9
Journal of Volcanology and Geothermal Research 65 (1995) 41-49 Leaching rates of rock-forming components through acidic alteration Kenji Nogami”,“, Minoru Yoshidab “Kusatsu-Shirane Volcano Observatory, Tokyo Institute of Technology, 641-36 Kusatsu, Agatsuma, Gunma, 377-17 Japan bDepartment of Chemistry, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, 152 Japan Received 7 January 1994; revised version accepted 18 August 1994 Abstract A series of experiments on the interactions of a glassy basaltic andesite with acidic solution in a flowing system were carried out. Leaching indices of seven components (Na, K, Ca, Mg, Fe, Al and Si) were defined to compare the relative leaching behaviour of these components at all reaction stages. At 160°C and using 0.24 N HzS04 solution, Na, Ca and Al were leached easily, compared with K, Mg, Fe and Si. Although Si concentrated in the final residual rock, it was not always the hardest component to leach. The leaching behaviour of these seven components in a glassy rock agreed with that in crystalline rock. Results of three experiments at 80, 120 and 160°C using 0.12 N HCl solution showed that the rise of temperature accelerated the leaching rate of each component, whereas the leaching index for each component was not affected by temperature. This indicated that the leaching processes for these seven components were independent of temperature. On the other hand, in a series of the experiments at 160°C using 0.24.0.12 and 0.0024 N HCl solutions to examine the effect of acidity, the change in acidity of the reacting solution affected not only the reaction rate but also the reaction processes of the components. Na, Ca, Fe and Al became hard to leach as acidity diluted and Si became easy to leach and comparable to these components. 1. Introduction In fumarolic and hydrothermal areas, rocks react with acid solutions. Rocks altered under acidic condi- tions become gradually enriched in SiOz as a result of the leaching of the other components, and finally change into SiOZ . nH,O, i.e., opaline silica (Minami et al., 1966; Ossaka, 1968). In order to simulate such processes, experiments were carried out by using ther- mal fluids and volcanic rocks whose chemical compo- sitions, mineralogy and textures were known (e.g., Minatoetal., 1959; Iwasakietal., 1964; Ossaka, 1968). * Comesponding author. Minato et al. ( 1959) soaked a block of andesite in hot strongly acid water over three months in the Tam- agawa Hot Spring Area, Akita, Japan. They showed that the proportions of Si02 and HZ0 present in the residual rock increased, whereas those of other com- ponents, especially A1203, CaO and Na,O decreased markedly. They observed the formation of three zones in the residual rock, according to the alteration mineral assemblages formed and also pointed out that plagio- clase was altered prior to pyroxenes in the intermediate zone. These facts correspond to the changes in the chemical composition of the residual rock. Many researchers have carried out experiments for rock and mineral alteration using acidic solutions, deionized water and electrolyte solutions in a batch 0377-0273/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIO377-0273(94)00039-l

Leaching rates of rock-forming components through acidic alteration

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Page 1: Leaching rates of rock-forming components through acidic alteration

Journal of Volcanology and Geothermal Research 65 (1995) 41-49

Leaching rates of rock-forming components through acidic alteration

Kenji Nogami”,“, Minoru Yoshidab “Kusatsu-Shirane Volcano Observatory, Tokyo Institute of Technology, 641-36 Kusatsu, Agatsuma, Gunma, 377-17 Japan

bDepartment of Chemistry, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo, 152 Japan

Received 7 January 1994; revised version accepted 18 August 1994

Abstract

A series of experiments on the interactions of a glassy basaltic andesite with acidic solution in a flowing system were carried out. Leaching indices of seven components (Na, K, Ca, Mg, Fe, Al and Si) were defined to compare the relative leaching behaviour of these components at all reaction stages. At 160°C and using 0.24 N HzS04 solution, Na, Ca and Al were leached easily, compared with K, Mg, Fe and Si. Although Si concentrated in the final residual rock, it was not always the hardest component to leach. The leaching behaviour of these seven components in a glassy rock agreed with that in crystalline rock.

Results of three experiments at 80, 120 and 160°C using 0.12 N HCl solution showed that the rise of temperature accelerated the leaching rate of each component, whereas the leaching index for each component was not affected by temperature. This indicated that the leaching processes for these seven components were independent of temperature.

