An analytical and experimental study of zoning in plagioclase

An analytical and experimental study of zomng in plagioclase ROBERT K. SMITH AND GAR3' E. LOFGREN

IXI -IOS

Smith, R. K. & Lofgren, G. E. 1983 0415: An atudytical and experimental study oJi zoning in plagioclase. Lithos, Vtd. 16, pp. 153-168. C|slo. ISSN 0024-4937. A detailed electron microprobe study has been conducted on tmtural and ex~n~entally grown zoned plagioclase feldspars. Discontit~ttous, sector, and ~:illatory che~aical zoning ~:.~rec~bserved s u p ~ n p o ~ d on continuous norma[ or revl;rse zoning trends. The relative aceuracy o1~3 egemeat (Na, Cad K) m~icroprobe traverses was found statistically to be 2 mole percent. Comparison of microprobe data on natural zoned plagioclase with .,oned plagiocl~s¢ grown in controlledl ©xperim¢:ats has shown that it may be possible to distinguish zonal development resulting from physio-chemical chan,~.:~sto the bulk magma from zoning related to local kh:tetic control on the growth of in6ividual crysllals.

Robert K. Smith, Department oJ Geosciences, University of Southern Coloraa'o. Pr~eblo, Colorado 81001: Present address: Division of E~,lrth and Physical Sciences, the University of To-r.a:r:at San Aattmio, San Antonio,. Texas 78285; Gary E. Lofgren, Geology Branch, SN6, NASA Johns,:~n~:~ace Center; Ho~'~or~, Texas 77058; 30th July, 198.7..

Plagioclase in plutonic and volcanic rocks is usually compositionally zoned. This zoning may be simple normal zoning, i.e. an An-rich core which grades continuously and smoothly to an Ab-rich rim~ ORen, however, the zoning is complex. There may be abrupt discontinuities with large compositional changes (10-30 An mole%)usually in a normal! sense, but sometimes with reversed trends (going outward from the core the crystal becomes increasingly An-rich). There may be fine scale (a few microns) oscillafioi~is in composition superimposed on a normal, re'verse, or constant compositional trend. Finally, there may be .compositional differences between differen~ crystallographically defined sectors of the crystal which have compositional boundlaries that resemble an hour glass (sector zoning), it is not unusual for all but the sector zoning to be present in a single crystal. All of the: compositional variations are caused by physio-chemical cha~tges which affect the magma in which these cr3tstals grow ~td are a record of those changes. If we could interpret those changes, much of the history .,3fthe enclosing magma body would be reveall,ed. Although theoretical models, especially for c,scillatory zoning, are numerous, critica~l d~ta showing :zoning profiles of individual crystals are surprisingly few, and experimental studies ai~te,d at reproducing zoning are even fewer. Not surprisingly it is not possible to fully evalua,ze tlheories of plagioclase zoning. 10 - ILithos2/83

During this investigation, 32 zoned p|agiociase crystals were analyzed by mea~s of 60 step-scan traverses. Of the plagioclase cr~'stals analyzed, 10 (18 stel~scan traverses) were experimentally grown and the remainder were from a variety of rocks ranging in composition from basalt to rhyodacite. ~hese data are used to evaluate the validity of ex~isting models of feldsp~r zoning. We will not attempt a thorough review of all models, nor even an in-depth description of sl~ecific models, but will outline only their salient features.. The fur flavor of each model can be obtained o~ly from the original papers (see also Smith 1974: 212-224). Models exist for norraal, reverse, discontinuous (stepped), os¢iUatory and sector zoning. Models for normal and discontinuous zoning are straight¢:~rward; those for sector and reverse zoning are complex, but reasonably well understood; and those for osciilato~¢ zoning, thLough more numerous, are the least satisfactery.

Experimental and analytical methods The electron microprol~¢ ~a~alys~s for Na, K, and Ca were carried out on ai~ AR[.-EMX-SM electron microprobe at the NASA Johnson Space Center, Houston, Texas. An electron beam of approximately 1 em in diameter was used with an acceleration potential of 15 Kv and a sample current of 0.02 ~A. Analyzed mineral standards

154 R. K. Smith & G. E. Lofgren

LITHOS 16 0983)

Table 1. Exl~mmental run conditions.

Zone

Temp. °C

Ruta 68, An 50, 10.0 wt. % Melt 1 2 3 4 5 Glass

Pressure Kb H,,O,

11200 1050 1000 950 900 850 -

Time Hrs

Average composidon An wt. %

Range of composition An wt. %

Average growth rate It/hour

17 24 24 49 47 73 -

91 84 79 68 53 ]3

82-89 74-82 64-70 -

2.5 4.7 0.9 I}.5 0.4 -

24 48 50 71 73 -

-

Tt, ~" 1 1 ( 1 0 ° C 6. ! 5.3 5.2 5. l 5.0 4.9 -

Run 74, An 40, 9.5 wi. % H 2 0 , TL ~ 1040°C Melt I

2 3 4 Glass

1100 950 9~} 850 800 -

6.2 5.0 4.~'~ 4.~ 45, -

72 60 48 30 8

-

-

58-63 45-49 -

1.4 0.6 0.3 0.3 -

Run 139, An 60, 7.1 ~vt.% H_,O Melted at i 2 ~ C for 7 hours. 5.3 Kb; d r o p p e d rapidly to 1150°C and then cooled at 4~C/hr to 80IFC, the pressure decreased s~,eadi!y with temperature from 5.3 to 4.7 Kb. Run 391. ,,in 40. 5.0 v~.. % HzO .Melted at 12C0"C for 15.5 hours. 5.9 Kb; dropped rapidlly to 1153~C and then cooled al 129°C/hr to 860°C. the pres,:ure decreased steadily ~4th temperature from 5.2 Kb at 1153°C ~o 4.7 Kb at 860~C. Run 618. An 37 A b 4 5 O r 18. lO.0 wt.%

1120

Melted at 11{J[~C for 20 he,its. 5.7 Kh: dropped rapidly to lq~}0°C and then cooled at 2°C/hr. to 500°C, the pressure dec: :ased steadily with temperature from 5.5 Kb at 1000°C to 3.4 Kb at 500°C.

