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U UNI V E RSI T Y O F C IN C INN A T I

08/10/2009 Date:

Gokce K. USTUNISIK I, , hereby submit this original work as part of the requirements for the degree of: Doctor of Philosophy

Arts&Sciences, Geology in

It is entitled: Application of Magma Recharge, Plagioclase Zoning, and Crystal Size

Distribution (CSD) Theory to Natural Solid-Liquid Equilibria

Gokce Ustunisik Student Signature:

This work and its defense approved by: Dr. Attila Kilinc Committee Chair: Dr. J. Barry Maynard

Dr. Warren D. Huff

Dr. David B. Nash

Dr. A. Umran Dogan

Approval of the electronic document:

I have reviewed the Thesis/Dissertation in its final electronic format and certify that it is an accurate copy of the document reviewed and approved by the committee. Attila Kilinc Committee Chair signature: Application of Magma Recharge, Plagioclase Zoning, and Crystal Size Distribution (CSD) Theory to Natural Solid-Liquid Equilibria

A dissertation submitted to the

Graduate School

of the University of Cincinnati

in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy (Ph.D.)

in the Department of Geology

of the College of Arts and Sciences by

Gokce K. Ustunisik

B.S., Ankara University, 2001 M.S., Ankara University, 2004 August 2009

Committee Chair: Dr. Attila Kilinc

OVERVIEW

During the last decade, insightful applications of thermodynamic calculations

embodied within the MELTS thermodynamic model of Ghiorso and Sacks (1995) have

greatly enhanced our understanding of the evolution of magmas. MELTS does the isobaric and isothermal constrained calculations by minimizing the Gibbs free energy for the system; temperature, pressure, fO2 constrained calculations by minimization of the ⎛ ∂G ⎞ Korzhinski potential ( L = G − n O2 ⎜ ⎟ ) for systems open to oxygen transfer. The ⎝ ∂nO2⎠ adiabatic calculations are done by minimization of the enthalpy subject to fixed pressure

and entropy (e.g. heat content). Applications of the MELTS calculations demonstrated in

several publications have shown how complex petrologic hypotheses can be tested to

yield quantitative and occasionally suprising results.

This doctorate research focuses on developing quantitative models for crystal

fractionation, magma recharge, magma mixing, compositional zoning in plagioclase by

applying the MELTS algorithm to natural solid-liquid equilibria, and the application of

Crystal Size Distribution (CSD) theory to compute crystal residence time in magma. This

dissertation is composed of three chapters.

In Chapter 1, the initial system parameters of parental magma (pressure,

temperature, water content, and oxygen fugacity) of the Small Hasandag volcano in

Central Turkey were constrained using the MELTS algorithm and then using the same

algorithm, the feasibility of isobaric fractional crystallization, magma recharge, and

isobaric-isenthalpic magma mixing was tested as the controlling process in the evolution

of the parental magma.

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In Chapter 2, the consequences of two different physical models of magma

dynamics on plagioclase zoning were determined. The consequences of magma pooling

at several levels within the crust before eruption (decompressional and isobaric fractional

crystallization) were explored. This process can produce normal, reverse and even oscillatory zoning in plagioclase. In another model, the effect of convection within a shallow magma chamber on plagioclase zoning was explored and was demonstrated that oscillatory zoning develops under these conditions.

In Chapter 3, the CSD theory was used to calculate the crystal nucleation rate, crystal growth rate and crystal residence time using the plagioclase and clinopyroxene

present in a single basaltic lava flow at the Small Hasandag volcano. Although crystal residence times using a single mineral in a single lava flow has been studied using the

CSD theory, it is not clear if the same crystal residence times can be obtained if more

than one mineral is used. The results of this part of my research show that residence times

calculated from the CSD theory gives the same crystal residence times whether a single

mineral or more than one mineral is used in the calculations. The results show that

plagioclase and clinopyroxene residence times overlap within the limits of error implying

that crystal residence times calculated by using the CSD theory either clinopyroxene or

plagioclase of the Small Hasandag volcano can be used in the calculation of residence

time.

ACKNOWLEDGEMENTS

I would like to gratefully acknowledge the assistance of all people who made a significant contribution to this dissertation. I am deeply grateful to my advisor for his patience, enthusiasm, advice, encouragement, and continuous support over the past four years without which this dissertation would not have come alive. I have greatly benefited from his experience and knowledge which helped me to learn how to think, how to define the problems, and how to approach them along my work.

I would like to thank to my committee members Dr. John Grover, Dr. David

Nash, Dr. Warren D. Huff, Dr. J. Barry Maynard, and Dr. A. Umran Dogan for their constructive criticism and valuable advice that were always essential to the completion of this work. I especially thank to Dr. J. Barry Maynard and Dr. Tammie Gerke for their help during the XRF analysis.

I should thank to the organizations that courteously provided funding for the research and travel. These include the Geological Society of America, the Department of

Geology at the University of Cincinnati for “Wycoff” and “Geology Alumni

Distinguished Doctoral” Fellowships, the University Research Council at the University of Cincinnati, and the Graduate Student Governance Association at the University of

Cincinnati.

I also thank to Dr. Arnie Miller and Dr. Lewis Owen for their encouragement and support during this work. A special thanks to Ana Cristina Londoño not only for her great friendship and continuous encouragement but also for her patience and invaluable time for her critics in my writings. I would also like to thank to Dr. Irem Yesilyurt, Murat

Akkus, Onur Conger, Sebnem Tosun, and Yalin Senyurt for their help in the field. Many

vi thanks to my friends who made an unforgettable and wonderful experience my life in

Cincinnati.

Last but not least, I am always thankful to my parents who continually encouraged and supported me with a great patience, unconditional love, and understanding of all times.

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TABLE OF CONTENTS

OVERVIEW……………………………………………………………………………...iii

ACKNOWLEDGEMENTS………………………………………………………………vi

LIST OF FIGURES…………………………………………………………………….....x

LIST OF TABLES………………………………………………………………………xvi

CHAPTER I: ROLE OF FRACTIONAL CRYSTALLIZATION, MAGMA

RECHARGE, AND MAGMA MIXING IN THE DIFFERENTIATION OF THE

SMALL HASANDAG VOLCANO, CENTRAL ANATOLIA, TURKEY

Abstract……………………………………………………………………………….1

1. Introduction………………………………………………………………………...3

2. Mineralogy of Small Hasandag Volcanic Rocks…………………………………...5

3. Chemical Composition of Small Hasandag Volcanic Rocks……………………….6

4. MELTS Calculations to Constrain the Initial System Parameters………………….7

4.1. Parental Magma Composition………………………………………………...8

4.2. Initial System Pressure………………………………………………………..9

4.3. Initial System Oxygen Fugacity………………………………………………9

4.4. Initial System Water Content………………………………………………..10

5. Testing Isobaric Fractional Crystallization Hypothesis…………………………...11

6. Testing Magma Recharge Hypothesis…………………………………………….13

7. Testing Isobaric-Isenthalpic Magma Mixing Hypothesis…………………………14

8. Conclusions………………………………………………………………………..16

9. Acknowledgements………………………………………………………………..18

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References……………………………………………………………………………18

CHAPTER 2: NEW INSIGHTS INTO THE PROCESSES CONTROLLING

PLAGIOCLASE ZONING

Abstract………………………………………………………………………………33

1. Introduction………………………………………………………………………34

2. Materials and Methods…………………………………………………………...37

3. Discussion of Results…………………………………………………………….39

3.1.MELTS Simulations to Demonstrate the Role of Total Pressure (Ptotal) and

Water Content of the Melt (wt% H2O) on Plagioclase Zoning……………………..39

3.2. Normal and Reverse Zoning under Decompressional Crystallization Followed by

Isobaric Cooling Conditions…………………………………………………………40

3.3.Oscillatory Zoning under Polybaric and Isothermal Convection Conditions……43

3.4. Partial Molal Volume Effect on Plagioclase Zoning and Calculation of Partial

Molal Volumes of Na2O and CaO………………………………………………...... 44

4. Conclusions………………………………………………………………………..46

5. Acknowledgements………………………………………………………………..48

References……………………………………………………………………………48

CHAPTER 3: CRYSTAL SIZE DISTRIBUTIONS (CSDs) in a BASALTIC FLOW

AT THE SMALL HASANDAG VOLCANO, CENTRAL TURKEY:

COMPARISON OF CALCULATED RESIDENCE TIMES WITH

PLAGIOCLASE AND CLINOPYROXENE CRYTALS

Abstract………………………………………………………………………………74

1. Introduction………………………………………………………………………75

2. The Small Hasandag Volcano……………………………………………………77

3. The Principles of the Crystal size Distribution (CSD) Theory…………………..78

3.1. Open System at Steady-State……………………………………………………79

4. Methods-Measuring the CSDs…………………………………………………...80

5. Results……………………………………………………………………………82

5.1. Plagioclase CSDs…………………………………………………………...... 82

5.2. Clinopyroxene CSDs……………………………………………………………84

5.3. Comparison of Residence Times………………………………………………..85

6. Conclusions………………………………………………………………………86

References……………………………………………………………………………87

APPENDIX………………………………………………………………………….98

LIST OF FIGURES

Chapter 1

Figure 1 Total alkali (Na2O+K2O wt %) vs. SiO2 (wt %) diagram (Le Bas et al. 1986) for

the Small Hasandag volcanic rocks.

Figure 2 Major oxides variation diagrams for the Small Hasandag volcanic rocks. a. SiO2 vs TiO2, b. SiO2 vs Al2O3, c. SiO2 vs FeO*, d. SiO2 vs MgO, e. SiO2 vs CaO, and f. SiO2 vs K2O.

Figure 3 Comparison of calculated melt compositions at a. P=1000 bars (open black

triangles), b. P=10 kbars (open black circles) at 2 wt% H2O and fO2=QFM+1, and c. P=1

bar (open black squares) with basaltic andesite, andesite, dacite, and rhyolite (black crosses) at 0 wt% H2O and fO2=QFM+1 in Na2O+K2O vs SiO2 space. Calculations are

carried out closed system isobaric fractional crystallization of parental basaltic andesite

(Mg#68, Table 1). Best agreement between computed melts calculations and the Small

Hasandag volcanic rocks is at P=1000 bars.

Figure 4 Comparison of calculated melt compositions at a. fO2=QFM+1 (open black

triangles), b. fO2=QFM+2 (open black circles), and c. fO2=QFM+3 (open black squares)

with basaltic andesite, andesite, dacite, and rhyolite (black crosses) at 2 wt% H2O and

P=1000 bars in MgO vs FeO* space. Initial system fO2 is best defined at fO2= QFM+1.

Figure 5 Comparison of calculated melt compositions at a. 0 wt% H2O (open black circles), b. 1 wt% H2O (open black squares), and c. 2 wt% H2O (open black triangles) with basaltic andesite, andesite, dacite, and rhyolite (black crosses) at P=1000 bars and

fO2= QFM+1 in SiO2 vs K2O space. Best agreement between computed compositions at

P=1000 bars and fO2= QFM+1 and Small Hasandag volcano is at 2 wt% H2O.

Figure 6 Comparison of melts generated from isobaric fractional crystallization of

basaltic andesite (Mg#68, Table 1) with 2 wt% H2O at 1000 bars and fO2= QFM+1 (open

black triangles) with composition of the Small Hasandag volcanic rocks (black crosses)

in a. SiO2 vs Ti2O, b. SiO2 vs Al2O3, c. SiO2 vs FeO*, d. SiO2 vs MgO, e. SiO2 vs CaO, f.

SiO2 vs K2O Harker diagrams.

Figure 7 a. SiO2 - MgO plot for the Small Hasandag compositions from basaltic andesite

to rhyolite, b. SiO2 - MgO plot for most of the data except the very low silica values to

focus on the discontinuities that are mostly concentrated in the SiO2 range of 62-65 wt%.

Figure 8 Comparison of melts generated from isothermal recharge followed by isobaric- isenthalpic mixing of dacite with rhyolite with composition of the Small Hasandag volcanic rocks (black crosses) in a. SiO2 vs Al2O3, b. SiO2 vs FeO*, c. SiO2 vs MgO, d.

SiO2 vs CaO, and e. SiO2 vs K2O Harker diagrams.

Figure 9 Calculated melt compositions with a. isobaric fractional crystallization of basaltic andesite and b. isothermal recharge followed by isobaric-isenthalpic mixing of dacite with rhyolite and the compositions of the Small Hasandag volcanic rocks in terms of total alkali-silica diagram are superimposed.

Figure 10 Comparison of melts generated from isothermal recharge followed by isobaric-isenthalpic mixing of dacite with rhyolite with composition of the Small

Hasandag volcanic rocks (black crosses) in SiO2 - MgO plot.

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Chapter 2

Figure 1 Multiple levels of magma chambers within the crust and magma is moving adiabatically among those levels and crystallizing at each level due to isobaric cooling.

Figure 2 The polybaric and isothermal convection of a parcel of magma in a single magma chamber.

Figure 3a The effect of decrease in total pressure (bars) on the development of an An-

rich zone (Yoder and Tilley 1962).

Figure 3b The effect of increase in water pressure (bars) on the development of an An-

rich zone (Yoder and Tilley 1962).

Figure 4 The inverse relationship between total pressure (bars) of the system and

anorthite content of plagioclase (mole%).

Figure 5 The direct relationship between water content in the melt (wt%) and anorthite content of plagioclase (mole%) at 1000 bars.

Figure 6 The change in total pressure (bars) with respect to solid mass (g.) under decompressional crystallization followed by isobaric cooling conditions.

Figure 7 The change in temperature (o C) with respect to solid mass (g.) under

decompressional crystallization followed by isobaric cooling conditions.

Figure 8 The change in dissolved water content of melt (wt%) with respect to solid mass

(g.) under decompressional crystallization followed by isobaric cooling conditions.

Figure 9a The change in anorthite content of plagioclase (mole%) with respect to solid mass (g.) under decompressional crystallization followed by isobaric cooling conditions.

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Figure 9b The anorthite and albite rich zones and formation of normal/reverse zoning in plagioclase under decompressional crystallization followed by isobaric cooling conditions.

Figure 10 The change in total pressure (bars) with respect to solid mass (g.) under polybaric -isothermal convection conditions.

Figure 11 The change in temperature (o C) with respect to solid mass (g.) under polybaric

-isothermal convection conditions.

Figure 12 The change in dissolved water content of melt (wt%) with respect to solid mass (g.) under polybaric -isothermal convection conditions.

Figure 13a The change in anorthite content of plagioclase (mole%) with respect to solid mass (g.) under polybaric -isothermal convection conditions.

Figure 13b The anorthite and albite rich zones and formation of oscillatory zoning in plagioclase under polybaric -isothermal convection conditions.

_ 3 Figure 14 Change inV Na2O (cm /moles) with the increase in pressure from 1000 bars to

2000 bars.

_ 3 Figure 15 Change inVCaO (cm /moles) with the increase in pressure from 1000 bars to

2000 bars.

Chapter 3

Figure 1 Simplified structural map of Turkey showing the main fault systems and volcanic provinces. The black rectangle is the CAV: Central Anatolian Volcanic

Province. WAV: West Anatolian Volcanics, GV: Galatean Volcanics, EAV: East

Anatolian Vocanics.

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Figure 2a The population density, n, is found by measuring the slope of the curve on the

cumulative number versus size plot.

Figure 2b The slope of the line on a plot of ln(n) versus L is the negative reciprocal of

the product of the residence time τ , and the crystal growth rate, G.

Figure 3 An example of the outlined plagioclase crystals by using IP Lab software and produced plagioclase maps colors indicating different class sizes.

Figure 4 An example of the outlined clinopyroxene crystals by using IP Lab software and produced clinopyroxene maps colors indicating different class sizes.

Figure 5 Plagioclase crystal size distribution (CSD) for Small Hasandag basalt. Linear regression of the data points gives a slope of -15.896 mm-1 and an intercept of 16.454 cm4

with a correlation coefficient of 0.98.

Figure 6 Clinopyroxene crystal size distribution (CSD) for Small Hasandag basalt.

Linear regression of the data points gives a slope of -29.075 mm-1 and an intercept of

16.676 cm4 with a correlation coefficient of 0.99.

LIST OF TABLES

Chapter 1

Table 1 Chemical composition of Small Hasandag volcanic rocks (basaltic andesite to rhyolite) in terms of weight percent of oxides (reported on anhydrous basis). Rocks have

been analyzed by XRF method.

Chapter 2

Table 1 Anhydrous chemical composition of Pu’u O’o basalt.

Table 2 Solid mass (g.), total pressure (bars), temperature (o C), dissolved water content

in the melt (wt%) and anorthite content (mole%) of plagioclase during decompressional

and isobaric crystallization intervals.

Table 3 Solid mass (g.), total pressure (bars), temperature (o C), dissolved water content

in the melt (wt%) and anorthite content (mole%) of plagioclase during polybaric and

isothermal crystallization intervals.

o 3 Table 4a Na2O (wt%), temperature ( C), pressure (bars), nNa2O (moles), and V (cm ). t

Table 4b CaO (wt%), temperature (o C), pressure (bars), nCaO (moles), and V (cm3). t

_ _ 3 3 o Table 5 V Na2O (cm /moles) andVCaO (cm /moles) at 1300 C and pressures of 1000

and 2000 bars.

Chapter 3

Table 1 Plagioclase Crystal Size Distribution (CSD) Table. “L interval” is the size range

of a group of measurements, in mm. “L mean” is the average measurement for that bin in

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mm. “L range” is the span of observed lengths for that bin in mm. “N” is the number of

2 3/2 3 crystals in that bin. “NA”=N/total area of measurement in mm and “NV”=NA in mm .

“n”=NV/L range and “ln(n)” = the natural log of n.

Table 2 Clinopyroxene Crystal Size Distribution (CSD) Table. “L interval” is the size

range of a group of measurements, in mm. “L mean” is the average measurement for that

bin in mm. “L range” is the span of observed lengths for that bin in mm. “N” is the

2 number of crystals in that bin. “NA”=N/total area of measurement in mm and

3/2 3 “NV”=NA in mm . “n”=NV/L range and “ln(n)” = the natural log of n.

LIST OF APPENDICES

Appendix A

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Chapter 1

Role of Fractional Crystallization, Magma Recharge, and Magma Mixing in the

Differentiation of the Small Hasandag Volcano, Central Anatolia, Turkey

Gokce Ustunisik1 and Attila Kilinc1

1 Department of Geology, University of Cincinnati, Cincinnati, OH, 45221-0013, USA

[In review for publication in Lithos]

Abstract:

During the last seven million years, eruptions of the Small Hasandag composite volcano in Central Anatolia, Turkey have produced calc-alkaline lavas ranging in composition from basalt to rhyolite. Published research on this volcano suggests that crystal fractionation and magma mixing are the two important processes controlling the differentiation of the Small Hasandag magmas. The shortcomings of these researches are that neither the intensive variables (P, T, fO2) nor the constraints under which the

presumed parental magmas evolved have been quantitatively evaluated.

In this study, the MELTS algorithm of Ghiorso and Sacks (1995) has been used to

determine the initial system parameters in terms of temperature (T), pressure (P), oxygen

fugacity (fO2), and water content (wt% H2O) and then the consequences of magma differentiation under closed system fractional crystallization, magma recharge, and magma mixing conditions have been evaluated separately. In order to determine the initial system parameters, approximately 100 isobaric fractional crystallization simulations of the parental basaltic andesite magma (Mg#68) were carried out in the pressure range of 1 bar to 10 000 bars, fO2 range of QFM+1 to QFM+3 and at water

contents from 0 to 4 wt%. The best agreement between the computed melt compositions

and the natural rocks was achieved at P=1000 bars, fO2=QFM+1, and 2 wt% water.

Computations with parental basaltic andesite at these initial system conditions and under

isobaric fractional crystallization generated melt compositions from basaltic andesite to

dacite that is very similar to observed lava compositions. Compositions more evolved

than dacites however, cannot be produced by closed system fractional crystallization

alone. This is because rhyolites generated by closed system fractional crystallization have

lower total alkali (Na2O+K2O) values compared to the Small Hasandag rhyolites.

Furthermore, natural rock compositions in the silica range of 62-65 wt% have discrete cycles of sudden increase and decrease in the MgO content in the range of 0.5-1 wt% which suggests the signs of magma replenishment.

This study shows that fractional crystallization and magma recharge in the composition range of basaltic andesite to dacite, followed by isobaric-isenthalpic mixing of dacite with the most differentiated rhyolite (Mg#46) generated melt compositions most closely resembling the entire compositional range of the Small Hasandag lavas, including the rhyolites. Therefore, the agreement between the liquid line of descent defined by the natural lavas and MELTS calculations and the agreement between the observed mineralogy of the rocks and calculated order of crystallization corroborate the conclusion that the fractional crystallization and magma recharge in the silica range from basaltic andesite to dacite followed by isobaric-isenthalpic mixing of dacite and rhyolite is the major controlling process in the differentiation of the Small Hasandag magmas.

Keywords Small Hasandag volcano. magma recharge. isobaric-isenthalpic magma

mixing. isobaric-isothermal magma mixing. MELTS algorithm

1. Introduction:

The Small Hasandag volcano is one of the three calc-alkaline volcanoes in Central

Anatolia (Hasandag Volcano, Small Hasandag Volcano, and Erciyes Volcano). It has

erupted many times during the past seven million years covering an extensive portion of

this region with its lava flows and pyroclastic materials (Daniel et al., 1998). It is an

excellent example of a subduction zone calc-alkaline volcano, and provides a well-

exposed suite of rocks ranging in composition from basalt to andesite, dacite, and

rhyolite.

