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The mechanism of myrmekite formation deduced from steady-diffusion modeling
based on petrography: Case study of the Okueyama granitic body, Kyushu, Japan
Takashi Yuguchi , Tadao Nishiyama
Department of Earth and Environment, School of Science, Graduate School of Science and Technology, Kumamoto University, 2-39-1, Kurokami, Kumamoto 860-8555, Japan
a b s t r a c ta r t i c l e i n f o
Article history:
Received 11 January 2008
Accepted 29 July 2008
Available online 12 September 2008
Keywords:
Myrmekite
The reaction rim
Steady-diffusion modeling
Sub-solidus reaction texture
Granitic rock
Myrmekite is an intergrowth texture consisting of vermicular quartz and albitic plagioclase (Ab93An7in this
study), typically occurring between K-feldspar and plagioclase. It occurs ubiquitously in both metamorphic
and granitic rocks; however, its genesis has been an enigma. This paper describes myrmekite's petrography
and discusses its genesis from the Okueyama granitic body (OKG), which is a young (14 Ma) granite in
Southwest Japan with no evidence of deformation after solidication. The genesis of a newly observed
texture, the reaction rim, will be also discussed in relation to myrmekite. The reaction rim is an albite layer
(Ab95An5) with no vermicular quartz between K-feldspar and plagioclase, and it occasionally makes a
composite texture with myrmekite. Both myrmekite and the reaction rim are accompanied by a diffusive
boundary layer (Olg-layer) with a mean composition of oligoclase (Ab75An25) in the rim of neighboring
plagioclase rim.
The overall reactions in an open system for the formation of myrmekite and that for the reaction rim are
derived based on the following two models: 1) one based on the assumption of conservation of solid volume
with arbitrarily specied closure components, and 2) the other based on the assumption of closure of AlO 3/2together with an arbitrarily specied volume factor. Steady diffusion modeling in an open system based on
the overall reaction thus derived denes the stability eld of myrmekite and of the reaction rim in terms of
the ratios of phenomenological coefcients (L-ratios). The steady diffusion models for the above two models
have essentially the same features. Myrmekite is stable for large values (>10) of LAlAl/LCaCa, for moderate
values ofLAlAl/LSiSi, and for only small values (b1) ofLAlAl/LNaNa. In the case of the reaction rim, the stabilityeld is much wider in a plot ofLAlAl/LCaCavs.LAlAl/LNaNa, and its dependence on LAlAl/LSiSiis stronger than that
of myrmekite. The reaction rim is stable only for large values ofLAlAl/LCaCa, which is consistent with the case
of myrmekite. Exchange cycles for myrmekite and the reaction rim show that the essential formation
mechanism is albitization of K-feldspar:
KAlSi3O8 NaO1=2 NaAlSi3O8 KO1=2;
which is coupled with albitization of plagioclase via diffusive transport of NaO 1/2and SiO2:
CaAl2Si2O8 NaO1=2 SiO2 NaAlSi3O8 CaO AlO3=2:
Formation of myrmekite requires more SiO2than development of the reaction rim; some of the SiO 2is given
by decomposition of K-feldspar and some is supplied from the environment to the boundary between K-
feldspar and plagioclase.
2008 Elsevier B.V. All rights reserved.
1. Introduction
Subsolidus reaction textures such as coronas, kelyphite, and reaction
zones have potentially provide records of pressure-temperature condi-
tions (e.g. Joanny et al., 1991), and also as a source of information
concerning diffusion and reaction kinetics that can be used to interpret
the duration and nature of metamorphism (e.g.Fisher, 1978). Symplec-
tite commonly occurs as a part of such subsolidus reaction textures (e.g.
hornblende and spinel symplectite in olivineplagioclase corona:
Nishiyama, 1983) and also as a breakdown or exsolution product of a
mineral (e.g., clinopyroxeneand spinel symplectite in olivine: Ashworth
and Chambers, 2000). Myrmekite is one such subsolidus reaction
texture,showing symplecticintergrowth of quratz and sodicplagioclase.
The genesis of myrmekite has been an important subject in petrology
because myrmekite occurs ubiquitously in granitic rocks and in pelitic
Lithos 106 (2008) 237260
Corresponding author. Present address: Mizunami Underground Research Center,
Japan Atomic Energy Agency, 1-64, Yamanouchi, Akeyo, Mizunami, Gifu, 509-6132,
Japan. Tel./fax: +81 96 342 3411.
E-mail address:[email protected](T. Yuguchi).
0024-4937/$ see front matter 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.lithos.2008.07.017
Contents lists available at ScienceDirect
Lithos
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / l i t h o s
mailto:[email protected]://dx.doi.org/10.1016/j.lithos.2008.07.017http://www.sciencedirect.com/science/journal/00244937http://www.sciencedirect.com/science/journal/00244937http://dx.doi.org/10.1016/j.lithos.2008.07.017mailto:[email protected] -
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gneisses. But its genesis has been also an enigma, because no
stoichiometric relation exists between the product (myrmekite) and
the reactants (plagioclase and K-feldspar).
This paper will discuss the mechanism of myrmekite formation in a
granitic system, taking the Okueyama granite (OKG) as an example. Two
types of myrmekite have been identied (Phillips, 1974). One is rim
myrmekite (Fig.1A), which is an intergrowth texture consisting of vermi-cular quartzandsodic plagioclase,and it develops betweenK-feldsparand
plagioclase. The other is intergranular myrmekite (Fig. 1B), which occurs
as a bleb between neighboring K-feldspar grains. Both types of myrekite
are observed in the Okueyama granite; however, the intergranular
myrmekite is very rare. Therefore, this paper concerns only the rim
myrmekite. Since myrmekite was rst described by Michel Levy in 1874,
various hypotheses for myrmekite have been proposed. Phillips (1974)
classied these hypotheses into six categories: 1) simultaneous or direct
crystallization, 2) replacement of K-feldspar by plagioclase, 3) re-
placement of plagioclase by K-feldspar, 4) solid state exsolution, 5)
incorporation of recrystallizing quartz in growing albite exsolved from K-
feldspar, and 6) miscellaneous hypotheses including combinations of
some of the above hypotheses. Recently one new hypothesis has been
proposed such that the myrmekiteforming reaction is triggered by the
combination of stress/strain concentration and uid inltration during
deformation (Tsurumi et al., 2003; Menegon et al., 2006). These seven
hypotheses will be briey reviewed and examined below.
1.1. The hypothesis of simultaneous or direct crystallization
The simultaneous or direct crystallization hypothesis is one of the
earliest, and it implies that myrmekite formed as the result of
simultaneous plagioclase and quartz crystallization from a melt or a
solution (Spencer, 1938).Barker (1970)argued against this hypothesis,
starting that myrmekite differs considerably from magmatic quartz
feldspar intergrowths such as granophyre and graphic granite in terms
of bulk composition as well as texture and occurrence. In particular, this
Fig.1. Photomicrographsshowingoccurrence of myrmekite and the reactionrim fromthe Okueyama granite.A: Rim myrmekite betweenplagioclase and K-feldspar.B: Intergranular
myrmekite occurring between two K-feldspar grains. C: The reaction rim between plagioclase and K-feldspar.
Fig. 2. The Okueyama granitic body. A: Locality map showingthe Okueyama granitic body(solid symbol) in Kyushu, and the distribution of felsic Miocene igneous rocks in southwest
Japan (afterNakada and Takahashi, 1979). B: Rock facies distribution and cross-section for the Okueyama granitic body (BG, biotite granite; HG, hornblende biotite granite; HGD,
hornblendebiotite granodiorite). Reprinted from Journal of Volcanology and Geothermal Resarch, Vol.29, Masaki Takahashi, Anatomy of a middle Miocene Valles-type caldera
cluster: geology of the Okueyama volcano
plutonic complex, southwest Japan, Page No. 33
70, Copyright (1986), with permission from Elsevier
.
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hypothesis does not explain why myrmekite occurs mostly between K-
feldspar and plagioclase. Myrmekite has not been considered a primary
igneous texture because it has been reported in various metamorphic
rocks (e.g. Shelley, 1964; Hall, 1966; Barker, 1970; Ashworth, 1972;
Shelley, 1973a,b; Phillips, 1980a; Nold, 1984). Myrmekite in granitic
rocks can be produced at the hydrothermal stage during cooling of the
granite body (e.g.Yuguchi and Nishiyama, 2007).
1.2. The replacement of K-feldspar by plagioclase hypothesis
The replacement of K-feldspar by plagioclase hypothesis is originally
based on Becke's (1908) model. Focusing on the relation between
anorthite content of the plagioclase and the volume of quartz in
myrmekite,Becke (1908)argued that myrmekite indicates the replace-
ment of K-feldspar at the sub-solidus stage by the followingtwo reactions:
KAlSi3O8 Na
orthoclase NaAlSi3O8 K
albite
and
2KAlSi3O8 Ca2
orthoclase CaAl2Si2O8
anorthite 4SiO2 K
quartz
The mixture of albite and anorthite components yields a sodicplagioclase and the silica precipitates as vermicular quartz. This model
may explain the genesis of the rim myrmekite but not of intergranular
myrmekite (Phillips, 1974). The myrmekitic plagioclase is albitic,
Ab93An7in our casewhich is inconsistent with this model.
1.3. The replacement of plagioclase by K-feldspar hypothesis
Drescher-Kaden (1948)proposed that myrmekite formed as a part of
reaction in which plagioclase is metasomatically replaced by K-feldspar.
The replacement requires excess silica as seen in the Becke's second
reaction above, and the source of this silica was discussed by
Bhattacharyya (1971, 1972)in that the residual silicain K-feldspar was
used to replace plagioclase in myrmekite from charnockitic rocks of
Eastern Ghtas, India. However, myrmekite commonly shows an invasiontexture in K-feldspar, as we will see later in the case of the Okueyama
granite, which contradicts this hypothesis.
1.4. The solid-state exsolution hypothesis
Schwanke (1909) proposed that K-feldspar has a hypothetical
silica-enriched An component (CaAl2Si6O16: now called Schwanke's
component). Exsolution of Schwanke's component may yield myrme-
kite by the following reaction:
CaAl2Si6O16 CaAl2Si2O8 4SiO2
Some petrologists (Spencer, 1945; Hall, 1966; Hubbard, 1966) had
supported this hypothesis because of the close occurrence of
myrmekite and perthite. However, Phillips (1974) stated that
Schwanke's component is purely hypothetical, and is proven neither
by experiments nor by crystallographic studies. This hypothesis does
not explain the albite-rich composition of myrmekitic plagioclase,either.
Castle and Lindsley (1993) proposed an exsolution model char-
acterized by a silica-pump. However, no hypothesis based on
exsolution can explain the characteristic occurrence of myrmekite
between plagioclase and K-feldspar.
1.5. The hypothesis of recrystallizing quartz incorporation in growing
albite exsolved from K-feldspar
The nexthypothesis considers incorporation of recrystallizingquartz
into growing albite (Shelley, 1964). Albite exsolved from K-feldspar
grows on the plagioclase seed crystal and encloses pre-existing rod-like
quartz structuresat the crush-zonesbetweenplagioclase and K-feldspar.
This hypothesis was criticized byAshworth (1972)based on the molarproportion of quartz in myrmekite.
