (8 ) 71 (10 ) 11 .7 (e l 1s2 (e ) 21 (10 )

1 . 3 3 ( 2 )r . 2 s ( 2 )L .28(2)1 . 2 e ( 2 )2 .8e( 5 )2 . 5 3 ( s )2 . 0 6 ( s )2 .64(6)2 . 5 9 ( 6 )z . r 3 ( 3 12 .14 (5 )2 . 1 7 ( 5 )2 . 2 3 ( 5 )

M t . G ibe le 23o

t . 7 6 ( 2 )1 .70(2)4 . s e ( ] )3 . 3 3 ( 8 )2 .s r (7 )3 .86( n )3 . 2 4 ( 6 )3 . 4 5 ( 6 )

40(44 2 ( 314 ( 30)23 ( 10 )

1 )6 l

142(7)6 7 ( 5 )

1 1 2 ( 6 )1 2 3 ( s 5 )144(7)1 6 7 ( s )154 (10 )

8 7 ( 3 )8 8 ( 2 )83 (4 )8 6 ( 4 )5 0 ( 1 )89 (4 )10 ( 20 )

84(r2)78 ( 13 )5e ( 10 )1 3 ( 7 )se( 6)

s2 (2 )78(12)90e 3 ( 5 )10( e )6e( i1 )r8 ( 8 )45(32\

Grande Caldeira 400o

Mt . G ibe le 5 l 0oT1 0 . r 30 ( 2 )T 2 0 . 1 3 2 ( 4 )M 0 . 1 2 8 ( 6 )9nt 9.112{q1uA2 u . . / . 5b tbJ0 s 0 . r 4 9 ( 4 )0 6 0 . 1 6 2 ( 5 )0 j 0 . 1 6 5 ( 4 )

Kakanui 230

3.04( 5 )2 . 9 3 ( s )

1 0 . 4 ( 4 )s . 6 ( 2 )s . e ( 3 )6 . 1 ( 2 )5 . 4 ( 2 )5 . 4 ( 2 )

rr2(4)102(e)179(2)9090

136 ( s )r 25 ( 30 )127 (r0)

123(4)83( 10)o 3 ( z i9090

1 0 7 ( 5 )? 4 / 1 ? \

s 1 ( 1 2 )

r 20 (4 )1 6 7 ( 8 )90

18018088 ( 10 )

120 ( 8 )133 (10 )

6 3 ( 4 )83(4)9020(4)

1 2 s ( 3 )10s(4)80(26)3e( 11 )

148 (4 )o o t 1 , l

090901 7 l E \

1 o o ( 1 7 )53 ( 10)

88 (4 )34 (6 )90e 6 ( 4 )e ( 3 )

76 (e )37 ( 30 )ee(e)

101 ( e )

8 7 ( 4 )10e(22)86 ( 3 )1e(e )e4 (e )5 7 ( 6 )5 5 ( 4 )87(7)o s ( 6 )

5e( 3 )

2 2 ( 4 )se(s )e 1 ( 2 )6 ( 4 )

8 1 ( 3 )s0( 3 )

100( 6 )39( 10)

Kakanui 750o

I t . = E ig r t h i s i nag ina ry d i sp l acemen t o f t he non -pos i t . i ve de f i n i t e e l l i p so idEs t ima ted s tanda rd dev ia t i ons i n pa ren theses re fe r t o t he ' l as t d i q i t s