Previous studies on the petrology and geochemistry of the Hasandag volcanics

have provided a detailed geological map of the Hasandag and the Small Hasandag

volcanoes, a discussion of the regional stratigraphy, descriptions of lava flows and

pyroclastic materials, and some age determinations based on K/Ar isotopes (Ercan et al.,

1990; Daniel et al., 1998; Aydar and Gourgaud, 1998). In their interpretations of the

petrogenesis of the Hasandag volcanics, these authors emphasized different processes.

For example, to explain the wide range on compositional diversity exhibited by volcanic

rocks, Aydar and Gourgaud (1998) suggested that fractional crystallization was the

governing process for evolution of Hasandag magma based on decreasing MgO and TiO2 and increasing Na2O and K2O with increasing SiO2. On the other hand, Daniel et al

(1998) suggested that magma mixing dominates the petrogenesis of intermediate

compositions (i.e. andesites and dacites) based on least-square calculations between

3 basaltic and rhyolitic end members. In addition to being contradictory, these conclusions do not provide a quantitative evaluation of the proposed processes.

A corollary of the fractional crystallization conclusion of Aydar and Gourgaud

(1998) based on linear trends shown in the Harker diagrams is that crystal fractionation processes under different initial state of a system conditions and different constraints follow the same path. If this assumption were true, fractional crystallization taking place under different initial state of the system would produce melts of the same composition.

This is clearly not true because crystal fractionation can take place under isobaric (Druitt and Bacon, 1989) or polybaric (Kuritani, 1999), isentropic (Blundy and Cashman, 2005), or even isochoric (constant volume) conditions and in each case path of magma evolution is different. In other words, even though Harker diagrams may suggest crystal fractionation, they do not give information about the initial state of the system. Therefore, even if crystal fractionation were the controlling process at the Small Hasandag volcano, the initial state of the system that produced the rocks under fractional crystallization constraint is still not known.

Fluid dynamics and thermodynamics of magma mixing suggest that this is a very complicated process and bringing two magmas together in a magma chamber does not necessarily result in mixing of these two magmas (Huppert and Sparks, 1980; Sparks and

Marshall, 1986; Russell, 1990). Magma mixing calculation as modeled by the least- square calculations of Daniel et al (1998) was based only on mass transfer of oxides between a mafic and a felsic magma to generate the intermediate hybrid compositions. In their calculations intensive variables of mixing (P, T, and fO2) are not specified and yet these variables can alter the results of the calculations significantly. Most importantly, in

a quantitative analysis of magma mixing, not only mass transfer but also heat transfer

between two magmas should be considered. Magma mixing in nature almost always

involves mixing of a more primitive magma at higher temperature with a more

differentiated magma at lower temperature. Thermodynamic principles applied to this

process require that the total heat content of the system must be constant and equal to the

sum of the enthalpies of the two magmas. Therefore, a realistic and geologically

reasonable modeling of magma mixing at a given depth must be carried out under isobaric-isenthalpic conditions (Dogan et al, 2007).

In this study, first the initial system state of the Small Hasandag parental magma

were determined in terms of P, T, wt% H2O, and fO2. Having constrained initial state of

the system, then magma evolution paths under isobaric fractional crystallization,

isothermal magma recharge followed by isobaric-isenthalpic magma mixing conditions

were calculated.

2. Mineralogy of Small Hasandag Volcanic Rocks:

Daniel et al., 1998 and Aydar and Gourgaud (1998) presented a very detailed

petrographic description of the Hasandag volcanics. The following is a brief description

of the petrographic analysis of the thin sections of the Small Hasandag volcanic rocks.

Porphyritic basaltic andesite shows some glomeroporphyrtic and intersertal

textures. The characteristic mineralogical composition includes plagioclase,

clinopyroxene, orthopyroxene, Fe-Ti oxides, and ±olivine as phenocrysts and microlitic

feldspar, orthopyroxene, and Fe-Ti oxides as microphenocrysts in the groundmass.

Plagioclase phenocrystals have some spongy zones at rim and at the center of the crystal

and extensive compositional zoning. Some clinopyroxene crystals exhibit sector zoning.

Porphyritic andesite and dacites show glomeroporphyrtic and intersertal textures.

Characteristic mineralogical assemblage in andesite and dacites includes plagioclase,

clinopyroxene, orthopyroxene, sanidine, Fe-Ti oxides, ±amphibole, ±biotite, and ±quartz

as phenocrysts and microlitic feldspar and Fe-Ti oxides as microphenocrysts in the

groundmass. Corroded plagioclase and orthopyroxene crystals and extensive

compositional and oscillatory zoning in plagioclase phenocryts are very common features

in the Small Hasandag andesites and dacites. The characteristic mineralogical

composition in rhyolites includes plagioclase phenocrystals and Fe-Ti oxides as

microphenocrysts in the groundmass. The presence of minor biotite and amphibole in

andesites and dacites indicates that initial magma composition have some water to

stabilize them at some stage in their differentiation.

3. Chemical Composition of Small Hasandag Volcanic Rocks:

In Table 1, 57 analyses of Small Hasandag volcanic rocks were presented ranging

in composition from basaltic andesite to rhyolite (Fig.1). Analyses were performed by X-

ray fluorescence (XRF) methods at department of Geology, University of Cincinnati.

Chemical compositions have been reported in anhydrous basis.

Harker diagrams in Figure 2 show that TiO2, Al2O3, FeO*, MgO, and CaO decrease and K2O increases with increasing SiO2 content. Although these linear trends

can be interpreted as representing either fractional crystallization of the parental basaltic

andesite or mixing of parental basaltic andesite with a rhyolitic magma, as stated earlier,

the identity and magnitude of intensive variables controlling either of these processes

cannot be recovered from these diagrams.

In order to model the evolution path of a magmatic system quantitatively it is

necessary to specify (1) initial conditions of the system in terms of its pressure (P),

temperature (T), oxygen fugacity (fO2) and water content (wt% H2O), and (2) constraints

under which magma evolution must proceed. Accordingly, first the physical parameters

of the parental magma were determined and then (1) isobaric fractional crystallization

and (2) magma recharge followed by isobaric-isenthalpic magma mixing were tested

using the MELTS algorithm (Ghiorso and Sacks, 1995) to model the evolution of the

Small Hasandag magmas.

4. MELTS Calculations to Constrain the Initial System Parameters:

MELTS algorithm of Ghiorso and Sack (1995) is widely used for modeling magmatic systems (Asimow et al., 2001; Kress and Ghiorso, 2004; Dogan et al., 2007).

In isobaric-isothermal computations Gibbs free energy of the system is minimized. In the

P, T, and fO2 constraint calculations, the MELTS algorithm minimizes the Korzhinki ⎛ ∂G ⎞ potential ( L = G − n O2 ⎜ ⎟ ) for systems open to oxygen transfer, and in adiabatic ⎝ ∂nO2⎠ calculations, it minimizes the enthalpy subject to fixed P and heat content. Once the

starting composition, initial system parameters, and the constraint on magma evolution are specified, MELTS calculates the composition of crystallizing minerals, the end- member compositions of solid solution minerals, and the composition of residual liquid at

each temperature and pressure.

To constrain the initial system parameters (P, T, fO2, and wt% H2O) of the Small

Hasandag parental magmas, the melt compositions that would be generated from a

parental basaltic andesite magma were calculated under isobaric fractional crystallization

conditions in the pressure range of 1 bar to 10,000 bars, fO2 range QFM+1 to QFM+3,

and H2O content=0-4 wt%. Compositions of calculated melts were then compared with

those of the Small Hasandag volcanic rock series. The results show that the basaltic

andesite parental magma with 2 wt% H2O evolving under fractional crystallization

conditions generates melts like those of the eruptive products of the Small Hasandag

volcano at a depth of about four kilometers below the surface (P~1000 bars). Following

is a brief explanation about determination of system parameters.

4.1. Parental Magma Composition:

A basaltic andesite (Mg#≈68, Table 1) is used as the anhydrous parental magma

composition. This is the most mafic of all the rocks have been studied and represents the

“most primitive” of all the rocks in the SiO2 -Na2O+K2O plot (Fig. 1). Although the role

of various water concentrations ranging from 0 wt% to 4 wt% will be discussed in the

“Initial System Water Contents’ section, to fix the initial system pressure and oxygen fugacity, 2 wt% water was added to the basaltic andesite and used that as the parental

magma composition in the MELTS calculations due to the existence of biotite and

amphibole in Small Hasandag lavas.

4.2. Initial System Pressure:

To constrain the pressure of parental magma composition, the compositions of

melts generated were calculated under fractional crystallization constraint at 1, 1000,

3000, 5000, and 10,000 bars. The best agreement between the calculated melt

compositions and the Small Hasandag volcanic rocks is attained at P=1000 bars (Fig. 3a).

The results show that the simulations at 1 bar can only produce the compositional

spectrum of the Small Hasandag from basaltic andesites to dacites but not the rhyolites

(Fig. 3c). At the very high pressure end of our computations, simulations at 10,000 bars

showed that although computed compositions can generate the whole spectrum of rocks

from basaltic andesite to rhyolite, computed rhyolite compositions have much lower

Na2O+K2O values than the natural rhyolites (Fig. 3b). Compositions generated at 3000

and 5000 bars generated a liquid line of descent similar to that of the Small Hasandag

rock spectrum in total alkali-silica diagram, but in MgO-TiO2, MgO-CaO, and SiO2-

Fe2O3 diagrams calculated and observed rock compositions differed significantly.

Calculations at 1000 bars faithfully reproduced the compositions of the Small Hasandag rocks ranging in composition from basaltic andesite to rhyolites in total alkali-silica as well as in oxide-oxide diagrams. On this basis, it was concluded that 1000 bars best represents the initial system pressure for the Small Hasandag magma.

4.3. Initial System Oxygen Fugacity:

Simulations were carried out at oxygen fugacity range of QFM+1 - QFM+3 using the basaltic andesite parental magma (with 2 wt% water) composition at 1000 bars.

Figure 4 shows the composition of melts produced at QFM, QFM+1 and QFM+2 buffer

conditions.

Comparison of calculated melt compositions with actual rock compositions of

Small Hasandag in MgO versus FeO* (total FeO) space, showed that initial system

oxygen fugacity is best defined at QFM+1 (Fig. 4a). Imposing one and two log units

above the QFM buffer conditions (QFM+1 and QFM+2) on the system, however, causes

lower degree of oxidation of iron from Fe+2 and Fe+3 and the melts generated do not

faithfully reproduce the composition of the Small Hasandag volcanic rocks (Fig. 4b and

4c).

4.4. Initial System Water Content:

Having constrained the both pressure and oxygen fugacity conditions, at P=1000

bars and fO2=QFM+1, next the effect of different water concentrations were evaluated ranging from 0 wt% to 4 wt% in SiO2 versus K2O space. Calculated melt compositions at

P=1000 bars, fO2=QFM+1 produced the similar compositions to Small Hasandag

magmas at H2O content=2 wt% (Fig. 5c). The results show that simulations under 2 wt%

H2O generate derivative melts which have higher SiO2 and lower K2O values than the

Small Hasandag natural rocks (Fig. 5a and 5b). The computations above 2 wt% H2O can only produce the compositional spectrum of the Small Hasandag andesites and dacites, but can not produce any rhyolites. This limits the amount of water in Small Hasandag magma to 2 wt%.

5. Testing Isobaric Fractional Crystallization Hypothesis:

Having constrained the initial system parameters of Small Hasandag magma, a

basaltic andesite composition (Mg#≈68, Table 1) at 1000 bars and fO2=QFM+1 with 2

wt% water was used as a starting material in open system fractional crystallization

calculations to test the hypothesis that “if the evolution of the Small Hasandag magma is

controlled by isobaric open system crystal fractionation process then calculations

involving the parental basaltic andesite magma with 2 wt% H2O at 1000 bars and

fO2=QFM+1 will produce a liquid line of descent identical to the observed liquid line of

descent on the Harker type diagrams”.

The liquidus temperature of the basaltic andesite magma at 1000 bars and

o fO2=QFM+1 is ≈1200 C. In the isobaric crystal fractionation computations, the

temperature of the magma is reduced 10 oC at each step of the crystallization process.

The calculated melt compositions under isobaric fractional crystallization conditions and the composition of the Small Hasandag rocks are shown in Fig. 6 in terms of SiO2 versus

TiO2, Al2O3, FeO*, MgO, and CaO bivariate plots. These figures show that isobaric

fractional crystallization of basaltic andesite magma can not produce liquid line of

descent that agrees well with the chemical trend of the Small Hasandag rocks. The

decrease in FeO* and MgO reflects crystallization of Mg rich olivine and orthopyroxene

(Fig. 6c and 6d). Decrease in TiO2 and FeO* is in response to crystallization of Fe-Ti

oxides (Fig 6a and 6c). Decrease in Al2O3 and CaO suggests crystallization of plagioclase

(Fig. 6b and 6e). The decrease in MgO and CaO reflects crystallization of clinopyroxene

(Fig. 6d and 6e). Although, the calculated melt compositions are in agreement with the

Small Hasandag rocks in some bivariate plots including SiO2-TiO2, SiO2-FeO*, SiO2-

CaO, and SiO2-K2O; there are still major discrepancies in SiO2-Al2O3 and SiO2-MgO plots. In calculations involving isobaric crystal fractionation of basaltic andesite, simulated melts compositions have much lower SiO2 and Al2O3 values compared to those

of the Small Hasandag (Fig. 6b). Similarly, computed melt compositions have lower SiO2 and MgO values than the Small Hasandag volcanic rocks (Fig. 6d).

Although isobaric fractional crystallization of the parental basaltic andesite can generate the compositions from basaltic andesite to dacite in total alkali-SiO2 diagram, the computations showed that the rhyolitic compositions produced by closed system fractionation have lower total alkali (Na2O+K2O) values compared to the natural rocks

(Fig. 3a). It is also noted that, in total alkali-SiO2 diagram, these higher alkali, higher

silica rhyolites are separated from the rest of the rocks and do not follow a linear

relationship with andesites and dacites. These observations coupled with the previous

workers’ field observation of presence of cognate inclusions and banding and thin section

observations of volcanic rocks (for example reverse zoning in plagioclase) support the conclusion that magma recharge and magma mixing may have played a significant role in the differentiation of the Small Hasandag magmas. Therefore, the hypothesis that the

mode of crystallization controlling the evolution of the Small Hasandag magmas is open

system fractional crystallization is rejected. Having rejected the fractional crystallization

hypothesis, the magma recharge and magma mixing hypotheses were tested seperately.

6. Testing Magma Recharge Hypothesis:

In SiO2 - MgO plot, Small Hasandag lavas show several fluctuations in MgO in

the SiO2 range of 62 to 65 wt% which can be interpreted as a clear sign of magma

recharge. Figure 7a shows the SiO2 - MgO plot for the Small Hasandag compositions

from basaltic andesite to rhyolite. Figure 7b shows the part of Figure 7a in the SiO2

interval of 62 wt% to 65 wt%. There are 12 major spikes in MgO in the silica range of

62-65 wt% and most of these spikes are in the range of 0.5-1% of MgO or even locally greater.

A physical model for the magma recharge process at the Small Hasandag volcano can be visualized as follows. Consider a shallow magma chamber in the crust connected

to a magma source, which is basaltic andesite in composition. Initially basaltic andesite

fills the shallow magma chamber and undergoes some fractional crystallization under

isobaric conditions. At this stage of evolution of this magma, small amount (about 5%)

basaltic andesite is injected to the magma chamber. Less evolved injected magma and

somewhat more evolved resident magma mix isothermally and the new magma starts

differentiating again under isobaric fractional crystallization conditions. This process is

repeated several times. At each injection of less evolved magma, the MgO content of the

mix magma increases and then isobaric fractional crystallization causes MgO to decrease.

This process of repeated magma recharge is thought what caused the MgO fluctuations in

the SiO2 – MgO plot shown in Figures 7a and 7b.

7. Testing Isobaric-Isenthalpic Magma Mixing Hypothesis:

Magma mixing can be treated as an isothermal or isenthalpic process.

Geologically isothermal process is a highly improbable case because it requires both the

resident magma and mixing magma be at the same temperature. Since magma mixing by

and large involves mixing of a more primitive magma (typically at a higher temperature)

with a more differentiated magma (typically at a lower temperature), isobaric-isothermal

conditions are unrealistic for magma mixing. Calc-alkaline volcanoes are open systems,

which mean that periodically less differentiated magma enters into the resident magma

chamber, causing mingling, mixing, or eruption (Sparks et al., 2000). In our opinion, a more realistic and geologically reasonable condition is keeping the enthalpy of the system constant and equivalent to the sum of enthalpies of the two magmas (isobaric-isenthalpic conditions).

To summarize the two-step model for the Small Hasandag volcano we explain the injection of basaltic andesite magma into a shallow magma chamber then repeated magma recharge process under isothermal conditions and finally the isenthalpic mixing of the last dacitic liquid with the rhyolitic magma which is common at the Hasandag volcanic province.

In order to model the evolution of the Small Hasandag volcano, Ghiorso and

Sacks (1995) MELTS software is used in this two-step differentiation process (isothermal magma recharge followed by isobaric-isenthalpic magma mixing). In the model, the starting temperature is selected at the liquidus temperature of the parental basaltic andesite (Mg#≈68, Table 1) and after it differentiated a little under isobaric conditions,

5% of the parental basaltic andesite is added to the remaining composition as the

differentiation proceeds until magma composition changed to most differentiated dacite.

Then, 5% hotter last dacitic composition is mixed with 95% of cooler rhyolitic magma

(Mg#≈46, Table 1) under isobaric-isenthalpic conditions (P=1000 bars, fO2=QFM+1). In

such a scenario, the dacitic magma cools and partially crystallizes while; the rhyolitic

magma is heated and some of its existing minerals may dissolve in the new mixed

magma. In this case, the heat released by crystallization of dacitic magma is used to heat

the rhyolitic magma. The MELTS algorithm calculates the composition of mixed melts

and coexisting minerals as the temperature of magma decreases at constant pressure.

These calculated melts ranged in composition from parental basaltic andesite to rhyolite.

In Figure 8, the melts generated by isothermal recharge of differentiated basaltic andesite until dacite followed by isobaric-isenthalpic magma mixing of this dacite with rhyolite

and the compositions of the Small Hasandag volcanic rocks are compared in terms of

major oxide Harker diagrams. In Figure 9 the calculated melt compositions with (a)

isobaric fractional crystallization of basaltic andesite and (b) isothermal recharge

followed by isobaric-isenthalpic mixing of dacite with rhyolite and the compositions of the Small Hasandag volcanic rocks in terms of total alkali-silica diagram are superimposed. The very good agreement between the calculated melt compositions and the Small Hasandag rocks supports the conclusion that isothermal recharge and isobaric- isenthalpic magma mixing is the controlling process for the chemical diversity of volcanic rocks at the Small Hasandag volcano (Fig. 8 and Fig. 9b). Also the computed melt compositions by isothermal recharge and isobaric-isenthalpic magma mixing and the natural rock composition in Small Hasandag are superimposed in SiO2 – MgO plot (Fig.

10). The isobaric-isothermal recharge of differentiated basaltic andesite to the remaining

magma during the differentiation from parental basaltic andesite to dacite has

successfully produced the discrete jumps in MgO content with the evolving SiO2. It is perhaps appropriate to discuss the rationale for isothermal mixing of less differentiated and somewhat hotter basaltic andesite magma with more differentiated and slightly cooler magma. Since only 5% of less differentiated is being added to 95% more differentiated magma, it will not significantly change the temperature of the cooler magma. Thus isothermal mixing at the temperature of the cooler magma is justified.

In order to determine the sequence of crystallization of minerals under isothermal recharge and isobaric-isenthalpic mixing conditions and to compare the generated minerals under this mixing model with the thin section observations of the Small

Hasandag rocks, MELTS algorithm is again used and allowed the mixed magma to crystallize. The sequence of crystallization of minerals as a function of temperature is recorded as the major minerals appearing in the order of olivine, orthopyroxene, plagioclase, clinopyroxene, and spinel.

The agreement between the liquid line of descent defined by the natural rocks and the MELTS calculations coupled with the agreement between the observed mineralogy of the rocks and calculated sequence of crystallization corroborate the conclusion that isothermal recharge followed by isobaric-isenthalpic magma mixing is the dominant process in the differentiation of the Small Hasandag magmas.

7. Conclusions:

The initial system parameters (P, T, fO2, and wt% H2O) of the Small Hasandag

magma were constrained by carrying out approximately 100 isobaric fractional

crystallization simulations of the most mafic basaltic andesite magma in the pressure range of 1 bar to 10,000 bars, fO2 range of QFM+1 to QFM+3 and at water contents from

0 to 4wt%. Using the comparison of calculated melts compositions and chemical

diversity by the natural rock data, the initial conditions of the Small Hasandag magma is

constrained to P=1000 bars, fO2=QFM+1, and H2O content=2 wt%. Based on these

initial system conditions, the MELTS algorithm is used to calculate the compositions of

melts formed from parental basaltic andesite magma under isobaric fractional

crystallization conditions (P=1000 bars). Results show that this process can generate a

wide range of compositions of the Small Hasandag volcanic rocks from basaltic andesite

to dacite, but not rhyolites. Moreover, in several Harker diagrams, the computed melt

compositions are in major disagreement with the chemistry of the Small Hasandag

volcanic rocks. Particularly, in SiO2 – MgO plot, the 0.5-1% jumps in the MgO content with the evolving silica can not be explained by simple fractional crystallization. In contrast, successive isobaric fractionation and magma recharge in the silica ranges of 62-

65 wt% (from basaltic andesite to dacite) followed by isobaric-isenthalpic magma mixing between dacite and rhyolite compositions at 1000 bars produced melt compositions that agree very well both with the chemistry and the mineralogy of the Small Hasandag volcanic suites. Calculations indicate that magma recharge followed by isobaric- isenthalpic magma mixing is the major controlling process in the evolution of the Small

Hasandag magmas.

