JOURNAL OF PETROLOGY
VOLUME 42
NUMBER 10
PAGES 1887–1910
2001
Minor Phases as Carriers of Trace Elements
in Non-Modal Crystal–Liquid Separation
Processes II: Illustrations and Bearing on
Behaviour of REE, U, Th and the PGE in
Igneous Processes
M. J. O’HARA∗, N. FRY AND H. M. PRICHARD
DEPARTMENT OF EARTH SCIENCES, CARDIFF UNIVERSITY, PO BOX 914, CARDIFF CF10 3YE, UK
RECEIVED SEPTEMBER 10, 1998; REVISED TYPESCRIPT ACCEPTED MARCH 16, 2001
becomes possible. Further complexities arise and the opportunities
for separation increase when two carrier-phases compete with differing
success for the same group of trace elements.
Minor phases which strongly concentrate selected trace elements,
termed here ‘carrier-phases’, release relatively large amounts of those
elements to the liquid phase when they are eliminated during partial
melting and glean relatively large amounts of those elements when
they first appear during progressive crystallization. It is characteristic
of such relationships that concentrations of the selected trace elements
in the bulk residues of partial melting will rise to a peak somewhat
before the last of the carrier-phase is eliminated during progressive
melting. In the liquids produced during equilibrium partial melting
a corresponding peak in the concentration of the trace element occurs
at the point where the carrier-phase is eliminated; the corresponding
peak in trace element concentration in the liquids produced by
accumulated perfect fractional melting is found somewhat above
that point. These peaks become more sharply accentuated as the
distribution coefficient of the trace element into the carrier-phase
increases. The highest trace element concentration in a partial melt
liquid product is found in the small drop of liquid produced during
perfect fractional melting at the point where the carrier-phase is
eliminated. Still higher concentrations may be found in the first
cumulates containing the carrier-phase which precipitate during
perfect fractional crystallization but the corresponding liquids do
not contain exceptionally high concentrations. Under favourable
conditions a large proportion of the available mass of a trace element
in a magmatic system may be transferred from the solid to the
liquid phases or vice versa with only a small change in the mass
fraction of liquid in and energy content of the system. Within that
range, separation of otherwise very similarly behaved trace elements
In a companion paper (O’Hara et al., 2001) the basic
features of non-modal melting or crystallization were
surveyed in systems where one or more of the solid
phases present in minor amounts strongly concentrates
certain trace elements. These minor ‘carrier-phases’ are
likely to release those elements to the liquid, or glean
them from the liquid, at some intermediate stage of the
melting or crystallization history.
Code has been written in Mathematica (Wolfram Research Inc., 1994) to implement the equations developed
in O’Hara et al. (2001) in order to calculate the cases
when two or three solid phases only are present. This
code (Electronic Appendix A) is available from the
Journal of Petrology Web site at http://www.petrology.
oupjournals.org. It has been used to produce the figures
Extended dataset can be found at
http://www.petrology.oupjournals.org
∗Corresponding author. E-mail: sglmjo@cardiff.ac.uk
 Oxford University Press 2001
KEY WORDS:
platinum; uranium; chromite; sulphide; distribution
coefficient
INTRODUCTION
JOURNAL OF PETROLOGY
VOLUME 42
below, which illustrate the quantitative detail of some
important principles of behaviour already derived
qualitatively in the semi-graphical treatment of the previous paper.
DISAPPEARANCE OR APPEARANCE
OF ONE CARRIER-PHASE IN TWOMAJOR-COMPONENT SYSTEMS IN
THE MIDDLE-f OR LOW-f STAGES OF
MELTING OR CRYSTALLIZATION
In much of the following discussion the values which
have been assumed for the crystal–liquid distribution
coefficients of trace elements with respect to the one or
two carrier-phases are such as to ensure that where a
carrier-phase is still present, the bulk and modal distribution coefficients remain significantly greater than
unity. Except where otherwise noted, the elements under
discussion are enhanced in concentration in the liquid
by further melting, or decreased by further crystallization,
provided that a carrier-phase is present. This is the
situation most relevant to the consideration of the behaviour of the platinum group elements (PGE) and of
uranium and thorium. The case of trace elements which
are only moderately compatible in the carrier-phases will
be considered in a later section.
The case of a system of two major components with
one carrier-phase is treated extensively at the outset to
illustrate the principal features of the behaviour. The
treatment is then extended to the case of systems of three
major components containing two competing carrierphases and concentrates on the additional or modified
features resulting from the introduction of the extra
phase.
Behaviour in a simple two-majorcomponent system with one carrier-phase
Figure 1 is a plot of the relative concentration of a trace
element which can be highly concentrated into a minor
carrier-phase in the products of a variety of processes.
The relative concentrations shown are those achieved
during non-modal melting or crystallization of a twosolid-phase mixture which contains 0·5% carrier-phase
in which the trace element of interest is partitioned
with a crystal–liquid distribution coefficient of 1000, and
99·5% of other phases in which that element has a
crystal–liquid distribution coefficient of 0·05. The modal
melting assemblage is assumed to contain 2% of the
carrier-phase. When 25% of the original solid material
has been melted, 2% of 25% = 0·5% of carrier-phase
has been consumed and it is consequently eliminated
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OCTOBER 2001
from the residue. The initial bulk distribution coefficient
for this element is >5·05 and the modal distribution
coefficient during the melting interval where two solid
phases coexist with liquid is >20·05. The plot is presented
at four scales to fully illustrate the details and there is an
extended commentary explaining the features of this plot
available on the Journal of Petrology Web site (Electronic
Appendix B).
Abbreviations summarized
Six important processes are represented by abbreviations
which are used repeatedly in the caption and description
of Fig. 1 and later in this paper. These are: APNMFC,
accumulated perfect non-modal fractional crystallization
(applies to average solids only, the conjugate liquid is the
same as the PNMFC product); APNMFM, accumulated
perfect non-modal fractional melting (applies to average
liquid only, the conjugate solid is the PNMFM residual
solid); ENMPC, equilibrium non-modal partial crystallization; ENMPM, equilibrium non-modal partial
melting; PNMFC, perfect non-modal fractional crystallization; PNMFM, perfect non-modal fractional
melting.
Concepts arising from Fig. 1
Initial, critical and dilution melting intervals; concentration,
critical and late crystallization intervals
Three intervals may be identified in the patterns of
varying concentrations in the ENMPM, APNMFM, ENMPC and PNMFC liquids. At low values of f there is an
initial melting or late crystallization interval in which the
carrier-phase is present and concentrations of the element
of interest in the liquid are either low or extremely low.
At high values of f there is a dilution or concentration
interval in which the concentrations of the element are
controlled principally by the mass fraction of the system
which is crystalline but does not contain the carrierphase; as f increases within this interval, the element of
interest is diluted by melting of the non-carrier-phase,
and as f decreases that element is concentrated in the
remaining liquid by extraction of the non-carrier-phase.
Within this interval relative concentrations of the element
of interest are uniformly greater than or equal to unity.
In a narrow range of f between the two above intervals
is a critical melting or crystallization interval located
immediately below and around (ENMPM, ENMPC,
APNMFC and PNMFC), or immediately above
(APNMFM) the critical value of f at which the carrierphase appears or disappears. Within this interval the
concentration of the element of interest changes rapidly
with increase or decrease in the value of f. This feature
is noticeably less emphasized in the case of APNMFM
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Fig. 1. Relative concentrations of elements and resultant bulk distribution coefficients plotted on the same vertical numerical scales for selected ideally behaved trace elements in the liquid
and solid phases during a variety of melting and crystallization processes in a hypothetical system with one carrier-phase. Data are plotted as a function of mass fraction of melt in the
system at four different vertical scales. Relative concentrations in the ENMPM liquid and residue and for the ENMPC liquid and precipitate are identical. Relative concentrations of an
element which is uniformly highly incompatible (d = 0·001) in the ENMPM liquid products are also shown as a guide to the effects of simple dilution or concentration in this figure. The
bulk distribution coefficient between the remaining solids and the melt during ENMPM is shown plotted against the same numerical scale as the relative concentrations.
O’HARA et al.
MINOR PHASES AS CARRIERS OF TRACE ELEMENTS, II
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liquids and relative concentrations peak at a slightly lower
value.