1.6. Combination of miscellaneous hypotheses
Ashworth (1972)discussed the possibility that both exsolution and
metasomatic replacement can form myrmekite simultaneously. In the
study of a two-feldspar migmatite suite, he found two kinds of myr-
mekite: one interpreted as a product of exsolution and the other as a
product of metasomatic replacement during retrograde regional meta-
morphism. Phillips (1980b) proposed a polygenetic myrmekite model
involving interaction between exsolution and metasomatic replacement
based on Ashworth's (1972)work. Clearly, no single hypothesis can
explain every kind of myrmekite, such as rim myrmekite and inter-
granular myrmekite. Each myrmekite requires a speci
c interpretation.
Fig. 3. Composite texture consisting of myrmekite and the reaction rim. Vermicular
quartz extends from plagioclase towards K-feldspar and terminates midway, making a
clear boundary with the reaction rim (albite layer free from vermicular quartz).
Fig. 4. Photomicrograph and sketch showing lateral transition from myrmekite to the
reaction rim at one grain boundary between plagioclase and K-feldspar in the Okueyama
granite.
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1.7. The hypothesis of deformation-triggered formation
Recently some petrologists focused on the relationship between myr-
mekite formation and deformation in metamorphic rocks. Tsurumi et al.
(2003) proposed that the myrmekite-forming reaction has been asso-
ciated with deformation during mylonitization of granite along the
Hatagawa Shear Zone in NE Japan.Menegon et al. (2006)suggested that
the formation of intergranular myrmekite was triggered by the combina-
tion of stress/strain concentration and
uid in
ltration during a ductileshear deformation in metagranites from the Gran Paradiso Unit (Western
Alps). Deformation may play an important role in the formation of
myrmekite in such strongly deformed rocks; however, the presence of
myrmekite in non-deformed rocks such as granites strongly suggests that
deformation cannot be an essential driving force in myrmekite formation.
This paper will present a detailed description of the rim
myrmekite, including its occurrence, texture, and composition. The
description itself will preclude some hypotheses discussed above.
Diffusion modeling of myrmekite growth based on our description can
provide deeper insights with which to examine the pre-existinghypotheses and present a new model for myrmekite genesis. The key
Fig. 5.Myrmekite between plagioclase and K-feldspar and their compositions. A: BSE image with the scanning line (above) and compositional prole (below) along the line. A steep
compositional gradient is observed in plagioclase near the boundary with myrmekite. B: OrAbAn compositional plot of core and rim of plagioclase, myrmekitic plagioclase and K-
feldspar rim.
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signature is the occurrence of the reaction rim (Fig. 1C) in the
Okueyama granite, which is an albite-rich rim of plagioclase with no
vermicular quartz, and which only develops between plagioclase and
K-feldspar (Yuguchi and Nishiyama, 2007). Transitional textures
transitional from the reaction rim to myrmekite are occasionally
observed in the Okueyama granite, suggesting that the reaction rim is
either a precursor of myrmekite or somethingwith a genesis similar to
that of myrmekite in its genesis. This paper will discuss differences
and similarities of myrmekite and the reaction rim based onpetrography and steady diffusion modeling, leading to an original
model describing their genesis.
2. Geological setting
The Okueyama granite (OKG) is located about 20 km south of the
Median Tectonic Line at the northern part of Miyazaki Prefecture, central
Kyushu (Fig. 2A). The Okueyama granite is one of the Miocene felsic
igneous rocks in theOuter Zone of SouthwestJapanwiththe ageof 14 Ma
(biotite KAr age, Shibata, 1978; whole rock RbSr age, Shibata and
Ishihara, 1979). The Okueyama granite intruded into the accretionary
prism called the Lower Shimanto Group of the Cretaceous (estimated byradiolarian fossils), in the Outer Zone of Southwest Japan (Miyazaki and
Okumura,2002). TheOkueyama granite is a botholithicpluton and is the
Fig. 6.The reaction rim between plagioclase and K-feldspar and their compositions. A: BSE image with the scanning line (above) and compositional prole (below) along the line. A
steep compositional gradient is observed in plagioclase near the boundary with the reaction rim. B: OrAbAn compositional plot of core and rimof plagioclase, the reaction rim and
K-feldspar rim.
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largest one (911 km2 on the surface) among several isolated stocks
forming the Okueyama granitic complex (Takahashi,1986). Its formation
represents the nal episode of magmatic activity in the Okueyama
volcanoplutonic complex (Takahashi, 1986). The Okueyama granite has
a at roof boundary and a steeply dipping wall boundary (Fig. 2B:
Takahashi,1986), providing a contact metamorphismon the surrounding
sediments graded from the biotite zone through the cordierite zone to
the orthopyroxene zone (Miyazaki and Okumura, 2002).
The Okueyama granite is a zoned granitic pluton formed by a singlemagma chamber, because the Okueyama granite has characteristic
vertical changes in its rock facies, mode and bulk chemical composition,
whichhave been interpreted to result from gravitational fractionation of
crystals (Takahashi,1986, 1987). The rock facies grade downward from a
biotite granite, through a hornblende biotite granite, to a hornblende
biotite granodiorite (Fig. 2B: Takahashi, 1986). K-feldspar and quartz
decrease monotonously downward, while plagioclase and mac miner-
als (hornblende and biotite) increase in the same direction (Takahashi,
1986). Hornblende does not occur in the upper part of the Okueyama
granite (above1070 m in the altitude). SiO2, K2OandK2O/Na2O decrease
monotonously downward from the roof, while other major oxides
increase in the same direction (Takahashi, 1986).
3. Petrography
Optical andchemicalfeatures of myrmekite andthe reactionrim were
observed using a polarization microscope and an SEM. Minerals were
analyzedwith an energy dispersive X-raymicro-analyzer(JEOL PC SEM
5600 combined with LINK ISIS) at Kumamoto University, operating at an
accelerating voltage of 20 kV and a beam current of 0.6 nA.
3.1. Myrmekite and the reaction rim
Myrmekite and the reaction rim formed by sub-solidus reactions
are observed between plagioclase and alkali feldspar in the Okueyama
granite (Yuguchi and Nishiyama, 2007). Myrmekite is an intergrowth
texture consisting of vermicular quartz and sodic plagioclase, whereas
the reaction rim is an albite-rich rim free of vermicular quartz.
Although myrmekite is relatively rare, the reaction rim is ubiquitous at
the rims of plagioclase in contact with K-feldspar. There is an invasion
texture of the myrmekite front and the reaction rim front into K-
feldspar (Fig.1). Myrmekite andthe reaction rimare good indicators of
the cooling process for the Okueyama granite as discussed byYuguchiand Nishiyama (2007). They showed that the mean width of
myrmekite changes from 10 m at the roof boundary to 100 m at
1000 m below the roof (at the altitude of 350 m, the lowest surface
exposure of the Okueyama granite) with a systematic downward
increment. The development of the reaction rim has the same
tendency with altitude as myrmekite.
A composite texture consisting of myrmekite and the reaction rim
is found in theOkueyamagranite(Fig. 3). Myrmekite in the plagioclase
side and the reaction rim in the K-feldspar side develop in parallel
between plagioclase and K-feldspar in this case. There is also a lateral
transition from myrmekite to the reaction rim at one grain boundary
between plagioclase and K-feldspar (Fig. 4). These textures imply that
the myrmekite and the reaction rim formed simultaneously during
the sub-solidus deuteric stage.Fig. 7.Plot of volume fraction of vermicular quartz in myrmekite against altitude.
Fig. 8.Schematic compositional prole of myrmekite and neighboring minerals (not to
scale). A diffusion boundary layer with a steep compositional gradient occurs between
plagioclase and myrmekite. The composition changes from Ab60An40to Ab93An7with a
mean of Ab75An25. The layer is approximated as a layer of constant composition of
Ab75An25, named the oligoclase layer (Olg-layer), and used for estimation of overall
reaction and steady diffusion modeling. The ratio of layer thicknesses is dened as the
Olg-layer: myrmekite=0.53: 1 based on observation.
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3.2. The chemicalcompositions of myrmekite and the neighboring minerals
Fig. 5A shows a BSE image and a concentration prole across
myrmekite from plagioclase to K-feldspar. The chemical composition
of plagioclase in contact with myrmekite changes fromAb60An40 atthe
core to the Ab80An20at the rim, with a rapid change in the transitional
layer adjacent to the myrmekite (about 30 m in thickness). This
transitional layer is named the oligoclase layer (Olg-layer) hereafter.
The composition of myrmekitic plagioclase is albitic and no less thanAb90. K-feldsparis Or90Ab10 withno Ancontent at the rim. Fig.5B plots
the core and rim compositions of plagioclase in contact with
myrmekite, the composition of myrmekitic plagioclase, and the rim
composition of K-feldspar in contact with myrmekite on OrAbAn
diagrams. These results indicate that plagioclase is almost homo-
geneous with a mean value of Ab59An39Or2, but that the Olg-layer in
contact with myrmekite shows a mean composition of Ab82An18. The
meancomposition of myrmekiticplagioclase is Ab93An7,andtherimof
K-feldspar in contact with myrmekite has a mean composition of
Or90Ab10. These values are constant in all samples collected fromvarious altitudes.
Fig. 9.Compositionvolume diagram in case of the largest proportion of varmicular quartz (A), the smallest proportion of vermicular quartz (B) in myrmekite, and the reaction rim
(C).fv =1 denotes volume constant between reactant and product. Positive and negative values in vertical axis represent inow and outow amounts in stoichiometric coefcients,
respectively.
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3.3. The chemical compositions of the reaction rim and the neighboring
minerals
Fig. 6A shows a BSE image and a concentration prole across the
reaction rim from plagioclase to K-feldspar. The chemical composition of
plagioclase in contact with the reaction rim ranges from Ab60An40 at the
core to Ab80An20at the rim, with a rapid change in a transitional layer
located at the rim (about 30 m in thickness). This transitional layer is
also named theOlg-layer as in thecase of myrmekite. The composition ofthe reaction rim is albitic, no less than Ab90. K-feldspar in contact with
the reaction rim is Or90Ab10with no An content at the rim. Figure plots
thecore andrim compositionsof plagioclase in contact with thereaction
rim, the composition of the reaction rim, and the rim composition of K-
feldspar in contact with the reaction rim on OrAbAn diagrams. These
results indicate that plagioclase in contact with thereaction rimis almost
homogeneous with a mean value of Ab59An39Or2, but that the Olg-layer
shows a mean compositionof Ab81An18Or1. The mean composition of the
reaction rim is Ab95An5, and the rim of K-feldspar in contact with the
reaction rim has a mean composition of Or91Ab9. These values are
constant in all samples collected from various altitudes.
Plagioclase in contact with other minerals such as quartz and
biotite does not show such a rapid compositional change as in the
vicinity of contact with myrmekite or with the reaction rim. For
example, plagioclase in contact with quartz has a gradual composi-
tional variation from Ab58An40Or2 at the core to Ab64An34Or2at the
rim. The rapid compositional change of plagioclase at the rim in
contact with myrmekite and also at the rim in contact with the
reaction rim implies that these textures are formed not by crystal-
lization but by sub-solidus reactions. The analyses of myrmekite and
the reaction rim show that the reaction rim has a composition very
similar to that of the myrmekitic plagioclase.
Fig. 10. Gradual change from myrmekite to the reaction rim at one grain boundary
between plagioclase and K-feldspar. A-1: Photomicrograph. A-2: Sketch. B: Measured
volume fractionof vermicular quartz in myrmekites L1L3and in thereaction rimL4. It
decreases from L1 (plagioclase side) to L3 (K-feldspar side).
