Quantitative Analysis
Analytical
Methods and Software
Quantitative analysis can be
performed by wavelength-dispersive spectrometry, energy-dispersive analysis, or
a combination of both. Most quantitative work is performed via the WDS. The software
package controlling microprobe automation is the SAMx XMAS+ä system. This is an extremely
versatile group of programs supporting both individual point
(manual mode) analysis or automated analysis of stored point locations
for unattended operation. Among many features, this package supports: (a) full
asynchronous control of all five WDS; (b) x-ray intensity acquisition modes
including simple intensity above mean background and integration of x-ray band
areas; (c) background acquisition methods including 2 point, 1 point &
slope, or none, with linear or curved background shape models; (d) the use of
multiple beam conditions (up to one for each different element); (e) automatic
or user-selected order of analysis on each spectrometer; and (f) analysis of up
to 40 elements. To this basic package, the SAMx IDFIXä package provides complete integration
of EDXA automation with standard WDS microprobe function and matrix correction
procedures.
Elements of interest are
usually treated as analytical unknowns, but elements present and not analyzed
for can be determined by stoichiometry or difference. If known, the
concentrations of any given element(s) can be entered manually, to permit
inclusion in the matrix correction calculations. Data reduction methods include
PAP and XPP (modified f (r z)) methods, and a ZAF algorithm.
Mass absorption coefficients from Heinrich (1986), except for those of the
light elements which are from Pouchou and Bastin. Element valences and compound
formula stoichiometry can be changed on a point-by-point basis during manual
analysis, or after automated analysis can be changed and the results
recalculated for all or selected groups of points off-line. For geologists, the
software permits the assignment of mineral groups for any chosen point or
group(s) of points during manual or automated analysis, permitting analysis and
formula calculations (both cations and end-member abundance for many solid
solutions) for many different mineral groups with a single analytical file.
Why Use
Wavelength Dispersive Spectrometry (WDS)?
Both WDS and EDXA (Energy
Dispersive X-ray Analysis) can be used to detect x-rays for analysis, but WDS
has superior resolving power for x-ray lines, and yields larger signal/noise
ratios. The superior resolution of WDS is demonstrated by comparing EDXA and
WDS spectra acquired from benitoite (BaTiSi3O9)
in the region of Ba and Ti x-ray emission. The Ti Ka and Ba La 1 peaks show complete overlap by EDXA
(left), but are well resolved by WDS (right). Thus, the superior resolution of
the WDS makes analysis of element pairs with overlapping emission lines (e.g.,
Ti & Ba or Ti & V) much more accurate, and larger signal/noise ratios
improve minimum levels of detection for minor and trace elements.
Analytical
Capabilities
Available
diffraction devices in our five WDS permit analysis of elements with Z ³ 5 (boron), producing common minimum
detection limits (MDL) in the 100-200 ppm range
(elemental basis) using counting times of 30-60 seconds on peak.
Some of the analytical
capabilities of the system are demonstrated by the analytical result below from
the analysis of a tourmaline group mineral [(Na,Ca)0-1(Fe,Mg,Mn,Al,Li)3Al6(BO3)3Si6O18(O,OH,F)4].
By constraining all of the elements with Z ³
5 in a material, light element components (such as Li, Be, or, in the case
below, H2O in the formula) can be deduced with reasonable accuracy
by the difference of analytical totals from 100%.
Point |
15: |
( -13186,-23943, -54), |
3 iterations------------BRTUR1-5 |
||||||
Element |
Wt% |
At% |
Ix/Istd |
Kratio |
Z.A.F. coefficients |
Ox% |
Cat# |
||
B |
3.06 |
5.59 |
0.8501 |
0.0026 |
0.9304 |
13.9802 |
1.0000 |
9.84 |
2.77 |
O |
47.68 |
58.81 |
|
|
|
|
|
0.00 |
0.00 |
F |
0.91 |
0.95 |
0.0869 |
0.0021 |
1.0266 |
4.2989 |
1.0001 |
0.91 |
0.47 |
Na |
0.70 |
0.60 |
0.0780 |
0.0029 |
1.0506 |
2.3362 |
0.9991 |
0.95 |
0.30 |
Mg |
8.75 |
7.10 |
0.2968 |
0.0600 |
1.0336 |
1.4201 |
0.9960 |
14.52 |
3.54 |
Al |
15.23 |
11.14 |
0.7453 |
0.0907 |
1.0687 |
1.5792 |
1.0028 |
28.77 |
5.54 |
Si |
17.36 |
12.20 |
0.4892 |
0.1781 |
1.0427 |
1.0601 |
0.9997 |
37.13 |
6.06 |
K |
0.01 |
0.01 |
0.0008 |
0.0001 |
1.1135 |
1.0998 |
0.9948 |
0.01 |
0.00 |
Ca |
2.83 |
1.39 |
0.2256 |
0.0248 |
1.1034 |
1.0343 |
0.9993 |
3.96 |
0.69 |
Ti |
0.51 |
2.10 |
0.0207 |
0.0041 |
1.2187 |
1.0151 |
0.9996 |
0.85 |
0.10 |
Mn |
0.02 |
0.01 |
0.0007 |
0.0002 |
1.2627 |
1.0000 |
1.0030 |
0.03 |
0.00 |
Fe |
0.29 |
0.10 |
0.0120 |
0.0024 |
1.2460 |
0.9976 |
1.0003 |
0.38 |
0.05 |
Sum |
97.35 |
100.00 |
|
|
|
|
|
97.35 |
19.52 |
Standard
Materials
Our inventory of standards
includes over 300 well-characterized reference materials, for intensity
calibrations on most of the elements from B (z = 5) to U (z = 92). These
include a large suite of natural and synthetic minerals (silicates, oxides,
carbonates, sulfides, phosphates, halides), natural and
synthetic glasses, pure elements (metals), element oxides, and metal alloys.
