worked example of batch melting: rb and srasimonet/ce30540/sp2017/lecture_10_new...worked example of...

Worked Example of Batch Melting: Rb and SrBasalt with the mode:

1. Convert to weight % minerals (Wol Wcpx etc.)

Table 9.2. Conversion from mode toweight percent

Mineral Mode Density Wt prop Wt%ol 15 3.6 54 0.18cpx 33 3.4 112.2 0.37plag 51 2.7 137.7 0.45

Sum 303.9 1.00

Worked Example of Batch Melting: Rb and Sr

Table 9.2. Conversion from mode toweight percent

Mineral Mode Density Wt prop Wt%ol 15 3.6 54 0.18cpx 33 3.4 112.2 0.37plag 51 2.7 137.7 0.45

Sum 303.9 1.00

Basalt with the mode:

1. Convert to weight % minerals (Wol Wcpx etc.)

2. Use equation eq. 9.4: Di = Σ WA Diand the table of D values for Rb and Sr in each mineral to calculate the bulk distribution coefficients: DRb = 0.045 and DSr = 0.848

Table 9.3 . Batch Fractionation Model for Rb and Sr

CL/CO = 1/(D(1-F)+F)DRb DSr

F 0.045 0.848 Rb/Sr0.05 9.35 1.14 8.190.1 6.49 1.13 5.730.15 4.98 1.12 4.430.2 4.03 1.12 3.610.3 2.92 1.10 2.660.4 2.29 1.08 2.110.5 1.89 1.07 1.760.6 1.60 1.05 1.520.7 1.39 1.04 1.340.8 1.23 1.03 1.200.9 1.10 1.01 1.09

3. Use the batch melting equation

(9.5)

to calculate CL/CO for various values of F

From Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

CC

1Di(1 F) F

L

O=

− +

4. Plot CL/CO vs. F for each element

Figure 9.3. Change in the concentration of Rb and Sr in the melt derived by progressive batch melting of a basaltic rock consisting of plagioclase, augite, and olivine. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Incremental Batch Melting

Calculate batch melting for successive batches (same equation)

Must recalculate Di as solids change as minerals are selectively melted (computer)

Fractional Crystallization1. Crystals remain in equilibrium with each

melt increment

CC

1Di(1 F) F

L

O=

− +

Rayleigh fractionationThe other extreme: separation of each crystal as it formed = perfectly continuous fractional crystallization in a magma chamber

Rayleigh fractionationThe other extreme: separation of each crystal as it formed = perfectly continuous fractional crystallization in a magma chamber Concentration of some element in the residual

liquid, CL is modeled by the Rayleigh equation:eq. 9.8 CL/CO = F (D -1) Rayleigh Fractionation

4. Plot CL/CO vs. F for each element


Other models are used to analyze Mixing of magmas Wall-rock assimilation Zone refining Combinations of processes

The Rare Earth Elements (REE)

Contrasts and similarities in the D values:All are incompatible

Also Note:

HREE are less incompatible

Especially in garnet

Eu can → 2+ which conc. in plagioclase

Table 9-1. Partition Coefficients (CS/CL) for Some Commonly Used Trace Elements in Basaltic and Andesitic Rocks

Olivine Opx Cpx Garnet Plag Amph MagnetiteRb 0.01 0.022 0.031 0.042 0.071 0.29 Sr 0.014 0.04 0.06 0.012 1.83 0.46 Ba 0.01 0.013 0.026 0.023 0.23 0.42 Ni 14.0 5.0 7.0 0.955 0.01 6.8 29.Cr 0.7 10.0 34.0 1.345 0.01 2.0 7.4La 0.007 0.03 0.056 0.001 0.148 0.544 2.Ce 0.006 0.02 0.092 0.007 0.082 0.843 2.Nd 0.006 0.03 0.23 0.026 0.055 1.34 2.Sm 0.007 0.05 0.445 0.102 0.039 1.804 1.Eu 0.007 0.05 0.474 0.243 0.1/1.5* 1.557 1.Dy 0.013 0.15 0.582 3.17 0.023 2.024 1.Er 0.026 0.23 0.583 6.56 0.02 1.74 1.5Yb 0.049 0.34 0.542 11.5 0.023 1.642 1.4Lu 0.045 0.42 0.506 11.9 0.019 1.563Data from Rollinson (1993). * Eu3+/Eu2+ Italics are estimated