8. Acknowledgments:

The authors are grateful to Stearn A. Morse at University of Massachusetts for his critical

and constructive comments in the earlier version of the manuscript.

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Table 1

Sample Number SiO2 TiO2 Al2O3 FeO* MnO MgO CaO Na2O K2O P2O5 Total Mg number GU-07-08 56.28 0.93 16.09 6.10 0.12 6.82 7.90 4.04 1.25 0.28 99.82 67.40 GU-07-07 64.23 0.65 17.31 4.14 0.09 1.72 5.38 3.48 2.42 0.21 99.64 66.03 GU-07-06 63.35 0.68 17.16 4.48 0.09 2.06 5.68 3.43 2.42 0.25 99.60 65.27 GU-06-11 59.33 0.77 18.18 5.32 0.10 3.83 6.93 3.54 1.53 0.22 99.75 56.16 GU-06-28 59.48 1.01 16.99 5.69 0.13 3.62 6.88 3.63 1.97 0.34 99.74 53.15 GU-06-03 62.08 0.56 15.76 3.99 0.09 2.10 9.93 3.05 2.24 0.29 100.08 48.44 GU-06-70 62.13 0.64 16.41 4.08 0.08 3.37 7.22 4.20 1.84 0.19 100.17 59.56 GU-06-73 61.85 0.68 17.50 4.66 0.10 2.38 6.64 3.10 2.39 0.27 99.59 47.68 GU-06-09 62.08 0.60 15.91 3.93 0.09 2.16 9.70 2.73 2.42 0.31 99.94 49.47 GU-06-13 62.10 0.66 16.92 4.68 0.10 2.67 6.19 4.10 2.15 0.25 99.82 50.40 GU-07-10 62.89 0.57 15.91 3.82 0.09 2.43 8.53 3.19 2.13 0.32 99.88 48.94 GU-06-32 62.06 0.68 18.06 4.24 0.09 2.10 6.48 3.36 2.19 0.30 99.56 46.82 GU-06-55 62.05 0.72 16.87 4.81 0.10 2.89 6.34 3.14 2.29 0.30 99.51 51.67 GU-06-23 62.46 0.60 17.03 3.92 0.09 2.03 7.91 3.28 2.28 0.26 99.86 48.05 GU-07-28 59.48 1.01 16.99 5.69 0.13 3.62 6.88 3.63 1.97 0.34 99.74 53.94 GU-06-37 62.45 0.62 18.05 4.47 0.10 2.23 5.98 3.41 2.01 0.25 99.58 47.10 GU-06-15 62.66 0.66 17.14 4.38 0.08 3.23 6.08 3.70 1.72 0.19 99.84 56.84 GU-06-52a 62.61 0.72 16.60 4.94 0.10 3.16 5.85 3.66 1.84 0.27 99.76 53.26 GU-06-08 62.81 0.67 17.08 3.96 0.09 2.03 5.87 5.04 2.09 0.30 99.94 47.70 GU-06-25 62.73 0.68 17.09 4.47 0.09 3.11 5.61 3.76 2.03 0.20 99.78 55.34 GU-06-48 62.95 0.63 16.32 3.91 0.07 3.55 6.47 4.21 1.73 0.21 100.04 61.78 GU-06-72 62.95 0.65 16.60 4.20 0.08 3.21 6.42 3.97 1.73 0.19 100.00 57.64 GU-06-10 62.89 0.57 15.91 3.82 0.09 2.43 8.53 3.19 2.13 0.32 99.88 53.12 GU-06-17 62.83 0.66 16.73 4.58 0.09 2.48 7.00 3.10 2.03 0.24 99.74 49.15 GU-06-49 63.02 0.62 16.71 4.14 0.08 3.18 6.14 4.09 1.81 0.19 99.97 57.83 GU-06-57 62.93 0.65 17.25 4.44 0.09 2.23 5.71 3.64 2.48 0.22 99.66 47.27 GU-07-09 63.15 0.74 16.23 4.66 0.09 2.94 5.49 4.27 2.04 0.26 99.89 52.96 GU-06-50 63.14 0.63 16.86 4.07 0.09 2.46 6.48 3.65 2.02 0.28 99.89 51.87 GU-06-01 63.39 0.56 16.18 3.78 0.08 1.96 7.76 3.64 2.31 0.26 99.94 48.11 GU-06-53 63.32 0.63 16.49 4.09 0.09 2.60 6.02 4.07 2.23 0.26 99.94 53.14

GU-06-05 63.40 0.65 16.82 4.16 0.08 3.03 5.49 4.13 1.90 0.20 99.87 56.46 GU-06-54 63.38 0.68 16.95 4.16 0.08 3.10 5.34 3.87 2.05 0.19 99.80 57.01 GU-06-51 63.25 0.65 17.12 4.40 0.10 2.27 5.83 3.23 2.43 0.26 99.80 47.95 GU-06-06 63.35 0.68 17.16 4.48 0.09 2.06 5.68 3.43 2.42 0.25 99.60 45.01 GU-06-52b 63.60 0.66 16.78 4.26 0.09 3.04 5.41 3.96 1.86 0.19 99.85 56.01 GU-06-56 63.67 0.64 16.75 3.89 0.08 2.83 5.33 4.01 2.24 0.27 99.71 56.47 GU-06-78 63.89 0.65 16.63 4.07 0.08 2.97 5.29 4.14 1.94 0.21 99.87 56.52 GU-06-12 63.84 0.63 16.96 4.17 0.09 1.97 5.53 4.01 2.31 0.23 99.75 45.67 GU-06-16 64.01 0.65 16.97 4.13 0.09 1.94 5.49 3.93 2.31 0.23 99.75 45.61 GU-06-07 64.23 0.65 17.31 4.14 0.09 1.72 5.38 3.48 2.42 0.21 99.64 42.61 GU-06-02 64.40 0.64 16.24 4.16 0.09 2.13 6.04 3.66 2.24 0.22 99.82 47.78 GU-07-12 64.56 0.63 16.24 4.36 0.09 2.63 5.29 3.94 2.05 0.16 99.94 51.83 GU-06-14 64.45 0.65 16.58 4.19 0.09 2.14 5.60 3.59 2.17 0.23 99.70 47.72 GU-06-04 64.66 0.64 16.16 4.18 0.09 2.00 5.53 3.90 2.41 0.23 99.80 46.03 GU-07-11 64.81 0.67 16.21 4.20 0.08 2.55 5.24 3.92 2.09 0.16 99.94 51.94 GU-07-38 65.52 0.56 16.42 3.89 0.08 2.29 4.91 3.83 2.21 0.16 99.86 51.18 GU-06-18 65.82 0.60 15.92 3.91 0.09 1.69 5.40 3.73 2.20 0.30 99.66 43.54 GU-07-18 66.23 0.52 15.64 3.55 0.08 2.36 4.72 4.44 2.26 0.19 99.98 54.17 GU-07-19 66.24 0.52 15.92 3.57 0.08 2.27 4.51 4.28 2.42 0.15 99.95 53.11 GU-07-05 67.91 0.28 13.47 2.17 0.06 1.21 8.70 2.73 3.83 0.08 100.45 49.90 GU-07-04 72.32 0.26 14.08 2.07 0.06 0.83 2.75 3.11 4.16 0.06 99.71 41.75 GU-07-22 72.88 0.25 14.45 1.65 0.06 0.73 2.17 4.33 3.32 0.08 99.93 44.20 GU-07-23 73.00 0.26 14.23 1.72 0.06 0.76 2.17 4.42 3.29 0.07 99.99 44.07 GU-07-01 73.19 0.27 13.78 1.92 0.06 0.79 1.88 3.15 4.51 0.07 99.62 42.47 GU-07-03 73.49 0.25 14.30 1.83 0.07 0.46 2.10 3.88 3.40 0.08 99.86 31.11 GU-07-26a 75.28 0.13 13.17 0.65 0.05 0.31 0.71 4.14 4.38 0.03 98.85 69.05 GU-07-26b 74.56 0.14 13.53 0.64 0.05 0.80 0.89 4.39 3.87 0.04 98.91 46.05 GU-07-25 75.95 0.10 13.27 0.62 0.06 0.12 0.86 4.23 3.86 0.05 99.11 25.18

10 O (wt %)

2 8

O+K 6 2

Na 4

0 40 45 50 55 60 65 70 75 80

SiO2 (wt %)

Fig. 1

a. b.

1.5 20.0

18.0 1.0

(wt %) (wt %) 16.0 2 3

0.5 O 2 TiO

Al 14.0

0.0 12.0 55 60 65 70 75 80 55 60 65 70 75 80

SiO2 (wt %) SiO2 (wt %)

c. d.

8.0 7.0 6.0 6.0 5.0 4.0 4.0 3.0 2.0 MgO (wt %) MgO FeO* (wt %) FeO* 2.0 1.0 0.0 0.0 55 60 65 70 75 80 55 60 65 70 75 80

SiO2 (wt %) SiO2 (wt %)

e. f.

12.0 6.0 10.0 8.0 4.0 6.0 O (wt %)

4.0 2 2.0 CaO (wt %) K 2.0 0.0 0.0 55 60 65 70 75 80 55 60 65 70 75 80

SiO2 (wt % ) SiO2 (wt % )

Fig. 2

a. P=1000 bars b. P= 10 kbars

fO2=QFM+1 fO2=QFM+1 16 16 14 14 12 12 10 10 O (wt %)O (wt

O (wt %) 2 8

2 8 6 6 O+K O+K 2

2 4 4 Na

Na 2 2 0 0 40 45 50 55 60 65 70 75 80 40 45 50 55 60 65 70 75 80

SiO2 (wt %) SiO2 (wt %)

c. P= 1 bar fO2=QFM+1

H2O=0% 16 14 12 10 O (wt %)

2 8 6 O+K

2 4

Na 2 0 40 45 50 55 60 65 70 75 80

SiO2 (wt %)

Fig 3.

a. b. at QFM+1 at QFM+2

10.0 10.0 8.0 8.0 6.0 6.0 4.0 4.0

FeO* (wt%) 2.0 FeO* (wt.%) FeO* 2.0 0.0 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 0.01.02.03.04.05.06.07.0 MgO (wt %) MgO (wt %)

c. at QFM+3

10.0 8.0 6.0 4.0

FeO* (wt %) (wt FeO* 2.0 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 MgO (wt %)

Fig. 4

a. b. 0% H2O 1% H2O

6.0 6.0

4.0 4.0 O (wt %) O (wt%) 2

2 2.0 2.0 K K

0.0 0.0 55 60 65 70 75 80 55 60 65 70 75 80

SiO2 (wt %) SiO2 (wt %)

c. 2% H2O

6.0

4.0 O (wt %)

2 2.0 K

0.0 55 60 65 70 75 80

SiO2 (wt %)

Fig. 5

a. b.

1.5 20.0

18.0 1.0

(wt %) (wt 16.0 3 (wt %) (wt 2 O 0.5 2 14.0 Al TiO 12.0 0.0 55 60 65 70 75 80 55 60 65 70 75 80 SiO2 (wt % ) SiO2 (wt % )

c. d.

8.0 7.0 6.0 6.0 5.0 4.0 4.0 3.0 2.0

2.0 MgO %) (wt FeO* (wt %) FeO* (wt 1.0 0.0 0.0 55 60 65 70 75 80 55 60 65 70 75 80 SiO2 (wt % ) SiO2 (wt % )

e. f.

12.0 6.0 10.0 8.0 4.0 6.0

4.0 O (wt % ) 2.0 2 CaO (wt % ) 2.0 K 0.0 0.0 55 60 65 70 75 80 55 60 65 70 75 80

SiO2 (wt % ) SiO2 (wt % )

Fig. 6

7.0

6.0

5.0

4.0

3.0 MgO (wt %) 2.0

1.0

0.0 56.3 62.1 62.9 62.5 63.0 62.9 63.4 63.7 64.4 65.5 72.3 75.3

SiO2 (wt % )

3.8

3.3

2.8

2.3 MgO (wt %)

1.8

1.3 62.0 62.3 62.7 62.9 63.2 63.5 63.9 64.5

SiO2 (wt %)

Fig. 7

20.0 8.0

18.0 6.0

(wt %) 16.0 4.0 3 O 2

Al 14.0 (wt %) FeO* 2.0

12.0 0.0 55 60 65 70 75 80 55 60 65 70 75 80

SiO2 (wt %) SiO2 (wt %)

7.0 12.0 6.0 10.0 5.0 8.0 4.0 3.0 6.0 2.0 4.0 MgO (wt %) MgO CaO (wt %) 1.0 2.0 0.0 0.0 55 60 65 70 75 80 55 60 65 70 75 80

SiO2 (wt %) SiO2 (wt % )

6.0

4.0 O (wt %)

2 2.0 K

0.0 55 60 65 70 75 80

SiO2 (wt % )

Fig. 8

a. P=1000 bars fO2=QFM+1, 2 wt% H2O

10 O (wt.%) O

2 8

O+K 6 2

Na 4

0 40 45 50 55 60 65 70 75 80

SiO2 (wt %)

b. P=1000 bars fO2=QFM+1, 2 wt% H2O

10 O (wt %)

2 8

O+K 6 2

Na 4

0 40 45 50 55 60 65 70 75 80

SiO2 (wt %)

Fig. 9

7.0

6.0

5.0

4.0

3.0 MgO %) (wt 2.0

1.0

0.0 56.3 62.1 62.9 62.5 63.0 62.9 63.4 63.7 64.4 65.5 72.3 75.3

SiO2 (wt % )

Fig. 10

Chapter 2

New Insights into the Processes Controlling Plagioclase Zoning

Gokce Ustunisik1 and Attila Kilinc1

1 Department of Geology, University of Cincinnati, Cincinnati, OH, 45221-0013, USA

[Submitted to American Mineralogist for publication]

Abstract:

Although plagioclase is the most abundant mineral in crustal rocks, the factors

controlling compositional zoning in plagioclase are not fully understood. The

composition of plagioclase crystallizing in a magma chamber depends upon physical

parameters such as temperature (T) and total pressure (Ptotal), as well as the water

content of the melt (wt% H2O). Using computational thermodynamic algorithms, the

changes in these physical parameters can be modeled under various differentiation

scenarios and their effects on plagioclase zoning can be quantitatively evaluated. The

effect of temperature, total pressure, and water content on plagioclase zoning has

previously been experimentally investigated in the albite-anorthite (Ab-An) system. In

this study, the effects of P, T and water content of the melt on plagioclase zoning were quantitatively investigated in a basaltic system using the MELTS algorithm.

Recent advances in computational geochemistry have opened the door to exploring the consequences of different crystallization conditions on plagioclase zoning.

Plagioclase zoning is reported in a basaltic magma under two different scenarios. The

first model involves a two-step crystallization process. In step one, magma moves decompressionally from a deeper to a shallower chamber while crystallizing plagioclase.

In step two, the magma pools in the shallower magma chamber and continues to 33

crystallize isobarically. If these two steps are repeated, the result is the development of

reverse, normal, and oscillatory zoning in plagioclase. In the second model, plagioclase

zoning is explored in a large magma chamber where magma crystallizes as it convects. In

this model plagioclase develops oscillatory zoning.

Zoning in plagioclase is interpreted in terms of the partitioning of Na2O and CaO

components between the melt and plagioclase phases. The results show that the partial

molal volume of Na2O in the melt is larger than that of CaO. This means that at a given

temperature with decreasing pressure Na2O partitions in favor of the melt making the

coexisting plagioclase more An-rich. Thus, isothermal decompression of magma results

in the development of reverse zoning in plagioclase.

Keywords MELTS, convection, normal zoning, reverse zoning, oscillatory zoning

1. Introduction:

The recognition that plagioclase crystals in volcanic and plutonic rocks preserve records of differentiation processes has attracted the attention of many researchers who

concentrated on deciphering the information contained in the plagioclase zones to

reconstruct the evolution of magmatic systems (Anderson 1984, Blundy and Schimizu

1991, Davidson and Tepley 1997, Stewart and Fowler 2001, Couch et al. 2001, Ginibre et

al. 2002, Ginibre et al. 2007). The composition and stability of plagioclase depends upon

pressure, temperature, and melt composition including its water content. Physical

conditions such as the decompressional movement of magma and magma mixing can cause variation in these parameters, which in turn, control plagioclase zoning. Therefore, the development of physical models to understand the role of intensive variables on

34 controlling the compositional zoning in plagioclase and linking these parameters to the magmatic processes remains a challenge.

There has been a considerable amount of analytical and theoretical effort aimed toward understanding the role of physical parameters in plagioclase zoning (e.g., optical analysis, Nomarski interference imaging, Back-scattered electron images (BSE) and microanalysis). Up until 1972, interpretations of plagioclase zoning were based primarily on thin section observations (Vance 1965, Bottinga et al. 1966). Since then, numerical modeling (e.g., Allegre et al. 1981) has provided additional insights into the kinetics of plagioclase growth and resorption. Experimental studies in the Ab-An system have elucidated the influence of P, T and melt composition including its H2O content (e.g.,

Drake and Weill 1975, Bindeman et al. 1998). With the development of the electron microprobe and other high resolution imaging techniques (Laser Interferometry,

Nomarski Differential Interference Contrast, or NDIC), the quantitative analysis of major elements at a resolution of a few microns and 2-D compositional maps have been made possible (Pearce and Kolisnik 1990).

Since Homma’s (1932) interpretation that oscillatory zoned plagioclase in andesitic lavas records thermally driven magmatic convection cycles, several researchers have tried to correlate zoning in plagioclase with various dynamic stages and processes within the magma chamber. Most of the previous studies and models have concentrated on linking zoning profiles to magma mixing or magma recharge. Examples include, recharge with complete chemical mixing (Singer et al. 1995), recharge involving variable recharge rates (Ginibre and Worner 2007), and recharge characterized only by thermal effects (Couch et al. 2001, Ruprecht and Worner 2007). Alternative models include

decompression driven crystallization (Humphereys et al. 2006, Blundy et al. 2006). These

studies, however, do not take advantage of combining dynamics of magma movement

within the crust with computational thermodynamics algorithms such as MELTS

(Ghiorso and Sack 1995) to quantitatively evaluate of the role of P, T, and water content

of the melt on plagioclase zoning. Here this approach is taken to develop models for

plagioclase zoning in a crystallizing magma rising adiabatically from a deeper chamber

into a shallower chamber where it continues to crystallize isobarically as well as in a

convecting magma chamber within the crust.

In this contribution, the consequences of applying two new differentiation

scenarios to the development of normal, reverse, and oscillatory zoning in a basaltic

magma is tested by using the MELTS algorithm of Ghiorso and Sack (1995). In the first

scenario, a crystallizing magma is modeled as rising adiabatically from a deeper to a

shallower magma chamber where it continues to crystallize isobarically and then rises

again adiabatically to even a shallower magma chamber (Fig.1). In many explosively

erupting volcanoes magma pooling followed by fractional crystallization is a common

process (Elsworth et al. 2008). Although the consequences of decompressional and

isobaric crystallization on plagioclase zoning have been discussed as separate cases in

previous studies (Kuritani 1999, Humphereys et al. 2006, Blundy et al. 2006), there is no quantitative evaluation of these processes where both are involved as magma moves toward the surface. This represents a gap in knowledge and thus the first objective is to fill that gap by quantitatively analyzing the consequences of decompressional uprise of magma followed by isobaric crystallization on plagioclase zoning. The second objective is to develop another model to relate plagioclase zoning to convection in a magma

36 chamber at a given depth (Fig. 2). In this model the plagioclase zoning is analytically monitored in a parcel of crystallizing magma at the bottom of the magma chamber that is repeatedly rising slowly toward the top by convection and then sinking back to the bottom. Although the temperature difference between the bottom and the top of the chamber is assumed to be small enough to model the plagioclase zoning isothermally, a temperature gradient from top to bottom of the chamber does not change the conclusions.

In both models, pressure dependent partitioning of Na2O and CaO between the melt and plagioclase controls the zoning of plagioclase.

2. Materials and Methods:

In our computations, a basalt composition is used from the Pu’u O’o eruption of

Kilauea Volcano, Hawaii (Garcia et al. 1992) and the MELTS algorithm of Ghiorso and

Sack (1995) is applied. The composition of this basalt is given in Table 1. The MELTS algorithm of Ghiorso and Sack (1995) which uses regular solution model is widely used for modeling magmatic systems (Steward and Fowlar 2001, Asimow et al. 2001, Kress and Ghiorso 2004, Dogan et al. 2007). In the MELTS algorithm, computations involving isobaric and isothermal processes are based on minimization of Gibbs free energy for all possible reactions under the constraints imposed on the system. On the other hand, in computations involving perfectly mobile components such as oxygen, MELTS uses the

Korzhinsky potential (L) where,

⎛ ⎞ ∂G L = G − n ⎜ ⎟ or O 2 ⎜∂ n ⎟ O ⎝ 2 ⎠ dL =−SdT + VdP + μ dn − n dμ ∑ i i O O 2 2 i,i≠O2

Once the starting composition and the initial system parameters (P, T, wt% H2O,

and fO2) are defined, different constraints on magma differentiation (isobaric, isothermal,

decompressional, polybaric crystallization) can be imposed on the system. MELTS

calculates the composition of crystallizing minerals and the composition of the coexisting

melt, including the weight percent of water at each P and T. MELTS also computes the

mole percent anorthite (XAn), albite (XAb) and sanidine (XOr) for a given P, T, and wt%

H2O. This allows to determine the effect of changing P, T, and wt% H2O conditions on

plagioclase composition, which is then used to describe the compositional zoning in

plagioclase.

