format and philosophy for collecting, compiling, and reporting

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


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


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.


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


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


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.


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).


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).


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.


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).


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.


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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