were used. All data were collected using 2 ~tm step-scan traverses; each point was irradiated for 20 seconds. Six element analyses v,ere completed using a M.A.C.-5 electron microprobe. X-ray intensities were measured with an electron beam diameter of approximately 1 .um using a 15 Kv acceleration potential and 0.015 ~tA sample current. Measure¢~ X-ray intensities were corrected for detector deadtime, background, and matrix effects using a Bence-Albee correction technique with alpha factors by Albee & Ray (1970). Mineral standards were used throughout. The experin~entally ~'own crystals analyzed in this .,,t~Jdv are previoudy described in Lofgren (1974a, b. 19~10}. The growth parameters are given in I'ab~c 1. avid include the initial melt ,:,~mposition, growth t~mperatme, cooling rate, and growth ralte data w?~ere avail able. 'irne major c~ement chemistry of the natural rock samples ll~at contaiin r~he c~stals studied are li~,~ted in Table 2. A majo.r concern of the analvtical method is

the precision of three element (Na, K, Ca) analyses with a 1 ~tm beam diameter using 2 ~tm stepscan traverses. Three approaches have been used to evaluate the., quality of the data: microscopic, six element electron microprobe analyses on selected crystals ~asing a different microprobe, and a statistical eval,aation. In the first method, plagioclase compositional variations were determined by microscopic measurement of optical extinction using Schustei's method (Schus~,er 1!880; Kohler 1942) and cornpared with microprobe data. Table 3 shows a direct comparison between microscopic and microprobe analv,~es 'inducted on two discontinuously zoned plagiocmse crystals (F:ig. 1). There is excellent chemical correlation belv,een the t w o methods. All abrupt compositional changes are quite evident optically as well as on the micro probe traverses,. The second ~aethod involved six elemer~t anal.yses (Na, K, Ca, AI, Si, and Fe) of four of ,:he crystals analyzed! for three element:;. The ofigi~a~

tlTHOS 16 (1983) Table 2.

Zo,,q#lgin plagioclase

Chemical analyses.

A

Wtt. %

M-714

M-229

M-513

SiO2 TiO2 AI?)~ Fe203 leo MnO

51.46 1.08 20.73 2.41 6.30

66.93 0.40 14.78 2.21 0.40

68.44 0.50 15.59 2.97 -

0.17

0.08

0.06

MgO

3.55 10.02 3.43 0.81 0.26 0.58

0.95 2.75 3.65 3.83 0.16 3.91

0.64 3.08 3.78 3.39 0.24 0.97

100.80

100.05

99.66

0.64 4.79 29.02 38.78 7.76

24.15 22.63 24).89 12.63 0.05

26.53 20.03 31.99 13.87 -

CaO Na20 K20 P205 H20 (total) Total

155

Norms (wt.%) Q or ab an di W O

hy c4 h m

mt il ru ap C rotal

--

--

13.12 -

--~ 3.49 2.05 0.57 100.22

--

2.34 -

1.59 -

1.94 0.39 0.76 0.35 96.14

2.97 0.13 0.43 0.52 0.62

B

98.69

traverse was located and multiple spot analyses performed along the traverse. Each individual spot analysis was then plotted directly on the original 2 ~tm step-scan traverse as shown in Figs. 2, 5B, 10B. In all instances less than a 2 An mole % difference is noted between the three and six eleme.nt microprobe analyses. This close chemical similarity implies that three element analyses are sufficiently accurate to study zoned plagioclase phenocrysts. A third major concern ~s the compositional significance of the vezy small, but sharp, microprobe compositional oscillations Ion the order of 1 to 2 An mole %) as noted along most of the micropzobe traverses. Whether such minor oscillations are evident optically is primarily a function of the crystallographic orientation of the crystal (compare Figs. 5 and 7). It ~s important, however, to know whether these s~aail oscillations reflect actual chemic~i variations within the

Fig. 1. Photomicrographs of discon linuouslly zoned plagioclase crystals used in the optical comparison o1 zone c o m l ~ t i o n s using Scihustefs method. [A] M-7/,4A, [B! M-5~3. Data and composhional comparisons are shown in Table 3. Crowed polarizels.

crystal, i.e. what An mo|e % change sl~ould be considered significant. In order to make 1his judgment, the accuracy of X-ray photon counting measurements as, they pertain to microprobe analyses of zoned plagioclase s were analyzed sta-

LITHOS 16 (198~)

156 R. K. Smith & G. E. Lofgren Fable 3. Micr~a:opic dalla.

Sample M-714 Zone Zone Zone Zone

1 2 3 4

M-513 Zone ! Zone 2 Zone 3

Extiaaction off (001 ~ or (010) (Schuster's method)

Composition (Schuste.r's method)

Composition (microprobe)

-

An An An An

An An An An

33" 26" 14° t o - 18° 9*

-- 31 ° - 15° to - 25 ° - 3 ° to - 8°

91 83 06 to An 70 53

A n 66 A n 48 to An 57 A n 39 to An 42

88 77 64 49

to to to to

An An An An

90.5 81 71 54

An 64 to An 65 An 51 to An 59 ~ n 36 to An 43

tistically (Appendix, Table 4, Fig. i3). The resuits of this analysis indicate that chemical variations of from 1-2 An mole % are significant in the present study.

Analyses of zoned plagioclase and evaluation of zoning model Discontitmous and reverse zoning A tyoical di.scontinuously zoned plagioclase phenecryst fr~m a fresh aa basalt (M-7!4) from Pacaya Volcano in Guatemala (Eichelberger et al. 1973) i~ shown in Fig. 3. This crystal has four sharply-defir:ed, concentric zones each more An poor than the previous zone. Chemical variations between the zones range from 10 to 15 An mole

D 80 70

N

3O

IO0. 90' ~0

80'

1

4 70-

~o

,~

6~

3 [2 ,~o ~oc~ ,~o

,,-o ~ e

~8~~ 200 220 ~ o

~o

2~o

~iceons

bO-

M 714A.T 2

2O ~0~ ~ 0

Wm

2~

40

60

80

K~0

Fig. 2 A 2gin ~_~cp-~:ar: ~raverse far Na, K. Ca with separate si× e|ement sp~n zlna~,/scs ~uperimr~scd (solid black c~rc~es} of a nm:urally ~w_cu~Tingplagiocla~ phenocryst (M-6tN}, Note the c~ose cc,rre[a~or hetv,,een the three element s t e p - ~ n t:raver~e and thc six clerr~c,~ s ~ analyses.

