EQUILIBRIUM IN GEOLOGICAL SYSTEMS - Chemical Fundamentals of Geology and Environmental Geoscience - page 37

Box 2.7 How a ternary diagram works

Three variables can be plotted in a two-dimensional graph
if they add up to 100%. Any composition in a three-compo-
nent system can therefore be represented in two dimen-
sions, usually in the form of a ternary diagram plotted on
special equilateral-triangle graph paper (Figure 2.7.1a).
The user labels each apex with one of the components, as
shown in Figure 2.7.1b.
Each apex represents 100% of the component with
which it is labelled (the Di corner, for example, represents
a composition consisting of 100% diopside). The side
opposite represents compositions that are devoid of that
component (in this case, a range of Ab-An mixtures).
Lines parallel to this edge are contours representing differ-
ent Di percentages from 0 (on the Ab-An edge) to 100%
(at the Di apex).

To plot a composition such as Di 72%, Ab 19%, An 9%
(note that the three co-ordinates must add up to 100%) 5 ,
rule a line horizontally across the diagram at the position
equivalent to 72% Di. Rule another line, parallel to the
Di-An edge, at the position corresponding to 19% Ab (be
sure to count this from the Di-An edge where Ab = 0%).
The intersection with the first line marks the composition
being plotted. Note that only two readings need to be plot-
ted; the third - being the difference from 100 - is not an
independent variable, but it is useful to read it off the
diagram (An = 9%) to check that the point has been plotted
accurately.
As with any plot showing mineral proportions, it is
essential to indicate whether the numbers relate to mass
% or molar proportions.

Di contour (%)
An contour (%)

Ab contour (%)

Di

100

9
10

90

20
30
40

80

72

70

60

50

50

60

40

70

30

80

20

90

10

100

Ab

An

100 90 80 70 60 50 40 30 20 10

19

%Ab

Figure 2.7.1 (a) Example of ternary graph paper with 100 mm sides (may be photocopied as needed). (b) how to plot a
three-component mixture in a ternary diagram.

The outcome of plotting three numbers that add up to less than 100% is a smaller triangle surrounding the target point, as illustrated
in Gill (2010), Fig. B1, p. 363. In such cases, each value should be multiplied by 100/ Tot (where Tot represents the initial total),
thereby scaling them up to values that do sum to 100%.

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