Preface ....................................................... xix
Acknowledgements .............................................. xxi
Glossary .................................................... xxiii
G.I Abbreviations of mineral names used in the text ........ xxiii
G.2 Other abbreviations and symbols used in the text ........ xxiv
Chapter 1 Geochemical data ..................................... 1
1.1 Introduction ............................................... 1
1.2 Geological processes and their geochemical signatures ...... 3
1.2.1 Processes which control the chemical composition
of igneous rocks .................................... 3
1.2.2 Processes which control the chemical composition
of sedimentary rocks ................................ 5
1.2.3 Processes which control the chemical composition
of metamorphic rocks ................................ 7
1.3 Geological controls on geochemical data .................... 9
1.4 Analytical methods in geochemistry ......................... 9
1.4.1 X-ray fluorescence (XRF) ........................... 10
1.4.2 Neutron activation analysis (INAA and RNAA) ........ 13
1.4.3 Inductively coupled plasma emission spectrometry
(ICP) .............................................. 13
1.4.4 Atomic absorption spectrophotometry (AAS) .......... 14
1.4.5 Mass spectrometry .................................. 14
Isotope dilution mass spectrometry (IDMS) .......... 15
Inductively coupled plasma emission mass
spectrometry (ICP-MS) .............................. 15
Spark source mass spectrometry (SSMS) .............. 15
1.4.6 Electron microprobe analysis ....................... 15
1.4.7 The ion microprobe ................................. 16
1.5 Selecting an appropriate analytical technique ............. 16
1.6 Sources of error in geochemical analysis .................. 17
1.6.1 Contamination ...................................... 17
1.6.2 Calibration ........................................ 18
1.6.3 Peak overlap ....................................... 18
1.6.4 Detecting errors in geochemical data ............... 18
Chapter 2 Analysing geochemical data .......................... 19
2.1 Introduction .............................................. 19
2.2 Averages .................................................. 21
2.3 Correlation ............................................... 22
2.3.1 The correlation coefficient ........................ 23
2.3.2 The significance of the correlation coefficient
(r) ................................................ 23
2.3.3 Assumptions in the calculation of the product-
moment coefficient of correlation .................. 24
2.3.4 Spearman rank correlation .......................... 25
2.3.5 Correlation matrices ............................... 26
2.3.6 Correlation coefficient patterns ................... 27
2.4 Regression ................................................ 28
2.4.1 Ordinary least squares regression .................. 29
2.4.2 Reduced major axis regression ...................... 31
2.4.3 Weighted least squares regression .................. 31
2.4.4 Robust regression .................................. 32
2.4.5 Some problems with traditional approaches to
correlation and regression ......................... 32
2.5 Ratio correlation ......................................... 33
2.5.1 An example of the improper use of ratio
correlation — Pearce element ratio diagrams ........ 34
2.5.2 Application to trace element diagrams .............. 36
2.5.3 Ratio correlation in isotope geology ............... 36
2.6 The constant sum problem .................................. 37
2.6.1 The consequences of closure ........................ 38
Correlating compositional data ..................... 38
The means of compositional data-sets ............... 38
Invalid escape routes .............................. 38
2.6.2 Aitchison's solution to the constant sum effect .... 38
An example — basalts from Kilauea Iki lava lake,
Hawaii ............................................. 41
The interpretation of log-ratios ................... 41
2.7 The interpretation of trends on triangular diagrams ....... 42
2.8 Principal component analysis .............................. 42
2.9 Discriminant analysis ..................................... 44
2.9.1 An example from igneous petrology .................. 44
2.9.2 Other applications of discriminant analysis ........ 45
2.10 Whither geochemical data analysis? ........................ 46
Chapter 3 Using major element data ............................ 48
3.1 Introduction .............................................. 48
3.2 Rock classification ....................................... 48
3.2.1 Classifying igneous rocks using oxide-oxide plots 49
The total alkalis-silica diagram (TAS) ............. 49
(a) Using TAS with volcanic rocks .................. 50
(b) A TAS diagram for plutonic rocks ............... 50
(c) Discrimination between the alkaline and
subalkaline series using TAS ................... 51
The K2O vs SiO2 diagram for the subdivision
of the subalkaline series ...................... 51