992 HARLOW: ANORTHOCLASE STRUCTURES

Table 9. Results of refinements of multi-site models for the M site

Grande Ca lde i ra 230 Ru R S i 9n i f . occup . xLeve l %

B E q u i v , M a j o rS p l i t t i n g

An i so t rop i c

Two Subs i tes

M t , G i b e l e 2 3 o

A n i s o t r o p i c

Two Subs i tes

Four Subs i tes

( n 1 i f ( n o . i a c 2

K a k a n u i 2 3 0

A n i s o t r o p i c

Two Subs i tes

Three Subs i tes

F o u r S u b s i t e s

Grande Ca lde i ra 4000

A n i s o t r o p i c

Two Subs i tes

Three Subs i tes

( n l i f q n o r i o < l

t ' l t . G ibe le 5100

Ani so t rop i c

Two Subs i tes

Three Subs i tes

F o u r S u b s i t e s

q ^ l i i q n a . i c c l

q n l i i S n a . i a ( 2

Kakanui 750o

An i so t rop i c

Four Subsi tes

F i ve Subs i t es

0.0406 0.0469

0 .0439 0 .0536

0 .0400 0 .0460 1 .014

0 .0516 0 .0579

0 .0599 0 .0709

0 .0519 0 .0586

0 .0512 0 .0572 1 .007

0.0430 0.0728

0 .0460 0 .0758

0 .0439 0 .0748

0 .0423 0 .0686

a.0221 0.1047

0.0221 0.1094 1.0002

0 .0210 0 .1082 1 .055

1 . 0

0 . 518 ( 18 )0.482

> 9 9 . 5 0 . 2 50 . 2 50 . 2 50 . 2 5

1 . 0

0 . s 0 1 ( 1 2 )0 .499

0 . 2 1 8 ( 7 )0 .481 ( 7 )0 . 301

> 9 9 , 5 0 . 2 50 . 2 50 . 2 50 . 2 5

0 . 2 7 4 3 ( 2 ) 0 . 0 0 5 1 ( 2 )

0 . 2 7 3 1 ( 5 ) 0 . 9 8 8 3 ( 5 )0 . 2 7 5 2 ( 5 ) 0 . 0 2 2 1 ( s )

0 . 2 7 8 3 ( 1 0 ) 0 . 9 7 1 1 ( e )0 .27 r0 ( s ) 0 .0026 (6 )o . 2 7 e t ( j ) 0 . 0 3 0 8 ( 6 )

0 .26e7 ( r3 \ 0 .0059 (9 )0 . 2 7 7 7 ( 8 ) 0 . 9 7 3 4 ( 5 )0 .2802 (8 ) 0 .0347 (5 )0 .2725 (13 ) 0 .0047 ( 10 )

0 . 2 7 9 6 ( 5 ) 0 . 0

0 .2 i 9 r (6 ) 0 .0148 (6 )

0 . 2 8 1 2 ( r 1 ) 0 . 00 .2755 (22 ) 0 .03 i0 (2e )

o . 2 7 s 7 ( 5 ) 0 . 00 . 2 7 9 7 0 . 0

0 .0351 0 .0488 r . 0

0.0406 0.0546 0.457(29)0 .543

0 .0327 0 .0412 1 .076 >99 .5 0 .675 (Na -Ca )0 . 3 2 5 ( K )

0 .0318 0 .0400 i . 106 >99 .5 0 .675 (Na -Ca )^ 0 .325

RMS 0isplacements (A) of Na-Ca Si te 1:

0 .2750 (2 \ 0 .0013 (2 ) 0 .1366 (2 ) 2 .36 (6 )

0 .2749 (6 ) 0 .9861 (9 ) 0 .1s65 (12 ) 0 .99 (13 ) 0 .43 (2 )0 .2749 (5 ) 0 .0130 (7 ) 0 .1214 (10 ) 0 .67 (11 )

0 .2750 (? ) 0 .0013 (1 ) 0 .1365 (2 ) 7 .20 (16 )0 .2750 0 .0013 0 .1365

' t . 46 (8 )

0 . 2 8 1 5 ( 7 ) 0 . 0 0 0 5 ( 5 ) 0 . 1 4 1 0 ( 1 0 ) 7 . 1 5 ( 1 6 ) 0 . 1 0 ( 1 )0 .2681 (8 ) 0 .0018 (3 ) 0 .1324 (8 ) 2 .39 (710 .089 (8 ) ? : 0 .248 (8 ) 3 : 0 .a50 (5 ) C = 0 .56 + Gene ra l

0 .0404 0 .0466 i . 005 >99 .5 0 .777 (Na -Ca )0 . 2 2 3 ( K )