Fig. 3. [A] Photomicrograph of a discontin~ou,.~ly zoned plagiodase feldspar phenocryst in a hypocrystalline basah porphyry from Pacaya Volcano, Guatemala. Crosse,5 polarizers. [B] The An content along the electron microprobe traverse .~,hown in A. Z~nes 1 (core zone) a~d 4 show a consta.~ to slig'l~ly reversed chemical trend and an overall normal trend respectively, while zones 2 and 3 show initial reverse trend,: followed by normal trends. Superimposed on this combined :everse and nor~aal zoning pauern are minor oscillations with differences as much as 7 moie % An. Da~.hed portion along th~ traverse represents either pits or fractures within the sample r~sulting in questionable analyses. Nume,ered zonal regioF,~s on this figure and subsequent figures correspond, in a~l cases, to ~ext descriptions

Zoning in ,plagioclase 157

LITHOS 16 0983)

A

100I10~0-i~'~--.

% ~' '

70 o

60-

~

,1.0o 30-

B

70.

li

-

~f

,

~,

,

,..

.

.~x '

,~

'

,'0o '

~'-~*" -

140

lUliCeORS UeS, T-!

Fig. 5. [A] Experimentally grown plagi~lase crystal showing discontinuous zoning (Table 1, run 68). Crosse~i polarizers. [Eq The An content along the electron microprobe traw:rse sl~town iu A. There are five, concentric, discontinuous zones each followed by reverse zoning trends. Solid circles are, six elemen,t spot analyses along the step-~can traverse, nole dose correspondence.

60"

50.

< ae 30. 20' 10

1213 20

aO

60

80

M-513,T-I Fig. 4. [A] Photomicrograph of ~ discontinuously zoned plagioclase phenocrys¢ in a l'~ypocry~,ta~llinedacite porphyry from California showing the ~ypical tabular plagioc~ase hab~it elongated parallel to the y axis, {01t~}. Crossed polarizers. IB! The An content along the electron microprobe traverse shown in A, There is a sharply defined, coml~asitional drop occurring between :,ones 1 and 2, culminating at a composition of An 57. Zone 2 shows a slight reverse trend and then a~ norma~l trend before the next discontinuous step to zone 3. The onset of zone 3 is marked by a change in coml~asition to less than An 40. which Li iollowed by a r e v e r e tread which changes to a normal trend near the edge of the crystal

%. The first three zones show both normal and reverse zoning while zone 4 shows a slight norreal trend. Oscillatory zoning is superimposed on the normal and reverse zoning in all zones. The revel~e zoning trends observed in zones 2 and 3 are present in most of the discontinuously zc,ned plagioclase phenocrysts in M-714. The rev,erse zoning has arrange of 4 to 15 An mole %. A traverse from a discontinuously zoned plagioclase crysll:al iin a hornblende-biotite dacite (M-513) from Cactus Mountain, California is shown in Fit, 4,. "]['hecrystal has thLee concentric, discontinuou? ,:ones each more All poor than the previous zon,:., wihich correlate well with another crystal 1 cm away in the same thin section. As previously observed in the Pacaya basalt, the discontinuous zoning shows both reverse and normal zoning trends with superimposed osci,llatio~-~swhich c~nnot be correlated from crystal to crystal. Reverse zoning trends are mo.~t obvious in zones 1 and 3. Minor osciilation:i are less prominent tt,~an in Fig. 3. An experimentaUy grown, disconlinuously zoned plagic,clas,e feldspar crystai is shown in Fig. 5 (see Lofgqen 1974b, Fig. 1B). This crystal

158 R. K. Smith & G. E. Lofgren

Lrrv',o:s 16 0983)

A

'3

'°

.

~--

,'o 5'0

~o

,o-,o-~go

i 100

Micron~s

#74.1"-1

/-~g. 6. [ A ] Exper{mentally grown plagioclase crys,:al displaying d~sconlinm.'us zoning ~ov,31 from a melt of different compositmn tllav shown in Fig. 5 (Table I. run 74). H'~e large decrease m An cnmen! at 3t} microns is an inclusion of melt in the cr~,~al. Crossed polarizers. [B] The An content along lhe electron microprobe traverse shown in A. Reverse zoning is less ~ron~mnced and lhe ouler zone is essentially homogeneOg|S.

consists of a sequence of five sharply-defined, concentric zones each more An poor than the pre,.ious zone. The variation in An content betwe~:n each zone ranges between I1 and 26 mole ';'~. Immediately following each rapid change in composition there is a reverse zonir, g trend that continues until the next discontinuo~Js step. The reverse zoning has a range of 3 to 17 An mole % with the ma~:imum amount r~oted in zones 2 and 3. The compos~,tional reverse zoning is least pronounced in the core and the outerm,m,t zone.

A microprobe traverse across an additional discontinuously zoned plagioclase crystal grown fl'om a melt of different composition is, shown in Fig. 6 (see Lofgren 1974b, Fig',. 1D). In this crys~tal, as previously noted in Fig. 5, immediately following each discontinuously prod~ced zot~e there is a continuous reverse zoning trend. Again, as in Fig. 5, the core and outermost zones show the least reverse zoni'ag; the other zone is nearly homogeneous. Discontinuous zoning ha:f perhaps the most obvious origin of any of the kinds of plagioclase zoning. It was recognized e'~dy that a rapid change of temperature or pressure (combined with loss of volatiles) could cause this type of zoning. It was also recognized that a change of pressure is more likely to happen fast enough to cause the obselreed sharp discontinuity (Phemister 1934) than a change in temperature. The experimentally produced discontin~aities are the product of rapid changes in temlperature. The magnitude of the compositional break is a direct function of the magnitude of the temperature change. A crystal doesn't know how an increased degree of supe~rcooling or supersaturation is induced; it merely responds to an increased driving force for crystallization. In experiments, temperature is ~Iheeasiest variable to change and has therefore been used in the presen~ study. In nature, a sudden pressure chm~ge would produce a similar discontinuity followed by renewed growth at either a lower or higher An content depending on water content (Wiebe 1968). Such discontinuities rnight also be D"oduced in a rapidly ascending magma, but again the accompanying pressure change, would cause the discontinuity. In the e×pefiments, each temperature change was followed by an isothermal period of crystallization. The crystal grown during this isothermal period is usually reversely zoned or occasionally unzoned, never normally zoned. In the magma which experien:es a sudden pressure change, there is likely to be a similar period of isothermal growth once the pressure is again constant. Similarly, the natural plagioclase crystals, as demonstrated earlier ip this paper, show a reverse zoning t~,..~d following most of the sharp discontinuities. The reverse zoning can be explained as a kineticaIly controlled response to a sudden, change in either the degree of supercooling or l:he, degree of supersaturation (Lofgren 1974b}. If the rapidly induced degree of supercooling is sufficiently large there is a strong probability that ~ontinued

