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Petrogenetic Models Fractional crystallization – major elements Mass balance: CPM = concentration in the parental melt C = concentration in differentiated melt CFCFCPMFMcum1 DM F = fraction of the melt remaining (1→0); CCii Lever rule: f PM FM ffc= (1– F) = degree of fractional fc ii crystallization CCcum FM Vojtěch Janoušek: Using whole-rock major- and trace-element data in interpretation of igneous rocks (after Cox et al. 1979) Trends produced by fractional crystallization of cumulate (cum) consisting of one (P), two (P–Q) or three (P–Q–R) minerals. PM = primary melt, FM = fractionated magma y Ax Fractional crystallization – major elements Fractional crystallization – major elements • Binary plots of major elements vs. SiO2 (Harker plots) or any other index of fractionation (e.g., MgO or mg#) often show linear relationships. Continuously evolving cumulate b Clinopyroxene C (9) • These trends on their own do not provide evidence for operation of fractional • Produces curved trends. S C (8) S (7) crystallization! CS C (8) wt.% L C (6) C (9) S L C (5) (5) C (7) • Partial melting or mixing would also produce linear trends (Wall et al. 1987). S CL L C (3) (4) L CaO C C (2) S L C (3) C (1) • However, the changes in fractionating assemblage result in inflections. S L C (2) C S 0 If present, they prove operation of fractional crystallization. C (1) y Ax S C (0) S Olivine SiO2 wt.% Reverse modelling • For reverse modelling of fractional crystallization, the composition of the primitive magma is considered to be a mixture of differentiated magma and cumulus crystals. ii i CCfCPM cum fc FM(1 f fc ) (after Wilson 1989) • Numerical solution is provided, for instance, by the least-squares method (Bryan et al. 1969). Harker plots for a suite of cogenetic volcanic rocks developing by fractional crystallization of olivine, clinopyroxene, plagioclase and apatite. 1 Classification of trace elements Classification of trace elements ionic potential = charge/radius Determines, which elements will be mobile in hydrous fluids and thus strongly enriched in arc magmas (being contributed by the subducted plate) Non-conservative elements Large Ion Lithophile Elements (LILE): Cs, Rb, K, Li, Ba, Sr, Pb... Conservative elements High Field Strength http://www.gly.uga.edu/railsback/FundamentalsIndex.html Elements (HFSE): Nb, Ta, Ti, Zr, Hf... (White 2005) Presentation of trace-element data Spiderplots 0 • Binary plots Plotting Chondrite (Boynton 1984) Po- 1 (original) a b • Log–log plots • Arrange elements logically • Histograms (more incompatible on the left) • Boxplots b • Divide each element’s R Rb (box and whiskers plots) concentration in the sample by (ppm) (ppm) • Box and percentile plots that in a reference material 200 400 600 800 100 • Plot y-axis using a log scale 0.05 0.10 0.20 0.50 ab 1 5 10 50 500 0.05 0.20 0.50 2.00 5.00 20.00 200 400 600 800 1000 1 5 10 50 500 Advantages/usage La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Sr Sr • Elimination of the Oddo-Harkins Po- 1 (normalized) c effect in the Solar System, the abundances of e even-numbered elements are greater t i r d than those of neighbouring odd- on h c E numbered ones + abundances generally E R / e decrease with increasing atomic number. l amp • Spiderplots allow representing S much of the sample’s composition on a single graph. La Pr Pm Eu Tb Ho Tm Lu 1 10 100 Ce Nd Sm Gd Dy Er Yb 2 Spiderplots Spiderplots – examples Standards for normalization 0 Standards for normalization MgO 5.8- 6 • Chondrites ( “Bulk Silicate Earth”) 6- 6.2 • Most primitive/least-altered sample 6.2- 6.4 6.4- 6.6 •Primitive Mantle 6.6- 6.8 6.8- 7 7- 7.2 • Mid-Ocean Ridge Basalts (NMORB) 7.2- 7.4 7.4- 7.6 7.6- 7.8 • Ocean-Island Basalts (OIB) Modifications 7.8- 8 8- 8.2 8.2- 8.4 • Averages of various crustal reservoirs, • Fields 8.4- 8.6 8.6- 8.8 8.8- 9 bulk, upper, lower… • Colour-coded by a certain 9- 9.2 a 9.2- 9.4 • Ocean Ridge Granites (ORG) 9.4- 9.6 parameter (SiO2, MgO…) La Pr Pm Eu Tb Ho Tm Lu 0.1 1 10 10 • Spider box plots Ce Nd Sm Gd Dy Er Yb • Spider box and percentile plots Rock/Chondrite (Boynton 1984) 0 0 1 0 1 b Multielement plots for metavolcanic 0.1 1 10 rocks from the Devonian Vrbno La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Group, Silesia (Czech Republic) Chondrite-normalized (Boynton 1984) (Janoušek et al. 2014) 1 REE patterns for dolerites from the Devonian Vrbno Group, Silesia La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Rock/NMORB (Sun and McDonough 1989) (SunRock/NMORB Two types of trace elements Behaviour of accessories – solubility concept Example – zircon “Dilute” trace elements (element partitioning) (Watson and Harrison 1983) • Trace elements that occur