Table 1
The equations in the steady diffusion modeling (Johnson and Carlson, 1990) applied to
myrmekite formation in case of volume ratio of myrmekitic plagioclase: vermicular
quartz= 2: 1 based on overall reaction (R1): conservation of solid volume and closure of
CaO
Fluxratio equations
bfor myrmekite >
0:93 LAlAlLNaNa
m
myKfsNaO1=2
0:07
LAlAlLCaCa
m
myKfsCaO
1:07 mmyKfsAlO3=2
2:93
LAlAlLSiSi
m
myKfsSiO2
0:93 LAlAlLNaNa
JKfsNaO1=2
0:07 LAlAl
LCaCa
JKfsCaO
1:07 JKfsAlO3=2
2:93 LAlAl
LSiSi
JKfsSiO2
0
SiO2my-Kfs =JSiO2
Kfs
bfor Olg layer>
0:75 LAlAlLNaNa
m
PlOlgNaO1=2
0:25
LAlAlLCaCa
m
PlOlgCaO
1:25 mPl
OlgAlO3=2
2:75
LAlAlLSiSi
m
PlOlgSiO2
0:75 LAlAlLNaNa
JPlNaO1=2
0:25
LAlAlLCaCa
JPlCaO
1:25 JPlAlO3=2
2:75
LAlAlLSiSi
JPlSiO2
0
mass balance equations
NaO1/2my-Kfs+0.10Or
my-Kfs +0.93Pl(m)my-Kfs =0
CaOmy-Kfs +0.07Pl(m)
my-Kfs =0
AlO3/2my-Kfs+Or
my-Kfs +1.07Pl(m)my- Kfs =0
SiO2my-Kfs+3Ormy-Kfs +2.93Pl(m)my- Kfs +Qtzmy-Kfs =0
KO1/2my-Kfs +0.90Or
my-Kfs =0
NaO1/2Olg-my+0.75Olg
Olg-my +0.93Pl(m)Olg- my =0
CaOOlg-my +0.25Olg
Olg-my+0.07Pl(m)Olg- my =0
AlO3/2Olg-my +1.25Olg
Olg-my +1.07Pl(m)Olg-my =0
SiO2Olg-my +2.75Olg
Olg-my +2.93Pl(m)Olg-my +Qtz
Olg-my =0
NaO1/2Pl-Olg +0.75Olg
Pl- Olg +0.60PlPl-Olg=0
CaOPl-Olg+0.25Olg
Pl-Olg+0.40PlPl-Olg =0
AlO3/2Pl-Olg+1.25Olg
Pl-Olg+1.40PlPl-Olg=0
SiO2Pl-Olg+2.75Olg
Pl-Olg+2.60PlPl-Olg =0
steady-diffusion equations
NaO1/2Pl-Olg +NaO1/2
Olg-my +NaO1/2my-Kfs =JNaO1/2
PlJNaO1/2
Kfs
CaO
Pl-Olg+CaO
Olg-my +CaO
my-Kfs =JCaO
PlJ
CaO
Kfs
AlO3/2Pl-Olg+AlO3/2
Olg-my +AlO3/2my-Kfs =JAlO3/2
PlJAlO3/2
Kfs
SiO2Pl-Olg+SiO2
Olg-my +SiO2my-Kfs =JSiO2
PlJSiO2
Kfs
boundaryux equations
JNaO1/2Pl =0
JNaO1/2Kfs =0.961
JCaOPl =0
JCaOKfs =0
JSiO2Pl =0
JSiO2Kfs =0.733
JAlO3/2Pl =0.489
JAlO3/2Kfs =0
extent reaction equation
Pl(m)Olg- my +Pl(m)
my- Kfs =1
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3.4. The volume fraction in myrmekite
The volume fractions of myrmekitic plagioclase and vermicular
quartz in myrmekite from 60 samples collected at various altitudes
were estimated from their areal fractions by simply assuming the
equivalence of areal and volume fractions. The area of myrmekitic
plagioclase and vermicular quartz inside a myrmekite were converted
to a binary image by image processing software(Scion image). Fig. 7
plots the volume fraction of vermicular quartz in myrmekite againstthe altitude. The maximal volume fraction is 0.4. The plot does not
show any systematic variation with the altitude.
4. Discussion
4.1. Overall reactions leading to formation of myrmekite
The outermost parts of plagioclase adjacent to myrmekite show a
rapid compositional change from the core composition (Ab60) to Ab93(Fig. 8), as described for the oligoclase layer (Olg-layer) above. The
Olg-layer may have formed simultaneously with the myrmekite,
because such an abrupt compositional change is absent in plagioclase
not associated with myrmekite. We believe that the Olg-layer
represents a diffusion boundary layer active during the formation of
myrmekite.
The reaction leading to formation of myrmekite will be discussed
using average compositions of the plagioclase core (Ab60), the Olg-
layer (Ab75), the myrmekitic plagioclase (Ab93) and the K-feldspar rim
(Or90Ab10). Because volume ratios of plagioclase and vermicularquartz are variable in myrmekite, ranging approximately from 2:1 to
4:1, we will consider these two extreme cases.
4.1.1. Case of the largest proportion of vermicular quartz
Molar ratios of minerals participating into the reaction can be
estimatedfrom the relative thicknessof the myrmekite andthe adjacent
Olg-layer, giving the ratio of myrmekitic plagioclase: vermicular quartz:
theOlg-layer= 1:2.2:0.793. Molar volumedata forend memberminerals
are taken fromHelgeson et al. (1978). Values for the plagioclase solid
solution were estimated by liner interpolation between albite and
Fig. 11. Stability eld of myrmekite with myrmekitic plagioclase: vermicular quartz=2:1 in volume fraction (shaded) in a plot ofLAlAl/LCaCaagainst LAlAl/LNaNa. A: Case of overall
reaction (R1) with assumptions of conservation of solid volume and closure of CaO. B: Case of overall reaction (R2) with assumptions offv =1.300 and closure of AlO3/2. Bold solid line
represents the condition of production of myrmekitic plagioclase and vermicular quartz in a constant proportion at the two boundaries (QtzPl-my/Pl(m)
P l- my =Qtzmy-Kfs/Pl(m)
Kfs-my). The dotted
line and the dot-and-dash line represent null production of Olg-layer for LAlAl/LSiSi =0.01 and 0.5, respectively.
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anorthite. Plagioclase and K-feldspar are assumed to be reactants and
myrmekitic plagioclase, vermicular quartz, and the Olg-layer are
products. No reaction in a closed system satises both of these mineral
compositions and the molar ratios; therefore we consider an open
system reaction as follows:
aAb60An40 bOr90Ab10 X 0:793Ab75An25 1:0Ab93An7 2:2Qtz Y
(a >0 andb > 0)
where X denotes the inux of chemical components through an
intergranular medium and Y indicates efux from the system. To
determine the stoichiometric coefcients a and b, and those of the
chemical components involved in X and Y, we need two additional
constraints. In the following considerations, we will discuss two cases;
that of constant solid volume and that of closure of AlO 3/2.
4.1.1.1. The constant volume replacement case. The assumption of
constant volume replacement (conservation of solid volume) may be
reasonable, because no deformation texture is observed around the
myrmekite. The conservation of solid volume is imposed as follows:
100:358a 100:718b 229:532
In addition to this, one more condition is necessary to determine the
absolute values ofa and b. The mass conservation (closure condition) of
one of four components (NaO1/2, CaO, AlO3/2, and SiO2) can be a candi-
date for such a condition. Among four possible combinations of the
conservation of solid volume and closure of one of four components,
only the conservation of solid volume and closure of CaO give positive
values ofaandb, as follows:
a 0:671 andb 1:611
Stoichiometric coefcients of mobile components are calculated
based on the values ofa and b, giving the following reaction:
0:671Ab60An40 1:611Or90Ab10 0:961NaO1=2 0:733SiO2
0:793Ab75An25 1:0Ab93An7 2:2Qtz 0:489AlO3=2 1:450KO1=2
(R1: conservation of solid volume and closure of CaO)
Thereaction (R1)shows thatthe myrmekiteand the Olg-layer formby
consumption of two feldspars with inux of SiO2 and NaO1/2 accom-
paniedby removal of AlO3/2 and KO1/2 through an intergranular medium.
4.1.1.2. The closure of AlO3/2 case. The closure of AlO3/2 may be a
reasonable assumption, because AlO3/2has been generally considered to
be immobile during metamorphism and metasomatism. Note that the
closure condition is not exactly identical to the immobility condition; the
closure component can be mobile within the myrmekite but shows
neither inow into nor outow from the myrmekite. This assumption of
AlO3/2 closure is incompatible withthe assumptionof theconstant volumereplacement as shown in Fig. 9A, in which the inow and outow of
components are plotted against the volume factorfv according to Gresens
(1967) under the assumption of AlO3/2closure. The volume factor is
dened as:
fv100:358a 100:718b 229:532 fv: volume factor
fv should take the value between 1.105 and 1.553 to guarantee the
positive values ofa andb. FollowingGresens (1967)we rst tried to
specify the magnitude offvto minimize the total inowand outow. At
fv=1.273, CaO also becomes a closure component together with AlO3/2.
This value gives, however, uphill diffusion of AlO3/2across the Olg layer
in thesteady diffusionmodelwhichwill be discussedlater. Therefore we
specifyfv =1.300 to avoid the uphill diffusion of AlO3/2. This value was
chosen by trial and error calculations for fvvalues near 1.273. Then we
get the following total reaction:
0:764Ab60An40 0:992Or90Ab10 0:967NaO1=2 2:349SiO2 0:793Ab75An25 1:0Ab93An7 2:2Qtz 0:037CaO 0:893KO1=2
(R2:fv =1.300 and closure of AlO3/2)
The behavior of open components is essentially the same as in the
case of R1; that is, NaO1/2and SiO2are consumed together with twofeldspars and KO1/2is evolved with the formation of myrmekite.
4.1.2. Case of the smallest proportion of vermicular quartz
In the second case of the smallest volume of vermicular quartz, we
have the following molar ratio; myrmekitic plagioclase: vermicular
quartz: Olg-layer=1: 1.1: 0.661. The same analysis as above gives the
following reaction:
0:588Ab60An40 1:314Or90Ab10 0:942NaO1=2 0:377SiO2 0:661Ab75An25 1:0Ab93An7 1:1Qtz 0:241AlO3=2
1:183KO1=2
(R3: conservation of solid volume and closure of CaO)
0:776Ab60An40 0:810Or90Ab10 0:879NaO1=2 1:400SiO2
0:661Ab75An25 1:0Ab93An7 1:1Qtz 0:075CaO 0:729KO1=2
(R4:fv = 1.200 (Fig. 9B) and closure of AlO3/2)
Although the values of stoichiometric coefcients are different in
some proportions, the behavior of mobile components is the same as
in the rst case.
Fig.12.Figures showing a procedure of measurement of volume fractions of vermicular
quartz (VQ) and myrmekitic plagioclase (MP) in arbitrarily divided three areas from Al
(plagioclase side) to A3 (K-feldspar side) in a myrmekite. A: Original image
(photomicrograph) of a myrmekite. B: Image of a myrmekite after removing those of
other minerals. C: A1, A2 and A3 are areas of a myrmekite arbitrarily divided into three
pieces, and the volume fractions of vermicular quartz and myrmekitic plagioclase in A1
and A3 are measured with an image processing software(Scion image).