Limits of
Detection, Accuracy, and Analysis Time
For most elements with z >
9, minimum detection limits (MDL, at 3-s
above mean background) down to 50 ppm on an elemental
basis are common, and can be lowered by almost an order of magnitude for many
trace components. The MDL are commonly higher for the ultralight
elements, with values of 500-1000 ppm common for B (z
= 5). Analytical accuracy for major and minor components, determined from
counting statistics, is often as low as 0.1% relative to the element
concentration. Inverse relationships between analysis time and MDL or accuracy
should be noted, such that decreased MDL and increased accuracy are
accomplished by the use of longer counting times. Consider that for most
elements analyzed using Ka x-ray lines,
elemental MDL in the 50-100 ppm range require on the
order of 30-60 seconds counting on peak (and an equal time on background).
Thus, an analytical routine comprised of 15 elements can commonly be achieved
in 3-5 minutes with MDL in this range.
Interference
Corrections
Even with the resolving power
of the WDS, there still are cases where x-ray line overlap cannot be avoided.
To alleviate these uncommon problems, the SAMx® analytical software
contains methods for correcting interferences based upon calibration from
standard materials.
Interference among first
order x-ray lines is
more common between pairs of elements with moderate to heavy atomic numbers (Z ³ 12) such as Ti & V or Ti &
Ba. The following example shows how the overlap of Ti Kb on V Ka
leads to a false V2O5 content of 1.92 wt.% in the analysis of titanite (CaTiSiO5).
Correction for this interference removes the fictive V as well as improving the
results of other major components by providing correct intensities used in the
matrix calculations.
|
Oxide |
Without Correction |
With
Correction |
Standard Value |
SiO2 |
30.65 |
30.65 |
30.65 |
|
CaO |
30.56 |
28.65 |
28.60 |
|
TiO2 |
40.85 |
40.62 |
40.75 |
|
V2O5 |
1.92 |
0.00 |
0.00 |
|
Total |
103.98 |
99.92 |
100.00 |
Interference among higher
order x-ray lines is
especially important for analyzing light elements. Shown below is the effect of
correction for third order P Ka
on F Ka in an REE-bearing apatite, Ca5(PO4)3(OH,F),
which is both a non-biologic mineral and the principal hard component of
vertebrate teeth and bone. Lack of correction results in fictive F contents
that are greater than the possible stoichiometric occupancy of F in the mineral
formula (which is about 3.73 wt.% F).
|
Oxide/anion |
Without
Correction |
With
Correction |
Standard Value |
CaO |
54.19 |
54.14 |
54.02 |
|
P2O5 |
40.82 |
40.86 |
40.88 |
|
F |
5.29 |
3.68 |
3.53 |
|
O=F |
-2.23 |
-1.55 |
-1.48 |
|
Total |
98.07 |
97.13 |
96.95 |
Data
Manipulation and Output
The XMAS+ä automation system provides for very
flexible treatment of analytical data. From any stored analytical file, the
user can select any or all information (raw x-ray intensities, intensities
relative to standards, K-ratios, element concentrations, oxide concentrations,
atomic proportions, cations, etc.) for output either to hardcopy or text file
(pre-formatted for Microsoft Excelä ). Moreover, the system permits the importation
of a new standard (including insertion of a new element and intensity
acquisition for points already analyzed), change of valence or formula
stoichiometry, and off-line recalculation of analytical results for all or
selected points within the file. Additional subroutines exist for sorting the
data, in which selected points can be grouped and averaged with user-selectable
levels of confidence (sigma) for statistics; the sorted groups of points can be
output to hardcopy, Excelä -compatible text
file, or a new XMAS+ä analytical file.
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