Zoqi~g in

LITHO$ ?~6 (1983)

growth will be at a composition more sodic than the composition predicted by the position of the solidus at that l:emperature. The reverse zoning trend is then the result of the system's attempt to approach the equilibrium condition as continued growth reduces the degree of supercooling in the system. It is easily seen that, depending on the magnitude of ~he rapidly induced degree of supercooling, the magnitude of the rever~e zoning will vary. In addition, if the system is cooling at a significant rate when the sudde~ change occurs, the normal zoning which results 'tom cooling will reduce, eliminate, or even cause a normal zoning trend. In the experiments any heat of crystallization is eliminated kt the; conl:rolletl envi:'onment; in nature it would add |Io the magnit~ede of the reverse zoning. Any significant elevation of temperature, however, would result in resorption of the already c~ystalliized ma!~.erial and would be apparent in the crystal.

p!agioch~s:e

159

A

"it ,~ 6o

*:l/

Oscillatory zoning Compositiona! data on osci~latodly zoned plagioclase determined by optical methodls are; few (Homma 1932; Phemister 1934, 1945; Larsen et al. 1938; Leedal 1952; Carr 1954; Ewart 1963; Panov 1968; Wiebe 1968); and compositional data determined by electron microprobe are even fewer (Hiirme & Siivola 1966; Klusman 1972; Subbarao et al. 1972; Pring!e et al. 1974; Sibley et al. 1976). We will, therefore, present additio~:~al electron microprobe data on oscillatory zoning trends associated with normal, reverse, and diiscontinuous zoning in both natuk-al and exlz~e,rimenta!ly grown plagioclase crystals. An oscillatory zoned plagioclase ph,enocrysll in a t~asalt from Chile wiith an overall normal zoning trend is shown in Fig. 7. In this example, oscillations are on the order of 1 to 2 An mole % (Fig. 7B). The overall compositional var/atiion for ~raverse T..1 (Fig. 7B) is fi'om An 59 to An 55 over a distance of 50 [~m. Approximately 120 [am distance from the above microprobe traverse a second analysis was run on the same crystal, traverse T-6 (F~g. 7C). This traverse shows the same normal, oscillatory zonii,g tread as traverse ~ I . However, major compositional differences exist between the two traverses which could not be accounted for by ~ector zoning because they are in the same sector. Traverse T-6 shows an overaU compositional variation from An 80 to An 57, and compared to traverse %1 has greater An mole %

2O

4O

6O

Microno

IO

100

M- SUB,T-1

20

40 60 80 K~) Mit:ronm I I | - SOO.T- @

Fig. 7. [A] Photomicrograph of an oscillatory zoned plagioclase feldspar phenocryst in a hypocrystalline basalt porplhyry fror,-I Chile. Crossed polarizers. [B] The An content along r.hc microprobe traverse on the left in A shows an overall normal zoning trend with minor oscillatiom. [C] This traverse shown on the right in A, displays a greater An variation, rcverse, a~d discontinuous zoning superimposed on a normal zoning trend Db,continuous zones occur at 64 pm and 52 pm respectively, with each sharp discontinuity followed by reverse zoaing. A normal zoning trend begins between 40 pm and l0 lmlL.

variations throughout. Sucb heroical variat'ions are confirmed optically; i.e. extinction anglte differences exist laterally along zones as ,Nell :~ the thickening and thinniing of these zones. Additi onal differences include a reverse zoning trend and discontinuous zones. Such chemical variations occurring laterally al.ong the same optically con,,,,,,~ the result of Iloca~ tinuous zone are most ,:1...i.. variations within the magma which are manifest.. ed in the crystal-liquid boundary kinetic~,~.. However, where different growth sectors of a~crys~,al are coacerned such compositional difle,rences may also be explained by the combination ,of crystal-liquid boundary kinetics and growth relationships between different crystal faces. In some of the crystals analyzed, oscillatory

LrrHos )6 0983)

160 R. K. Smith & G. E. Lcfgren A

/

:1

i [

Microns

~

2;L~B,T- 4

F/g. 8. [A] Photomicrograph of a plagioclase phenocryst displ~,/ing rhythmic oscillations in a hypocrysta!line ~:rachyte porp~,)r), from near the Hoover Dam. Arizona:. Crossed polarizers. [B] The An c~ament along the microprobe traverse shown in A. Rhythmic osdllatioas are well displayed.

zoning is superimposed on what would be an otherwise homogeneous crystal. Such crystals commonly have both large and :~mall scale oscillations. The large scale os~fillatiionsstand out and are of nearly constant composition. Two exampies are described below. The first examgle is a plag{oclase cu~stal (Fig.

A

8, M-229B) in a trachyte from near the Hoover Dam, Arizona. It displays rhythmic oscillations superimposed on an average chemical background of An 32. Each successive rhythmic oscillation, at 50, 150, and 195 ttm respectively, is followed by a normal and more gradual decrease in the An content compared to tl~e rather sharp increase; in An content preceding each oscillation. There is a slight (approximately 2 An mole %) dropr between successive peak heights from the crysl:al interior toward the rim. Relatively smaller oscillations from 2 to 6 An mole % occur between the three major rhythmic spikes. The second example is shown in Fig. 9, and is in a basalt from Chile: (M-600). This crystal has a norm~ly zoned central core, An 50 to An 30, with an outer zone containing four rhythmic osdilations. The rhylthmic oscillations occur on a relative/ly constant chemical background with a mean of approximately An 35. The numerous microprobe traverses (Fig. 9A) completed on this phenocryst, provide an excellent opportunity to correlate the four major rhythmic oscillations on two crystal ~aces. Of the four separate rhythmic spikes, three are within 5 to 7 An mole % of one another (Figs. 9B, 9C); i.e. all three lie between An 48 arid An 55. The fourth and outermost spike has a composition of An 43, Between these four An-rich, rhythmic oscillations on face (100) (F:ig. 9A), there are minor oscillation,,; with compositions ranging between An 3:8 and An 30. These minor oscillations on face (100) show excellent correlation between traverses T-1 and T-5

70'

C

60.

