GeolCarp_Vol65_No4_257

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GEOLOGICA CARPATHICA

, AUGUST 2014, 65, 4, 257—271 doi: 10.2478/geoca-2014-0017

Distribution of elements among minerals of a single

(muscovite-) biotite granite sample – an optimal approach

and general implications

VOJTĚCH JANOUŠEK

1,2

, TOMÁŠ NAVRÁTIL

, JAKUB TRUBAČ

1,2

, LADISLAV STRNAD

FRANTIŠEK LAUFEK

and LUDĚK MINAŘÍK

Czech Geological Survey, Klárov 3/131, 118 21 Prague 1, Czech Republic;

vojtech.janousek@geology.cz; jakub.trubac@geology.cz; frantisek.laufek@geology.cz

Institute of Petrology and Structural Geology, Charles University in Prague, Albertov 6, 128 43 Prague 2, Czech Republic

Institute of Geology, Academy of Science, Rozvojová 269, 165 00 Prague 6, Czech Republic; navratil@gli.cas.cz; alex@gli.cas.cz

Laboratories of the Geological Institutes, Charles University in Prague, Albertov 6, 128 43 Prague 2, Czech Republic;

ladislav.strnad@natur.cuni.cz

(Manuscript received January 17 2014; accepted in revised form June 5, 2014)

Abstract: The petrography and mineral chemistry of the coarse-grained, weakly porphyritic (muscovite-) biotite Říčany
granite (Variscan Central Bohemian Plutonic Complex, Bohemian Massif) were studied in order to assess the distribu-
tion of major and trace elements among its minerals, with consequences for granite petrogenesis and availability of
geochemical species during supergene processes. It is demonstrated that chemistry-based approaches are the best suited
for modal analyses of granites, especially methods taking into account compositions of whole-rock samples as well as
their mineral constituents, such as constrained least-squares algorithm. They smooth out any local variations (mineral
zoning, presence of phenocrysts, schlieren…) and are robust in respect to the presence of phenocrysts or fabrics. The
study confirms the notion that the accessory phases play a key role in incorporation of many elements during crystalli-
zation of granitic magmas. Especially the REE seem of little value in petrogenetic modelling, unless the role of acces-
sories is properly assessed and saturation models for apatite, zircon, monazite±rutile carefully considered. At the same
time, the presence of several P-, Zr- and LREE-bearing phases may have some important consequences for saturation
thermometry of apatite, zircon and monazite.

Key words: modal analyses, trace-element residence, ICP-MS, Central Bohemian Plutonic Complex, Říčany granite.

Introduction

The  distribution  of  chemical  elements  among  minerals  in  a
single  granite  specimen  represents  a  fundamental  and  in-
triguing problem, which, however, has attracted surprisingly
little attention in the current literature (e.g. Gromet & Silver
1983;  Sawka  1988;  Evans  &  Hanson  1993;  Wark  &  Miller
1993; Bea 1996). Still, a good understanding of the net con-
tributions  of  individual  phases  to  the  whole-rock  chemical
budget is a necessary prerequisite should any relevant petro-
genetic  modelling  be  undertaken.  Moreover,  particular  host
minerals show variable resistance to alteration and/or weath-
ering, thus controlling the degree to which the given element
could be mobilized into the environment.

For such studies, reliable and precise concentration data in

small sample volumes are crucial. The data must be sufficient to
minimize the effects of inhomogeneities in the analysed mate-
rial (for individual minerals it could be the presence of zoning,
inclusions, alteration zones…). The required precision is often
far beyond the limits of the electron microprobe microanalysis
(EMPA); the prohibitive cost effectively rules out the ion
probe as well. Fortunately the ICP-MS technique enables a
reliable determination of sub-ppm amounts of elements both in
the solution (dissolved whole-rock powders or monomineralic
separates) and in situ, using the laser-ablation (LA) apparatus.

In addition, an accurate estimate of the mineral modal pro-

portions has to be made. Theoretically this should pose no
problem, given that the modal analyses have provided a ba-
sis for classification of holocrystalline igneous rocks for over
eighty years (Niggli 1931; Johannsen 1932, 1937, 1938, 1939;
Streckeisen 1974; Le Maitre 2002).

The classical technique relies on counting of individual

mineral grains over a regular grid, either in a standard thin sec-
tion  or  a  polished  rock  slab.  More  sophisticated  alternatives
include computer-aided image analysis, powder X-ray diffrac-
tion  (P-XRD)  and  chemistry-based  mathematical  approaches
(normative  recalculations  or  statistical  methods  employing
the chemistry of the bulk rock and its mineral constituents).

The current paper initially focuses on methodological is-

sues  connected  with  obtaining  a  modal  analysis  representa-
tive  of  a  large,  coarse-grained  granite  sample.  The  various
methods  are  compared  and  the  most  trustworthy  approach/
modal  data  chosen  (Appendix 1*).  Then,  using  a  combina-
tion of EMPA with (LA) ICP-MS data, an attempt is made to
identify the principal mineral hosts for individual elements,
evaluating  the  relative  contributions  of  each  of  them  to  the
whole-rock  budget.  Finally  we  discuss  the  general  implica-
tions  for  obtaining  modal  analyses  of  coarse-grained  rocks,
modelling  of  igneous  processes,  obtaining  reliable  whole-
rock trace-element analyses and saturation thermometry.

* – Appendices 1—5 (only as a Supplement in the electronical

version; www.geologicacarpathica.com)

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of biotite, quartz and oligoclase (an ‘hourglass’ texture of
Pivec 1970).

Plagioclase occurs as subhedral prismatic crystals with

common albite law twin lamellae, on average 1.2—2.0 mm
across. Apart from those enclosed within the K-feldspar,
they are of uniform oligoclase composition (An

11—19

; Appen-

dix 2) and are usually chemically unzoned.

Biotite forms subhedral flakes on average 0.5—0.75 mm (up

to 1.2 mm) across, with a strong pleochroism: X – straw yel-
low, Y = Z – dark rusty-brown. Pleochroic haloes around
submicroscopic inclusions are very distinct and common.
Biotite is often associated with grains of magnetite (Fig. 2b).

Anhedral quartz grains with weak undulose extinction are

up to 2 mm across.

