Mass conservation and elemental fractionation - Geochemistry: An Introduction - page 26

3

Enstatite

Forsterite

2

1

Quartz

0

1 2 3

C SiO 2

Figure 2.3 There cannot be three independent vectors in a two-dimensional space. A third mineral, therefore,

requirestheretobeareaction.Hereforsterite enstatite. This eliminates the deficient

mineral, either quartz or forsterite. Units are numbers of oxide molecules per gram-formula weight.

+ quartz ⇔

Component 1

( B / D ) 2
( B / D ) 1

5

4

25

5

3

1

2

0.2

0.04

1

Component 2

1 2 3 4 5

( C / D ) mixture

Figure 2.4 When concentration ratios or isotope ratios are plotted, the mixture or fractionation is not

generally given by straight lines but by hyperbolas whose concavity depends on the abundance
ratios of the elements in the denominator in the components of the mixture.

C 0 represents the fraction of element B residing in phase
j . Equation 2.8 is a closure condition equivalent to (2.5) , but this time restricted to element
B. Let us now compare the combination of ratios in a mixing process using (2.9 ). It can
be seen that, unlike the weights f j assigned to the concentration balance (2.6) , weights
ϕ

B
j

f j C j /

where the weight ϕ =

B

j assigned to the ratio balance are dependent on the element in the denominator of the
ratio. Therefore, in ratio/ratio diagrams, mixtures do not generally form straight lines but
hyperbolas ( Fig. 2.4 ). A mixture relation like this is linear only if the denominator element