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structure that accommodates either Mg or Fe, but not
Si. For every Si atom in the olivine structure, there have
to be two divalent atoms present, each of which can be
either Mg or Fe. Another way to symbolize this con-
straint is to write the formula as (Mg,Fe)
2
SiO
4
, in which
'(Mg,Fe)' represents an atom of either Mg or Fe. One
can now express the composition of an olivine as a
combination of just two components:
metallic iron (for example in certain meteorites). The
amount of oxygen present is no longer determined
solely by the metals present, as it would be in a system
consisting entirely of silicates. One cannot express the
composition of metallic iron as a mixture of oxides, so
one must resort to using four components, Mg, Fe, Si
and O, in order to describe all possible compositions in
this
quaternary
system.
In this topic, the general practice will be to refer to
components by means of their chemical formulae. This
avoids confusion between phases and components,
which can arise when a phase (for example the mineral
quartz) happens to have the same chemical compos-
ition as one of the components (SiO
2
) in the same sys-
tem. However, in other topics it is quite common for
end-member names to be used in this way as well (for
example, 'forsterite' for Mg
2
SiO
4
).
Mg SiO eSiO
2
4
2
4
Mineralogists call these components the 'end-mem-
bers' of the olivine series, and give them the names
forsterite (Fo) and fayalite (Fa) respectively.
In analysing the arithmetic of chemical equilib-
rium between minerals, it is important to formulate
the components of a system in such a way as to mini-
mize their number, as the definition implies. What
constitutes the minimum number depends upon the
nature of the system. In an experiment involving
the melting of an olivine crystal on its own, the comp-
osition of the melt, though different from the solid, still
conforms to the olivine formula X
2
SiO
4
. The comp-
ositions of both phases present, olivine and melt, can
therefore be expressed as proportions of only two
components, Mg
2
SiO
4
and Fe
2
SiO
4
(Box 2.4). Systems
consisting of only two components are called
binary
systems.
If, however, olivine coexists with, let us say, orthopyr-
oxene, the formulation of components becomes less
straightforward. Orthopyroxenes are composed of the
same four elements as olivine, but they combine in
different proportions. The general formula of ortho-
pyroxene, X
2
Si
2
O
6
, reveals an X:Si ratio (1:1) lower than
for olivine (2:1). The composition of a pyroxene cannot
therefore be expressed in terms of just the two olivine
end-members. To represent the separate compositions
of olivine and orthopyroxene in this system, three
components will be needed:
Equilibrium
It is useful to distinguish between two aspects
of equilibrium: thermal equilibrium and chemical
equilibrium.
Thermal equilibrium
All parts of a system in thermal equilibium have
the
same temperature
: in these circumstances heat flowing
from one part of the system, A, to another part, B, is
exactly balanced by the heat passing from part B to
part A, so there is no
net
transfer of heat. Net heat
transfer only occurs when there is a difference in tem-
perature between different parts of the system.
Chemical equilibrium
This describes a system in which the distribution of
chemical components among the phases of a system
has become constant, showing no net change with
time. This steady state does not mean that the flow of
components from one phase to another has ceased:
equilibrium is a dynamic process. An olivine sus-
pended in a magma is constantly exchanging comp-
onents with the melt. At melt temperatures, atoms will
diffuse across the crystal boundary, both into the crys-
tal and out of it into the liquid. If the diffusion rates of
element X in and out of the crystal are unequal, there
will be a net change of the composition of each phase
with time, a condition known as
disequilibrium
. Such
Either Mg SiO eSiO SiO
Or
:
2
4
2
4
2
:
MgOFeO
SiO
2
The identity of the components is less important here
than their number. A system like this requiring three
components to express all possible compositions is
said to be
ternary
.
There are circumstances in which four components
would be necessary, such as when olivine coexists with
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