bgt: a fortran 77 computer program for biotite–garnet geothermometry

BGT: a FORTRAN 77 computer program for biotite±garnet geothermometry

p

T.N. Jowhar*

Wadia Institute of Himalayan Geology, 33 General Mahadeo Singh Road, Dehra Dun 248 001, U.P., India

Received 1 December 1996; received in revised form 8 November 1998; accepted 8 November 1998

1. Introduction

Reconstruction of the P±T±t path followed by crus-

tal rocks during orogeny has assumed greater signi®-

cance. The P±T conditions can be calculated using

di�erent geothermometers and geobarometers, each of

which usually has several experimental and empirical

calibrations. The calculation of each geothermometer

or geobarometer is generally a laborious process

because of the complexity of the algebraic expressions

used.

Partitioning of Mg and Fe between coexisting biotite

and garnet is known to be signi®cantly dependent on

temperature of equilibration. Because of the common

occurrence of this mineral pair in medium to high

grade metamorphic rocks, the biotite±garnet Mg±Fe

exchange geothermometer ®nds wide application and

at present at least 20 di�erent calibrations are avail-

able. Some of the biotite±garnet geothermometric

equations are non-linear and can only be solved with

iterative methods, e.g. calibrations of Hodges and

Spear (1982), Indares and Martignole (1985) and

Holdaway et al. (1997).

Several models for biotite±garnet geothermometry

have been published since 1976. In order to select the

most appropriate model for any speci®c use as well as

to facilitate further application of biotite±garnet

geothermometry, it is desirable to be able to compare

the results of all previous calibrations. The program

BGT was prepared in FORTRAN 77 language for this

purpose. It includes the following 20 di�erent calibra-

tions of the biotite±garnet geothermometer:

1. Thompson (1976).2. Goldman and Albee (1977) second parameter sol-

ution.

3. Goldman and Albee (1977) ®fth rank solution4. Perchuk (1977).5. Ferry and Spear (1978).

6. Perchuk (1981).7. Hodges and Spear (1982).8. Pigage and Greenwood (1982).

9. Perchuk and Lavrent'eva (1983).10. Ganguly and Saxena (1984, 1985).11. Indares and Martignole (1985) model A.12. Indares and Martignole (1985) model B.

13. Perchuk et al. (1985).14. Hoinkes (1986).15. Aranovich et al. (1988).

16. Williams and Grambling (1990, 1992) model 3.17. Dasgupta et al. (1991).18. Bhattacharya et al. (1992) using the mixing par-

ameters for the pyrope±almandine asymmetricregular solution of Hackler and Wood (1989).

19. Bhattacharya et al. (1992) using the mixing par-

ameters for pyrope±almandine asymmetric regularsolution of Ganguly and Saxena (1984).

20. Holdaway et al. (1997).

2. Thermodynamic relationships for biotite±garnet

geothermometer

The thermodynamics of Mg±Fe partitioning betweenbiotite and garnet has been presented by Saxena

Computers & Geosciences 25 (1999) 609±620

0098-3004/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved.

PII: S0098-3004(99 )00004-7

Short Note

pCode available at http://www.iamg.org/CGEditor/

index.htm

* Tel.: +91-135-627-387; fax: +91-135-625-212.

E-mail address: [email protected] (T.N. Jowhar)

(1969), Ganguly and Kennedy (1974), Thompson(1976), Ganguly and Saxena (1984, 1987) and

Dasgupta et al. (1991). The equilibrium conditions atP and T for the Mg±Fe exchange between garnet andbiotite according to the following reaction:

Fe3Al2Si3O12

Almandine� KMg3AlSi3O10�OH �2

Phlogopiteÿÿ*)ÿÿ

Mg3Al2Si3O12

Pyrope� KFe3AlSi3O10�OH �2

Annite

�1�

can be written as (Dasgupta et al., 1991)

DG 0�1,T � � PDV� 3RT ln KD � 3RT ln�gMg=gFe�Grt

ÿ 3RT ln�gMg=gFe�Bt � 0�2�

where DG(1,T )0 is the free energy change of the reaction

at 1 bar and T; DV is the molar volume change at 1

bar and 298 K; KD=(XMg/XFe)Grt/(XMg/XFe)

Bt=distribution coe�cient and g is the activity coe�cient.In Appendix A the biotite±garnet geothermometric

equations of di�erent calibrations are given for readyreference.