The biotite may also be overgrown by scarce primary mus-

covite (up to 0.2 mm across). Also the plagioclase encloses
some small (0.1—0.2 mm) flakes of muscovite, at least some
of which appear to be of primary magmatic origin.

According to our microscopic and EPMA study and previ-

ous  work  of  Kodymová  &  Vejnar  (1974),  the  granite  con-
tains  significant  proportions  of  rutile  (0.1 mm).  Small
apatite (0.1—0.2 mm) prisms or needles are often enclosed by
biotite (Fig. 2c). Euhedral crystals of titanite (0.1 mm), brown
to  reddish  in  colour,  and  euhedral  dipyramidal  crystals  of
zircon (0.2 mm), pink to pale brown are less common acces-
sories. Monazite (0.2 mm) usually occurs in forms aggregates
of spherical grains. Magnetite (0.1 mm) occurs mostly in an-
hedral fragments, only rarely forming octahedra, up to 0.5 mm
across. Ilmenite (0.1 mm) forms black opaque grains of non-
metallic lustre, sometimes lamellated. Subangular hedral zir-
con-like ABO

-type phase (up to 0.1 mm across) represents a

newly encountered, rather rare accessory mineral. It occurs in
plagioclase, very often together with monazite (Fig. 2d).

Modal proportions

Petrographic approaches

In the present case, both the conventional point counting

and image analysis of the stained slab (Fig. 3a—b; see Appen-
dix 1  for  full  analytical  details  on  all  methods  used)  were
taken  to  approximate  well  the  mineral  proportions  in  the
studied  sample’s  matrix,  as  no  sizeable  K-feldspar  pheno-
crysts  are  present  in  the  hand  specimen.  The  results  do  not
differ  greatly (Table 1). The image analysis (Fig. 3c—e) indi-
cates somewhat higher amounts of biotite (9.0 vs. 7.3 vol. %:
image  analysis  vs.  conventional  point  counting,  plagioclase
(31.2 vs. 27.1 vol. %) and quartz (38.1 vs. 32.8 vol. %), at the
expense  of  the  K-feldspar  (21.8  vs.  25.0 vol. %).  Unfortu-
nately  the  contents  of  kaolinite  could  not  be  determined  by
the image analysis. This mineral largely resisted staining and
was thus counted, at least in part, as plagioclase.

Chemical methods

For sample Žer-1, the following mesonormative composi-

tion (‘Improved Granite Mesonorm’ of Mielke & Winkler
1979) is obtained (wt. %): Or 29.1, Pl (Ab + An) 36.8,

Table 1:

Estimates

modal

percentages

(vol.

and

wt.

original

data

bold)

the

individual

minerals

the

Říč

any

granite

Žer-1.

–

Data

mineral

densities

used

recalculation

wt.

vol

(or

vice

versa

)

are

from

Robie

al.

(1967),

whole-rock

density

the

Říčan

granite

from

Hejtman

(1948).

Original

data

are

bold.

–

For explanation of the individual methods (point-counting, imag

e analysis, least-squares calculation and XRD), see text. For m

ore detailed outcome of the constrained least-squares method,

see

Table

–

‘Improved Granite Mesonorm’ of

Mielke & Winkler (1979).

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Fig. 3. Photograph of the polished hand specimen of the sample
Žer-1, of natural appearance (a) and stained (b). The remaining im-
ages are separated colour components corresponding to the plagio-
clase (c) K-feldspar (d) and quartz with biotite (e). Box in figure (b)
indicates the area used for image analysis (c—e).

SiO

70.34

TiO

0.36

14.64

0.62

FeO

0.94

MgO

1.14

MnO

0.024

CaO

1.36

SrO

0.046

BaO

0.126

0.015

3.71

5.55

0.145

0.153

0.06

0.016

S tot

<0.005

0.51

<0.05

F(ekv)

–0.064

S(ekv)

–0.001

Total

99.69

A/CNK

1.00

O/Na

1.50

Table 2: Whole-rock major- and
minor-element analysis of the stud-
ied sample (wt. %).

A/CNK =
= m olar Al

/(CaO + Na

O + K

uncorrected for apatite.
K

O/Na

O ratio is given by weight.

For whole-rock trace-element com-
position, see Appendix 4.

Qtz  25.2,  Bt  5.8,  Ap  0.34,  Mgt  0.9,  Ilm  0.34,  Cal  0.14  and
Crn  0.54  (Table 1).  The  negligible  proportion  of  normative
corundum  is  in  line  with  the  subaluminous  nature  of  the
sample (A/CNK  ~ 1.0 – Table 2). Normative calcite and co-
rundum  were  further  not  considered  as  they  do  not  corre-
spond to mineral phases present in the rock.

The approximate proportions of the main rock-forming

minerals (wt. %) were also obtained by the constrained least-
squares (LSQ) method (Albarède 1995) implemented in the
GCDkit.  The  whole-rock  chemical  composition  and  typical
EMP analyses of the main rock-forming minerals served as
an  input  (Table 3).  Phosphorus,  not  present  in  appreciable
amounts in any of the main phases but representing an essen-
tial structural component in two common accessories, apatite
and monazite, was disregarded. The low sum of squared re-
siduals  (R

= 0.071) indicates an excellent fit. The propor-

tions of K-feldspar (29.4 wt. %) and plagioclase (36.6 wt. %)
are closely comparable to the mesonorm; but the quartz per-

Table 3: Constrained least-squares approximation to the modal composition (wt. %).

–

Shown are real electron microprobe analyses of the main rock-forming minerals (see Appendix 2).

–

The observed whole-rock concentrations (Table 2) and the best estimate by the constrained least-squares method, with the correspond-

ing differences (residuals).

–

The sum of squared residuals indicating a goodness of fit.