Below is a discussion of the results based on MELTS simulations that show (1)

the effect of total pressure (1 bar and 10 kbars) in a dry system (0 wt% H2O) and the

effect of water content (0 wt% and 1.5 wt% H2O) at 1000 bars on plagioclase zoning, (2)

the development of normal, reverse, and oscillatory zoning under decompressional

crystallization followed by isobaric cooling in multiple magma chambers, (3) the

development of oscillatory zoning under polybaric-isothermal crystallization simulating

convection in a single magma chamber, and (4) calculation of partial molal volumes of

Na2O and CaO in the melt.

3. Discussion of Results:

3.1. MELTS Simulations to Demonstrate the Role of Total Pressure (Ptotal) and

Water Content of the Melt (wt% H2O) on Plagioclase Zoning:

The effect of decreasing total pressure and increasing water pressure on the zoning of plagioclase in the Ab-An system has been studied by Yoder and Tilley (1962).

Figures 3a and 3b show that for a given temperature decreasing total pressure (from 10

Kb to 1 bar) or increasing water pressure (from 0 to 150 bars) results in an increase in the

An-content of plagioclase, which can be used to explain the development of reverse zoning in this system. Here, the consequences of decreasing pressure and increasing water content on the An-content of plagioclase (mole% An) are extended to a multicomponent basaltic melt at fO2~QFM (Fig. 4 and Fig. 5).

Isobaric crystallization is computed at every 5 oC starting from the liquidus

temperature of the Pu’u O’o basalt of 1160 oC at 1 bar and 1320 oC at 10 kbars and the

plagioclase composition is recorded at each stage. The anorthite content of plagioclase

decreases in response to isobaric cooling both at 1 bar and 10 kbars (Fig. 4). As shown in

Figure 4, if a basaltic magma cools isobarically (either at 1 bar or 10 Kb) the An content

of plagioclase decreases with decreasing temperature resulting in normal zoning in

plagioclase. On the other hand, if crystallization of plagioclase takes place when the

magma is rising or when the total pressure on the magma is decreasing, reverse zoning

develops. For example, at 1100 oC, the An content of plagioclase increases from 34

mole% to 54 mole% with a decrease in total pressures from 10 kbars to 1 bar, implying that a decrease in the total pressure at constant temperature causes reverse zoning in

plagioclase. The An content of plagioclase increases 20 mole% per 10 kbar decrease in

total pressure or 0.002 mole% / bar.

The relationship between water content of the melt and the An content of

plagioclase is shown in Figure 5. At a constant total pressure of 1000 bars crystallization

along the QFM buffer is computed in the dry basaltic magma as well as in the basalt

magma containing 1.5 wt% H2O. The liquidus temperature of the dry basaltic magma at

o o 1000 bars is 1170 C and that of basaltic magma containing 1.5 wt% H2O is 1120 C.

Figure 5 shows that the An content of plagioclase decreases with decreasing temperature

at 1000 bars in both the dry basaltic melt and in the basaltic melt with 1.5 wt% H2O, suggesting that in either a dry or water-bearing magma, isobaric crystallization results in normal zoning. Figure 5 also shows the effect of increasing water content of magma on the An content of plagioclase at a given temperature. For example, at Pt =1000 bars and

T=1050 oC, the An content of plagioclase increases from 38 mole% to 68 mole% with an

increase in water content from 0 wt% to 1.5 wt%. These results suggest that at a given P

and T a more calcic plagioclase will crystallize in a water-bearing magma compared to a

dry magma. This figure also suggests that it is possible to develop oscillatory zoning in

plagioclase if the water content of the melt fluctuates.

3.2. Normal and Reverse Zoning under Decompressional Crystallization followed by

Isobaric Cooling Conditions:

The first model involves several cycles of decompressional crystallization

followed by isobaric crystallization. Using the solid mass as a measure of the degree of

crystallization, Table 2 lists the changes in total pressure (P, bars), temperature (T, oC),

wt% H2O in the melt, and the An content (mole% An) in plagioclase during

decompressional and isobaric crystallization intervals. At a given pressure the solidus

temperature of a water-bearing magma is lower than that under dry conditions. A

corollary of this is that when a hydrous magma degasses the remaining liquid must

crystallize rapidly. Figure 6 shows the change in total pressure under decompressional

and isobaric crystallization conditions. Starting with 63.48 wt% crystallization, the

system is allowed to decompress adiabatically (under isentropic constraint). During this

process the total pressure decreases from 4000 bars to 3850 bars (Fig. 6) while the

temperature decreases, as expected, very little from 844.38 oC to 843.60 oC (Fig. 7), but

the dissolved water content stays constant at 8.09 wt% (Fig. 8). The net result of

decompressional crystallization is an increase in the anorthite content of plagioclase (Fig.

9a and 9b) or the development of reverse zoning. This part of the model represents

crystallization of magma during its adiabatic rise. Once this magma enters a magma

chamber at a given depth, it continues to crystallize under isobaric conditions. Between

63.48 wt% and 63.68 wt% crystallization, the pressure is kept constant at 3850 bars (Fig.

6) while the temperature is allowed to drop from 843.60 oC to 841.60 oC (Fig. 7). The result of isobaric crystallization at 3850 bars is a decrease in the anorthite content of plagioclase (Fig. 9a and 9b) and an increase in the dissolved water content from 8.076

wt% to 8.121 wt% (Fig. 8). During this stage, normal zoning develops. Then the magma

ascends again from a depth equivalent to 3850 bars to a depth equivalent to 3750 bars

adiabatically (Fig. 6) with a temperature drop of 0.7 oC (Fig. 7). During this process the dissolved water content stays constant at about 8.12 wt% (Fig. 8). Plagioclase crystals show an increase in the An content (reverse zoning) due to a decrease in total pressure

(Fig.9a and 9b). When the magma reaches the magma chamber at about 3750 bars (Fig.

6) it isobarically cools again (Fig. 7). An increase in the dissolved water content from

8.126 wt% to 8.146 wt% (Fig. 8) causes a decrease in the anorthite content resulting in normal zoning (Fig. 9a and 9b). In the final stage, the system is allowed to rise adiabatically from a depth equivalent to 3750 bars to a depth equivalent to 3700 bars

(Fig. 6). During this step the temperature content of the melt stays constant at about 840

oC as shown in Figure 7 as does the water content (8.15 wt%) as shown in Figure 8.

Decompressional crystallization under adiabatic conditions produces a reverse zoning in

plagioclase due to the decrease in total pressure and increase in the dissolved water

content (Fig. 9a and 9b). If the process is limited to just adiabatic uprise, then only

reverse zoning can develop. On the other hand, if process is limited to just isobaric

cooling only normal zoning can develop. The net result of crystallization of plagioclase

during adiabatic uprise followed by isobaric cooling repeated more than once is the

development of oscillatory zoning.

During decompressional crystallization intervals, the An content of plagioclase

increases due to two separate effects: decrease in total pressure and increase in the water

content of the melt. In order to analyze the relative contribution of each factor, we calculated the change in anorthite content during the first decompressional crystallization interval. With a decrease in total pressure of 150 bars (from 4000 to 3850 bars), the

anorthite content of plagioclase increases approximately 0.4 mole%. Since the effect of

decrease in total pressure increases anorthite content 0.002 mole%/ bar; 0.3 mole% of the

0.4 mole% increase is due to the decrease in total pressure and the remaining 0.1 mole%

increase is due to the presence of water in the melt.

3.3. Oscillatory Zoning under Polybaric and Isothermal Convection Conditions:

The second model involves polybaric and isothermal convection of magma

simulating the consequences of a density driven convection within a single magma

chamber in the crust. Consider a parcel of melt in a convecting magma chamber (Fig. 2).

Melt crystallization takes place in response to decreasing pressure on the ascending limb of convection followed by more crystallization as the parcel of magma sinks to the bottom of the magma chamber along the descending limb of convection. If the temperature gradient in the magma chamber is small, the process can be modeled as an isothermal and polybaric process using the MELTS algorithm.

In the modeling, the Pu’u O’o basalt which was used in the decompressional and isobaric crystallization model reported above is again chosen. The magma chamber is assumed to be at a depth between 14 and 15 kilometers below the surface of the earth, and has a total pressure of 3750 bars on top and 4000 bars at the bottom. Crystallization is assumed to take place along the QFM buffer. Table 3 shows the changes in total

o pressure (P, bars), temperature (T, C), wt% H2O in the melt, and the An content of

plagioclase (mole% An) during polybaric and isothermal crystallization steps. Variations

in total pressure, temperature, and dissolved water content of the melt as a function of

solid mass crystallized are given in Figures 10, 11, and 12, respectively. Along the ascending limb of convection in the magma chamber during polybaric crystallization causes a decrease in total pressure from 4000 bars to 3750 bars (Fig.10) and the dissolved water content of the melt increases (Fig.12). The decrease in total pressure and increase in dissolved water content produces an increase in the anorthite content of plagioclase during the polybaric crystallization intervals (Fig. 13a and 13b). Along the descending

limb of the convection crystallization continues while the total pressure increases from

3750 bars to 4000 bars (Fig. 10) and the dissolved water content of the melt increases

(Fig. 12). The increase in total pressure (Fig. 10) causes a decrease in the anorthite

content of plagioclase as shown in Fig. 13a and 13b. The trends shown in Figure 13a

indicate development of reverse zoning when magma is ascending from the bottom of the

chamber to the top of the chamber and development of normal zoning when magma is

descending from the top to the bottom of the chamber. Thus for each cycle of convection

a reverse and a normal zone can develop. If convection continues several cycles, the net

result is the development of oscillatory zoning in plagioclase.

3.4. Partial Molal Volume Effect on Plagioclase Zoning and Calculation of Partial

Molal Volumes of Na2O and CaO:

During the decompressional crystallization intervals of our decompressional

crystallization and isobaric cooling model and during the polybaric convection intervals

in the polybaric and isothermal convection model, the An content of the plagioclase

increases as the total pressure on the magma decreases. Since changes in the Ab/An ratio

of plagioclase are related to the amount of Na2O and CaO in plagioclase, zoning must be

controlled by the partial molal volumes of Na2O and CaO in the melt. In other words, as

the pressure decreases, the component with the larger partial molal volume partitions in

favor of the melt making the coexisting plagioclase more An rich.

In order to evaluate the role of Na2O and CaO on zoning in plagioclase, the partial

molal volumes of these oxides were calculated at two pressures (1000 bars and 2000

bars) using the MELTS algorithm of Ghiorso and Sack (1995).

By definition, the partial molal volume of an oxide in a melt is the change in the total volume per mole of that particular oxide added to the melt under constant temperature, pressure, and number of moles of other oxide components. Therefore, the partial molal volume of an oxide is the slope of the plot of the total volume of melt as the amount of the oxide is changed with all other variables held constant. The partial molal

_ _ volume of Na2O (V Na2O ) and CaO (VCaO ) can be expressed as below:

_ ⎡ ⎤ V Na2O = ∂V /∂n P,T,n (1) ⎣⎢ t Na2O ⎦⎥ j

_ VCaO = ∂V /∂n P,T,n (2) []t CaO j

Where,

V = Total volume of melt (cm3) t

nNa2O = Number of moles of Na2O

nCaO = Number of moles of CaO

P = Pressure (bars)

T = Temperature (oC)

nj =number of moles of all other components

The partial molal volumes of Na2O and CaO in the Pu’u O’o melt were calculated in order to understand the effect of increase in total pressure on the partial molal volume of each oxide. Computations of the partial molal volumes of Na2O and CaO were made above the liquidus temperatures of the Pu’u O’o basalt at 1000 and 2000 bars. In the calculation of the partial molal volume of Na2O we kept the pressure, temperature and number of moles of all components constant and increased only the number of moles of

Na2O by 0.04, 0.09 and 0.12, and calculated the change in the total volume of the system.

Similarly in the calculation of the partial molal volume of CaO, the pressure, temperature,

and number of moles of all components were kept constant and only the number of moles

of CaO was increased by 0.18, 0.23 and 0.27 moles, and then the change in the total

volume of the system was calculated (Table 4a and 4b). In plots of V vs. nNa2O and V t t vs. nCaO the slopes of the lines are equal to the partial molal volumes of Na2O and CaO,

_ 3 respectively (Fig 14 and 15). V Na2O is 30.297 cm /mole at 1000 bars and 30.303

_ 3 3 cm /mole at 2000 bars which is effectively constant. VCaO is 19.363 cm /moles both at

1000 bars and 2000 bars (Table 5).

The relationship between compositional changes in plagioclase and pressure in

terms of partial molal volumes of Na2O and CaO in the melt can now be interpreted.

Figures 6 and 10 show that as pressure on the magma increases, the mole percent of

anorthite in plagioclase decreases. This is because, with increasing pressure, Na2O, which has a larger partial molal volume compared to that of CaO, goes into plagioclase resulting in a more albitic plagioclase. Conversely, with decreasing pressure, CaO, which has a

smaller partial molal volume, goes into plagioclase resulting in a more anorthitic

composition. This interpretation supports the conclusion reached by Ghiorso and

Carmichael (1987) earlier.

4. Conclusions:

The effects of changing total pressure and water content of the melt on the

development of compositional zoning in plagioclase have been extended from the simpler

Ab-An system to a more complex rock system. Computations using a basaltic composition and the MELTS algorithm of Ghiorso and Sack (1995) demonstrate the effect of total pressure and water content on plagioclase zoning. The results concerning the role of changing total pressure and water pressure on plagioclase zoning support the conclusions reached from a study of the Ab-An system (Yoder and Tilley 1962) but extends it into more complex rock systems. Decreasing and increasing total pressure on a dry rock system causes development of reverse and normal zoning, respectively whereas increasing water content causes the development of reverse zoning. A corollary of this is that if the water content of the melt fluctuates, crystallizing plagioclase will develop oscillatory zoning.

Having determined the role of total pressure and water content of the melt on the development of normal and reverse zoning in plagioclase, two possible mechanisms under which normal, reverse, and oscillatory zoning can occur were proposed. In the first model (decompressional crystallization followed by isobaric cooling), several cycles of crystallization during ascent followed by crystallization in a magma chamber at a given depth within the crust are simulated. In this model plagioclase crystals can develop reverse, normal and even oscillatory zoning in response to changes in total pressure and the water content of the melt. In the second model (convection under polybaric and isothermal crystallization), polybaric convection of a magma body in a single magma chamber is simulated. Crystallization along the ascending and descending limbs of convecting melt can produce reverse and normal zones, respectively in each cycle, and if there are several cycles the net result is development of oscillatory zoning in plagioclase.

5. Acknowledgments:

The authors are grateful to Mark Ghiorso of OFM Research Inc. for his constructive comments in the earlier version of the manuscript.

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Table 1.

Oxide wt%

SiO2 50.44

TiO2 3.11

Al2O3 13.67

Fe2O3(t) 12.73

MnO 0.18

MgO 5.91

CaO 9.97

Na2O 2.62

K2O 0.67

Total 99.33

Table 2.

Solid mass Pressure Temperature Water Content of Anorthite (g.) ( bars) (o C) Melt Content (wt%) (mole%) Decompressional 63.56 4000 844.38 8.093 47.42 63.58 3950 843.82 8.097 47.51 63.56 3900 843.52 8.093 47.62 63.54 3850 843.23 8.088 47.74 Isobaric 63.48 3850 843.6 8.076 47.78 63.68 3850 841.6 8.121 47.35 Decompressional 63.68 3850 841.6 8.121 47.35 63.68 3800 841.24 8.121 47.42 Isobaric 63.71 3750 840.89 8.126 47.48 63.79 3750 839.89 8.146 47.26 Decompressional 63.79 3750 839.89 8.146 47.26 63.80 3700 839.54 8.147 47.33

Table 3.

Solid mass Pressure Temperature Water Content of Anorthite (g.) ( bars) (o C) Melt Content (wt%) (mole%) Polybaric 63.56 4000 844.38 8.09 47.42 63.96 3750 839.38 8.18 47.61 Isothermal 63.96 3750 839.38 8.18 47.61 64.02 3800 839.38 8.20 47.46 64.09 3850 839.38 8.21 47.31 64.15 3900 839.38 8.23 47.16 64.22 3950 839.38 8.24 47.02 64.28 4000 839.38 8.26 46.87 Polybaric 64.28 4000 839.38 8.26 46.87 64.36 3950 838.38 8.27 46.91 64.44 3900 837.38 8.29 46.94 64.51 3850 836.38 8.31 46.98 64.59 3800 835.38 8.33 47.02 64.66 3750 834.38 8.35 47.06 Isothermal 64.66 3750 834.38 8.35 47.06 64.73 3800 834.38 8.36 46.91 64.79 3850 834.38 8.38 46.76 64.86 3900 834.38 8.39 46.62 64.93 3950 834.38 8.41 46.47 64.99 4000 834.38 8.42 46.32 Polybaric 64.99 4000 834.38 8.42 46.32 65.07 3950 833.38 8.44 46.36 65.14 3900 832.38 8.46 46.40 65.21 3850 831.38 8.48 46.44 65.29 3800 830.38 8.50 46.48 65.36 3750 829.38 8.51 46.51 Isothermal 65.36 3750 829.38 8.51 46.51 65.43 3800 829.38 8.53 46.37 65.49 3850 829.38 8.55 46.22 65.56 3900 829.38 8.56 46.08 65.63 3950 829.38 8.58 45.93 65.69 4000 829.38 8.60 45.79

Table 4a.

Na2O Temperature Pressure nNa2O V (wt%) (o C) (bars) (moles) t (cm3) 2.62 1300 1000 0.04 36.69 5.62 1300 1000 0.08 38.07 8.62 1300 1000 0.12 38.99 2.62 1300 2000 0.04 36.49 5.62 1300 2000 0.08 37.85 8.62 1300 2000 0.12 39.22

Table 4b.

CaO Temperature Pressure nCaO V (wt%) (o C) ( bars) (moles) t (cm3) 9.97 1300 1000 0.18 36.69 12.97 1300 1000 0.23 37.58 15.97 1300 1000 0.27 38.47 9.97 1300 2000 0.18 36.49 12.97 1300 2000 0.23 37.38 15.97 1300 2000 0.27 38.27

Table 5.

_ _ Temperature Pressure VCaO V Na O o 3 2 ( C) (bars) (cm /moles) (cm3/moles) 1300 1000 19.363 30.297

1300 2000 19.363 30.303

DECOMPRESSIONAL

ISOBARIC

DECOMPRESSIONAL

ISOBARIC

DECOMPRESSIONAL

ISOBARIC

Figure 1.

P= 3750 bars

POLYBARIC ISOTHERMAL

P= 4000 bars

Figure 2.

r An=72 wt% An=58 wt% Ptotal=1 ba Ptotal=10 Kb

Figure 3a.

O=150 2 bars

PH An = 88 wt% Ptotal=1 bar An = 72 wt%

Figure 3b.

Total Pressure - Anorthite Content relationship

1300

1200 Ptotal =10 kbars C) o

1100

Ptotal =1 bar

Temperature ( 1000

900 30 35 40 45 50 55 60 34 54 Albite Mole Percent Anorthite

Figure 4.

Water Content - Anorthite Content relationship

1300

1200 Ptotal = 1000 bars 0 wt% H2O C)

o 1100

1000

900 Ptotal = 1000 bars Temperature ( 1.5 wt% H2O 800

700 35 40 45 50 55 60 6568 70 38 Albite Mole Percent Anorthite

Figure 5.

Solid Mass - Total Pressure relationship

4050

4000 Decompressional 3950 Crystallization Decompressional Crystallization

3900 (An) (An) 3850 Decompressional Crystallization Isobaric Isobaric 3800 Crystallization Crystallization Total Pressure (bars) Pressure Total (An 3750 ) (An) (An) 3700

3650 63.56 63.58 63.56 63.54 63.48 63.68 63.68 63.68 63.71 63.79 63.79 63.80 Solid Mass (g.)

Figure 6.

Solid Mass - Temperature relationship

844.50

844.00 Isobaric 843.50 Crystallization C) o 843.00 Decompressional (An) Decompressional Crystallization 842.50 Crystallization Decompressional (An) 842.00 Crystallization (An) 841.50 Isobaric (An Temperature ( Crystallization ) 841.00 840.50 (An) 840.00 839.50 63.56 63.58 63.56 63.54 63.48 63.68 63.68 63.68 63.71 63.79 63.79 63.80 Solid Mass (g.)

Figure 7.

Solid Mass - Water Content of Melt relationship

8.154

Isobaric 8.134 Crystallization Decompressional Crystallization Decompressional (An) (An) Crystallization (An) 8.114 Isobaric Crystallization

Decompressional (An) 8.094 Water Content of Melt (wt%) Crystallization (An)

8.074 63.56 63.58 63.56 63.54 63.48 63.68 63.68 63.68 63.71 63.79 63.79 63.80 Solid Mass (g.)

Figure 8.

Solid Mass - Anorthite Content relationship

47.80 Decompressional 47.75 Crystallization 47.70 (An) 47.65 Decompressional Crystallization 47.60 (An) 47.55 Isobaric 47.50 Isobaric Crystallization Crystallization 47.45 (An) Decompressional 47.40 (An) Crystallization

Anorhite Content (mole%) 47.35 (An) 47.30 47.25 1 2 3 4 5 47.20

63.56 63.58 63.56 63.54 63.48 63.68 63.68 63.68 63.71 63.79 63.79 63.80

Solid Mass (g.)

Figure 9b. Figure 9a.

Solid Mass - Total Pressure relationship

4050 Polybaric Polybaric 4000 Crystallization Crystallization (An) (An) 3950

3900

3850

Total Pressure (bars) Total Pressure 3800 Isothermal Isothermal Isothermal Crystallization 3750 Crystallization Crystallization (An) (An) 3700 (An)

9 9 .09 44 5 7 .99 .36 49 4. 4. 5. 63.56 63.96 64 64.22 64.28 6 6 64.66 64. 64.93 64 65.14 65.29 65 6 65.63 Solid Mass (g.)

