Table Of ContentSvenMaa10e
Principles of
Igneous Petrology
With 291 Figures
Springer-Verlag
Berlin Heidelberg New York Tokyo
Professor Dr. SVEN MAAL0E
Department of Geology
University of Bergen
Allegaten 41
N-50l4 Bergen
ISBN 978-3-642-49356-0 ISBN 978-3-642-49354-6 (eBook)
DOl 10.1007/978-3-642-49354-6
Library of Congress Cataloging in Publication Data. Maall'Je, S. (Sven), 1943- . Princi
ples of igneous petrology. Includes index. 1. Rocks, Igneous. I. Title. QE461.M216
1985 552'.1 84-26829
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© Springer-Verlag Berlin Heidelberg 1985
Softcover reprint of the hardcover 1st edition 1985
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tective laws and regulations and therefore free for general use.
8700 Wiirzburg.
2132/3130-543210
Dedicated to
Peter J. Wyllie for his inspiration
Preface
Igneous petrology was to some extent essentially a descriptive sci
ence until about 1960. The results were mainly obtained from field
work, major element analyses, and microscopical studies. During the
1960's two simultaneous developments took place, plate tectonics
became generally accepted, and the generation of magmas could
now be related to the geodynamic features like convection cells and
subduction zones. The other new feature was the development of
new analytical apparatus which allowed high accuracy analyses of
trace elements and isotopes. In addition it became possible to do ex
perimental studies at pressures up to 100 kbar.
During the 1970's a large amount of analytical data was obtained
and it became evident that the igneous processes that control the
compositions of magmas are not that simple to determine. The
composition of a magma is controlled by the compositions of its
source, the degree of partial melting, and the degree of fractionation.
In order to understand the significance of these various processes the
relationship between the physical processes and their geochemical
consequences should be known. Presently there are several theories
that attempt to explain the origin of the various magma types, and
these theories can only be evaluated by turning the different ideas
into quantitative models. We will so to speak have to do some book
keeping for the various theories in order to see which ones are valid.
the present book is intended as an introduction to the more fun
damental aspects of quantitative igneous petrology.
Apart from using quantitative analysis as an evaluation of ideas,
the application of physicochemical equations has a much more sig
nificant potential. Many if not most igneous processes can not be ob
served, and will never be observed. Processes like convection in the
mantle and magma chambers, dyke propagation, and magma ac
cumulation in the mantle can not be observed directly. These and
other processes can only be understood by developing quantitative
models. Hence, the application of physical and chemical principles,
by using equations and various constants, is mandatory for the
understanding of the generation of magmas.
The attempt to convert an idea into equations is frequently a dif
ficult task, and this represents a real challenge for the present gener
ation of the students of igneous petrology. It is hoped that the pres-
VIII Preface
ent book will assist the graduate students to a quantitative treatment
of petrology, although the present book only represents a beginning.
Clearly in order to bring further development to igneous pet
rology it is nescessary to apply physicochemical principles. However,
the new ideas, the creative insight, is hardly attained by reading text
books on physics. There is still a lot left for the individual petrologist
to discover without the direct aid of the exact sciences, but some
training in these will no doubt prove most useful.
The present book is dedicated to Peter J. Wyllie, because he in
many ways has added to the author's understanding of petrology as
well as experimental work. I would also like to thank Dr. Jim V. P.
Long, Cambridge, whose technical skill in constructing complicated
apparatus like ion and microprobes has been a great experience.
Further I would like to thank some of my Danish colleagues for
their kindness and inspiration, my thanks goes to Dr. Tom S. Peter
sen, Dr. Ib S0rensen, and Dr. Ella Hoch.
Bergen, April 1985 S. Maa10e
Contents
I Monary Systems . . . . 1
1 Introduction. . . . . . 1
2 Monary Phase Relations . 2
3 Phase Changes Within the Upper Mantle. 7
II Binary Systems. 12
1 Introduction. . 12
2 The Phase Rule 12
3 The Lever Rule 12
4 Binary Isomorphous Systems. 14
5 Equilibrium Crystallization . 16
6 Fractional Crystallization . . 18
7 Influence of Additional Components and Pressure . 20
8 Partial Melting. . . . . . . . . . . . . 22
9 Binary Isomorphous System with Minimum 22
10 Eutectic Systems . . . . . . . . 24
11 Partial Melting. . . . . . . . . 25
12 Eutectic System with Solid Solution 25
13 Partial Melting. . . . . . 26
14 Peritectic Systems . . . . 27
15 Equilibrium Crystallization 28
16 Fractional Crystallization . 28
17 Partial Melting. . . . . . 29
18 Peritectic System with Solid Solution 29
