Full text of DOI:10.1007/s004100100298

Contrib Mineral Petrol %2002) 142: 436±448
DOI 10.1007/s004100100298
Catherine Ginibre á Andreas Kronz á Gerhard Worner
High-resolution quantitative imaging of plagioclase composition
using accumulated backscattered electron images:
new constraints on oscillatory zoning
Received: 25 October 2000 / Accepted: 8 July 2001 / Published online: 30 August 2001
Ó Springer-Verlag 2001
Abstract Oscillatory zoning in plagioclase is investigat- thermal minerals %Shore and Fowler 1996). The mineral
ed at small scale %£10 lm) using accumulated back- most frequently investigated for oscillatory zoning is
scattered electron %BSE) images as high-resolution plagioclase because it is ubiquitous in igneous rocks
imaging method. Combined with electron microprobe and its zoning in anorthite content is readily observed
quantitative analysis, gray-value pro®les across these under optical microscope. ``Oscillatory zoning'' in pla-
images can be calibrated for An-content with a resolu- gioclase is found in various volcanic rocks ranging in
tion of 0.5 mol% An. Applied to oscillatory-zoned composition from basaltic %Anderson 1984; Kuritani
crystals, this new application of BSE imaging allows 1998), to andesitic and rhyolitic %Nixon and Pearce
better characterization of zoning patterns along a pro®le 1987; Pearce and Kolisnik 1990; Singer et al. 1995) as
and quanti®cation of wavelength, amplitude, and shape well as in intrusive rocks %Wiebe 1968; Loomis and
of the oscillations. We also obtain high-resolution in- Welber 1982; Blundy and Shimizu; 1991; Brophy et al.
formation on the morphology of growth zones bound- 1996).
aries. This approach allows us to better classify the
Zoning in plagioclase is characterized by changes in
di€erent types of ``oscillations'' and concentric zoning. An-content, with variations generally ranging from 1 to
Dissolution is more frequent than usually recognized. over 30 mol% An. The analytical methods used to
Major resorption surfaces crosscut several growth zones. characterize this zoning in previous studies and their
Irregular 5±10-lm saw-tooth zones are delimited by characteristics are summarized in Table 1. Quantitative
faint wavy dissolution surfaces and must be distin- pro®les with analytical precision of ‹1 mol% An at
guished from small-scale oscillations %£1±3 lm) with variable spatial resolution %£3 lm) are obtained by
straight boundaries. This suggests at least two mecha- electron microprobe %EMP) point analysis. Quantitative
nisms for the formation of these zoning patterns: faint EMP analyses are also commonly used to calibrate the
oscillations are probably caused by local kinetic control other quantitative methods, such as EMP X-ray pro®le
whereas wavy dissolution surfaces involve magma of Ca, Na %Kuo and Kirkpatrick 1982; Loomis and
chamber dynamics.
Welber 1982; Smith and Lofgren 1983; Kuritani; 1998),
and laser-interferometry %Nixon and Pearce 1987; Pearce
et al. 1987; Pearce and Kolisnik 1990). Other techniques
such as optical microscopy and Nomarsky interference
contrast microscopy %NDIC) provide high-resolution
images of zoning %Anderson 1983; Nixon and Pearce
1987; Pearce et al. 1987; Pearce and Kolisnik 1990;
Singer et al. 1995). However, none of these methods
combine two-dimensional morphological and quantita-
tive compositional information. For this reason, most of
the studies combine imaging %NDIC) and compositional
measurement %EMP point analysis and/or laser inter-
ferometry). This has the disadvantage that the pro®le
and the image have di€erent spatial resolutions, which
prevents an accurate correlation. As a result, very few
studies quantitatively investigate in detail small-scale
oscillations £10 lm in natural samples %Anderson
1984).
Introduction
One of the most spectacular zoning patterns in crystals
consists of ®ne concentric euhedral zones of contrasting
compositions, usually referred to as ``oscillatory zon-
ing''. It is common in many igneous as well as hydro-
C. Ginibre %&) á A. Kronz á G. Worner
GZG, Abteilung Geochemie, Goldschmidtstr. 1,
37077 Gottingen, Germany
E-mail: cginibr@gwdg.de
Editorial responsibility: T.L. Grove

437
Table 1 Comparison of methods used for the characterization of compositional zoning in plagioclase
Method
Imaging
Quantitative analysis
Optical microscopy
Good contrast; spatial resolution of about
1 lm; for details varying with depth, the
limiting factor is the thickness of the
thin section %30 lm)
Di€erences of 1±2 mol% An can be
measured. However, the values are
determined for each zone. No continuous
pro®les can be obtained
Electron microprobe
quantitative analysis
Nomarski di€erential
interference contrast
Quantitative mapping would be
Pro®les: spatial resolution generally coarser
than 5 lm. Compositional resolution: 1% An
No quantitative information
time-consuming and is never used
Imaging of the surface. Very good contrast,
spatial resolution comparable to that of
optical microscopy. The image is sensitive
to etching process and to the state of
the surface before etching
Laser interferometry
2-D information given by parallel
pro®les %interference fringes)
Pro®les must be calibrated using EMP
quantitative analyses. Resolution: 2 lm,
2.5 mol% An
Wavelength dispersive
spectrometry pro®le %Ca)
Mappings are time-consuming and
have lower spatial resolution than
other imaging methods, rarely used to
characterize plagioclase zoning
Pro®les must be calibrated using EMP
quantitative analyses. Resolution: 2±5 lm,
1±2 mol% An
Backscattered electron
imaging
Imaging of the surface of the sample
%1 lm). The signal/background ratio
of normal BSE images is low but can
be improved by accumulating several
images of the same part of the sample.
