Geology Reference
In-Depth Information
Table 8.3
The mineral formula and site occupancies of an olivine
1
2
3
4
5
Oxide
RMM of oxide
Analysis as mass
% oxides*
Analysis as moles
of oxides
†
Moles of oxygen
(as O
2-
)
‡
Cations per
4 oxygens
§
Site totals
SiO
2
60.09
39.41
0.6558
1.3116
1.0008
Z site sum:
1.001
}
FeO
71.85
16.46
0.2291
0.2291
0.3496
MnO
70.94
0.21
0.0030
0.0030
0.0046
Y site sum:
1.998
MgO
40.32
43.27
1.0732
1.0732
1.6378
CaO
56.08
0.23
0.0041
0.0041
0.0063
99.58
2.6210
4
2 6210
×
=
.
* See Box 8.4.
†
Column 1 divided by relative molecular mass.
‡
Column 2 × number of oxygens per molecule (=2 for SiO
2
, 1 for the rest)
§
Column 2 × 4/2.6210.
Table 8.3 shows how this calculation is carried
out. The oxide analysis is written in column 1. The
first step is to calculate the number of
moles
of each
oxide present. This is achieved by dividing each
oxide mass percentage by the
relative molecular
mass (RMM)
of the oxide concerned, entering the
results in column 2. Because column 1 contains the
number of grams of each oxide in 100 g of the
olivine (i.e. mass percentage), column 2 contains
the
number of moles
per 100 g.
3
Multiplying each entry in column 2 by the number
of oxygen atoms in the corresponding oxide formula - 2
for SiO
2
, 1 for the other oxides - gives the number of
moles of O
2−
associated with each oxide (column 3).
Adding these up tells us that 100 g of sample con-
tains total of 2.6210 moles of O
2−
. Our objective, how-
ever, is to calculate the numbers of cations associated
with 4 moles of O
2−
. Multiplying each entry in col-
umn 2 by 4 ÷ 2.6210 = 1.5261 gives us the number of
moles of each oxide which together contain 4 moles
of O
2−
(column 4). As each oxide molecule contains
only one atom of metal, the figures in column 4 also
indicate the numbers of cations equivalent to a total
of 4 oxygens.
The results in column 4 show two notable features.
The first entry is a number very close to 1.0000. It rep-
resents the number of silicon atoms present for every
four oxygen atoms in the olivine structure, and it ind-
icates that the Z-sites in olivine are filled with silicon
alone. Secondly, the remaining entries in column 4 add
up to 1.998. These elements collectively represent the
average contents of the two Y-sites associated with
every group of four oxygens in olivine. These concl-
usions allow us to write the complete chemical for-
mula for the olivine, showing in what proportions the
elements occupy each type of site:
(
)
Mg
Fe
Ca Mn
Si O
(8.1)
1 638
.
0 350
.
0 006
.
0 005
.
1 001
.
4
The close correspondence of the total site occupan-
cies to the whole numbers of the ideal formula of oli-
vine (Y
2
ZO
4
) is additional reassurance of an accurate
analysis.
Amphibole analysis
Table 8.4 shows the formula calculation for an amphi-
bole analysis.
The sites available in the amphibole structure
(Box 8.5) are summarized by the formula:
(
)
ABCZO H
2
5
8
22
2
although in many amphiboles the large A site is partly
or wholly vacant. The following points should be noted:
(a) The formula of an amphibole is normally written
with 24 oxygens (including OH), so the analysis is
recalculated on this basis.
3
The logic here is analogous to dividing a bag of apples among
a group of children: it is more useful to know the
number
of
apples in the bag than their weight.
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