70,

'°j3

60

.50" 40"

~

30' edge

4C

~30

20. I0, 20

40

60

80

I00

P~:|©ro.s M - OO0,,T- 1

20 40 60 ~|©rOnS

M - 60@,T.- 7

t;/l? ~ Phommicro~aph of a plagioc|a~e phenocr~ st i~ a hypocto'stalline basah porphyry from Chile. [A] Shows number, location, v.a,J cxtcr~t of ~h.e microprobe lraverses. Crosse'd potafizen, [B] and [C] The An content al,3ng microprobe traverses 1 and 7 reS.l:~;ctiv¢y sh<~wl~in A.

(Fig. 13). However, traverse T-7 (Fig. 9 C ) n o r mal to face (001) shows a COml:~letelack ot! minor oscillations be'tween the fo,ar major spikes. Such minor cherrhcal variations occurring on the different crysta:ll faces may be due to crystal-lgquid boundary kinetics and the ra~e of crystal growth of these faces. An alternative e~planation is that, due; to the very small area bet,,veen major o~:illations on face (001), any minor chemical ~lariations that may be present there are not recorded because of the microprobe beam spot size. • i ~ n e d plagi[oclase crystals displaying oscillato~/zoning have also been grown experimentally in controlled cooling experiments (Lofgren 1980). An experimentally grown p~agioclase crystal displaying oscilllatory zoning is shown in Fig. 10 (run condill:ions are given in Table 1). The osc!iltatory zoning is very fine with small compositional variations ~ranging from 1 to 2 An mole %. Such small compositional variations have been observed both optically and by the electron microprobe awd are superimposed on a normal zoning trend which is initially fl;~t with rapidly decreasing An content toward the rim (Fig. 10). Osc;illations produced experimentally are best developed in the An 40-60 bulk compositional range. Oscillatory zoning consisting of successive and at times rhythmic compositional variations from core to margin of a plagioclase crystal has been a subject of discussion for many years (e.g. Harloff 197.7; Bowen 1928; Homma 1932; Phemister 1934; Hills 1936; Carr 1954; Vance 1962; Botfinga et al. 1966; Sibley et al. 1976; Haase et al. 1980; Allegre et al. 1981). Theories for Ithe origin of oscillatory zoning can be divided• into two main groups. One group of theories is based on repeated changes in crystal-liquid equilibrium as a result of sudden changes of temperature, pressure, water saturation, and melt composition. The second group of theories is based on disequilib~rium growth of the crystal, which appears to be the dominant growth mode of oscillaltory zoning in the crystals analyzed here. Allegre et aL (1981) critique the existing disequilibrium growth models and find them lacking in ::)ne critical ingredient, the driving force flal l, o r an explanation of, the oscillatory behavior. All the: models explain a plausible .~ingle cycle of crystaUization, but do not adequately accom~t for repetition of the cycle. Allegre et al. (1981.) attempt to explain the repeating cycles by po:s.tulating that, for a crystal whose growth ihas, slowed because of the changing melt composition at ~he

161

z, omng in plagioclase

L I T H O S 16 (le~3)

A

100.

I$

9080-

70I:

6o-

30" 2010-

I0

20

30 40 50 KI i © r @,n •

bO

70

#139,T-

2

Fig. I0. [A] E×perimentaily grown plagioclase crystal (Table ~, run 139). Crossed polarizers. [B] Ttle Ae content along tl~e microprobe traverse shown in A. Fine-scale, o,lciBat¢,~y zonit~g apparent in the traverse is not seen ~ptically in A because of the position of the e×tinction band. Ose~llato,ry zoning is obscarred optically only as the microscope stage ~is rotated. Solid circles represent six element analy~e.~; along the step-scan traverse, note close correlation.

in,terrace, there is a characteristic time |or structural rearrangement before the growth taste can increase. They provide a mathematical for;mulatiotJ of the growth equatio~ whirr: they claim dee~:, provide for true oscillatory behavior, with the incorporation of the characte~isfc delay time. lit is clear tha'~ the experimental growth of oscillatory zones in plagioclase woul,d, at this

162 R. K. Smit~ & G. E. Lofgren

B

,oo]

Lmios 16 (]983)

C

I00

90' 80-

70-

70 G

~'0 °'

60" 50"

40-

40"

30-

30-

20"

20-

t

10',

\ O,.e, 2c

Microns

# 61a.1"-1

time. aid i~ the evaluation of the models. If the prediction of Atlegre et ai. is true. however, the ~,r~wth rate for oscillatorily zoned crystals would be 'very slow, perhaps too slow for laboratory cxperiment~ttion. This may explain the difficulty one of the authors CGEL) has had growling oscilRat,~rily zoned crystals i~a the laboratory. '.')~fly in one experiment out of more than 50 attempts have oscil!atorily zoned plagioclase crystal.,; been uown. This experiment, however, was n t>t at the s~ov,,est cooling rate attempted, as the model of A~legre et al. (1981) would saggest it should be. The experimentally produced oscillatofily zoned crystals resemble the zoning described by

7-'

-7o -70o

Ui©rone #618,T-2

Fig. !!. [A] Experimentally grown plagioclase crystal showing sector zoning (Table !l. run 6181. Crossed polarizers. [B] The An content along the microprobe traverse on the left in A showing relatively symmetrical normal zoning trcnas. [C] Shows a normal zoning trend in the (001) d::reclion (traverse on the right in A).

Gutmann (1977)in basaltic plagioclase, but do not mimic any of the oscillatorily zoned c~3,stals examined in this study. Before the oscilLliatory zoning mechanism and the environmen,ts in which the different styles and magnitudes of oscillatory zoning are produced can be adequately understood, the models must acc~rately e):plain the variations in magnitude and style of the oscillatory zoning.