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4.2. Overall reactions leading to formation of the reaction rim
The reaction rim is also accompanied by the Olg-layer as
discussed in the petrography section. The Olg-layer has a steep
compositional gradient in it, probablycaused by diffusionduring thereaction rim formation. We will take an average composition of the
Olg-layer as Ab75An25, toderive thereaction leading to theformation
of the reaction rim. Other compositions used for the derivation are:
Ab60An40 for host plagioclase, Ab95An5 for the reaction rim, and
Or90Ab10 forK-feldspar. A molarratioof thereaction rimand theOlg-
layer is calculated to be 1: 0.529 based on the volume ratio. Thus the
following reaction can be assumed:
aAb60An40 bOr90Ab10 X 1:0Ab95An5 0:529Ab75An25 Y
(a >0 andb > 0)
We need two auxiliary conditions to obtain the values of
stoichiometric coefcients. As in the case of the myrmekite, we
will consider two cases: constant solid volume and closure of
AlO3/2.
4.2.1. The constant volume replacement case
The conservation of solid volume is employed, giving the followingrelation:
100:35a 100:718b 153:138
The other condition will be one of four mass conservation (closure
condition) equations of NaO1/2, CaO, AlO3/2, and SiO2. Among four
possible combinations of the two conditions, the following three give
results consistent with the observation that plagioclase is consumed
more than K-feldspar (abb).
0:456Ab60An40 1:066Or90Ab10 0:967NaO1=2 0:021SiO20:007AlO3=2
1:0Ab95An5 0:529Ab75An25 0:959KO1=2
(R5: conservation of solid volume and closure of CaO)
Fig. 13. Exchange cycle for myrmekite with the largest volume fraction of vermicular quartz (myrmekitic plagioclase: vermicular quartz=2:1). A. Case of overall reaction (R1):
conservation of solid volume and closure of CaO for LAlAl/LNaNa =0.3,LAlAl/LCaCa=96.628, andLAlAl/LSiSi =0.5. B. Case of overall reaction (R2): fv =1.300 and closure of AlO3/2for LAlAl/
LNaNa =1.0, LAlAl/LCaCa =14.663, and LAlAl/LSiSi =0.4. Amounts of minerals and components produced and consumed are represented by positive and negative values in moles,
respectively. Thin arrows denote moving directions of components and bold arrows the directions of zone growth. Open uxes are designated by vertical arrows.
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0:473Ab60An40 1:049Or90Ab10 0:958NaO1=2 0:028SiO2 1:0Ab95An5 0:529Ab75An25 0:944KO1=2 0:007CaO
(R6: conservation of solid volume and closure of AlO3/2)
0:402Ab60An40 1:120Or90Ab10 0:994NaO1=2 0:021CaO0:028AlO3=2
1:0Ab95An5 0:529Ab75An25 1:008KO1=2
(R7: conservation of solid volume and closure of SiO2)
Although we have no reasoning to determine which reaction is the
most appropriate, we see a feature common to the above three
reactions such that the reaction rim is formed by consumption of two
feldsparsassociated with the inuxof NaO1/2 together with removal of
KO1/2. Inux of SiO2is also required in the former two reactions, but
the amounts are small.
4.2.2. The closure of alo3/2case
Fig. 9C shows a compositionvolume relationship under the con-
dition of AlO3/2closure. The volume factor is given as:
fv 100:358a 100:718b 153:138
fvshould take the value between 0.889 and 1.248 to guarantee a > 0
and b >0. Herewe chose the value of 1.020 forfv, which does not result
in the uphill diffusion of AlO3/2in the steady diffusion model.
0:547Ab60An40 0:946Or90Ab10 0:924NaO1=2 0:146SiO2 0:529Ab75An25 1:0Ab95An5 0:851KO1=2 0:036CaO
(R8:fv =1.020 and closure of AlO3/2)
This reaction (R8) forms the reaction rim under almost constant
volume by consuming two feldspars, NaO1/2and SiO2 together with
evolving KO1/2. The amount of SiO2 necessary for this reaction issmaller than that in the case of myrmekite (R2 and R4).
The myrmekite-forming reaction requires a volume increment.
The larger the proportion of vermicular quartz is in the myrmekite,
the larger the volume increment becomes in the myrmekite-
forming reaction. The reaction rim can form with no volume change
or with only a small volume increment. The reaction rim occurs
much more frequently in the Okueyama granite than the myrmekite,
suggesting that the reaction with volume increment (the case of
myrmekite) is not likely to occur easily in the granitic system under
cooling.
4.3. Myrmekite and the reaction rim
The question arises: what causes the difference in products(myrmekite and the reaction rim) given the same reactants (plagio-
clase and K-feldspar)? Reactions discussed above imply the following:
1) myrmekite will form when some amount of silica inows into the
grain boundary between plagioclase and K-feldspar; 2) the reaction
rim will form when the inux of silica is smaller than that required for
myrmekite formation; and 3) the greater the inux of silica, the more
the volume fraction of vermicular quartz in myrmekite increases. Thus
the difference between formation of myrmekite and the reaction rim
results from the amount of silica available for the reaction between
plagioclase and K-feldspar.
This hypothesis will help interpret the development of a composite
texture consisting of myrmekite and reaction rim. Fig.10 is an example
of such a composite texture, showing a gradual development from
myrmekite to reaction rim between plagioclase and K-feldspar. Four
layers (L1 to L4) can be recognized in this texture, based on the
proportion of vermicular quartz. The volume fraction of vermicular
quartz decreases from 0.245 in L1 to 0.094 in L3. L4 (the reaction rim)
is free from vermicular quartz. After some amounts of silica owed
into the intergranular medium between plagioclase and K-feldspar,
the myrmekite L1 richest in quartz formed, which was followed by
successive formation of lower-quartz myrmekite layers L2 and L3.
Finally after silica was used up, the reaction rim formed. This
interpretation can be also applied to the composite texture showninFig. 3.
Table 2
The equations in the steady diffusion modeling (Johnson and Carlson, 1990) applied to
myrmekite formation in case of volume ratio of myrmekitic plagioclase: vermicular
quartz=2:1 based on overall reaction (R2): fv =1.300 and closure of AlO3/2
Flux-ratio equations
bfor myrmekite >
0:93 LAlAlLNaNa
m
myKfsNaO1=2
0:07
LAlAlLCaCa
m
myKfsCaO
1:07 mmy
KfsAlO3=2
2:93
LAlAlLSiSi
m
myKfsSiO2
0:93 LAlAlLNaNa
JKfsNaO1=2
0:07
LAlAlLCaCa
JKfsCaO
1:07 JKfsAlO3=2
2:93
LAlAlLSiSi
JKfsSiO2
0
SiO2my-Kfs =JSiO2
Kfs
bfor Olg layer>
0:75 LAlAlLNaNa
m
PlOlgNaO1=2
0:25
LAlAlLCaCa
m
PlOlgCaO
1:25 mPlOlgAlO3=2
2:75
LAlAlLSiSi
m
PlOlgSiO2
0:75 LAlAlLNaNa
JPlNaO1=2
0:25
LAlAlLCaCa
JPlCaO
1:25 JPlAlO3=2
2:75
LAlAlLSiSi
JPlSiO2
0
mass balance equations
NaO1/2my-Kfs+0.10Or
my-Kfs +0.93Pl(m)my-Kfs =0
CaOmy-Kfs +0.07Pl(m)
my-Kfs =0
AlO3/2my-Kfs+Or
my-Kfs +1.07Pl(m)my-Kfs=0
SiO2my-Kfs+3Or
my-Kfs +2.93Pl(m)my-Kfs +Otz
my-Kfs =0
KO1/2my-Kfs+0.90Ormy-Kfs =0
NaO1/2Olg-my +0.75Olg
Olg-my +0.93Pl(m)Olg-my =0
CaOOlg-my +0.25Olg
Olg-my+0.07Pl(m)Olg-my =0
AlO3/2Olg-my +1.25Olg
Olg-my +1.07Pl(m)Olg-my =0
SiO2Olg-my +2.75Olg
Olg-my +2.93Pl(m)Olg-my +Qtz
Olg-my =0
NaO1/2Pl-Olg +0.75Olg
Pl-Olg+0.60PlPl-Olg= 0
CaOPl-Olg+0.25Olg
Pl-Olg +0.40PlPl-Olg= 0
AlO3/2Pl-Olg +1.25Olg
Pl-Olg+1.40PlPl-Olg =0
SiO2Pl-Olg+2.75Olg
Pl-Olg+2.60PlPl-Olg =0
steady-diffusion equations
NaO1/2Pl-Olg +NaO1/2
Olg-my +NaO1/2my-Kfs=JNaO1/2
PlJNaO1/2
Kfs
CaOPl-Olg+CaO
Olg-my +CaOmy-Kfs =JCaO
PlJCaO
Kfs
AlO3/2
Pl-Olg +AlO3/2
Olg-my+AlO3/2
my-Kfs =JAlO3/2
PlJAlO
3/2
Kfs
SiO2Pl-Olg+SiO2
Olg-my +SiO2my-Kfs=JSiO2
PlJSiO2
Kfs
boundaryux equations
JNaO1/2Pl =0
JNaO1/2Kfs =0.967
JCaOPl =0.037
JCaOKfs =0
JSiO2Pl =0
JSiO2Kfs =2.349
JAlO3/2Pl =0
JAlO3/2Kfs =0
extent reaction equation
Pl(m)Olg-my +Pl(m)
my-Kfs= 1
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4.4. Steady diffusion modeling of myrmekite and the reaction rim
Myrmekite and the reaction rim are textures formed by diffusion-
controlled growth, because both textures have sharp boundaries at
their contacts with plagioclase and K-feldspar.
Here we will employ a steady diffusion model (Fisher, 1973; Joesten,
1977; Nishiyama, 1983) to clarify the interplay between diffusion and
reaction in forming these textures. The steady diffusion model is a
remarkable method for revealing a stability of the texture in terms of theratio of phenomenological coefcients (L-ratio). Because reactions
forming these textures are in an open system as discussed above, an
open system version (Johnson and Carlson, 1990; Ashworth and Birdi,
1990; Ashworth and Sheplev,1997; Fukuyama et al., 2004) of the steady
diffusion model will be applied. Basic postulates of the steady diffusion
model are: 1) mineral assemblages andmineral compositions areconstant
throughouteach layer, 2) the systemis in local equilibrium (a steadystate)
and diffusion of a component through an intergranular medium is driven
by its chemical potential gradient, and 3) chemical reactions occur only at
layer boundaries and no reaction occurs within the layers.
4.4.1. Steady diffusion model for myrmekite
The following models assume the Olg-layer is a layer with a constant
composition of Ab75 byaveraging the internalconcentration gradient. We
will take NaO1/2, CaO, AlO3/2, and SiO2 as reaction-controlling compo-
nents because neither myrmekite nor plagioclase contains appreciable
amounts of KO1/2. The overall reactions derived in the previous sectionsare pre-requisites of themodels, andthe amounts of open components in
the overall reactions are taken as boundary uxes (Johnson and Carlson,
1990).