Figure 10.

Solid Mass - Temperature relationship

845.30 Polybaric 843.30 Polybaric Crystallization Crystallization

C) 841.30

o (An) (An) 839.30

837.30

835.30 Isothermal Isothermal 833.30 Crystallization Crystallization Isothermal Temperature (T, Temperature 831.30 (An) Crystallization (An)

829.30 (An) 827.30

825.30

6 96 28 59 66 93 29 49 63 3.56 6 63. 64.09 64.22 64. 64.44 64. 64. 64.79 64. 64.99 65.14 65. 65.3 65. 65. Solid Mass (g.)

Figure 11.

Solid Mass - Water Content of Melt relationship

8.70 Polybaric Polybaric 8.60 Crystallization Crystallization (An) 8.50 (An) Isothermal 8.40 Crystallization Isothermal 8.30 (An) Isothermal Crystallization Crystallization 8.20 (An) Water Content of Melt (wt%) Melt of Content Water (An) 8.10

8.00

9 6 .09 .22 5 6 .79 .93 .29 .36 4. 63.56 63.96 64 64 64.28 64.44 6 64. 64 64 64.99 65.14 65 65 65.49 65.63 Solid Mass (g.)

Figure 12.

Solid Mass - Anorhite Content relationship

47.75 47.55 Polybaric Crystallization Polybaric 47.35 (An) Crystallization 47.15 (An) 46.95 Isothermal Crystallization 46.75 Isothermal (An) 46.55 Crystallization

46.35 (An) Isothermal

Anorhite Content (mole%) Content Anorhite Crystallization 46.15 (An) 45.95 45.75

6 3 .96 .09 .28 .59 .79 14 3 6 5. 5. 63.56 63 64 64.22 64 64.44 64 64.66 64 64.93 64.99 6 65.29 6 65.49 65. Solid Mass (g.) Figure 13b.

Figure 13a.

39.50

39.00

y = 30.297x + 35.383 38.50 R2 = 0.9998 )

3 38.00 P = 1000 bars 37.50 Vt (cm y = 30.303x + 35.175 R2 = 0.9996 37.00

P = 2000 36.50 bars

36.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

nNa2O (moles)

Figure 14.

39.00

38.50

38.00 y = 19.363x + 33.188 2

) R = 0.9997 3

(cm 37.50 t P = 1000 V bars 37.00 y = 19.363x + 32.988 R2 = 0.9997

36.50 P = 2000 bars 36.00 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 nCaO (moles)

Figure 15.

Part 3

Crystal Size Distributions (CSDs) in a Basaltic Flow at the Small Hasandag

Volcano, Central Turkey: Comparison of Calculated Residence Times of Plagioclase and Clinopyroxene Crystals

Gokce Ustunisik1 and Attila Kilinc1

1 Department of Geology, University of Cincinnati, Cincinnati, OH, 45221-0013, USA

Abstract

Crystal Size Distribution (CSD) analysis has been used to calculate the residence

times of plagioclase and clinopyroxene crystals from a single basaltic flow in Small

Hasandag volcano, Central Turkey. In addition to crystal residence time, τ (s); crystal

nucleation density, no (#.cm-4) and crystal nucleation rate, J (#.cm-3.s-1) have also been

evaluated. The CSDs of plagioclase and clinopyroxene crystals from this basaltic flow

yields a linear relationship when the natural logarithm of the number of crystals of a

given size interval per unit volume is plotted against mean crystal length, Lmean. The slope

of this line, -1/G.τ , is controlled by the crystal growth rate, G (cm/s) and the crystal

residence time, τ (s) in the magma chamber.

For plagioclase crystals the observed slope of -158.65 cm-1 and the intercept of

16.454 correspond to a crystal residence time of 1.99 years (±0.60 years) and a nucleation

rate of 2.84x106 cm-3.s-1, using the crystal growth rate of plagioclase as 10-10 cm/s

(Cashman, 1988). Using the published growth rate of 10-10 cm/s (Congdon, 1991) for

clinopyroxene crystals, the observed slope of -290.75 cm-1 and the intercept of 16.676

gives a crystal residence time of 1.09 years (±0.33 years) and a nucleation rate of

4.74x106 cm-3.s-1. Uncertainty in the residence times is estimated as ±30% by Mangan

(1990) and once this uncertainty factor is applied to the calculated values, the residence

times for plagioclase and clinopyroxene crystals slightly overlap; implying that in calculation of magma residence times either plagioclase or clinopyroxene of the Small

Hasandag volcano can be used as a reliable proxy.

Keywords: CSD, Plagioclase size distribution, Clinopyroxene size distribution, Crystal residence time, Small Hasandag

I. Introduction

The theoretical basis of crystal size distribution was initially developed by chemical engineers (Randolph and Larson, 1971) and gained widespread attention in geological sciences through the early works of Marsh (1988) and Cashman and Marsh

(1988). Many of the early studies have been concerned with the calculation of residence

times in magma chambers (Cashman, 1993; Higgins, 1996a; Higgins, 1996b; Mangan,

1990; and Resmini et al., 1995). Cashman and Marsh (1988), Hort et al. (1993), Resmini

and Marsh (1995), Hort et al. (1999), Zeig and Marsh (2002) have applied the crystal size

distribution (CSD) studies to basaltic systems. Cashman (1988) provided estimates of

crystal nucleation and growth rate in natural systems using CSD measurements and steady-state models suggested that magma residence time can be calculated from the

slope of the CSD once the growth rate is known. Mangan (1990) used olivine CSDs to

estimate residence times for Kilauea lavas and found agreement with times independently

75 estimated by Wright and Fiske (1971) using geochemistry and eruption histories. Resmini et al. (1995) calculated the residence time in a sequence of comagmatic lava flows in

Dome Mountain, Nevada to estimate the overall magma storage for the Dome system.

Quantitative evaluation of possible crystal fractionation by crystal settling, crystal floatation, resorption of small crystals, crystal breakage, or accumulation were made possible by examining the curvature of the CSD profile independently from the chemical data (Marsh, 1988; Armienti et al., 1994; Marsh 1998; Higgins 1996b).

These previous studies based on CSD calculations focused on extracting information from igneous rocks about a variety of processes including magma residence times, local magmatic cooling rates, solidification processes, and magma ascent rate.

However, there is not any research on the calculation of crystal residence time by using more than one mineral from the same lava flow. The objective of this contribution is to test the following hypothesis: If the crystal residence time of a mineral is related to the slope and crystal growth rate, then two minerals crystallizing from the same magma must yield, within the error limits, the same crystal residence time. To test this hypothesis, the plagioclase and clinopyroxene from a single basalt flow were usedd, after verifying by

MELTS calculations that the two minerals crystallized 20oC apart (1166.30 and 1146.30 oC).

Below is a brief description of the geology of the Small Hasandag volcano, followed by the principles of the CSD theory and its application to plagioclase and clinopyroxene crystals in the Small Hasandag basalts.

2. The Small Hasandag Volcano

Small Hasandag Volcano is one of two terminal cones of the double-peaked

Hasandag stratovolcano, which is located in Central Anatolia, Turkey (Fig. 1). It is of

particular interest to the understanding of the evolution of Central Anatolian Volcanism

through time. Hasandag volcano has erupted violently in the past and is still considered

an active volcano. Its products (lava flows and pyroclastic materials) cover a large

portion of the Central Anatolian Volcanic region with a total volume of 354 km3 and the

area of extent of 760 km2. The Small Hasandag portion of this volcano provides a well- exposed suite of calc-alkaline rocks ranging in composition from basalt to rhyolite but dominantly andesite and dacite.

The mafic lavas at Small Hasandag volcano were originally noted by Ercan et al.

(1990) and later described in detail by Aydar and Gourgaud (1998). A compherensive discussion of the geology of the area was given by Aydar and Gourgaud (1998) and

Daniel et al. (1998). Based on previous studies four evolutionary stages have been recorded in the history of Small Hasandag volcano (Aydar and Gourgaud, 1998). These are Stage 1: Kecikalesi volcano, 13 Ma, Stage 2: Paleovolcano, 7 Ma, Stage 3:

Mesovolcano, 1Ma, and Stage 4: Neovolcano <1Ma. The basaltic lavas are found in almost each stage either as monogenetic vents (cinder cones and maar) or as lava flows

(Mesovolcano and Neovolcano) (Aydar and Gourgoud, 1998).

The basaltic composition (GU-07-17) used in this study for the CSD measurements is from massive, vesicle-free Neovolcano basalts. Petrographic examination shows the major mineralogy includes olivine, clinopyroxene, plagioclase, and Fe-Ti oxides. Oscillatory zoned plagioclase crystals and large clinopyroxene

77 xenocrysts are observed in these basalts. The xenocrystals of clinopyroxene were excluded from the CSD measurements.

3. The Principles of Crystal Size Distribution (CSD) Theory

The fundamental concept in crystal size distribution analysis is the development of a histogram of the number of crystals per unit size per unit volume (N) as a function of crystal size (L). This kind of a measurement can be directly made from a thin section using a computer-based image analysis system. Conversion of two-dimensional measurements based on number of crystals per unit size range per unit area in a thin section to three-dimensional measurements based on number of crystals per unit size range per unit volume of the rock is made by using stereological corrections (Higgins,

2000). The population density can be calculated by finding the slope of the cumulative curve with respect to crystal size (i.e., n=dN/dL) (Fig. 2a). A distribution of the natural log of the population density of crystals [ln(n)] versus crystal size (L) gives a slope of -1/

G.τ and the y-intercept of ln(no), where G is the average growth rate and τ is the residence time of that particular mineral in the magma and no is the nucleation density

(Fig. 2b). CSD measurements can show evidence for crystal fractionation and crystal accumulation/settling mechanisms with concave-down and concave-up curvatures, respectively. While the above formulations are developed for a steady-state system, the solution for the non-steady state batch-cooling model where magma is allowed to cool and crystallize completely has the same form as the steady-state solution (Marsh, 1988,

Cashman and Marsh, 1988). In the formulation of crystal size distribution theory, growth rate (G) has been taken to be independent of crystal size. Although constant growth rate

78 is observed in many systems, it is not a necessary assumption in CSD theory. The role of non linear growth rate on CSD has been studied by Marsh (1988). Marsh (1988) has characterized size-dependent growth by discussing the deviation of CSDs from the classical pattern and having curvature at small crystal sizes while having straight segment at larger sizes. It is also well established that, the processes such as textural coarsening produces curvature in CSD in smaller crystals due to the size-dependent growth rate

(Higgins, 2006a).

In CSD calculations, the system is accepted as open system at steady-state. The following is a brief discussion of an open system under steady-state conditions.

3.1. Open System at Steady-State:

CSD theory is based on a steady-state population balance that monitors the number of crystals in a specific size range brought in by the influx of magma and the number of crystals of this size range leaving the magma chamber due to the out flux of magma. The fundamental equation for steady state conditions is shown in below:

dn/dL + n/ G.τ = 0 (1) where τ = V/Q is the recharge or the residence time of crystals in the system, V=volume of magma and Q=influx rate. The integration of equation 2 gives a log-linear relationship:

L ln( n ) =− + ln( n ) (2) G τ o where the logarithm of the number density of crystals of a given size range per unit volume ln(n)is related to crystal growth rate (G, cm/s), crystal residence time in the magma chamber ( τ , s), crystal size ( L, cm) and logarithm of crystal nucleation density ln(no) (Marsh, 1988, Cashman and Marsh, 1988). Thus, a plot of ln(n) against L gives a straight line with a negative slope which is equal to

1 slope = − (3) Gτ

Therefore, if the crystal growth rate is known then the crystal residence time in the

magma chamber, τ , can easily be calculated. Since no can be obtained from the y-

intercept and G from the slope, nucleation rate, J can be calculated by using the

following equation.

J = no. G (4) where J is in #.cm-3.s, no is in #. cm-4 and G is in cm/s.

4. Methods - Measuring the CSDs

To calculate the crystal nucleation density, crystal nucleation rate, and magma

residence time in Small Hasandag volcano, a basaltic composition (GU-07-17) is used in

this study for the crystal size distribution measurements. This basalt contains olivine,

clinopyroxene, plagioclase, and Fe-Ti oxides. Among these phases, plagioclase and

clinopyroxene crystals have been chosen for crystal size distribution analysis since these

are the most abundant crystals in the composition.

The CSDs for plagioclase and clinopyroxene are measured by using computer-

based image analysis system. A digital camera attached to a petrographic microscope equipped with image analysis software – IP Lab v. 9.3 was used for size measurements of plagioclase and clinopyroxene crystals. One representative thin section from Small

Hasandag basalts (GU-07-17) was used for the measurements. This sample is from the massive and vesicle free regions of the basaltic rocks of Small Hasandag. Major, minor axes plus area of 830 plagioclase and 540 clinopyroxene crystals were measured. The

large plagioclase and clinopyroxene xenocrysts present in the sample were excluded from

the CSD analyses.

Twenty-eight images covering the entire thin section were captured and these images were used to measure major and minor axes, as well as the area of plagioclase and

clinopyroxene crystals. Using the IP lab software each plagioclase and clinopyroxene

crystal was carefully outlined (Fig. 3 and Fig. 4). Only unfragmented crystals were used

for the selection and measurement of crystal size distribution analysis in order to

eliminate size measurement errors due to fragmentation.

One challenging aspect of crystal size analysis is the calculation of the population

density that is represented by the two-dimensional (2D) projection. This value is

volumetric in dimension and cannot be directly measured in thin sections. Therefore, the

two-dimensional calculations must be converted to three-dimensional (3D) CSDs. Since

not all crystals can be assumed perfectly spherical, many investigators have used

stereological transformations from 2D to 3D to get volume normalized population

densities. There are several methods of this conversion used in the literature (Cashman

and Marsh, 1988; Sarda and Graham, 1990; Peterson, 1996; Higgins, 2000; Castro et al.,

2003; Duchene et al., 2008). One of most widely used methods is to raise the number

density in area to the three-halves power (Cashman and Marsh, 1988). Mangan (1990)

used olivine crystals to calculate the magma residence time for the 1959 eruption of the

Kilauea volcano in Hawaii. Mangan’s (1990) data indicate that magma residence times

3/2 which are calculated by converting 2D to 3D using NV = (NA) are in agreement (within

±30% error limits) with times independently estimated by Wright and Fiske (1971) using

the geochemistry and eruption histories. In our measurements, the number density of

crystals per unit volume of rock is also calculated as the number of crystals per unit area

3/2 of rock raised to the three-halves power (NV = (NA) ) as recommended by Cashman and

Marsh (1988).

Once the crystal size data are obtained by image analysis, the data is converted to centimeters using an established conversion factor based on the objective lens magnification (10X). Then, for that given thin section the crystal size dimensions are sorted into “bins” based on the mean maximum length of the crystals. These bins are

n-1 defined using the geometric series, an=a1(r) with r=0.794 and a1=length of the major

axis of the largest crystal. This bin width ensures that there are a sufficient number of

crystals in each bin. Each bin used in our calculations contains at least one crystal, and

there are no gaps with empty bins. The collected data was analyzed using Excel for

further calculations and for the construction of CSD diagrams.

The crystal size distribution data for plagioclase and clinopyroexene crystals are plotted on a natural logarithm of population density [ln(n)] versus mean crystal size

(Lmean, cm.) diagram following Marsh (1988), where the population density is the

number of crystals within a size range per unit volume divided by the width of that size

range.

5. Results

5.1. Plagioclase CSDs:

The crystal size distribution of 830 plagioclase crystals is presented in Figure 5.

Table 1 shows the L interval, the size range of a group of measurements; L mean, the

average measurement for that bin; L range, the span of observed lengths for that bin; N,

the number of crystals in that bin; NA, the l area of measurement; NV ; n range; and ln (n)

for outlined plagioclase crystals. The upper plot in Figure 5 displays the raw data and the

lower plot shows the results of linear regression applied to the data. The vertical line to

the left (Lmean <0.008 cm) in the lower plot marks the crystal sizes that are fewer than 10

crystals per unit volume of rock since the CSD based on such a small number of crystals

is generally not even and do not represent the true size distributions at those small crystal

sizes. Similarly the two crystal classes to the right of the vertical line (Lmean >0.043 cm)

are also not included in the regression in order to eliminate the effect of the xenocryst

population on CSD calculations. The deficiency of small (Lmean <0.008 cm) and large crystals (Lmean >0.043 cm) on the left and right hand side of the CSD plot has been

confirmed qualitatively by petrographic observations.

Linear least-square regression of the data in Figure 4 gives a slope (1/G.τ ) of

-158.65 cm-1 and an intercept (no) of 2.84x1016 #.cm-4. Assuming a crystal growth rate

of 10-10 cm/s similar to that observed for plagioclase in near-surface basaltic magmas by

Cashman (1988); the calculated residence time for the magma using plagioclase crystals

is 1.99 years (±0.60 years). The calculated nucleation rate (J) is 2.84x106 #.cm-3.s-1. The

o characteristic crystal size (Lc) defining the CSD by Lc= G. τ , where ln (n/n ) is equal to

1, is calculated as 0.063 cm.

A visual inspection of the CSD profile of plagioclase is linear showing no sign of

either crystal fractionation or accumulation. The decrease in the spectra at small crystals sizes for the first 4 crystal classes (e.g., as Lmean approaches to 0) and the concave up tail

for the last 2 crystal classes (e.g., Lmean>0.042 cm) are not considered in the regression

analyses due to the fewer number of crystals at these size ranges.

5.2. Clinopyroxene CSDs:

The crystal size spectrum for a total of 540 clinopyroxene crystals is shown in

Figure 6. Table 2 shows L interval, the size range of a group of measurements; L mean,

the average measurement for that bin; L range, the span of observed lengths for that bin;

N, the number of crystals in that bin; NA, the total area of measurement; NV; n range;

and ln (n) for outlined clinopyroxene crystals. Figure 6 displays an upper plot composed

of raw data and a lower plot composed of the results of linear regression applied to the

data. All except the smallest and largest crystals were included in the regression analysis.

The vertical line on the left in the lower plot at Figure 6 marks the crystal sizes smaller

than 0.008 cm. Although there is representative number of crystals at sizes < 0.008 cm,

since CSD based on such a small number of crystal classes are not reflective of the true

CSD at those crystal sizes, we did not included those crystal classes in the regression

analysis. Consequently, the crystal classes to the right of the vertical line (Lmean >0.028

cm) on the CSD plot are not included in the regressions. Although the CSD profile at

0.030 cm shows a kink which might be indicative of the two stages of clinopyroxene crystallization, petrographic observations of large clinopyroxene xenoliths and clumping of crystals and the deficiency of the number of crystals counted at those crystal classes

(Lmean >0.028 cm) in Table 3 confirms that these data points should not be included in the

CSD profile.

In Figure 6 a linear least-square regression of the data gives a slope (1/G.τ ) of

-290.75 cm-1 and an intercept (no) of 4.74x1016 #.cm-4. For clinopyroxene crystals, the

crystal growth rate of 10-10 cm/s from Congdon (1991) was used. Thus the calculated residence time for magma based on clinopyroxene crystals is 1.09 years (±0.33 years)

6 -3 -1 and the nucleation rate (J) is 4.74x10 #.cm .s . The characteristic crystal size (Lc),

where ln (n/no) = 1, is calculated as 0.034 cm.

A clear linear correlation exists between the mean crystal size and the population density of clinopyroxene crystals based on the CSD profile in Figure 6. Once the decrease in the spectra at small crystals classes and the concave up tail for the last 4 crystal classes are not considered in the regression analyses because of the deficiency of number of crystals at these size ranges, the CSD profile for clinopyroxene has neither the signs of crystal fractionation nor accumulation.

5.3. Comparison of Residence Times:

As discussed above, a constant growth rate of 10-10 cm/s (Cashman, 1988 and

Congdon, 1991) is used respectively for plagioclase and clinopyroxene to calculate their

residence times in Small Hasandag volcano. Considering the basalt used in the CSD

calculations is the most parental composition to the rest of compositions ranging from basaltic andesite to rhyolite and the most representative of magma that existed in the chamber, the residence time calculated by plagioclase and clinopyroxene crystals should

give the most approximate residence time for the basaltic flow in Small Hasandag volcano.

The residence times determined by plagioclase and clinopyroxene from the linear portions of the CSDs are 1.99 years (±0.60 years) and 1.09 years (±0.33 years) respectively. Uncertainty in the residence times is estimated as ±30% by Mangan (1990).

Once this uncertainty factor is applied to the calculated values, the residence time by plagioclase and clinopyroxene crystals which indicates either plagioclase or

clinopyroxene from this basaltic flow in Small Hasandag can be used for the calculation

of residence time of the magma.

6. Conclusions

Crystal Size Distributions (CSDs) for plagioclase and cliopyroxene in a basaltic

lava from Small Hasandag volcano in Turkey show a linear relationship between the

population density of crystals and the mean crystal length within the size range

considered. Using the published growth rate of 10-10 cm/s for both plagioclase and

clinopyroxene (Cashman, 1988 and Congdon, 1991) and employing a steady-state model,

the residence time determined by plagioclase and clinopyroxene crystals are 1.99 years

and 1.09 years respectively. Based on a ±30% uncertainty in residence time calculations,

our results show that both plagioclase and clinopyroxene are crystallized from a single

magma source.

A visual inspection of the CSD profile for both crystals indicates a single stage of crystallization. Although the CSD profile for clinopyroxene shows a change in the slope

at the characteristic crystal size of 0.030 cm, with the petrographic observations of clumping of large clinopyroxene xenoliths and the deficiency of number of crystals

counted at those crystal classes, these data points were not included in the CSD profile.