Sector zoning Sector zoned phgioclase crystals have be.~;n growl1 experiment~lly (Figs. 11 and i2). ~icro-

Zot~ing in plagi~7,chue 163

LITHOS 16 (1983)

A

,°! 60" 5040-

,t:

3o2010-

¢*o"

Fig. 12. [A] Photomicrograph of cxperimentaUy grown sector zoned crystal (Table !, run 391). Crossed polarizers. [B] The An content along the microprobe traverse ~how~t in A. Note the sharp composition change at the secto¢ boundary.

probe traverses on two crystals are shown. In Fig. 11, traverses at right angles show a normal zoning trend in each sector. The sector boundaries are evident because of diffe~rences in e.xtinclion betweer~ the s,',~.ctorscaused by differences in composition. It can be seen in the traverses that

tlhe core part of the (0'~0) sector (Fig. 11B) is more calcic 1than the core part of the (~i01) sector. l ~ e compositional difference is maiint~ined along the sector boundary. This feature is better illustrated in Fig. 12. qTne traverse (Fi[~,. 12) cuts across two sector boundaries. The ca,rapositionai profile (Fig. 12B) shows the sharp co~llp~sitional dispari~.y between sect:ors. The (00I) sector is ~bout An 50 while the (010) sectolr i::!~ali~,mut An 60 at the sector boundary and zoned ~,ormally to An 45 ~o 48 at ~:he edge of the crystal,. Sector zoned plagioelase is rare in ~aature, but has been described and analyzed by Bll,yan (1974) in basalts from the ocean floor. He found that, as in the experiments, the (010) sectors were more An-r~ch than the (001) sectors, tie also found that FeO and MgO were enriched ~n~ the (010) sector. Individui~i sectors were normally :tuned. The model:g fc.r sector zoning have; t~een developed primarLr:y for clinopyroxene, but have been applied to other minerals such as staurolile, quartz, andalusite, and epidote. Only Dowty (1976) mentions ptagioclase. The models are based on an interplay of structur~:l control and growth rate in a disequilibrium growth environment. Some workers emphasize the importance of structural control (Hoilister & Bence 1967; Hollister 1970; Nakamura 1973; Dowty 1976) and others emphasize the differences in growth rates of different crystal faces in the discquilibrium erwironment (Wass 1973; Leung 1974; Downes 1973). The most successful model appears to be that of Dowty (1976), wnich is based primar.ily on the nature and number of ~he crystal sites available on the different faces during growth. Impurities will be adsorbed in these sites and then trapped as they are covered b~ the next layer of atoms. For the impurities to be trapped the growth must be sufficiently rapid to prevent the adsorbed cations from leaving t'hese s~tes they are temporarily occupying. For the sector zoning observed "in the cxpefime.nts where the faster growing (~B(~l) ~eetor is too,re Na-rich and the slower growing (010) sector is ~rnore Ca-rich, a model basec! on faster l,qowth rates incorporating more iml~,~riry (in this ~'a~,e Na) would appear to be; sufl~icient. This model would not explain, h.~weverr, the preferential incorporation of FeO and IvlgO iin the (010) ~ie~-torobserved by Bryan (197,~1,)or the preferenlti~l inc~,~oration of' trace e~e~aents in the (010) sector observed b~ Shimazu (1981),. The modei of Dowl':y (1976) has four 4/9 sites c,n the :~urface of least bonding for the (010) face, while the

164 R. K. Smith & G. E. Lofgren surface of least bonding on (001) exposes.only two 4/9 sites. The 4/9 sites would prefer Ca, Mg, Fe and other trace elements to sodium even at the slower growth rate extant on the (010) face relative to (001). The magnitude of the growth rate disparity between the faces and the variation of the absolute growth rate on (010) would affect the magnitude of the compositional differences between the faces. In the experiments, crystals gyown at cooling rates nero l°C/hr showed little, i~' a~ty, compositional variation across the sector boundary in the few cases where a sector boundary is present. Crystals grown at faster cooling rates showed a larger compositional disparity between sectors (Fig. 12; Lofgren 198;0). The rarity of se~tor zoned plagioclase (Bryan 1974) ,nay we![l be explained by the relatively rapid c~oling :rate (l°C,~ar is a relatively rapid cooling rate except in lava flows) required to produce sector zoniing.

Normal zoning Normal zoning is most simply defined as a change of chemicM composition from a more calcic core to a le~s calcic rim of a plagiociase crystal. The l:,attern ,can be simple: a smooth curve from core to rim, or complex, containing all or most of the different varieties of plagio. ,Aase zoning. It is the simple, smooth profile which we are discussing here. Klusman (1972) has presented a model where Ca partitioning between liquid and solid :f011ows a logarithmic .distribution law with an exponentia~ factor which varies as a function of liquid com0osition. The resulting zoning profile is initially flat (of constant composition) over approximately the inner 2/3 of the crystal followed by a rapid decrease in CaO content 0ncrease m Na20 content) towards the e~ge of the crystal. Piagioclase crystals grown in slowly cooled experiments (.~2°C,,hr) have such profile:s (Figs. I~L i i ~. Plagioc~ase c~'ystals grown in more rapid.. ly cc~ci~d experiments have more linear profiles (Fig. l iC, !2B). Lofgren (1973, 1!~80, Fig. 12) sh¢~ws ;~ :,erie~ of normal zoning c,~mpositional pr¢ff~les from crystals grown at different cooling rates. With increasing cooling rate the profile is more liaear and mc~re restricted in compositional rar~ge. [f grown sufficier~tly rapidly, the resulting microli :ic plagic~ase will be nearly he,mogeneous aed have grown at a composition not greatly dissimilar from that which uses all the feldspar

LITHOS 16 (1983) components in the melt, i.e. the equilibrium composition. The Klusman raoclel for logarithmic distribution thus applies to crystals grown under near interface equilibrium conditions. Evans & Moore (1968) reported a more restrieced range of plagioclase zoning (An~0 to An42)in crystals from the chilled margin oiF a lava lake in Hawai; compared to crystals from the center of the lava lake (An.Ort to Or~Ab3aAn3). These data are consistent with the experimental results and show the importance of kinetic control of plagioclase composition. In the more rapidly cooled lava, the plagioclase nucleates at a lower temperatme and thus has a less An-rich core (ANT0,compared to Anrr). The faster cooling rate also inhibits continued growth (An,2 compared to Or64 Ab33An3 for a rim composition ). In the more slowly ,cooled lava, plagioclase can nucleate at a higher An composition and continues to grow to lower temperatures ~md thus shows a larger zoning range. Lofgren & Gooley (1977) show examples of slowly cooled experiments which produced feldspars sirn,lar to those descdbed by Evans & Moore from the center of the lava lake.