Perfect fractional melting and the critical
melting spike
During perfect fractional melting the initial melting interval can be recognized, but neither of the other two
intervals exist. Instead, the most conspicuous feature of
the PNMFM liquids is the extraction interval marked by
the asymmetric critical melting spike of concentration
peaking at the critical value of f, which is followed at
higher f by an interval of severe depletion.
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OCTOBER 2001
at which high concentrations of the highly incompatible
element are achieved in the liquid phase. The effects are
shown here for the cases of ENMPM (Fig. 2a), which
is identical to that for ENMPC, and APNMFM (Fig.
2b)—that for the PNMFC liquid is visually similar to
these two figures. In all four cases the mass fraction of
melt, developed or remaining, at the critical melting or
crystallization interval increases as the mass fraction of
the carrier-phase in the initial bulk composition increases,
but the magnitude of the step in concentration achieved
at the critical interval is at the same time greatly reduced.
Effect of varying mass fractions of carrierphase on ENMPM, PNMFM residues,
ENMPC, PNMFC and APNMFC
precipitates
Perfect fractional crystallization and the
critical crystallization spike
During perfect fractional crystallization the concentrations in the precipitated solids display an interval
of mild concentration at high f before the appearance of
the carrier-phase, a critical concentration spike in the
crystal assemblage precipitated immediately after the
appearance of the carrier-phase, and an extreme depletion interval at low f after rapid extraction of the
element of interest into the earliest cumulates.
Varying the mass fraction of the carrierphase
Figure 2 presents six perspective views of the surface of
liquid or solid compositions generated in different nonmodal melting or crystallization processes as the melt
fraction increases from 0·001 at the front left to 0·999
at the back right face in each case. The modal melting
assemblage is assumed to contain 2% of the carrierphase, and the crystal–liquid distribution coefficients for
the element of interest were set at 1000 in the carrierphase and 0·05 in the other phases. The mass fraction
of the carrier-phase has been allowed to vary from zero
at the front right face of each figure to 0·03 (3%) at the
back left face of each figure. With this choice of parameters the elimination or appearance of the carrier-phase
takes place at all values of f between 0·001 and 0·999,
and for mass fractions between 0·02 and 0·03 the noncarrier-phase is eliminated before, or begins to crystallize
after, the carrier-phase.
Effect of varying mass fractions of carrierphase on ENMPM, ENMPC, APNMFM and
PNMFC liquids
Varying the (very low) mass fraction of the carrier-phase
in the initial solid alters the mass fraction of total melting
The effects of varying the (very low) mass fraction of the
carrier-phase in the source region on the behaviour of
the highly compatible element in the solid residues or
precipitates are shown here for the case of ENMPM
(Fig. 2c), which is identical to that for precipitates in
ENMPC. The results for PNMFM or APNMFM, which
are also identical to one another, are visually indistinguishable from Fig. 2c at these scales. As the mass
fraction of the carrier-phase in the initial bulk composition
increases in all four cases, the build-up in relative concentration of the element of interest in the solids at the
boundary between the critical interval and the initial
concentration or late crystallization interval (low-f region)
increases, and the magnitude of the step in concentration
achieved in the residues at the critical interval is greatly
enhanced. The greater the mass fraction of total solid at
the critical interval, the smaller the change in concentration in that solid necessary to balance a large
change in the necessarily small mass fraction of liquid.
The effects of varying the (very low) mass fraction of the
carrier-phase in the source region on the behaviour of
the highly compatible element in the APNMFC precipitates are shown in Fig. 2d.
The situation for the instantaneous PNMFC precipitates is very different and is shown in Fig. 2e. Negligible concentrations of the element of interest are
generated in the precipitates before the entry of the
carrier-phase (right-hand half of the figure). Very high
concentrations of the element of interest are found in
the first crystals of the carrier-phase to precipitate and
in the bulk precipitate at this point. Fractional crystallization of this precipitate rapidly eliminates significant
concentrations of the element of interest from all the
later residual liquids (left half of figure). The steep-sided
ridge (arête) feature is poorly represented in this figure
because of the interplay between a very narrow region
of extreme high values and the grid of sampling points
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MINOR PHASES AS CARRIERS OF TRACE ELEMENTS, II
Fig. 2. Relative concentration of an element which is highly compatible in a single carrier-phase, in the liquids and solids produced during a
variety of crystal–liquid processes. Results are expressed as a function of the mass fraction of melt and of the mass fraction of the solid system
which is composed of the carrier-phase. Further discussion in the text.
used for the preparation of this figure—in fact the height
of the arête increases dramatically towards the front
corner of the figure because the concentrations in the
liquids from which the modal assemblage starts to fractionate are increasing in this direction (compare Fig. 2a
and b). Precipitate compositions are related to these
concentrations in the liquids by the modal distribution
coefficient at the critical interval, which is constant
throughout the region of the arête and the left-hand side
of the figure.
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Effect of varying mass fractions of carrierphase on PNMFM liquids
Figure 2f shows the varying location of the spike of
concentration which is produced in PNMFM liquids
as the mass fraction of the carrier-phase changes. The
arête feature is again poorly represented in this figure
because of the interplay between a very narrow region
of extreme high values and the grid of sampling points
used for the preparation of this figure. In fact, the
height of the arête increases dramatically towards the
back corner of the figure because the concentrations
in the residual solids from which the melt increments
are to be developed are increasing in that direction
(Fig. 2c). Liquid compositions are related to these
concentrations by the bulk distribution coefficient in
the critical interval. The bulk distribution coefficient
also increases towards the back of the figure because
of the higher ratio of carrier-phase to main phase on
entering the critical interval. At more than 0·02 initial
mass fraction of carrier-phase, the bulk distribution
coefficient increases to 1000 at the critical melting
value because the main phase is totally consumed first.
Varying the modal melting proportions
The effect of reducing the modal melting proportion of
the carrier-phase is, in terms of the overall topography
of each of these diagrams in Fig. 2, broadly analogous
to increasing the carrier-phase mass fraction. The critical
interval or spike moves to higher values of f. Other
variations of parameters modify the absolute values of
relative concentration but not the overall topography of
these diagrams.
Varying the distribution coefficient of trace
elements in the carrier-phase
Figures 3 and 4 present a number of plots for a specific
choice of starting composition different from that used
in preparing Figs 1 and 2. The initial bulk composition
is now assumed to contain 1·5% of the carrier-phase,
with the modal melting assemblage containing 6% of the
carrier-phase. All elements are assumed to have d =
0·001 in the main phase. This choice of parameters was
made in the interests of convenience and clarity in the
diagrams.
Figure 3 plots the relative concentrations achieved in
the liquid and solid products of the ENMPM, ENMPC
and APNMFM processes and the solids of the APNMFC
process as a function of the mass fraction of liquid, f, in
the system. Figure 4 presents comparable data for the
liquids and solids of the PNMFC and the liquids of the
PNMFM processes. These figures illustrate the effect of
varying the distribution coefficient of the element of
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OCTOBER 2001
interest in the carrier-phase upon the concentrations
achieved and, less obviously, upon the ratios of these
elements to one another and to a highly incompatible
element.
For any element which has dcarrier-phase >1·0 and dmain
phase <1·0, there exists a pair of values of these distribution
coefficients such that dm = 1·0 for any specified set of
modal melting proportions. When this condition is satisfied the relative concentration of the element of interest
in the liquid products of ENMPM, PNMFM and
APNMFM will all be constant at 1/0dbs at all values of f
up to that of the critical value of f at which the carrierphase is eliminated. This may readily be shown by making
the required substitution for dm = 1 in the simplified form
of the equations in Electronic Appendix A appropriate to
first-stage melting of a binary mixture. The effect is
shown by the horizontal dotted lines in Fig. 3a and c.
During ENMPC (Fig. 3a) the subsequent residual liquid
products after commencement of crystallization of the
carrier-phase then preserve whatever relative concentration they inherit at the critical value of f from
earlier processes in the system. A similar situation is
observed in residual liquids of PNMFC (Fig. 4a) and also
in the liquid products of PNMFM (Fig. 4f ), although
here the form of the curve is extremely sensitive to small
changes in the value of dm. In the system postulated in
preparing Figs 3 and 4, dm is 1·0 when dcarrier-phase =
16·653 and dmain phase = 0·001, and consequently 0dbs =
0·2508. This then results in a uniform relative concentration in the liquids of 3·988.