4.4.1.1. Case of the largest proportion of vermicular quartz based on
overall reaction (R1). Table 1shows a list of equations of the steady
diffusion model for the case of the largest proportion of vermicularquartz
(myrmekitic plagioclase: vermicular quartz=2:1 in volume) based on the
Fig. 14. Stability eld of myrmekite with myrmekitic plagioclase: vermicular quartz=4:1 in volume fraction (shaded) in a plot ofLAlAl/LCaCa against LAlAl/LNaNa. A. Case of overall
reaction(R3): conservation of solidvolumeand closure of CaO.B. Caseof overallreaction(R4):fv =1.300 andclosureof AlO3/2. Boldsolid linerepresents thecondition of production of
myrmekitic plagioclase and vermicular quartz in a constantproportion at thetwo boundaries (QtzPl-my/Pl(m)
Pl-my =Qtzmy-Kfs/Pl(m)
Kfs-my). The dotted line andthe dot-and-dashline represent null
production of Olg-layer forLAlAl/LSiSi =0.01 and 0.5, respectively.
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overall reaction (R1). The system of simultaneous equations was solved
with the help of Maple mathematical software by taking the ratios of
phenomenological coefcients (L-ratios) as parameters. The result shows
that myrmekite will grow towards both sides, consistent with the
observations, when L-ratios satisfy the following ve conditions:
mmyKfsPlm >0 :
LAlAlLNaNa
b 2:318 : : :1
mmyKfsQtz >0 :
LAlAlLCaCa
> 284:984
LAlAlLNaNa
17:748 : : :2
mOlgmyPlm
>0 : LAlAl
LCaCa
> 328:331
LAlAlLNaNa
118:210 : : :3
mOlgmyQtz >0 :
LAlAlLCaCa
b 410:603
LAlAlLNaNa
308:885 : : :4
mOlgmyOlg b
0 : LAlAl
LCaCa
> 8:236
LAlAlLNaNa
68:601
LAlAlLSiSi
38:667 : : :5
See Appendix A for the list of symbols used in this paragraph.
Because only the last condition depends on LAlAl/LSiSi and the other four
depend only on LAlAl/LCaCa and LAlAl/LNaNa, we will discuss the stability of
myrmekite on a plot ofLAlAl/LCaCavs.LAlAl/LNaNa. The shaded area inFig.
11A represents the stability eld of myrmekite satisfying these
conditions.
The lowest boundary of the eld with respect to LAlAl/LCaCa is
determined by the last condition, which is dependent on LAlAl/LSiSi.The limiting case LAlAl/LSiSi =0.01 gives the widest area, becoming
narrower with increasing value ofLAlAl/LSiSi. For reference the case of
LAlAl/LSiSi =0.5 is shown by a dashed-dotted line in Fig. 11A.
To further constrain the stability eld of myrmekite we examined
the volume fraction of vermicular quartz at the boundary with K-
feldspar and also at the boundary with the Olg-layer. After dividing
myrmekite arbitrarily into three sub-layers (the A1 layer adjacent to
the Olg-layer; the A2 layer in the central part; andA3 layer, adjacent to
K-feldspar), thevolume fraction of vermicular quartz in each layer was
measured with image-processing software (Scion image). The result
shown inFig. 12indicate that the volume fraction is almost the same.
Thus we have the following relationship:
mmyKfsQtz =m
myKfs
Pl m
mOlgmyQtz =m
Olgmy
Pl m
Fig. 15.Exchange cycle for myrmekite with the smallest volume fraction of vermicular quartz (myrmekitic plagioclase: vermicular quartz=4:1). A. Case of overall reaction (R3):
conservation of solid volume and closure of CaO for LAlAl/LNaNa = 0.116,LAlAl/LCaCa=50.0, andLAlAl/LSiSi =0.5. B. Case of overall reaction (R4): fv =1.200 and closure of AlO3/2for LAlAl/
LNaNa =0.9, LAlAl/LCaCa =10.713, and LAlAl/LSiSi =0.3. Amounts of minerals and components produced and consumed are represented by positive and negative values in moles,
respectively. Thin arrows denote moving directions of components and bold arrows the directions of zone growth. Open uxes are designated by vertical arrows.
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This equation gives a linear relation betweenLAlAl/LNaNaand LAlAl/
LCaCa:
LAlAlLCaCa
366:454
LAlAlLNaNa
206:564
LAlAlLCaCa
> 0;
LAlAlLNaNa
> 0
: : :6
A thick solid line inFig.11A within the shaded area represents this
relationship.
This result implies that myrmekite is stable for only small values of
LAlAl/LNaNaand for large values ofLAlAl/LCaCa. In other words, the stable
formation of myrmekite meansLNaNa > LAlAlLCaCain the intergranu-
lar medium. Although the relations are not shown in Fig. 11A,
combining of5 and 6 gives
LAlAlLCaCa
366:454
LAlAlLNaNa
206:564
LAlAlLCaCa
> 0;
LAlAlLNaNa
> 0;
LAlAlLNaNa
b0:183
LAlAlLSiSi
0:448
: : :7
These relationships further mean thatLAlAl/LSiSib2.445.
Fig. 13A shows an exchange cycle for myrmekite in the case of
LAlAl/LNaNa =0.300, LAlAl/LCaCa =96.628, and LAlAl/LSiSi =0.500, satisfy-
ing 7. The boundary reaction between plagioclase and the Olg-layer
consumes plagioclase, SiO2, AlO3/2, and NaO1/2 removes CaO, andforms the Olg-layer. Myrmekite grows towards both sides, consum-
ing the Olg-layer, SiO2, AlO3/2, NaO1/2, and CaO at one boundary and
consuming K-feldspar, NaO1/2, andCaO togetherwith removing SiO2,
AlO3/2, and KO1/2at the other boundary. This exchange cycle shows
the counterintuitive uphill diffusion of AlO3/2 from K-feldspar
towards An40 plagioclase across the Olg layer.
4.4.1.2. Case of the largest proportion of vermicular quartz based on
overall reaction (R2). Table 2shows a list of equations of the steady
diffusion model based on the overall reaction (R2) while assuming
fv=1.300 and closure ofAlO3/2. Theresultshowsthat myrmekitewill grow
towards both sides whenL-ratios satisfy the following six conditions:
mmy
KfsPl m >0 : L
AlAlLNaNa
b1:316 : : :8
mmyKfsQtz >0 :
LAlAlLCaCa
> 945:347
LAlAlLNaNa
777:775 : : :9
mOlgmyPlm
>0 : LAlAl
LCaCa
> 341:211
LAlAlLNaNa
16:984 : : :10
mOlgmyQtz >0 :
LAlAlLCaCa
> 130:210
LAlAlLNaNa
637:153 : : :11
mOlgmyOlg b 0 :
LAlAlLCaCa
> 5:838
LAlAlLNaNa
30:590
LAlAlLSiSi
5:556 : : :12
mmyKfsQtz =m
myKfsPlm
mOlgmyQtz =mOlgmyPlm
LAlAlLCaCa
1522:892
LAlAlLNaNa
1537:555
LAlAlLCaCa
> 0;
LAlAlLNaNa
> 0
: : :13
A thick solid line (13) inFig. 11B represents a stability eld of
myrmekite that is located within the shaded area satisfying 812. The
stable formation of myrmekite means LNaNa > LAlAlLCaCa in the
intergranular medium.
Fig. 13B shows an exchange cycle for myrmekite in the case of
LAlAl/LNaNa =1.000,LAlAl/LCaCa = 14.663 andLAlAl/LSiSi = 0.400, satisfying
13. The boundary reaction between plagioclase and the Olg-layer
consume plagioclase, SiO2and NaO1/2, removes AlO3/2and CaO and
forms the Olg-layer. Myrmekite grows towards both sides, consum-
ing the Olg-layer, SiO2, AlO3/2, NaO1/2, and CaO at one boundary and
consuming K-feldspar, NaO1/2 and CaO together with removal of
SiO2, AlO3/2 and KO1/2 at the other boundary. This exchange cycle
does not show the uphill diffusion of AlO3/2across the Olg-layer that
was observed inFig. 13A.
4.4.1.3. Case of the smallest proportion of vermicular quartz based on
overall reactions (R3) and (R4). The same procedure as above was
applied to the case of smallest proportion of vermicular quartz in
myrmekite(myrmekitic plagioclase: vermicular quartz=4: 1) based on
the overall reactions (R3) and (R4). The result is shown inFig. 14. The
stabilityeld of myrmekite (Fig.14A) based on the overall reaction (R3)
(conservation of solid volume and closure of CaO) is far more restricted
than that in theformercase(R1: conservation of solid volumeand closure
of CaO; Fig. 11A), however, the basic relations among L-ratios are similar.The stability eld of myrmekite (Fig. 14B) based on overall reaction (R4)
(fv=1.200 and closure of AlO3/2) is more enlarged than that in the former
case (R2: fv =1.300 and closure of AlO3/2; Fig. 11B), however, the basic
relations amongL-ratios are also similar. Comparison ofFigs. 11 and 14
tells us that larger values ofL-ratios are preferable for the formation of
Table 3
The equations in the steady diffusion modeling (Johnson and Carlson, 1990) applied to
thereactionrim formation in case of overall reaction(R5): conservation of solid volume
and closure of CaO
Fluxratio equations
bfor reaction rim>
0:95 LAlAlLNaNa
m
recKfsNaO1=2
0:05
LAlAlLCaCa
m
recKfsCaO
1:05 mrecKfsAlO3=2
2:95
LAlAlLSiSi
m
recKfsSiO2
0:95 LAlAlLNaNa
JKfsNaO1=2
0:05 LAlAl
LCaCa
JKfsCaO
1:05 JKfsAlO3=2
2:95 LAlAl
LSiSi
JKfsSiO2
0
bfor Olg layer>
0:75 LAlAlLNaNa
m
PlOlgNaO1=2
0:25
LAlAlLCaCa
m
PlOlgCaO
1:25 mPlOlg
AlO3=2
2:75
LAlAlLSiSi
m
PlOlgSiO2
0:75 LAlAlLNaNa
JPlNaO1=2
0:25
LAlAlLCaCa
JPlCaO
1:25 JPlAlO3=2
2:75
LAlAlLSiSi
JPlSiO2
0
mass balance equations
NaO1/2rec-Kfs +0.10Or
rec-Kfs+0.95Pl(r)rec-Kfs =0
CaOrec-Kfs+0.05Pl(r)
rec-Kfs =0
AlO3/2rec-Kfs+Or
rec-Kfs+1.05Pl(r)rec-Kfs=0
SiO2rec-Kfs+3Or
rec-Kfs+2.95Pl(r)rec-Kfs =0
KO1/2rec-Kfs+0.90Orrec-Kfs=0
NaO1/2Olg-rec+0.75Olg
Olg-rec+0.95Pl(m)Olg-rec =0
CaOOlg-rec+0.25Olg
Olg-rec+0.05Pl(m)Olg-rec=0
AlO3/2Olg- rec +1.25Olg
Olg-rec+1.05Pl(m)Olg-rec =0
SiO2Olg-rec+2.75Olg
Olg-rec+2.95Pl(m)Olg-rec =0
NaO1/2Pl-Olg +0.75Olg
Pl- Olg +0.60PlPl-Olg=0
CaOPl-Olg+0.25Olg
Pl-Olg+0.40PlPl-Olg=0
AlO3/2Pl-Olg +1.25Olg
Pl-Olg+1.40PlPl-Olg=0
SiO2Pl-Olg +2.75Olg
Pl-Olg+2.60PlPl-Olg=0
steady-diffusion equations
NaO1/2Pl-Olg +NaO1/2
Olg-rec+NaO1/2rec-Kfs=JNaO1/2
PlJNaO1/2
Kfs
CaOPl-Olg+CaO
Olg-rec+CaOrec-Kfs=JCaO
PlJCaO
Kfs
AlO3/2
Pl-Olg+AlO3/2
Olg-rec+AlO3/2
rec- Kfs =JAlO3/2
PlJ
AlO3/2
Kfs
SiO2Pl-Olg +SiO2
Olg-rec+SiO2rec-Kfs=JSiO2
PlJSiO2
Kfs
boundary ux equations
JNaO1/2Pl =0
JNaO1/2Kfs =0.967
JCaOPl = 0
JCaOKfs = 0
JSiO2Pl =0
JSiO2Kfs =0.021
JAlO3/2Pl =0
JAlO3/2Kfs =0.007
extent reaction equation
Pl(r)Olg-rec+Pl(r)
rec-Kfs =1
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myrmekite richer in vermicular quartz. Fig. 15 is an example of the
exchange cycle with the smallest proportion of vermicular quartz based
on overall reaction (R3) in the case of LAlAl/LNaNa=0.116, LAlAl/LCaCa =
50.000, and LAlAl/LSiSi =0.500(Fig. 15A) and overall reaction (R4) in the
case of LAlAl/LNaNa =0.900, LAlAl/LCaCa =10.713, and LAlAl/LSiSi=0.300 (Fig.