Whole rock

Plagioclase

Pl14

K-feldspar Kfs1

Biotite Bt14

Quartz Real

Estimated

Residual

Squared

residual

SiO

64.05

64.16

37.50

99.86

70.34

70.44

–0.10

0.010

TiO

0.00

3.33

0.00

0.36

0.31

0.05

0.002

21.76

18.47

14.80

0.02

14.64

14.78

–0.14

0.019

FeOt

0.04 0.03 17.26

0.00

1.50

1.64

–0.14

0.018

MnO

0.05

0.03

0.24

0.00

0.02

0.05

–0.02

0.001

MgO

0.00 0.00 13.35

0.00

1.14

1.25

–0.11

0.011

CaO

3.87

0.01

0.04

0.00

1.36

1.42

–0.06

0.004

9.42

0.96

0.14

0.00

3.71

3.75

–0.04

0.001

0.40

15.61

9.47

0.00

5.55

5.61

–0.06

0.004

wt. %

36.6 %

29.4 %

9.3 %

24.7 %

R sqr

0.071

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Fig. 6. Chondrite (Boynton 1984)-normalized REE spiderplots for the individual minerals. Zrn-l = zircon-like ABO

-type phase. Grey field

denotes the total variation in the dataset.

Feldspars and kaolinite

K-feldspar is characterized by roughly double enrichment

of Ba, Rb and Pb over the whole-rock abundances; also Sr is
slightly elevated (Fig. 5a). The plagioclase contains rather
high Sr and Be (see Navrátil et al. 2002; Navrátil 2003). On
the other hand, concentrations of transition metals and high
field strength elements (HFSE) in both feldspars are very
low. The kaolinite is stripped of much of the original K-feld-
spars’ large-ion lithophile (LILE) budget, and contains only
Cd, Pb and Ta in amounts exceeding those in the whole rock.

The plagioclase contains more than twice as much REE as

the  K-feldspar  (81.3  vs.  26.6 ppm).  Still  the  patterns  are  of
similar  shape,  featuring  a  high  degree  of  LREE  over  HREE
enrichment and sizeable positive Eu anomalies (Fig. 6a). The
feldspars share normalized Eu contents nearly identical to the
whole  rock  but  the  concentrations  of  the  remaining  REE  are
significantly  lower.  The  limited  REE  mobility  in  course  of
weathering of feldspars resulted in significantly higher appar-
ent concentrations in the residual kaolinite (

ΣREE ~191 ppm).

Only Eu contents approach those of the host rock and thus the
Eu anomaly turns to a strongly negative one.

Biotite and muscovite

The biotite is classified as phlogopite with 13.7—17.2 wt. %

total Al

(Al

1.10—1.18 and Al

0.16—0.27 apfu) and is

relatively Mg-rich (Mg/(Fe

+ Mg = 0.57—0.59). The content

of Al

for muscovite is 31.3 wt. % total (Al

1.44 and

3.44 apfu). Both micas are slightly enriched in Rb, Mn

(see Navrátil et al. 2007), Ni, Co, Zn, Nb and Ta. Elevated

contents  of  Cd,  Th,  U,  Zr  and  Hf  are  also  characteristic  of
muscovite.  The  main  differences  lie  in  the  total  REE  con-
tents (7.3 ppm for biotite vs. 3396 ppm for muscovite). The
muscovite REE pattern is steep, with a much higher degree
of  LREE/HREE  enrichment  compared  to  biotite  (Fig. 6a).
The Eu anomaly is negative in both cases.

Accessory minerals

Apatite: As shown by EMPA, the main minor constituents

in apatite are Mn, Fe and Cl. It is further characterized by an
enrichment of Mn, Cd and U (Fig. 5b). The Pb contents are
close to those in the whole rock. Apatite is rich in REE, and
the MREE in particular (

ΣREE=3962 ppm; Fig. 6b). A neg-

ative Eu anomaly is characteristic.

Zircon: This mineral is rather Hf poor (0.01—0.02 apfu) but

contains high concentrations of other HFSE, such as Nb and
Ta. Zircon is a major Cd, Zn, Ni and Co bearing-phase. High
concentrations  of  U  with  Th  are  typical,  as  well  as  high
ΣREE (2615 ppm) and parabolic, convex-up chondrite-nor-
malized  pattern  with  elevated  HREE  contents  (Fig. 6b).
While  the  Eu  anomaly  is  negative,  the  Ce  anomaly,  typical
of most igneous zircons (Hoskin & Schaltegger 2003), is ab-
sent.  This,  together  with  a  rather  low  degree  of  HREE  en-
richment, might reflect the presence of inclusions (see fig. 1
in Hoskin & Schaltegger op. cit.) or an admixture of the zir-
con-like (Zrn-l) phase.

Monazite: Monazite shows large concentrations of P, Zr

and Hf. Enrichment in radioactive elements is characteristic,
with Th prevailing over U. Pb contents are also high. This
mineral is enriched in REE, and especially LREE, with Ce

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being the most abundant (

ΣREE=91,205 ppm; Fig. 6b). A

deep negative Eu anomaly is characteristic.

Rutile: Rutile (TiO

> 98 wt. %) is a major transition metal-

bearing phase (Ni, Co and Cd); it displays elevated U and Th
contents. High HFSE concentrations (Zr, Hf, Nb and Ta) are
also typical. It is a REE-rich mineral (

ΣREE=7358 ppm)

with a fair degree of LREE/HREE fractionation and a deep
negative Eu anomaly.

Ilmenite and magnetite: Both minerals are characterized

by high contents of metals (Mn and Cd, less enriched Pb, Zn,
Co and Ni) as well as HFSE. The U and Th contents are also
somewhat elevated (Fig. 5b). The minerals are enriched in
REE (

ΣREE for ilmenite is 2735 ppm, for magnetite

3818 ppm), and the LREE in particular (Fig. 6b). The Eu
anomaly is deeply negative in both cases.

Titanite: Titanite shows low Al (0.09—0.11 apfu) and Fe

(0.03—0.03 apfu) contents. It is enriched in HFSE (Zr, Hf, Th
and U, less so Nb and Ta). Elevated Cd contents are also
typical. On the other hand, the LILE (Ba, Rb and Sr) are de-
pleted compared to the whole rock (Fig. 5b). The

ΣREE is

high (21,314 ppm) and the REE pattern relatively steep
(Fig. 6b) with a pronounced negative Eu anomaly.