Rar

e Ea

rth E

lem

ents

REE DiagramsPlots of concentration as the ordinate (y-axis)

against increasing atomic number Degree of compatibility increases from left to right

across the diagram (“lanthanide contraction”)

Con

cent

ratio

n

La Ce Nd Sm Eu Tb Er Dy Yb Lu

-3

-2

-10

1

2

34

5

6

7

89

10

11

0 10 20 30 40 50 60 70 80 90 100

Atomic Number (Z)

Log

(Abu

ndan

ce in

CI C

hond

ritic

Met

eorit

e) HHe

Li

Be

B

C

N

O

FSc

FeNi

Ne MgSiS

CaAr

Ti

PbPtSn BaV

K

NaAlP

Cl

ThU

Eliminate Oddo-Harkins effect and make y-scale more functional by normalizing to a standard estimates of primordial mantle REE chondrite meteorite concentrations

Chart2

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

90

92

H

He

Li

Be

B

C

N

O

F

Sc

Fe

Ni

Ne

Mg

Si

S

Ca

Ar

Ti

Pb

Pt

Sn

Ba

V

K

Na

Al

P

Cl

Th

U

Atomic Number (Z)

Log (Abundance in CI Chondritic Meteorite)

10.4456042033

9.434568904

1.7566361082

-0.1366771399

1.3263358609

7.0043213738

6.4955443375

7.3765769571

2.9258275746

6.5365584426

4.7589118924

6.0310042814

4.9289076902

6

4.0170333393

5.711807229

3.719331287

5.0043213738

3.5763413502

4.7860412102

1.5340261061

3.3802112417

2.4668676204

4.1303337685

3.9800033716

5.9542425094

3.3521825181

4.6928469193

2.717670503

3.1003705451

1.5774917998

2.0755469614

0.8169038394

1.7930916002

1.0718820073

1.6532125138

0.8506462352

1.3710678623

0.6665179806

1.0569048513

-0.1561445774

0.4065401804

0.2695129442

-0.4634415574

0.1430148003

-0.3133637307

0.206825876

-0.735182177

0.5820633629

-0.5100415206

0.6821450764

-0.0457574906

0.6720978579

-0.4294570601

0.652246341

-0.3506651413

0.0553783314

-0.7775436633

-0.0820221174

-0.5880437621

-1.0118871597

-0.4814860601

-1.2196826879

-0.4042833801

-1.051098239

-0.6006724678

-1.4225082002

-0.6057234732

-1.4353339357

-0.8124792792

-1.6840296545

-0.876148359

-1.2865094569

-0.1706962272

-0.1797985405

0.1271047984

-0.7281583935

-0.468521083

-0.735182177

0.4983105538

-0.8416375079

-1.474955193

-2.0457574906

Sheet1

at nosymbolmeteors/msolar

1H10.44560420332.79E+101.0027900000000

2He9.4345689042.72E+091.002720000000

3Li1.756636108257.10.3520.0108761329

4Be-0.13667713990.730.810.5911971831

5B1.326335860921.20.9019.1388888889

6C7.00432137381.01E+071.0010100000

7N6.49554433753.13E+061.003130000

8O7.37657695712.38E+071.0023800000

9F2.92582757468431.02858.0535714286

10Ne6.53655844263.44E+061.003440000

11Na4.75891189245.74E+041.0057581.9334389857

12Mg6.03100428141.07E+061.001074000

13Al4.92890769028.49E+041.0084768.9814814815

14Si61.00E+061.001000000

15P4.01703333931.04E+040.9810175.9425493716

16S5.7118072295.15E+050.99510749.656121045

17Cl3.71933128752401.045468.6907020873

18Ar5.00432137381.01E+051.00101000

19K3.576341350237701.003762.6510721248

20Ca4.78604121026.11E+041.0061292.7444794953

21Sc1.534026106134.21.0034.3106796117

22Ti3.380211241724001.012429.2089249493

23V2.46686762042931.00291.5422885572

24Cr4.13033376851.35E+041.0013476.2323943662

25Mn3.980003371695500.979308.2278481013

26Fe5.95424250949.00E+051.02919174.434087883

27Co3.352182518122501.002254.5824847251

28Ni4.69284691934.93E+041.0049300

29Cu2.7176705035220.99514.6651053864

30Mn3.100370545112600.991246.4516129032

31Ga1.577491799837.80.9234.7808306709

32Ge2.07554696141190.94111.7878787879

33As0.81690383946.56

34Se1.793091600262.1

35Br1.071882007311.8

