American Mineralogist, Volume 71, pages I 126-1 128, 1986
Limitations on the interpretation of biotite substitutions
from chemical analysesof natural samples
Davro A. Hrcwrrr
Department of Geological Sciences,Virginia Polytechnic Institute and State University, Blacksburg,Virginia 24061, U.S.A.
JiincnN Arnncnr
Mineralogisch-Petrographisches
Institut, Universitiit Basel,Basel, Switzerland
Ansrru,cr
Biotites, as well as other phases,are sufficiently complex chemically that there are numerous sets of linearly independent exchangecomponents with which to describe the
composition of a naturally occurring crystal. Even after complete chemical analysis,this
leads to ambiguities in the correlation of exchangecomponents with valid substitution
mechanismsin complex phases.The best means of identifuing valid substitutions are by
the observation of simple endmember compositions, the investigation of compositional
changesin zoned crystalsor petrogeneticsequences,and by direct experimental synthesis.
INrnonucrrou
Studiesof the crystal chemistry of biotite, particularly
those investigating the substitution of Ti, frequently try
to define individual substitutions as important in producingthe chemicalcomposition of panicular phases.This
has led to disagreementamong various researchersas to
which substitutions are important and how the compositions of biotite should be expressedin terms of endmembers.
The purpose of this paper is to present an analysis of
biotite compositions using the methods presented by
Thompson (1982) applied along the lines of a similar
treatment of biotites by Labotka (1983). We will show
againthat any common biotite can be representedin terms
of an additive componentand a limited number of linearly
independent exchangecomponents. Furthermore, there
are numerous sets of viable exchangecomponents that
can be used, and the substitutions touted will depend on
the particular choice of exchange vectors. Finally, although it has been widely understood that incomplete
analyses-especially those neglecting FerO, and HrOwill lead to ambiguities regardingbiotite substitutions, it
can also be demonstratedthat even with complete biotite
analyseswe are unable to make unique substitution models.
Brorrrn coMPoNENTS
of the phase in this structural arrangement.As pointed
out by Thompson (1982) and Labotka (1983),there are
numerous ways of expressingtheserestrictions.The standard structural formula givesthe number of moles of each
of the l8 components in such a way that chargebalance
and the crystal-chemicalintegrity of the biotite are maintained. A more useful approach,becausewe are trying to
simplify our expressionof the biotite composition, is to
define one set of equations basic to the crystal chemistry
of biotite and then a smaller set of exchangecomponents
with which to describe the composition of the phase
(Thompson, 1982;Labotka, 1983).
The first group ofequations defining the biotite structure for these 18 components is
(l)
K+Na*Ca*tr(XID:2
Mg * Fe2** Mn2* + Fe*r(VI)
(2)
+ AI(VI) + Ti + tr(VI) : 6
(3)
si+A(I\o+Fe3+(IV):3
(4)
o+oH+F+cl:24
2 positive charges: ) negativecharges (5)
Labotka (1983) shows that using a single additive component, suchas phlogopite, is equivalent to thesefirst five
equationsas long as the additional exchangecomponents
are charge-balanced.Therefore,we need to define only l3
exchangecomponents:The choiceof these l3 is arbitrary,
Based on crystallographic information, summarized
most recently by Hazen and Burnham (1973) and Bailey
(1984), the structural formula for biotite, normalized to
24 anions and including the commonly discussedsubstitutions, can be expressedas shown in Table 1.
Altogether theseamount to l8 components.By analogy
with the phaserule, the variance of the systemequalsthe
number of variables minus the number of equations relating those variables: Therefore, we must place l8 restrictions on the systemin order to definethe composition
l 0-l l 26$02.00
0003-o04x/86/09
tt26
in biotite
Table1. Commoncomponents
Two interlaver sites
KMgSiO
Na
Ca
!(xil)
Six octahedral sites
Eight tetrahedral sites
Fe2*
Fe3.(Vl)
A(vr)
Ti
Mn
A(lV)
Fe$(lV)
Twenty-four
anions
nryt)
Note: !n reters to a vacancy of coordinationnumber n.
OH
F
cl
tr27
HEWITT AND ABRECHT: INTERPRETATION OF BIOTITE SUBSTITUTIONS
but all of the original 18 components must be included
and the exchangesmust be linearly independent and
charge-balanced.The first group ofthese can be expressed
as simple two-element exchanges:
NaK-,
FeMg-,
MnMg-,
Fe3*AI(IV)-,
FOH_,
cloH_,
(6)
(7)
(8)
(e)
(10)
(l l)
The choice of the remaining components is not so well
defined. There are many possibilities, and the particular
choice that is made will influence any interpretation on
substitutionsthat might be attempted. In our comparison
we will use two very similar setsof exchanges,both containing only commonly quoted mica substitutions (given
in parenthesesin the following lists). Even though more
divergent sets can easily be constructed, the minor differencesbetweenthesetwo setsare sufficient to yield significantly ditrerentresultswhen applied to natural biotites.