0 .0402 0 .0467 1 .008 >99 . s 0 .777 (Na -ca )^ 0 . 2 2 3 ( K )

R l4S D i sp lacemen ts (X ) o f Na -Ca S i t e

0 .2743 (? ) 0 .0033 (2 ) 0 .1353 (3 ) 2 .8e (5 )

0 . 2 7 3 L ( 5 ) 0 . e 8 9 0 ( 5 ) 0 . 1 5 s 9 ( 8 ) 0 . 6 3 ( 1 1 ) 0 . 5 1 ( 1 )0 . 2 7 5 7 ( 5 ) 0 . 0 1 9 1 ( 6 ) 0 . i 1 2 6 ( e ) 0 . 6 6 ( 1 1 )

0 .2734 (24 ) 0 .0056 (23 ) 0 .1437 (26 ) 0 .00 . 2 7 7 0 ( r o ) 0 . e 7 7 3 ( 5 ) 0 . 1 7 1 5 ( 1 6 ) 0 . 7 6 ( 1 1 ) 0 . 8 6 ( 2 )0 .2808 (10 ) 0 .0286 (5 ) 0 .1001 (15 ) 0 .760 .?697 (24 ) 0 .0018 (23 ) 0 .1261 (25 ) 0 .0

o .?743 (2 ) 0 .0033 (2 ) 0 .1353 (3 ) 4 .27 (13 )0 .2743 0 .0033 0 . i 353 7 .26 (55 )

0 . 2 7 3 3 ( s ) 0 . 0 0 3 3 ( 5 ) 0 . i 3 6 0 ( 8 ) 3 . 9 6 ( 1 1 ) 0 . 0 7 ( 3 )0 .280s (23 ) 0 .0028 (16 ) 0 .1326 (30 ) 8 .46 (53 )

1 : 0 .085 (7 ) 2 : 0 . I 29 ( I 0 \ 3 : 0 . 356 (4 ) C = 0 ' 84 + P ro l a te

0 .0415 0 .0674 1 .035 >99 .5 0 .675 (Na -Ca ) 0 .2889 (20 ) 0 .0^ 0 .32s (K ) 0 .2688 (24 ) o .o

R l ' lS 0 i sp l acemen ts (X ) o f Na -Ca S i t e l : 0 . 18 (1 ) 2 : 0 ' 38 (1 ) 3 : 0 . 4 6 ( 2 ) c = 0 . 2 9 + o b l a t e

1 . 0

0 . 5

0 .644 ( 53 )0 . 178

1 . 01 7 > 99 . 5 0 .675 ( Na -Ca )0 . 3 2 5 ( K )

0 . r 350 ( 3 ) 4 .27 (8 )

0 . 1 6 0 4 ( 7 ) 0 . 7 6 ( 1 0 ) 0 . s e ( i )o .1oe4 (7 ) 0 .73 (10 )

0 . i 8 1 6 ( 1 4 ) 0 . 2 2 ( 4 )0 . 1 3 e 1 ( l o ) 0 . 2 2 1 . 0 0 ( 2 )0 .0977 ( 10 ) 0 .22

0 . r 5o4 ( 12 ) 0 . 00 . i 763 ( 10 ) 0 .22 (8 ) 1 .oo (2 )0 .0e72 (L0 l 0 .220 . 1 1 8 5 ( 1 2 ) o . o

0 . 1 3 6 6 ( 7 ) 4 . s 6 ( 1 6 )

0 . 1 3 s 6 ( 7 ) 3 . 5 e ( 1 3 ) 0 . 3 8 ( 1 )

o .15oo (26 ) 2 .54 (22 )0 . r 0 1 7 ( 3 8 ) 2 . 7 7 0 . 8 1 ( 3 )

0 . 1 3 6 8 ( 7 ) 1 0 . 1 ( 1 )0 . 1 3 6 8 4 . 6 ( 3 )

0 . 1 3 5 2 ( 3 0 ) 1 0 . 3 ( 6 )0 . 1 3 6 5 ( 2 6 ) 4 . ? 5 ( 2 2 \ o . r 7 ( 3 )