Spatial resolution: 0.5 lm
Pro®les must be calibrated using EMP
quantitative analyses. Compositional
resolution £ 0.5 mol% An. The quantitative
information is two-dimensional so that
pro®les may be directly compared with
the zone morphology
Most studies distinguish irregular or rounded re- %1980). These are faint oscillations %1±2 lm/1±2% An)
sorption surfaces, often correlated between di€erent and are also interpreted as being a result of kinetic
crystals %Loomis and Welber 1982), from euhedral os- control.
cillatory zoning, which cannot be correlated between
Despite this abundant literature on the topic, the in-
crystals. Many authors attempted to interpret zoning in terpretation of oscillatory zoning remains controversial.
plagioclase in terms of processes that occur in the One reason is the lack of an unequivocal de®nition of
magma chamber %see reviews in Pearce 1994; Shore and oscillatory zoning. It appears that each author uses the
Fowler 1996).
term in a di€erent sense and there is consensus neither
Major resorption surfaces are generally attributed to on the shape, nor on the wavelength and amplitude of
profound changes in temperature, pressure, melt com- the variation. Whereas some authors %e.g. Smith and
position, and water content in the magma at large scale Brown 1988) consider only periodic oscillations on a
caused, for example, by magma recharge %Nixon and micrometer scale, others consider that these oscillations
Pearce 1987; Davidson and Tepely 1997). Minor re- ``need not need to be regular or harmonic'' %Shore and
sorption surfaces are attributed to local e€ects of minor Fowler 1996). Between these extremes, authors describe
changes in the same parameters caused by magma dy- or model more or less regular ``oscillations'', ranging
namics %convection). ``Oscillatory zoning'' is generally from 1±5 lm and 1±2 mol% An to 10±100 lm
attributed to local kinetic e€ects in a boundary layer at and 5±15 mol% An. The shape of many pro®les
the crystal±melt interface. Dynamic e€ects and recharge described consists mostly of asymmetrical variations or
processes are generally well accepted, although rates and ``saw-tooth patterns''.
details of such processes are still poorly understood.
These problems in de®ning oscillatory zoning are
Kinetic e€ects are even more dicult to constrain and probably caused by %1) the variability of such zoning
have been theoretically and numerically modeled %Haase patterns in plagioclase and in other minerals, and
et al. 1980; Allegre et al. 1981; Lasaga 1982; Loomis %2) the analytical diculty in characterizing small-scale
1982; Ortoleva 1990; L'Heureux and Fowler 1994; Wang zoning patterns. A good characterization of natural
and Wu 1995; L'Heureux and Fowler 1996a, 1996b). zoning should provide %1) high-resolution quantitative
Other interpretations involve the periodic destruction of An pro®les to be compared with An pro®les calculated
this boundary layer %Loomis 1982; Anderson 1984). by numerical models, and %2) two-dimensional infor-
Numerous experimental studies of plagioclase equilibria mation that shows the morphology of the zones, which
%Yoder et al. 1957; Johannes 1978; Housh and Luhr may help to distinguish possible resorption surfaces
1991) and growth kinetics %Lofgren 1974, 1980; Kirk- from growth zones. None of the techniques discussed
patrick et al. 1979; Muncill and Lasaga 1987, 1988) have above satis®es both conditions together.
been performed and used to explain zoning patterns.
The present study demonstrates that accumulated
Oscillations in experimentally grown plagioclase are BSE images provide a powerful quantitative imaging
described in one single run of Lofgren's experiments tool for plagioclase major element zoning. The spatial

438
resolution is £1 lm and thus equivalent to or even Syenite cumulate from the Laacher See
better than other imaging methods %NDIC). Further-
more, gray scales of such BSE images can be calibrated The Laacher See Tephra %Eifel, Germany) consists of
in terms of An content. The compositional resolution 6.3 km3 ma®c to highly di€erentiated phonolite erupted
can be as small as 0.5 mol% An. The quantitative 12.9 ka ago and represents an inverted zoned magma
pro®les obtained can be compared directly with the chamber %Worner and Schminke 1984a, 1984b; Bogaard
two-dimensional information.
1995; Harms and Schminke 2000). Late in the eruption,
This approach has been used here to study zoning crystal-rich ``nodules'' were ejected. These cumulates are
patterns in a typical ``oscillatory-zoned'' plagioclase interpreted by Tait %1988) and Tait et al. %1989) as the
%andesine) from a dacite %Parinacota volcano, Chile). crystallized wall of the magma chamber. Compositions
We will re®ne the classi®cation between small-scale range from ma®c %pyroxene + amphibole) to felsic
oscillations and larger-scale resorption events %Pearce %syenite cumulates). Oscillatory zoning in plagioclase
and Kolisnik 1990), and provide a tool to better un- crystals is very rare in these cumulates. Sample 15616 in
derstand magma chamber processes. We distinguish %1) one of the few where ®ne oscillatory zoning is present in
low amplitude oscillations that are possibly true peri- plagioclase. It belongs to group 1-intermediate-type 2 of
odic oscillations, %2) saw-tooth patterns, which make Tait %1988) and contains two feldspars, pyroxene, and
up most of the usually described ``oscillatory zoning'', amphibole, and small amounts of interstitial glass. The
and %3) major resorption surfaces. The newly de®ned investigated crystal is shown in Fig. 1. The core is ex-
zoning types can be better interpreted in terms of re- tensively patchy zoned, similar to crystals found in the
sponsible dynamic and kinetic processes, as recorded in Laacher See pumices, and may have crystallized before
the growing crystals. The other sample studied here is accumulation. However, the rim, intergrown with other
a cumulate plagioclase from a phonolitic magma crystals %pyroxene, plagioclase), must have crystallized
chamber %Laacher See, Eifel, Germany). It shows in situ. This rim is strongly normally zoned with weak
only low-amplitude oscillations, probably from kinetic superimposed oscillations, which can be seen under the
controls.