On the other hand, in a series of the experiments at 160°C using 0.24.0.12 and 0.0024 N HCl solutions to examine the effect of acidity, the change in acidity of the reacting solution affected not only the reaction rate but also the reaction processes of the components. Na, Ca, Fe and Al became hard to leach as acidity diluted and Si became easy to leach and comparable to these components.

1. Introduction

In fumarolic and hydrothermal areas, rocks react

with acid solutions. Rocks altered under acidic condi-

tions become gradually enriched in SiOz as a result of

the leaching of the other components, and finally

change into SiOZ . nH,O, i.e., opaline silica (Minami et

al., 1966; Ossaka, 1968). In order to simulate such

processes, experiments were carried out by using ther- mal fluids and volcanic rocks whose chemical compo- sitions, mineralogy and textures were known (e.g.,

Minatoetal., 1959; Iwasakietal., 1964; Ossaka, 1968).

* Comesponding author.

Minato et al. ( 1959) soaked a block of andesite in

hot strongly acid water over three months in the Tam-

agawa Hot Spring Area, Akita, Japan. They showed

that the proportions of Si02 and HZ0 present in the

residual rock increased, whereas those of other com-

ponents, especially A1203, CaO and Na,O decreased markedly. They observed the formation of three zones

in the residual rock, according to the alteration mineral

assemblages formed and also pointed out that plagio-

clase was altered prior to pyroxenes in the intermediate zone. These facts correspond to the changes in the

chemical composition of the residual rock. Many researchers have carried out experiments for

rock and mineral alteration using acidic solutions,

deionized water and electrolyte solutions in a batch

0377-0273/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIO377-0273(94)00039-l

Page 2: Leaching rates of rock-forming components through acidic alteration

42 K. Nogami, M. Yoshida /Journal of Volcanology and Geothermal Research 65 (1995) 41-49

and/or flowing system controlling pH values, temper- ature, flow rates and other reaction conditions (e.g., Kamiya, 1960; Chiba, 1962; Seyfried and Bischoff, 1979; Muir and Nesbitt, 1992; Walther and Woodland, 1993).

Recent studies of rock-water interaction have been focused on the kinetics of mineral dissolution in elec- trolyte solutions (e.g., Brady and Walther, 1989; Dove and Crerar, 1990; Walther and Woodland, 1993) and observations of altered mineral surfaces using a variety of spectroscopic procedures (e.g., Hellmann et al., 1990; Muir and Nesbit, 1992). Sanemasaet al. ( 1972) investigated the dissolution reaction of olivine in inor- ganic acids at various temperatures. They estimated activation energy according to the Arrhenius plots and discussed effects of anions on activation energy. Dove and Crerar (1990) examined the kinetics of quartz dissolution in deionized water and electrolyte solutions. They also obtained data on activation energy and showed the effects of electrolytes on reaction rates.

However, to investigate rock alteration processes under acidic conditions only by kinetics of the disso- lution of individual phases is not the full story because volcanic rocks are aggregates of minerals and glass whose dissolution rates will be mutually affected by coexisting phases.

In this work, experiments with acid solutions in a flowing system reproduce the leaching of rock-forming components and provide the basis for a method to investigate the leaching behaviour of these compo- nents. The experiments are also aimed to analyse the effects of temperature and acidity on leaching proc- esses.

2. Experimental

2.1. Material

The sample used is anonporphyritic basaltic andesite collected from a lava flow (LC- 1) of Miharayama, Izu- Oshima, which erupted in 1986. Small amounts of min- ute crystals of plagioclase and opaque mineral are scattered in its glassy groundmass. Fujii et al. ( 1988) and Nakano et al. ( 1988) reported that the microphen- ocrysts in the basaltic andesite comprise less than l- 2%. They concluded that the microphenocryst assem- blage is plagioclase (An,,_,,) + clinopyroxene (augite and pigeonite) + orthopyroxene (bronzite and hyper- sthene) and that plagioclase, clinopyroxene, titanifer-

Table 1

Composition (wt.%) of45-74 pm fraction of sample used as starting material and LC- 1 lava from Izu-Oshima

Starting material LC-I”

SiO, 54.64 TiOZ I .26

Al,03 14.43

FeOb 13.20

CaO 9.08

MgO 4.15

MnO 0.22

NazO 2.2 1

K,O 0.48

P,Os 0.10

Total 99.77

Analyses by X-ray fluorescence.