Summary Discontinuous zoning has been reproduced experimentally by rapid changes of temperature. The magnitude of tile discontinuous (compositional) drop is a direct result of the magnitude of the temperature drop. NaturaIly formed plagioclase crystals with dis,=ontinuous zoning are more likely to be produced by a rapid change in pressure. Both the number of observed discontinuous ;,ones and the chemical composition of each discontinuous zone from crystal to crystal can be correlated. Such .correlation between plagioclases containing discontinuous zoning supports a mechanism of physical changes external to :he magma, e.g. pressure, temperature, and water :~amration. Although reverse zoning is not commonly re.. ported in natural igneous plagioclase feldspars, i!I is obse~rved in the discontinuous zoning expefi. meres. After each rapid temperature drop a per/od of isothermal cE¢statfization followed. Re.verse zoning resulted during most of these periods c,f ~sotherma] growth. We have shown that in natural plagioclases this reverse zoning also occur,; after most sharp discontinuities. Here again~ as in the cam for discontinuous zoning,

,Zoning in plagiocla'se 165

LrrHos i6 (1983)

60' 50,

40. $0 ,~T..5

//

- ;

•-

I

60"1 ~

,!'

1

I I 1

SO. 4@,

I:

$0 JT'-4.

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l

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SO,

'°i 3,

"--

i!

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\,

~-=.,I==..,=i=.=--,~

2O

4@ 60 80 M|cr@n$

1 O0

Fig. 13. Four separate microprobe traverses (see Fig. 9A for locations on crystal) selected to teslt statistically the si_lmificance of the very s:rnall, but sharp, microprobe compositional oscillations. On each traverse microscopically correlatable minor oscillations are numbered 1, 12, a'ad 3 (solid and dashed I,ines).

sudden pressure changes would most likely be followed by isothermal growth at constantt pre~;sure and therefore result in the possibility of reverse zoning. The reverse zoning is explained as a kine~tically controlled response to a sudden change in either the degree of supercooling or the degree of supersaturation. Plagioclase crystals displaying oscillatory zoning have been produced in controlled coo~ing

expez'iments. Miicroprobe and optical anal~yseson oscillatory zoned crystals o,f natural and experimental plagiodase show a complete lack of correlation between oscillatory zoning in plagioclases h,~)m crystal to crystal within a given thin section. This lack of correlation between different oscillatory zoned plagioclases and the ability to produce, o~_'~iato~ryzoning in constant coeling rate experiiments suggest a formation mechanism rq~lated ~.o l':he kineTiies of crystal growth. Mo~;t models for oseillato:~,yzoning explain a plausiible single cyeh; oscillation, but only that of AUegre et al. (1981) adeqt~ately accounts for ~repetition of the cycle. Sector zoning in plagioclase is also rarely seen in naturally grown fel',dspa;rs; Bryan (1974) describes one ,of the few occurrences. Secrtor-zoned plagioclase cqcstals were not observed in the natural rock specimens studied here, but have been observed in~ experimentally grown plagic,clages. In both the natural and synthetic plagioclase crystals, the (t~l) sector is the most No-rich and the fastest growing while the (0i0) sector is the most Ca-rich and the slower growing. The (010) section, however, is usually enriched in traceelements, whiich c(mtradicts the simple growth rate m(,del Dowty (1976) appears to have the most sucoessful hypothesis; his model is based on the nature and number of the crystal sites available on the different faces during the growth. Normal =,oning iin plagiodase feld~,;pars ha,; been ,.;uccessto!!y reproduced experimentally. The normal zon'ing profile and the composition range were foand to vary with the cooling rate. At slow cooling rates (--2°C/hr) the pllagioclase compositional; profile shows little if any zoning until the outer portion of the crystal is reached. In this case the normal zoning profile closely follows the Klusman (1972) ~nodel for Ca partitioning between :.iquid and solid, which varies as a function of the liquid composition. Normally zened plagioclase crystals grown at increasingly more rapid cooling rates show that the zoning profile bec¢,mes more linear and more restricted in compositional range. In general, the faster the cooling rate, the more restricted will be the zoning interval

Appendix Statistical evaluation of the micr~probe data A statistical a~aalysis procedure tor X-ray co,rating measurem,ents mus" adq:tress two problems. X-ray photons are randomly er.aitted f,,om tlhe irradiated sample, causing the X-ray intensity

~,

R. g. Smith & G. E. Lofgren

LITHOS

F a b ~ 4. Statistical analysis. Traverse 1 : i An % between 48 and 76 ltrn

T r o v e , s : T-2 A n % I~eatween 3~ and 54 Otto

36.6

36.8 37.2 36.3

36.9 37.3 33.8 36.8 35.2 36.4 38.4 36.3 34.3 32.8 31.7 / 34.8 36.5 34.0

Zt3ne 1 Z~one 2

Zone 3

Traverse T-4 A n % between 42 and 64 t~n

Traverse T-5 A n % between 50 and 74 am

36.7 37.5 37.1 33.0---.__ 38.1 37.8 ~ 3 5 . 5 _~A.8- . - . . . ~ . . ~ . ~ 3 7 . 3 ~ 3 5 .

37.2 36.1 37.2 37.0 36.5 1

36.9

37.9

37.9 35.5 33.6 ..,, 33.0 - ' - ' ~ 36.1 35.6

~

" 37.0~..~.....36. 37.2 34.8 32.8 - ~ _ 36.8 - " - " ' - 3 4 . 5 36.7

i 35.45 35.73 36.46 s 1.85 1.70 1.45 i for total population = 36.03_; s for total population = 1.57.

7

37.3 37.0 36.6 36.7

36.60. 0.92

Standard deviation o r Z scores

Zone ~ Zone 2 Zone 3

-0.89 -0.14 -2.G3

-1.61 --9.55 -1.61

--9.66 --0.37 -2.52

-1.63 0.11 -2.28

X--tl

where x = An %, at 2'.one !. 2. 3; u = mean of total population of each tn~verse, and s s = standard deviation of total population of each traverse. z = ~

t Tcs; Traverse T- l T-2 TJ T-5

Zone 1 33.8 33.0 35.5 ;5. ! ~4.35 1.16 -2.13

s t

Zone 2 35.2 34.8 37.0 36.7 35.93 t.09 -0.13

Zone 3 31.7 33.0 32.8 34.5 33.00 !.15 -3.84

~-U

t= ~ ~her,e ~ = mean for zones I+ 2. and 3; u = mean for total lx~pulation of traverses T-I, Ts/Vn 2. T-4. and T-5. s = standard deviation fur total population of traverses, T - I , T-2. T-4, and T-5, and n = sample size br~, in present study). Sign T e s t - Z o n e /