The relative concentrations in the corresponding solid
phases for PNMFC (Fig. 4c and e) display no composition
variation with varying f, at a concentration of 3·988 for
dcarrier-phase = 16·653, because in this system it has been
assumed that dm is constant and the precipitate composition is linked to the liquid composition by this distribution coefficient, here constrained to be equal to 1·0.
In this system any element which has dcarrier-phase <66·6
has 0dbs <1·0. This is the condition which determines
whether the relative concentrations in the residuum
during partial melting decline from the outset (see the
appropriate curves in Fig. 3b and d) or increase from
the outset and pass through a maximum located at a
value of f as discussed in the extended commentary
on Fig. 1 above. Solid compositions during ENMPM
or during ENMPC are related to the liquid compositions
directly or indirectly by the value of the bulk distribution
coefficient, which is itself a function of f. Consequently,
there are in general no uniform or linearly varying
relationships between f and relative concentrations to
be observed in these solids.
General features evident in Figs 3 and 4 are the later
retention, later peaking of concentration, and higher peak
concentrations of the most highly compatible elements in
the residues of partial melting (Fig. 3b, d and f ) relative
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MINOR PHASES AS CARRIERS OF TRACE ELEMENTS, II
Fig. 3. Plot similar to that in Fig. 1, but for a different starting composition, showing relative concentrations of elements for selected ideally
behaved trace elements of widely varying distribution coefficient in the liquid and solid phases, in a hypothetical system with one carrier-phase,
during a variety of equilibrium and accumulated perfect fractional melting and crystallization processes. Data are plotted as a function of mass
fraction of melt in the system at a variety of horizontal and vertical scales. Further description in the text. Numbers against curves indicate the
distribution coefficient which applies.
to less highly compatible elements. These are complementary to the later and sharper increase of the
more highly incompatible elements in the ENMPM and
APNMFM liquids (Fig. 3a, c and e). Ratios of the most
highly compatible elements to less compatible elements
begin to change rapidly once the value of f has exceeded
that at which the curve of concentration for the less
compatible element has passed through the condition
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NUMBER 10
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Fig. 4. Plots comparable with those in Fig. 3, for the cases of liquids and solids produced in perfect fractional melting and crystallization
processes. (Note the change in the range of distribution coefficients used in Fig. 4f.)
where the second differential, ∂2C/∂f 2, of relative concentration has passed through zero—in the case illustrated this takes place in the main at f > >0·2. With
appropriate change of terminology, the same is true
for liquids and precipitates of ENMPC and PNMFC,
although in the latter case the effects in the solids are
extreme.
In the case of PNMFM liquids and of PNMFC precipitates the peak concentrations achieved increase conspicuously as the distribution coefficient into the carrierphase increases (Fig. 4c, 4 and e), and the range of
f across which strong peaking occurs is considerably
narrowed. These features lead to crossing of the curves
and consequently to the inversion of ratios between highly
compatible elements, mostly within a very narrow interval
of f.
FRACTIONAL MASS OF AN
ELEMENT IN THE SOLID AND
LIQUID PHASES; RATES OF
TRANSFER OF THAT MASS DURING
MELTING AND CRYSTALLIZATION
PROCESSES
For purposes such as the prediction or estimation of ore
reserves and the evaluation of heat production within
the crust, interest is focused not so much upon the
concentration of an element in the carrier-phases as upon
what fraction of the total mass of an element in the
system is contained within the mobile liquid or the
sedentary solid phases at each stage of a process. This
quantity is readily calculated by multiplying the relative
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O’HARA et al.
MINOR PHASES AS CARRIERS OF TRACE ELEMENTS, II
energy into or out of the system will be reflected in
transfer of an element between the liquid and solid phases
or vice versa. In ideal modally melting systems with ideal
trace element behaviour throughout, we have
(1) for the rate of transfer into the liquid phase during
equilibrium processes,
∂ fractional mass
∂
f
d
=
=
∂f
∂ f [d+f (1−d)] [d+f (1−d)]2
(2) for the rate of transfer into the accumulated perfect
fractional partial melting liquid during fractional melting
processes,
∂ f [1−(1−f )1/d ] (1−f )(1/d )−1
∂ fractional mass
=
=
∂f
∂f
f
d
(3) for the rate of transfer from the residual liquid
into the solids with declining f during perfect fractional
crystallization,
∂
∂ fractional mass
=
f . f d−1=d.f d−1.
∂f
∂f
Fig. 5. Fraction of the total mass of an element in the system which
is in the liquid phase, expressed as a function of the mass fraction of
melt. (a) shows results during equilibrium partial melting (EPM) (or
crystallization) by continuous lines, perfect fractional crystallization
(PFC) by dashed lines and perfect fractional melting (PFM) by dotted
lines in a simple modally melting system with ideal trace element
behaviour throughout. The cases for trace elements with d = 0·05 and
d = 10 uniformly in the solid present are illustrated. (b) shows results
for the case where a carrier-phase is present and is eliminated at 0·25
mass fraction of melting. The continuous lines are for concentrations
of a trace element in liquids produced in ENMPM with d = 0·05 in
all solid phases at all stages of melting, and for d = 10 and d = 1000
in the carrier-phase only. The dashed lines illustrate liquids produced
in PNMFC, and dotted lines are for liquids produced in APNMFM.
Further description in the text.
concentration of the element in the liquid or solid part
of the assemblage by the mass fraction of the system which
is currently composed of that part of the assemblage, i.e.
as f times the concentration in the liquid, or as (1 − f )
times the average concentration in the solid phases.
Results of such calculations for simple modally melting
systems are presented in Fig. 5a and results for a selected
non-modally melting system in Fig. 5b.
The first differentials of these quantities with respect
to the mass fraction of melting are measures of the rates
of transfer of fractional mass of an element between the
solid and liquid phases at any value of f, i.e. at any given
stage in the melting or crystallization process. They
measure the ‘efficiency’ with which a given transfer of
With these simple assumptions the sign of each of these
differentials does not change across the range of f from
zero to unity; that is, the transfer of the element is always
from the solid to the liquid in the first two cases and
from liquid to solid in the third case. Some representative
plots prepared from these functions are presented in
Fig. 6a.
This unidirectional transfer continues to hold true
during non-modal melting provided that there are no
incongruent reaction relationships between crystals and
liquid, particularly those which might cause the appearance and disappearance of a carrier-phase at an
intermediate stage during the partial melting or crystallization history. The differentials of the relevant functions can be obtained from the expressions derived in
the companion paper (O’Hara et al., 2001), but Fig. 6b
has been prepared using numerical differentiation at an
interval of 10−5 in f.
Figures 5 and 6 confirm what may also be inferred from
the results for element concentrations. During melting,
elements which are incompatible or become incompatible
as a result of changes in the stable crystalline assemblage
are then rapidly transferred to the liquid phase over a
small range of f; that is, with great efficiency over a
small range of energy input. Elements which are highly
compatible in a carrier-phase are scarcely transferred to
the liquid phase at all until a threshold of f (i.e. of energy
input) has been crossed at which the carrier-phase melts
out completely. During partial crystallization, elements
which are incompatible are retained in the liquid and
are only transferred to the solids in the final stages of
crystallization, or are very rapidly eliminated from the
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products of equilibrium melting. In the present case we
present results for a two-stage equilibrium non-modal
melting process only. The equations given by O’Hara et
al. (2001) and Mathematica code available from the
Journal of Petrology Web site can be used to model more
complex situations.
Two-stage ENMPM and spidergrams
A plausible scenario invokes the remelting of source
materials which are themselves the residues of an earlier
partial melting event. Inspection of Fig. 4 will demonstrate
that the most dramatic effects upon the concentrations
of elements which are strongly concentrated into a carrierphase will be encountered when the first-stage melting
event approaches, but does not quite achieve, the elimination of that carrier-phase. The residues will show
significantly disturbed concentrations and ratios, which
are then handed on to the second event products. Moreover, because the mass fraction of the carrier-phase has
been much reduced in the first event, the concentration
spike associated with its elimination in the second event
will occur at low mass fractions of melting and will result
in high concentrations of the elements of interest in the
liquids.
Fig. 6. Rates of mass transfer from the solid to the liquid phase or
vice versa in the processes depicted in Fig. 5. Rates are expressed as
fraction of the mass of an element transferred per fraction of whole
system transferred from solid to liquid state or vice versa. Line ornaments
in (a) and (b) are the same as in Fig. 5a and b, respectively. Further
discussion in the text.
liquid immediately following the appearance of a carrierphase in the crystallization sequence.