15B), which represent a point on the thick solid lines in Fig. 14. Basic
features of the each exchange cycle are the same as those in the former
case.
4.4.2. Steady diffusion modeling of the reaction rim
Steadydiffusion modeling of thereactionrim will be based on overall
reactions (R5), (R6) and (R7). Because we have no indication of which
reaction is most appropriate, we will discuss all the cases separately. As
in the case of myrmekite, NaO1/2, CaO, AlO3/2and SiO2are selected as
reaction-controlling components because no KO1/2is contained in the
reaction rim.
4.4.2.1. A model based on overall reaction (R5): conservation of solid
volume and closure of Cao. All the steady diffusion model equations
are listed inTable 3. The solutions show that the reaction rim grows
towards both sides whenL-ratios satisfy the following relations:
mrecKfsPlr >0 : L
AlAl
LNaNa
b11:474 LAlAl
LSiSi
1:361 : : :1
mOlgrecPl r >0 :
LAlAlLCaCa
> 687:927
LAlAlLNaNa
27:02
LAlAlLSiSi
4:06 : : :2
mOlgrecOlg b0 :
LAlAlLCaCa
> 7:420
LAlAlLNaNa
59:620
LAlAlLSiSi
2:367 : : :3
Fig. 16A shows a stability eld (shaded area) of the reaction rim
satisfying the above relations on a plot ofLAlAl/LNaNavs.LAlAl/LCaCa. The
stability eld depends also on LAlAl/LSiSi, and two cases, LAlAl/LSiSi =0.01
(A1) and 0.5 (A2), are also shown. As LAlAl/LSiSi increases, the stability
eldbecomes wider. Thedependence on LAlAl/LSiSi is stronger than in the
case of myrmekite. Thereaction rimis stable only forlarge valuesofLAlAl/
LCaCa, which means LAlAlLCaCa. This result is consistent with that of the
case of myrmekite.
Fig. 17A shows an example of the exchange cyclefor the reaction rim
with values of LAlAl/LCaCa =40.0, LAlAl/LNaNa = 0.40, and LAlAl/LSiSi =0.50,
which satisfy the stability conditions 13. The Olg-layer formed by
consuming plagioclase, SiO2, AlO3/2, and NaO1/2 together with removing
CaO. The reaction rim formed by consuming all the four reaction-
controlling components at the boundary with the Olg-layer, and by
consuming NaO1/2 and CaO together with removing KO1/2 at the
boundary with K-feldspar.
4.4.2.2. A model based on overall reaction (R6): conservation of solid
volume and closure of AlO3/2. The same model as above based on
overall reaction (R6) gives a stability eld shown inFig. 16B and an
example of the exchange cycle in Fig. 17B. The stability eld is very
similar to the model based on overall reaction (R5). The only
difference is the lower limit with respect to LAlAl/LNaNa. We see no
large difference in the exchange cycle when compared to that based
on overall reaction (R5).
4.4.2.3. A model based on overall reaction (R7): conservation of solid
volume and closure of SiO2. This case gives a somewhat different
from the above two cases. The stability eld shown in Fig. 16C is
narrower than those of the other two cases, especially at larger values
ofLAlAl/LSiSi (Fig.16C2). The basic features of the exchange cycle showninFig. 17C are almost the same as those of the other two cases.
All three models for the reaction rim growth discussed above show
the common features: 1) The open components move in the same
directions in all exchange cycles, and 2) the amounts of reactants and
products at each boundary are almost the same. The reaction rim
stabilityeld shows anareamuch wider than thatof myrmekitein a plot
ofLAlAl/LCaCavs.LAlAl/LNaNa, and it is remarkably dependent on LAlAl/LSiSi.
Allexchangecycles based on thesemodels show uphilldiffusionof AlO3/2across the Olg layer.
4.4.2.4. A model based on overall reaction (R8): fv=1.020 and closure of
AlO3/2. A set of the steady diffusion model equations (Table 4) gives
the stability eld shown inFig.16D. The basic features of the stability
eld shown inFig. 16D are almost the same as those of the three cases
Fig.16. Stability eld of the reaction rim in a plot ofLAlAl/LCaCaagainstLAlAl/LNaNa. A: Case of overall reaction (R5) with assumptions of solid volume conservation and closure of CaO
(A1:LAlAl/LSiSi =0.01 and A2: LAlAl/LSiSi =0.5). B: Case of overall reaction (R6) with assumptions of solid volume conservation and closure of AlO3/2(B1: LAlAl/LSiSi =0.01 and B2: LAlAl/
LSiSi =0.5). C: Case of overall reaction (R7) with assumptions of solid volume conservation and closure of SiO2(C1:LAlAl/LSiSi =0.01 and C2:LAlAl/LSiSi =0.5). D: Case of overall reaction
(R8) with assumptions offv =1.020 and closure of AlO3/2(D1: LAlAl/LSiSi =0.01 and D2: LAlAl/LSiSi =0.5).
253T. Yuguchi, T. Nishiyama / Lithos 106 (2008) 237260
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based on overall reactions R5
7. Fig. 17D shows an example of theexchange cycle for the reaction rim with values of LAlAl/LCaCa =40.0,
LAlAl/LNaNa =0.40, andLAlAl/LSiSi =0.50. The Olg-layer consumes plagio-
clase, SiO2, and NaO1/2together with removing AlO3/2and CaO. The
reaction rim consumes all the four reaction-controlling components at
the boundary with the Olg-layer, and consumes NaO1/2and CaO and
removing KO1/2at the boundary with K-feldspar. This exchange cycle
does not show uphill diffusion of AlO3/2across the Olg layer, which is
observed inFig. 16AC.
4.5. Driving force for formation of myrmekite and the reaction rim
Exchange cycles for myrmekite and the reaction rim show that
their principal formation mechanism is albitization of K-feldspar and
plagioclase. At the contact with K-feldspar the essential reaction is
written as:
KAlSi3O8 NaO1=2 NaAlSi3O8 KO1=2; R9
which is equivalent to an ion exchange reaction between K-feldspar
and albite (Orville, 1963). This reaction proceeds irreversibly from the
left to the right. At the same time the following reaction occurs at the
contact with plagioclase:
CaAlSi2O8 NaO1=2 SiO2 NaAlSi3O8 CaO AlO3=2; R10
which forms myrmekitic plagioclaseand alsothe Olg-layer. Therefore, the
driving force for myrmekite and the reaction rim formation will be the
introduction of NaO1/2with or without SiO2 into the grain boundary
between K-feldspar and plagioclase. The difference between myrmekite
and the reaction rim can be explained as follows; Almost all orthoclase
componentsin K-feldsparare converted to albite by (R9) in the case of the
reaction rim, whereas only 55 to 75% (by mole fraction) of the same
component is transformed to albite by (R9). The remaining orthoclasecomponent decomposes into oxides, from which SiO2 precipitates as
quartz together with SiO2 supplied from the exterior in the case of
myrmekite. Thereforethe differenceis mostlydue to theextent of reaction
(R9), which is determined by the amount of NaO1/2 available for the
reaction. In other words, the introduction of NaO1/2into the boundary
between K-feldspar and plagioclase will make K-feldspar unstable,
resulting in formation of albite with or without quartz. Further, inow
of SiO2 into the boundary favors the formation of myrmekite. (R9) is
coupledwithalbitization of plagioclase(R10) byexchangeof SiO2 (Figs.13,
15 and 17), and therefore both myrmekite and the reaction rimform only
between K-feldspar and plagioclase.