We will ®rst present our samples, techniques and re-
optical microscope.
sults and then compare them to the existing model for
oscillatory zoning and discuss the relevance of these
models for zoning patterns of plagioclase in natural
systems.
Analytical techniques
All analyses were performed on a JEOL 8900 RL elec-
tron microprobe at Gottingen. Zoning patterns were
documented by backscattered electron %BSE) images.
Details of the technique are given in the Appendix. The
accumulation of several images of the same area of the
Samples
Dacite from the Parinacota volcano
Parinacota volcano %north Chile) belongs to the
Central Volcanic Zone of the Andes and has been
investigated by Worner et al. %1988), Davidson et al.
%1990), and Worner et al. %2000). It consists of a
Pleistocene to Recent calc-alkaline stratocone with
compositions ranging from basaltic andesites to
rhyodacites. We chose a dacite from a ``Old Cone''
lava dome %PAR-130, see Worner et al. 1988) for our
investigation. The mineralogy consists of plagioclase,
amphibole, two pyroxenes, rounded biotite, and Ti±Fe
oxides in a groundmass of glass with microliths of
pyroxene, plagioclase and alkali-feldspar. Plagioclase
phenocrysts have compositions ranging from An25 to
An55. The phenocryst population consists of two
types. The majority comprises 1±2 mm large crystals
showing oscillatory zoning throughout the crystal with
only few resorption zones. Some smaller crystals show,
in addition, several more extensive resorption zones.
The crystal investigated here %PAR-130-P3) is repre-
sentative of the large oscillatory zoned phenocrysts.
Between various crystals of this type, however, we did
not observe an obvious correlation of individual
zones.
Fig. 1 BSE image of the cumulate LS 15616 showing the analyzed
plagioclase crystal P1. The box indicates the location of the high-
resolution image %Fig. 2)

439
sample increases the signal/noise ratio. Quantitative
point analyses of major elements are used to calibrate
the gray scale of the BSE-images in terms of An content.
An example of the high-resolution BSE image and An-
calibrated pro®les is shown in Fig. 2 for the Laacher See
sample %LS 15616). Gray scale pro®les with superim-
posed EMP quantitative point analysis are given in Fig. 3
for the Parinacota dacite %PAR 130-P3).
Results: ``oscillatory'' zoning patterns
The diversity of zoning patterns is seen in the pheno-
crysts from dacite PAR-130. One type %low amplitude
oscillations) is particularly well seen in the rim of the
cumulate crystal LS15616-P1.
The images and resulting pro®les have a composi-
tional resolution down to 0.5 mol% An and a spatial
resolution down to 0.5 lm. Characteristics of BSE im-
ages are compared with other analytical techniques in
Table 1. This shows that our approach is the only
method that allows quantitative two-dimensional docu-
mentation of the plagioclase zoning pattern with such
a spatial and compositional resolution at the scale of
interest.
Dacite PAR-130
Crystal PAR-130-P3 is shown as a BSE image in Fig. 3
along with a quantitative An pro®le and an An-cali-
brated gray scale pro®le from the accumulated BSE
images. These accumulated images and corresponding
pro®les are shown in detail in Fig. 4a, b. Comparison of
the detailed An pro®le with the two-dimensional image
shows various types of zoning patterns as described
below.
A few major resorption surfaces %R) are observed,
which cross cut several 5-to 50- lm-wide growth layers
at the corners of the growing crystal. They are charac-
terized by wavy, highly irregular layers of up to 5 lm
width, which are richer in An by 5±10 mol%. These are
similar to those obtained in dissolution experiments of
plagioclase %Tsuchiyama 1985; Johannes et al. 1994;
Nakamura and Shimakita 1998; Hammouda and Pi-
chavant 2000). However, compositional discontinuities
Fig. 3 a BSE-image of plagioclase crystal PAR-130-P3. Major
resorption surfaces are indicated by arrows. Dashed lines show
Fig. 2 a High-resolution BSE image and b corresponding An- the location of quantitative pro®les, thin-lined boxes represent the
calibrated gray scale pro®les of crystal LS15616P1. Despite location of the accumulated BSE images and thick-lined boxes the
polishing artifacts, small-amplitude oscillations %0.5% An) are part of the images shown in Fig. 4. b An-calibrated gray scale
seen both on the image and the three parallel pro®les. Sampling pro®le %line) and quantitative point analyses %squares). Details of
width %100 pixels) of the pro®les is shown on L1 %white dashed line) the gray scale pro®le are shown in Fig. 4a, b

440
Fig. 4 a High-resolution BSE
images and corresponding
An-calibrated gray scale pro®le
of PAR-130-P3. Examples for
the features described in the text
are indicated on the images and
on the pro®les. Major resorp-
tion surfaces %R) with calcic
overgrowth is best seen at
170 lm. Minor resorption
surfaces %r) separates individual
normal zones in saw-tooth
patterns %STR). The STR
present on this part of the
pro®le are very narrow %5 lm)
and thus not typically asym-
metrical. Small-amplitude
oscillations %LAO) are seen at
420 lm. b High-resolution BSE
images and corresponding
An-calibrated gray scale pro®le
of PAR-130-P3 continued. The
comparison of two parallel
pro®les between 510 and 610 lm
show the lateral variability of
the pro®les. Typical STR
pattern with superimposed
LAO is seen between 610 and
680 lm. High-frequency, high-
amplitude An variations %HFA)
with wavy zone boundaries
occur in the outermost 20 lm
grown during eruption
in crystals from PAR-130 never exceed 10 mol% An, in opposite sense %i in Fig. 4). The contact with the
contrast with discontinuities of up to 30 mol% An, previously grown zone is sharp and straight, suggesting
which are reported in the literature %Nixon and Pearce simple continued growth.