7. References

Armienti, P., Pareschi, M.T., Innocenti, F., and Pompolio, M., 1994. Effects of magma storage and ascent on the kinetics of crystal growth. Contributions to Mineralogy and

Petrology 115, 402-414.

Aydar, E., Gourgaud, A., 1998. The geology of Mount Hasan stratovolcano, Central

Anatolia, Turkey. Journal of Volcanology and Geothermal Research 85, 129-152.

Cashman, K.V., and Marsh, B.D. 1988. Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization II. Makaopuhi lava lake. Contributions to

Mineralogy and Petrology, 99: 292-305.

Cashman, K.V. 1993. Relationship between plagioclase crystallisation and cooling rate in basaltic melts. Contributions to Mineralogy and Petrology, 113: 126-142.

Castro, J. M., Cashman, K. V., and Mangan, M. T., 2003. A technique measuring 3D crystal size distributions of prismatic microlites in obsidian. American Mineralogist, 88,

1230-1240.

Congdon, R. D., 1991. The solidification of the Shonkin Sag Laccolith: Mineralogy, petrology, and experimental phase equilibria. Unpublished Ph.D. dissertation, Johns

Hopkins University, 316 pages.

Daniel, C., Aydar, E., Gourgaud, A., 1998. The Hasan Dagi stratovolcano (Central

Anatolia, Turkey): Evolution from calc-alkaline to alkaline magmatism in a continental collision zone. Journal of Volcanology and Geothermal Research, 87, 275-302.

Duchene, S., Pupier, E., DeVeslud, C. L., and Toplis, M. J., 2008. A 3D reconstruction of plagioclase crystals in synthetic basalt. American Mineralogist, 93, 893-901.

Ercan, T., Tokel, S., Can, B., Fisekci, A., Fujitani, T., Notsu, K., Selvi, Y., Olmez, M.,

Matsuda, J.I., Yildirim, T., Akbasli, A., 1990. The origin and evolution of the Cenozoic volcanism of Hasandagi-Karacadag area (Central Turkey) (in Turkish). Bulletin of

Geomorphology 18, 39-54.

Higgins, M.D., 1996a, Crystal size distributions and other quantitative textural measurements in lavas and tuff from Mt Taranaki (Egmont volcano), New Zealand,

Bulletin of Volcanology, 58, 194-204.

Higgins, M.D., 1996b, Magma dynamics beneath Kameni volcano, Greece, as revealed by crystal size and shape measurements, Journal of Volcanology and Geothermal

Research, 70, 37-48.

Higgins, M. D., 2000, Measurement of crystal size distribution, American Mineralogist,

85, 1105-1116.

Hort, M., Marsh, B.D., and Spohn, T., 1993, Igneous layering through oscillatory nucleation and crystal settling in well-mixed magmas, Contributions to Mineralogy and

Petrology, 114, 425-440.

Hort, M., Marsh, B.D., Resmini, R.G., and Smith, M.K., 1999, Convection and

crystallization in a liquid cooled from above: An experimental and theoretical study,

Journal of Petrology, 40, 1271-1300.

Mangan, M.T. 1990, Crystal size distribution and the determination of magma storage

times: The 1959 eruption of Kilauea volcano, Hawaii. Journal of Volcanology and

Geothermal Research, 44: 295-302.

Marsh, B., 1988, Crystal size distribution (CSD) in rocks and the kinetics and dynamics

of crystallization I. Theory, Contributions to Mineralogy and Petrology, 99, 277-291.

Peterson, T.D. 1996, A refined technique for measuring crystal size distributions in thin

section. Contributions to Mineralogy and Petrology, 124: 395-405.

Randolph, A.D. and Larson, M.A., 1971, Theory of particulate processes, Academic

Press, New York, NY, 251.

Resmini, R.G. and Marsh, B.D., 1995, Steady-state volcanism, paleoeffusion rates, and magma system volume inferred from plagioclase crystal size distributions in mafic lavas;

Dome Mountain, Nevada, Journal of Volcanology and Geothermal Research, 68 (4), 273-

296.

Sarda, P. and Graham, D., 1990, Mid-ocean ridge popping rocks: implications for

degassing at ridge crests. Earth and Planetary Science Letters, 97: 268-289.

Zeig, M.J. and Marsh, B.D., 2002, Crystal size distributions and scaling laws in the quantification of igneous textures, Journal of Petrology, 43 (1), 85-101.

Table 1

L Interval L Mean L Range N NA NV n ln(n) 0.0721-0.0572 0.065 0.015 2 5.624 13.338 889.224 6.790 0.0572-0.0454 0.051 0.012 1 2.812 4.716 392.985 5.974 0.0454-0.0361 0.041 0.009 14 39.370 247.030 27447.761 10.220 0.0361-0.0286 0.033 0.007 19 53.431 390.560 55794.287 10.929 0.0286-0.0227 0.026 0.006 40 112.486 1193.019 198836.499 12.200 0.0227-0.0181 0.021 0.005 69 194.038 2702.906 540581.281 13.200 0.0181-0.0143 0.016 0.004 114 320.585 5740.036 1435009.107 14.177 0.0143-0.0114 0.013 0.003 135 379.640 7397.041 2465680.324 14.718 0.0114-0.0090 0.010 0.002 129 362.767 6909.425 3454712.738 15.055 0.0090-0.0072 0.008 0.002 108 303.712 5292.892 2646445.832 14.789 0.0072-0.0057 0.007 0.001 96 269.966 4435.721 4435720.992 15.305 0.0057-0.0045 0.006 0.001 59 165.917 2137.152 2137151.890 14.575 0.0045-0.0036 0.005 0.001 32 89.989 853.655 853654.903 13.657 0.0036-0.0029 0.004 0.001 6 16.873 69.308 69308.141 11.146 0.0029-0.0023 0.003 0.001 1 2.812 4.716 4715.822 8.459

Table 2

L Interval L Mean L Range N NA NV n ln(n) 0.1142-0.0907 0.102 0.024 1 2.812 4.716 200.673 5.302 0.0907-0.0720 0.081 0.019 3 8.436 24.504 1310.381 7.178 0.0720-0.0572 0.065 0.015 2 5.624 13.338 901.240 6.804 0.0572-0.0454 0.051 0.012 3 8.436 24.504 2076.621 7.638 0.0454-0.0360 0.041 0.009 3 8.436 24.504 2606.822 7.866 0.0360-0.0286 0.032 0.007 10 28.121 149.127 20152.348 9.911 0.0286-0.0227 0.026 0.006 6 16.873 69.308 11747.142 9.371 0.0227-0.0180 0.020 0.005 14 39.370 247.030 52559.541 10.870 0.0180-0.0143 0.016 0.004 19 53.431 390.560 105556.759 11.567 0.0143-0.0114 0.013 0.003 37 104.049 1061.353 365983.882 12.810 0.0114-0.0090 0.010 0.002 58 163.105 2083.048 867936.835 13.674 0.0090-0.0072 0.008 0.002 91 255.906 4093.732 2274295.829 14.637 0.0072-0.0057 0.006 0.002 90 253.093 4026.439 2684292.739 14.803 0.0057-0.0045 0.005 0.001 77 216.535 3186.350 2655291.549 14.792 0.0045-0.0036 0.004 0.001 70 196.850 2761.878 3068752.916 14.937 0.0036-0.0028 0.003 0.001 38 106.862 1104.671 1380838.157 14.138 0.0028-0.0023 0.003 0.001 11 30.934 172.047 344093.442 12.749

EURASIAN PLATE

Figure 1

dN/dL= n N (L)

Size (L, mm)

Figure 2a

ln(no)

Slope = -1/G τ

-4 ln(n) (#.cm )

Size (L, mm)

Figure 2b

Figure 3

Figure 4

18.00 16.00 plagioclase 14.00 12.00 10.00

ln(n) ln(n) 8.00 6.00 4.00 2.00 0.00 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Lmean (cm)

18.00 16.00 plagioclase 14.00 12.00

10.00 y = -158.65x + 16.454

ln(n) ln(n) 8.00 R2 = 0.9816 6.00 4.00 2.00 0.00 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Lmean (cm)

Figure 5

17.00 clinopyroxene 12.00

7.00 ln(n) ln(n) 2.00

-3.00

-8.00 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Lmean (cm)

17.00 clinopyroxene 12.00

7.00 y = -290.75x + 16.676

ln(n) 2 2.00 R = 0.9868

-3.00

-8.00 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Lmean (cm)

Figure 6

APPENDIX A

Crystal size distribution data for GU-07-17 basalt sample

Plagioclase Crystal Size Distribution Data Sample Name: GU-07-17 Major Axis Minor Axis Perimeter Area (µm2) (µm) (µm) (µm) 25.85 20.24 75.05 403.62 30.06 15.26 75.45 356.64 31.29 20.44 85.88 490.11 31.51 25.55 95.25 621.02 32.52 12.91 77.87 326.74 32.99 23.84 98.49 593.84 33.91 21.79 95.60 560.39 36.04 34.18 117.64 932.17 36.66 16.72 90.46 460.02 36.70 28.39 111.23 795.49 36.76 19.27 93.41 553.07 37.34 25.60 104.98 746.48 37.56 17.21 94.19 489.04 37.68 22.05 101.49 645.07 38.23 18.38 96.22 538.16 38.30 33.35 119.54 986.95 38.85 17.38 94.25 515.74 39.33 13.92 90.12 415.37 39.36 22.42 102.92 685.51 39.74 16.13 97.40 484.06 39.88 20.72 104.53 631.06 39.95 15.63 93.90 482.64 40.01 18.67 100.79 580.25 40.56 34.21 131.96 1018.31 40.61 26.88 112.79 848.88 40.76 24.66 110.18 762.39 41.00 34.50 126.38 1080.00 41.25 26.10 115.82 791.22 41.37 27.24 116.72 863.83 41.45 16.11 98.53 510.40 41.97 25.24 115.45 818.62 42.35 20.22 104.23 660.95 42.72 34.99 134.00 1122.86 42.88 24.12 117.04 765.30 43.08 20.06 106.49 663.09 43.38 28.37 120.35 951.39 44.76 17.81 111.83 615.04 44.97 16.87 104.48 577.11 44.98 26.34 119.75 914.02

45.16 36.71 139.16 1270.66 45.62 36.48 140.45 1255.64 45.63 24.27 122.02 786.95 45.78 28.94 124.99 1024.00 45.82 18.48 109.47 649.21 46.15 17.16 107.51 605.43 46.18 23.03 117.68 824.32 46.40 44.06 157.86 1537.60 46.93 24.87 122.97 899.13 46.99 29.04 127.51 1065.64 47.13 18.74 113.80 675.39 47.24 37.63 147.86 1316.28 47.57 20.33 114.40 748.51 47.62 17.29 110.56 640.89 47.69 18.54 115.97 678.04 48.12 17.35 113.30 640.89 48.25 18.03 116.15 630.43 48.99 22.08 118.79 836.07 49.02 37.95 146.65 1431.89 49.51 18.61 120.06 696.19 50.79 15.78 114.57 559.52 50.89 27.54 134.60 1077.91 51.31 14.41 111.89 571.26 51.32 34.88 160.47 1328.32 51.36 21.77 124.99 824.32 51.36 28.38 135.17 1112.62 51.40 15.47 117.28 611.84 51.52 23.33 126.26 917.22 51.61 28.54 135.51 1137.50 51.72 18.36 124.83 700.48 51.75 25.41 130.89 977.02 51.80 19.52 121.27 776.27 51.93 15.67 117.00 599.07 52.11 17.19 119.56 678.04 52.48 33.17 161.93 1287.01 52.73 21.07 124.88 862.76 52.73 23.29 131.04 938.58 53.02 31.10 144.83 1223.23 53.37 28.01 137.89 1137.18 53.47 25.49 135.42 1050.69 53.88 25.39 134.64 1051.77 53.91 33.25 153.11 1282.82 54.09 31.91 151.00 1319.77

100

54.62 49.66 184.13 2037.67 54.72 22.39 134.70 946.17 54.79 33.22 152.21 1394.52 54.82 36.36 157.24 1517.02 54.83 36.19 157.20 1529.06 55.02 21.35 132.00 907.61 55.22 28.88 144.93 1199.18 55.74 28.00 143.84 1178.83 55.83 18.28 129.22 782.68 56.18 23.13 139.41 961.00 56.74 34.51 166.06 1454.29 56.75 26.63 143.54 1143.59 56.75 17.91 130.93 755.99 57.15 18.28 131.14 813.65 57.20 53.77 199.03 2289.64 57.34 31.02 156.74 1357.15 57.40 14.44 124.04 638.53 57.52 22.09 134.96 973.81 57.56 25.02 143.59 1068.50 57.93 23.37 139.16 1042.15 57.98 42.05 169.05 1860.07 58.30 25.44 143.19 1103.01 58.45 26.64 146.42 1213.82 58.54 25.96 153.25 1058.04 59.16 21.45 135.98 962.07 59.48 21.05 136.59 965.27 59.68 19.83 135.82 900.14 60.06 20.36 138.05 924.69 60.50 23.32 145.65 1079.52 60.53 18.47 138.66 852.09 60.56 20.50 146.36 904.41 60.57 51.06 188.95 2366.19 60.74 18.89 138.16 880.92 60.75 21.00 138.51 978.08 60.82 40.76 174.08 1857.93 60.87 51.67 197.61 2405.70 61.06 29.52 157.63 1364.37 61.14 26.33 149.33 1221.54 61.37 25.80 150.43 1216.20 61.44 24.38 148.57 1146.79 61.52 41.33 180.47 1950.83 61.54 25.05 149.03 1089.13 61.81 36.91 182.39 1674.28

101

61.91 20.15 143.59 946.05 61.92 32.32 161.29 1526.92 62.08 18.87 142.63 873.44 62.26 17.72 136.34 833.93 62.46 48.62 210.16 2064.01 62.51 33.33 164.42 1568.57 62.89 28.59 159.91 1329.38 63.25 20.98 142.79 1033.61 63.38 37.54 173.35 1806.62 63.99 26.56 156.63 1313.37 64.15 36.15 173.02 1757.56 64.18 40.15 181.24 1928.41 64.26 31.70 161.14 1558.84 64.26 41.01 179.72 2014.90 64.69 33.59 168.77 1652.93 64.99 18.23 145.50 894.80 65.01 26.85 158.60 1306.87 65.21 30.60 170.30 1509.84 65.37 16.24 140.83 821.12 65.50 48.66 194.13 2448.41 65.51 21.79 152.90 1104.04 65.52 20.25 145.21 1028.27 65.82 22.44 152.86 1142.73 65.89 26.30 161.27 1308.03 66.20 47.01 193.33 2403.57 66.48 41.91 187.84 2149.44 66.58 25.33 165.76 1213.00 66.62 22.20 156.19 1090.20 66.94 39.53 181.14 2006.35 66.97 22.47 155.09 1115.83 66.97 23.44 158.79 1218.00 66.99 26.35 164.90 1325.11 67.09 36.13 183.25 1830.17 67.15 35.55 175.50 1839.03 67.19 25.28 161.04 1301.62 67.67 49.68 207.69 2479.38 67.98 40.13 197.82 1991.40 68.23 25.69 162.04 1359.28 68.45 23.56 164.50 1178.83 68.47 28.24 161.64 1497.02 68.51 13.78 143.14 717.55 69.06 19.66 154.33 1048.56 69.14 22.73 160.58 1206.59

102

69.35 56.92 216.24 3031.94 69.39 17.85 151.31 924.22 69.49 52.10 219.20 2688.66 69.57 32.16 186.13 1662.53 69.69 18.13 159.12 956.73 69.78 36.82 187.13 1939.08 70.08 19.08 158.55 1009.05 70.11 43.81 197.21 2334.16 70.15 21.45 162.39 1129.71 70.56 17.19 153.31 900.14 70.61 33.21 177.34 1800.27 70.77 36.96 187.57 1940.44 70.85 30.41 172.56 1645.44 70.94 29.79 171.71 1627.29 71.04 45.79 201.64 2450.55 71.07 17.23 153.61 933.24 71.18 36.18 189.22 1968.67 71.21 25.51 171.41 1358.21 71.25 35.84 187.86 1858.89 71.25 33.23 189.55 1761.83 71.85 14.18 154.33 747.44 71.89 18.25 162.23 997.30 71.94 45.26 200.43 2508.21 71.96 13.96 147.88 745.31 72.29 41.83 198.84 2249.91 72.40 18.12 156.78 1013.32 72.47 33.48 186.92 1826.97 72.62 42.64 227.90 2071.49 72.69 48.58 210.74 2684.83 72.85 25.83 178.74 1365.42 72.94 24.84 168.70 1377.43 73.49 21.58 165.86 1174.56 73.73 27.79 184.57 1528.52 73.77 59.14 227.05 3368.84 73.99 45.33 219.13 2302.18 74.05 22.28 172.27 1188.44 74.28 22.71 168.32 1279.20 74.53 24.82 171.62 1405.20 74.72 26.93 177.49 1499.24 74.87 17.64 158.85 985.90 74.96 36.31 204.58 2067.22 75.26 22.64 175.69 1268.52 75.72 16.89 164.29 980.22

103

75.72 44.23 214.83 2533.24 75.81 35.54 193.44 2098.18 76.12 21.01 170.70 1156.40 76.20 36.92 208.15 2123.81 76.22 23.50 177.05 1304.82 76.33 19.38 162.35 1052.83 76.43 15.61 160.78 883.05 76.72 28.83 187.13 1678.55 76.82 34.00 200.49 1900.64 76.90 34.06 195.19 1891.03 77.17 53.93 229.82 3147.81 77.20 29.63 183.68 1664.43 77.68 34.16 193.00 2017.81 78.00 54.77 223.57 3290.18 78.22 32.71 189.64 1948.69 78.26 28.17 184.40 1660.39 78.36 23.65 176.61 1428.69 78.61 51.25 240.01 2793.31 78.66 42.33 214.04 2412.11 78.79 26.09 184.42 1565.11 79.15 27.36 187.96 1669.66 79.18 30.13 185.84 1837.64 79.33 52.57 225.03 3191.90 79.51 29.25 187.94 1691.36 79.54 36.35 197.51 2232.72 79.66 32.36 197.15 1997.94 79.72 24.86 182.69 1526.92 80.01 20.75 178.83 1266.10 80.29 24.11 185.52 1510.91 80.31 30.35 200.18 1823.76 80.66 24.48 179.13 1517.31 80.82 19.43 175.86 1154.27 80.84 41.74 212.74 2591.50 80.86 26.76 193.12 1651.85 80.98 36.69 214.25 2245.54 81.22 51.13 237.53 2819.70 81.30 46.82 225.33 2883.00 81.32 16.93 176.86 1037.88 81.45 21.16 180.54 1296.42 81.51 26.26 191.12 1633.70 81.96 34.17 216.02 1935.88 81.98 50.52 235.53 3088.40 82.02 31.22 197.86 1896.37

104

82.28 28.48 198.33 1791.98 82.31 22.66 181.97 1367.51 82.83 36.55 209.11 2277.57 82.95 19.93 180.99 1253.55 82.96 32.14 203.52 1955.10 83.02 32.53 202.73 2018.85 83.64 27.51 303.28 623.58 83.88 23.76 190.75 1532.70 84.31 29.21 204.56 1802.41 84.43 23.31 191.71 1519.45 84.54 27.45 193.27 1760.76 84.66 37.55 219.28 2346.97 84.89 36.11 206.29 2370.47 85.45 19.58 182.44 1240.76 85.63 36.68 223.81 2374.74 86.11 42.33 217.61 2826.41 86.30 46.65 236.46 2985.51 86.35 37.35 219.03 2449.48 86.53 26.48 203.60 1741.54 86.64 23.48 195.06 1525.85 86.86 20.59 190.31 1311.05 86.95 19.24 185.96 1233.28 87.57 38.47 221.26 2443.07 87.81 32.87 216.96 2132.35 87.90 30.00 204.94 2037.32 88.00 47.02 232.89 3190.52 88.23 26.16 200.85 1694.56 88.30 17.99 184.96 1133.98 88.32 58.96 340.99 3137.13 88.35 36.17 222.46 2431.33 88.36 50.79 246.90 3403.01 88.40 32.93 214.25 2213.50 88.59 21.72 192.81 1471.40 88.84 48.90 236.88 3343.21 88.87 15.84 189.20 1021.86 88.98 45.23 237.59 3109.37 89.00 35.76 219.49 2372.60 89.08 26.20 205.98 1797.07 89.08 29.72 217.04 2016.76 89.13 46.40 238.03 3103.03 89.32 47.57 236.88 3259.92 89.75 47.86 237.34 3315.45 89.82 49.63 259.36 3354.96

105

89.96 23.02 194.00 1541.87 90.11 22.71 200.77 1544.20 90.36 20.17 192.25 1336.14 90.43 33.57 217.95 2317.87 90.44 24.72 204.42 1630.50 90.50 27.58 211.68 1860.07 90.75 41.95 232.95 2883.00 90.92 38.41 240.24 2587.22 90.94 18.90 194.44 1209.79 91.12 26.08 212.48 1760.76 91.16 46.29 234.95 3203.40 91.35 36.50 235.96 2339.50 91.63 26.50 206.76 1782.57 91.80 27.42 211.93 1904.91 91.92 29.46 220.86 2026.64 92.10 27.36 209.67 1905.94 92.57 39.78 230.49 2792.24 92.67 26.87 203.73 1872.88 92.85 25.85 212.33 1757.56 92.97 28.99 211.49 2073.62 93.10 27.87 219.34 1970.76 93.11 22.31 201.79 1533.33 93.15 34.81 218.44 2492.19 93.26 32.86 236.21 2234.86 93.32 47.88 257.33 2963.98 93.38 34.68 218.55 2503.94 93.42 33.72 222.96 2393.96 93.64 26.41 210.81 1884.63 93.88 50.38 251.64 3617.63 93.91 40.50 253.33 2834.95 94.00 25.54 208.95 1813.09 94.02 61.53 311.28 4212.30 94.09 36.91 228.51 2621.06 94.09 28.42 222.58 1801.34 94.66 26.68 214.50 1885.69 94.71 21.38 202.91 1469.26 94.80 27.12 211.49 1769.31 95.20 24.85 214.73 1762.71 95.32 24.08 216.77 1653.99 95.34 59.73 286.33 4158.99 95.58 31.75 223.06 2348.04 95.90 40.45 249.53 2731.37 95.99 62.56 274.02 4634.15