Zircon-like ABO

-type phase: The results of the EMPA of

the zircon-like ABO

-type phase are summarized in Appen-

dix 5. Because of the relatively high Th contents, crystals are
metamict  and  altered,  and  yield  low  analytical  totals.  The
analysed phase appears to be a member of the zircon—thorite
solid solution series (0.27—0.33 apfu Th, 0.49—0.55 apfu Zr),
with substitution of Si by P (0.22—0.24 apfu) in the tetrahedral
position B. The phase is highly enriched in Fe (0.03—0.23 apfu)
and Ca (0.20—0.22 apfu. The Fe and Ca atoms, which proba-
bly  enter  the  crystal  structure  during  self-amorphization  and
interactions  with  circulating  fluids,  could  be  positioned  in

channels running parallel to the c axis of the crystal structure
(Geisler et al. 2002, 2003). Silica removal accompanied by a
hydration by post-magmatic, low-T fluids is also very probable.

Discussion

Modal analysis

Main rock-forming minerals

The choice of the most appropriate method for estimating

modal  abundances  of  the  main  rock-forming  minerals  was
governed  by  comparison  of  the  observed  and  calculated
model whole-rock contents of the major- and minor-element
oxides,  as  well  as  the  most  common  among  the  LILE  (Ba,
Rb and Sr, which are hosted in granites mostly by feldspars
and  micas  –  Hanson  1978).  Examining  Fig. 7,  it  is  clearly
seen that the constrained LSQ method provides the most accu-
rate  estimate.  As  this  approach  does  not  give  good  assess-
ments of contents of minor phases, no muscovite was included
in the calculation and 0.2 wt. % of this mineral was added on
the basis of the point counting. The ‘best’ modal proportions
of  the  main  rock-forming  minerals  are  thus  estimated  to  be:
0.365 Pl, 0.293 Kfs, 0.247 Qtz, 0.093 Bt and 0.002 Ms.

As for the rock classification in the QAP triangle (Fig. 8)

(here essentially the vol. % of Kfs, Pl and Qtz recast to 1),
the modal estimates by all methods yield comparable results
and the studied rock classifies consistently as monzogranite.
Still, the image analysis and, to some extent, point counting
tend to overestimate somewhat the Q proportion, whereas
the P-XRD approach results in a slightly lower 100*P/(A + P)
ratio of 47 % (other methods giving 55—59 %).

Fig. 7. Bar plots of calculated whole-rock contents of major- and minor-element oxides (a) and selected LILE (Rb, Sr and Ba) (b) calculated
from representative mineral analyses (Appendices 2 and 4) and modal abundances estimated on the basis of the P-XRD, granite mesonorm,
constrained least-squares (LSQ), image analysis of the stained thin slab and point counting of a standard thin section (Table 1). The best
agreement with the whole-rock contents (vertical orange lines) is achieved by the LSQ method.

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Fig. 8. QAP (quartz, K-feldspar, plagioclase) triangle of Streckeisen
(1974)  comparing  previous  modal  analyses  of  the  Říčany  granite
(Steinocher  1950,  1953;  Palivcová  1965)  with  those  obtained  for
sample  Žer-1  in  course  of  the  present  study  by  various  methods.
If necessary, the results were recast to vol. %.

Zr Nb La

Nd Eu Yb Y P

wt. %

2.875 1.166 1.431 0.661 0.473 0.314

0.314

Mnz

1.442 10.761 0.046

0.098 0.641 0.838 0.661 0.524 0.046

Zrn 0.032 0.116 2.459 2.882 3.780 0.550 1.240

0.032

0.327

0.081

0.655 0.634 3.543 0.691 1.391

0.081

Mgt

14.835 10.647 1.121

2.544 13.639 8.811 7.978

1.121

Ttn

1.443 9.563

0.343

0.260 0.498

0.340

0.255

0.255

Table 4: Maximum contents of selected accessory minerals (wt. %).

(ppm) Ap

Mnz Zrn Rt Real

Calc.

1.2 10086.7

453122.0 44550.4 145.5 145.5

0.1

35.3 3288.9 4675.2 3.8 4.6

424.5 26574.3

496.4 1861.8 12.2 13.5

1105.0 13148.3

446.9 2031.7 12.9 10.2

18.3

40.8 6.9 7.4

0.3

0.1

72.2 57.0 86.9 69.1

0.5 0.3

1173.8 839.3 447.3 398.7 5.5 4.2

186228.0 111734.2

0.0

17.5 585.4 585.4

Estimated modal
proportions (wt. %)

0.290 %

0.040 %

0.023 %

0.082 %

Table 5: Modal percentages of the most abundant accessories (wt. %) estimated by the unconstrained least-squares method.

–

Real mineral analyses are summarized in the

Appendix 2.

–

The whole-rock composition not accounted for

by the main rock-forming minerals. See text for
discussion.

–

Estimated modal percentages obtained by the

least-squares approach.

–

Composition of a mixture (ppm) calculated using

these mineral proportions.

Accessory phases

After subtracting the elements hosted by the main rock-

forming minerals (not only hosted incorporated in the lattice,

Estimates are based on an assumption that the given
mineral contains the full whole-rock inventory of the
individual elements, after subtracting those hosted by
the main phases (0.365 Pl, 0.293 Kfs, 0.247 Qz, 0.093 Bt
and 0.02 Ms). Minima for each mineral are shown in
bold; these represent maximum possible contents of
each phase (last column).

but  also  contained  in  small  inclusions,  fluid  inclusions  or
sorbed  at  grain  boundaries,  interfacial  films  etc.),  the  rest  of
the whole-rock chemical inventory has to be accounted for by
the accessories. A crude estimate of a maximum modal abun-
dance can be made using trace-element characteristics of the
individual minerals. Assuming that such a phase accommodates
the entire whole-rock inventory of the given element, these are
as follows (Table 4, elements in brackets being the most restric-
tive ones): apatite  < 0.314 wt. % (P), monazite  < 0.046 wt. %
(La),  zircon  < 0.032 wt. %  (Zr),  rutile  < 0.081 wt. %  (Nb),
magnetite  < 1.121 wt. % (La) and titanite  < 0.255 wt. % (Y).

For some minerals, these constraints should approach the

real modal abundances; the others contain no unique essen-
tial structural component, and instead share their trace-ele-
ment load with other mineral phase(s). For instance, the
maximal apatite content is likely to be overestimated, as part
of P resides in monazite. Likewise, the LREE hosted in min-
erals other than monazite can hardly be neglected.

