www.elsevier.com/locate/chemgeo
Chemical Geology 2
Format and philosophy for collecting, compiling, and reporting
microprobe monazite ages
M.L. Williams *, M.J. Jercinovic, P. Goncalves 1, K. Mahan
Department of Geosciences, University of Massachusetts, Amherst, MA 01003, United States
Received 18 January 2005; received in revised form 13 July 2005; accepted 26 July 2005
Abstract
Microprobe monazite dating has been increasingly used to constrain the timing of deformation and metamorphism because of
the potential to date very small monazite domains (down to 5 Am or less) in structural and petrologic context. This paper presents
an analytical strategy, presentation format, and error considerations for microprobe monazite dating. The strategy involves high-
resolution compositional mapping to delineate compositional domains within monazite crystals. Then for each compositional
domain, a series of Th, U and Pb analyses are made, and a single date and error are calculated. The number of analyses in each
domain is determined by the desired statistical precision of the date. Results from several monazite grains are typically combined
and, along with textural relationships, are used to build an argument that the dates constrain the age of a deformation or
metamorphic event. The total error involves three components: short-term random error (dominated by counting statistical
uncertainty), short-term systematic error (uncertainty in background correction, conductive coating variation, and calibration),
and long-term systematic error (uncertainty in standard composition, mass absorption factors, decay constants, etc.). In homoge-
neous compositional domains, short-term random errors (2j) of less than 10 m.y. can be obtained from five to ten analyses.
However, short-term systematic error, mainly background estimation uncertainty, would typically result in a doubling of the
magnitude of random error. Microprobe dates are presented as a single Gaussian probability distribution for each domain, along
with representative compositional maps. It is recommended that a consistency standard be analyzed during each analytical session
and the results be reported along with those from the unknown. This proposed strategy and format are compatible with those of
other geochronological techniques; they incorporate analytical limitations associated with trace, as opposed to major element,
microprobe analysis, and will allow better comparisons to be made between labs and between different geochronological
techniques.
D 2005 Elsevier B.V. All rights reserved.
Keywords: Monazite; U–Pb dating; Electron microprobe; Trace element analysis
1. Introduction
Monazite dating using the electron microprobe has
become increasingly popular over the past decade, es-
0009-2541/$ - see front matter D 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.chemgeo.2005.07.024
* Corresponding author. Fax: +1 413 545 1200.
E-mail address: [email protected] (M.L. Williams).1 Present address: Departement de Geosciences, Universite de
Franche-Comte, 25000 Besancon, France.
pecially as a tool for constraining the age of deformation
and metamorphic events (Suzuki and Adachi, 1991,
1998; Montel et al., 2000; Terry et al., 2000; Simpson
et al., 2000; Shaw et al., 2001; Williams and Jercinovic,
2002; Asami et al., 2002; Cheong et al., 2002; Pyle and
Spear, 2003a; Hibbard et al., 2003; Tickyj et al., 2004;
Foster et al., 2004; Goncalves et al., 2004).
The power of the technique comes from the in situ,
non-destructive nature coupled with high spatial reso-
25 (2006) 1–15
2 For this contribution, we use the term bdateQ to refer to a number
alculated from an appropriate age equation. It may or may not have
eological significance. The term bageQ is used for a result (date or
eighted mean of dates) that is interpreted to have geological signif-
ance, that is, to represent a true geological time span since a
articular event.
M.L. Williams et al. / Chemical Geology 225 (2006) 1–152
lution. Age information is acquired from the same thin
sections from which petrologic or microstructural rela-
tionships are obtained. The spatial resolution is impor-
tant because high-resolution X-ray compositional maps
of monazite grains generally reveal significant compo-
sitional zoning, which can be remarkably complex
(Williams and Jercinovic, 2002; Pyle and Spear,
2003a). Compositional domains can be linked to micro-
structures, metamorphic minerals, or metamorphic reac-
tions, allowing specific timing constraints to be placed
on stages in the structural or metamorphic history
(Terry et al., 2000; Simpson et al., 2000; Foster et al.,
2000; Williams and Jercinovic, 2002; Pyle and Spear,
1999; Foster et al., 2004; Dahl et al., in press). Al-
though core domains may be large enough to be dated
by ion probe or other isotopic means, dates on narrow
rim domains or irregularly shaped internal domains
require the micron-scale resolution that only the micro-
probe can provide. Thus, although less precise than
isotopic methods, microprobe dating is now an essential
part of monazite geochronology.
Microprobe monazite dating requires the precise
measurement of Th, U, and Pb, along with Y and any
other elements needed for interference correction. Al-
though Th and Y can be present as bmajorQ elements, U
and Pb concentrations in monazite are typically on the
order of 100s to 1000s of ppm (i.e., trace components)
and are, therefore, a challenge for electron probe micro-
analysis (EPMA). Because uncertainties associated with
microprobe dates are particularly dependent on precise
and accurate trace element analyses, a significant
amount of attention has been paid to analytical issues
such as interference correction, background estimation,
and standard characterization (Scherrer et al., 2002;
Jercinovic and Williams, 2005; Pyle et al., 2005). In
parallel, several strategies for data presentation and error
analysis have been developed, ranging from simple
application of major-element methodology to regression
techniques that involve large numbers of analyses and
subsequent statistical discrimination of age populations
(e.g., Asami et al., 1996; Montel et al., 2000; Cocherie
and Albarede, 2001; Williams and Jercinovic, 2002).
The diversity of processing schemes and analytical
approaches has tended to limit the rigorous comparison
of data between laboratories and with other geochrono-
logic techniques for which analysis and processing
methodologies are relatively well accepted (e.g., con-
cordia diagrams, Wetherill et al., 1956; Terra–Wasser-
burg diagrams for U–Pb geochronology, Tera and
Wasserburg, 1972; Ludwig, 2003).