0 . 0 0 . 1 4 0 6 ( 1 0 ) 1 0 . 4 ( 4 )

o .o 0 .0792 (37 ) 3 .32 (18 )0 . 0 0 . 1 6 6 4 ( 3 7 ) 3 . 3 20 . 0 5 4 4 ( 2 1 ) 0 . 1 4 e 5 ( 3 0 ) 3 . 3 2 1 . 4 1 ( 4 )

o .o 0 .0601 (70 ) 3 .93 (26 )0 .0 0 .2082 (86 ) 3 .e30 . 0 5 1 6 ( 2 1 ) 0 . 1 4 7 e ( 3 1 ) 3 . e 3 1 . 3 4 ( s )0 .0 0 .131 .2 (47 ) 0 .5

0 .0343 0 .0467 1 .0 0 .2780 (3 ) 0 .0

0 .04 i3 0 .0592 0 .5 0 .2780 (4 ) 0 .0156 (4 )

0 .0373 0 .0544 0 .327 (32 , 0 .2806 (14 ) 0 .00 . 3 3 6 0 . 2 7 6 7 ( 8 ) 0 . 0 2 0 4 ( 7 )

0 .0354 0 .0505 0 .25 0 .2707 ( I 9 l 0 . 00 .25 0 .2774 (21 ) 0 .00 . 2 5 0 . 2 8 L e ( 1 7 ) 0 . 0 2 5 e ( 5 )

0 .0336 0 .0454 1 .020 >99 .5 0 .777 (Na -ca ) 0 .2780 (3 ) 0 ' 00 .223 (K ) 0 .2780 0 .0

0 .0326 0 .0437 I . 051 >99 .5 0 .777 (Na -Ca ) 0 .2862 (8 ) 0 .0^ 0 .223 (K ) 0 .259 r (?1 . ) o .o

R IYS D i sp ' l acemen ts (A ) o f Na -Ca S i t e 1 : 0 .154 (9 ) 2 : 0 .338 (9 ) 3 : 0 '

0 . r 3 7 2 ( 4 ) 4 . 5 e ( 7 1

0 . 1 3 7 0 ( 5 ) 3 . 3 8 ( 1 0 ) 0 . 4 0 ( 2 )

o . r 7 3 s ( 3 5 ) 2 . r 7 ( L t )0 . 1 1 9 0 ( 1 8 ) 2 . r 7 0 . 5 3 ( 3 )

0 . 0 e 4 4 ( 2 0 ) r . 7 1 ( 1 1 )0 . 1 7 3 2 ( 2 2 ) r . 7 Lo . r4o1 (14 ) 1 .71 . 0 .67 (2 \

0 .1371 (4 ) 7 .90 (27 )0 .13 i1 4 .62 (39 )

0 . 1 4 1 8 ( 1 4 ) 7 . 8 4 ( 2 3 ) 0 . 2 0 ( 3 )0 . L 2 6 7 ( 2 4 ) 4 . 1 8 ( 2 5 )4 0 0 ( 7 ) C = 0 . 2 5 + 0 b l a t e

1 . 0>50. 0.285(22)

0 . 3 7 0 ( 2 s )0 . 1 7 2

> 9 9 . 5 0 . 1 9 3 ( 2 4 )0 .194 (26 )0 . 1 e 8 ( 1 e )0.2r8

0.2839(7 )0 .2776120 )0 .2804 ( 1e )0.2944(23)

0 . 2 8 3 7 ( 3 0 )0 .2840 ( 34 )0.295?(2r ' )0 . 2732 ( r9 )

E s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s r e f e r t o l a s t d i g i t s

independent quarter-atom subsites with partiallyconstrained (two fixed and two refined, but equal)isotropic thermal parameters (B's) and each with aNa/K ratio equal to the overall value. The geometryof subsite positions is essentially the same as thatfor the high-albite model (Ribbe et al., 1969). withtwo inner sites close to the centroid for the anisotro-pic model and two outer sites aligned with thecavity elongation (Fie. 9). The value of B for theinner sites, M12 and M26, w€ls optimized at 0.0,obviously an unrealistic approximation, but roughlyequivalent to a single central site with a cylindricalellipsoid of electron density distribution. The maxi-mum distance between subsites, M16-M2u, de-creases and unconstrained B's increase with in-creasing Or content. Models for the most K-richanorthoclase do not converge in least-squares re-finement with more than three M-subsites, andnone of these models are an improvement over theanisotropic model.