There are obvious potential implications of these simple
truths for the consideration of the following: (1) the
extraction of the PGE from the upper mantle; (2) the
precipitation of the PGE within solidifying magmas to
form ore bodies; (3) the distribution and ratios of the
heat-producing elements U and Th within the continental
crust; (4) the separation of U and Th from the other
principal heat-producing element K in the crust; (5)
estimation of heat flow from the upper mantle beneath
continents; (6) the design of industrial processes for the
extraction and concentration of appropriate elements.
REMELTING OF PARTIALLY
RESIDUAL SOURCE REGIONS AND
EFFECTS ON THE RATIOS OF
HIGHLY COMPATIBLE ELEMENTS
In simple systems a number of imperfect partial melting
processes yield liquid products closely resembling the
Concentration as a function of d at fixed
values of f ′ in second-stage ENMPM
liquids
Let us consider the residue from a previous 0·175 mass
fraction ENMPM event which had affected a source
material containing 0·015 mass fraction of carrier-phase,
when the modal melting assemblage contains 0·06 mass
fraction of that carrier-phase. Let f ′ be the mass fraction
of second-phase ENMPM liquid formation. Figure 7a
plots the variation of relative concentration of an element
in the newly developed liquid phase as a function of f ′.
Results are presented for eight values of the distribution
coefficient. We observe that when the element is only
moderately compatible (d < >20 with this choice of
parameters) relative concentrations fall consistently as f ′
increases, with at most only a faint inflection at the point
of elimination of the accessory phase. Strong ‘peaking’
is restricted to those elements of high d whose bulk
distribution coefficients are initially q1.
The changing concentrations and ratios of the elements
are plotted as pseudo-spidergrams in Fig. 7b and c. The
vertical axes are concentration in the liquid phase relative
to the concentration of 1·0 for each element assumed in
the original source material before first event melting.
The long horizontal axis measures the mass fraction of
liquid produced in the first event (Fig. 7b) or in the
second event (Fig. 7c) where the value of f ′ is the mass
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MINOR PHASES AS CARRIERS OF TRACE ELEMENTS, II
maximum possible concentration, and the curve is approximately a straight horizontal line. Relative concentrations decline almost uniformly by dilution as further
melting of the main phase matrix takes place. At low f,
the most compatible elements (highest d) have relative
concentrations lower than in the source region.
In the second ENMPM event (Fig. 7c) the residual
solid, now to become the new solid source material, has
inherited strong depletion of the highly incompatible
element, moderate depletion of the concentrations of
elements with d <20 into the carrier-phase, and moderate
to pronounced enrichments of trace elements with d q
20 into the carrier-phase—the pseudo-spidergram for
this solid material is of the type which is evident in the
dilution phase at the back of Fig. 7c. The liquids produced
at low values of f ′ by second-stage ENMPM of the
residue (front part of Fig. 7c) display marked peaking of
relative concentrations among those elements which are
only moderately compatible in the carrier-phase and
have bulk distribution coefficients in the second event
which are <1·0 (even though they may have been >1·0
at the start of the first event as a result of the higher
mass fraction of carrier-phase present). Elements whose
bulk distribution coefficients were <1·0 in the first event
are relatively depleted in the second event liquids. Elements whose bulk distribution coefficients remain high
even in the second event continue to be held in the
residue until the carrier-phase is finally eliminated at f ′
> 0·09.
Fig. 7. (a) Concentrations of ideally behaved trace elements during
second-stage melting of the residue from a previous batch melting
event. Key: [1] d = 10 000; [2] d = 3000; [3] d = 1000; [4] d =
300; [5] d = 100; [6] d = 30; [7] d = 10; [8] d = 0·001. (b) displays
the pseudo-spidergrams of element concentrations developed in the
liquids of the first melting episode. (c) displays the pseudo-spidergrams
in the liquids developed in the second melting event. An arrowhead in
(b) marks the spidergram for the 17·5% equilibrium melt of the original
source composition; the front face spidergram in (c) represents the first
drop of melt in equilibrium with the isolated residue of that 17·5%
melting event. Further discussion in the text.
fraction of the first event residue which is now remelted.
The short horizontal axis is mostly logarithmic for the
values of distribution coefficient in the carrier-phase, but
the results for d = 0·001, log d = −3, have been plotted
arbitrarily at the left-hand end of each scale.
ENMPM of an undepleted source produces liquids
having pseudo-spidergrams with strongly negative but
progressively decreasing slopes (Fig. 7b)—the higher the
distribution coefficient, the lower the relative concentration of the element concerned—at all values of
melt formation up to f = 0·25 at which the accessory
phase holding the highly compatible element would be
eliminated from the original source. Thereafter, the elements concerned are all in the liquid and at their
ADDITIONAL FEATURES AND
MODIFICATIONS IN THREE-MAJORCOMPONENT SYSTEMS WITH TWO
COMPETING CARRIER-PHASES
Features have been explored in a very simple system
containing at the solidus 0·94 mass fraction of the main
phase which does not accommodate the elements of
interest and 0·06 mass fraction of carrier-phases 2 and
3 combined. Assumptions made about the distribution
coefficients of eight elements and about the modal melting
proportions of the phases in the various possible equilibria
between crystals and liquid are shown in Table 1.
Variation in proportions among the solid
phases
Figure 8a illustrates the variations in the mass fractions
of the three solid phases as a function of the value of the
ratio of carrier-phase 3 to the combined mass of carrierphases at the solidus, and of the mass fraction, f, of liquid
developed in the system. With these simple assumptions,
carrier-phase 3 is eliminated along a line, the left arm of
1897
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NUMBER 10
OCTOBER 2001
Table 1: Assumed modal melting proportions and distribution coefficients used in the preparation of
Figs 8–16
Modal melting proportions
Crystal–liquid distribution coefficients for elements [1]–[8] in illustrated equilibria
1+2+3 3
1+2 2
1+3 2
[1]
Main phase 1
0·90
0·94
0·94
Carrier-phase 2
0·05
0·06
Carrier-phase 3
0·05
t
t
t
[2]
0·001
[3]
0·001
[4]
0·001
0·001
[5]
[6]
0·001
[7]
0·001
[8]
0·001 0·001
10000
3000
1000
300
100
30
10
0·001
10
30
100
300
1000
3000
10000
0·001
0·06
an inverted-V shaped locus, where it is the first phase to
be consumed during partial melting or the third phase
to appear during partial crystallization. This line is the
locus of a critical value, fc2, of melt fraction extending
from the lower left corner of the figure to a central point
at carrier-phase ratio 0·5, f = 0·6. Where carrier-phase
3 is more abundant, it is also eliminated along a line
extending as a nearly collinear segment, the right arm
of a V-shaped locus, which is that of a critical value, fc1,
extending exactly to the rear corner of the figure. Along
this line the relatively abundant carrier-phase 3 in the
solid composition is the second carrier-phase to be consumed during melting or the first to precipitate during
partial crystallization. An analogous pair of boundaries
marking the elimination or appearance of carrier-phase
2 extends from the lower right corner of the figure to
the near central point and on to the top left corner. The
main phase is the sole crystal species coexisting with
liquid in the triangular area towards the centre top of
the figure, and is the only liquidus phase in the system
chosen, except at two end members of the variation in
initial composition which happen to be each cotectic for
main phase and one or other carrier-phase because of
the initial assumptions.
Figure 8b and c plots the variations in solid phase
proportions in the residues from ENMPM of one particular bulk composition, which has an assumed ratio of
0·33 carrier-phase 3 in the total carrier-phases. Carrierphase 3 in this composition is eliminated at f = 0·4,
carrier-phase 2 at f = 0·725. Other features of this
particular composition are further displayed in subsequent figures.
Variations in the bulk distribution
coefficient
The bulk distribution coefficients of the first seven elements in Table 1 vary as a result of the melting behaviour
of this selected composition, as displayed in Fig. 9 at two
scales. For two of the elements ([6] and [7]), which
are strongly concentrated into carrier-phase 3 but not
strongly concentrated into carrier-phase 2, the bulk distribution coefficient has fallen close to, or below, 1·0 at
the elimination of carrier-phase 3; all bulk distribution
coefficients have fallen to 0·001 at the elimination of
carrier-phase 2.