Regarding the opaque phases, ilmenite and magnetite are

the possible carriers of the ferromagnetic properties in the
granite. It is worth stressing that the mean magnetic suscepti-
bility of the Říčany granite is low (13.13—105.3

×10

—6

[SI]:

Trubač et al. 2009) and thus the rock must contain only a
very limited amount of ferromagnetic component. Moreover,
in the constrained LSQ calculation, the whole-rock Fe bud-
get is exhausted by biotite and residual TiO

is as low as

0.05 wt. %  (Table 3).  According  to  petrographic  investiga-
tion (Kodymová & Vejnar 1974), rutile seems to be the most
important  Ti-bearing  accessory.  Ilmenite,  magnetite  and  ti-
tanite were therefore not taken into further consideration, in
accordance  with  the  microscopic  and  electron-microprobe
studies showing all three phases to be rather rare. The modal
abundance of the zircon-like ABO

phase remains unknown

as the complete trace-element data are not available.

In order to assess the abundances of the remaining acces-

sory minerals (Ap, Mnz, Zrn and Rt), the unconstrained LSQ
method was applied to the outstanding trace-element inven-

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Residence in individual minerals

Returning to Fig. 9, one can examine the residence of par-

ticular elements in detail. Silica is hosted almost equally by
quartz (35 wt. % of its whole-rock abundance), plagioclase
(33 %), and somewhat less by K-feldspar (27 %). Bulk Ti,
Fe and Mg are held by biotite, whereby rutile contains a fifth
of the whole-rock TiO

. Much of the MnO is also accounted

for by biotite but almost a third is hosted by K-feldspar. As
expected, the main reservoirs for Al

are the feldspars

(Pl: 52 %, Kfs: 38 %). Surprisingly little Al, however, resides
in biotite (10 %), owing to its small modal abundance. Most
of the CaO and Na

O are bound to plagioclase ( ~ 90 %); only

10 % of the former is stored in apatite and 8 % of the latter in
K-feldspar. Part of the Na

O contents in K-feldspar is to be

ascribed to small plagioclase inclusions observed during pet-
rographic studies. For K

O, K-feldspar is clearly the key host

(81 %), biotite accounting for a mere 16 % of the whole-rock
budget. The main reservoir for P is apatite; monazite’s con-
tribution is small, close to 7 %.

Concerning the LILE, Rb is accumulated by K-feldspar

(55 %),  biotite  comes  second  (24 %)  and  plagioclase  third
(20 %).  The  two  feldspars  represent  almost  equally  impor-
tant  Sr  reservoirs  (Pl:  57 %,  Kfs:  42 %).  The  bulk  of  Ba  is
concentrated  in  K-feldspar  (83 %);  both  biotite  (12 %)  and
plagioclase (5 %) are rather unimportant. The overwhelming
majority  of  Be  (79 %)  is  located  in  plagioclase;  K-feldspar
and biotite share the rest. Lead is another element for which
the feldspars are the main hosts (Kfs: 61 %, Pl: 37 %).

The most important LREE reservoirs are monazite (41 % La)

and plagioclase (33 % La), while muscovite, K-feldspar,
rutile and apatite seem to be much less significant. The bulk of
Eu is accounted for by the feldspars (Kfs: 50 % and Pl: 38 %);
the apatite contribution represents a mere 8 %. On the other
hand, apatite is the most important host for the middle and
heavy REE as well as Y. Less significant HREE-bearing phase
is rutile. Surprisingly, zircon and monazite do not rank among
important sinks for HREE, owing to their scarcity.

Regarding the radioactive elements, both feldspars seem to

incorporate  much  U  (Kfs:  35  and  Pl:  25 %).  Among  accesso-
ries,  rutile  accounts  for  over  20 %  of  both  Th  and  U.  Almost
equally  significant  for  Th  are  K-feldspar,  monazite  and  rutile,
less so plagioclase (15 %) and muscovite (13 %). Minerals such
as zircon and apatite play only marginal roles in hosting the ra-
dioactive  elements,  unlike  probably  the  newly  recognized  zir-
con-like ABO

phase, even though its role cannot be quantified.

Among the HFSE, the zircon contains only ~ 70 % of the

total Zr and Hf; with rutile accounting for the rest. About
60 % of the Nb and Ta budget are hosted by biotite. We can
only speculate that this may be in the form of submicroscopic
inclusions; for rutile remains approximately one fifth of the
whole-rock inventory.

General implications

Modal analysis

Petrographic techniques: In studies of granitic rocks, un-

stained thin sections are best suited for most textural obser-

vations, as well as description of optical properties and iden-
tification  of  mafic  minerals.  In  many  cases,  however,  it  is
difficult to determine some of the colourless phases, particu-
larly if the feldspars are not twinned or their grains are small.
One way out is to use cold-stage cathodoluminescence (CL),
in  which  the  (mostly)  blue  K-feldspars  are  easily  distin-
guished from ochre—yellow plagioclases and almost non-lu-
minescent  quartz  (Marshall  1988;  Janoušek  et  al.  2000a,
2004).  CL  also  facilitates  rapid  determination  and  mapping
of  some  accessory  phases,  such  as  of  apatite,  monazite  and
zircon.  Nowadays  largely  neglected,  staining  turns  K-feld-
spars  yellow  and  plagioclase  white,  also  facilitating  point
counting (Gabriel & Cox 1929; Hollocher 2013).

Obtaining a statistically valid modal analysis by point

counting of a standard thin section can be troublesome, espe-
cially  for  coarse-grained  or  porphyritic  rocks  (Chayes  &
Fairbairn 1951; Chayes 1954, 1965; Hutchison 1974). In or-
der to maximize the counted area in these cases, it was pro-
posed to use rock slabs or point count directly on the outcrop
(e.g. Hutchison 1974) – but such methods are cumbersome
and seldom used. Clearly, the situation becomes even more
complicated  when  the  rock  possesses  a  fabric,  as  one  deals
essentially  with  a  2D  section  of  a  three-dimensional  aniso-
tropic body.