P [ + ] = .5

| | o . 'am = tlj+~. l]~: ttm2-tl;+ ne

H o : Uzone I : u:ml H i : lJz,me l < Uo~l

PI+~>.5

in - Zone 1 373 - 33.8 ?#,~ - 33.O 3~ ~ - 35.5 ~+=,.5 - 35.] : +~umber of + signs |i I'L.~ ~:uc:

= = = =

Difference 3.5 3.3 2.6

=

I J4

Sign

Zone ! 33.8 33.1} 35.5

-- O u t - 36.8 - 37.8

= DifJeren.:e

+ + +

-

37.~

=-!.8

-'t"

35. I

-

37.9

= -2.g

---3.0 = --4.8

P[x ~- Oj = (4) +~ = ~'Sr~' ¢.5)" = :~25 t t , / s i g n s of difter,:ncc.,, the ~ame P = .5 1{~: sign~, o~ differcnc.es different P # .5 ~; = rmmber of c~a ages P{z~0!=

4

t5!+t'5;'

= ~/4)25 :~me.~ 2 and 3 ~t,ekl the same re+~ultg.

Sign

--

--

16 (1983)

Zoning h~Idagioclase

LITHOS 16 (1983) to fluctualte in a statistical manner above and below a mean ~,alue. If there were no beam damage to the samph; surface, the longer the sample is exposed to the radh~tion sourco the more accurate the calculated mean intensity willlbe for every quadrupling of the count time. However, because the electron beam does alter the surface characteristics of the sample during a scan, this prevents the rechecking of the traverse a second time. Thi~ inability to remeasu~re the exact traverse eliminates the possibility of computi~g the mean and standard deviation of the microprobe traverse composition by normal statistical methods. Therefore, to have a valid statistical analysis between micropro~ ~,traverses, these two problems must be accounted for. The ~nability to remeasure the exact microprobe traverse can be overcome by using multiple microprobe traverses across the same zones in the same p hgioclase crystal. To test the accuracy of ILhe statistical approach a zoned plagioclase crystal had to be chosen for which nt~qerous electron micropro~ traverse~ had been conducted and for which small microprobe compositional oscillations, to be checked statistically, could 17e ob.;erved microscopically and therefore correlated from tra~'erse to traverse. The zoned plagioclase crystal shown in Fig. 9A was chosen because it met the criteria listed above. All microprobe traverses and the location of each are shown in Fig. 9A. In order to test the validity of the small co:nposilional oscilledoh~ in this particular zoned plagioclase crystal, a region bounded by the two major zonal gpikes correlated by dashed lines in Fig. 13 was ch~;en. F,,~ur separate microprobe traverses (~s shown in Fig. 13) were c h s e n for the statistical an~dysis. Because ~icroprobe traverses "1-4 and T-5 were run separately under different beam currents compared with traverses T-1 and T-2, normal X-ray photon counts for Ca, Na, and K from each of these four regions could not be used for statisticall ar~alysis. However, the computed An mole % from the raw data can be used. Therefore. Table 4 lists all An mole % from each of the four traverses used for various statistical analyses. ~:Llso listed in Table 4 are the means and standardt deviations for each population of the four mic,oprobe traverses, as well as the mean and standard devir-tion for the total population of traverses T-I, T-2, T-4, and T-5. Standard deviations or Z scores for the three separate and visually correl atable minor o~ciilati~r,s are also listed in Table 4 (compare -'ig. 13 noting tee exact three zones in questiot~L Becaose the sample size was so small the null hypothesis was also tested using the conservative t test. "['he null hypothesis, in this case, states that the mean of each zone is equal to the mean ,)f the total population observed. All t scores for the mean of ZOtles I, 2, and 3 are listed in Table ,~i. The siignificance one usuall ~ associates with normal btatis:ical X-ray measurement accuracy is as follows: (1) if differences exceed three or more standard deviations, this difference is cor,sidered significant at the 95% or better confidence level, (2) tf the difference ts exceeded by two standard deviations or more. this difference is considered significant at the 90% confidence level, and (3) if the difference does not exceed one standard deviat2on, the difference is ,considered non-significant. From an examination of Table 4, it can be seen that standard deviation differences from -0.¢36 to - 1 . 6 3 (t . . . . 2.13). - 0 . 5 5 ~o 0.11 (t= - 0 13), and - 1.61 ~,) - 2 . 5 2 (t = - 3.84) exist fo~' zones 1, 2, and 3 res~ctively. Under normal circumstance~; zones 1 aad 3 would be considered significant (at the 90% and 95% confidence level, respectively), while zone 2 would be considered aon-significant. However, because correla6on tetween these m,,~or An variations can be made easily with the mi~-ro~,ope f~r zone 2, one must reeva.~uate ~he significance of the standard deviations for zone 2 (see Table 4).

16'7

Hypothesis testing using the non-parametric sign te~t (i.e. no assumptions about the population are m3d~) was also conducted on the An mole % data listed in Table 4. In this test one only Ic~)k~;at patterns; i.e. positive o r negative values (slopes and not the magnitude tbetween An mole % differences). The sign tes~t~:~rzone I shot,s a small probability (6%) that there is no pattern of differences; telling us that we can expec: a negative ar, d a positive slope on either sick; of our microscopically observable and correlatable zone. ~a other words there is a 'valley' that can be traced for zone 1 ,from traverse to traverse. The 94% confidence !~vei is all that c ~ be expected based on the present sample size. Sign tests for zones 2 and 3 yield the ,exact same results. Therefore: based on the standard deviation differences (Z scores), t tests, and sign tests (Table 41~, combined with the visual colrelatiot: of those minor zones labeled I1, 2, and 3 in Fig. 13, minor An chemical variations from 1 to 2 An mole % are consideied to he significant in the present study.

Acknowledgements. - This work was supported by NASA grant NSG-9051. Microprobe analyses we,re performed at the Johnson Space Center, Houston, Texas with the assistance of Roy Brown. J. Eichelberger supplied sample (M-714) from Pacaya Volcano in Guatemala.. Laboratory data were collected with the assistance of D. L. Whitley, G. X. Hernandez, M. R. Florez, J. L. Cook, L. N. Goessman, and M. K. Story. We thank Roger W. Johnson for reviews and discussion concerning all statistical analyses; however, we assume all responsibility for interpretations and conclusions reache0. We al~o appreciate the usefu~ comments and suggestions by' Maynard Slaughter. Comments from an unknown reviewer improved the manuscript. Pat Vigil and Florence McClary typed the manuscript.

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