A BASIC program to recast garnet end members

Computerx & GeoJciences Vol. 13. No. 6. pp. 655--658. 1987 Printed in Great Brttaln. All rights reserved

00q8-3004i87 $3.00 + 0.(30 Copyright ,.~ 1987 Pergamon Journals Lid

SHORT NOTE A BASIC P R O G R A M TO R E C A S T G A R N E T END M E M B E R S CHARLES R. KNOWLES Idaho Geological Survey. University of Idaho. Moscow. ID 83843. U.S.A. (Received 17 November 1986; revised 22 Mat' 1987)

INTRODUCTION

This program written in BASIC recasts oxide-weight percent analyses of garnets into the six more abundant garnet end-member minerals. When the ferric and ferrous ions have been analyzed the program will add any titanium to the ferric amount and place the combined quantity in the tetrahedral site ofandradite. If only total iron has been analyzed, as might be obtained from a microprobe or X-ray fluorescence mcthods, the input is made as all fcrrous and the program will use an empirical scheme to split the iron into ferrous and ferric components before rccasting the end members. I)IS(,US,NION Mineral analysis using most analytical methods available today results in data of elemental composition and does not give oxide molecular percentages or valences. Analysis by microprobe, X-ray fluorescence, instrumental neutron activation, and several other methods do not distinguish between ferrous and ferric ions. Elemental analyses generally are reduced to oxide weight percentages by gravimetric factors. This program, written in BASIC, will use oxide chemistry as input and transform these data to garnet end members for the six abundant naturally occurring varieties. These end-member garnets are uvarovite, pyrope, grossular, andradite, almandine, and spessartine. Although uvarovite (the Cr end member garnet) is not as abundant as the other five, most garnets contain some chromium; therefore, this mole fraction is considered more important than any of the minor phases. The end-member recasting is performed using the method of Rickwood (1968). Rickwood used many different mineral species as well as the six most abundant. These synthetic mineral species and extremely rare varieties do not aid most researchers studying natural materials. The nine most generally analyzed elements are used in this program. The rare occurrence of elements such as V, Zr, and Y will need to be treated separately using the Riekwood method, when 655

they are present. His treatment of Ti in the mineral schorlomite was considered one of the most important of the rare minerals but for simplicity was not added to these calculations. Titanium is considered to be in the tetrahedral site in most situations. Consequently in this program the Ti is added to the ferric ion and treated as the tetrahedral equivalent. This treatment of Ti obviously will cause some errors in the rare instance, but the ilmenite and futile mineral inclusions that seem ubiquitous in garnets present a larger error. The use of schorlomite was rejected because of these Ti contaminations. From infrared studies by Rossman (1986) on hydrogrossulars as well as other garnets, it was determined that the hydroxyl component may not be as important as previously believed. The water seems to be mostly adsorbed water. Rossman determined that the weight percentage of water in the lattice seldom exceeded 0.25%. This program ignores the water contribution. Even though the electron microprobe and X-ray fluorescent analytical methods cannot analyze for ferrous or ferric ions. the need exists, particularly for the garnets, to split the total iron into the two valence states. This program allows for the splitting of the ferrous and ferric ions using an empirical method, it was decided to take existing published data and apply a scheme to the six mineral species that might give a better result than assigning either all Fe 2~ or Fe ~'. The data published in Deer, Howie, and Zussman (I 962) were used. It was seen that an allocation could be made for the iron ions when the other elements were considered, if the chromium is large, all of the iron is present as ferric ions. The following scheme was used: ifCr > Mg + Mn + Fe, then iron is assignedall Fe ~* if C a > 20 and AI > I0. iron is split 50°/, Fe '÷ and 5 0 0 Fe ~÷, ifCa > 20 and AI < I0. iron is split 5*/, Fe 2+ and 9 5 0 Fe ~*, if Ca < 20 and AI > 12. iron is split 95% Fe '* and 5% Fe 3~'. ifCa < 20, AI < 12, and Mn > 20, all iron is set to Fe ~~ , ,

Short Note

656

if Ca < 20, AI < 12, M n < 20, and Mg > 10, iron is set 95% Fe:" and 5% Fe 3~, if none of the conditions are met, than all Fe is Fe: +.

This scheme is about 90% effective in allocating the ferrous-ferric fractions. If the iron is assigned as all ferrous or as all ferric, the errors are larger in more situations than if this empirical method is used. A better method might be to use a linear regression and maximize the value of the total percentage of cations allocated to end members. The scope of this program does not warrant this lengthy mathematical treatments.

REFERENCES

Deer, W. A., Howie, R. A., and Zussman, J., 1962. Rock forming minerals Vol. I. onho- and ring silicates: Longroans. Green & Co.. London. England. p. 75-112. Rickwood, P. C.. 1968, On recasting analyses of garnet into end member molecules: Contrib. Minerology and Petrology, v. 18, no. 2. p. 175-198. Rossman, G. R., 1986, The hydrous content of garnets (abst.): Abstracts and Program of the Fourteenth General Meeting of the International Mineralogical Association, Stanford, California, p. 213.