19 Equilibrium Crystallization 29
20 Fractional Crystallization 30
21 Partial Melting. . 30
22 Congruent System . 31
23 Binary Exsolution . 32
24 Liquid Immiscibility 34
25 Principles of Construction 36
III Ternary Systems 39
1 Introduction. . 39
2 Gibbs' Triangle 39
3 Coordinate Transformations 40
x Contents
4 Space Diagram and Projection 42
5 Ternary Eutectic System . 43
6 Crystallization . . . 44
7 Partial Melting. . . 45
8 Ternary Lever Rules 46
9 Swanson's IT Rule . 47
to The Tangent Rule 47
11 Quantitative Analysis - Trend Estimate 48
12 Binary and Ternary Congruent Compounds 50
13 Crystallization Vectors 51
14 Ternary Peritectic System . 53
15 Equilibrium Crystallization 54
16 Fractional Crystallization . 58
17 Partial Melting of Composition Z 60
18 Solid Solution . . . .,. . . 61
19 One Solid Phase ..... . 61
20 Albite-Anorthite-Silica System 64
21 Equilibrium Crystallization 64
22 Fractional Crystallization . 66
23 Solid Solution - Two Solids 67
24 Equilibrium Crystallization 68
25 Fractional Crystallization . 69
26 Solid Solution - Peritectic System . 69
27 Types ofUnivariant Curves in Ternary Systems 72
28 Eutectic Crystallization . . . 72
29 Eutectic-Peritectic Transition 72
30 Peritectic Crystallization. . . 74
31 Peritectic-Eutectic Transition 74
IV Pseudobinary Systems 75
1 Introduction. . . . . 75
2 Rhines Phase Rule . . 75
3 Ternary Eutectic System . 75
4 Ternary System with a Congruent Compound. 77
5 Ternary System with an Incongruent Compound 77
6 Ternary System with Two Incongruent Compounds 79
7 Pseudo binary Joins Within the Ternary Systems
Wollastonite-Enstatite-Alumina 79
V P-TDiagrams ....... . 84
1 Pressure-Temperature Diagrams 84
2 Eutectic System . . . . . . . 84
3 Congruent-Incongruent Transition 85
4 Congruent Compound . 86
5 Ternary Eutectic System . 88
6 Lherzolite . 89
7 Tholeiite . . . . . . . 91
Contents Xl
VI Schreinemakers' Phase Theory 92
1 Introduction. . . . . . . . 92
2 Variance ........ . 92
3 The P-T-x Diagram for a Binary Eutectic System 94
4 The Bounding Theorem . . . . . 97
5 Morey-Schreinemakers' Theorem. 99
6 The Overlap Theorem. . . . . . 100
7 Principle of Opposition . . . . . 100
8 Arrangement of Univariant Curves 101
9 Monary Systems . . 103
10 Binary Systems. . . 103
II Degenerate Systems 106
12 Ternary Systems . . 108
13 Examples of Ternary Chemographs 110
14 Quaternary'Systems ..... . 113
VII Gas-Bearing Systems 114
I Introduction. . . . 114
2 Binary and Multicomponent Phase Relations 116
3 P-T Diagrams of Rock-H 0 Systems . . . 124
2
4 Phase Relations in the Presence of Carbon Dioxide 126
5 CaO-MgO-C0 127
2 •••
6 Carbonation Reactions . 128
7 Liquid Immiscibility . . 133
8 Gas Contents of Magmas 134
9 Nominal Anhydrous Minerals 137
VIII Oxygen Fugacity 140
1 Introduction. . . 140
2 Equations of State for Gases 141
3 Ideal Gases . . . . . . . 142
4 Mixtures of Ideal Gases . . 143
5 Van der Waals' Equation of State 143
6 Reduced Equation of State. . . 144
7 Fugacity ......... . 145
8 Fugacity of Van der Waals' Gas. 146
9 Coefficient of Fugacity from Reduced Parameters 147
10 Solid Buffers. . . . . . . . . . . . . . . . 148
IX Partial Melting . 152
I Introduction. . 152
"2 Parameters Controlling Primary Magmas 153
3 Estimation of Primary Magma Compositions 153
4 Partial Melting in a Ternary Eutectic System 154
5 Partial Melting of Lherzolite . . . . . . . ISS
XII Contents
6 Melting Curves of Lherzolite . . . . . . . . . 156
7 Partial Melting of a Granitic Composition . . . 159
8 Influence of Pressure on the Liquid Composition 160
9 Partial Melting by Adiabatic Ascent . . . . . 162
10 Adiabatic Ascent of a One-Component System 162
11 Adiabatic Ascent of a Ternary System . . . . 164
12 Partial Melting of Lherzolite . . . . . . . . 167
13 Geochemical Relationships of Partial Melting. 169
14 Types of Partial Melting . . . . . . 169
15 Batch Melting, One Solid Phase. . . 170
16 Fractional Melting, One Solid Phase. 172
17 Critical Melting . . . . . . . . . 173
18 The Distribution Coefficient for a Multiphased
Assemblage . . . . . . . 174
19 Treui1's Method . . . . . 177
20 R/I Discrimination Method 179
X Fractional Crystallization . 182
1 Introduction. . . . . . . 182
2 Phase Relations of Fractional Crystallization 184
3 Thermal Barriers . . . . . . . . . . 188
4 The System Albite-Orthoclase-Quartz 191
5 Rayleigh Fractionation . . . . . 192
6 Types of Fractional Crystallization 193
7 Perfect Fractional Crystallization . 194
8 Partial Fractional Crystallization . 199
9 The Calculation Procedure for a General Fractionation
Formula of Binary Systems 201
10 Olivine Fractionation in Basalts 203
11 Trace Element Fractionation 206
12 Analysis of Trends . . . . . . 208
13 Trend and Control Lines 209
14 The Minimal Enrichment Ratio qJ • 212
15 Analysis of the Fractionate. . . . 214
16 The Linear Equation Method and the Least Square
Method ........ . 215
17 Statistics of Chemical Data. 219
XI Magma Kinetics . . . 230
1 Diffusion . . . . . . 230
2 The Diffusion Process . 230
3 Temperature Dependence of D 235
4 Pressure Dependence of D. . 236
5 Diffusion in Gases and Liquids 237
6 Diffusion in Solids . 241
7 Diffusion Equations 242