“Data from Fujii et al. ( 1988).

“Total iron as FeO.

54.15

I .24

14.56

14.09

9.02

4.07

0.20

2.05

0.47

0.10

99.95

ous magnetite and brownish glass exist in the groundmass.

The sample was crushed in an agate mortar and sieved to obtain the 45-74 pm fraction. The separated sample was then washed with ethanol to eliminate very fine particles and was used as the starting material. Chemical compositions of LC-1 lava and the starting material used in the experiments are shown in Table 1. Segregation due to sieving is negligible.

2.2. Procedure

Parts of an instrument for high-performance liquid chromatography were assembled into an apparatus for the experiments (Fig. 1) . The apparatus has a pump with a built-in damper whose maximum pressure is 7

Fig. 1. Apparatus used for rock-acid solution interaction. 1 = acid

solution; 2 = teflon tube; 3 = power switch; 4 = pump switch; 5 = dis- play 6 = pump; 7 = damper; 8 = heater; 9 = Pyrex column; 10 = heat

controller; 11 = valve; 12 = thermometer.

Page 3: Leaching rates of rock-forming components through acidic alteration

Table 2

K. Nogami, M. Yoshido / Joumal of Volcanology and Geothermal Research 65 (1995) 4149 43

Experimental conditions of EXP- 1 to EXP-6

EXP-I EXP-2 EXP-3 EXP-4 EXP-5 EXP-6

Rock weight (g) 3.750 3.750 3.750 3.750 3.750 3.750

Reaction temp. (“C) 160 80 120 160 160 160

Pressure (kg/cm’) 2-3 2-3 2-3 2-3 2-3 2-3

Reacting solution 0.24 N H,SO, 0.12 N 0.12 N 0.12 N 0.24 N 0.0024 N HCI HCI HCI HCI HCI

Total reaction time (min) 5520 1440 1440 1440 1440 1440

kg/cm*. A Pyrex column of 10 mm inner diameter and 50 mm long was used for the reaction vessel. Samples of 3.750 g occupied about 80% of the capacity of the vessel. The column was connected to a Teflon tube via a glass filter supported with a Teflon stopper and heated with a 100 W mantle heater. The thermometer of the controller was set between the heater and the reaction vessel. HCl and H,S04 solutions were used as the acid media in the experiments and the acidity of solutions ranged from 0.0024 to 0.24 N. In preliminary experi- ments, differences in leaching behaviour of the com- ponents between HCl and H2S04 used as reaction fluids were not distinguishable in the same H30+ concentra- tion. The flow rate of the acid solution was controlled with both an adjuster and a valve. Reaction tempera- ture, run time and other experimental conditions are summarized in Table 2.

Sample solutions were collected continuously in fractions. Based on the results of previous works (e.g., Iwasaki et al., 1976)) the decrease in the concentrations of dissolved components was expected to be rapid at the early stage of experiment and become slower. Therefore, the times taken for collecting solutions per fraction were extended as the reactions progressed. The first four fractions were collected at hourly intervals and the others a few hours apart.

2.3. Chemical analysis

Seven components - Na, K, Ca, Mg, Fe, Al and Si - in the solution were analysed by the following meth- ods: Na and K with flame photometry; Ca, Mg and Si with ICP emission spectrometry; Fe and Al with col- orimetry using 2,2’-bipyridine and 8-quinolinol, respectively.

3. Analysis of leached fluids

Data for EXP-1 performed at 160°C are given in Table 3. The flow rates ranged from 1.10 to 1.38 g/ min with 1.21 g/min as average. It was difficult to keep the flow rate more precisely constant because the pack- ing condition of the sample changed as grains dissolved and secondary minerals, mainly opaline silica, were formed.

The leached proportion P,(i) of component X, from the first to the ith fraction, is expressed by Eq. ( 1 ), where X is Na, K, Ca, Mg, Fe, Al and Si:

i W,(k)

P,(i) =k=IR x100 (1) x

R, is the weight of component X present in the starting material and W,(k) is the amount of component X leached in the solution of the kth fraction. P,(i) indi- cates the degree of leaching of component X from the original sample.

