Interpreting SrœNd isotopic data from magmatic and metamorphic ...

Vojtěch Janoušek:
Interpreting Sr–Nd isotopic data: numerical recipes
originated from the same magma by various degrees of fractional crystallization only preserve
identical initial isotopic ratios (forming horizontal lines).
Eqs [6.2] and [6.4] can be, after eliminating c M , combined into a formula for f. The parameter f can
be calculated if the isotopic compositions and element concentrations for both end-members as well as
the isotopic composition of the presumed hybrid are known:
f
=
I
M
( c
A
cB
− c
( I − I )
B
B
) − I
A
M
c
A
+ I
B
c
B
[6.6]
Exercise 6–2
Plot the theoretical mixing hyperbola between granite and basalt, whose compositions
are given below. Calculate the 87 Sr/ 86 Sr ratio of a mixture, containing 50 % of the
granite. Calculate proportion of the granite in a mixture that has 87 Sr/ 86 Sr = 0.71200.
A: granite B: basalt
Sr 160 ppm 318 ppm
87 Sr/ 86 Sr 0.73691 0.70362
Hints:
! Calculate the Sr concentrations (eq. [6.2]) and isotopic composition (eq. [6.4]) of the hybrid
for various proportions of the granite (f = 0–1)
! Plot the results in the Sr– 87 Sr/ 86 Sr diagram
! Check the results in the 1/ Sr– 87 Sr/ 86 Sr plot — they should form a straight line
! Proportion f of the granite end-member is obtained using eq. [6.6].
B2 Using a pair of different isotopic ratios (Sr–Nd)
Taking into account that [6.2]
c = c f + c ( 1−
f )
M
A
B
the equation [6.4] can be rewritten as:
I
Ac
A
f + I
BcB
(1 − f )
I
M
= [6.7]
c f + c (1 − f )
A
Both Sr and Nd isotopic compositions can be calculated for pre-set values of the parameter f and the
corresponding mixing hyperbola plotted in the 87 Sr/ 86 Sr – 143 Nd/ 144 Nd space.
General equation of this mixing hyperbola is derived from two equations [6.7], one for Sr and one for
Nd, by solving both equations for f and equating the results:
B
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