Liquid compositions during ENMPM or
ENMPC of the selected composition
Figure 10a is a plot of the concentration of the various
elements in the ENMPM liquid as the mass fraction of
melting proceeds in the selected composition discussed
above. Elements [1]–[3] are those most strongly concentrated into carrier-phase 2—they are released extensively into the liquid only when that carrier-phase is
eliminated. Element [4] is equally at home in either
carrier-phase—its concentration in the liquid is just sensitive to the elimination of carrier-phase 3 but the main
release of this element to the liquid has to wait until the
second carrier-phase is eliminated. Elements [5] and [6]
have a distinct preference for carrier-phase 3 rather
than carrier-phase 2, hence their concentrations are
significantly affected by the elimination of phase 3, although carrier-phase 2 can still provide a home for
them in the residue. Their concentrations in the liquid
consequently do not peak until carrier-phase 2 is eliminated. Element [7], which is overwhelmingly concentrated into carrier-phase 3 and only mildly
concentrated into carrier-phase 2, displays a marked peak
of concentration at the elimination of carrier-phase 3.
We observe the complicated pattern of variation in the
inter-element ratios at values of f just below that of the
elimination of carrier-phase 3 up to that of the elimination
of carrier-phase 2.
Solid compositions during ENMPM or
ENMPC of the selected composition
Figure 10b is a plot of the relative concentration of the
various elements in the ENMPM (or ENMPC) solids as
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O’HARA et al.
MINOR PHASES AS CARRIERS OF TRACE ELEMENTS, II
Fig. 8. (a) Diagram illustrating the variations of the mass fractions of the main phase and the two carrier-phases in the residue of partial melting,
as a function of the mass fraction, f, of melt in the system and of the ratio of the carrier-phases in the solid composition. Contours of the mass
fractions of the main and carrier-phases in the developing solid assemblage are indicated. Further description in the text. (b) The continuous
line is the plot of the variation in the mass fraction of the major phase in the residuum during ENMPM of an initial composition comprising a
mass fraction of main phase 1 of 0·94, and with a ratio of carrier-phases defined by phase 3/(phase 2 + phase 3) = 0·3333, expressed as a
function of the mass fraction of partial melt. The mass fraction of the total system which is composed of main phase declines sharply to zero at
f = 1·0 [dashed curve in (b)]. (c) Plot of the variation in the mass fractions of carrier-phases 2 and 3 in the residuum (conspicuous curves) as a
function of the mass fraction of partial melt. The mass fraction of the total system which is composed of each phase is shown by the lower line
in each pair. Further discussion in the text.
the mass fraction of melting or crystallization proceeds
in the selected composition. Elements [1]–[3] are those
most strongly concentrated into carrier-phase 2—their
relative concentrations peak in the solids only as carrierphase 2 nears elimination during melting. Element [4]
is equally at home in either carrier-phase—its concentration is just sensitive to the elimination or appearance of carrier-phase 3 but the main transfer of this
element into or out of the solid takes place at values of
f just below that at which carrier-phase 2 is eliminated
during melting or first appears during crystallization.
Elements [5] and [6] have a distinct preference for
carrier-phase 3 rather than carrier-phase 2, hence their
concentrations are significantly affected by the elimination of carrier-phase 3, although carrier-phase 2 can
still provide a home for them in the residue. Their
concentrations in the solid consequently peak at the
elimination of carrier-phase 3, and element [5] displays
a second peak as the elimination of carrier-phase 2
is approached. Element [7], which is overwhelmingly
concentrated into carrier-phase 3 and only mildly concentrated into carrier-phase 2, displays a marked peak
of concentration in the solids at the elimination of carrierphase 3. We observe again the complicated pattern of
variation in the inter-element ratios at values of f just
below that of the elimination of carrier-phase 3 up to
that of the elimination of carrier-phase 2.
We observe particularly the way in which the concentration of the elements [1]–[5] in the solids passes
through a peak just after the carrier-phase 2 has appeared
during crystallization. Initially, the bulk distribution coefficient for these elements is below unity (Fig. 9) while
the mass fraction of carrier-phase in the bulk solids
remains small, and the elements behave for a while as
though still mildly incompatible. With advancing crystallization this situation is soon reversed as the amount
of carrier-phase deposited increases, thereby contributing
more to the composition of the solids and to the bulk
distribution coefficient. The element becomes increasingly compatible and the concentrations in the solid
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Fig. 9. Variations in the bulk distribution coefficient as a function of
mass fraction of liquid formed during ENMPM of the composition
illustrated in Fig. 8b and c, displayed at two different vertical scales.
Distribution coefficients into carrier-phases 2 and 3 are given in Table
1. Further discussion in the text.
and liquid then decrease as the mass of solid increases.
This peak is encountered at successively longer intervals
of crystallization after the appearance of the carrierphase as the compatibility of the element decreases. In
the case of element [5] a second peak is encountered
after the entry of carrier-phase 3 at f = 0·4. Elements
[6] and [7] display no peak before the appearance of
the carrier-phase 3. The reverse of this process during
ENMPM has been explained in connection with an
earlier figure.
A point of some importance in geochemical modelling
is that the bulk distribution coefficients for the seven
elements considered are all high and broadly similar in
the low f stage of the process, all low and similar in the
high f stage, but diverge greatly and evolve independently
in the intermediate stage.
PNMFM and PNMFC
Enough has been said in an earlier section to enable the
reader to envisage the styles of behaviour which will be
encountered during PNMFM and PNMFC of the selected
composition.
NUMBER 10
OCTOBER 2001
Fig. 10. Plots of relative concentrations of elements [1]–[7] in the
liquid (a) and bulk residual solid phases (b) during ENMPM of the
composition displayed in Fig. 8b and c. Further discussion in the text.
Effect of varying the ratio of the two
carrier-phases in the selected composition
Figure 11 displays plots of the surfaces of concentration
of ideally behaved trace elements in the liquid phase,
relative to their concentrations in the source material
undergoing ENMPM. They are plotted as a function of
the mass fraction of partial melt liquid produced (in 20
steps of 0·0499 between 0·001 at front left face and 0·999
at back right face) and as a function of the ratio of the
mass fraction of carrier-phase 3 to the total mass fraction
of the carrier-phases (in 25 steps of 0·04 between 0·0 at
the back left face and 1·00 at the front right face). Total
mass fraction of the carrier-phases is fixed at 0·06, i.e.
the assemblage initially contains 0·94 mass fraction of
main (silicate) phase 1 which does not accept the elements
under consideration.
Data are plotted in Fig. 11a for element [1], which is
very strongly compatible in carrier-phase 2 but only
mildly compatible in carrier-phase 3. The crest of the
scarp feature running diagonally across the surface marks
the locus along which carrier-phase 2 is eliminated and
most of trace element [1] is released into the liquid. In
the triangular facet on the near part of the dip slope of
the surface, carrier-phase 3 is still present and retains a
little of element [1] until its elimination at a locus running
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O’HARA et al.
MINOR PHASES AS CARRIERS OF TRACE ELEMENTS, II
Fig. 11. Plots of the concentration of ideally behaved trace elements in the liquid phase, relative to their concentration in the source material
undergoing equilibrium non-modal partial melting, as a function of the mass fraction of partial melt liquid produced and as a function of the
ratio of the mass fraction of carrier-phase 3 to the total mass fraction of the carrier-phases. Distribution coefficients into carrier-phases 2 and 3,
respectively, are: in (a) element [1] 10 000 and 10; in (b) element [2] 3000 and 30; in (c) element [3] 1000 and 100; in (d) element [4] 300 and
300, in (e) element [7] 10 and 10 000 (as given in Table 1). (e) is a mirror image of (a) solely because of the symmetry in the assumed parameters.
Further description in the text.
from the back right corner of the figure to approximately
the centre of the figure. The triangular facet of the dip
slope which runs from the centre down to the back right
face of the figure is the region where major phase 1 is
the sole remaining solid and the concentration of the
trace element [1] is modified solely by dilution as more
of phase 1 melts.
Figure 11b plots data for element [2], which is strongly
compatible in carrier-phase 2 and moderately compatible
in carrier-phase 3. The crest of the scarp feature running
diagonally across the surface marks the locus along which
carrier-phase 2 is eliminated and much or most of trace
element [2] is released into the liquid. Features of this
surface have evolved from those of Fig. 11a but a similar
commentary applies.