1987; Singer et al. 1995) in other natural samples.
Superimposed on the normal zones of STR, faint
The most striking zoning pattern is a Saw-Tooth repeated variations % £2 mol% An, £1±5 lm) with
pattern with Resorption %STR): this pattern consists of straight boundaries are recognized as Low Amplitude
repeated, mostly normally zoned growth layers, 5±20 lm Oscillations %LAO), both on the pro®le and on the im-
wide, separated by wavy boundaries followed by a sharp age. Amplitude and wavelength are close to the analyt-
increase in An. They are generally slightly rounded at ical resolution and, thus, it is not possible to determine
the crystal edges. A thin calcic line is often present at the whether these variations are truly periodic. However,
zone boundary and resembles that observed at major they seem more regular and periodic than STR and they
resorption surfaces. All these features indicate that these are, therefore, considered as possible true oscillations in
zone boundaries are in fact resorption surfaces. How- the following discussion.
ever, most of them represent only a minor resorption
The outermost 20 lm exhibit High-Frequency %3 lm
event %r in Fig. 4) because they a€ect only one growth in wavelength), high-Amplitude %10 mol% An) oscilla-
layer. The resulting An pro®le shows peaks that are tions %HFA). Although narrower, they are very similar
dominantly asymmetrical, and only some of the smallest to the STR type with a similar amplitude %5±8 mol%
peaks %in both width and An content) are almost sym- An) and a sharp wavy boundary, as well as very ®ne
metrical.
superimposed oscillations %LAO) within individual
Some growth layers at the same scale of 5±10 lm are zones. Again, recognition of the exact shape of the An
inversely zoned forming a saw-tooth pattern in the pro®le is limited by the short wavelength, close to the

441
Fig. 4b %Contd.)
spatial resolution. We interpret these zones as a special %Fig. 5b) shows two clear wavelengths at 21.2 and
case of STR, which is restricted to syn-eruption fast 10.6 lm. These zoning patterns can therefore be
growth %see Discussion).
regarded as true oscillations.
Cumulate LS15616
Discussion
Low-amplitude %0.5 mol% An) oscillations %LAO) are
also found in the rim of the plagioclase crystals of cu- The zoning patterns observed here are similar to oscil-
mulate sample LS15616, but with a larger wavelength lations described in the literature %Pearce and Kolisnik
%10±20 lm) than in PAR-130 P3 %Fig. 2). Zone bound- 1990). They include normal and inverse saw-tooth pat-
aries are straight and transitions are smooth. These os- terns %STR) with 10±20 lm width and 5±10% An
cillations are superimposed on a strong normal zoning amplitude, and low amplitude oscillations %LAO) with
%from An55 to An43). Again, the shape of the oscillations 1±20 lm wavelength and 0.5±2 mol% An amplitude.
is not clearly de®ned because of the low signal/noise Large discontinuities in the An pro®le, with up to 30±
ratio. In order to better characterize the nature of these 40 mol% An contrast %Nixon and Pearce 1987) and large
oscillations, we considered the residual signal obtained patchy resorbed zones are absent in our samples. Both
by subtracting the pro®le, averaged over 20 lm %wave- types %STR and LAO) are present within a single crystal
length of the oscillations), from the initial pro®le. The from the Parinacota dacite. By contrast, the rim of the
result is shown in Fig. 5a. The wavelength of the crystal from the Laacher See cumulate shows only LAO,
oscillations decreases slightly toward the rim. Fourier which have two superimposed wavelengths, which are
analysis of the residual pro®le between 60 and 140 lm larger than in PAR-130-P3 %21.2 and 10.6 lm).

442
zoning by local kinetic e€ects and to try to develop the
best numerical model for these oscillations. Several ex-
perimental %Lofgren 1974, 1980; Kirkpatrick et al. 1979;
Muncill and Lasaga 1987, 1988) and theoretical %Kirk-
patrick 1981; Baronnet 1984; Cashman 1990) studies
have shown the importance of kinetics in growth pro-
cesses. Crystal growth rate depends on melt supersatu-
ration or undercooling at the crystal±melt interface.
When the system is suciently undercooled with a cor-
respondingly high crystal growth rate, element di€usion
is too slow to replenish the melt at the interface. A
chemical boundary layer then develops, where the su-
persaturation is lower than in the bulk melt. This in-
¯uences the composition of the growing crystal. Kinetic
models of oscillatory zoning are based on this compe-
tition between interface and di€usion kinetics %see
review in Pearce 1994). These models, however, never
imply resorption because the melt is always saturated in
plagioclase. Because resorption at the scale of STR
zoning patterns %5±20 lm) has rarely been recognized in
previous studies, thermodynamic models that include
repeated destabilization of the plagioclase to explain
such oscillations have been rejected by most authors.
