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Figure 3. Comparison of influence of phase
assemblage on the precision of the bulk analy-
sis. Precision = percentage of the oxide value
represented by the relative standard deviation
(RSD*100). Elements that occur dominantly in
one phase are more affected as grain size
increases relative to beam size because they
are more likely to be undersampled.

Fig. 5A). Here “order” reflects the extent of Figure 4. Comparison of sampling number with modeled bulk compositions. Solid line represents
short- or long-range ordering in the glass/ grain size << beam size; dotted line represents grain size >> beam size; dashed line is the true elec-
melt, which is unknown. For XAS mea- tron probe microanalysis oxide value. Modeled and true bulk values are approached within ~10
surements a beam/order size ratio of 950 analyses for fine-grained samples (solid line) with larger beam spot sizes. Significantly more analy-
was used (beam size = 950 pixels; ordering ses are needed when the sample is coarse-grained (dotted line). (A) Al2O3. (B) FeO. (C) MgO. (D) Gore
size = 1 pixel; Fig. 5B) because our model Mountain garnet outcrop. Circles represent the 1.5 cm diameter of possible Raman or laser-induced
has maximum beam size of 1000 that results breakdown spectroscopy analytical dimensions. Note the difficulty in sampling a representative
in full sample coverage. bulk composition even at these relatively large analytical sizes in a coarse-grained material.
For comparison, with a 2 μm diameter beam size, 7,500 electron probe microanalysis or X-ray
Beam Dimensions absorption spectroscopy spots would fit the diameter of each individual circle; for a 0.2 nm diame-
ter beam size, 75,000,000 electron energy loss spectroscopy spots would fit the diameter of each
Even when grain size is small, as in individual circle.
either crystallographic dimensions of a
mineral or short range order in melts, vari- analysis will sample a large, nearly repre- covers nearly the whole sampling area,
ations in analytical spot size also result in sentative number of atoms (Fig. 5B), and multiple analyses lead to increased analyti-
sampling challenges. For example, the the calculated redox value approaches that cal overlap, resulting in oversampling of
redox state of a melt (glass) can be calcu- of the true value (Table 2). Multiple analy- the minor elements. This would not occur
lated from its Fe3+/Fe ratio (e.g., Kilinc et ses are still required to adequately cover in a natural sample of near “infinite”
al., 1983; Kress and Carmichael, 1991). the sample area and reduce standard devia- dimension.
Measured Fe3+ concentration must be rep- tions, but they do not significantly improve
resentative of the bulk system to be inter- the match to the actual data (Table 2). The DISCUSSION
pretable. Our model simulates truly ran- apparent decrease in the precision of the
dom melts (Figs. 5A and 5B), but natural Fe2O3/FeO ratio with more analyses Using spot analyses to return representa-
silicate glasses may exhibit short range observed in Table 2 is an artifact of the tive data on a bulk sample thus requires
ordering on ~1–2 nm scales (e.g., Mysen model dimensions; when a single analysis consideration of several issues: the miner-
and Richet, 2005). If beam size is much alogy or scale of ordering in a glass,
smaller than the short range ordering in the
melt (e.g., STEM-EELS), a single analysis Figure 5. Modeled basaltic “melts.” Black squares are the sampling
may sample only one atom (Fig. 5A), gen- areas (20). (A) Electron energy loss spectroscopy measurements:
erating no representative information on the beam/order size ratio = 0.1 (beam size = 10 pixels; order size = 100
redox state of the bulk system (Table 2). pixels). (B) X-ray absorption spectroscopy measurements: beam/
Multiple analyses with this 0.1 beam/order order size ratio = 950 (beam size = 950 pixels; order size = 1 pixel).
ratio may never actually sample all of the
elements present (Fig. 5A). Even with an
impractically large number of analyses per
single sample (n = 50), true bulk glass
redox ratio is elusive (Table 2). Oxidation
state of the sample cannot be quantified
accurately without excessively large num-
bers of analyses.

When analytical beam size is several
orders of magnitude greater than the short
range order in the melt (e.g., XAS), a single

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