3. Program description

The program BGT is written in ANSI standard,FORTRAN77. Program BGT consists of a main pro-gram and 20 subroutines. It computes temperatureusing 20 di�erent calibrations of biotite±garnet

geothermometer (calibrations listed in Appendix A).The program does not take into account the compo-sitional limits of applicability of each individual cali-

bration and proceeds on to compute temperature.The evaluation of reliability of individual calibrationsis not the purpose of this paper, for which one is

advised to consult the references cited in this paper.The size of the source code BGT.FOR is 39521 bytes.The program was implemented on an IBM PC com-

patible microcomputer (80386DX and Intel Pentium)using MS-DOS operating system version 6.22. Theexecutable code of the program BGT.EXE was gener-ated using Microsoft FORTRAN 77 Optimizing

Compiler version 5.00. The size of the executablecode BGT.EXE is 54972 bytes. This computer pro-gram will run on any IBM compatible microcom-

puter.The input data required for this program is (for

each biotite±garnet pair):

Sample number.Fe2+, Mg, Mn, Ti, AlIV, AlVI, Ca cations of bio-tite.

Fe2+, Mg, Ca, Mn cations of garnet.

Pressure, P, in bars.

All data are accessed by the program using free for-mat READ statements; an ASCII data ®le is requiredfor data input (e.g. TEST.DAT). Any number of

samples can be put in one data ®le, but they should bein the order mentioned next. Data required for properprogram execution is as follows:

Line 1: sample number. Any characters in column 1to 65.

Line 2: biotite cations in the following order (separ-ated by comma): Fe2+, Mg, Mn, Ti, AlIV, AlVI, Ca.Line 3: garnet cations in the following order (separ-ated by comma): Fe2+, Mg, Ca, Mn.

Line 4: pressure, P, in bars.

Program output is directed to a separate ASCII ®le

(e.g. TEST.OUT) and consists of the following:

1. Input data for each sample.

2. The following recalculated values for biotite andgarnet:

XMGGAR=XMgGrt=[Mg/(Mg+Fe)]Grt

XFEGAR=XFeGrt=[Fe/(Mg+Fe)]Grt

XMGBIO=XMgBt =[Mg/(Mg+Fe)]Bt

XFEBIO=XFeBt=[Fe/(Mg+Fe)]Bt

XMG/XFE GARNET=(XMg/XFe)Grt=(Mg/

Fe)Grt

XMG/XFE BIOTITE=(XMg/XFe)Bt=(Mg/Fe)Bt

KD=KD=(XMg/XFe)Grt/(XMg/XFe)

Bt=(Mg/

Fe)Grt/(Mg/Fe)Bt

LNKD=log(KD)XPY=XPrp

Grt=Mg/(Fe+Mg+Ca+Mn)

XAL=XAlmGrt =Fe/(Fe+Mg+Ca+Mn)

XGR=XGrsGrt=Ca/(Fe+Mg+Ca+Mn)

Table 1

Test sample data. Sample JS3883 from Chipera and Perkins

(1988), sample 78B from Hodges and Spear (1982)

Sample Biotite Garnet

JS3883 78B JS3883 78B

Cations per 22 oxygens cations per 24 oxygens

Fe2+ 2.245 2.320 Fe2+ 3.983 4.448

Mg 2.528 2.262 Mg 0.744 0.540

Mn 0.000 0.015 Ca 0.354 0.148

Ti4+ 0.251 0.163 Mn 0.871 0.648

AlIV 2.493 2.511

AlVI 0.665 1.008

Ca 0.029 0.018

JS3883, P=5000 bar

78B, P=3760 bar

T.N. Jowhar / Computers & Geosciences 25 (1999) 609±620610

XSP=XSpsGrt=Mn/(Fe+Mg+Ca+Mn)

XPH=XPhlBt =Mg/(Fe+Mg+Ti+AlVI)

XANN=XAnnBt =Fe/(Fe+Mg+Ti+AlVI)

3. Temperature for biotite±garnet geothermometer

using 20 di�erent calibrations.