The purpose of this paper is to propose an analytical
philosophy and data reduction strategy for microprobe
monazite dating that is particularly appropriate for con-
straining the timing of deformation and metamorphic
events in older rocks (older than several hundreds of
millions of years). The analytical approach is statisti-
cally based, and in many ways, is similar to the phi-
losophy used for other geochronologic techniques. In
essence, it involves repeated Th, U and Pb analyses
(samples) of a single monazite compositional domain
(one population) with the number of analyses limited
by the desired statistical precision of the date. This
could be compared to the cycles of measurements
(series of blocks) during mass spectrometric analysis.
The result is a single date, based on multiple measure-
ments, for each compositional domain. We refer to this
approach as a bbottom-upQ approach in that interpreta-
tions are based on combining results from specific
grains with specific textural relationships in order to
build a more general data set. Top-down approaches
(i.e., Suzuki and Adachi, 1991; Montel et al., 1996,
2000; Cocherie and Albarede, 2001) that begin with
large composite data sets and subsequently attempt to
deconvolute meaningful ages or relationships are nec-
essary in certain cases. However, these approaches are
limited by the small size and compositional complexity
of many monazite grains and by the relatively large
uncertainties that can make discrimination of events
difficult. It is hoped that the proposed strategy will
begin the process of standardizing microprobe monazite
geochronology and establishing a format that will allow
comparison and integration of data among microprobe
laboratories and especially, between the microprobe and
other geochronological techniques (IDTIMS, SIMS,
LA-ICPMS).
2. Background
Monazite is a rare-earth element bearing phosphate
mineral, (Ce,La,Nd,Th)PO4, that generally contains sig-
nificant amounts of Th and U and typically, little initial
Pb (Parrish, 1990). By assuming that all of the Pb is
radiogenetic, and that the isotopes of uranium are pres-
ent in their relative crustal abundances, a geological
date2 can be calculated from the total abundances of Th,
U, and Pb (e.g., Suzuki and Adachi, 1991; Montel et
al., 1996; Williams et al., 1999; Cocherie et al., 1998).
The validity of these assumptions has been discussed
c
g
w
ic
p
M.L. Williams et al. / Chemical Geology 225 (2006) 1–15 3
and evaluated by a number of workers and will not be
discussed here. For the purpose of this paper, it is
relevant to note that a large number of studies have
now produced geologically reasonable ages using the
microprobe, and analyses of the same samples by mi-
croprobe and by isotopic means have produced compa-
rable results (Montel et al., 1996; Williams et al., 1999;
Dahl et al., 2005).
One of the most useful and important characteristics
of monazite is that it typically contains distinct com-
positional domains with relatively sharp boundaries.
Although sector compositional zoning (crystallograph-
ically controlled growth zoning) is not uncommon,
compositional domains are typically interpreted in
terms of generations of monazite growth (Williams
and Jercinovic, 2002; Pyle and Spear, 2003a,b; Gibson
et al., 2004). The domains may reflect different meta-
morphic reactions that produce (or consume) monazite
and possible fluid-flow or deformation events that lead
to dissolution and precipitation of monazite during one
or more tectono-metamorphic events. Because Pb dif-
fusion is extremely slow (Cocherie et al., 1998; Crow-
ley and Ghent, 1999; Seydoux-Guillaume et al., 2002;
Cherniak et al., 2004), monazite generations may rep-
resent points along the prograde or retrograde P–T
history (Pyle and Spear, 2003a; Foster et al., 2004;
Gibson et al., 2004), and not necessarily the thermal
or deformational peak. Importantly, the compositional
domains can, in many cases, be linked to deformation
fabrics or metamorphic textures and thus allow timing
constraints to be placed on specific parts of the tectonic
history (Williams and Jercinovic, 2002). For example,
comparison of monazite generations inside and outside
of porphyroblasts can constrain the timing of porphyr-
oblast growth (Foster et al., 2000). Monazite domains
with kinematically significant shapes or locations can
constrain the timing of deformation events (Shaw et al.,
2001). One ultimate goal is to balance monazite gen-
erations into specific metamorphic reactions in order to
directly date the reactions (Spear and Pyle, 2002; Pyle
and Spear, 2003a,b; Gibson et al., 2004). In each case,
the power of the approach comes from the fact that
specific monazite domains or generations can be linked
to specific geologic events.
Once monazite generations have been identified
through high-resolution compositional mapping, it is
necessary to evaluate and select the most appropriate
technique for constraining the age. This depends on the
nature of the geologic questions being asked. In situa-
tions with relatively young monazite or when extremely
high precision is required, single- or partial-grain
IDTIMS techniques may be necessary, bearing in
mind that some mixing of domains may be inevitable.
Where domains are large, ion probe or laser ICPMS
techniques may be suitable. However in many cases,
compositional domains, especially rim domains and
overgrowths that are likely to be most directly linked
to fabrics and textures, are too small for ion beam or
laser techniques, and would be overwhelmed by larger
domains if whole grains were analyzed. Under these
circumstances the microprobe is an appropriate tool for
monazite geochronology as long as the Pb concentra-
tion is high enough (due to age or high Th/U concen-
tration) to allow the necessary statistical resolution.
2.1. Major vs. trace element analysis: distinct
approaches for distinct applications
Thorium is typically, but not always, present in mon-
azite at the weight percent (i.e., major element) level.
However, U, Pb, and Y, all critical for monazite analysis
and error evaluation, are typically present at the 100s to
1000s of ppm level, and thus represent a special chal-
lenge for the electron microprobe. Analytical precision
in EPMA depends upon the ability to distinguish char-
acteristic X-ray counts (bpeak countsQ) generated from
an element of interest from background X-rays (contin-
uous spectrum) and from X-rays generated from other
interfering peaks. Because major element analyses typ-
ically involve large peak/background ratios (10–100 or
more), small uncertainties in background intensity esti-
mation or approximations concerning correction proce-
dures and sample preparation may not result in dramatic
inaccuracies in the final concentration. However, trace
element analyses typically involve peak/background ra-
tios between 1 and 3, greatly magnifying the importance
of background estimation, and allowing otherwise
minor interfering peaks to become major analytical
hindrances. In this case, the application of major ele-
ment analytical techniques can lead to large uncertain-
ties at best, and at worst, to meaningless results. Most of
these issues are treated in more detail elsewhere (Scher-
rer et al., 2002; Jercinovic and Williams, 2005; Pyle et
al., 2005). However, several are particularly important
for error estimation, and thus to the analytical strategy.