36Kr1.653212513845

37Rb0.85064623527.091.087.6808333333

38Sr1.371067862323.50.9923.2593856655

39Y0.66651798064.641.014.6818018018

40Zr1.056904851311.41.0011.3563218391

41Nb-0.15614457740.6981.010.7079714286

42Mo0.40654018042.550.982.4979591837

44Ru0.26951294421.861.011.8804395604

45Rh-0.46344155740.3441.030.3534678899

46Pd0.14301480031.390.991.3818235294

47Ag-0.31336373070.4860.760.3684193548

48Cd0.2068258761.611.061.7014772727

49In-0.7351821770.1842.020.3724878049

50Sn0.58206336293.820.933.5700934579

51Sb-0.51004152060.3090.960.2971153846

52Te0.68214507644.81

53I-0.04575749060.9

54Xe0.67209785794.7

55Cs-0.42945706010.372

56Ba0.6522463414.490.964.3274660633

57La-0.35066514130.4461.020.4534333333

58Ce0.05537833141.1360.961.0936645963

59Pr-0.77754366330.16690.910.1519217949

60Nd-0.08202211740.82791.020.8447959184

62Sm-0.58804376210.25821.030.266185567

63Eu-1.01188715970.09730.940.0918944444

64Gd-0.48148606010.331.050.3454205607

65Tb-1.21968268790.06030.300.0182727273

66Dy-0.40428338010.39420.960.3770608696

67Ho-1.0510982390.08890.520.046228

68Er-0.60067246780.25080.980.24552

69Tm-1.42250820020.03780.040.0014538462

70Yb-0.60572347320.24791.140.2818231579

71Lu-1.43533393570.03676.330.2324333333

72Hf-0.81247927920.1541.210.1856438356

73Ta-1.68402965450.0207

74W-0.8761483590.1331.630.2171029412

75Re-1.28650945690.0517

76Os-0.17069622720.6751.050.7092391304

77Ir-0.17979854050.6610.990.651350365

78Pt0.12710479841.341.071.4357142857

79Au-0.72815839350.1871.220.2275542169

80Hg-0.4685210830.34

81Tl-0.7351821770.1841.100.2019512195

82Pb0.49831055383.150.902.8426829268

83Bi-0.84163750790.144

90Th-1.4749551930.03351.500.05025

92U-2.04575749060.009

CI chondrite from Anders and Grevesse

&A

Page &P

Sheet1

&A

Page &P

Atomic Number

Ratio solar/chondrite

&A

Page &P

CI Chondrite

solar system

&A

Page &P

H

He

Li

Be

B

C

N

O

F

Sc

Fe

Ni

Ne

Mg

Si

S

Ca

Ar

Ti

Pb

Pt

Sn

Ba

V

K

Na

Al

P

Cl

Th

U

Atomic Number (Z)

Log (Abundance in CI Chondritic Meteorite)

What would an REE diagram look like for an analysis of a chondrite

meteorite?

0.00

2.00

4.00

6.00

8.00

10.00

56 58 60 62 64 66 68 70 72

sam

ple/

chon

drite

LLa Ce Nd Sm Eu Tb Er Yb Lu

?

Divide each element in analysis by the concentration in a chondrite standard

0.00

2.00

4.00

6.00

8.00

10.00

56 58 60 62 64 66 68 70 72

sam

ple/

chon

drite

LLa Ce Nd Sm Eu Tb Er Yb Lu

REE diagrams using batch melting model of a garnet lherzolite for various values of F:

Figure 9.4. Rare Earth concentrations (normalized to chondrite) for melts produced at various values of F via melting of a hypothetical garnet lherzolite using the batch melting model (equation 9.5). From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Europium anomaly when plagioclase is a fractionating phenocryst

or a residual solid in source

Figure 9.5. REE diagram for 10% batch melting of a hypothetical lherzolite with 20% plagioclase, resulting in a pronounced negative Europium anomaly. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Normalized Multielement (Spider) DiagramsAn extension of the normalized REE technique to a broader spectrum of elements

Fig. 9.6. Spider diagram for an alkaline basalt from Gough Island, southern Atlantic. After Sun and MacDonough (1989). In A. D. Saunders and M. J. Norry (eds.), Magmatism in the Ocean Basins. Geol. Soc. London Spec. Publ., 42. pp. 313-345.