Results of the test sample data listed in Table 1

(input data ®le TEST.DAT) are presented in AppendixB.All the calculations used in the present program

have been tested and reproduce the results given bythe authors, where available.

4. Program availability

The source code BGT.FOR, executable codeBGT.EXE and sample test data ®le TEST.DAT are

available from the author by sending a nonformatted3.5 inch ¯oppy disk. The program is also available byanonymous FTP from FTP.IAMG.ORG, or via

Internet from www.iamg.org/CGEditor/index.htm.

Acknowledgements

I thank Dr. Dexter Perkins and an anonymousreviewer for reviewing this manuscript and o�ering

valuable and helpful comments. I am also thankful toDr. V.C. Thakur, Director, Wadia Institute ofHimalayan Geology, Dehra Dun for encouragementand permission to publish this paper.

Appendix A. Biotite±garnet geothermometric equations

of di�erent calibrations

T is in degrees Kelvin, P is in bars and R=1.9872

cal molÿ1 degÿ1. All Fe as Fe2+.

A.1. Thompson (1976)

T � �2739:646� 0:0234P ��ln KD � 1:56�

where

KD � �XMg=XFe�Bt

�XMg=XFe�Grt

A.2. Goldman and Albee (1977)Second parameter solution:

ln KD � ÿ0:257�20:015�1000 ln aQM � 0:522�20:134�

Fifth rank solution:

ln KD �26664ÿ0:0177�20:010�1000 ln aQ

M ÿ 1:22�20:14�X GrtMn

ÿ2:14�20:13�X GrtCa � 1:40�20:09�X Bt

Fe

�0:942�20:109�X BtTi ÿ 1:59�20:21�X Bt

Al�VI �ÿ0:492�20:068��

37775where

1000ln aQM � 5:57�106=T 2�

KD � �Mg=Fe�Grt=�Mg=Fe�Bt

XBtFe � Fe=�Fe�Mg�

XBtTi � Ti=�Fe�Mg�Mn� Ti� AlVI�

XBtAl�VI � � AlVI=�Fe�Mg�Mn� Ti� AlVI�

XGrtMn � Mn=�Fe�Mg�Mn� Ca�

XGrtCa � Ca=�Fe�Mg�Mn� Ca�

A.3. Perchuk (1977)

T � 3416:4=�ln KD � 2:30128�where

KD � �XMg=�1ÿ XMg��Bt��1ÿ XMg�=XMg�Grt

XMg � Mg=�Mg� Fe�Mn�

A.4. Ferry and Spear (1978)

T � 12454� 0:057P

4:662ÿ 3R ln K

where

K � �Mg=Fe�Grt=�Mg=Fe�Bt

T.N. Jowhar / Computers & Geosciences 25 (1999) 609±620 611

A.5. Perchuk (1981)

T � �3650=�ln KD � 2:57�� 252:25�X GrtMn ÿ 0:035�

where

XGrtMn � Mn=�Mg� Fe�Mn�

XGrtMg � Mg=�Mg� Fe�Mn�

KD � �XMg=�1ÿ XMg��Bt��1ÿ XMg�=XMg�Grt

A.6. Hodges and Spear (1982)

T � 12454� 0:057P

4:662ÿ 3R ln K1

where

K1 � �aPrp=aAlm�Grt=�aPhl=aAnn�Bt

� �XPrp=XAlm�Grt=�XPhl=XAnn�Bt � �gPrp=gAlm�

� gPrp

gAlm

�� exp

26664��3300:0ÿ 1:5T ��X 2

Grs � XAlmXGrs � XGrsXSps � XPrpXGrs�RT

�WMgMn�X 2Sps � XGrsXSps � XAlmXSps � XPrpXSps�

RT

37775

XPrp � Mg=�Fe�Mg� Ca�Mn�

XAlm � Fe=�Fe�Mg� Ca�Mn�

XGrs � Ca=�Fe�Mg� Ca�Mn�

XSps � Mn=�Fe�Mg� Ca�Mn�

XPhl � Mg=�Fe�Mg� Ti� AlVI�

XAnn � Fe=�Fe�Mg� Ti� AlVI�

WMgMn � 0

A.7. Pigage and Greenwood (1982)