5. Conclusions
All the hypotheses heretofore proposed for the origin of myrmekite
were critically examined in the study. Our petrographical study of
myrmekite from a young granitic body with no deformation after
solidication precludes most of preexisting models such as the model of
direct crystallization, the model of solid state exsolution and the model of
deformation-triggered formation. Only a model involving replacement of
K-feldspar by plagioclase is consistent with the occurrence of the rim
myrmekite, our major concern in this paper,but thismodel fails to explain
the albite-rich composition of myrmekitic plagioclase. In this paper we
presented a new model for the genesis of the rim myrmekite and the
reaction rim, which is a texture with some similarityto the rimmyrmekite
in its occurrence and origin. Systematic development of myrmekite
accordingto thedepthof thegranitic body(Yuguchi and Nishiyama, 2007)
indicates that myrmekite forms by a sub-solidus reaction during thedeuteric stage, together with other sub-solidus textures such as
patchperthite and the reaction rim. Our diffusion model based on a
detailed petrographical study claried how and why myrmekite occurs
typically between K-feldspar and plagioclase. One model using the
assumption of solid volume conservation gives an exchange cycle with
uphill diffusion of AlO3/2across the Olg layer. The other model, with an
AlO3/2closure condition, can give an exchange cycle with no such uphill
behavior if the volume factor is larger than unity (the volume increases
Table 4
The equations in the steady diffusion modeling (Johnson and Carlson, 1990) applied to
thereaction rimformation in caseof overallreaction (R8):fv =1.020and closureof AlO3/2
Fluxratio equations
bfor reaction rim>
0:95 LAlAlLNaNa
m
recKfsNaO1=2
0:05
LAlAlLCaCa
m
recKfsCaO
1:05 mrecKfsAlO3=2
2:95
LAlAlLSiSi
m
recKfsSiO2
0:95 LAlAlLNaNa
JKfsNaO1=2
0:05
LAlAlLCaCa
JKfsCaO
1:05 JKfsAlO3=2
2:95
LAlAlLSiSi
JKfsSiO2
0
bfor Olg layer>
0:75 LAlAlLNaNa
m
PlOlgNaO1=2
0:25
LAlAlLCaCa
m
PlOlgCaO
1:25 mPlOlgAlO3=2
2:75
LAlAlLSiSi
m
PlOlgSiO2
0:75 LAlAlLNaNa
JPlNaO1=2
0:25
LAlAlLCaCa
JPlCaO
1:25 JPlAlO3=2
2:75
LAlAlLSiSi
JPlSiO2
0
Mass balance equations
NaO1/2rec-Kfs + 0.10Or
rec-Kfs+0.95Pl(r)rec-Kfs=0
CaOrec-Kfs +0.05Pl(r)
rec-Kfs =0
AlO3/2rec-Kfs +Or
rec-Kfs+1.05Pl(r)rec-Kfs=0
SiO2rec-Kfs +3Or
rec-Kfs+2.95Pl(r)rec-Kfs= 0
KO1/2rec-Kfs +0.90Or
rec-Kfs= 0
NaO1/2Olg- rec +0.75Olg
Olg-rec+0.95Pl(m)Olg-rec =0
CaOOlg-rec+0.25Olg
Olg-rec+0.05Pl(m)Olg- rec = 0
AlO3/2Olg- rec +1.25Olg
Olg-rec+1.05Pl(m)Olg- rec =0
SiO2Olg-rec+2.75Olg
Olg-rec+2.95Pl(m)Olg- rec =0
NaO1/2Pl-Olg +0.75Olg
Pl- Olg +0.60PlPl-Olg=0
CaOPl-Olg+0.25Olg
Pl- Olg +0.40PlPl-Olg=0
AlO3/2Pl-Olg +1.25Olg
Pl- Olg +1.40PlPl-Olg=0
SiO2Pl-Olg +2.75Olg
Pl- Olg +2.60PlPl-Olg= 0
steady-diffusion equations
NaO1/2Pl-Olg +NaO1/2
Olg-rec +NaO1/2rec-Kfs =JNaO1/2
PlJNaO1/2
Kfs
CaOPl- Olg +CaO
Olg-rec+CaOrec-Kfs=JCaO
PlJCaO
Kfs
AlO3/2Pl-Olg+AlO3/2
Olg-rec +AlO3/2rec- Kfs =JAlO3/2
PlJAlO3/2
Kfs
SiO2Pl-Olg +SiO2
Olg-rec+SiO2rec-Kfs =JSiO2
PlJSiO2
Kfs
boundary ux equations
JNaO1/2Pl =0
JNaO1/2Kfs =0.924
JCaOPl =0.036
JCaOKfs =0
JSiO2Pl =0
JSiO2Kfs =0.146
JAlO3/2Pl =0
JAlO3/2Kfs =0
extent reaction equation
Pl(r)Olg-rec+Pl(r)
rec-Kfs=1
Fig. 17.Exchange cycle of the reaction rim. A: Case of overall reaction (R5) with assumptions of solid volume conservation and closure of CaO forLAlAl/LNaNa =0.4,LAlAl/LCaCa=40.0 and
LAlAl/LSiSi =0.5. B: Case of overall reaction (R6) with assumptions of solid volume conservation and closure of AlO 3/2forLAlAl/LNaNa =0.4,LAlAl/LCaCa =40.0 andLAlAl/LSiSi =0.5. C: Case of
overall reaction (R7) with assumptions of solid volume conservation and closure of SiO2forLAlAl/LNaNa =0.4,LAlAl/LCaCa=110.0 andLAlAl/LSiSi =0.5. D: Case of overall reaction (R8) with
assumptions offv =1.020 and closure of AlO3/2forLAlAl/LNaNa =0.4,LAlAl/LCaCa =40.0andLAlAl/LSiSi =0.5. Amounts of minerals and components produced and consumed arerepresented
by positive and negative values in moles, respectively. Thin arrows denote moving directions of components and bold arrows the directions of zone growth. Open uxes are
designated by vertical arrows.
255T. Yuguchi, T. Nishiyama / Lithos 106 (2008) 237260
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due to the formation of the myrmekite). We have no denite criteria at
present to determine which model is more appropriate. However, the
essential feature is the same in bothmodelsdecomposition and partial
albitization of K-feldspar and albitization of plagioclase triggered by
introduction of NaO1/2and SiO2 into the boundary between the two
minerals. Albitization of K-feldspar itself can occur everywhere around
the K-feldspar crystal; however, the key signature for myrmekite
formation is a coupling between decomposition and partial albitization
of K-feldspar and albitization of plagioclase by the following reactions:
KAlSi3O8 NaO1=2 NaAlSi3O8 KO1=2albitization of K feldspar
KAlSi3O8 KO1=2 AlO3=2 3SiO2decomposition of K feldspar
and
CaAl2Si2O8 NaO1=2 SiO2 NaAlSi3O8albitization of plagioclase
The coupling between the reactions is maintained by diffusive
transport of NaO1/2and SiO2. The increase in activity of NaO1/2in the
grain boundary between K-feldspar and plagioclase destabilize both
minerals, leading to albite formation. Additional increments in SiO2activity due to the inux of SiO2and/or decomposition of K-feldspar
favors formation of myrmekite; otherwise the reaction rim forms.
Acknowledgements
We are grateful to Dr. H. Isobe for his assistance in electron-probe
works. This paper has been beneted from a critical and constructive
review byan anonymous reviewer. The editorialhandlingand comments
by Prof. IanBuick is also appreciated. This workwasnanciallysupported
by a Grant-in-Aid for Scientic Research (B: 14340164 and A: 17204045)
to T.N. from the Japan Society for the Promotion of Science and also a
Grant-in-Aid from the Fukada Geological Institute to T.Y.
Appendix A. List of symbols for steady-diffusion model
bBoundary between myrmekite and K-feldspar>
Pl(m)my-Kfs Stoichiometric coefcient of myrmekitic plagioclase(Pl(m))
at the boundary between myrmekite and K-feldspar
Ormy-Kfs Stoichiometric coefcient of orthoclase at the boundary
between myrmekite and K-feldspar
Otzmy-Kfs Stoichiometric coefcient of vermicular quartz at the bound-
ary between myrmekite and K-feldspar
NaO1/2my-Kfs Stoichiometric coefcient of NaO
1/2at the boundary between
myrmekite and K-feldspar
CaOmy-Kfs Stoichiometric coefcient of CaO at the boundary between
myrmekite and K-feldspar
AlO3/2my-Kfs Stoichiometric coefcient of AlO
3/2at the boundary between
myrmekite and K-feldspar
SiO2my-Kfs
Stoichiometric coefcient of SiO2at the boundary betweenmyrmekite and K-feldspar
KO1/2my-Kfs Stoichiometric coefcient of KO
1/2at the boundary between
myrmekite and K-feldspar
bBoundary between Olg-layer and myrmekite >
Pl(m)Olg-my Stoichiometric coefcient of myrmekitic plagioclase(Pl(m))
at the boundary between Olg-layer and myrmekite
OlgOlg-my Stoichiometric coefcient of oligoclase at the boundary bet-
ween Olg-layer and myrmekite
QtzOlg-my Stoichiometric coefcient of vermicular quartz at the
boundary between Olg-layer and myrmekite
NaO1/2Olg-my Stoichiometric coefcient of NaO
1/2at theboundarybetween
Olg-layer and myrmekite
CaOOlg-my Stoichiometric coefcient of CaO at the boundary between
Olg-layer and myrmekite
AlO3/2Olg-my Stoichiometric coefcient of AlO
3/2at the boundary between
Olg-layer and myrmekite
SiO2Olg-my Stoichiometric coefcient of SiO
2at the boundary between
Olg-layer and myrmekite
bBoundary between plagioclase and Olg-layer >
PlPl-Olg Stoichiometric coefcient of host plagioclase at the bound-
ary between plagioclase and Olg-layer
OlgPl-Olg Stoichiometric coefcient of oligoclase at the boundary
between plagioclase and Olg-layer
NaO1/2Pl-Olg Stoichiometric coefcient of NaO
1/2at theboundary between
plagioclase and Olg-layer
CaOPl-Olg Stoichiometric coefcient of CaO at the boundary between
plagioclase and Olg-layer
AlO3/2Pl-Olg Stoichiometric coefcient of AlO
3/2at the boundary between
plagioclase and Olg-layer
SiO2Pl-Olg Stoichiometric coefcient of SiO
2at the boundary between
plagioclase and Olg-layer
b
Boundary
ux >
JNaO1/2Kfs Flux of NaO
1/2at the boundary between myrmekite and K-
feldspar
JNaO1/2Pl Flux of NaO
1/2at the boundary between plagioclase and Olg-
layer
JCaOKfs Flux of CaO at the boundary between myrmekite and K-
feldspar
JCaOPl Flux of CaO at the boundarybetween plagioclase and Olg-layer
JAlO3/2Kfs Flux of AlO
3/2 at the boundary between myrmekite and K-
feldspar
JAlO3/2Pl Fluxof AlO
3/2at the boundary between plagioclase andOlg-layer
JSiO2Kfs Flux of SiO
2at the boundary between myrmekite and K-
feldspar
JSiO2
Pl Flux of SiO2
at the boundary between plagioclase and Olg-layer
Appendix B
The equations in the steady diffusion modeling (Johnson and
Carlson,1990) applied to myrmekite formation in case of volume ratio
of myrmekitic plagioclase : vermicular quartz=4 : 1 based on overall
reaction (R3): conservation of solid volume and closure of CaO.
Flux-ratio equations
bfor myrmekite>
0:93 LAlAlLNaNa
m
myKfsNaO1=2
0:07
LAlAlLCaCa
m
myKfsCao
1:07 mmyKfsAlO3=2
2:93 LAlAl
LSiSi m
myKfsSiO2 0:93
LAlAl
LNaNa JKfsNaO1=2
0:07 LAlAlLCaCa
JKfsCaO
1:07 JKfsAlO3=2
2:93
LAlAlLSiSi
JKfsSiO2
0
mmyKfsSiO2
JKfsSiO2
bfor Olg-layer>
0:75 LAlAlLNaNa
m
PlOlgNaO1=2
0:25
LAlAlLCaCa
m
PlOlgCaO
1:25 mPlOlgAlO3=2
2:75 LAlAl
LSiSi
m
PlOlgSiO2
0:75
LAlAlLNaNa
JPlNaO1=2
0:25 LAlAlL
CaCa
JPlCaO 1:25 J
PlAlO3=2 2:75
LAlAlL
SiSi
JPlSiO2 0
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mass balance equations
mmyKfsNaO1=2
0:10mmyKfsOr 0:93mmyKfsPlm 0
mmyKfsCaO 0:07m
myKfsPlm 0
mmyKfsAlO3=2
mmyKfsOr 1:07mmyKfsPlm 0
m
myKfsSiO2 3m
myKfsOr 2:93m
myKfsPlm m
myKfsQtz 0
mmyKfsKO1=2
0:90mmyKfsOr 0
mOlgmyNaO1=2
0:75mOlgmyOlg 0:93mOlgmyPlm
0
mOlgmyCaO 0:25m
OlgmyOlg 0:07m
OlgmyPlm 0
mOlgmyAlO3=2
1:25mOlgmyOlg
1:07mOlgmyPlm
0
mOlgmySiO2
2:75mOlgmyOlg 2:93m
OlgmyPlm
mOlgmyQtz 0
mPlOlgNaO1=2
0:75mPlOlgOlg 0:60mPlOlgPl 0
mPlOlgCaO 0:25m
PlOlgOlg 0:40m
PlOlgPl 0
mPlOlgAlO3=2
1:25mPlOlgOlg 1:40mPlOlgPl 0
mPlOlgSiO2
2:75mPlOlgOlg 2:60mPlOlgPl 0
steady-diffusion equations
mPlOlgNaO1=2
mOlgmyNaO1=2 mmyKfsNaO1=2
JPlNaO1=2 JKfsNaO1=2
mPl
OlgCaO mOlg
myCaO mmy
KfsCaO JPlCaOJKfsCaO
mPlOlgAlO3=2
mOlgmyAlO3=2
mmyKfsAlO3=2
JPlAlO3=2JKfsAlO3=2
mPlOlgSiO2
mOlgmySiO2
mmyKfsSiO2
JPlSiO2 JKfsSiO2
boundaryux equations
JPlNaO1=2 0
JKfsNaO1=2 0:942
JPlCaO 0
JKfsCaO 0
JPlSiO2 0
JKfsSiO2 0:377
JPlAlO3=2 0:241
JKfsAlO3=2 0
extent reaction equation
mOlgmy
Plm
mmyKfs
Plm
1
Appendix C
The equations in the steady diffusion modeling (Johnson and
Carlson,1990) applied to myrmekite formation in case of volume ratio
of myrmekitic plagioclase : vermicular quartz = 4 : 1 based on overall
reaction (R4):fv =1.200 and closure of AlO3/2
.