3.2.2 Classifying igneous rocks using the norm ........... 52
Cation norms ....................................... 57
Norm calculations and the oxidation state of
iron ............................................... 57
Basalt classification using the Ne-Di-OI-Hy-Q
diagram of Thompson (1984) ......................... 57
Granite classification using the Ab-An-Or diagram
of O'Connor (1965) ................................. 58
The Q'(F')-ANOR diagram of Streckeisen and
Le Maitre (1979) ................................... 60
3.2.3 Classifying igneous rocks using cations ............ 61
The R1-R2 diagram of de la Roche et al. (1980) ..... 61
The Jensen cation plot (Jensen, 1976) .............. 63
3.2.4 The chemical classification of sedimentary rocks ... 64
Arenite/wacke ...................................... 64
Mudrocks ........................................... 65
3.2.5 Discussion ......................................... 66
3.3 Variation diagrams ........................................ 66
3.3.1 Recognizing geochemical processes on a major
element variation diagram .......................... 66
Fractional crystallization ......................... 67
Assimilation and fractional crystallization ........ 69
Partial melting .................................... 69
Mixing lines in sedimentary rocks .................. 69
The identification of former weathering
conditions from sedimentary rocks .................. 70
Mixing in metamorphic rocks ........................ 71
Element mobility ................................... 71
Artificial trends .................................. 73
3.3.2 Selecting a variation diagram ...................... 73
Bivariate plots .................................... 73
(a) Harker diagrams — bivariate plots using
SiO2 along the x-axis .......................... 73
(b) Bivariate plots which use MgO on the x-axis .... 74
(c) Bivariate plots using cations .................. 74
(d) Bivariate plots using the magnesium number ..... 74
Triangular variation diagrams ...................... 74
(a) The AFM diagram ................................ 75
(b) Problems in the use of the AFM diagram ......... 76
3.3.3 Interpreting trends on variation diagrams .......... 78
Extract calculations ............................... 78
Addition-subtraction diagrams ...................... 79
Trends showing an inflection ....................... 79
Scattered trends ................................... 79
A computer-based approach to mixing calculations ... 81
3.3.4 Modelling major element processes in igneous
rocks .............................................. 82
3.3.5 Discussion ......................................... 84
3.4 Diagrams on which rock chemistry can be plotted together
with experimentally determined phase boundaries ........... 84
3.4.1 The normative albite-orthoclase-quartz diagram -
the 'granite system' ............................... 86
Water-undersaturated equilibria .................... 88
The presence of anorthite .......................... 88
3.4.2 The silica-undersaturated portion of the
normative nepheline—kalsilite—silica diagram -
the 'nepheline syenite system' .................... 88
3.4.3 Basaltic experimental systems ...................... 89
CMAS diagrams ...................................... 90
(a) Projecting rock compositions into CMAS ......... 91
(b) Interpreting CMAS diagrams ..................... 93
Diagrams based upon the Yoder-Tilley (1962) CIPW
normative tetrahedron .............................. 94
(a) Projections in the tholeiite basalt
tetrahedron OI-PI-Di-Q ......................... 94
(b) The normative Ne-Di-OI-Hy-Q diagram ............ 96
(c) The low-pressure tholeiitic basalt phase
diagram (Cox et al., 1979) ..................... 97
(d) Problems with CIPW normative projections ....... 99
3.4.4 Experimental systems for calc-alkaline rocks ....... 99
The olivine-clinopyroxene-silica projection of
Grove et al. (1982) ................................ 99
The projections of Baker and Eggler(1983, 1987) .... 99
3.4.5 Discussion ........................................ 100
Chapter 4 Using trace element data ........................... 102
4.1 Introduction ............................................. 102
4.1.1 Classification of trace elements according to
their geochemical behaviour ....................... 102
Trace element groupings in the periodic table ..... 102
Trace element behaviour in magmatic systems ....... 103
4.2 Controls on trace element distribution ................... 104
4.2.1 Partition coefficients ............................ 106
Measuring partition coefficients .................. 106
Physical controls on the value of partition
coefficients in mineral-melt systems .............. 107
(a) Composition ................................... 107
(b) Temperature ................................... 107
(c) Pressure ...................................... 111
(d) Oxygen activity ............................... 113
(e) Crystal chemistry ............................. 113
(f) Water content of the melt ..................... 115
(g) Selecting a partition coefficient ............. 115