These are discussed briefly below.
Background analysis is particularly critical. For trace
elements, small uncertainties in background estimates
are extremely significant (Fialin et al., 1999; Goldstein
et al., 2003; Reed, 1993; Jercinovic and Williams,
2005). First, the background spectrum, obtained from
wavelength dispersive spectrometers (intensity as a
function of wavelength), is distinctly curved, reflecting
the combination of the natural shape of the continuous
M.L. Williams et al. / Chemical Geology 225 (2006) 1–154
X-ray emission spectrum and curvature due to chang-
ing spectrometer efficiency as a function of diffraction
geometry. The resulting curvature for PET monochro-
mators in the range of 0.40–0.65 sin-theta units (U,
Th, Pb first-order M lines) is concave upward, with
intensity decreasing with wavelength (Fig. 1). Al-
though less apparent over short wavelength distances,
this curvature obviously results in overestimation of
background intensity if linear interpolations of mea-
surements made on either side of the peak of interest
are used (Fig. 1). In addition, any small interferences
in the region chosen for background measurement can
lead to further overestimation. Because many such
interferences are possible in compositionally complex
materials such as monazite, and because they can be
produced from very small (unrecognized?) amounts of
the interfering element, it is not possible to pick fixed
background offset positions appropriate for all analy-
ses, even if curvature were not an issue. It is essential
to select background on the basis of a detailed, high-
resolution scan of the peak and background region
(Fig. 1). Either raw background scan data or data
Th Mζ 1
Pb Mβ
Pb M5-O3 Pb Ma1,2
Au Mγ
Au M3-N4
Y Lg2,3Th M1-O3 (2) T M4-N3 Pb M4-O2h
Th M2-O4 (2)
Th Mζ2
La Lα 1 (2)La Lα 2 (2)
La Lβ1 (2)
La Lβ4 (2)La Lb3 (2)Ce Lη (2)
Ce Lα 1 (2) Ce Lα 2 (2)
Pr Lα 1 (2)
Pr Lα 2 (2)
Sm Ll (2)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
55000 56000 57000 58000 59000 60000 61000 620
Wavelength (sin-θ ∗ 105)
I (cp
s/nA
)
Bkg 2
Bkg 1
Pb region (PET) - Elk Mtn. (Wards) Monazite
Fig. 1. Sample spectrometer wavelength scan used for interference analysi
2005). Scan shows the Pb region (0.55–0.64 sin-h) of the spectrum using a
filtering. Inset shows the specific location of the Pb Ma peak, used for
interpretations of background: Solid line—exponential regression through se
Bkg-2. Dotted line—linear regression using Bkg-1. Background values deter
independent constraints (i.e., IDTIMS). Linear extrapolations from Bkg-2 an
Bkg-2 and 60 m.y. for Bkg-1. Note that Bkg-1 is a region that would comm
using an approach modeled after major-element analysis. However, all poin
explanation, see Jercinovic and Williams (2005).
smoothed by an appropriate low-pass filter, such as
a Savitzky Golay filter (Savitzky and Golay, 1964;
Jercinovic and Williams, 2005) are then used for
regression using an appropriate model (polynomial
or exponential, as determined by the quality of the
fit). The regression model is then used to calculate the
background intensity under the peak and an associated
background uncertainty. A secondary benefit of the
scanning approach is that it allows assessment of
interferences in both peak and background regions.
At this stage in the development of EPMA geochro-
nology, new monazite components and fluorescences
are still being recognized, and the scans allow an
explicit evaluation of the spectrum.
Conductivity and beam damage are also issues to
be considered when high current density and long
counting times are employed. Jercinovic and Williams
(2005) showed that standard carbon coating is not
adequate to prevent surface damage and compositional
change even during count times as short as 5 min,
assuming typical high current (ca. 200nA), focused
beam analysis.
00 63000 64000
Wavelength (sin-θ ∗ 105)
Upper Bkg
Regressed Bkg -Exponential Fit
Bkg-2
Two-point BkgLinear Fit
PbMα1
Pb region (PET) - Elk Mtn. (Wards) Monazite
0.18
0.20
0.22
0.24
0.26
0.28
58500 59000 59500 60000 60500 61000 61500 62000
I (cp
s/nA
)
Bkg-1
s and background selection (modified from Jercinovic and Williams,
standard PET crystal. Heavy line is smoothed using Savitsky-Golay
monazite geochronology. The figure and inset show three possible
lected regions of the spectrum. Dashed line—linear extrapolation from
mined by exponential regression (solid line) yield dates consistent with
d Bkg-1 yield results significantly younger than expected: 30 m.y. for
only be selected for background measurement (offset=ca. 0.1 sin-h)ts in this region are significantly above true background. For detailed
M.L. Williams et al. / Chemical Geology 225 (2006) 1–15 5
Greater stability can be achieved by use of coating
materials with higher electrical and thermal conductiv-
ities (e.g., gold), but care must be taken to minimize
coating thickness differences between standards and
unknowns and to obtain a thickness that produces
adequate film continuity for the sample in question
(Jercinovic and Williams, 2005). However, some vari-
ation due to slight differences in coating thickness are
expected and incorporated into error analysis.
2.2. Top-down vs. bottom-up approaches
Current monazite analysis strategies are broadly
categorized into two types. The first, referred to here
as btop-downQ, involves collection of large numbers of
analyses from multiple compositional domains, and
then the use of regression or other statistical analysis
to distinguish important age populations. These in-
clude the pseudo-isochron (CHIME) method of
Suzuki and Adachi (1991, 1998) and subsequent
refinements therein (e.g., Rhede et al., 1996; Cocherie
et al., 1998; Cocherie and Albarede, 2001), and the
age histogram method of Montel et al. (1996, 2000).