Our observations now show that ``oscillatory zoning''
in plagioclase is very variable in style and cause, and,
therefore, must be classi®ed as at least two di€erent
types: STR and LAO. Kinetic numerical models up to
now have considered observed ``oscillations'' of 1 to
10% An in amplitude and 1 to 100 lm in wavelength,
which apparently includes both STR and LAO types.
However, STR ``oscillations'' are not true oscillations
and exhibit evidence for repeated resorption at a scale as
small as 5±20 lm. Therefore, they cannot be explained
by existing kinetic models, which produce periodic os-
cillations and consider only growth. Models for STR
zoning patterns should include resorption and produce
non-periodic variations. Such kinetic models are pres-
ently not available. In contrast, LAO zoning may rep-
resent true oscillations for which kinetic models in fact
exist because they have a regular wavelength and do not
show observable resorption. Furthermore, LAO pat-
terns also occur in crystals grown in a quiescent envi-
ronment %cumulates) or superimposed on STR patterns,
thus favoring local kinetics over external thermody-
namic control.
Fig. 5 a Residual An pro®le of the crystal from LS515616: the
pro®le was smoothed by averaging the values over 20 lm and then
subtracted from the original signal. The resulting pro®le was also
smoothed by averaging over 2 lm in order to reduce the noise.
b Normalized power spectrum of the residual pro®le obtained by
fast Fourier transform. Two distinct wavelengths are recognized
both on the pro®le and on the power spectrum
Accumulated BSE images allow one to identify many
more resorption surfaces than are usually recognized,
separating zones as narrow as 5 lm. Only Nixon and
Pearce %1987) describe minor resorption surfaces every
10±20 lm. We found possible true oscillations without
resorption only with very low amplitude %LAO).
A similar classi®cation between small-and large-scale
oscillations was made by Pearce and Kolisnik %1990) in a
larger range of rock types. They distinguish small-scale
oscillations %type I), which they attribute to kinetic ef-
fects, from larger oscillations that show resorption %type
II) caused by changes in the bulk melt %temperature,
composition, etc). However, their type I generally has
saw-tooth-shaped pro®les and ranges in composition
from <1 to 10% An, which typically overlaps the range
of our STR patterns. Therefore, we suspect that their
classi®cation and interpretation may have overlooked
dissolution surfaces in type-I oscillations because of a
poorer resolution of the imaging method. We now dis-
cuss the relevance of theoretical models for the types of
zoning that we observed. We will show that kinetic
models do not apply to the most striking STR-patterns.
LAO-patterns, however can be explained by some
kinetic models whereas others are clearly inadequate.
In the recent literature on oscillatory zoning, there
seems to be a consensus to explain planar ``oscillatory''
We now discuss ®rst dynamic models for STR and
related HFA patterns, and then models that involve
local kinetic models for LAO zoning patterns. The
model of Loomis %1982), which involves both local ki-
netic and dynamic e€ects, is discussed for the interpre-
tation of the inverse zoning.
Saw-tooth patterns: equilibrium models and magma
chamber dynamics
Equilibrium models assume that the growing crystal is in
equilibrium with the surrounding melt. The dependence
of crystal composition on the physical %P, T) or com-

443
positional %water content, magma composition) param- resorption by Singer et al. %1995). For 100-lm-spaced
eters is determined by phase equilibria. Several studies resorption surfaces, they calculate that this could occur
have shown their in¯uence on An content of the crystal in laminar convection cells of 100 m diameter. Their
%Yoder et al. 1957; Johannes 1978; Loomis and Welber calculations applied to 10-lm-spaced resorption would
1982; Housh and Luhr 1991). Housh and Luhr %1991) give 10-m convection cells, which may be too small. In
investigated intermediate compositions and obtained a addition, laminar convection may not allow sucient
slope of the solidus of around 5 °C/% An.
mixing. The observation of ``R''-type resorption surfaces
Mechanisms thought to cause repeated changes in the and STR oscillations suggests that both are dynamically
environment of a growing crystal involve magma controlled, the width of the zones being related to the
chamber dynamics. %1) Repeated magma recharge re- nature and scale of convection.
sults in temperature increase, followed by composition
The HFA oscillations at the rim of the crystal cor-
changes if mechanical and chemical mixing is sucient. respond to the last phase of crystallization, during or
%2) Gradients in temperature and composition are ex- after eruption, where rapid growth rates are expected.
pected in magma chambers, at least in the thermal/ Kinetic processes will thus play a more important role
chemical boundary layer %Marsh 1989). Movement of there. However, the repeated resorption surfaces that
the crystals along these gradients by convection can suggest a dynamical origin of STR-type are also present
produce periodic changes in T, water content, bulk in HFA, suggesting a similar process. The narrower
composition, and, to a lesser extent, P, depending on the spatial scale at presumed higher growth rates indicates
scale of the convection.
much shorter time-scales. If this interpretation is correct,
The latter mechanism was proposed by Homma an increase in the turbulence of the magma prior and/or
%1932) to explain oscillatory zoning and has been during magma ascent and eruption could explain more
invoked more recently by some authors to explain rapid movements and changes in the magma composi-
repeated minor %Singer et al. 1995) or major %Pearce and tion and temperature at the contact of the crystals.