Table2. Calculated
biotiteformulae
FD-12Si
A(rv)
A(vr)
Ti
Fe'3*
Fee+
Mg
Mn
qvt)
Na
K
!(xil)
F
OH
ot
5.42
2.58
0.67
0.35
0.44
2.78
1.22
0.14
0.40
0.00
0.15
1.86
-0.01
0.02
0.39
3.17
20.42
Au Sable-t
5.587
2.413
0.243
0.636
0.000
2.786
2.321
0.015
-0.001
0.005
0.040
1.971
-0.016
0.275
0.165
2.435
21.125
. Dodgeet al.(1969).
'- Bohten
et al.(1980).
by difference
basedon 24 anions.
f Calculated
We will comparethesesetsof equationsfor two natural
biotites that have been analyzed for all the elements in
ExchangeSet I
our original list except oxygen.Table 2 lists the structural
formulae for both biotites calculated on the basis of 24
CaAI(IV)IL,Si_,
(Clintonite)
(r2) anions. The first is an analysis(FD-12) of a biotite from
the Taft Granite in the Sierra Nevada reported by Dodge
(Talc)
(l 3)
sitr(xrr)K,A(rv)_,
et al. ( I 969). The secondis an analysisofa granulite-facies
A(IV)A(VDFe_,Si_,
(Al-Tschermak's) (14) metamorphic biotite from the Adirondacks (Au Sable)for
Fe3*(VI)OFe-,OH
(Fe oxy-annite)
(15) which Bohlen et al. (1980) have reported both a complete
,
Titr(VI)Fe-,
(Ti-vacancy)
(16) chemical analysisand structural determination.
Table 3 compares the vector coefficients necessaryto
A(IV),TiFe-,Si-,
(Ti-Tschermak's) (17)
describe
the biotites with the two different sets of ex(Ti
TiOrFe-,OH-,
(18)
oxy-annite)
changesusing phlogopite (24 anions) as the additive component. The first eight exchangesneed not be compared
ExchangeSet II
becausethey are the same and yield identical results for
both
sets.Even though there are only two differencesin
(Clintonite)
CaAI(IV)IL,Si-,
(12)
last
five exchangecomponents, there are significant
the
(Talc)
sitr(xll)rL,A(rv)_,
(13)
diferences in the apparentsubstitutions.Looking at sam(Al-Tschermak's) (14)
Al(IV),TiFe_,Si ,
ple FD-12, just three exchangesout ofthe last five in Set
Fe3*(VI)OFe-,OH-,
(Fe oxy-annite)
(15) I account for most of the necessarychangesin composiAl(v!,tr(vr)Fe,
(Muscovite)
(16) tion. Those substitutions are the Al-Tschermak's, Ti-va(Ti-Tschermak's) (17) cancy, and Fe oxy-annite exchanges,all of which have
Al(IV),TiFe_,Si_,
AI(VI)OFe ,OH_,
(Al oxy-annite)
(18) beenshownto be important substitutionsby experirnental
synthesisand/or have beencommonly proposedas major
substitutions in biotite (Rutherford, 1973; Forbes and
Applrca,tloN To NATURALBToTITES
Flower, 1974; Wones, 1963).Using ExchangeSet II we
How do these different sets of equations describe the see that the same material is equally well expressedby
compositions of natural biotites? Both work equally well major amounts of Ti-Tschermak's, muscovite, and Fe
and are accurate to the degree that the original analyses oxy-annite exchangeswith a small negativeamount of Alare accurate.If they are applied to incomplete analyses, Tschermak'ssubstitution. Thesetoo are well-acceptedmica
particularly those neglectingFerOr, H2O, F, and Cl, some substitutions and give an equally good desoription ofthe
coefficientsof the exchangevectors must be falsely set to biotite; however, we get a very different view of the imzero, and the results obtained are questionable at best. portance of particular substitutions than we got with ExClever treatment of the data and choicesof the exchange changeSet I.
componentscan alleviate some of the problems, but the
A similar result is obtained when we look at the data
coefficientsofthe vectors chosencan only be reliable for for the Au Sablebiotite. This has been cited as a biotite
the part of the biotite analyzed.and not for the whole.
demonstrating the importance of the Ti oxy-annite sub-
l r28
HEWITT AND ABRECHT:INTERPRETATIONOF BIOTITE SUBSTITUTIONS
from phlogopite
Table3. Vectorcoefficients
Set I
FD-12
Au Sable
NaK-l
FeMg_1
MnMg-,
Fe,*Al(lV)_l
FOH_1
0.15
4.64
0.14
0.00
0.39
0.040
3.664
0.015
0.000
0.165
o.275
0.005
-0.016
0.243
0.000
-0.001
0.074
0.563
cloH_1
Clintonite
Talc
Al-Tschermak's
Fe oxy-annite
TLvacancy
Ti-Tschermak's
Ti oxy-annite
o.02
0.00
-0.01
0.67
0.44
0.40
-0.04
-0.01
stitution, although Bohlen et al. (1980) only refer to it as
one of the substitutions that might be considered. The
vector coefficients in Table 3 using the Set I exchange
componentsgrve very similar results to those in Table 7
ofthe Bohlen et al. (1980) paper. However, an equally
good representationof the Au Sablebiotite is given without any Ti oxy-annite substitution by using the exchange
componentsin Set IL Here the Al oxy-annite substitution
replacesthe Ti oxy-annite substitution; we seeno reason
why the latter substitution should be any more or less
valid than the former. No experimental or observational
data are currently available to give preferenceto either
substitution.