Partition coefficients in basalts and basaltic
andesites ......................................... 116
Partition coefficients in andesites ............... 117
Partition coefficients in dacites and rhyolites ... 117
4.2.2 Geological controls on the distribution of trace
elements .......................................... 119
Element mobility .................................. 120
Partial melting ................................... 121
(a) Batch melting ................................. 121
(b) Fractional melting ............................ 122
Crystal fractionation ............................. 124
(a) Equilibrium crystallization ................... 124
(b) Fractional crystallization/Rayleigh
fractionation ................................. 124
(c) In situ crystallization ....................... 127
Contamination ..................................... 127
(a) AFC processes ................................. 127
(b) Zone refining ................................. 130
Dynamic models .................................... 130
(a) Dynamic melting ............................... 130
(b) The RTF magma chamber ......................... 131
Sedimentary processes ............................. 132
4.3 Rare earth elements (REE) ................................ 133
4.3.1 The chemistry of the REE .......................... 134
4.3.2 Presenting REE data ............................... 135
(a) Difficulties with chondnte normalization ...... 136
(b) Choosing a set of normalizing values .......... 136
REE ratio diagrams ................................ 137
NASC normalization for sediments .................. 137
Rock normalization ................................ 137
4.3.3 Interpreting REE patterns ......................... 137
REE patterns in igneous rocks ..................... 138
REE patterns in sea and river water ............... 140
REE patterns in sediments ......................... 140
(a) Clastic sediments ............................. 140
(b) Chemical sediments ............................ 141
4.4 Normalized multi-element diagrams or incompatible
element diagrams (spider diagrams) ....................... 142
4.4.1 Multi-element diagrams for igneous rocks .......... 142
Primordial (primitive) mantle-normalized spider
diagrams .......................................... 142
Chondrite-normalized spider diagrams .............. 143
MORB-normalized spider diagrams ................... 145
Which spider diagrams do we use? .................. 147
Interpreting multi-element diagrams for igneous
rocks ............................................. 148
4.4.2 Multi-element diagrams for sediments .............. 148
Interpreting multi-element diagrams for
sediments ......................................... 149
4.5 Platinum metal group element (PGE) plots ................. 150
4.5.1 Presenting PGE data ............................... 151
Chondrite normalization ........................... 151
Primitive mantle normalization .................... 152
4.5.2 Interpreting PGE patterns ......................... 153
4.6 Transition metal plots ................................... 154
4.7 Bivariate trace element plots ............................ 156
4.7.1 The selection of trace elements in igneous rocks
for plotting on bivariate graphs .................. 156
Incompatible element plots ........................ 157
(a) Identification of igneous source
characteristics from incompatible element
plots ......................................... 157
(b) Identification of igneous source
characteristics from incompatible element
ratio-ratio plots ............................. 157
(c) Calculation of partition coefficients from
reciprocal concentration trace element
plots ......................................... 158
Compatible element plots .......................... 158
4.7.2 Bivariate plots in sedimentary rocks .............. 159
4.8 Enrichment-depletion diagrams ............................ 159
4.9 Modelling trace element processes in igneous rocks ....... 160
4.9.1 Vector diagrams ................................... 161
4.9.2 Modelling on multivariate diagrams ................ 162
4.9.3 Petrogenetic modelling - examples ................. 166
Partial melting ................................... 166
Crystal fractionation ............................. 166
Crustal contamination and AFC processes ........... 166
Open system processes ............................. 167
Magma and source mixing ........................... 168
Demonstrating element mobility .................... 168
4.9.4 Inversion techniques using trace elements ......... 168
Constraining fractional crystallization using an
inversion method .................................. 169
Constraining partial melting using an inversion
method ............................................ 170
4.9.5 A final comment on geochemical modelling .......... 170
Chapter 5 Discriminating between tectonic environments
using geochemical data ............................. 171
5.1 Introduction ............................................. 171
5.1.1 Discriminant analysis ............................. 171