Both of these methods have the advantage that a large
number of measurements are used to calculate ages,
and thus, errors (precision) are potentially quite small.
However, these methods have the disadvantage that
distinct compositions (and possibly ages) are invari-
ably mixed. In fact, a range of compositions is re-
quired for the pseudo-isochron approach. Domains of
different composition may or may not differ in age,
and the large error associated with a single measure-
ment can make it extremely difficult to distinguish age
populations. Nevertheless, under certain circum-
stances, such as dating large monazite grains with
growth or sector zoning, these methods can be effec-
tive and satisfactory.
An alternative approach, here called bbottom-upQanalysis, is at the core of the method proposed here,
and is similar to that used by Pyle and Spear (2003a),
Williams et al. (1999), Shaw et al. (2001), and others. It
involves detailed measurements restricted to specific
compositional domains and/or grains. Interpretations
of ages of geologic events are made by combining
and comparing the individual results based on statistical
arguments and on textural or microstructural evidence
(implying in-situ analysis of monazite in thin sections
rather than in separates). We suggest that the method
described below is more suitable for distinguishing
metamorphic and deformational events, and is most
compatible with the greatest strength of the electron
microprobe: its spatial resolution.
3. Proposed analytical strategy
The essence of the method proposed here is that
numerous data points (analyses) are collected from
each monazite compositional domain in order to pro-
duce a single date with an associated error. Each do-
main is bsampledQ repeatedly until the precision of the
resulting date reaches an acceptable value, or until all of
the available domain area has been analyzed.
The proposed analytical strategy is built upon, and
entirely dependent upon, compositional X-ray maps.
Backscattered electron maps, although useful in some
cases, can be rather insensitive to variations in elements
other than Th, and thus, can miss important composi-
tional domains. It is critical to recognize and character-
ize compositional domains within monazite grains in as
many petrological and structural settings as possible.
We strongly recommend full-thin-section compositional
mapping for Ce or La, along with a texturally revealing
element base map such as Mg, Al, etc., in order to
identify all monazite grains coarser than several
microns, and to classify them with respect to texture
and/or fabric (Williams and Jercinovic, 2002). Then,
high-resolution compositional maps are produced from
a number of grains in each basic setting. Raw X-ray
maps are processed in two ways. First, maps are pro-
cessed individually, by adjusting the gray or color scale,
to distinguish subtle intra-crystalline compositional dif-
ferences (Fig. 2a). Second, maps from all grains in a
thin section or rock sample are processed together (i.e.,
using a single color table for all grains) so that concen-
tration levels and zoning characteristics can be com-
pared from grain to grain (Fig. 2b). This presumes that
all grain maps have been collected with identical elec-
tron optical settings and pixel count times. Simulta-
neous processing allows direct comparison of the
major compositional populations in a thin section, and
when combined with textural and microstructural set-
ting, helps in the formulation of the analytical strategy
for the section or rock as a whole. Also, age maps,
constructed from raw compositional maps, can be ex-
tremely useful for evaluating broad age characteristics
of compositionally zoned grains (Williams et al., 1999;
Goncalves et al., 2005).
Once compositional domains have been character-
ized, major element analyses can be made within each
major domain type, unless major and trace elements are
analyzed simultaneously. The major element analyses
are necessary for matrix correction during trace element
runs. However, geochronologic results are not strongly
affected by variation in monazite composition (Pyle et
al., 2005), and at present, it is considered adequate to
Fig. 2. Compositional maps of four monazite grains (1–4): (a) processed independently and (b) processed simultaneously (i.e. with a single look-up
table). Top grain is an inclusion in garnet; all other grains are matrix grains. Note that there are three fundamental domains: (1) cores of inclusion
grains and inner core of matrix grain-3 (D1); (2) matrix core domains (D2-bluegreen); (3) rims of matrix grains, especially near cordierite (D3). The
outer, Y-rich rims are interpreted to represent monazite growth during garnet breakdown (rims tend to be thicker near cordierite pseudomorphs).
Note that matrix grain-3 has a fundamentally different Th content and may represent a different generation or possibly a different bulk
compositional domain in the host rock.
M.L. Williams et al. / Chemical Geology 225 (2006) 1–156
characterize each basic domain type, but not every
domain. If mapping and major element analyses are
carried out on carbon-coated sections, then the coating
is stripped by re-polishing, and recoated with gold for
trace element analyses. Background scan acquisitions
are then carried out in each compositional domain to be
dated. Because conductivity can vary as a function of
location within the thin section, nature of surrounding
phases, grain boundary characteristics, variations in the
conductive coating, etc., it is necessary to make a
background scan in every domain of each grain.
Again, incorrect background values can propagate to
age errors of 10s of m.y. Background scans are ana-
lyzed and modeled as discussed above, and a back-
ground value is determined for each trace element (i.e.
ThMa, PbMa, UMh, plus YLa, and KKh for interfer-
ence correction) in each domain.
Using the regressed background values and appro-
priate major element compositions, trace element anal-
yses are made within each domain. Analyses are
M.L. Williams et al. / Chemical Geology 225 (2006) 1–15 7
repeated within each compositional domain until (1) an
acceptable age error has been achieved, or (2) the
available analysis area has been exhausted. Although
EPMA is non-destructive, the number of analyses can
be limited in very small domains because of surface
contamination and other effects involving the conduc-
tive coating (Jercinovic and Williams, 2005). As dis-
cussed below, the standard deviation of the mean
(SDOM) is a useful measure of random error in homo-
geneous domains, and a relatively small number of
analyses (5–10 using analytical conditions summarized
below) are generally required to yield a stable uncer-
tainty on trace element analyses and a 2r random error
on dates of approximately 1% (Fig. 3).