Figure 11c displays results for element [3], which is
compatible in carrier-phase 2 and moderately compatible
in carrier-phase 3. Most features of this surface may
be understood from the previous commentary. In the
triangular facet on the near part of the surface, carrierphase 3 is still present and retains a substantial amount
of element [3] until its elimination at a locus running
from the back right corner of the figure to approximately
the centre of the figure. This facet represents an extended
concentration interval in the partial melting history.
Data are plotted in Fig. 11d for element [4], which is
equally compatible in both carrier-phases and its features
may be understood from the previous commentary. We
observe that high relative concentrations of the compatible element in the liquid in this case are only achieved
when both carrier-phases have been eliminated. The
highest concentration is achieved at the lowest mass
fraction of melting when both carrier-phases are eliminated simultaneously. Figure 11e displays the situation
for an element which is mildly compatible in carrierphase 2 and very highly compatible in carrier-phase 3,
and is the mirror image of Fig. 11a.
Figure 12a–e shows plots for the relative concentrations
in the solids complementary to the liquids shown in Fig.
11a–e. They should be examined in the light of the
description of Fig. 11 and of earlier figures, but are
presented here without further commentary.
RATIOS OF THE HIGHLY
COMPATIBLE ELEMENTS IN LIQUID
AND SOLID PRODUCTS OF ENMPM
OR ENMPC
Now let us consider the effects of competition between
two contrasted carrier-phases upon the ratios of the
compatible trace elements. The discussion below refers
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NUMBER 10
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Fig. 12. Plots complementary to those in Fig. 11, but for the concentration of ideally behaved trace elements in the bulk solid phases, relative
to their concentration in the source material undergoing equilibrium non-modal partial melting or crystallization. Distribution coefficients into
carrier-phases 2 and 3, respectively, are: in (a) element [1] 10 000 and 10; in (b) element [2] 3000 and 30; in (c) element [3] 1000 and 100; in
(d) element [4] 300 and 300, in (e) element [7] 10 and 10 000. (e) is a mirror image of (a) solely because of the symmetry in the assumed
parameters. Further description in the text.
exclusively to ENMPM, but the relationships are the
same for ENMPC.
Ratios of concentrations of other elements
to that of element [1] in the selected threemajor-component composition
Figure 13 is a plot analogous to that in Fig. 10 above,
and for the same bulk composition, illustrating the changing ratios of concentration of elements [2]–[7] divided
by that of element [1] during ENMPM of an assemblage
with mass fraction of the major phase 1 in the initial
assemblage of 0·94 and mass fraction of carrier-phase 3
equal to one-third of the combined carrier-phases.
Figure 13a is drawn for the ENMPM liquids and
represents the results of dividing the concentration on
each of the other curves in Fig. 10a by the concentration
on the lowest curve. Figure 13b is drawn for the ENMPM
solids and represents the results of dividing the concentration on each of the other curves in Fig. 10b by the
concentration on the highest curve. We note particularly,
in both liquids and solids, the complex changes in the
compatible element ratios which are encountered immediately below the elimination of carrier-phase 3 at
f = 0·4; the substantial changes in all the ratios during
the progressive elimination of carrier-phase 2; the strongly
defined peaks in the liquids of the ratios of those elements
which were preferentially concentrated into the carrierphase 3 when it is eliminated; and the pronounced
minimum in the ratios at the final approach to the point
of elimination of carrier-phase 2 (when most of element
[1] is finally released into the liquid). At higher values of
f all of the compatible elements originally held in the
carrier-phases have been released to the liquid and their
ratios in both liquid and solid are 1·0.
Ratios of two elements of strongly
contrasted behaviour in the carrier-phases
throughout the three-major-component
system
Figure 14a is a plot of the logarithm of the ratio of the
concentration of an ideally behaved trace element [7] in
the liquid phase, divided by that of another trace element
[1] of strongly contrasted behaviour with respect to the
carrier-phases. Results are displayed as a function of the
mass fraction of partial melt liquid produced (in 20 steps
of 0·0499 between 0·001 at front left face and 0·999 at
back right face) and as a function of the ratio of the mass
fraction of carrier-phase 3 to the total mass fraction of
the carrier-phases in the solid initial composition (in 25
steps of 0·04 between 0·0 at the back left face and 1·00
at the front right face). Total initial mass fraction of the
carrier-phases is fixed at 0·06, i.e. the assemblage initially
1902
O’HARA et al.
MINOR PHASES AS CARRIERS OF TRACE ELEMENTS, II
Fig. 13. Plot similar to Fig. 10 and for the same starting composition,
displaying the ratios of concentrations of elements [2]–[7] divided by
the concentration of element [1] in the liquid and bulk residual solid
phases during ENMPM of the composition displayed in Fig. 8b and
c. Further discussion in the text.
contains 0·94 mass fraction of main (silicate) phase 1
which does not accept the elements under consideration.
It should be noted that Fig. 14a is rotated 40° clockwise
when looking down the vertical axis relative to all the
presentations in Figs 11 and 16. Figure 14b is rotated
50° anti-clockwise relative to Figs 11 and 16.
Carrier-phase 2 is still present everywhere to the left
of and behind the feature running diagonally across the
surface from front corner to back corner in Fig. 14a; to
the right of the analogous feature in Fig. 14b. Carrierphase 3 is present everywhere on the near side of the
diagonal feature from back left to front right of Fig. 14a;
to the far side of the analogous feature in Fig. 14b. Both
carrier-phases are present in the area of the triangular
shelf in the mid-left of Fig. 14a which slopes up gently
from its near edge and passes through height of unity
(log = 0) along the left to right median plane of the
figure. In this region of combinations of the parameters,
the retention of different trace elements by the two phases
approximately balances out and there is little difference
between the ratio in the liquid generated and that in the
source material; an analogous feature appears at midright in Fig. 14b.
Fig. 14. Ratios of concentration of element [7] divided by that of
element [1] in the liquid (a) and the bulk residual solids (b) throughout
the system for which simple concentration data are displayed in Figs
11 and 12. It should be noted that the vertical scale in the upper figure
represents a total range of about 106 in the value of the ratio, whereas
that in the lower figure represents a total range of about 103 in that
value. (a), which represents the surface in Fig. 11e divided by that in
Fig. 11a, is rotated about 40° clockwise about the vertical axis looking
downwards relative to Fig. 11. (b), which represents the surface in Fig.
12e divided by that in Fig. 12a, is viewed from the opposite direction
relative to (a)—mass fraction of melting increases to the left and
amounts of carrier-phase 3 increase away from the viewer. Further
description in the text.
In the remote triangular segment of Fig. 14a carrierphase 2 is still present, strongly retaining trace element
[1] in the solid phase. Carrier-phase 3, which was strongly
retaining trace element [7] in the first region discussed,
is now absent, hence the ratio of concentration of trace
element [7] to that of trace element [1] in the liquid
phase is everywhere high although it declines as the
mass fraction of melting increases to the right and then
decreases abruptly as carrier-phase 2 is totally consumed.
In the right-hand triangular segment of Fig. 14a neither
carrier-phase is present. Both of these trace elements are
1903
JOURNAL OF PETROLOGY
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then highly incompatible in the remaining major phase
1, hence the ratio of these two elements is everywhere
close to 1·0 (log = 0). The triangular area in the front
of Fig. 14a is one in which carrier-phase 2 is absent but
carrier-phase 3 is still present. Melting out of carrierphase 2 has released most of trace element [1] to the
liquid but trace element [7] is still strongly retained in
carrier-phase 3. The ratio of trace element [7] divided
by that of trace element [1] in the liquid phase is
consequently extremely low.
Figure 14b displays, from a diagonally opposed perspective viewpoint, the comparable data for the ratios
in the solid residues of the ENMPM process. In the
foreground, sections from right towards left of the surface
are of the type displayed in left to right orientation in
the lowest curve [7] of Fig. 13b although there is a
change in geometry resulting from the change to logarithmic scales. The diagonal trough across the surface
in this sector results from the fact that virtually all of
element [7] is in the liquid whereas almost all of element
[1] is still held in the residue until the elimination of
carrier-phase 2. The origin of the sharp arête feature at
the elimination of carrier-phase 3 in the back left part
of this figure lies in the retention of element [7] in
the residual carrier-phase 3 almost up to the point of
elimination of this phase, whereas almost all of element
[1] has been transferred to the liquid by this point.
Attention is directed to those regions, particularly near
the centre of Fig. 14a, where both carrier-phases are
consumed almost simultaneously and the ratio of the two
elements in the liquid phase is extremely sensitive to
small variations in the mass fraction of melting or in the
ratio of the two carrier-phases in the source material.