5.1.2 Immobile trace elements ........................... 172
5.1.3 Tectonic environments ............................. 172
5.1.4 Using discrimination diagrams ..................... 173
5.2 Discrimination diagrams for rocks of basaltic to
andesitic composition .................................... 174
5.2.1 Trace element discrimination diagrams ............. 174
The Ti-Zr, Ti-Zr-Y and Ti-Zr-Sr diagrams (Pearce
and Cann, 1973) ................................... 174
(a) The Ti-Zr-Y diagram ........................... 174
(b) The Ti-Zr diagram ............................. 176
(c) The Ti-Zr-Sr diagram .......................... 178
(d) Discussion .................................... 179
Other discrimination diagrams using Ti-Zr-Y-Nb
variations ........................................ 180
(a) The Zr/Y-Zr diagram for basalts (Pearce and
Norry, 1979) .................................. 180
(b) The Ti/Y-Nb/Y diagram (Pearce, 1982) .......... 180
(c) The Zr-Nb-Y diagram (Meschede, 1986) .......... 180
(d) The causes of Ti-Zr-Y-Nb variations in
basalts from different tectonic settings ...... 182
The Th-Hf-Ta diagram of Wood (1980) ............... 182
The Ti-V diagram of Shervais (1982) ............... 184
The La-Y-Nb diagram of Cabanis and Lecolle
(1989) ............................................ 184
Diagrams which preferentially select
volcanic-arc basalts .............................. 186
(a) The Cr-Y diagram (Pearce, 1982) ............... 186
(b) The Cr-Ce/Sr diagram .......................... 187
Distinguishing between different types of
volcanic-arc basalt ............................... 188
The K2O/Yb-Ta/Yb diagram ......................... 189
Diagrams which distinguish between different
types of volcanic-arc andesite (Bailey, 1981) ..... 190
Diagrams which discriminate between the alkali
basalt and tholeiitic magma series ................ 190
(a) The TiO2-Y/Nb diagram (Floyd and
Winchester, 1975) ................................. 190
(b) The P2O5-Zr diagram
(Floyd and Winchester, 1975) .................. 191
(c) The TiO2-Zr/P2O5 diagram
(Floyd and Winchester, 1975) .................. 192
(d) The Nb/Y-Zr/P2O5 diagram
(Floyd and Winchester, 1975) .................. 192
(e) Discussion .................................... 193
5.2.2 Discrimination diagrams for basalts based upon
major elements .................................... 193
The F1-F2-F3 diagrams of J.A. Pearce (1976) ....... 194
The MgO-FeO-AI2O3 diagram of Т.Н. Pearce
et al. (1977) ..................................... 196
5.2.3 Discrimination diagrams for basalts based upon
minor elements .................................... 196
The TiO2-K2O-P2O5
diagram of Т.Н. Pearce et al.(1975) ............... 196
The MnO-TiO2-P2O5 diagram
of Mullen (1983) .................................. 198
The K2O-H2O diagram of Muenow et al.
(1990) ............................................ 199
5.2.4 Discrimination diagrams for basalts based upon
clinopyroxene composition ......................... 200
5.3 Discrimination diagrams for rocks of granitic
composition .............................................. 201
5.3.1 Discrimination diagrams for granites based upon
Rb-Y-Nb and Rb-Yb-Ta variations (Pearce et al.,
1984) ............................................. 202
The Nb-Y and Ta-Yb discrimination diagrams ........ 204
The Rb-(Y + Nb) and Rb-(Yb + Та) discrimination
diagrams .......................................... 204
5.3.2 Discrimination diagrams for granites based upon
Hf-Rb-Ta variations ............................... 205
5.3.3 A measure of arc maturity for volcanic-arc
granites .......................................... 205
5.4 Discrimination diagrams for clastic sediments ............ 206
5.4.1 Discrimination diagrams for clastic sediments
using major elements .............................. 207
The sandstone discriminant function diagram
(Bhatia, 1983) .................................... 207
Bivariate plots as sandstone discrimination
diagrams (Bhatia, 1983) ........................... 208
The K2O/Na2O vs SiO2
sandstone-mudstone discrimination diagram
(Roser and Korsch, 1986) .......................... 208
Provenance signatures of sandstone-mudstone
suites using major elements (Roser and Korsch,
1988) ............................................. 208
5.4.2 Discrimination diagrams for clastic sediments
using trace elements .............................. 209
Greywackes ........................................ 209
Spider diagrams as discriminants of tectonic
setting for shales (Winchester and Max, 1989) ..... 209
Provenance studies (Cullers et ai, 1988) .......... 210
5.4.3 Discussion ........................................ 211
5.5 Tectonic controls on magmatic and sedimentary
geochemistry ............................................. 212
5.5.1 An expert system for identifying the tectonic
environment of ancient volcanic rocks (Pearce,
1987) ............................................. 213
5.5.2 Do tectonic discrimination diagrams still have
a function? ....................................... 213
