Example: Quantitative Chemical Analysis of Ancient Glass
 
Above: Various glass artifacts from Egypt. Source: Malter Galleries.
I rarely post quantitative elemental data here because, well, a table of numbers is less interesting than pretty X-ray maps.  I don't want people to forget, however, that, with a little work, an electron microprobe can acquire very good quantitative data.  Our electron microprobe can determine the abundance of each element from beryllium (Z = 4) to uranium (Z = 92) using the wavelength-dispersive spectrometers (WDS).  Using suitable standards and conditions, measurements can have less than 1% relative error, and the detection limits are usually range from 30 to 300 ppm (though I have pushed the detection limits into single-digit ppms in a few case).  An area as small as 1-micron on a sample's surface is analyzed, and typical analyses take only a minute or two.
This example involves quantitative analysis of samples from the Corning Museum of Glass.  This museum has the world’s most complete glass collection, housing over 45,000 objects from the last 3500 years.  Their collection has artifacts from the Near East, Asia, Europe, and the Americas dating from ancient until modern times.  The museum houses a full-sized replica of an ancient Egyptian furnace as well.  Several examples of their glass artifacts can be viewed on the museum's collections page (http://www.cmog.org/collection/).
I had nine samples from the Corning Museum: three samples of three different ancient glass compositions.  These samples were tiny fragments, only a few dozen or hundred microns in diameter.  Each sample, composed of a few fragments, was placed in one hole of a bronze holder.  Then epoxy was poured around the tiny fragments, and the samples were polished using microscopic diamonds to produce flat surfaces.
Below: Secondary-electron image of the samples; field of view is about 4-mm wide.
I assigned numbers to each of the nine samples, as illustrated below:
Below: SE image of the same glasses with their numbering from Sample #1 to #9.  
I set out to determine if I could distinguish the three different glass compositions.  I began with scans to identify the elements present, and I then conducted five quantitative analyses on each sample.  The analytical conditions were rather typical.  The mean data (in weight %) for each sample are below:
 
#1
#2
#3
#4
#5
#6
#7
#8
#9
Ag2O
0.01
0.01
-
-
0.01
0.03
0.01
0.01
0.01
Al2O3
4.45
4.46
4.46
0.92
0.92
0.92
0.97
0.96
0.98
BaO
0.12
0.05
0.10
11.18
11.33
11.23
0.48
0.51
0.47
CaO
8.32
8.35
8.36
4.91
5.02
4.95
4.82
4.84
4.84
Cl
0.18
0.17
0.12
0.07
0.09
0.09
0.11
0.08
0.09
CoO
0.04
0.03
0.04
0.20
0.18
0.17
0.18
0.17
0.19
Cr2O3
-
-
0.01
-
-
-
0.01
-
0.02
CuO
2.69
2.66
2.60
1.22
1.19
1.19
1.23
1.28
1.25
FeO(T)
0.32
0.39
0.34
0.29
0.31
0.31
1.08
1.06
1.02
K2O
1.09
1.09
1.09
2.97
2.98
2.96
3.06
3.03
3.11
MgO
1.02
1.05
0.99
2.77
2.84
2.81
2.63
2.63
2.67
MnO
0.26
0.24
0.27
0.01
-
-
0.98
1.02
1.02
Na2O
16.79
16.68
16.63
1.29
1.24
1.30
14.15
14.06
14.04
NiO
0.08
0.12
0.11
0.01
0.03
-
0.04
0.02
0.03
P2O5
0.94
0.95
0.89
0.12
0.11
0.10
0.08
0.13
0.11
PbO
0.51
0.48
0.51
37.08
36.42
36.63
0.16
0.18
0.05
SO3
0.41
0.44
0.39
0.11
0.08
0.06
0.13
0.13
0.12
Sb2O5
0.55
0.56
0.53
0.21
0.24
0.23
2.03
2.03
2.04
SiO2
61.99
62.35
62.35
34.42
34.60
34.60
65.77
65.84
65.92
SnO2
-
0.01
0.00
0.10
0.12
0.15
0.12
0.12
0.11
SrO
0.19
0.20
0.20
0.48
0.47
0.46
0.38
0.39
0.38
TiO2
0.11
0.06
0.10
1.22
1.21
1.24
0.83
0.81
0.76
ZnO
0.27
0.28
0.29
0.14
0.10
0.13
0.10
0.13
0.13
ZrO2
0.06
0.07
0.00
0.03
0.05
0.01
0.02
-
-
Total
100.40
100.67
100.37
99.77
99.53
99.58
99.37
99.43
99.36
I plotted the 45 measurements to look for clusters in the data.  I was hoping to establish which of the nine samples belonged to the three different glass compositions.  Clusters appeared in a plot of silicon, lead, and magnesium...
... and in a plot of strontium, potassium, and manganese...
... and in several other plots I tried.  Now I had the three different glass compositions, and I knew which samples belonged to each one -- I have labeled each of them below as either A, B, or C:
Below: SE image of the glass samples with their identifications as Group A, B, or C.  
Careful inspection of the above secondary-electron (SE) image reveals some clue about these compositions: the samples labeled 'C' are a little brighter than the others.  SE imaging shows mostly topographic contrast -- it is the imaging mode used by SEMs to produce highly magnified images of, for instance, spiders or salt grains.  The SE detectors, though, can pick up low-energy backscattered electrons (BSE), which show compositional contrast -- a brighter area has higher average atomic number than a darker area.  The glass samples of Group C are the ones containing high concentrations of barium (BaO = 11 wt %) and lead (PbO = 37 wt %).  There aren't any brightness differences between A and B because their mean atomic numbers are so close.
Because these glass samples came from the Corning Museum of Glass, their compositions had been determined previously by a research scientist at the museum, Dr. Robert H. Brill.  If you have not heard of Robert Brill, he's an expert on ancient glass and its composition.  According to the museum website, Brill "is responsible for conducting chemical analyses and other scientific investigations of ancient glass in order to determine when and where it was made, what it was used for, and how it was traded."  His current focus is glass unearthed at sites on the Silk Road, spanning from the Mediterranean to East Asia.  In 1999, Brill also authored the book Chemical Analysis of Ancient Glasses, a two-volume reference (888-pages long!) that compiles his chemical analyses of thousands of Egyptian, Mesopotamian, Hellenistic, Roman, Indian, Islamic, and medieval glass fragments.
So how do my analyses compare to Brill's data?  Below is a comparison.  Two things to keep in mind: (1) ancient glasses are often somewhat heterogeneous, so microscopic fragments might not be exactly representative of the complete item, and (2) this was my initial attempt for the glass samples -- microprobe analysis can be an iterative process as one finds the proper conditions and standards to use for a particular material.
 
A - Brill
A - Frahm
B - Brill
B - Frahm
C - Brill
C - Frahm
Ag2O
0.003
0.009
0.01
0.001
0.003
0.004
Al2O3
1.14
0.97
4.21
4.47
1.02
0.92
B2O3