This document discusses Pearce Element Ratio (PER) diagrams, which are a type of variation diagram used to model magmatic evolution. PER diagrams plot element ratios rather than oxide weights, preserving true elemental variations. They allow testing of hypotheses about fractionation by seeing if rock compositions fall along lines representing fractionation trends. An example PER diagram is presented showing fractionation of anorthite and forsterite. While PER diagrams can eliminate bad hypotheses, they can only support but not prove good ones. Overall, PER diagrams provide a quantitative way to investigate magmatic processes like fractionation and accumulation.

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(Winter Chapter-
9)
Pearce Element
Ratio
A variation diagram for evaluating hypothesis on model of
magmatic evolution
Presenter
Sujan Raj Pandey
Roll No.05
M.Sc. 1st Semester
Central Department of Geology

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Variation Diagrams
 The chemical compositional variation of igneous rocks has been
used to interpret the series of related rocks and model the trend of
variation.
 There is no single best way to display the data using parameters
that show systematic variation to investigate the underlying causes.
 So, different diagrams have been approached to understand the
causes, these diagrams are what we term variation diagrams.
 Types: a) Bivariate Plots like Harker Diagram, PER
b) Ternary Diagram

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Previous Approach
 Previous approaches, which are still in used
today defines the variation diagram on plotting of
oxide-oxide wt.% comparisons.
 Initial, Harker Diagram (Harker,1900) uses plot of
wt. % of silica as abscissa against the other major
oxides in a rectangular graph to evaluate specific
differentiation mechanism.
 A ternary variation diagram plots three
components, usually normalized to 100, on a
triangular graph, which is generally equilateral but
may be right-angled (AFM diagrams).

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Limitations to Previous Approach
 But, this oxide-oxide wt.% variation diagram are limited as;
a) Only qualitative rather than quantitative.
b) Limits for solid solution as wt.% is not easily related to
mineral of chemical composition.
c) The wt.% oxide data suffer constant sum effect (Chayes,
1964).
d) The data are in a weight percent basis, the elemental
variations due to crystallization are no longer apparent and
the absolute relationships of the masses are lost and not
recoverable.
e) It cannot discriminate between the rival hypothesis

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Pearce Element Ratio (PER)
 Pearce (1968), proposed a method for using chemical data to indicate
phase extracted from evolving liquid by plotting element ratio or molar
ratio diagram.
 This molar ratio approach, designed to model processes of
fractionation and accumulation in igneous systems is termed as
Pearce Element Ratio.
 It is also a bivariate plot, but between the two element ratio, where
denominator of the ratio is always same for both axes and is a single
element.
 Pearce element ratios preserve information related to variations in
absolute units.

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Pearce Element Ratio (PER)
 Their defining characteristic is a denominator formed from
concentrations of elements that enter the minerals crystallizing from
igneous melts in negligible amounts i.e. conserved elements.
 The numerators are linear combination of elements that reflect the
chemical change in the melt-solid system caused by segregation
and accumulation of mineral assemblage.
 PER diagrams ensure that the true elemental variations are
represented whether expressed against other element ratios or a
physical dimension.

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Mathematical Relation
 Mathematically, the element ratios are calculated in two steps.
a. First, all the wt.% oxides are converted to the element fraction
(ei) by;
𝑒𝑖 =
𝑤𝑖𝐴𝑖
𝑀𝑤𝑖
;
where 𝑤𝑖 is wt.%, 𝐴𝑖 is no. of cation in the oxide formula and
𝑀𝑤𝑖 is molecular weight of oxide i.
b. Then, Pearce element ratio of element i is;
PERi =
𝑒𝑖
𝑒𝑧
where 𝑒𝑧 is conserved element or trace?.

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PER Approach to Test Hypothesis
 Specification of the mineral assemblage allows us to create a model
such that the compositions of melts and solid assemblages will fall on
a line with the model slope. So we approach as following procedure:
i. A single rock composition is held to plot the model slope( of 1,2 ) in
Pearce ratio space.
ii. Now, if we select the fixed point on model slope line representing melt
composition at the beginning of crystallization then,
iii. The points of PER fall down slope for the residual melt and
iv. The points of PER will fall up-slope for crystal-melt mixtures.
v. When the pattern of points doesn’t conform to the slope, then it suggest
the no fractionation of mineral.
 Thus, the trend of fractionation and accumulation can be visualize,
but this doesn’t prove that a particular mineral is fractionating or even
at work.

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Example of PER Plot
 The diagram was designed to describe the Pearce element ratios in
the melts generated by fractionation (loss) of anorthite (CaAl2Si2O8)
and forsterite (Mg2SiO4) from the initial melt.

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Example of PER Plot
 The Pearce
element ratio
coordinates of the
initial melt are
shown with a
black star.
 The ratios derived
from the
compositions of
the solids plus
trapped melt are
shown by filled
circles.

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Conclusion
 Pearce element ratio uses element ratio to test hypotheses of mineral
fractionation in a set of cogenetic analyses.
 Pearce element ratio variation diagrams can be employed to identify
the phases involved in igneous differentiation., to estimate the molar
proportions of phases and to place limits on the compositions of the
phases involved.
 The Harker diagram shows all the components varying with SiO2,
suggesting a very complex differentiation mechanism. PER diagrams,
on the other hand, show the essential simplicity of the processes.
 To determine the exact variation between components, weight per-
cent comparisons be discontinued (wherever possible) in favor of
molar ratio comparisons in which one of the components (the divisor)
is a constant.

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Conclusion
 The PER approach is a good way to test hypotheses and can serve
to eliminate a bad hypothesis, but it can only support, not prove, a
good one.
 When scattered data on Harker type diagrams suddenly become
linear on PER diagrams, one should not jump to the conclusion that
this correlation necessarily demonstrates that a particular mineral is
fractionating.
 Rather, it should be treated as a suggestion, to be evaluated using
other textural and chemical criteria.

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Thank You