Chapter 6 Using radiogenic isotope data ...................... 215
6 1 Introduction ............................................. 215
6.2 Radiogenic isotopes in geochronology ..................... 215
6.2.1 Isochron calculations ............................. 216
Pb isotope isochrons .............................. 218
Fitting an isochron ............................... 218
Errorchrons ....................................... 219
The geochron ...................................... 219
6.2.2 Model ages ........................................ 220
T-CHUR model ages ................................ 221
T-depleted mantle (DM) model ages ................ 221
Assumptions made in the calculation of model
ages .............................................. 221
6.2.3 Interpreting geochronological data ................ 224
Blocking temperatures ............................. 224
Concepts of geological age ........................ 225
(a) Cooling age ................................... 226
(b) Crystallization age ........................... 226
(c) Metamorphic age ............................... 226
(d) Crust formation age ........................... 226
(e) Crust residence age ........................... 226
The interpretation of whole-rock ages ............. 226
(a) The Rb-Sr system .............................. 226
(b) Pb isotopes ................................... 227
(c) The Sm-Nd system .............................. 227
The interpretation of mineral ages ................ 226
(a) Rb-Sr mineral ages ............................ 228
(b) Argon methods ................................. 228
(c) Sm-Nd mineral ages ............................ 229
(d)U-Pb dating of zircon .......................... 229
The interpretation of model ages .................. 229
6.3 Radiogenic isotopes in petrogenesis ...................... 231
6.3.1 The role of different isotopic systems in
identifying reservoirs and processes .............. 232
6.3.2 Recognizing isotopic reservoirs ................... 234
Oceanic mantle sources ............................ 237
(a) Depleted mantle (DM) .......................... 237
(b) HIMU mantle ................................... 237
(c) Enriched mantle ............................... 237
(d) PREMA ......................................... 241
(e) Bulk Earth (Bulk Silicate Earth - BSE) ........ 241
(f) The origin of oceanic basalts ................. 241
(g) Trace elements and mantle end-member
compositions .................................. 241
Continental crustal sources ....................... 241
(a) Upper continental crust ....................... 242
(b) Middle continental crust ...................... 242
(c) Lower continental crust ....................... 242
(d) Subcontinental lithosphere .................... 242
Seawater .......................................... 243
6.3.3 The evolution of mantle reservoirs with time -
mantle evolution diagrams ......................... 244
The evolution of Sr isotopes with time ............ 244
The evolution of Nd isotopes with time ............ 247
The evolution of Pb isotopes with time ............ 248
6.3.4 The epsilon notation .............................. 249
Calculating epsilon values ........................ 249
(a) Epsilon values calculated for an isochron ..... 250
(b) Epsilon values for individual rocks at the
time of their formation ....................... 251
(c) Epsilon values for individual rocks at the
present day ................................... 253
Epsilon values for Sr isotopes .................... 253
Calculating the uncertainties in epsilon values
when they are determined for isochron diagrams .... 254
The meaning of epsilon values ..................... 254
The fractionation factor fSm/Nd ................... 255
Epsilon-Nd time plots ............................. 255
6.3.5 Isotope correlation diagrams ...................... 256
Using isotope correlation diagrams and epsilon
plots to recognize mixing processes ............... 257
(a) Mixing between sources ........................ 257
(b) Mixing in a magma chamber ..................... 258
Applications to contamination ..................... 259
(a) Contamination of magmas by the continental
crust ......................................... 259
(b) Crustal contamination and AFC processes ....... 260
(c) Contamination with seawater ................... 260
Isotope vs trace (and major) element plots ........ 261
6.3.6 Mantle-crust geodynamics .......................... 263
Plumbotectonics ................................... 263
Geodynamics ....................................... 263
Chapter 7 Using stable isotope data .......................... 266
7.1 Introduction ............................................. 266
7.1.1 Notation .......................................... 266
7.1.2 Isotope fractionation ............................. 267
7.1.3 Physical and chemical controls on stable isotope
fractionation ..................................... 268
7.2 Using oxygen isotopes .................................... 270
7.2.1 Variations of δ18O in nature ...................... 270