Chondrite-normalized spider diagrams are commonly organized by (the author’s estimate) of increasing incompatibility L ← R

Different estimates →different ordering (poor standardization)

MORB-normalized Spider Separates LIL and HFS

Figure 9.7. Ocean island basalt plotted on a mid-ocean ridge basalt (MORB) normalized spider diagram of the type used by Pearce (1983). Data from Sun and McDonough (1989). From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Application of Trace Elements to Igneous Systems

1. Use like major elements on variation diagrams to document FX, assimilation, etc. in a suite of rocks More sensitive → larger variations as process

continues

Figure 9.1a. Ni Harker Diagram for Crater Lake. From data compiled by Rick Conrey. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Contrasts and similarities in the D values:All are incompatible

Also Note:

HREE are less incompatible

Especially in garnet

Eu can → 2+ which conc. in plagioclase



Rar

e Ea

rth E

lem

ents

2. Identification of the source rock or a particular mineral involved in either partial melting or fractional crystallization processes



Rar

e Ea

rth E

lem

ents

Garnet concentrates the HREE and fractionates among them

Thus if garnet is in equilibrium with the partial melt (a residual phase in the source left behind) expect a steep (-) slope in REE and HREE

Shallow (< 40 km) partial melting of the mantle will have plagioclase in the resuduum and a Eu anomaly will result

0.00

2.00

4.00

6.00

8.00

10.00

56 58 60 62 64 66 68 70 72

sam

ple/

chon

drite

La Ce Nd Sm Eu Tb Er Yb Lu

67% Ol 17% Opx 17% Cpx

0.00

2.00

4.00

6.00

8.00

10.00

56 58 60 62 64 66 68 70 72

sam

ple/

chon

drite


57% Ol 14% Opx 14% Cpx 14% Grt

Garnet and Plagioclase effect on HREE

0.00

2.00

4.00

6.00

8.00

10.00

sam

ple/

chon

drite

60% Ol 15% Opx 15% Cpx 10%Plag


Element Use as a Petrogenetic Indicator

Ni, Co, Cr Highly compatible elements. Ni and Co are concentrated in olivine, and Cr in spinel and clinopyroxene. High concentrations

indicate a mantle source, limited fractionation, or crystal accumulation.

Zr, Hf Very incompatible elements that do not substitute into major silicate phases (although they may replace Ti in titanite or

rutile). High concentrations imply an enriched source or extensive liquid evolution.

Nb, Ta High field-strength elements that partition into Ti-rich phases (titanite, Ti-amphibole, Fe-Ti oxides. Typically low

concentrations in subduction-related melts.

Ru, Rh, Pd,

Re, Os, Ir,

Pd

Platinum group elements (PGEs) are siderophile and used mostly to study melting and crystallization in mafic-ultramafic

systems in which PGEs are typically hosted by sulfides. The Re/Os isotopic system is controlled by initial PGE

differentiation and is applied to mantle evolution and mafic melt processes.

Sc Concentrates in pyroxenes and may be used as an indicator of pyroxene fractionation.

Sr Substitutes for Ca in plagioclase (but not in pyroxene), and, to a lesser extent, for K in K-feldspar. Behaves as a compatible

element at low pressure where plagioclase forms early, but as an incompatible element at higher pressure where

plagioclase is no longer stable.

REE Myriad uses in modeling source characteristics and liquid evolution. Garnet accommodates the HREE more than the LREE,

and orthopyroxene and hornblende do so to a lesser degree. Titanite and plagioclase accommodates more LREE. Eu2+ is

strongly partitioned into plagioclase.

Y Commonly incompatible. Strongly partitioned into garnet and amphibole. Titanite and apatite also concentrate Y, so the

presence of these as accessories could have a significant effect.

Table 9.6 A Brief Summary of Some Particularly Useful Trace Elements in Igneous Petrology

Trace elements as a tool to determine paleotectonic environment

Useful for rocks in mobile belts that are no longer recognizably in their original setting

Can trace elements be discriminators of igneous environment?

Approach is empirical on modern occurrences Concentrate on elements that are immobile

during low/medium grade metamorphism

Figure 9.8 Examples of discrimination diagrams used to infer tectonic setting of ancient (meta)volcanics. (a) after Pearce and Cann (1973), (b) after Pearce (1982), Coish et al. (1986). Reprinted by permission of the American Journal of Science, (c) after Mullen (1983) Copyright © with permission from Elsevier Science, (d) and (e) after Vermeesch (2005) © AGU with permission.

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worked example of batch melting: rb and srasimonet/ce30540/sp2017/lecture_10_new...worked example of...

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