mimerquita

8/9/2019 Mimerquita

1/24

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]

8/9/2019 Mimerquita

2/24

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

.

238 T. Yuguchi, T. Nishiyama / Lithos 106 (2008) 237260

8/9/2019 Mimerquita

3/24

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.

239T. Yuguchi, T. Nishiyama / Lithos 106 (2008) 237260

8/9/2019 Mimerquita

4/24

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.


8/9/2019 Mimerquita

5/24

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.


8/9/2019 Mimerquita

6/24

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.


8/9/2019 Mimerquita

7/24

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.


8/9/2019 Mimerquita

8/24

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


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


8/9/2019 Mimerquita

9/24

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.


8/9/2019 Mimerquita

10/24

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


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).


8/9/2019 Mimerquita

11/24

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


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.


8/9/2019 Mimerquita

12/24

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


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


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


CaOOlg-my +0.25Olg

Olg-my+0.07Pl(m)Olg-my =0

AlO3/2Olg-my +1.25Olg


SiO2Olg-my +2.75Olg

Olg-my +2.93Pl(m)Olg-my +Qtz

Olg-my =0


Pl-Olg+0.60PlPl-Olg= 0

CaOPl-Olg+0.25Olg

Pl-Olg +0.40PlPl-Olg= 0

AlO3/2Pl-Olg +1.25Olg


SiO2Pl-Olg+2.75Olg




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


JNaO1/2Pl =0

JNaO1/2Kfs =0.967

JCaOPl =0.037

JCaOKfs =0

JSiO2Pl =0

JSiO2Kfs =2.349

JAlO3/2Pl =0

JAlO3/2Kfs =0


Pl(m)Olg-my +Pl(m)

my-Kfs= 1


8/9/2019 Mimerquita

13/24

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.


8/9/2019 Mimerquita

14/24

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.


8/9/2019 Mimerquita

15/24

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


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


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


SiO2Olg-rec+2.75Olg




CaOPl-Olg+0.25Olg




SiO2Pl-Olg +2.75Olg




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


Pl(r)Olg-rec+Pl(r)

rec-Kfs =1


8/9/2019 Mimerquita

16/24


8/9/2019 Mimerquita

17/24

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.


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).


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).

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-

8/9/2019 Mimerquita

18/24


8/9/2019 Mimerquita

19/24

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


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


CaOrec-Kfs +0.05Pl(r)

rec-Kfs =0

AlO3/2rec-Kfs +Or


SiO2rec-Kfs +3Or

rec-Kfs+2.95Pl(r)rec-Kfs= 0

KO1/2rec-Kfs +0.90Or

rec-Kfs= 0

NaO1/2Olg- rec +0.75Olg


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



CaOPl-Olg+0.25Olg




SiO2Pl-Olg +2.75Olg

Pl- Olg +2.60PlPl-Olg= 0



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


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.

http://-/?-http://-/?-

8/9/2019 Mimerquita

20/24

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


AlO3/2my-Kfs Stoichiometric coefcient of AlO



SiO2my-Kfs

Stoichiometric coefcient of SiO2at the boundary betweenmyrmekite and K-feldspar

KO1/2my-Kfs Stoichiometric coefcient of KO



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


AlO3/2Olg-my Stoichiometric coefcient of AlO



SiO2Olg-my Stoichiometric coefcient of SiO

2at the boundary between


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


AlO3/2Pl-Olg Stoichiometric coefcient of AlO



SiO2Pl-Olg Stoichiometric coefcient of SiO

2at the boundary between


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


8/9/2019 Mimerquita

21/24


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


mPlOlgSiO2



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


JPlNaO1=2 0

JKfsNaO1=2 0:942

JPlCaO 0

JKfsCaO 0

JPlSiO2 0

JKfsSiO2 0:377

JPlAlO3=2 0:241

JKfsAlO3=2 0


mOlgmy

Plm

mmyKfs

Plm

1

Appendix C


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


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


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


8/9/2019 Mimerquita

22/24


mPlOlgNaO1=2

mOlgmyNaO1=2

mmyKfsNaO1=2


mPlOlgCaO m

OlgmyCaO m

myKfsCaO J

PICaOJ

KfsCaO

mPlOlgAlO3=2

mOlgmyAlO3=2 mmyKfsAlO3=2

JPlAlO3=2 JKfsAlO3=2

mPlOlgSiO2

mOlgmySiO2 mmyKfsSiO2

JPlSiO2 JKfsSiO2


JPlNaO1=2 0

JKfsNaO1=2 0:879

JPlCaO 0:075

JKfsCaO 0

JPlSiO2 0

JKfsSiO2 1:400

JPlAlO3=2 0

JKfsALO3=2 0


m

OlgmyPlm m

myKfsPlm 1

Appendix D


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


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


OlgrecPlm 0

mPlOlgNaO1=2


mPlOlgCaO 0:25m

PlOlgOlg 0:40m

PlOlgPl 0

mPlOlgAlO3=2

1:25mPlOlgOlg 1:40m

PlOlgPl 0

mPlOlgSiO2

2:75mPlOlgOlg

2:60mPlOlgPl

0


mPlOlgNaO1=2

mOlgrecNaO1=2 mrecKfsNaO1=2


mPlOlgCaO m

OlgrecCaO m

recKfsCaO J

PlCaOJ

KfsCaO

mPLOlgAlO3=2

mOlgrecAlO3=2

mrecKfsAlO3=2 JPlAlO3=2

JKfsAlO3=2

mPlOlgSiO2

mOlgrecSiO2

mrecKfsSiO2 JPlSiO2

JKfsSiO2


JPlNaO1=2 0

JKfsNaO1=2 0:958

JPlCaO 0:007

JKfsCaO 0

JPlSiO2 0

JKfsSiO2 0:028

JPlAlO3=2 0

JKfsAlO3=2 0


mOlgrecPl

r

mrecKfsPlr 1


8/9/2019 Mimerquita

23/24

Appendix E


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


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


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



mPlOlgNaO1=2

mOlgrecNaO1=2 mrecKfsNaO1=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


JPlNaO1=2 0

JKfsNaO1=2 0:994

JPlCaO 0

JKfs

CaO

0:021

JPlSiO2 0

JKfsSiO2 0

JPlAlO3=2 0

JKfsALO3=2 0:028


mOlgrecPlr

mrecKfsPlr 1

References

Ashworth, J.R., 1972. Myrmekite of exsolution and replacement origins. GeologicalMagazine 109, 4562.

Ashw

mimerquita

Documents