0.0
0.5
1.0
1.5
2.0
2.5
Pb
UTh
1 2 43 5 6 7 8 9 10Number of Points in Weighted Mean
95%
Con
f. (
% o
f wei
ghte
d m
ean)
475
485
495
505
515
525
0
5
10
15
20
1 2 43 5 6 7 8 9 10Number of Points in Weighted Mean
Dat
e (m
.y.)
95%
Con
fiden
ce (
2σ)95% Confidence
(2σ)
a)
b)
Fig. 3. (a) Uncertainties associated with trace element analyses as a
function of number of repeated measurements made in a homoge-
neous compositional monazite domain. Data from consistency stan-
dard GSC-8153 tabulated in Table 1. Uncertainties are 2r, and shown
as percentages of total concentration. Analytical conditions: 600 s,
200 nA, 15 kV, gold coating. (b) U–Th–Pb date and 95% confidence
interval as a function of number of measurements made in a homo-
geneous compositional monazite domain. Data from Table 1. Note:
five to ten analyses are sufficient to stabilize uncertainty and date. For
standard GSC-8153 (ca. 500 Ma), 2r short-term random error of 5
m.y. is achieved with 6 analyses.
At the beginning of each analytical session (i.e.,
each time a monazite calibration is made), it is im-
portant that at least one, and preferably several, stan-
dard grains be dated along with the unknown grains.
In the best situation, this would be a standard grain for
which trace element compositions and the geological
age have been constrained independently. However,
such standards are not currently available. For the
present, analyses are made from a standard with rea-
sonably well-known age, here called a bconsistencystandardQ. These results are used to constrain day-to-
day variability and long term reproducibility. During
the infancy of microprobe dating, it is useful for
identical bconsistency standardsQ to be used in differ-
ent microprobe laboratories in order to compare tech-
niques and results.
4. Uncertainty considerations
As with all geochronological or geochemical analy-
ses, error analysis is critical for evaluating the signifi-
cance or usefulness of the results. For many types of
analyses, the total error is conveniently broken into two
components: precision and accuracy. For microprobe
monazite geochronology as proposed above, there are
at least three error components: (1) short-term random
errors (counting uncertainty); (2) short-term systematic
error (background, sample coating and calibration
effects); and (3) long-term systematic errors.
Assuming that repeated analyses are made within a
single compositional domain, random error includes a
variety of factors including X-ray production and
counting variation, spectrometer reproducibility, ther-
mal effects during analysis, current variation, counter
drift, subtle compositional variation, and others (Pyle et
al., 2005). Of these, X-ray counting is probably the
most significant. Error in age estimates due to counting
uncertainty can be quantified by propagating estimated
X-ray counting uncertainty first, through the equations
used in computation of elemental concentration and
then, through the age equation. The magnitude of the
propagated counting uncertainty varies with count rate
(a function of concentration and acquisition parameters)
of the critical elements, Th, U, and Pb, and as shown by
a number of workers, can be quite large for a single
trace element analysis, i.e., greater than 50 m.y. (Pyle et
al., 2005). However, this uncertainty is significantly
reduced when dates are based on multiple analyses
within a single compositional domain, rather than eval-
uating the error on a single point acquisition. Common-
ly, a 2r SDOM on the order 1.0% for U, Th, and Pb
(and less than 10 m.y. when propagated through the age
M.L. Williams et al. / Chemical Geology 225 (2006) 1–158
equation) can be obtained from as few as five measure-
ments. Other contributions to short-term random errors
can either be minimized or managed to some degree.
For example, laboratory temperature and detector pres-
sure can be controlled. Analytical routines can be de-
veloped such that spectrometers are stationary during a
series of measurements, and gold coating can substan-
tially reduce surface damage and instabilities (electrical
and compositional) within the excitation volume (Jerci-
novic and Williams, 2005).
The SDOM, i.e. standard deviation of the mean
(Taylor, 1997; Bevington and Robinson, 2003), is a
very useful estimate of random error for multiple mea-
surements from individual compositional domains. Es-
sentially, the SDOM evaluates the confidence interval
associated with a quantity obtained by averaging re-
peated samples of a single population. That is, it
describes the deviation of successive estimates of the
mean taken from the same population. It is essential
that the analyses are carried out in a single composi-
tional domain, or in statistical terms, that the micro-
probe has sampled a single (normally distributed)
population. It is for this reason that compositional
Table 1
Typical microprobe monazite data set from one homogeneous domain of co
Consistency Standard: GSC-8153Pt
Th 1σ U 1σ
1 64,586 621 2519 302 64,570 621 2442 303 64,738 623 2589 314 64,561 621 2475 305 64,677 622 2465 306 64,411 620 2440 307 64,726 623 2541 308 64,766 623 2436 309 64,779 623 2476 3010 64,832 624 2465 30Simple Mean 64,665 622 2485 30Std-Dev 129 50Weighted Mean 64,664 248495% Conf. 197 9SDOM 41 16Date (From trace element weighted means)
Propagating Trace uncertainties through age equa1 Weighted Uncertainty2 SDOM-Trace Elements
With Bkg Uncert.^ 64,664 393 2484 19
Ten trace element measurements were made in determining the date for this
using the method of Taylor (1997). SDOM=standard deviation of the mean
trace element data. Measurements were done at 200 nAwith 600 s count tim
be 1% (see text for discussion).
*Data in gray are typically not shown or calculated; domain age and
^Background uncertainty (short-term systematic uncertainty) includes 1% u
maps, not BSE images, are so critical. We use SDOM
to estimate uncertainties associated with repeated trace
element analyses (i.e. uncertainties associated with a set
of Th, U, Y, and Pb analyses in one domain), and then
propagate these uncertainties through the age equation
in order to estimate the short-term random error asso-
ciated with a date for a particular compositional do-
main. We have compared SDOM associated with
repeated compositional analyses to uncertainties deter-
mined by propagating counting statistical error and
found them to be similar if not identical in most cases
(Table 1). Williams et al. (1999) showed this same
similarity for repeated dates determined from single
compositional domains. The similarity reflects the fact
that the short-term random error is dominated by count-
ing uncertainty. When the SDOM is larger than the
propagated error from counting statistics, one might
suspect that fine compositional heterogeneities are sig-
nificant (i.e., see Seydoux-Guillaume et al., 2003) or
that other components of short-term random error have
not been minimized.