The situation for the bulk solids is analogous.
Trace elements which are less compatible
than the controlling element in the carrierphase
This issue has been addressed above at the end of the
simple graphical treatment relating to Figs 1–3. Figures
3 and 4 illustrate how a less compatible component will
behave relative to more compatible components in the
carrier-phase. Effects upon the ratios of those elements
may be inferred from these figures. These effects are
further illustrated for elements [5]–[7] in a more complex
situation in Fig. 13, where the concentration of element
[1], the denominator in each ratio plotted, is the most
highly compatible element in carrier-phase 2 which is
finally consumed at f > 0·735 and elements [5]–[7] are
only made available in significant amounts when carrierphase 3 is eliminated at f = 0·4.
Figure 14 illustrates two extreme cases where element
[7] is much less compatible than element [1] in carrierphase 2, whose presence dominates effects in the back
NUMBER 10
OCTOBER 2001
half of Fig. 14a and the front half of Fig. 14b. Element
[1], on the other hand, is much less compatible than
element [7] in carrier-phase 3, whose presence dominates
effects in the front half of Fig. 14a and the back half of
Fig. 14b.
SPIDERGRAM EVOLUTION IN
LIQUID AND SOLID PRODUCTS OF
ENMPM AND ENMPC IN THE
SYSTEM OF THREE MAJOR
COMPONENTS
The effects which the variations of concentration and
ratio have upon the appearance of pseudo-spidergrams
for the seven compatible elements in the liquid and solid
products of ENMPM or ENMPC are displayed in Figs
15 and 16.
Figure 15 displays the evolution of the pseudo-spidergrams (bold curves) in the liquid products of partial
melting for elements [1]–[7] in 11 steps of partial melting
between 0·001 (front left face) and 0·999 (back right face)
at nine values of the ratio of carrier-phase 3 to the sum
of carrier-phases in the source composition, when the
main phase is 0·94 mass fraction of the whole initial
material. This choice of values of f avoids the meaningless
results at f = 0·0 in Fig. 15 and at f = 1·0 in Fig. 16.
It should be noted that the relative concentrations are
here plotted directly, not as their logarithms. Where both
carrier-phases have been melted out completely (back
right of the intermediate figures) the spidergram is flat
and mildly enhanced relative to the height of 1·0 throughout the dilution interval. A very wide variety of patterns
can be obtained at widely varying mass fractions of
melting at the low and intermediate values of f in
response to the changing ratio of the contrasted carrierphases.
Figure 16 displays complementary data for the residues
of partial melting. The change in the vertical scale should
be noted. In the first and last of these figures parts of
the spidergram for f = 0·999 are off-scale. Particular
interest attaches to these patterns as potential starting
points for second-stage partial melting.
CONSEQUENCES OF MORE
SOPHISTICATED MELTING OR
CRYSTALLIZATION MODELS
The relatively simple processes of non-modal melting
and crystallization discussed above all represent idealized
and special cases of the processes which probably occur
in nature. This section surveys some modifications of the
distinctive features of those processes which are likely to
1904
O’HARA et al.
MINOR PHASES AS CARRIERS OF TRACE ELEMENTS, II
Fig. 15. Pseudo-spidergrams (bold curves) for concentrations of elements [1]–[7] in the liquid phase at nine selected values of the initial ratio,
r, of carrier-phases in the source composition as the mass fraction of liquid increases in 11 steps. The rapid changes in form of the spidergrams
with variation in mass fraction of melting within each diagram and with variation in initial carrier-phase ratio between diagrams should be
noted. It should be recalled also that the arbitrary spacing of the 11 selected values of melt fraction in each diagram cannot be expected to
capture the most extreme spidergrams which can be generated. Further explanation in the text.
result from the introduction of more complicated or more
sophisticated models of melting or crystallization.
Small packet and integrated crystallization
of a molten mantle
The small packet and integrated crystallization of a
molten mantle in a full-sized planet would be subject to
the same principles as are outlined below for the more
appropriate case of smaller magma bodies. Integrated
crystallization is less likely to be an important factor
during crystallization of a molten mantle. Carrier-phase
precipitation is unlikely to be triggered in the early and
middle stages when the mass fraction of liquid returned
from each packet is likely to be large, unless immiscible
metal or sulphide liquids are involved, or some of the
oxide structures precipitated at the high pressures in the
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NUMBER 10
OCTOBER 2001
Fig. 16. Pseudo-spidergrams (bold curves) for concentrations of elements [1]–[7] in the bulk residual phases at selected values of the initial
ratio, r, of carrier-phases in the source composition as the mass fraction of liquid increases in 11 steps. Observations and cautions attached to
Fig. 15 apply here also; readers should note additionally the change in the relative concentration scale and the fact that the diagrams in the
second, third and fourth positions are not drawn for the same values of the initial ratio as are the corresponding diagrams in Fig. 15. Further
explanation in the text.
lower mantle can act as carrier-phases for particular
groups of trace elements.
A considerably more complicated situation is posed by
a partly molten planet which is still growing by accretion
at the same time as it is undergoing phase separation
through liquid immiscibility and partial crystallization.
The body of liquid is continuously replenished with
primitive (chondritic) material at a rate which is initially
high relative to the size of the liquid body but later
diminishes to insignificance. Phase separation might take
place initially at low pressures and with low pressure
gradients within the molten body; at a later stage pressures
and pressure gradients would be high. The chondritic
input material could sustain the budget of siderophile
elements in the silicate liquid despite the continuing
reduction of the melt by evolution of carbon- and sulphuroxide gases and separation of metal phase. At some
point, however, these reactions might be inhibited by the
1906
O’HARA et al.
MINOR PHASES AS CARRIERS OF TRACE ELEMENTS, II
increasing pressure and pressure gradient in the melt,
allowing the siderophile element budget of the outer
layers to be augmented by the later accreting material
despite the separation of a substantial metal core.
Small packet and REXM melting of the
solid mantle
Chrome spinel and sulphide may be present in the upper
mantle in small amounts as carrier-phases for the PGE.
Trace amounts of phases rich in REE, U and Th may
also be present. Small packet melting (O’Hara & Fry,
1996b, p. 920) of the upper mantle will gradually raise
the content of elements in the residue which are highly
compatible in a carrier-phase, with little change in their
ratios one to another, provided that the average mass
fraction of melt extracted is insufficient to approach
carrier-phase elimination. If carrier-phase elimination is
achieved in each small packet which is processed, the
content in the residue of these same elements will decline
gradually, again with little discrimination between them.
In some melting regimes there may be a steady flow
of relatively undepleted mantle into the regime and of
relatively depleted mantle out of the melting regime
(O’Hara, 1993, 1995). This flow may maintain a budget
of highly compatible elements which can be extracted
into successive liquid batches despite achievement of
carrier-phase elimination within the melting regime.
Integrated melting from shaped melting
regimes
Integrated melting regimes (O’Hara, 1985, 1995; Plank
& Langmuir, 1992) will mix together partial melt
products, some proportion of which have been derived
at values of f less than the critical value(s) required to
liberate the highly compatible elements from their
carrier-phase(s). This will obviously dilute the peaking
of concentration predicted from the behaviour of the
simple systems reviewed above. It may also smear
the geochemical effects associated with carrier-phase
elimination across a range of other geochemical parameters such as the concentrations and ratios of elements
which are truly highly incompatible throughout most
of the melting history. A melting regime may be
described by low values of the power factor, n (O’Hara,
1985, and 1995, especially Fig. 10), implying a melting
regime where the contribution from peripheral regions
with low mass fractions of melting is large, yet the
average mass fraction of melting may still be high
provided that the maximum mass fraction of melting
in the central region is sufficiently high. Then the high
concentrations of PGE contributed from the central
axis of the melting regime could be combined with
relatively high concentrations and discriminated ratios
of the highly incompatible elements contributed by the
extensive periphery. This latter feature would seem to
point to very low mass fractions of partial melting.
Opportunities to eliminate carrier-phases and incorporate high concentrations of their highly compatible
trace elements into the liquid will be maximized when
the melting regime is described by high values of the
power factor parameter n combined with relatively
high values of average f. In these circumstances there
could be low concentration and little discrimination of
highly incompatible elements.