7.2.2 Oxygen isotope thermometry ........................ 271
Calibration of oxygen isotope thermometers ........ 272
Tests of isotopic equilibrium ..................... 274
Applications ...................................... 276
(a) Low-temperature thermometry ................... 276
(b) High-temperature thermometry .................. 277
7.2.3 Oxygen isotope-radiogenic isotope correlation
diagrams .......................................... 278
Recognizing crust and mantle reservoirs ........... 278
Recognizing crustal contamination in igneous
rocks ............................................. 279
Recognizing simple crystal fractionation in
igneous rocks ..................................... 281
7.3 Fingerprinting hydrothermal solutions using oxygen and
hydrogen isotopes — water-rock interaction ............... 282
7.3.1 Hydrogen isotopes ................................. 283
7.3.2 Calculating the isotopic composition of water
from mineral compositions ......................... 285
7.3.3 The isotopic composition of natural waters ........ 285
(a) Meteoric water ................................ 285
(b) Ocean water ................................... 287
(c) Geothermal water .............................. 288
(d) Formation water ............................... 288
(e) Metamorphic water ............................. 289
(f) Magmatic water ................................ 289
7.3.4 Quantifying water/rock ratios ..................... 289
7.3.5 Examples of water-rock interaction ................ 291
(a) Interaction between igneous intrusions and
groundwater ................................... 292
(b) Interaction between ocean-floor basalt and
seawater ...................................... 292
(c) Water-rock interaction in metamorphic
rocks ......................................... 292
(d) Water-rock interaction during the formation
of hydrothermal ore deposits .................. 294
(e) Diagenesis of clastic sediments ............... 294
7.4 Using carbon isotopes .................................... 294
7.4.1 The distribution of carbon isotopes in nature ..... 295
Controls on the fractionation of carbon isotopes .. 295
7.4.2 Combined oxygen and carbon isotope studies of
carbonates — δ18O vs δ13C plots .................... 296
Limestone diagenesis .............................. 297
Hydrothermal calcite .............................. 300
7.4.3 The δ13C composition of seawater .................. 300
7.4.4 Biogeochemical evolution .......................... 300
7.4.5 Carbon isotopes in CO2 ............................ 301
CO2 dissolved in igneous melts ................... 301
CO2 in metamorphic fluids ........................ 301
(a) Granulites .................................... 301
(b) The origin of metamorphic graphite ............ 301
CO2 in gold-mineralizing fluids .................. 302
CO2 fluid-rock interaction ....................... 302
7.4.6 Carbon isotope thermometry ........................ 302
The calcite-graphite δ13C thermometer ............. 302
The CO2-graphite thermometer ..................... 303
7.5 Using sulphur isotopes ............................. 303
7.5.1 The distribution of sulphur isotopes in
nature ...................................... 304
7.5.2 Controls on the fractionation of sulphur
isotopes .................................... 306
Sulphur isotope fractionation in igneous
rocks ...................................... 306
Sulphur isotope fractionation in
sedimentary rocks .......................... 306
(a) The bacterial reduction of sulphate
to sulphide ............................ 306
(b) The bacterial oxidation of sulphide
to sulphate ............................ 307
(c) The crystallization of sedimentary
sulphate from seawater - evaporite
formation .............................. 307
(d) The non-bacterial reduction of
sulphate to sulphide ................... 307
Sulphur isotope fractionation in
hydrothermal systems ....................... 308
Sulphur isotope fractionation between
sulphide and sulphate phases — sulphur
isotope thermometry ........................ 308
7.5.3 Using sulphur isotopes in igneous petrogenesis .... 311
(a) Outgassing of SO2 ............................ 311
(b) Contamination ................................. 312
(c) Crystal fractionation ......................... 312
7.5.4 Using sulphur isotopes to understand the genesis
of hydrothermal ore deposits ...................... 312
Modern hydrothermal mineralization at mid-ocean
ridges ............................................ 312
Ancient hydrothermal mineralization ............... 313
(a) High-temperature inorganic reduction of
seawater sulphate ............................ 314
(b) Low-temperature organic reduction of
sulphate ...................................... 314
(c) Low-temperature bacteriological reduction
of sulphate ................................... 315
(d) Sulphur of magmatic origin .................... 315
References .................................................... 316
Index ......................................................... 344
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