In our case, the approach using the stained polished slab is

superior, as it represents an area larger than the standard sec-
tion (ca. 119 vs. 6 cm

). The current work confirms that the

tedious point-counting of the stained sample can be success-
fully replaced by computer-aided image analysis. However,
this method also brings about some new problems, for exam-
ple, some degree of ambiguity caused by alteration of the
feldspar.

P-XRD: The Rietveld method has been widely used for

quantitative  phase  analysis  of  various  geological  materials
and  industrial  products  (Madsen  &  Scarlett  2009  and  refer-
ences  therein).  This  full-pattern  profile  fitting  method  has
several  advantages  over  other  diffraction  approaches  to
quantitative phase analysis using at most a few of the stron-
gest reflections from each phase in the mixture (Bish & Post
1989). Nevertheless, the application of the Rietveld method
to geological materials still poses significant problems. The
most  pronounced  difficulties  are  micro-absorption  effects,
complex  preferred  orientation,  various  chemical  substitu-
tions in minerals and also the presence of structural defects.

Our estimate of modal composition obtained by P-XRD is

probably  biased  by  the  defective  structure  of  kaolinite,
which  is  affected  by  planar  disorder.  Considering  the  com-
plexity of the diffraction pattern, the large number of reflec-
tions  and  presence  of  significant  preferred  orientation,  the
results  from  P-XRD  are  reasonable,  in  other  words  they  are
comparable to other approaches. The advantage of the P-XRD
method over standard petrographic techniques is that it rep-
resents,  like  the  chemical  approaches,  the  whole  volume  of
the homogenized sample.

Chemical methods: For the sample Žer-1, the bulk-rock

analysis represents ~ 30 kg, or over 11,000 cm

of the rock,

and thus should be robust to the presence of fabrics, pheno-
crysts and local inhomogeneities such as schlieren. Major-
element or norm-based schemes (Streckeisen & Le Maitre

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GEOLOGICA CARPATHICA, 2014, 65, 4, 257—271

1979; De La Roche et al. 1980; Debon & Le Fort 1988) have
been  preferred  by  many  authors  for  classification  purposes.
However,  some  normative  recalculations  involve  minerals
not  encountered  in  common  felsic  plutonites  and  thus  their
use is not straightforward (e.g. CIPW and Catanorm – Hut-
chison 1975). For this reason, Mielke & Winkler (1979) de-
veloped  their  ‘Improved  Mesonorm’,  designed  specifically
for granitic rocks.

With the spread of personal computers, mathematical

methods became popular. They attempt to find the best esti-
mate  of  modal  proportions  based  on  major-  and  minor-ele-
ment analyses of the large whole-rock sample and its typical
mineral  constituents.  As  usually  the  number  of  chemical
components  exceeds  that  of  the  mineral  phases,  there  is  no
unique solution and the algorithms rely on the least-squares or
linear programming approaches (e.g. Wright & Doherty 1970;
Le Maitre 1981; Laube et al. 1996; Paktunc 1998; Janoušek et
al. 2006). Potential pitfalls could lie in the choice of typical
mineral  compositions  and/or  the  weathering/alteration  ef-
fects. The methods are also rather insensitive to the presence
of minor/or accessory phases, whose contents have to be as-
sessed separately.

Here the results obtained by mesonormative and LSQ ap-

proaches are closely comparable for felsic minerals (Fig. 8).
The amount of biotite, however, is nearly half (5.8 vs.
9.3 wt. %, respectively), and much lower also than estimates
by the remaining methods. The reason probably lies in the
fact that the mesonorm also estimates the proportion of mag-
netite and ilmenite, whereby in the LSQ calculation the sole
iron-bearing phase is biotite. The normative contents of the
opaque phases seem overestimated by the mesonormative al-
gorithm, especially that of magnetite (0.9 %).

Taken together, several of the methods employed here to

estimate  the  modal  proportions  of  the  main  rock-forming
minerals have yielded comparable results. It is necessary to
stress that the current case is a particularly favourable one, as
no significant zoning of mineral phases, not even of plagio-
clase,  has  been  observed  in  the  Říčany  Pluton.  Moreover,
K-feldspar  phenocrysts  in  the  studied  sample  are  small  and
sparse.  Still,  the  constrained  LSQ  method  (Albarède  1995)
was  found  superior  to  all  other  approaches.  The  obtained
percentages of the main rock-forming minerals compare well
with  the  modal  analyses  determined  previously  by  conven-
tional  point  counting  (Steinocher  1950,  1953;  Palivcová
1965) (Fig. 8).

Petrogenetic modelling

Collectively, the four accessories, apatite, monazite, zircon

and rutile host more than half of the total LREE and over
three quarters of the HREE + Y, Zr and Hf of the studied gran-
ite sample. The cases of Th, U, Ti, Ni, Co, Nb and Ta are sim-
ilar, albeit not so extreme. This confirms the notion that the
accessories are often crucial in controlling the behaviour of
many elements in granitic systems (e.g. Mittlefehldt & Miller
1983; Miller & Mittlefehldt 1984; Bea 1996). Particularly
the REE are of little value in petrogenetic modelling of frac-
tional crystallization of the main rock-forming minerals, un-
less the role of accessories is properly assessed.

Determination of the whole-rock trace-element abundances

Some 10—30 % of the whole-rock HREE, U, Th, Nb, Ta, Ti,

Cd, Co and Ni, and even more of Zr and Hf, are contained in
the resistant accessories, zircon and rutile. Thus the pressure
bomb or sample fusion are absolutely essential in sample de-
composition, if these elements are to be determined quantita-
tively (e.g. Potts 1987; García de Madinabeitia et al. 2008 and
references therein). Using a combined HF, HCl and HNO

at-

tack is clearly inadequate and will induce low total REE con-
tents and artificially increased degrees of LREE/HREE
fractionation. Alas such cases are by no means rare – for in-
stance, the acid decomposition casts serious doubts on some
of the results by Minařík et al. (1998).

Saturation thermometry

Our study provides some interesting implications for the

accessory  phase  saturation  thermometry  commonly  used  in
the  granite  studies  (see  Janoušek  2006  and  Anderson  et  al.
2008 for review). As in Říčany phosphorus is hosted nearly
exclusively by apatite (86 % of the whole-rock contents), the
saturation  thermometry  involving  this  mineral  should  apply
be applicable. Indeed the temperature calculated for the un-
corrected whole-rock P

content and that based on apatite-

hosted P

are both mutually closely comparable (946 vs.