106

96.28 30.74 222.77 2234.86 96.36 21.46 214.60 1566.43 96.43 20.56 208.70 1481.01 96.48 22.22 204.83 1632.02 96.51 27.67 217.84 1897.44 96.78 25.62 220.78 1909.08 96.87 49.01 250.09 3598.41 97.51 34.56 234.31 2339.50 98.08 23.07 224.88 1687.09 98.14 50.75 259.22 3821.29 98.48 51.95 281.64 3771.39 98.51 37.66 239.15 2844.56 98.69 27.47 223.16 2070.42 99.24 26.79 228.30 1956.12 99.34 48.25 257.38 3621.90 99.36 62.96 289.59 4397.36 99.56 25.85 223.82 1946.71 99.61 25.70 236.51 1927.34 99.63 39.83 248.50 2960.85 99.75 35.78 239.05 2614.99 99.99 54.12 295.19 3710.53 100.07 24.45 224.58 1845.12 100.11 32.97 235.18 2543.69 100.16 19.70 220.60 1483.14 100.21 28.90 230.18 2154.77 100.30 64.21 279.69 4895.76 100.47 19.74 214.92 1427.62 100.87 40.48 260.41 3085.88 100.93 23.94 217.02 1785.71 100.97 49.98 258.95 3915.54 101.07 54.57 276.29 3995.62 101.35 38.73 254.77 2723.90 101.76 72.26 300.33 5596.54 101.80 62.70 297.48 4542.68 101.86 46.55 253.46 3659.24 101.95 29.36 227.44 2214.57 101.96 26.48 225.00 2054.40 102.05 71.42 311.76 5297.24 102.18 44.97 259.72 3426.09 102.41 27.35 228.05 2084.30 102.72 23.12 221.81 1775.71 102.75 28.14 229.51 2097.11 103.21 27.95 232.43 2192.15

107

103.42 45.11 274.73 3485.22 103.44 48.91 267.51 3861.08 103.70 20.91 223.03 1494.01 104.07 32.48 249.74 2579.24 104.43 24.07 239.02 1840.07 104.69 33.95 251.93 2632.07 104.72 34.95 254.71 2810.39 104.83 73.49 334.18 5231.04 105.19 39.23 253.60 3158.49 105.33 44.32 259.59 3618.70 105.67 39.74 250.05 3177.71 105.83 35.69 291.41 2626.73 106.30 21.01 233.24 1679.07 106.40 42.73 257.23 3412.62 106.45 44.19 277.84 2978.03 106.71 22.17 227.49 1752.22 107.00 54.74 297.87 4392.13 107.11 34.72 254.43 2669.15 107.11 55.58 302.60 4329.84 107.17 27.65 238.59 2134.90 107.34 43.26 266.48 3388.06 108.51 29.13 240.88 2162.09 109.04 30.22 250.58 2449.48 109.18 25.11 243.23 2091.78 109.19 49.38 275.88 4055.42 109.20 55.75 321.26 4361.87 109.58 60.58 302.27 5100.98 109.66 47.71 282.86 3926.88 109.97 47.83 287.79 3914.47 110.24 50.60 273.33 4325.57 110.65 28.73 249.94 2376.87 110.95 93.97 359.55 7446.68 111.03 48.97 283.17 4131.80 111.10 49.03 285.71 4169.67 111.16 38.02 258.78 3212.94 111.28 31.57 258.55 2560.53 111.38 36.09 276.72 2567.74 111.59 77.64 341.34 6529.46 111.63 26.32 241.78 2225.25 111.70 73.74 400.01 5736.10 112.13 44.39 275.63 3841.15 112.34 102.14 422.40 6819.77 113.61 27.26 259.16 2313.68

108

113.74 34.21 261.95 2789.38 113.77 80.35 335.68 6808.27 113.86 28.59 248.61 2416.38 113.94 73.02 332.10 6189.34 114.33 49.56 293.89 4259.36 114.95 34.01 264.58 3026.08 115.15 62.43 333.20 5346.36 115.25 58.07 327.25 4627.37 115.41 36.81 273.62 3086.94 115.51 30.66 260.41 2727.10 115.52 50.78 291.20 4491.07 115.75 53.44 299.72 4749.47 115.96 34.82 258.06 3081.61 116.08 29.56 266.63 2215.64 116.42 62.76 316.40 5486.24 116.45 63.01 341.71 5259.89 116.74 36.92 272.91 3275.94 117.04 39.60 269.76 3521.53 117.10 54.99 315.31 4399.24 117.34 101.88 463.30 8163.23 117.80 44.55 289.53 3992.42 117.95 24.60 247.80 2099.25 118.29 48.17 296.46 4181.42 118.46 72.57 348.61 6419.48 118.98 65.01 333.60 5650.68 119.18 28.55 264.56 2600.04 119.40 65.67 361.41 4631.55 119.42 17.77 245.60 1551.48 119.62 31.13 270.34 2684.39 119.64 22.67 262.33 1981.79 119.78 27.94 263.75 2546.65 120.03 36.09 281.39 3154.21 120.34 43.55 284.87 3919.81 120.41 34.10 274.39 3174.50 120.56 29.09 272.25 2579.75 121.55 82.49 353.60 7633.17 121.81 49.32 301.18 4598.92 121.89 36.52 279.63 3366.70 122.57 24.93 256.71 2276.50 122.84 30.49 291.99 2660.90 122.88 27.69 272.80 2574.01 123.13 20.83 258.57 1948.81 123.38 18.70 257.90 1742.61

109

123.49 31.40 278.45 2984.44 124.04 78.56 386.85 7085.77 124.15 36.83 282.66 3381.65 124.20 40.47 289.30 3790.61 124.55 35.61 293.06 3338.94 124.57 64.41 331.32 6212.33 125.09 57.42 341.14 5336.75 125.44 49.10 304.58 4620.27 125.45 44.17 311.78 4079.53 125.71 52.16 316.34 4717.28 125.77 38.18 319.93 3503.46 125.88 52.84 340.03 4901.10 126.05 80.15 371.48 7611.21 126.83 19.71 273.22 1875.02 127.05 21.33 272.72 2019.17 127.07 22.56 260.35 2034.12 127.09 35.25 285.62 3457.46 127.35 31.09 281.28 3026.71 127.44 26.10 277.50 2520.69 127.51 40.43 299.97 3835.46 127.91 29.47 281.87 2563.73 128.06 29.19 282.20 2817.61 128.40 38.25 294.55 3752.29 128.61 25.26 277.04 2402.50 128.77 39.48 296.09 3753.24 129.12 27.98 291.24 2639.88 129.22 59.49 345.45 5701.93 129.44 30.73 292.91 2895.81 129.46 42.91 318.21 4228.40 129.59 42.00 299.01 4124.82 129.61 37.60 303.14 3644.32 130.11 47.58 338.82 4522.04 130.18 30.68 303.18 2982.30 130.40 63.60 358.92 5987.56 130.41 36.33 304.24 3429.23 130.50 26.01 299.23 2334.16 130.67 32.70 300.11 2805.05 130.71 53.00 319.15 5206.48 130.91 76.67 402.49 6887.16 131.02 44.42 324.87 4120.55 131.38 23.28 276.63 2282.91 131.49 43.55 318.61 4267.91 131.54 24.16 287.84 2400.46

110

131.75 50.53 328.80 5069.81 131.97 79.64 374.53 7921.84 132.37 27.82 292.42 2806.11 132.39 41.80 307.17 4156.89 132.50 38.74 301.43 3728.68 132.79 30.99 298.71 2683.32 133.21 48.45 340.34 4641.63 133.29 62.40 342.87 6344.73 133.39 23.38 274.92 2150.50 133.44 68.01 406.79 6382.10 134.63 40.81 341.28 3854.68 134.78 86.85 673.00 7086.37 135.26 56.58 340.19 5736.10 135.42 29.53 286.19 2676.92 135.45 21.22 289.25 2203.89 135.49 80.63 395.30 8306.24 135.83 32.96 298.26 3057.05 136.10 40.54 323.66 4137.64 136.26 66.07 385.69 6154.67 136.31 21.65 270.82 2104.59 136.33 32.51 307.00 3315.27 136.53 85.54 415.18 8746.16 136.71 36.69 355.07 3069.58 136.83 21.16 278.60 2152.68 137.25 28.72 299.44 2977.57 137.34 30.42 300.07 3112.57 137.49 81.73 390.05 8350.02 137.90 26.28 292.81 2639.55 138.11 50.77 336.56 4795.39 138.37 40.78 313.43 4101.48 138.48 39.09 319.44 4101.48 138.80 38.41 313.06 3873.90 139.03 21.08 293.41 2177.20 139.27 27.73 303.02 2943.07 139.75 61.17 356.77 6477.89 139.96 38.12 334.95 3836.52 140.16 30.09 312.18 3155.28 140.62 40.74 332.58 4213.45 140.72 66.14 407.63 6749.72 141.06 24.42 309.28 2557.28 141.28 39.33 319.61 4032.48 141.30 44.71 339.17 4585.04 141.36 96.00 428.52 10408.69

111

141.49 35.19 320.65 3794.88 141.96 38.33 324.66 3889.91 142.15 58.63 356.77 6316.97 142.30 71.34 389.65 7648.49 142.35 21.22 308.96 2282.91 142.64 38.13 324.18 4193.16 142.66 25.83 308.21 2785.83 143.16 31.71 305.48 3149.94 143.42 29.18 308.50 3060.25 143.45 32.60 326.42 3463.73 143.46 73.79 401.36 8098.02 143.51 25.21 284.97 2349.11 143.88 48.15 336.68 5375.19 144.15 76.05 395.10 7891.94 144.66 32.91 322.74 3540.75 144.96 54.12 349.48 5981.69 145.56 84.23 421.34 9110.27 146.21 29.31 328.38 3233.23 146.41 66.27 388.06 7342.04 146.64 29.49 315.69 3196.93 146.72 55.54 369.23 6007.31 146.75 55.66 408.85 5401.88 146.78 37.86 335.06 4291.40 146.98 41.44 357.63 4322.36 147.06 28.76 532.91 1099.81 147.29 54.55 386.43 5648.82 147.30 32.70 323.66 3283.42 147.78 31.08 318.11 3076.27 148.20 45.65 347.81 5042.04 148.24 35.65 332.18 3616.56 148.38 61.62 388.19 5861.05 148.74 31.72 325.56 3380.58 149.16 51.84 394.01 5440.76 149.16 27.17 317.71 2773.02 149.27 52.65 364.43 5724.09 149.61 36.11 359.31 3750.19 149.84 26.11 325.60 2891.84 149.98 29.51 329.79 3321.54 150.12 34.81 331.76 3871.76 150.42 84.08 472.43 8187.72 150.46 36.65 338.94 4034.57 151.27 31.50 337.92 3573.85 151.42 42.44 363.76 4555.14

112

153.88 32.16 335.90 3628.31 153.90 57.37 387.90 6364.98 154.45 59.87 384.90 6955.69 154.76 27.52 325.68 3154.26 154.80 33.77 355.16 3750.03 154.80 81.17 459.60 9495.20 154.82 16.49 310.59 1930.54 154.83 48.07 433.36 5423.24 154.96 39.37 349.59 4307.41 155.15 97.24 532.67 8599.88 155.19 39.60 353.32 4561.54 155.35 30.72 344.89 3531.14 155.57 33.41 360.76 3612.29 155.73 38.91 360.59 3455.33 155.77 36.54 350.53 4077.44 156.31 48.46 391.40 5586.61 156.42 109.04 474.49 12980.97 157.41 53.36 412.60 6150.40 158.10 64.04 405.01 7659.17 158.31 40.18 361.01 4736.66 158.74 68.69 440.26 7794.17 158.83 63.67 383.72 7797.31 159.48 35.63 605.24 1276.55 159.52 69.52 412.17 8346.81 159.82 89.51 434.22 10674.57 160.56 34.11 345.27 3918.74 161.43 38.29 378.40 4646.97 161.75 53.78 393.06 6282.39 161.96 42.24 380.81 4990.15 162.03 37.32 353.11 4178.85 162.54 43.49 386.80 5048.70 162.71 46.29 376.27 5530.02 162.72 24.19 332.84 2808.25 162.72 43.39 416.18 4640.56 163.55 78.65 431.30 9565.15 163.77 83.95 496.40 9763.75 164.52 27.04 350.09 3201.31 164.86 46.09 382.80 5704.23 165.04 30.63 344.39 3731.38 165.42 38.27 364.39 4574.05 166.40 67.76 448.58 8260.32 166.48 73.62 446.44 8747.67 166.91 48.34 390.67 5883.45

113

166.97 29.25 346.63 3532.21 167.40 46.49 381.28 5931.50 167.45 43.95 380.69 5379.46 167.97 40.28 382.87 4572.22 168.13 55.44 631.34 1330.45 168.41 47.49 423.36 5603.69 168.56 46.41 382.21 5861.05 169.29 55.83 418.82 6144.38 169.56 45.79 404.73 5536.95 169.62 25.18 356.67 3159.55 169.66 25.68 355.31 3106.16 169.75 79.81 465.21 10022.16 169.77 102.30 477.45 13037.56 170.37 53.87 406.43 6905.50 170.38 35.68 371.21 4524.17 170.93 45.81 418.36 5676.30 171.23 135.63 640.39 16734.21 171.32 40.33 373.64 4656.58 171.52 42.50 401.57 5320.73 172.32 43.63 445.78 4824.22 172.65 36.93 377.17 4221.99 173.62 42.31 419.57 4932.06 174.64 77.56 479.29 10139.61 174.76 93.93 539.92 11346.20 174.83 46.08 409.09 6132.24 174.89 29.54 372.33 3773.52 175.52 78.32 462.45 9932.21 176.28 79.34 469.86 10633.99 176.55 44.36 397.33 5844.32 176.60 40.36 397.77 5241.72 177.10 41.79 416.20 5425.38 177.86 146.93 596.06 19317.63 178.01 45.59 392.49 6031.87 178.20 55.40 462.51 6883.96 178.29 56.01 484.49 5762.77 178.52 124.39 572.30 16091.23 178.81 75.74 466.97 10330.55 180.79 66.55 553.84 7409.31 180.87 38.01 401.22 4897.89 181.60 27.20 388.20 3485.68 182.99 109.72 512.99 15319.65 183.08 35.99 396.25 4960.88 183.14 39.19 404.11 5219.29

114

183.16 73.46 504.82 9849.62 184.53 39.53 409.57 5445.66 184.87 52.18 422.92 6795.33 186.59 72.89 502.89 9395.87 187.04 93.25 591.92 12936.12 187.80 61.28 460.65 8555.03 187.90 79.06 522.09 9856.65 188.14 48.78 443.75 6351.39 188.98 81.60 540.73 11459.38 189.21 44.85 440.00 5691.25 189.31 36.52 411.26 5191.93 190.26 49.69 442.20 6451.51 190.27 60.43 465.28 8748.30 190.42 42.58 434.58 5589.81 190.74 30.21 396.08 4135.50 191.79 22.30 379.54 3174.50 193.66 35.82 423.08 5119.79 194.05 46.72 432.20 6725.93 195.44 57.97 491.71 8232.56 195.81 63.38 472.38 9327.03 196.19 79.02 585.81 10997.57 196.48 38.24 424.20 5746.78 196.83 59.34 485.53 8763.25 197.00 63.32 622.10 7520.35 197.48 114.19 554.62 17019.30 198.09 45.33 451.19 6780.38 198.61 40.84 459.42 5536.42 198.69 32.82 406.78 3781.56 200.29 68.00 490.31 9683.67 201.11 36.50 454.49 5375.94 201.20 64.46 504.15 9593.98 201.23 95.82 564.47 14461.97 201.54 38.54 445.10 5320.73 201.57 51.31 498.89 7630.34 201.72 24.48 396.92 3228.96 202.25 66.81 507.33 9571.55 202.90 75.95 526.84 10920.16 204.02 79.10 528.24 11940.61 206.03 33.20 423.28 5107.18 207.07 40.77 449.09 5414.70 208.75 48.77 509.91 7399.70 209.47 76.41 625.13 10765.33 209.87 65.85 490.27 10367.05

115

210.93 38.61 466.20 6124.77 211.50 31.97 446.39 4958.76 211.95 69.49 555.79 10660.92 212.00 66.98 539.60 9731.72 212.27 43.07 497.20 6667.20 213.34 83.80 564.76 12940.39 214.23 22.48 437.99 3633.65 215.17 31.23 453.65 5161.61 215.43 68.31 521.52 8049.97 215.48 73.23 573.73 11206.32 215.93 54.10 500.55 8687.44 216.19 20.65 442.51 3068.53 219.83 33.06 466.77 5411.49 219.97 77.32 547.99 13004.46 220.60 30.23 453.57 4854.12 222.34 39.51 465.46 6077.79 222.38 77.95 554.57 12660.63 223.37 68.01 536.47 11316.30 223.85 60.96 541.38 9808.60 224.29 39.71 491.11 6434.43 224.60 35.84 489.23 6064.97 226.34 44.76 480.42 7600.44 228.37 46.35 520.37 7286.06 229.88 42.79 496.08 7112.46 230.00 51.73 523.63 8857.21 232.44 44.56 518.36 7921.72 232.51 38.05 511.13 6417.34 232.95 71.06 561.02 12516.48 233.70 58.70 537.43 10119.32 234.43 83.89 618.86 14237.56 234.58 118.27 716.94 20309.12 235.23 38.62 525.38 6795.33 235.41 54.95 531.38 9796.85 239.09 39.00 497.48 6412.03 239.56 45.25 503.27 7812.93 241.34 84.69 609.99 15035.37 243.45 44.07 514.77 8181.31 244.33 57.62 576.78 9815.12 244.70 71.73 573.83 11983.48 246.26 70.11 576.79 12875.26 246.59 28.30 516.40 4973.43 248.77 108.19 825.21 19294.73 249.18 164.75 733.49 31661.80

116

251.45 43.32 522.59 8308.56 252.10 69.50 587.92 12766.34 255.69 34.41 539.69 5962.47 258.32 42.51 573.47 8058.51 262.79 55.11 629.62 10902.00 263.52 61.44 610.25 11345.72 263.78 66.67 613.18 13045.03 263.91 48.73 579.29 9826.62 264.52 118.87 1082.28 2198.68 264.53 93.02 687.51 17285.19 265.80 65.78 625.33 13502.04 267.63 101.87 680.88 20463.95 267.74 63.13 614.72 12420.49 268.18 65.10 588.06 13063.18 270.78 35.75 546.64 7076.16 271.07 41.69 579.93 8501.64 277.62 38.49 618.04 8029.68 283.95 54.31 607.79 11092.71 284.51 124.86 1099.85 19183.81 289.20 36.53 612.71 7778.49 292.20 82.01 722.02 17278.91 292.84 81.61 678.23 18270.73 293.65 36.40 612.21 7549.18 297.07 35.24 599.75 7251.27 302.45 41.97 621.53 8317.98 306.76 67.39 691.42 14909.82 309.47 45.58 625.20 9554.47 311.85 46.25 647.44 10474.82 313.74 62.78 730.96 13426.23 316.95 53.26 688.08 10420.44 325.29 54.12 745.17 12432.13 331.93 43.39 737.47 9243.75 332.10 85.93 865.31 18539.78 333.67 101.13 780.29 25021.22 343.10 66.32 726.80 17034.25 343.45 55.10 738.52 14211.04 354.55 71.39 797.00 19045.94 359.83 91.08 856.14 24086.92 366.74 57.55 792.39 14754.54 369.09 64.32 947.46 15907.74 370.70 111.84 986.60 30188.19 375.02 78.74 856.22 20899.60 381.31 57.94 790.28 15892.79

117

385.18 50.43 814.76 14139.50 390.28 124.66 1047.74 35551.64 394.92 76.84 890.26 20973.70 399.32 90.92 945.24 26537.46 400.09 64.23 896.91 18525.93 402.65 95.91 1048.90 25168.57 404.65 58.21 839.35 17460.83 408.47 58.08 882.37 16017.72 416.75 68.75 964.20 20954.06 454.58 65.59 950.52 20330.71 654.87 83.15 1457.76 35366.91 720.72 91.09 1492.33 45446.73