DrscussroN
Thompson (1982) has demonstrated the vector approach to compositional analysisof minerals and has made
it clear that there are many combinations of exchange
vectors that lead to the same composition. Whether or
not particular vectors correspond to crystal-chemically
valid substitutions may be an important question, but it
is usually not answerableby analysisof complex natural
phases.Other criteria must be used to determine an independentset of important substitutions. Three kinds of
data seemmost likely to yield this information. First, the
natural occurrenceof compositions related to a principal
additive componentby a single"simple" exchangevector.
The occurrencesof these endmember phases provide
valuable information on the validity of particular vectors
as substitutions, although any single substitution may be
a combination oftwo or more other substitutions.It seems
reasonable,however, that we should choose the set of
substitutions that representsthe least common denominators. Second, changesin compositions of phasesthat
occur as zoned crystals or in petrogenetic sequencecan
be directly related to appropriate substitutions. In these
samples there is the added advantage of being able to
define initial and final compositions and therefore the
vectors that relate them. This allows us to examine more
complex phase compositions, but we should still search
for simple changesin composition if we want to identify
the most fundamentalsubstitutions.Finally, experimental
methods can be useful in establishingsubstitutions. The
l00o/osynthesisand persistenceof a phase on the com-
Set ll
NaK_r
FeMg-,
MnMg_1
Fe3tAl(lV)-1
FOH_,
ctoH,
Clintonite
Talc
Al-Tschermak's
Fe oxy-annite
Muscovite
Ti-Tschermak's
Al oxy-annite
FD-12
Au Sable
0.15
4.64
0.14
0.00
0.39
0.02
0.00
-0.01
-0.11
0.44
0.40
0.35
-0.02
0.040
3.664
0.015
0.000
0.165
0.275
0.005
-0.016
-0.880
0.000
-0.001
0.636
1.125
position of a panicular substitution are compelling evidencefor its validity. With lessthan 1000/osynthesis,accurate microanalysis is a necessityand often shows the
phase composition located off the planned substitution
vector. It has been our experiencethat this is especially
true for biotites and that often there is no unique set of
simple vectors leading to the measured composition in
these multiphase experiments (Abrecht and Hewitt, in
prep.).
In summary it must be remembered that there is no
generallyvalid correlation betweenexchangecomponents
and substitution mechanisms.For complex phases,multiple equivalentsetsofexchangecomponentsare available
to describe the phase compositions. Additional information must be obtained in order to choosea set or sets
of exchangecomponentsthat are also valid substitutions
for the phasein question.
R-nrnnnNcns
and structuresof the micas'
Bailey,S.W.(1984)Classification
Societyof AmericaReviewsin Mineralogy,13,
Mineralogical
t-12.
E.J.(1980)CrystalchemD.R.,andEssene,
Bohlen,S.R.,Peacor,
istry of a metamorphicbiotite and its significancein water
barometry.ArnericanMineralogist,65, 55-62.
Dodge,
F.C.W.,Smith,V.C.,andMays,R.E.(1969)Biotitesfrom
graniticrocksofthe centralSierraNevadabatholith,California. Journalof Petrology,10,25U27l.
Forbes,W.C.,and Flower,M.F.J.(1974)Phaserelationsof tiran-phlogopiteKrM&TiAl,Oro(OH)o:A refractoryphasein the
Irtters, 22,6046.
uppermantle?EarthandPlanetaryScience
Hazen,R.M., and Burnham,C.W. (1973)The crystalstructure
of oneJayerphlogopit0and annite.AmericanMineralogist,
58.889-900.
Labotka,T.C. (1983)Analysisof the compositionalvariations
Minnesota.
from northeastern
of biotite in pelitic hornfelses
AmericanMineralogist,68, 900-914.
Rutherford,M.J. (1973)The phaserelationsof the aluminous
Journalof
iron biotitesin thesystemKAlSiOo-AlrOr-Fe-O-H.
Petrology,14, 169-179.
and
An algebraic
Thompson,J.B.,Jr. (1982)Compositionspace:
geometricapproach.MineralogicalSocietyof AmericaReviewsin Mineralogy,10, I-32.
Wones,D.R. (1963)Physicalpropertiesof syntheticbiotiteson
AmericanMineralogist,48, 1300thejoin phlogopite-annite.
r32r.
Ocronrn 2, 1985
MaNuscnrrr REcETvED
Mav 16, 1986
M,o'NuscnrprAccEPTED