Kolisnik 1990) resorption surfaces. In contrast, large
In contrast to the complex resorption-rich zoning of
and prominent resorption with An variations of up to plagioclase from lavas, plagioclase crystals from La-
40% %Singer et al. 1995; Davidson and Tepley 1997) are acher See cumulates are characterized, at least in their
generally related to major magma chamber recharge outer part, by the absence of saw-tooth patterns and
events. We will show below that medium, non-periodic evidence of resorption. This is consistent with the
STR ``oscillations'' and their related small-scale resorp- absence of convection expected in the more quiescent
tion interfaces considered here can not be explained by environment where crystals accumulate. An alternative
magma recharge.
explanation could be that initial zoning patterns of
In sample PAR-130, STR ``oscillations'' exhibit higher amplitude, such as STR, have been almost com-
resorption interface at only 5-to 10-lm spacing. The pletely erased by di€usion in the crystal. However, we
dependence of plagioclase composition on pressure is observed these low amplitudes in the outer 200 lm of the
small. Any pressure changes, for example caused by to crystal whereas larger contrasts are seen in the core.
convection in typical magma chambers below strato- Furthermore, the time needed to compositionally
volcanoes, may reach 1 kb at most. This limits the e€ect equilibrate 20-lm-wide zones is >104 years at 1,100 °C
of pressure. The most plausible cause for resorption is, %Grove et al. 1984). It would be at least two orders of
therefore, thermal and compositional changes. For the magnitude larger at the temperature of phonolite
observed variations in An concentration %compositional %<880 °C, Worner and Wright 1984, Berndt et al. 2001).
shift £ 5 mol% An), the temperature dependence of An This is much longer than the time estimated for the
reported above would imply temperature di€erences of whole history of the Laacher See volcano %Tait et al.
only 5±25 °C.
1989; Bourdon et al. 1994).
If magma recharge were responsible for the STR
oscillations, then there would have to be hundreds of
small recharge events regularly timed during the growth Low-amplitude oscillations: kinetic models
time of any plagioclase crystal with only minor changes
in the melt composition. This is inconsistent with con- Before discussing the relevance of the models we would
ventional wisdom on the rate and volume of magma like to draw attention to two points. First, all kinetic
recharge events %Nixon and Pearce 1987; Davidson and models assume a boundary layer at the crystal±melt
Tepley 1997).
interface, which necessitates a suciently high crystal
High-frequency, small temperature changes imply, at growth rate and thus sucient undercooling. However,
a local scale, mixing, crystal dispersion, or the e€ect of a the undercooling of natural magmas is not well con-
thermal or compositional gradient. This is consistent strained but is likely to be rather small %Cashman 1990).
with the results of the trace element study in the same The existence of a boundary layer at the crystal±melt
crystal %Ginibre et al. 2001), which also argue for local interface has been reported by Bottinga et al. %1966) in
mixing. One possible process for this is convection plagioclase-bearing basalt. However, this occurs in an
within the magma chamber. Laminar convection has erupted lava and it is not clear whether this gradient
been suggested as an explanation of repeated minor existed over the whole crystallization history of the

444
crystal, or was formed only during eruption and rapid patterns at high growth rates, however, they do not
cooling. Second, as shown above, models that involve involve resorption. No small-scale symmetrical oscilla-
kinetics should be designed to only explain LAO pat- tions are reported in the results, but the model was not
terns and this restricts the range of amplitudes and designed to produce this type of oscillation.
wavelengths expected to be reproduced by the models.
The model of Allegre et al. %1981) also uses a phe-
This is important because oscillations may be obtained nomenological approach to explain oscillations. They
in many non-linear dynamical models that consider assume a delay in the response that the growth rate gives
di€erent parameters %e.g., undercooling, partition coef- to a change in the liquid concentration at the interface,
®cient) with variable values. Thus, it is not important and they introduce an additional di€erential equation to
that oscillations can be obtained. The important ques- describe it. The regular steady-state solution is similar
tion is: are conditions and results in fact applicable to to that of Lasaga %1982). Superimposed smooth asym-
natural samples that have been positively identi®ed to be metrical damped oscillations are obtained through
kinetically controlled? It is of little value to apply ex- perturbations of small amplitude. The amplitude of os-
isting kinetic models to explain STR-oscillations. Our cillations is that of the initial small perturbation and the
LAO patterns may be an appropriate candidate for ki- wavelength is not constrained by the model. A low
netically controlled oscillations. The wavelength ranges damping factor is favored by low degrees of supersatu-
between 1±20 lm and the amplitude is 0.5±2 mol% An. ration. The resulting oscillations may be comparable to
The pro®le shape, which is, unfortunately, not well de- our observations. However, because it is a phenome-
®ned, shows no clear asymmetry. Thus, we discuss here nological model, several parameters %wavelength,
the relevance of the existing models to the observed amplitude) are not constrained. Theoretical and experi-
LAO oscillations, which may be kinetically controlled.
mental constraints are needed to assess whether the
Existing numerical models mainly di€er by the as- mechanism %delay in the response of growth rate to
sumption on partitioning of Ab and An components liquid concentration) really occurs in natural magmas.
between melt and crystal under non-equilibrium condi-
An additional model %Anderson 1984) for oscillatory
tions. Some models assume that the growing crystal is in zoning proposes a combination of kinetic and dynamic
equilibrium with the adjacent melt. A general solution models. In a supersaturated liquid, a local boundary
for the growth equations in these conditions is given by layer is formed at the crystal±melt interface. It is as-
Lasaga %1982). With such assumptions, L'Heureux and sumed that the growing crystal is in equilibrium with the
Fowler %1994, 1996a, 1996b) obtained oscillations in melt composition regardless of temperature. The peri-
their models. However, the resulting amplitudes and odic destruction of the boundary layer, caused by a
wavelengths are too high %³10 mol% An, ³40 lm). shear pulse caused by the e€ect of tides on pressure,
Furthermore, their models needs particular conditions brings more supersaturated melt to the crystal surface.