Considering the difference in the relative massand ionic radius of potassium and sodium, it islikely that the two cations will behave dissimilarlyin intermediate alkali feldspar structures as wasfound by De Pieri and Quareni (1973) and Fenn andBrown (1977). The smaller sodium should be morefree to vibrate or rattle in the expanded cavity of analkali feldspar of intermediate composition, where-as potassium, with its greater mass and radius,should be relatively fixed in the center of the alkalicavity. Thus a model similar to that of De Pieri andQuareni (1973), here called a split-species model,consisting of an isotropic potassium site and ananisotropic sodium (and calcium) site, with occu-panices determined by bulk composition, was test-ed and yielded both a significantly improved R-factor and realistic temperature factors (see Table9). The resulting RMS displacements for the sodiumportion of the model are even larger than those formodels using a single anisotropic atom and a multi-ple subsite solution of the sodium site may beindicated. However, no further modeling was at-tempted. Small differences in the positions of theNa and K subsites are not considered to be signifi-cant.

The uniqueness of these multiple partial-atommodels is open to debate. Generally the resultspresented here are comparable to those of Winter etal. (1979) for high albite, particularly with respect tosodium anisotropy. They found no compelling rea-son to accept a static subsite model based on fourdiscrete Si,Al ordering schemes for subsites. In

HARLOW: ANORTHOCLASE STRUCTURES 993

fact, considering the 12 nearest T atoms bonded tothe 9 nearest oxygens around the M site of an alkalifeldspar, there are 110 configurations which haveno Al-O-Al bonds (the aluminum avoidance princi-ple) and have neutral charge (Al:Si : 1.3). Thisnumber increases by 390 if + I electron/M-sitecharge is allowed. These possibilities obviouslysuggest that four discrete domains are unlikely andthat local configurations tend to smear out the locusof M sites. Further studies of polarized single-crystal vibrational spectra or a low-temperaturestructure refinement would be useful in evaluatingthe nature of the M-site. The data presented hereshow that the electron distribution is not normal fora single-site model. If thermal vibration is the cause,there is either more than one node to the vibration,i.e., there is some type of positional disorder thatmay change with time, or the motion is anharmonic.Introduction of potassium into the Na-feldsparstructure causes expansion of the average alkaliatom cavity so that the sodium may reach greaterdisplacements (either thermal or positional) fromthe M-site centroid. Also the presence of potassiumchanges the distribution of electron density suchthat it is not modelled well by a single averagedatom. Consequently, even more than for the feld-spars studied by De Pieri and Quareni (1973), theuse of models with separate K and Na(Ca) sites isnecessary to achieve a reasonable description of thestructures. Splitting of the M-site into many sub-sites is not demanded but is perhaps reasonable.

In the high-temperature structures the magnitudeof apparent thermal motion for the M-site occupantis greater than for the room-temperature structures.The apparent motion is constrained to be symmetricacross the (010) mirror plane on which the M sitelies, and the delocalization can be adequately de-scribed by a real anisotropic model. Thus, there isless reason to attempt models with mutliple partialatoms. However, such modeling was performed tobe consistent with the room-temperature resultsand with the four-site model proposed by Okamuraand Ghose (1975) and Prewitt et al. (1976) for highalbite and the two-site model of Winter et al. (1979)for monalbite.