118

Clinopyroxene Crystal Size Distribution Data Sample Name: GU-07-17 Major Axis (µm) Minor Axis (µm) Perimeter (µm) Area (µm2) 23.94 19.94 71.67 373.72 23.97 23.40 77.65 437.02 24.18 18.71 70.07 349.20 24.55 19.84 72.38 379.06 24.89 20.79 74.41 404.61 26.33 25.08 83.82 514.67 26.42 26.16 87.63 523.79 27.18 23.03 81.99 490.34 28.07 20.38 79.94 445.38 28.10 25.52 89.41 552.04 28.41 26.43 90.77 582.34 28.81 24.46 86.89 548.84 28.96 23.96 89.31 537.09 29.26 27.98 93.69 639.60 29.43 21.73 85.88 491.18 29.70 23.37 87.17 538.43 29.93 22.45 90.27 484.77 30.06 24.37 90.66 567.70 30.27 25.91 91.48 610.77 30.55 24.37 90.16 583.01 30.65 26.89 95.95 637.75 31.41 22.31 89.32 531.11 31.45 28.56 99.79 695.12 31.77 27.76 98.68 688.72 31.82 24.79 93.91 604.30 32.22 26.04 96.55 646.12 32.85 31.83 110.37 799.77 33.09 27.25 97.93 702.60 33.15 31.66 108.12 813.40 33.25 17.29 85.23 427.61 33.53 26.81 100.04 697.35 33.56 24.50 96.97 629.99 33.57 31.96 107.55 829.66 33.93 29.01 106.09 760.26 33.96 32.08 111.69 827.53 34.21 18.43 89.81 480.50 34.26 29.32 105.33 768.44 34.32 23.87 96.20 636.71 34.33 30.77 107.91 817.92 34.40 20.89 90.87 556.20 34.57 27.36 101.59 736.03 34.78 32.19 110.79 857.43 34.87 27.25 102.09 743.35 35.00 28.23 103.18 773.67 35.03 31.94 110.58 864.90 35.09 29.99 107.30 822.19 35.23 24.61 102.21 658.82 35.52 19.79 90.62 542.43

119

35.83 28.96 112.70 780.99 36.26 23.68 103.27 652.41 36.66 28.42 108.05 812.58 37.20 29.24 111.36 843.72 37.31 26.74 105.33 780.99 37.45 34.58 118.85 1001.58 37.46 31.11 114.36 903.34 37.79 31.08 114.86 908.68 37.96 29.56 111.96 872.99 37.97 30.20 112.35 895.99 37.97 22.89 101.60 662.02 38.20 36.40 125.37 1065.36 38.21 36.24 123.92 1078.95 38.34 35.14 122.33 1047.59 38.54 29.94 115.10 875.08 39.00 34.83 123.88 1051.77 39.05 26.69 110.27 791.44 39.16 33.78 121.66 1015.46 39.17 29.93 115.82 891.59 39.48 36.09 128.36 1090.45 39.69 34.49 120.84 1060.13 39.74 28.77 112.90 889.46 39.82 34.88 125.95 1062.44 40.29 34.81 123.88 1092.34 40.63 28.66 118.49 870.90 40.66 29.88 119.54 938.86 40.70 34.75 125.68 1086.27 40.76 34.17 123.38 1090.20 41.03 29.00 121.59 885.54 41.04 28.22 118.39 858.49 41.19 35.63 131.64 1113.69 41.27 37.18 131.04 1193.78 41.37 25.55 111.61 824.90 41.47 36.09 129.08 1163.88 41.75 33.28 126.52 1059.09 41.75 31.21 125.65 972.74 41.76 35.84 129.22 1146.79 41.89 33.05 125.47 1048.63 41.94 23.50 108.32 762.17 42.10 38.77 134.57 1274.93 42.47 34.26 130.37 1115.54 42.48 28.78 117.99 938.58 42.54 29.90 133.40 950.36 42.63 36.34 130.54 1205.52 42.75 35.53 131.71 1151.09 42.78 33.32 127.86 1096.61 42.86 34.90 130.16 1135.41 42.90 29.60 120.20 985.56 42.96 30.59 123.98 1001.58 43.01 36.88 131.71 1239.96 43.02 38.67 135.45 1287.01 43.03 31.28 126.87 1022.50

120

43.20 26.87 119.95 794.43 43.21 35.22 131.54 1169.22 43.33 28.64 126.90 912.95 43.34 30.95 124.84 1010.12 43.36 35.43 131.04 1201.25 43.63 29.04 124.44 962.07 43.68 32.45 126.40 1091.27 43.81 25.55 122.78 824.90 43.88 22.41 112.06 767.39 43.97 34.51 133.61 1151.09 43.99 37.32 152.81 1129.71 44.02 32.28 134.04 1062.22 44.15 34.79 132.31 1170.96 44.27 34.93 133.56 1196.98 44.37 36.79 135.53 1253.57 44.51 41.32 144.04 1404.13 44.51 36.40 140.77 1187.37 44.55 37.14 140.16 1232.22 45.03 37.10 139.04 1215.91 45.08 36.57 135.78 1280.27 45.18 24.16 116.79 834.31 45.68 37.43 144.29 1287.74 45.70 35.66 137.24 1255.71 45.86 42.43 145.50 1514.11 45.96 29.52 125.19 1053.90 46.18 35.71 135.90 1282.82 46.24 39.11 141.79 1400.97 46.26 35.73 136.28 1269.59 46.32 44.88 150.54 1621.95 46.92 38.99 145.00 1418.01 46.97 37.34 140.84 1338.24 47.25 36.39 141.52 1327.25 47.44 25.80 131.39 908.68 47.67 39.52 146.97 1382.15 48.03 39.21 149.79 1446.84 48.08 33.62 138.09 1240.76 48.11 36.78 141.98 1351.81 48.84 38.85 147.57 1459.51 48.84 33.67 140.14 1245.19 48.86 29.68 132.45 1111.36 48.94 35.71 140.01 1356.08 48.98 28.11 132.85 1042.15 49.12 27.04 127.33 1026.68 49.17 42.65 154.10 1633.07 49.22 32.22 139.51 1179.89 49.41 26.28 196.39 401.47 49.51 31.68 137.49 1196.98 49.74 43.06 155.99 1648.65 49.82 41.45 152.31 1572.84 49.97 34.83 144.37 1310.01 49.98 44.73 164.22 1630.97 50.03 42.53 153.92 1656.12

121

50.08 26.76 129.02 1041.31 50.18 29.28 136.99 1126.51 50.36 30.88 139.66 1159.61 50.50 43.85 157.20 1722.32 50.50 32.06 146.61 1175.62 50.52 37.12 146.97 1446.84 50.59 34.35 143.08 1299.49 50.78 34.50 142.08 1363.33 50.98 35.04 147.57 1369.60 51.04 43.95 160.48 1697.89 51.08 24.20 127.23 951.40 51.12 29.48 140.38 1133.32 51.32 26.32 130.68 1054.96 51.89 26.14 136.65 937.81 52.24 37.69 150.49 1514.11 52.44 39.42 157.24 1568.57 52.48 44.66 162.69 1810.95 52.51 26.81 136.13 1019.73 52.80 33.36 148.68 1334.72 52.92 38.32 155.44 1510.74 53.14 23.76 130.33 979.15 53.31 47.25 172.02 1945.49 53.31 35.49 150.39 1459.65 53.52 42.26 162.43 1747.02 53.58 50.07 173.02 2091.78 53.60 40.29 159.66 1621.95 53.69 43.36 165.36 1774.65 53.86 34.91 154.27 1384.91 54.10 43.23 164.40 1782.12 54.15 32.54 155.13 1332.59 54.18 37.53 154.13 1563.23 54.21 39.60 160.44 1651.88 54.30 35.23 150.14 1483.14 54.39 45.64 170.91 1855.80 54.43 42.60 170.60 1741.54 55.00 48.51 174.84 2027.71 55.22 28.09 145.80 1187.37 55.46 35.55 160.43 1469.26 55.53 50.74 181.78 2185.09 55.63 46.53 176.61 1977.52 55.70 48.99 182.75 2006.35 56.77 41.95 164.61 1802.41 56.83 25.05 141.02 1070.98 56.84 40.98 169.61 1755.39 56.92 41.42 163.98 1827.53 57.29 46.52 180.69 2026.17 57.33 39.01 162.98 1699.98 57.93 48.96 178.47 2149.44 57.94 40.03 164.96 1796.00 58.13 36.08 157.65 1630.50 58.17 37.82 169.16 1609.02 58.25 49.85 198.07 2022.37

122

58.51 46.65 175.59 2130.22 58.54 44.18 178.97 1848.32 58.56 38.01 165.51 1682.82 58.63 49.85 193.08 2036.25 58.73 47.31 182.42 2129.68 58.75 50.96 189.86 2317.87 58.89 33.45 158.29 1458.47 59.32 53.78 207.24 2339.50 59.41 37.66 161.23 1751.15 59.88 48.31 182.60 2236.99 60.16 47.04 179.72 2185.74 60.19 49.58 183.83 2283.36 60.21 37.44 175.80 1595.26 60.57 42.30 179.22 1904.91 60.66 40.58 176.10 1869.35 60.84 26.73 151.56 1206.50 60.92 53.53 195.55 2523.16 61.09 26.57 154.88 1191.64 61.20 43.81 175.79 2085.77 61.28 46.86 190.56 2156.86 61.28 48.42 186.59 2264.76 61.32 32.99 171.66 1455.38 61.47 53.23 200.54 2447.51 61.53 42.80 192.05 1894.44 62.18 48.92 192.37 2341.64 62.22 43.24 180.08 2100.32 62.52 31.32 162.32 1499.24 62.67 38.28 174.70 1803.48 62.88 50.76 193.23 2439.87 62.90 46.35 183.35 2255.15 62.95 50.80 204.63 2362.82 63.02 34.30 163.75 1683.89 63.26 53.67 207.05 2416.38 63.40 46.61 182.60 2293.59 63.52 26.95 156.35 1270.28 63.53 45.36 181.74 2238.06 63.60 50.20 191.37 2458.02 63.69 51.33 201.70 2424.92 63.75 37.57 190.81 1475.20 63.76 32.02 165.17 1561.97 63.79 51.93 196.90 2544.51 63.80 31.73 166.47 1547.33 63.90 39.07 189.61 1822.30 64.03 34.55 167.92 1691.61 64.03 51.18 196.61 2461.23 64.24 29.73 161.48 1453.25 64.70 60.02 216.21 2921.44 64.82 35.91 170.81 1781.05 65.10 53.22 205.48 2610.72 65.14 49.72 207.77 2279.18 65.40 47.20 189.82 2367.00 65.57 53.36 207.46 2678.56

123

65.60 41.09 192.98 2060.81 65.89 38.76 177.97 1940.15 66.29 56.80 211.58 2858.44 66.41 37.26 177.65 1889.21 66.56 45.43 193.74 2283.36 66.83 55.27 209.77 2753.84 66.89 53.58 208.91 2774.09 67.00 56.82 213.73 2886.20 67.06 45.00 194.29 2230.59 67.38 36.02 182.75 1840.85 67.38 51.01 202.45 2561.60 67.73 51.53 203.21 2680.12 67.98 50.01 198.03 2632.07 68.33 49.52 200.08 2604.33 68.41 46.26 201.85 2380.08 68.43 31.63 173.02 1563.23 68.72 54.64 212.08 2895.81 69.16 33.84 174.29 1801.34 69.24 38.75 187.57 1882.94 69.42 67.86 236.05 3651.92 69.62 54.13 205.63 2923.57 69.68 62.80 224.23 3367.77 69.84 48.49 205.62 2477.83 69.90 34.44 188.80 1815.22 70.26 35.54 191.37 1888.90 70.47 37.92 189.05 1990.34 71.02 24.80 167.38 1304.82 71.04 53.75 212.04 2933.18 71.48 48.31 203.92 2626.73 71.96 40.63 202.96 2049.06 72.08 34.24 186.12 1876.67 72.11 47.01 207.95 2562.67 72.22 32.54 178.32 1801.34 72.45 51.08 226.67 2655.56 72.57 48.87 201.92 2771.61 73.07 41.54 200.64 2297.86 73.17 70.02 264.64 3748.97 73.27 53.80 219.03 3007.93 73.35 30.87 178.41 1739.41 73.35 60.52 326.42 664.94 73.72 57.37 216.07 3284.48 73.88 50.46 223.47 2805.07 73.99 61.88 246.87 3465.82 74.22 53.14 217.93 3043.44 74.32 42.68 201.70 2432.40 74.72 43.70 201.35 2546.65 74.74 30.83 184.67 1580.79 74.77 54.41 223.23 3107.23 74.92 49.30 221.56 2729.24 75.13 49.02 211.96 2785.20 75.53 53.53 229.71 3103.03 75.69 45.19 230.18 2445.21

124

75.72 69.64 259.91 3666.75 75.85 45.81 232.04 2512.48 76.10 30.94 188.80 1773.58 76.30 43.95 207.69 2533.84 76.46 50.87 224.67 2938.89 76.66 68.53 252.66 4038.33 76.67 37.61 197.92 2169.72 76.75 49.25 216.63 2930.53 77.35 32.75 191.61 1888.17 77.36 51.59 224.67 2979.66 77.45 50.81 228.61 2909.69 77.61 52.98 221.03 3144.85 77.75 52.06 228.76 3069.86 77.75 34.80 194.94 2014.90 77.95 59.34 235.84 3582.92 78.01 68.75 251.28 4166.47 78.04 47.64 230.35 2094.13 78.35 41.99 210.68 2411.04 78.67 39.68 207.62 2231.09 78.90 45.72 222.16 2550.92 79.02 62.50 251.20 3781.00 79.25 69.69 262.68 4030.86 79.46 39.74 209.36 2248.74 79.59 50.03 229.11 2973.76 79.70 45.07 218.84 2747.39 79.89 53.29 236.63 3095.49 79.99 40.22 208.82 2431.33 80.21 55.55 240.76 3293.03 80.48 58.80 257.34 3489.50 80.88 48.70 224.31 2925.30 80.94 44.21 222.52 2721.76 81.37 62.83 249.68 3932.62 81.51 44.93 214.25 2847.76 81.73 47.43 222.29 2936.80 82.06 55.64 239.83 3472.09 82.06 36.82 209.61 2294.65 82.11 27.33 199.57 1708.44 82.33 32.84 200.89 2100.32 82.64 43.86 223.33 2528.50 83.08 34.90 206.59 2115.27 83.12 44.83 228.92 2814.66 83.28 48.59 229.32 3092.28 83.54 49.92 243.63 2810.29 83.77 36.34 217.08 2230.04 84.02 65.86 280.11 3987.08 84.13 52.73 235.63 3382.72 84.37 62.12 252.70 4050.08 84.44 45.64 233.35 2852.03 84.58 26.92 194.13 1729.80 84.70 41.70 215.15 2729.24 84.81 71.30 266.30 4676.86 84.90 58.41 259.04 3532.73

125

85.10 53.24 246.75 3431.84 85.68 64.86 254.02 4306.35 85.96 41.76 218.47 2748.61 86.14 65.71 276.69 4049.01 86.17 64.69 284.60 3680.63 86.41 42.84 227.86 2765.54 87.59 72.85 284.36 4799.87 87.95 64.91 273.27 4279.65 88.18 51.70 242.02 3398.91 88.30 48.63 259.43 3090.49 88.53 46.32 242.58 3137.13 88.93 53.55 267.32 2987.64 89.25 49.56 234.50 3385.32 89.61 73.16 297.25 4797.52 89.65 42.77 232.64 2934.25 89.83 80.43 297.34 5488.85 90.02 57.10 258.05 3933.69 90.04 43.50 247.00 2767.68 90.04 66.45 280.62 4168.60 90.05 58.62 264.22 3882.97 90.15 48.75 236.52 3406.21 90.38 56.26 264.06 3847.43 90.55 85.51 347.40 4922.45 90.70 53.00 273.52 3512.99 90.87 52.47 246.86 3664.61 91.68 52.13 254.31 3632.58 91.82 45.08 239.26 2809.32 92.10 78.29 291.90 5529.63 92.94 29.23 218.74 1936.95 93.30 48.93 255.73 3289.13 93.38 76.62 306.58 5493.71 93.41 70.74 279.01 5108.25 93.50 50.14 245.65 3635.78 93.78 70.97 299.38 4966.23 93.90 83.63 312.03 5870.64 94.37 39.23 231.89 2875.52 94.84 48.53 256.44 3425.43 95.11 56.59 268.78 3912.34 95.36 73.65 295.58 4969.44 95.59 50.65 260.63 3424.00 95.82 51.76 261.93 3773.52 95.86 77.48 325.86 4964.02 96.20 62.43 271.10 4640.56 96.27 67.66 313.28 4650.17 96.55 47.99 261.97 3266.33 97.02 92.55 324.33 6938.42 97.36 77.05 302.49 5748.91 97.36 57.73 260.28 4331.97 97.43 59.41 291.01 4295.67 97.54 47.00 260.26 3300.50 98.11 95.32 335.81 7068.69 98.12 73.20 451.53 4049.01

126

98.63 51.00 293.58 3474.55 98.66 86.94 326.69 6561.53 98.88 64.08 287.69 4763.35 99.30 38.09 241.56 2799.71 99.77 45.27 252.84 3452.23 99.80 63.93 320.24 4690.75 99.91 82.21 368.21 4293.53 100.30 41.69 260.93 2983.37 100.78 54.26 267.11 4039.80 100.81 48.42 262.33 3627.24 101.74 47.47 260.62 3660.34 102.12 70.76 299.63 5523.61 103.89 33.72 245.40 2653.43 104.63 57.75 289.95 4627.75 104.95 57.69 294.33 4502.82 107.73 69.91 344.52 5074.84 108.67 95.45 405.35 7459.49 109.38 105.25 415.68 8517.66 110.06 79.96 355.56 6444.04 110.38 70.85 330.70 5942.60 110.48 74.09 329.09 6197.70 110.90 60.16 301.64 5034.57 110.97 96.55 353.05 8325.46 111.05 33.89 259.91 2456.96 111.45 62.70 300.88 5391.21 111.49 52.97 291.64 4364.95 112.30 33.53 256.44 2860.58 112.90 53.20 287.44 4575.09 113.17 52.43 287.59 4501.75 113.92 93.28 363.03 8202.66 113.96 52.42 290.35 4604.36 115.58 66.45 322.85 5441.39 116.00 76.72 349.32 6583.91 116.53 63.16 324.81 5438.67 117.36 60.98 325.79 5238.51 117.80 59.87 317.58 5231.66 117.89 53.03 296.69 4703.56 118.12 86.31 342.51 7948.53 120.37 77.32 356.73 6738.74 120.57 87.39 363.37 8060.65 122.11 105.23 411.08 9750.30 122.56 70.59 334.95 6582.44 122.97 63.49 330.04 5509.76 123.01 46.65 319.74 4160.06 123.63 70.83 353.66 6576.44 123.68 88.18 366.52 8410.88 124.31 55.87 367.96 4785.78 125.42 93.31 424.56 8108.70 125.60 65.62 368.83 5203.28 126.93 45.96 303.91 4440.89 127.87 47.55 331.63 3816.24 128.37 67.43 360.57 6414.14

127

128.49 52.52 326.83 5019.62 130.84 70.48 353.95 6797.47 131.16 85.66 444.76 6706.71 131.40 50.99 343.16 4969.44 132.89 61.91 339.34 6326.58 133.18 78.73 382.68 7827.87 133.30 89.82 425.06 8959.72 133.32 123.35 505.70 12147.03 133.46 86.44 384.80 8603.08 134.31 82.87 365.86 8681.80 136.05 116.37 452.19 11786.12 136.88 46.11 354.70 4183.55 137.91 86.08 433.76 8606.28 139.68 80.36 409.86 7742.45 141.04 97.43 425.22 10512.27 143.84 75.24 386.12 8367.10 144.05 111.02 434.86 12355.25 146.21 86.75 429.54 9656.98 146.47 97.49 458.96 9602.88 148.36 68.54 392.24 7627.13 152.97 42.33 357.25 4639.49 156.33 126.43 539.73 14458.77 157.58 59.39 387.23 6899.98 160.14 79.91 421.57 9655.91 162.44 94.02 462.92 11382.50 163.50 111.17 538.97 11533.06 164.65 57.01 422.26 6737.67 164.97 78.47 417.93 9811.80 165.92 99.50 474.61 12404.37 166.09 67.52 424.28 8443.98 167.53 107.54 602.61 10472.76 167.84 94.41 487.81 11956.97 171.40 102.20 494.05 13161.42 173.59 90.52 506.18 11552.28 181.28 142.76 561.18 19648.17 192.95 82.25 548.41 11033.34 199.86 133.13 628.01 19111.07 200.03 152.59 668.61 22429.03 204.66 131.00 680.58 20047.52 207.26 97.19 554.76 14984.12 207.29 148.17 824.70 21680.15 208.91 85.83 609.53 12061.61 210.06 186.35 740.74 28618.56 210.68 159.46 652.51 25095.96 216.13 173.17 705.19 28299.30 223.98 170.69 819.44 28753.23 225.48 188.89 724.39 32079.23 226.20 100.13 648.45 15552.80 228.34 105.34 760.30 15482.77 242.31 188.24 753.18 35149.09 246.35 138.77 737.84 23114.17 264.03 144.75 750.11 27488.85

128

273.09 91.60 678.03 17627.93 278.17 124.62 912.19 23297.83 286.77 167.23 831.99 36018.26 286.95 242.16 972.57 52371.26 293.04 159.99 908.52 35810.04 296.10 256.37 1196.96 50241.05 306.36 271.36 1035.07 60848.34 308.39 191.80 989.64 42610.71 319.11 257.28 1533.55 54674.46 322.19 176.68 1404.12 2905.42 333.80 238.05 1003.96 60846.21 343.13 289.63 1682.93 69378.81 369.19 168.56 957.22 46060.70 375.65 281.23 1187.90 82238.05 408.20 148.17 1039.50 44587.17 476.73 329.93 2589.16 97823.33 493.86 376.90 1552.60 141737.80 511.49 270.17 1494.95 106484.80 608.66 329.63 1759.21 152341.90 627.94 482.98 2251.27 235816.90 789.53 495.58 3754.13 7810.79 818.39 450.38 2458.96 268161.50 878.19 394.28 2456.67 253929.10 1142.45 755.86 3874.97 652327.40

129