on the partition coecient of anorthite. The conditions The resulting new plagioclase grows from a more ma®c
described in L'Heureux and Fowler %1994) only occur in composition and is thus more calcic. However, the
plagioclase with An £50. In L'Heureux and Fowler growth rate needed to grow one 1-to 20- lm-wide zone
%1996a, 1996b), the parameter KD, which must be per day is approximately 10±9 to 2. 10±8 cm/s, which is
smaller than 1 in order to produce oscillations is, in fact, much faster than the generally accepted although poorly
KD="csAn)/clAn)/%csAb/clAb) where the superscripts s and constrained 10±10 to 10±11 cm/s %Cashman 1990). Fur-
l respectively refer to the solid and the liquid. In local thermore, the assumption of equilibrium composition in
equilibrium, this KD is always larger than 1, so this the growing crystal still has to be veri®ed.
model fails to produce oscillations under realistic
conditions.
In conclusion none on the existing kinetic models
satisfy the observed small amplitude oscillations: some
Other models %Haase et al. 1980; Ortoleva 1990; of them %L'Heureux and Fowler 1994, 1996a, 1996b;
Wang and Wu 1995) consider that the partitioning be- Haase et al. 1980; Ortoleva 1990; Wang and Wu 1995)
tween Ab and An is controlled by the interface attach- are ruled out by the scale and amplitude of the oscil-
ment kinetics of both components, which, in turn, lations whereas, two others %Allegre et al. 1981;
depend on the composition of the existing crystal. The Anderson 1984) may be plausible but are too poorly
oscillations obtained also have amplitudes that are too constrained.
high %40 to 80 mol% An) and asymmetric saw-tooth
pro®les with sharp peaks that do not match the observed
LAO pro®les. Adding small random variations in An- Inverse zoning patterns and kinetics
concentration in the melt far from the crystal does not
in¯uence the amplitude of the resulting variations Another model that combines kinetics and small-scale
%Holten et al. 2000).
dynamics is that of Loomis %1982). In contrast to the
Pearce %1994) proposed a phenomenological numeri- model of Anderson %1984), Loomis %1982) assumes that
cal model based on the idea of Sibley et al. %1976). He the growing plagioclase has the solidus composition at
assumed that growth occurs with a constant partition the temperature considered. Water rejected in the
coecient, but only if the supersaturation in the melt boundary layer during crystal growth plays a dominant
exceeds a certain value. This model produces saw-tooth role: it locally reduces the liquidus and solidus temper-

445
through constructive comments. This study was part of the DFG-
funded SFB 468.
atures together with local undercooling and, thus, in-
creases the An content in the growing crystal. Such a
process could explain the rare inverse zones found in the
PAR-130-P3. An initial supersaturation could be caused
by an external cause, such as the disturbance of an ex-
isting water-rich boundary layer, or temperature drop,
degassing, etc. Inverse zoning then occurs when the
system comes back to equilibrium through the local
chemical evolution of the melt because of crystallization.
The width of the inverse zones in Loomis' model %50±
200 lm) is, however, larger than the 10-lm-wide inverse
zones observed in our sample.
It should be noted that this model is neither com-
patible with that of Anderson %1984), nor with that of
Allegre et al. %1981) because it assumes a di€erent par-
titioning law at the crystal interface. More experimental
data are needed to determine the actual partitioning law
in disequilibrium growth.
Appendix: An-calibrated accumulated BSE images
Principle
Backscattered electrons are emitted close to the surface
of the sample: The sampling depth depends on the mean
atomic number of the material and is £1 lm for feld-
spars %Goldstein et al. 1992). The emission intensity of
BSE depends mainly upon the mean atomic number of
the sample. In plagioclase, this is related to the Ca/Na
ratio and thus to An content. The in¯uence of K content
is discussed later. Other elements, such as Fe, Ba, and Sr
have variations of at most a few hundred ppm in the
investigated plagioclase crystals %Ginibre et al. 2001)
and, therefore, cannot signi®cantly a€ect BSE intensity.
Other e€ects may in¯uence the BSE signal. For ex-
ample, electron channeling a€ects BSE intensity de-
pending on crystal lattice orientation independently
from compositional variations. This is a common
problem in plagioclase because of polysynthetic twins.
However, this artifact can be readily recognized and
avoided by careful choice of the crystal section. Artifacts
caused by an imperfect surface polish are randomly
oriented and add to the statistical noise. They are gen-
erally small compared with the An signal but become
more important in low contrast images as shown in
Fig. 2a %LS-15616-P1). Irregularities in carbon coating,
especially as a result of quantitative analysis spots are
also seen in BSE and, therefore, images must be acquired
prior to quantitative point analysis.
Spatial resolution of the BSE signal depends mainly on
the sampling volume of BSE. The backscattered intensity
may be calculated as a function of the distance from the
beam impact point %Goldstein et al. 1992). This represents
a transfer function of the BSE signal, which will be con-
voluted with the initial compositional information to give
the resulting image. For the mean atomic number of
feldspar, the radius within which 80±90% of BSE intensity
is emitted, is about 1 lm at 15 kV acceleration voltage. In a
more practical sense, the spatial resolution is the mini-
mum distance at which two zones of di€erent composition
are seen. However, this spatial resolution depends on the
contrast and is, therefore, not independent of the com-
positional resolution. On the basis of the ®nest observed
zones, spatial resolution is estimated to be 0.5 lm in PAR-
130-P1 for contrasts of 1±2 mol% An %see below). Near
the limit of resolution, the pro®le is smoothed by the
transfer-function of the BSE signal.