931 °C according to the model of Harrison & Watson 1984).
The fact that they are unrealistically high for a granitic mag-
ma can be related to the sensitivity of the algorithm to exact
determinations of P

contents, as the isotherms converge

rapidly for increasingly acidic compositions (see fig. 3a in
Janoušek 2006).

Zircon incorporates a mere 62 % of the whole-rock Zr

budget (Fig. 9), the rest being hosted by other phases, most
importantly the early crystallizing rutile. The zircon satura-
tion thermometry (Watson & Harrison 1983) thus yields a
liquidus temperature estimate (784 °C) ca. 40 °C higher than
that calculated for the corrected Zr concentration.

The case of monazite is more complex, though. The model

of Montel (1993) includes additional parameters apart from
the  temperature,  major-element  and  LREE  contents  of  the
magma. One is the fraction of REE phosphates in the mona-
zite but this can be directly measured (the average for Říčany
monazite is 89.5 mol %). More difficult to constrain are the
water  contents  of  the  magma.  Fortunately,  the  effect  is  not
great  (738 °C  is  obtained  for  3 wt. %  H

O; 761—724 °C for

1—5 wt. % H

O).

Plagioclase represents an important sink for LREE, with

monazite  containing  some  21—41 %  of  the  whole-rock  in-
ventory. This brings problems for the LREE-based monazite
thermometry.  While  the  uncorrected  LREE  content  yields
738 °C,  the  corrected  content  gives  barely  668 °C,  that  is
about 70 °C less (for 3 wt. % H

O in the magma melt). Such

a corrected temperature seems to be too low for a granitic
magma. However, one should take into account the petrolog-
ical evidence indicating that the monazite saturation level
was probably reached early, prior to the onset of the plagio-
clase crystallization. Thus using the uncorrected temperature
seems more justifiable here.

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Conclusions

The study of the petrography and mineral chemistry of a

single large sample of coarse-grained, weakly porphyritic
(muscovite-) biotite granite from the Říčany intrusion
(Czech Republic) has yielded the following conclusions:

1. The methods taking into account the whole-rock com-

position  as  well  as  the  true  mineral  chemistries  (linear  pro-
gramming  or  constrained  least  squares)  are  particularly
suitable  for  modal  analyses  of  granitic  rocks.  The  modes
then represent a large volume of sample and thus (i) smooth
out any local variations, such as small-scale crystal accumula-
tion, (ii) account for the presence of phenocrysts, and (iii) are
insensitive to shaped-preferred orientation/fabric.

2. Accessory phases control the behaviour of many trace el-

ements in differentiation of felsic granitic systems. Clearly the
REE are of little value in petrogenetic modelling of the main
rock-forming minerals fractionation, unless the role of acces-
sories is properly assessed and existing saturation models for
apatite, zircon, monazite ± rutile are carefully considered.

The fact that many of the essential structural components

(P, Zr, LREE) used in apatite, zircon and monazite saturation
thermometry are incorporated into other minerals may lead
to significant overestimation of the liquidus temperatures. In
the present case, the saturation temperatures for zircon
would be overestimated as ca. 40 °C due to significant con-
tents of Zr in the early crystallized rutile. However, the cor-
rection for monazite (—70 °C) probably should not be applied
as most of the extra LREE are hosted by plagioclase, a rela-
tively late mineral.

In the studied sample, over 80 % of the whole-rock Zr and

Hf and ca. 10—30 % of HREE, U, Th, Nb, Ta, Ti, Cd, Co and
Ni are contained in resistant accessory phases Zrn and Rt.
Thus the pressure vessel or sample fusion – and not merely
a combined acid attack – are absolutely essential in sample
decomposition if these elements are to be determined quanti-
tatively.

Acknowledgments:  This  manuscript  benefited  from  insight-
ful comments by I. Broska, an anonymous reviewer and han-
dling  editor  I.  Petrík,  as  well  as  from  careful  editing  by    E.
Petríková. The authors are indebted to Z. Korbelová for assis-
tance  at  the  electron  microprobe  and  J.K.  Novák  (both  Geo-
logical Institute, Czech Academy of Sciences, Prague – GLI)
who  carried  out  the  point  counting  analysis.  V.  Sedláček
(GLI) did the mineral separations, P. Hasalová (Czech Geo-
logical  Survey)  helped  with  staining  of  feldspars.  Janoušek
and Trubač acknowledge the support by the Grant Agency of
the  Czech  Republic  (GAČR,  No.  P210/11/1168)  and  Czech
Ministry of Education, Youth and Sports (Project LK 11202);
Minařík  and  Navrátil  were  supported  from  institutional
Project No. RVO67985831. This study is a part of the Ph.D.
research of Jakub Trubač.

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www.geologicacarpathica.com

GEOLOGICA CARPATHICA

, AUGUST 2014, 65, 4

Electronic supplement

Analytical techniques

Sampling

The whole-rock sample Žer-1 ( ~ 30 kg) was collected in

the  Žernovka  quarry, ca.  850 m  NNW  of  the  namesake  vil-
lage  off  the  pluton’s  center  (Fig. 1c,  GPS  50°0’22.64” N;
14°44’56.13” E). Its bulk was crushed by a steel jaw crusher,
homogenized and ground in an agate mill at the Laboratories
of  the  Institute  of  Geology,  Czech  Academy  of  Sciences,
v.v.i. (CAS).

Mineral separation

The crushed material ( < 500 µm) was floated on a Wilfley

shaking  table.  The  heavy  fraction  was  filtered  on  glass  frit,
rinsed  with  ethanol  and  air  dried.  The  light  fraction  was
dried  at  105 °C  and  was  used  for  separation  of  the  main
rock-forming minerals. The fraction between 63 and 250 µm
thereof  served  for  magnetic  separation  of  biotite.  The  biotite
separate  was  finally  cleaned  in  acetylene  tetrabromide  with
density of 2.54 kg . m

—3

The quartz separate was obtained after biotite separation by

flotation using ANP1 (amino nitro paraffin) agent. K-feldspar
was separated in bromoform solution (2.59 kg . m

—3

). The

material with density greater than 2.54 kg . m

—3

was plagio-

clase. Following the separation of quartz and orthoclase,
muscovite separation was achieved in bromoform with den-
sity 2.74—2.84 kg . m

—3

. Kaolinite was isolated by centrifuga-

tion of the fine fraction ( < 25 µm) in bromoform.