T � 1586X GrtCa � 1308X Grt

Mn � 2089� 0:00956P

0:78198ÿ ln k

where

K � �XMg=XFe�Grt=�XMg=XFe�Bt

XGrtCa � Ca=�Fe�Mg� Ca�Mn�

XGrtMn � Mn=�Fe�Mg� Ca�Mn�

A.8. Perchuk and Lavrent'eva (1983)

T � 7843:7� DV�Pÿ 6000�1:9872 ln KD � 5:699

where

DV � ÿ0:0577

KD � �XMg=XFe�Bt=�XMg=XFe�Grt

A.9. Ganguly and Saxena (1984, 1985)

T �

A� �WFeMg�XFe ÿ XMg� � DWCaXCa � DWMnXMn�Grt=R

ln KD ÿ DS 0=Rÿ ln�gFe ÿ gMg�Bt

where

A � 1175� 9:45P �kbar�


DS 0=R � ÿ0:782

W GrtFeMg �W Fe±Mg

H �Mg=�Mg� Fe2��Grt

�WMg±FeH �Fe2�=�Mg� Fe2��Grt


WFe±MgH � 200

WMg±FeH � 25002500

WS � 0

DWCa � 30002500

DWMn � 30002500

A.10. Indares and Martignole (1985)Model A:

T �

24 �12454� 0:057P� 3�ÿ454X BtAl ÿ 6767X Bt

Ti��3�3300ÿ 1:5T �X Grt

Ca �4:662ÿ 5:9616 ln KD

35Model B:

T �

24 �12454� 0:057P� 3�ÿ1590X BtAl ÿ 7451X Bt

Ti��3�3000�X Grt

Ca � X GrtMn��

4:662ÿ 5:9616 ln KD

35where

XBti � i=�Fe�Mg�Mn� AlVI � Ti �,

i � Fe, Mg, Mn, AlVI, Ti

XGrtj �j=�Fe�Mg�Mn� Ca�,

j � Fe, Mg, Mn, Ca

KD � �XMg=XFe�Grt=�XMg=XFe�Bt

A.11. Perchuk et al. (1985)

T � 3720� 2871X GrtCa � 0:038P

ln KD � 0:625X GrtCa � 2:868

where


XGrtCa � Ca=�Fe�Mg� Ca�Mn�

A.12. Hoinkes (1986)

T � 2089� 0:00956P

0:7821ÿ ln K1 ÿ 2:978X GrtCa � 5:906�X Grt

Ca �2

where

K1 � �XMg=XFe�Grt=�XMg=XFe�Bt

XGrtCa � Ca=�Mg� Fe� Ca�Mn�

A.13. Aranovich et al. (1988)

T �"3873:1� 2871X Grt

Ca � 0:0124Pÿ 957NBtAl

ln KD � 2:609� 1:449X GrtCa � 0:287NBt

Al

#where


XGrtCa � Ca=3

XGrtMg � Mg=3

XGrtFe � Fe=3

NAlBt is the number of Al in octahedral coordination of

biotite formula calculated per 11 oxygens

A.14. Williams and Grambling (1990, 1992)Model 3:

T �

264 �ÿ17368ÿ 79:5P �kbar� � 1579ÿW GrtMgFe�XAlm ÿ XPrp�

ÿ12550�XGrs� ÿ 8230�XSps��R�ln KD ÿ 0:782ÿ ln�Fe2�Bt=FeTot,Bt��

375


where

KD � �XMg=XFe�Grt=�XMg=XFe�Bt

WGrtMgFe �WFe±Mg�XPrp=�XPrp � XAlm�� WMg±Fe�XAlm�XPrp � XAlm��

WFe±Mg � 695

WMg±Fe � 2115, R � 8:3143 J K ÿ1 molÿ1

�Fe2�Bt=FeTot,Bt� � 0:90

XPrp � Mg=�Fe�Mg� Ca�Mn�

XAlm � Fe=�Fe�Mg� Ca�Mn�

XGrs � Ca=�Fe�Mg� Ca�Mn�

XSps � Mn=�Fe�Mg� Ca�Mn

A.15. Dasgupta et al. (1991)

T �24 4301� 3000X Grt

Ca � 1300X GrtMn ÿ 495�XMg ÿ XFe�Grt ÿ 3595X Bt

Al�VI �

ÿ4423X BtTi � 1073�XMg ÿ XFe�Bt � 0:0246P=�1:85ÿ R ln KD�

35where

KD � �Fe=Mg�Bt=�Fe=Mg�Grt � �Mg=Fe�Grt=�Mg=Fe�Bt

XGrtMg � Mg=�Mg� Fe2� � Ca�Mn�

XGrtFe � Fe2�=�Mg� Fe2� � Ca�Mn�

XGrtCa � Ca=�Mg� Fe2� � Ca�Mn�

XGrtMn � Mn=�Mg� Fe2� � Ca�Mn�

XBtMg � Mg=�Mg� Fe� AlVI � Ti �

XBtAl�VI � �

XAlÿ �Si� AlIV� where Si� AlIV � 3 per formula unit

XBtTi � Ti=�Mg� Fe� AlVI � Ti �


XBtFe � Fe=�Mg� Fe� AlVI � Ti �

A.16. Bhattacharya et al. (1992)Using the mixing parameters for the pyrope±almandine asymmetric regular solution of Hackler and Wood (1989):

T�HW� �

2666664�20286� 0:0193Pÿ f2080�X Grt

Mg�2 ÿ 6350�X GrtFe �2

ÿ13807�X GrtCa ��1ÿ X Grt

Mn� � 8540�X GrtFe ��X Grt

Mg��1ÿ X GrtMn�

�4215�X GrtCa ��X Grt

Mg ÿ X GrtFe �g � 4441�2X Bt

Mg ÿ 1��13:138� 8:3143 ln KD � 6:276�X Grt

Ca ��1ÿ X GrtMn��

3777775Using the mixing parameters for pyrope±almandine asymmetric regular solution of Ganguly and Saxena (1984):

T�GS� �

2666664�13538� 0:0193Pÿ f837�X Grt

Mg�2 ÿ 10460�X GrtFe �2

ÿ13807�X GrtCa ��1ÿ X Grt

Mn� � 19246�X GrtFe ��X Grt

Mg��1ÿ X GrtMn�

�5649�X GrtCa ��X Grt

Mg ÿ X GrtFe �g � 7972�2X Bt

Mg ÿ 1��6:778� 8:3143 ln KD � 6:276�X Grt

Ca ��1ÿ X GrtMn��

3777775where


XGrtMg � Mg=�Mg� Fe2� � Ca�Mn�

XGrtFe � Fe2�=�Mg� Fe2� � Ca�Mn�

XGrtCa � Ca=�Mg� Fe2� � Ca�Mn�

XGrtMn � Mn=�Mg� Fe2� � Ca�Mn�

XBtMg � Mg=�Mg� Fe2��

A.17. Holdaway et al. (1997)

T � 41952� 0:311P� G� B

10:35ÿ 3R ln KD

where R=8.31441

G � 2XMgXFe�WGrtFeMg ÿWGrt

MgFe� � X2FeW

GrtMgFe ÿ X2

MgWGrtFeMg

B � ÿWBtMgFe�XFe ÿ XMg�

WGrtFeMg � ÿ24166� 22:09Tÿ 0:034P

WGrtMgFe � 22265ÿ 12:40T� 0:050P

WBtMgFe � 40719ÿ 30T


Appendix B


References

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bgt: a fortran 77 computer program for biotite–garnet geothermometry

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