Results of these subsite (averaged alkali atom)models are given in Table 9 and show no measur-able improvement over the anisotropic approach.However, the subsite modeling does suggest thereis less delocalization of electrons (fewer subsites)with decreasing temperature and/or increasing Orcontent (consistent with the room-temperature re-

994

finements). Also the fact that these multiple partial-atom models do not result in better refinementsindicates that the use of displacive disorder isprobably not an adequate model in these high-temperature structures.

A large central positive residual on several differ-ence Fourier maps suggested a "split-species"model as used for two room-temperature struc-tures. Thus, a model using an isotropic potassiumand an anisotropic sodium (calcium) site was at-tempted. The refinements produced a significantlybetter R factor than any other model (Table 9). Theresulting anisotropic site for the Na,Ca contributionis slightly less oblate and has a slightly largeranisotropy than the totally-averaged site, with theresiduals on the difference Fourier section beingnoticeably smaller. Consequently, a model involv-ing distinct M-site species with different thermalparameters is reasonable and consistent with thedata. M-O bond distances for the split sites in themonoclinic high-temperature structures suggest adistorted five- or six-fold coordination, with the Matoms being displaced towards the ends and sides ofthe alkali cavity (Table 10).

Conclusions

Refinement of three anorthoclase structures atroom-temperature (K-analbites) and at high-tem-

Table 10. M-O distances for models with split M subsites (in A)

t ' l Subsites ont OnZ 0g 0g 0p Average

Mona lb i te 9800 ( l l i n te r e t a l . , 1979)

N a 1 2 . 5 s ( 2 ) 2 . 4 4 ( I l 2 . 7 s ( 2 ) 2 . e 1 ( 2 \ 2 . 6 8 ( ? \ 2 . 8 6 7- 2 . 9 5 ( 2 \ 3 . 1 1 ( 2 ) 3 . 3 s ( 2 ) 2 . s s ( 2 )

l i lona ' lb i te 9800 (0kamura and Ghose, 1975)

H a 1 ( m ) 2 . 7 3 ( 8 ) 2 . 5 1 ( 9 ) ? . 6 8 ( 9 \

N a z ( m ) 2 . 7 4 ( 5 \ 2 . 5 1 ( 7 )

Na3 2 .s4(5) 2 .40(4) 2 .71(10) 2 .70 2 . 6 0 ( 1 0 )

Mt . G ibe le 5100

t r 1 ( m ) 2 . 7 3 ( 2 \ 2 . s 2 ( 2 )

r '42(m) 2 .75(2) 2 .51 . (2 )

M 3 2 . 5 7 ( 2 ) 2 . 4 7 ( ? \3 . 0 0 { 2 )

Kakanu i 750o

l u l r ( m ) 2 . 8 4 ( 3 ) 2 . 4 8 ( 3 )

t ' t 2 ( m ) 2 . 8 1 ( 3 ) 2 . s 2 ( 4 \

r i f3 2 .47 (3 ) 2 .46(3)3 . 3 0 ( 3 )

Sp l i t Spec ies

Grande ca lde i ra 4000

N a ( c a ) 2 . 8 4 ( l ) 2 . 4 5 1 2 |K 2 .73(2) 2 .6 r (2 )

l l t . G ibe le 510o

N a ( C a ) 2 . 8 0 ( 1 ) 2 . 4 1 ( 1 ) 2 . e s ( 1 ) 3 . 1 0 ( 1 ) 2 . 8 7 ( r \ 2 . 8 7 1

K 2 . 6 s ( 2 ) 2 . 6 r ( 2 ) 2 . 8 s ( 2 \ 3 . 2 3 ( 2 ) 2 . 8 3 ( 2 ) 2 . 8 6 5

HARLOW : ANORTHOCLASE STRUCTURES

2 .7112 ) 3 .18 (1 ) 3 .07 (2 ) 2 .8763 .13 (2 ) 3 . i 6 (2 ) 2 .65 (? ) 2 .8782 . ss (2 ) 2 .87 (1 ) 2 .68 (2 . t 2 . 8813 . r 6 ( 2 ) 3 . 4 0 ( 1 ) 3 . 0 6 ( 2 )