Conclusion
High quality accumulated BSE images, which are possible
withthenewgenerationofelectronmicroprobes,providea
major improvement in imaging and analysis of major ele-
ment zoning in plagioclase. This makes more accurate
quanti®cation of small-scale zoning patterns possible.
Our observations show at least two types of oscilla-
tory zoning at scales smaller than 20 lm, 5±10 mol%
An, which both correspond to the type I oscillations of
Pearce and Kolisnik %1990). This indicates that higher
resolution imaging allows for a better distinction of os-
cillatory zoning types. STR patterns are non-periodic
saw-tooth-shaped ``oscillations'' characterized by re-
sorption surfaces. We attribute this type of oscillations
to dynamic processes such as %turbulent) convection,
which includes resorption phases, as assumed for the
type II oscillations of Pearce and Kolisnik %1990). Only
LAO patterns %amplitude <2% An) may be true oscil-
lations caused by a kinetic e€ect. They are also found in
a plagioclase crystal derived from a cumulate. Among
the existing models, that of Allegre et al. %1981) is closest
to these particular oscillations, but needs to be better
tested for its applicability if magmatic parameters and
conditions are to be extracted.
The oscillations described here are representative for
the sample studied. However, it can not be excluded that
the characteristics %amplitude and wavelength) of both
types of oscillations vary in other systems %di€erent melt
composition, magma chamber dynamics, etc.), or even
that other types exist that have yet to be recognized. A
systematic study using accumulated BSE images of
plagioclase in a large range of systems %volcanics to
cumulates and various compositions) should allow us to
generalize the di€erent types of oscillatory zoning and
the di€erent processes that produce them.
Image acquisition
Particular attention was given to obtaining a high-
quality polish of the thin sections because the state of the
Acknowledgements We would like to thank George Bergantz for
stimulating discussions and helpful comments on a early version of
the manuscript. Two anonymous reviewers provided valuable input surface has a large in¯uence on the quality of the images.

446
Fig. 6 Calibration lines for four
accumulated BSE images of
PAR 130-P3: anorthite content
from the quantitative analyses
is plotted against the luminance
of the corresponding points on
the images. It can be seen that
the quality of the correlation
varies between di€erent images
An acceleration voltage of 15 kV and a beam current of exact positioning of the sampling area on the image.
20 nA were used for all images. By accumulating 10±30 Such points were excluded from the calibration.
BSE images of the same part of the sample, a higher Measured luminance of quantitative measurement
signal/background ratio was obtained. This increases the points are plotted against An content for each image and
compositional resolution.
Gray scale pro®les
are shown in Fig. 6 for four images of PAR-130-P3.
There is a good linear correlation between the individual
quantitative point analyses %10 to 15 points) and BSE
gray scale %luminance) measured on the image at the
same spot. Each image is individually calibrated for An
content using the determined linear correlation. An-
calibrated pro®les over the entire crystal from core to
rim are then obtained by combining individual
calibrated gray scale pro®les.
The e€ect of K2O concentration is accounted for in
the linear calibration because the K2O content is al-
most linear with An in the compositional range of one
image. As is seen in Fig. 6, the quality of the correla-
tion varies between the images. This is explained as
follows: in contrast to lateral variations, di€erences in
sampling depth between BSE signal and quantitative
analysis can not be corrected for. They are generally
small because growth zones are almost normal to the
section, but the e€ect is larger when zone boundaries
are wavy. This e€ect is the most important source of
uncertainty in the calibration. The images with the
poorest correlation are those with wavy boundaries
%image 5).
Gray scale %or luminance) pro®les normal to planar
growth zones are measured on the accumulated BSE
images using image analysis software %Optimas). Each
point of the pro®le represents the luminance averaged on
a sampling area. For each image, width %normal to the
pro®le direction) and length %parallel to the pro®le di-
rection) of the sampling units are chosen to be large
enough to reduce noise, but small enough not to average
di€erent compositions. They thus depend on the width
and lateral variability of the growth zones. We chose
sampling areas of 100 pixels %width)´5 pixels %length) for
the image of the Laacher See cumulate feldspar %15616)
and of 8 pixels %width)´3 pixels %length) for all images of
PAR-130-P3.
Calibration
The measuring points of quantitative analysis are seen
on subsequent simple BSE images and thus can be lo-
cated precisely on the accumulated BSE images. Image
analysis is then performed as for the pro®le. For the Precision and accuracy
calibration, the luminance was averaged over the area
corresponding to each measurement point, which has a The precision of the An-calibrated pro®le is the com-
diameter of 5 or 2 lm. This allows us to take into ac- positional resolution and depends only on the quality of
count the di€erent lateral spatial resolutions of EMP the BSE images and gray scale pro®les and not on the
quantitative analyses and the BSE signal. For some calibration. Figure 2 compares three parallel pro®les
measurements points located on a zone boundary, the from the image of LS15616 and shows that, despite
result of gray scale determination is very sensitive to the polishing artifacts, they di€er by less than 0.5 mol% An

447
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% £1 lm). The pro®le observed is therefore smoothed
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