The change of the leached proportion of each com- ponent with time is shown in Fig. 2. The seven com- ponents fall into two groups: one comprising Na, Ca and Al, showing the higher leached proportions; and the other, for K, Mg, Fe and Si, having less leaching. The leached proportions of Na, Ca and Al increase very sharply until about 1000 min but gradually afterwards, whereas the leached proportions of K, Mg, Fe and Si increase gradually throughout the experiment.

The amounts of the components present in the resid- ual rock obviously continued to decrease with time and the chemical and mineralogical compositions of the reacting solid material changed as the reaction pro- ceeded. Accordingly, it is impossible to determine the relative facility with which the components leached at a particular reaction time from the leached proportions.

Page 4: Leaching rates of rock-forming components through acidic alteration

44 K. Nogami, M. Yoshida / Journal of Volcanology and Geothermal Research 65 (1995) 4149

A AI 0 Na

l cs A Fe 0 Si UK . Mg

v-

0 2000 4000 6000

Reaction time (min.)

Fig. 2. Change in leached proportions of Na, K, Ca, Mg, Fe, Al and Si vs. reaction time, resulting from leaching of these components from rock under acidic conditions in EXP- 1.

However, in order to compare the relative behaviour of the components at all reaction stages, we define a leaching index, Z,(i) , of component X in fraction i as:

z,(i) =s,(i) R,(i)

where S,(i) is the ratio of the amount of component X to the sum of seven components in the solution after the reaction to yield fraction i. R,(i) is a ratio of the amount of the component X to the sum of the amounts of seven components in the rock before the reaction to yield fraction i. Rx and W,(i) from Eq. ( 1) provide the amounts of the components present in the rock before the reaction to yield the ith fraction. The larger the leaching index, the more easily the component was leached.

The variations of the leaching indices of the seven components against time are shown in Fig. 3. The indi- ces of Na, Ca and Al are all above unity as these com- ponents were most easily leached. Those of K and Mg are lower than 1, although both gradually increase with time. The index of Fe gradually increases to be above 1 after about 4000 min. These variations mean that the

Table 3 Concentration (in mg/kg) of major components in solution samples from EXP-I at 160°C using 0.24 N H,SO,

Fraction No.: I 2 3 4 5 6 7 8

Total reaction time (mm) 60 120 180 240 435 960 1200 1440 Reaction time fraction per (min) 60 60 60 60 195 S25 240 240 Wt. of solution (g) 82.55 82.18 80.48 19.52 241 663 304 309 Flow rate (g/min) 1.38 1.37 1.34 1.33 I .27 I .26 1.27 I .29

Na 69.7 51.6 50.0 45.3 40.9 18.7 8.58 5.80 K 3.95 2.16 2.08 1.96 I .82 0.97 0.70 0.52 Ca 256 171 161 151 127 57.8 28.5 19.7 Mg 11.8 5.36 5.32 5.33 5.37 3.60 3.31 3.20 Fe 147 113 105 98.2 91.6 56.2 16.4 30. I Al 389 283 263 241 209 92.3 44.4 21.5 Si 183 125 126 129 139 130 124 113

Fraction No. 9 10 II 12 13 14 IS 16

Total reaction time ( min ) 1680 1800 2400 2520 2880 3000 4080 5520 Reaction time fraction per (min) 240 120 600 120 360 120 1080 1440 Wt. of solution (g) 295 151 751 147 421 146 1349 1588 Flow rate (g/min) 1.23 1.26 1.25 1.23 1.17 1.22 I .25 1.10

Na 5.22 4.16 2.44 2.18 2.18 2.00 I .5 I 1.41 K 0.56 0.52 0.41 0.50 0.57 0.54 0.50 0.63 Ca 17.2 15.0 9.80 8.81 9.37 8.88 6.22 7.62 Mg 3.65 3.93 3.41 3.62 4.22 4.02 3.95 5.64 Fe 29.6 27.8 20.0 19.7 21.1 18.9 15.6 18.3 Al 22.8 18.2 10.5 8.62 8.63 7.04 5.25 4.56 Si 118 117 88.1 84.6 84.2 69.9 41.3 33.9

Page 5: Leaching rates of rock-forming components through acidic alteration

K. Nogami, M. Yoshida /Journal of Volcanology and Geothemal Research 65 (199s) 4149 45

A 0

P I¶

-0 2ow 4066 6666 Reaction time (min.)