APPENDIX 10 REM GARNET END MEMBER RECASTING ZO REM BY CHARLES R. KNOWLES 3~ REM 40 REM THIS PROGRAM USES RICKWOOD'S(1968) METHOD FOR GARNET END MEMBER RECASTING 14 REM OF THE MORE COMMON NATURAL OCCURING GARNETS UVAEOVITE, ANDRADITE, PYROPE bO REM SPESSARTINE, GROSSULAR, AND ALMANDINE. 25 REM THERE ARE NO END MEMBERS WITH WATER OR OTHER RARE AND SYNTHETIC 60 REM END MEMBERS. THE Ti IS ADDED TO Fo+++ AS IF ALL IS GOING INTO 70 REM THE TETRAHEDRAL SITE OF ANDRADITE AND NONE INTO SCHORLOMITE. 45 REM INPUT IS AS OXIDES. IF ALL Fe IS ADDED AS FeO AND INPUT Fe203 AS 0.0 80 REM THE PROGRAM WILL SPLIT UP THE Fe EMPIRICALLY INTO 90 REM FeO AND Fe203 FROM DATA FOUND IN DEER 1962. IF THE AMOUNT OF 1OO REM Cr IS LARGER THAN Mg+Mn+Fe++ THEN Fe IS ASSIGNED ALL Fe AS Fe+++ llO REM IF Ca>20 AND AI20 AND AI>IO Fe IS SPLIT 50% Fe÷++ AND 50% Fe+÷ 13~ REM IF CA<20 AND AI>I2 Fe IS SPLIT 5% Fe+++ AND 95% Fe++ 140 REM IF Ca<20,ALlO FE IS SPLIT 5% Fe+++ AND 95% Fe++ 150 REM IF Ca<20,AL20 THEN FE IS SPLIT 0% Fe++÷ AND all Fe÷÷ 160 REM IF THE ABOVE CONDITIONS ARE NOT SATISFIED, ALL IRON IS SET TO Fe÷+ 17~ REM THIS SCHEME IS ABOUT 90% GOOD WHEN COMPARING IT TO DEER '62 18~ REM

190 REM 20~I CLEAR 210 CLS 22M INPUT"PLEASE TYPE IN THE SAMPLE NUMBER--";ZZ$ 230 INPUT " S i O 2 : " ; Q ( O ) 24M INPUT "TiO2:";Q(6) 250 INPUT "AI203:";Q(1) 260 INPUT "Cr203:";W(7) 270 INPUT "Fe203:";Q(2) 280 INPUT " F e O : " ; Q ( 3 ) 290 INPUT "MnO=";Q(8) 3~O INPUT "MgO:";Q(4) 31Z INPUT "CaO=";Q(5) 320 FOR I= O TO 12:LPRINT:NEXT 330 LPRINT"THIS IS SAMPLE NUMBER "ZZS:LPRINT:LPRINT 340 LPRINT"SiO2 ="Q(O):LPRINT"TIO2 ="Q(6) 350 LPRINT"AI203:"Q(1):LPRINT "Fe203:"Q(2) 360 LPRINT"Cr203="Q(7):LPRINT"FeO ="Q(3) 370 LPRINT"MnO ="Q(8):LPRINT"MgO ="Q(4) 380 LPRINT"CaO ="Q(5) 390 LPRINT" 4OO REM 41Z REM 420 REM **'''''*'*''MOLECULAR WEIGHTS OF OXIDES 430 REM 44Z REM 450 LET T(O):SZ.O848:REM SIO2 460 LET T(6):79.89881:REM TIO2 470 LET T(1):IOI.9612:REM A1203 480 LET T(7):I51.9902:REM Cr203 490 LET T(3):71.8464:REM FeO 50@ LET T(2)=I59.69:REM Fe203 510 LET T(8)=70.9374:REM MnO 530 LET T(4):40.3044:REM MgO 530 LET T(5):56.O794:REM CaO 54~ IF Q(2):O THEN 580 ELSE 760 550 REM 560 REM 570 REM 580 REM "*''''**CALCULATE THE FERROUS FERRIC PROPORTIONS ~.gv~ REM

WHEN FE+÷+:O

S h o n Note

657

5~ 610 620 630 640 650 660

REM EEM IF Q(7)>Q(4)+Q(8)+Q(3) THEN 750' IF Cr>Mg+Mn+Fe++ LET Q(3):Q(3)*.77732 IF Q(5)>20 THEN 690 ' IF CaO > 20 IF Q(1)>I2 THEN 730 ' IF A1203 > 12 IF Q(8)>20 THEN 720 ' IF Mn >20 6 7 0 IF Q(4)>10 THEN 710 ' IF Mg >10 6 8 0 GOTO 7 6 0 690 IF Q(1)Q(2)) AND (Q(6)>I) THEN 1020 670 FOR 1:O TO 8:LET Q(I):(Q(1)/TOT)/T(1) 880 NEXT I 890 LET Q ( 1 ) : Q ( 1 ) ~ 2 : L E T Q ( 7 ) : Q ( 7 ) * 2 : L E T Q(2):Q(2)*2 900 LET Q ( 2 ) : Q ( 2 ) + Q ( 6 ) : Q ( 6 ) : O 910 FOR 1:O TO 8 920 TOTAL:TOTAL+Q(1) 930 NEXT 940 LET I:5:LET J:7:LET K:O:LET L:I 950 LET RX:Q(1)/3:LET RY:Q(J)/2:LET RZ:Q(K)/3 960 IF (RX
THIS IS SAMPLE NUMBER TEST OF DEER et. al. ALMANDINE SiO2 = TIO2 = A1203= Fe203= Cr203= FeO

37.39 .16 20.72 .83 O

= 36.36

il

658

Short Note MnO MgO

CaO

: .86 : 3.85 = .41

THE TOTAL OF THE ELEMENTS

IS

I~.58

THE REMAINING SILICON IS 5.301655E-e3 THE I~EMAINING IRON IS: 4.O58838E-O3

THE PERCENTAGE OF CATIONS ALLOCATED TO END MEMBERS

THE MOLECULAR PERCENTAGES UVAROVITE

O.~

ANDRADITE

1.19

PYROPE

15.48

GPESSARTINE

1.97

GROSSULAR

O.ZO

ALMANDINE

81.37

ARE AS FOLLOWS:

IS: 98.98