2 .58 (4 ) 3 .1s (2 ) 3 .38 (5 ) 2 , s413 .36 (5 ) 3 .21 (3 ) 2 .54 (5 \ 2 .e302 . 6 7 ( 3 ) 2 . s e ( 3 ) 2 . 6 1 ( 3 ) 2 . 8 6 33 .46 (4 ) 3 .34 (4 )

2 .92 (2 ) 3 .07 (1 ) 2 .e3 (1 ) 2 .8992 . s4 (2 ) 3 .16 (1 ) 2 .83 (1 ) 2 .882

perature (K-monalbites) reveal the followingpoints:

(1) Room-temperature cell parameters indicate alarge degree of Si,Al disorder consistent with mono-clinic topochemistry. High temperature measure-ments show that these samples do become metrical-ly monoclinic.

(2) Extrapolations of cos2a values predicts 0136as the composition for the displacive transformationto monoclinic symmetry at room temperature,which is comparable to estimates of Bambauer etal. (1978), Hovis (1980) and Kroll et al. (1980).Extrapolations for cos2(AT-O-T) yield an equiva-lent result.

(3) T-O-T angles and M-O distances increase inaverage value and the variance for the averagesdecreases with increasing Or content at room tem-perature. This shows a trend to a more regularlycoordinated M-site as in the sanidine structure. Athigh temperature in K-monalbites, increase in Orcontent and temperature have similar effects uponthe alkali feldspar structure, except that K-rich K-monalbites always have a wider and shorter M-sitecavity than Na-rich ones. This feature is due to thestrong capacity of K to expand the average alkalication cavity.

(4) An increase in apparent-thermal-motion mag-nitudes is correlated with the addition of An contentand is probably a result of increased local displace-ment of atoms from the average sites due to theinfluence of added Ca and Al in the feldspar struc-ture.

(5) Anisotropic thermal models of the M site areunreal at room temperature but, similar to the caseof high albite (Ribbe et al., 1969, Wainwright inSmith, 1974) and analbite (Winter et al., 1979),maximum apparent motion is parallel to the cavitylength and minimum motion is parallel to a*, thehighly constrained direction of M-Oa2 and M-Oa1bonding. Modeling with multiple isotropic partialatoms suggests structures equivalent to that ofRibbe el al. (1969) for high albite or Winter et al.(1979) for analbite-four M subsites of which twoare greatly displaced from the average centroidparallel to the cavity elongation. These models areless applicable as Or content increases and proba-bly represent an average of many local geometricconfigurations rather than a domain texture. How-ever a "split-species" model, using a separateisotropic site for K and an anisotropic site forNa(Ca), yields real thermal parameters with signifi-cantly improved weighted R factors, further sup-Est imated s tandard dev ia t ions in paren theses re fe r to the las t d ig i ts

porting the conclusions of De Pieri and Quareni(1973) and Fenn and Brown (1977\ on the differentnature of K and Na in intermediate alkali feldspars.Nonetheless, the large anisotropy and displacementmagnitudes of the Na(Ca) portion of the site suggestpositional disorder as in high albite or analbite forthese refinements. For the high-temperature struc-tures multiple partial-atom sites do not provideimprovement in modeling of the M-site over ananisotropic apparent thermal motion model. "Split-species" models for the more potassic crystals yielda better match to the data than the other approach,but do not yield the same degree of improvement asfound in the room-temperature structures.

AcknowledgmentsI want to thank Gordon E. Brown, James B. Thompson, Jr.

and the late David R. Waldbaum for stimulating my interest inthe feldspars in general and this topic in particular. I am indebtedto Eric Dowty and Dan Appleman who offered support andcriticism throughout the project. This paper was benefitted fromthe thoughtful reviews and suggestions of Drs. Hans-UlrichBambauer, Maryellen Cameron, Phillip Fenn and Herbert Kroll.This research was supported by National Science FoundationGrant NSF-DES-00527 (Eric Dowty, Principal Investigator).

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Manuscript received, May 29, 1981;acceptedfor publication, June 1, 1982.