in small amounts in the crystal lattice, and their activity is proportional to their concentration (Henry 1803). • The coefficient of proportionality depends on the nature of the mineral but not Zr on the concentration of the element. C 12900 lnZrn 3.80 0.85( M 1) • Modelled by element partitioning between crystals and liquid. C Zr T L sat Essential Structural Constituents (solubility concept) • Essential Structural Constituents (ESC) form a substantial part of the crystal T = temperature in K lattice of certain accessory minerals. Zr = 497644 ppm (49.7 wt. %) is the CZrn e.g., Zr in zircon, P in apatite or P, Th and LREE in monazite amount of Zr in an ideal zircon M = whole-rock chemical parameter • The Henry’s Law is not applicable. based on cation fractions: • Empirical approach, using experimentally determined mineral solubility in a Na K 2 Ca silicate melt. M Al Si 3 Partition coefficient Partition coefficient HORNBLENDE CLINOPYROXENE GARNET 100 hbl/L cpx/L grt/L 50 KD K D KD rhyolite Partition coefficient compatible elements KD » 1 Depends on: concentrate into the mineral rather rhyolite dacite 10 • magma composition than in the melt basalt min/ L Cmin 5 dacite (acid/basic, water >1 : COMPATIBLE K rhyolite D D K contents...) incompatible elements K « 1 1 dacite CL D • temperature remain in the melt 0.5 basalt basalt • pressure Partition coefficient 0.1 0.05 • mineral < 1 : INCOMPATIBLE • mineral stoichiometry D 0.01 K Does not depend on: La Ce Nd SmEuGd Dy Er Yb Lu La Ce Nd SmEuGd Dy Er Yb Lu La Ce Nd SmEuGd Dy Er Yb Lu (composition) • concentration of the given element Measurement: plagioclase • oxygen fugacity 10 concentration of any other elements • (Bulk analysis of mineral separates 0.9 ab (Eu in plagioclase) in the system 5 and glass or matrix) 0.8 –13 fO2 =10 • In-situ measurement in f =10–10 1 O2 0.7 –8 fO =10 phenocrysts and glass 0.5 2 (Sr) Bulk distribution coefficient Pl/L D –6 D Pl/L K fO =10 (ion probe, LA ICP MS,…) 0.6 2 Databases of KD values: ln K • Rollinson (1993) • Experiments (doped material) 0.1 DKd X 0.5 i i • GERM website • Calculations (lattice strain model) 0.05 i (http://earthref.org/KDD/). 0.4 Pl/L Ln KD (Sr) = 1521/T – 9.909 0.01 6.8 6.9 7.0 7.1 7.2 La Ce Nd Sm Eu Gd Dy Er Yb Lu 104/T (K–1) Partition coefficients Fractional crystallization C0 = concentration in the parental melt Rayleigh equation C = concentration in differentiated melt C L L F (1)D F = fraction of the melt remaining (1→0); C (1– F) = degree of fc 0 D = bulk distribution coefficient for the crystallizing phases ‘Forbidden domain‘ Instantaneous solid: c 1 L cDcDcFinst (1) D c0 F sL0 Bulk cumulate: 1 F D ccs 0 Mineral/melt distribution coefficients for REE in dacites and rhyolites (Hanson 1978) 1 F 4 Fractional crystallization Equilibrium crystallization The identification of fractionating phases is C = concentration in the parental melt Melt development: 0 facilitated by log–log plots of CL = concentration in differentiated melt whole-rock trace-element C F = fraction of the melt remaining (1→0); concentrations, in which the 0 CL (1– F) = degree of fractional originally exponential Rayleigh D FD(1 ) crystallization trends are converted to linear D = bulk distribution coefficient for the ones: crystallizing phases log(cL ) log(cD0 ) ( 1 ) log( F ) For granitoids are commonly Regardless of its exact mechanism used Rb, Sr, Ba whose (fractional/equilibrium), distribution coefficients (K ) are D crystallization quickly depletes relatively well known compatible elements from the melt. (Hanson 1978). Ba vs Sr patterns for the Kozárovice (diamonds) and Blatná (squares) intrusions of the Central Bohemian Plutonic Complex, Czech Republic (Janoušek et al. 2000) (White 2005) Fractional crystallization – behaviour of Fractional melting accessories C0 = concentration in the (unmelted) source Melt development: CL = concentration in the melt 1 1 F = degree of melting CS D (1F ) D = bulk distribution coefficient after C0 melting (residue) At any moment, the instantaneous liquid equilibrates with the solid residue. The composition of a single melt increment is: 1 C 1 1 L (1F ) D CD0 Average composition of the (aggregated) melt: C 1 1 L 1(1)F D CF0 Watson & Harrison (1984); Hoskin et al. (2000); Janoušek (2006) 5 Distinguishing between fractional Batch melting crystallization and partial melting C0 = concentration in the (unmelted) source PM Melt development: 50 CL = concentration in the melt Co C F = degree of melting Fractional 0 F Pa rtial melti 20 C r ng L D = bulk distribution coefficient after a c DF(1 D ) t Batc i h melting (residue) ) o n β a l 10 c r y s Ni ppm t Log ( All the melt is formed, and then separated in a single batch.
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