Table 1 shows a summary of several methods of
estimating the short-term random error associated with
nsistency standard GSC-8153
May 26, 2005
Pb 1σ Date* 1sig* 2sig*
1626 11 497 8.1 16.31602 11 492 8.1 16.21599 11 486 8.0 16.01632 11 500 8.2 16.41600 11 490 8.1 16.21604 11 493 8.1 16.31624 11 495 8.1 16.21615 11 494 8.1 16.21613 11 493 8.1 16.21645 11 502 8.2 16.41616 11 494 8.1 16.2
15 4.71616 494
3 2.6 5.25 1.5 2.9
494tion:
2.4 4.82.1 4.2
1616 7 494 5.1 10.2
domain. Weighted mean and 95% confidence interval were calculated
of the ten measurements. Date was calculated from weighted means of
e. Background was determined by regression; uncertainty estimated to
uncertainty are calculated from trace element weighted means.
ncertainty on regressed background estimate (see text for discussion).
3 The goal here is to illustrate the components of uncertainty. The
absolute magnitudes depend strongly on the particular electron mi
croprobe utilized, the composition of the particular monazite, and on
analytical conditions. In addition, some of the numbers reported in
Fig. 3 were produced as the techniques were evolving and are
somewhat larger than what might currently be expected.
M.L. Williams et al. / Chemical Geology 225 (2006) 1–15 9
trace element analyses and with calculated dates from a
relatively homogeneous monazite standard. Dates and
propagated uncertainties are included for individual
analyses for illustration here (grey-shaded area), but
are not recommended for general presentation. Presen-
tation data would generally come from the data includ-
ed in dark box. Trace element concentrations for each
compositional domain are calculated from the weighted
mean of the individual analyses. However, because
uncertainties are similar from analysis to analysis, sim-
ple means are nearly identical to weighted means.
Uncertainties associated with trace element analyses
and the calculated date can be calculated from the
weighted data (Taylor, 1997) or can be estimated
using the SDOM. In this case, the SDOM associated
with the data is significantly smaller than the weighted
uncertainty (1.5 vs. 2.6 1r). We suspect that this
reflects a component of positive error correlation in
the age equation. No correlation was assumed in prop-
agating uncertainties, but correlations would be inher-
ently included in the SDOM or the individual dates.
Short-term systematic error is reflected in day-to-day
reproducibility (i.e., from analytical session to session),
but not in a single set of analyses. The largest of these
uncertainties involves background estimation (see also
Jercinovic and Williams, 2005). If background values
are estimated on the basis of high-resolution wave-
length scans, then uncertainties arise from high-fre-
quency noise in the scan, from differences in
regression models, from choice of domains included
in the regression, and others. Work is in progress to
characterize and limit these uncertainties as much as
possible by improving the regression and analysis soft-
ware and procedures, and also by establishing the op-
timal conditions for scan acquisition (number of points,
dwell time, scan range, etc.). However, repeated anal-
yses using procedures summarized in Jercinovic and
Williams (2005) suggest that uncertainties in the back-
ground estimates based on regression are on the order
of 0.5–1.0%. These uncertainties can be propagated
through trace element concentration and age calcula-
tions, but the various uncertainties are likely to be
correlated to some extent, and the degree of correlation
can strongly affect the result. Assuming negative cor-
relation (worst case scenario), background uncertainties
of 0.5–1.0% can lead to a total short-term error of
approximately twice the magnitude of the short-term
random error. It should be noted that if background
values are not based on scanning, but instead on two-
point linear estimation, errors associated with trace
element analyses can be very large and propagate to
age uncertainties of 50 or 100 m.y. or more (Jercinovic
and Williams, 2005). Further, there is no way to eval-
uate the magnitude, or even direction, of the error.
Additional contributions to short-term systematic error
involve variations in coating thickness and continuity,
as well as conductivity variation in the sample itself.
Incorrect calibration of the instrument presents another
potential source of short-term systematic error, which
can be easily reduced by evaluating results from a
bconsistency standardQ (see below).
Short-term systematic error is, to a first order,
assessed by comparing consistency standards, of similar
composition to the unknown, over a period of time
involving a number of calibrations, sample coatings,
and background estimations. It is recommended that
consistency standards be analyzed before and after
each analytical session. Fig. 4 shows results from a
single relatively homogeneous standard, GSC-8153,
over a period of several months. Each date reflects 4–
10 analyses in a small area of the standard. Dark error
bars represent 2r, short-term, random errors, determined
by propagating uncertainties associated with each trace
element (Th, U, Pb) through the age equation. The
weighted mean of dates including only short-term ran-
dom errors (498F3) yields a large and unsatisfactory
MSWD (N15) (Wendt and Carl, 1991), indicating that
error associated with individual dates has been under-
estimated. The variation, from analytical session to an-
alytical session, reflects the short-term systematic error
(primarily background estimation and variation in con-
ductive coating). Gray error bars (Fig. 4) represent the
total short-term error (i.e. count-related and 1.0% back-
ground uncertainty) propagated through the age equa-
tion. These estimates characterize essentially all of the
deviation in the total population (MSWD=2.6).3 The
small amount of error not included (i.e. the fact that the
MSWD is not even smaller) probably reflects a combi-
nation of small session-to-session variations, perhaps
dominated by variations in gold coat quality and
thickness.
Long-term systematic error concerns the overall ac-
curacy of the age estimate and incorporates systematic
errors that are reproducible from session to session.