Fig. 3. Leaching indices of Na, K, Ca, Mg, Fe, Al and Si in EXP-1 which indicate the relative ease of leaching for the seven components, plotted against reaction time.

proportions of K, Mg and Fe present in the residual rock increased as the alteration progressed. The leach- ing index of Si becomes higher than 1 after about 1500 min, continues to increase until about 3000 min and then starts decreasing. This indicates that Si is not always the hardest element to be leached. Indeed, at the halfway stage of alteration, Si leached out more easily than K, Mg and Fe though it concentrated in the final residual rock.

Residual rock

I , I

0 20 40 60

28 (Cu Ku ) I degree

Fig. 4. XRD patterns of starting and residual rocks used in EXP- 1. PI= plagioclase; Ti = titaniferous magnetite.

K, Mg, Fe and Si were harder to leach than Na, Ca and Al. Although the rock used in the experiments is glassy and nonporphyritic, this tendency agrees with the alteration of crystalline phases shown by Minato et al. ( 1959).

XRD patterns of the starting material and the residual rock of EXP-1 are shown in Fig. 4. Major minerals identified in the starting material are plagioclase and titaniferous magnetite. These minerals are also present in the residual rock, but the diffraction peaks of plagi- oclase are smaller. Broad peaks for SiOz. nH,O appear from 20 to 30” of 28. Sulfate minerals, such as anhy- drite, gypsum and alunite, are not observed in the resid- ual rock. These facts are in harmony with the results of the analysis of the solutions.

.i 30 A

B g A : 20

A0

E

L

a

$10 ,P

:”

0 b4 PB !

0 500 1000 Reaction time (min.)

Fig. 5. Effect of reaction temperature on leached proportions of Na, K, Ca, Mg, Fe, Al and Si. Change in leached proportions of seven components are plotted against reaction time in EXP-2, -3 and -4 using0.12NHCl. (a) 80°C. (b) 120°C. (c) 160°C.

Page 6: Leaching rates of rock-forming components through acidic alteration

46 K. Nogami, M. Yoshida / Journal of Volcanology and Geothermal Research 65 (1995) 4149

0 2 4 6 6 0 10 20 30

0.6, I 3-

0.0 4 I 04 4 0 1 2 3 0 10 20 30

0.6, 1 4-

0.0 4 I 0 4

LeachLl proportion (%) 6

Fig. 6. Leaching indices of Na, K, Ca, Mg, Fe, Al and Si plotted against leached proportions in EXP-2. -3 and -4. 0 =8O”C; l = 120°C;

Cl = 160°C.

4. Effect of reaction conditions on relative leaching facility

4.1. Reaction temperature

In order to examine the effects of temperature on the leaching behaviour of all components, three experi- ments: EXP-2, -3 and -4 were carried out using 0.12 N HCl solution for 24 h at 80,120 and 160°C respectively (Table 2).

The leached proportions of the seven components as

a function of time at 80, 120 and 160°C, are shown in Fig. 5, b and c, respectively. These figures indicate that the higher is the reaction temperature, the larger are the leached proportions of all the components. In each experiments, the leached proportions of Na, Ca and Al show similar patterns and increase sharply with time, while the proportions of K, Mg, Fe and Si increase gradually.

Page 7: Leaching rates of rock-forming components through acidic alteration

K. Nogami, M. Yoshidn /Journal of Volcanology and Geothermal Research 65 (1995) 41-49 47

(b):O.lZN

z A

z 30. A

r A : 8

::

g 20. P

Reaction time (min.)

Fig. 7. Effect of acidity of HCI solution on leached proportions of Na, K, Ca, Mg, Fe, Al and Si. Changes in leached proportions of seven components am plotted against reaction times in EXP-4, -5 and-6at 160°C. (a) 0.0024N. (b) 0.12N. (c) 0.24N.

In EXP-2, -3 and -4, the leached proportions of all the components increase as the reaction temperature rises. This indicates that the chemical composition of the reacting solid after the same reaction time varies with temperature. In order to compare the relative facil- ity of the components leached at the same reaction stage, it is necessary to examine the leaching indices of the components against the leached proportions.