Fluxration equations
bfor myrmekite>
0:93 LAlAlLNaNa
m
myKfsNaO1=2
0:07
LAlAlLCaCa
m
myKfsCaO
1:07 mmyKfsAlO3=2
2:93 LAlAl
LSiSi
m
myKfsSiO2
0:93
LAlAlLNaNa
JKfsNaO1=2
0:07 LAlAlLCaCa
JKfsCaO
1:07 JKfsAlO3=2
2:93
LAlAlLSiSi
JKfsSiO2
0
mmyKfsSiO2
JKfsSiO2
bfor Olg-layer>
0:75 LAlAlLNaNa
m
PlOlgNaO1=2
0:25
LAlAlLCaCa
m
PLOlgCao
1:25 m
PlOlgAlO3=2
2:75 LAlAl
LSiSi
m
PlOlgSiO2
0:75
LAlAlLNaNa
JPlNaO1=2
0:25 LAlAlLCaCa
JPlCaO
1:25 JPlAlO3=2
2:75
LAlAlLSiSi
JPlSiO2
0
mass balance equations
mmyKfsNaO1=2
0:10mmyKfsOr 0:93mmyKfsPlm 0
mmyKfsCaO 0:07m
myKfsPlm
0
mmyKfsAlO3=2
mmyKfsOr 1:07m
myKfsPlm 0
mmyKfsSiO2
3mmyKfsOr 2:93mmyKfsPlm
mmyKfsQtz 0
mmyKfsKO1=2
0:90mmyKfsOr 0
mOlgmyNaO1=2
0:75mOlgmyOlg 0:93mOlgmyPlm 0
m
OlgmyCaO 0:25m
OlgmyOlg 0:07m
OlgmyPlm 0
mOlgmyAlO3=2
1:25mOlgmyOlg
1:07mOlgmyPlm
0
mOlgmySiO2
2:75mOlgmyOlg 2:93mOlgmyPlm
mOlgmyQtz 0
mPlOlgNaO1=2
0:75mPlOlgOlg 0:60mPlOlgPl 0
mPlOlgCaO 0:25m
PlOlgOlg 0:40m
PlOlgPl 0
mPlOlgAlO3=2
1:25mPlOlgOlg 1:40m
PlOlgPl 0
mPlOlg
SiO2 2:75mPlOlg
Olg
2:60mPlOlg
Pl
0
257T. Yuguchi, T. Nishiyama / Lithos 106 (2008) 237260
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steady-diffusion equations
mPlOlgNaO1=2
mOlgmyNaO1=2
mmyKfsNaO1=2
JPlNaO1=2 JKfsNaO1=2
mPlOlgCaO m
OlgmyCaO m
myKfsCaO J
PICaOJ
KfsCaO
mPlOlgAlO3=2
mOlgmyAlO3=2 mmyKfsAlO3=2
JPlAlO3=2 JKfsAlO3=2
mPlOlgSiO2
mOlgmySiO2 mmyKfsSiO2
JPlSiO2 JKfsSiO2
boundaryux equations
JPlNaO1=2 0
JKfsNaO1=2 0:879
JPlCaO 0:075
JKfsCaO 0
JPlSiO2 0
JKfsSiO2 1:400
JPlAlO3=2 0
JKfsALO3=2 0
extent reaction equation
m
OlgmyPlm m
myKfsPlm 1
Appendix D
The equations in the steady diffusion modeling (Johnson and
Carlson, 1990) applied to the reaction rim formation in case of overall
reaction (R6): conservation of solid volume and closure of AlO3/2
.
Fluxration equations
bfor reaction rim>
0:95 LAlAlLNaNa
m
recKfsNaO1=2
0:05
LAlAlLCaCa
m
recKfsCao
1:05 mrecKfsAlO3=2
2:95 LAlAl
LSiSi
mrec
KfsSiO2
0:95 LAlAlLNaNa
JKfsNaO1=2
0:05 LAlAlLCaCa
JKfsCaO
1:05 JKfsAlO3=2
2:95
LAlAlLSiSi
JKfsSiO2
0
bfor Olg-layer>
0:75 LAlAlLNaNa
m
PlOlgNaO1=2
0:25
LAlAlLCaCa
m
PlOlgCao
1:25 mPlOlgAlO3=2
2:75 LAlAl
LSiSi
m
PlOlgSiO2
0:75
LAlAlLNaNa
JPlNaO1=2
0:25 LAlAl
LCaCa J
PlCaO 1:25 J
PlAlO3=2 2:75
LAlAl
LSiSi J
PlSiO2 0
mass balance equations
mrecKfsNaO1=2
0:10mrecKfsOr 0:95mrecKfsPlr 0
mrecKfsCaO 0:05m
recKfsPlr 0
mrecKfsAlO3=2
mrecKfsOr 1:05mrecKfsPlr 0
mrec
KfsSiO2 3mrec
KfsOr 2:95mrec
KfsPlm 0
mrecKfsKO1=2
0:90mrecKfsOr 0
mOlgrecNaO1=2
0:75mOlgrecOlg 0:95mOlgrecPlm
0
mOlgrecCaO 0:25m
OlgrecOlg 0:05m
OlgrecPlm
0
mOlgrecAlO3=2
1:25mOlgrecOlg 1:05m
OlgrecPlm 0
mOlgrecSiO2
2:75mOlgrecOlg 2:95m
OlgrecPlm 0
mPlOlgNaO1=2
0:75mPlOlgOlg 0:60mPlOlgPl 0
mPlOlgCaO 0:25m
PlOlgOlg 0:40m
PlOlgPl 0
mPlOlgAlO3=2
1:25mPlOlgOlg 1:40m
PlOlgPl 0
mPlOlgSiO2
2:75mPlOlgOlg
2:60mPlOlgPl
0
steady-diffusion equations
mPlOlgNaO1=2
mOlgrecNaO1=2 mrecKfsNaO1=2
JPlNaO1=2 JKfsNaO1=2
mPlOlgCaO m
OlgrecCaO m
recKfsCaO J
PlCaOJ
KfsCaO
mPLOlgAlO3=2
mOlgrecAlO3=2
mrecKfsAlO3=2 JPlAlO3=2
JKfsAlO3=2
mPlOlgSiO2
mOlgrecSiO2
mrecKfsSiO2 JPlSiO2
JKfsSiO2
boundaryux equations
JPlNaO1=2 0
JKfsNaO1=2 0:958
JPlCaO 0:007
JKfsCaO 0
JPlSiO2 0
JKfsSiO2 0:028
JPlAlO3=2 0
JKfsAlO3=2 0
extent reaction equation
mOlgrecPl
r
mrecKfsPlr 1
258 T. Yuguchi, T. Nishiyama / Lithos 106 (2008) 237260
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Appendix E
The equations in the steady diffusion modeling (Johnson and
Carlson, 1990) applied to the reaction rim formation in case of overall
reaction (R7): conservation of solid volume and closure of SiO2.
Fluxratio equations
bfor reaction rim>
0:95 LAlAlLNaNa
mrecKfsNaO1=2
0:05 LAlAlLCaCa
mrecKfsCao
1:05 mrecKfsAlO3=2
2:95 LAlAl
LSiSi
m
recKfsSiO2
0:95
LAlAlLNaNa
JKfsNaO1=2
0:05 LAlAlLCaCa
JKfsCaO
1:05 JKfsAlO3=2
2:95
LAlAlLSiSi
JKfsSiO2
0
bfor Olg-layer>
0:75 LAlAlLNaNa
m
PlOlgNaO1=2
0:25
LAlAlLCaCa
m
PlOlgCaO
1:25 mPlOlgAlO3=2
2:75 LAlAl
LSiSi
m
PlOlgSiO2
0:75
LAlAlLNaNa
JPlNaO1=2
0:25
LAlAlLCaCa
J
PlCaO
1:25 J
PlAlO3=2
2:75
LAlAlLSiSi
J
PlSiO2
0
mass balance equations
mrecKfsNaO1=2
0:10mrecKfsOr 0:95mrecKfsPlr 0
mrecKfsCaO 0:05m
recKfsPlr 0
mrecKfsAlO3=2
mrecKfsOr 1:05mrecKfsPlr 0
mrecKfsSiO2
3mrecKfsOr 2:95mrecKfsPlr 0
mrecKfsKO1=2
0:90mrecKfsOr 0
mOlgrecNaO1=2
0:75mOlgrecOlg 0:95mOlgrecPlm
0
mOlgrecCaO 0:25m
OlgrecOlg
0:05mOlgrecPlm
0
mOlgrecAlO3=2
1:25mOlgrecOlg
1:05mOlgrecPlm
0
mOlgrecSiO2
2:75mOlgrecOlg 2:95m
OlgrecPlm
0
mPlOlgNaO1=2
0:75mPlOlgOlg
0:60mPlOlgPl
0
mPlOlgCaO 0:25m
PlOlgOlg 0:40m
PlOlgPl 0
mPl
OlgAlO3=2 1:25mPl
OlgOlg 1:40mPl
OlgPl 0
mPlOlgSiO2
2:75mPlOlgOlg 2:60mPlOlgPl 0
steady-diffusion equations
mPlOlgNaO1=2
mOlgrecNaO1=2 mrecKfsNaO1=2
JPlNaO1=2 JKfsNaO1=2
mPlOlgCaO m
OlgrecCaO m
recKfsCaO J
PlCaOJ
KfsCaO
mPlOlgAlO3=2
mOlgrecAlO3=2
mrecKfsAlO3=2 JPlAlO3=2
JKfsAlO3=2
mPlOlg
SiO2 m
Olgrec
SiO2 mrecKfs
SiO2 JPl
SiO2JKfs
SiO2
boundaryux equations
JPlNaO1=2 0
JKfsNaO1=2 0:994
JPlCaO 0
JKfs
CaO
0:021
JPlSiO2 0
JKfsSiO2 0
JPlAlO3=2 0
JKfsALO3=2 0:028
extent reaction equation
mOlgrecPlr
mrecKfsPlr 1
References
Ashworth, J.R., 1972. Myrmekite of exsolution and replacement origins. GeologicalMagazine 109, 4562.
Ashw