These include uncertainty in the quality and character-
ization of standards, the quality of interference algo-
rithms, the accuracy of ZAF factors, and others
(including dead time correction, beam current measure-
-
450
460
470
480
490
500
510
520
530
540
550
Mean with 2SD498 +/- 8 Ma
Weighted Mean (w/ 95% conf.)498 +/- 3 Ma
Dat
e (M
a)
Session3/29/05 5/2/05 5/21/05 6/2/05
Consistency Standard - GSC-8153
Short-tern random error
Total short-term error (including bkg. error)
Fig. 4. Dates from consistency standard, GSC-8153 (ca. 500 Ma, W. Davis, personal communication, 2005) over a period of months. Black error
bars include only short-term random error (counting uncertainties). Gray error bars include both counting uncertainties and uncertainties associated
with background determination (see text for discussion). The weighted mean of all dates is 498F3 Ma (light gray inner rectangle). The MSWD
(Wendt and Carl, 1991) is 15 if only short-term random (counting) errors are included, and 2.6 if short term systematic (background) errors are
included. Note that many workers take a value of MSWDb3 to signal an acceptable weighted mean or isochron (Wendt and Carl, 1991). The two-
sigma standard deviation of all means is 8 m.y. (darker gray outer rectangle).
M.L. Williams et al. / Chemical Geology 225 (2006) 1–1510
ment, decay constants, etc.) as well as assumptions
regarding the electron microprobe analysis, especially
at high sample current in materials that have low bulk
thermal and electrical conductivity. Long-term system-
atic error cannot be evaluated by examining the distri-
bution of analyses alone. Therefore, potential sources of
systematic error should be reduced to a negligible level
independently by better characterization of standards,
improved analytical protocols, etc. However, because
standards tend to contain high concentrations of the
element(s) of interest (10s of wt.%), uncertainties asso-
ciated with the composition of the standards are rela-
tively insignificant. The true accuracy of the interpreted
age can only be assessed by investigating well-dated
standards. Standard characterization is currently under-
way, but as noted above, it is difficult to compare the
results from different geochronologic techniques be-
cause the actual volume of material that is investigated
is different from technique to technique.
5. Presenting and integrating results
A single date and error estimate should be reported for
each monazite compositional domain. As noted above,
we recommend that individual analyses be referred to as
bmeasurementsQ or banalysesQ, but not as dates. Al-
though computationally feasible, it may not be useful
to report a date or error for each analysis (similarly, error
is not reported for individual blocks during isotopic
analysis). In fact, such uncertainties are misleading in
that they suggest a very low precision that should not be
compared with results of other geochronologic techni-
ques (see below). This is consistent with the approach
used in many other analytical techniques, where individ-
ual measurements are accumulated until an acceptable
level of precision has been achieved (e.g., IDTIMS).
Results (i.e., the mean, or weighted mean, date and
2r error) associated with a set of analyses within a
single monazite compositional domain are represented
by a normal probability distribution with an area of
unity (Fig. 5a,b). The width of the Gaussian distribution
is a direct graphical representation of the short-term
random error (i.e. SDOM of trace analyses propagated
through the age equation). Results from multiple com-
positional domains can be shown on the same plot (Fig.
5b) as results from different monazite grains (Fig. 6).
Interpretations concerning which of the distributions
(compositional domains) can or should be grouped as
a single geologic event can be made on a purely statis-
tical basis by a Chi-squared test: i.e., at what confidence
can two sample distributions be said to represent the
same population? However, these interpretations are
perhaps best initiated on the basis of textural, micro-
structural, and compositional arguments. Commonly,
monazite can be assigned to generations based on
texture, fabric, and composition before the trace ele-
ment analyses are carried out. Regardless of how
groupings are established, weighted means can be cal-
2000
1980
1960
1940
1920
1900
1880
1860
184099W-34-2
m2
1922 +/-10 Ma(random error)n=5
Ma
5 µm m2
Th Mα
550
530
510
490
470
450Ma Consistency Std. (GSC 8153)
495 +/-2 Ma (random error)n = 7
3-month mean (496 Ma) with 2x standard deviation (8 m.y.).
core
rim
1750
1950
1775
1800
1825
1850
1875
1900
1925
a
b
Fig. 5. (a) Single monazite date from a small (8–10 Am diameter) monazite inclusion in garnet. The date is represented by a Gaussian distribution
calculated from a set of five analyses (circles) from a single compositional domain along with the random error for that set of analyses. The
random error is calculated from the standard error of the mean for the trace element analyses, propagated through the age equation. Square shows
the location of the background scan. The date also includes results from a consistency standard (GSC-8153) that was gold-coated with the dated
sample and analyzed in the same analytical session. It is also recommended to include compositional maps showing the domain of interest and
the location of the analyses that make up the date. (b) Dating multiple domains within a single monazite crystal. Squares represent location of
background scans. Circles represent trace element analytical spots. The number of analyses within each domain is determined by the required
precision or by the amount of area available for analysis. Note that here, only four or five analyses in each domain are required to demonstrate
that the domain dates are significantly different. Note: elongate monazite are aligned in the fabric of the (ca 1850 Ma) Legs Lake shear zone
(Mahan, 2005).
M.L. Williams et al. / Chemical Geology 225 (2006) 1–15 11
culated with associated errors to represent the compos-
ite results. As a matter of terminology, one might
denote an individual distribution as a bdateQ (i.e., a
calculated number) and a weighted mean as an bageQ,that is, a number with interpreted geologic significance.
However, individual dates (distributions) might also be
interpreted as ages.
In addition to the presentation of a date for each
compositional domain, the results obtained on the
bconsistency standardQ should also be presented or
reported. This allows a measure of confidence in the
results, at least compared to other results from the same
laboratory. However, because background estimates are
made separately on the unknown and the consistency
Fig. 6. Example of multi-monazite age calculation. Interpreted age of exhumation of highgrade granulites along the Legs Lake shear zone,
Saskatchewan (Mahan, 2005). High-Y rims are interpreted to have grown during decompression and garnet consumption. The age (1850 Ma) is
calculated as the weighted mean of four dated high-Y rim domains (approximately 5–10 Am wide). The 2r propagated random error is 8 Ma;
propagated random error and short term systematic (i.e. background) error is 17 Ma (see text for discussion). Inset: results from consistency standard
(GSC-8153) and multi-month running average with 2r standard deviation.