Relations between the leaching indices for all com- ponents and their leached proportions in EXP-2, -3 and -4 are summarized in Fig. 6. Plots of the leaching indi- ces versus the leached proportions for each component follow the same curve in all the experiments. Although the rise of temperature causes an increase of the leached proportions of the components, relative facility of the components to be leached is independent of tempera-

ture between 80 and 160°C. These results indicate that only the reaction rates change with reaction tempera- ture, whereas the reaction processes do not essentially change.

4.2. Acidity of solution

Hellmann et al. ( 1990) examined the pH depend- ence on dissolution rate and the leached layer thick- nesses of albite. They showed that deepest leaching occurred at acid pH, lesser leaching at basic pH and little leaching at neutral pH. To investigate the effects of H30+ concentration in the acid pH region on the relative facility of the components to be leached, we carried out two experiments: EXP-5 and -6. Except for acidity, experimental conditions are the same as those given in EXP4 (Table 2),

The leached proportions of all components as a func- tion of time are shown in Fig. 7a, band c, using 0.0024, 0.12 and 0.24 NHCl solutions, respectively. The seven components in EXP-4 and -5 fall into two groups according to their leached proportions: one for Na, Ca and Al showing the higher proportions and the other, for K, Mg, Fe and Si, having the lower proportions. The components in EXP-6 are divided into four groups according to the leached proportions: one for Na, sec- ond for Ca and Al, third for K and Si and fourth for Mg and Fe.

Plots of leaching indices of the seven components versus their leached proportions in EXP4, -5 and -6 are summarized in Fig. 8. In EXP-4 and -5, each com- ponent follows the same trend and the change of acidity from 0.24 to 0.12 N do not noticeably affect the facility of the components to be leached. In EXP-6 using 0.0024 N HCl solution, the plots of the indices of Na, Ca, Al and Fe follow trends quite different from those in EXP-4 and -5. The leaching indices of these com- ponents decrease, while the index of Si increases and becomes comparable to the indices for Na, Ca and Al. These results indicate that not only the reaction rates but also the reaction processes change in accordance with the change in the acidity of the reacting solution, from 0.12 to 0.0024 N.

5. Conclusions

Experimental studies on the hydrothermal alteration of glassy basaltic andesite under conditions of high

Page 8: Leaching rates of rock-forming components through acidic alteration

48 K. Nogami, M. Yoshidn / Journal of Volcanology and Geothermal Research 65 (1995) 4149

2.8 ‘r I 41 I

0 5 10 15 20 0 20 40 60

0.8 G

0.61

0.01 0 2 4 6

0 10 20 30

0.0 ---_-I 0

LeAed prbDportionl;%) 20

Ca

Fig. 8. Leaching indices of Na, K. Ca, Mg, Fe, AI and Si plotted against leached proportions in EXP-4. -5 and -6. 0 = 0.24 N; 0 = 0.12 N; A = 0.0024 N.

temperature and strong acidity indicate that Na, Ca and

Al are leached out quickly compared with K, Mg and Fe. Si is mostly concentrated in the residual rock, but it is not always the hardest component to be leached

out. Their leaching behaviours for glassy and nonpor-

phyritic rock used in the present experiments coincide

with those of crystalline rock previously reported.

The reaction temperature markedly affects the

leached proportion of the components, however, plots of the leaching indices against the leached proportions

of the components follow the same trends regardless of

temperature. This indicates that an increase of the reac- tion temperature activates the leaching of the compo-

nents, although the reaction mechanisms do not necessarily change. On the other hand, the acidity of the solutions strongly affects both the leached propor- tions and the leaching indices. The trends of the indices against the proportions of almost all the components depend upon the acidity. This indicates that not only the reaction rates but also the reaction processes are affected by changes in acidity of the reacting solutions.

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K. Nogami, M. Yoshidn /Journal of Volcanology and Geothermal Research 65 (1995) 41-49 49

Acknowledgements

We would like to express our appreciation to Pro- fessor Masahiro Yamamoto of Okayama University for giving permission to use the ICP emission spectrome- ter. We also thank the members of Fujii Laboratory of University of Tokyo for analysing the rock sample. We are deeply indebted to Professor Emeritus Joyo Ossaka of Tokyo Institute of Technology for valuable discus- sions and instructive suggestions. Finally we thank the two reviewers for their constructive comments on the manuscript.

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