The above comments concentrate on features of the
liquid products of integrated melting regimes. When the
local partial melting process approaches perfect fractional
partial melting and the source material undergoing partial
melting was initially inhomogeneous with respect to the
distribution and ratios of trace element carrier-phases, it
is to be expected that the residues might display extreme
variations in those trace element ratios. There may be
some evidence for this in the behaviour of Ba, U and
Th in rocks of the granulite facies Scourie complex, NW
Scotland. These rocks may be the residuum of fractional
partial melting of continental crust with virtual elimination of K-feldspar, the carrier-phase for Ba and competition between zircon, allanite and monazite, present
in widely varying proportions, for U and Th (O’Hara &
Yarwood, 1978; Cohen et al., 1991). Comparable effects
on the ratios of light to heavy REE can also be anticipated
in the partial melting of pelites when there is competition
for these elements between monazite and xenotime (Andrehs & Heinrich, 1998). Space does not allow the pursuit
of these points further in this contribution.
Magma recharge and carrier-phase
saturation
Magma recharge, accompanied by mixing of the more
primitive and more evolved magmas, may be a common
feature in long-lived magma chambers. There is a high
probability that such mixing will result in a mixed magma
which is in equilibrium neither with the same crystal
assemblage as the former evolved magma in the chamber,
nor with the mineral assemblage stable at the liquidus
of the primitive magma added to the chamber (e.g.
Walker et al., 1979). This obviously complicates any
attempt to compute the crystallization history.
The complications acquire major significance in the
context of this paper if such magma recharge results in
the transient or enhanced precipitation of one or more
carrier-phases whose presence would not be anticipated
in a simple closed system process. This has been suggested
for the specific case of chromite in the large layered
gabbro complexes (Irvine, 1977) but might also affect
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sulphide precipitation in those bodies (Naldrett & von
Gruenewaldt, 1989).
Integrated crystallization of magma bodies
Those effects upon the highly compatible elements which
are associated with carrier-phase appearance will be
smeared across a range of values of other parameters
(such as the concentration of a truly incompatible element)
by integrated partial crystallization (O’Hara & Fry, 1996a,
1997). In the precipitates, carrier-phase precipitation may
be restricted to limited portions of the crystallization zone
when there is lateral melt integration as well as or instead
of vertical integration.
Small packet crystallization of magma
bodies
Small packet crystallization (Langmuir, 1989; O’Hara &
Fry, 1996b) processes the magma by partially crystallizing
a succession of small batches and returning the residual
liquid to mix with the main body of magma before
repeating the process. One important factor in the present
context is whether or not the amount of crystallization
within each packet is sufficient to trigger the precipitation
of the carrier-phase. There is a critical difference here
between simple uniform mass fraction crystallization of
each batch, which may be less likely to trigger that
precipitation, and integration of the residual liquid from
a crystallization zone within which the mass fraction of
crystallization varies from very high to very low, which
practically guarantees that carrier-phase precipitation will
be encountered through part of the zone. However, if
the carrier-phase is precipitated in either case, only very
small amounts of the highly compatible elements will
survive into the residual liquid which remixes with the
main body of the magma—consequently, these elements
are removed slowly and with little inter-element discrimination from the body of the magma as a whole. In
the cumulate sequence a predictable consequence of
small packet crystallization which does trigger carrierphase precipitation would be the multiple replication of
units containing carrier-phases highly enriched in the
elements of interest (e.g. the PGE) with little discrimination.
Periodically recharged, periodically tapped,
continuously fractionated (RTXC)
crystallization of magma bodies
RTXC crystallization (O’Hara, 1977, 1993; O’Hara &
Mathews, 1981) continually recharges the magma body
with all elements in the added primitive magma batches.
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OCTOBER 2001
If the crystallization process between these recharges fails
to trigger carrier-phase precipitation then the elements
of interest are likely to concentrate like other incompatible
elements in the residual liquid. This effect is maximized
when the rate of liquid escape from the magma chamber
is low and the rate of crystallization is as high as permitted
by the constraint that the carrier-phase should not precipitate. Once the carrier-phase does start precipitating,
most of the resident elements of interest are likely to be
eliminated from the magma body in the next few cycles.
After that the budget of these elements in the magma
body will be controlled by what is resupplied by each
primitive magma batch and removed in each crystallization cycle. The features of the complementary
cumulates are fundamentally different from those predicted during small packet crystallization.
SUMMARY AND CONCLUSIONS
From the above discussion a recipe of igneous processes
may be written for achieving a high concentration of
an element which is highly compatible in a carrierphase (the comments are of general application but
the case of the PGE is uppermost in our minds). This
concentration would be maximized in a bulk rock by
the following chain of events, however unlikely they
may seem individually:
(1) provision of a source region in which the ratio of
the element of interest to the elements which stabilize
the carrier-phase is relatively high, and the absolute
amount of carrier-phase present is such that carrierphase elimination during partial melting will occur at
relatively low values of f.
(2) First-stage partial melting of the original source
region falling short of elimination of the carrier-phase by
ENMPM, with liquid removal and achievement of the
maximum possible concentration of the element of interest in the residuum as discussed in connection with
Fig. 1 above. It should be noted, however, that eventual
total yield from a given mass of source region may be
optimized by accepting a slightly lower concentration
than the peak in a larger mass fraction of residuum
accompanied by reduced concentration in this first-stage
liquid extract. High values of the relevant 0dbs and dm
obviously help here.
(3) Second-stage partial melting by a near-perfect nonmodal fractional melting process with isolation of melt
batches produced at or close to the final elimination of
the carrier-phase.
(4) Melt movement accompanied by geochemical or
phase equilibria changes which delay the appearance of
the carrier-phase during subsequent crystallization.
(5) Otherwise perfect fractional crystallization of the
liquid in a periodically refilled, periodically tapped
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O’HARA et al.
MINOR PHASES AS CARRIERS OF TRACE ELEMENTS, II
magma chamber operating with small mass fractions of
liquid escape relative to the mass fraction crystallized in
each cycle, and this mass fraction of crystallization just
inadequate to trigger carrier-phase precipitation until a
late stage in the history of the magma body. A high value
of the relevant dm once carrier-phase precipitation has
commenced obviously helps here.
(6) Separation of the carrier-phase from the main
phase in that precipitate by any process leading to crystal
sorting. This might be purely mechanical, but such
separation would undoubtedly be promoted if late inputs
of parental magma into a far evolved magma chamber
resulted in the formation of a mixed magma with the
carrier-phase on its liquidus and complementary cumulate layers very rich in that carrier-phase.
Some of the predictions from the considerations in this
paper may appear somewhat paradoxical. The source
region, which is richest in the carrier-phase and may
contain the highest bulk concentration of the element of
interest, is in practice less likely to yield partial melts
with high concentrations of the highly compatible element. This is because carrier-phase elimination will not
occur until higher, perhaps normally unattainable, mass
fractions of partial melting have been achieved.
During progressive partial melting the highest concentrations of the highly compatible element in both the
carrier-phase and the silicate matrix minerals will be
observed at the point of final elimination of the carrierphase, when the highly compatible element concentration
of the residue has already been greatly reduced; that is,
in the case of the PGE, when there is barely a trace of
chromite or sulphide left in the residual mantle assemblage.
Turning from the issue of concentration to that of
the ratios of trace elements which are highly compatible
in one or more carrier-phases, the considerations in
this paper require that significant variations in the
ratios of, for example, the PGE, of U and Th, or of
light and heavy REE should be observed in some
silicate melts even when there is only one carrierphase in the source solid or precipitated cumulate,
provided that the partial melting or crystallization
processes involve little integration of melts which
represent different mass fractions of partial melting or
crystallization. The anticipated variability of ratios
should be much more prominent when there has been
competition between two highly contrasted carrierphases during the melting or crystallization process.
However, these effects would be much subdued in the
liquid products if integration of melts across melting
or crystallization regimes with widely variable mass
fractions of melting or crystallization were the norm.
Such variations in ratios should be preserved to a
greater extent in the residues of partial melting processes
which locally at least approximate to perfect fractional
partial melting, or in the cumulates of partial crystallization processes which locally at least approximate
to perfect fractional crystallization.
ACKNOWLEDGEMENTS
We wish to thank J. R. Cann, K. G. Cox, C. Herzberg,
R. K. O’Nions, D. C. Presnall, D. M. Shaw and M.
Wilson for their efforts as readers of an earlier version
of this paper, which led to significant improvements in
substance and presentation.
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