M.L. Williams et al. / Chemical Geology 225 (2006) 1–1512
standard, the results from the consistency standard
cannot be directly used to adjust the results from the
unknown (as might be done on an X-ray fluorescence
spectrometer). Fig. 6 represents a suggested microprobe
monazite presentation format. The data come from
Mahan (2005), and represent an attempt to date exhu-
mation of a large granulite facies terrain in northern
Saskatchewan. High-Y monazite rims are interpreted to
have grown during decompression and garnet resorp-
tion (Mahan, 2005). The figure shows compositional
maps (processed with the same look-up table) and the
locations of all analyses. Each rim domain corresponds
with a single normal distribution, and a single monazite
date. The weighted mean of several domains represents
the interpreted age for the monazite rim growth (and
thus the retrograde metamorphism and deformation).
M.L. Williams et al. / Chemical Geology 225 (2006) 1–15 13
Also shown are two dating sessions, before and during
analysis, of the consistency standard, in this case, GSC-
8153 (ca. 500 Ma; William Davis, personal communi-
cation, 2005).
6. Discussion and conclusions
The essence of the monazite dating strategy
involves: (1) delineating homogeneous compositional
domains by X-ray mapping in monazite crystals and
identifying those domains that can provide constraints
on a particular geologic process or question, (2) ana-
lyzing (bsamplingQ) the composition of each relevant
domain a number of times (as dictated by the required
precision) in order to produce a single mean date and
error estimate for that domain, and (3) combining se-
lected dates from separate domains in specific structur-
al/petrologic settings, using a weighted mean or other
statistical procedure, in order to place constraints on
geologic features or events of interest. This approach is
similar to that used by other geochronological or geo-
chemical techniques. By IDTIMS geochronology, mul-
tiple measurements of the same unknown isotopic ratio
are repeated (or continuously sampled) to obtain the
required precision. Then, results from multiple fractions
are plotted on appropriate diagrams and commonly
combined (regressed) to calculate a best age of a par-
ticular rock or event.
It might seem logical, at least for some geochrono-
logical techniques, to begin by collecting a general data
set from a number of grains in order to get a sense of
the range of dates preserved and to assess the statistical
significance of each, i.e., top-down approach. For mon-
azite geochronology of metamorphic rocks, however,
this has not proven to be the best strategy. As noted by a
number of workers, monazite would be expected to
grow at a number of points along a P–T path (Pyle
and Spear, 2003a; Foster et al., 2004; Gibson et al.,
2004). Most metamorphic reactions probably produce
or consume a small amount of monazite because dif-
ferent silicate phases contain different amounts of rare
earth elements. In addition, fluid flow or infiltration
events, perhaps linked to deformation pulses or meta-
morphic reactions, may also lead to monazite growth or
dissolution. Ultimately, a very broad array of monazite
generations (and monazite ages) may be present in a
suite of metamorphic rocks. The critical goal is to link
some phase of monazite growth to a deformation or
metamorphic event so that the date can be interpreted to
constrain the age of the event. The most important
monazite generations may not be the most abundant,
and in fact, important generations may be extremely
rare or even unique in a particular thin section. Because
of the large error associated with individual dates,
important populations may be obscured in composite
data sets.
For these reasons, the bbottom-upQ approach is best
suited to dating deformation and metamorphic events.
By identifying essentially all monazite grains in a thin
section, or suite of thin sections, it is possible to evaluate
a large number of grains and distinguish populations on
the basis of textural, microstructural, or compositional
setting from the outset. Then, once populations have
been identified, a strategy for dating can be developed
based on the particular tectonic problem being
addressed. If necessary, statistical arguments can be
used to evaluate whether two populations are signifi-
cantly different at some level of confidence. In many
situations, however, it may never be necessary to com-
bine the results from separate populations of monazite.
Microprobe monazite geochronology occupies a
unique place within the spectrum of geochronologic
techniques. The spatial resolution of the electron
probe and the in-situ nature of the technique make it
ideal for constraining the age of small monazite
domains, especially those that can be linked to geologic
events in the host rock. The precision and accuracy of
the technique are improving with developments in an-
alytical software and hardware, standards, and proce-
dures, but it is likely that it will never have the precision
of isotopic methods such as IDTIMS. In addition, there
is no means for assessing the concordancy or internal
consistency of microprobe dates, and thus, the accuracy
of the results may always have a greater measure of
error compared with isotopic methods. As with all
analytical data, careful attention to error is critical.
The analytical strategy and presentation format pro-
posed here are particularly appropriate for evaluating
the number and general distribution of monazite growth
events and for asking questions such as, bat what
confidence can one date be interpreted to be different
than anotherQ? However, the impact of the results can
be significantly increased by combining the microprobe
results with results from a technique such as IDTIMS
with great analytical precision but less spatial resolu-
tion. In many cases, the two techniques can be com-
pletely complementary (Baldwin et al., in press).
Isotopic methods can, under optimal circumstances,
provide the absolute accuracy of the chronology,
while microprobe results can identify and clarify
mixed ages and incorporate the implications of small
rim or core domains that may be minor in volume but
critical for constraining some aspect of the geologic
history.
M.L. Williams et al. / Chemical Geology 225 (2006) 1–1514
Acknowledgments
Research for this paper was partially supported
under NSF grant: EAR-0004077 for the development
of hardware, software, and techniques of microprobe
monazite analysis. In addition NSF grant EAR-
0310215 provided an opportunity to test and refine
this methodology. We thank Bill Davis, Geologic Sur-
vey of Canada, for helpful discussions and for provid-
ing our current consistency standard, GSC-8153.
Discussions with S.A. Bowring, B. Davis, P. Bickford,
D. Gibson, P. Dahl, and many others were extremely
helpful. We thank both anonymous reviewers for in-
sightful comments and suggestions. [RR]
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