The dried heavy fraction from the shaking table was sieved

on a 315 µm nylon sieve. The fine fraction was used for sepa-
ration of heavy minerals – zircon and monazite. Apatite was
recovered from the heavy fraction by centrifugation in methyl-
eniodide with density 3.18—3.25 kg . m

—3

. Magnetite was ob-

tained from the dark part of the heavy fraction by magnetic
separation with the intensity of magnetic field set to 0.2 A.

Electron microprobe and BSE imaging

The analyses of the major rock-forming and selected acces-

sory minerals were done with a fully automated CAMECA
SX-100 electron microprobe, employing

Φ(ρz) correction

procedure (Merlet 1992) at the CAS. All analyses were per-
formed at an acceleration voltage of 15 kV but with different
beam currents and spot sizes chosen according to the mineral
type. Thus 20—40 nA and a spot size of 10 µm were employed
for analyses of apatite, titanite, rutile, monazite, magnetite, il-
menite and zircon—thorite solid solution. For feldspars, micas

and quartz, the beam current was 10—15 nA and spot size
2 µm. Minor-element interferences have been checked rou-
tinely and corrected for by measuring the corresponding stan-
dards. All the mineral abbreviations are after Kretz (1983).

Whole-rock major- and minor-element analyses

The major-element whole-rock analysis of the whole-rock

sample was undertaken by wet chemistry in the laboratories of
the Czech Geological Survey, Prague – Barrandov. Further
analytical details are given in Dempírová (2010); the relative
2

σ uncertainties were better than 1 % (SiO

), 2 % (FeO),

5 % (Al

, K

O and Na

O), 7 % (TiO

, MnO, CaO), 6 %

(MgO) and 10 % (Fe

, P

). Interpretation and plotting

of the whole-rock geochemical data was done by the R-lan-
guage package GCDkit (Janoušek et al. 2006).

Trace-element analyses

Solution ICP-MS analyses

The trace-element analyses of mineral separates and

whole-rock samples were carried out after modified total di-
gestion in mineral acids (HF + HClO

) and borate fusion

(Na

+ Na

) in Pt crucibles followed by solution

nebulization ICP-MS PQ3 VG Elemental at Charles Univer-
sity in Prague. All the chemicals involved were reagent
grade (Merck, Germany) and the acids were double distilled.
Deionized water from a Millipore system (Milli-Q Academic,
USA) was used for all dilutions.

The measured data were processed on-line using VG Plas-

maLab software, applying corrections for instrumental drift.
The analytical precision for all the elements analysed ranged
from 0.5 to 5 % relative. The accuracy of this analytical
method was checked using the G-2 and BCR-2 reference ma-
terials (USGS, USA). Trace-element ICP-MS analyses fol-
lowed the methods of Strnad et al. (2005).

In-situ laser ablation analyses

In-situ trace-element analyses were performed on a qua-

drupole-based  ICP-MS  Thermo  Fisher  X-Series  II  (Charles
University) coupled to a NewWave UP 213 laser microprobe
(NewWave Research; USA) operating at output wavelength
of 213 nm. All samples were prepared as polished thin sec-
tions. The data were acquired in the time-resolved and peak
jumping  mode  with  one  point  measured  per  mass  peak  and
processed  off-line  by  Thermo  Fisher  PlasmaLab  software
2.5.11  321.  The  raster  pattern  was  linear,  approximately

JANOUŠEK et al.: Distribution of elements among minerals of a single (muscovite-) biotite granite sample – an opti-
mal approach and general implications

Appendix 1

GEOLOGICA CARPATHICA

GEOLOGICA CARPATHICA, 2014, 65, 4

JANOUŠEK et al.: Distribution of elements among minerals of a single granite sample

×400 µm. External calibration of the laser-ablation analy-

ses was done using standards NIST 610 and 612 (Pearce et al.
1997). For internal standardization

Si concentrations based

on electron microprobe measurements were applied. Data re-
duction  included  correction  for  the  gas  blank,  the  internal
standard  and  a  calibration  check;  the  data  were  processed
off-line  in  a  MS  Excel  spreadsheet-based  program.  For  de-
tails on analytical protocol and correction strategy see Strnad
et al. (2005).

Modal analyses

Point counting

Point counting was done on a thin section 3

×2 cm using a

standard optical microscope. The total number of points
counted was 4890.

Image analysis of stained rock slab

The rock sample was stained according to the method of

Gabriel & Cox (1929). The polished sample surface was ex-
posed to fumes of HF for about 15 min., then treated with a
concentrated solution of sodium cobaltinitrite for another
10 min., rinsed and dried. This reaction forms a yellow coat-
ing on K-feldspar and white on plagioclase; quartz remains
unaffected.

The image analysis was performed on a scanned stained

polished rock slab (ca. 17

×7 cm). The abundance of mineral

phases was estimated on the basis of pixel colour analysis by
Quick Photo Micro 2.2 software. Dark—black areas were at-
tributed to biotite, grey and greyish glassy-like colour to
quartz, white to plagioclase and yellow to K-feldspar.

Powder X-ray diffraction

A powder sample was prepared by grinding in an agate mill

and, subsequently, in an agate mortar. The powder X-ray dif-
fraction pattern was collected in a conventional Bragg-Bren-
tano geometry on the Philips X’Pert diffractometer equipped
with graphite secondary monochromator. The CuK

radiation

was used. To minimize the background, the sample was
placed on a flat low-background silicon wafer. Data were ac-
quired in the angular range 3—90° 2

Θ, with a step interval of

0.02° and a step-counting time of 9 s. A divergence slit of 0.5°
and a receiving slit of 0.1 mm were used.

The quantitative phase analysis of the sample was per-

formed using the Rietveld method (Young 2000). Refinement
was done by minimizing the sum of the weighted squared dif-
ferences between observed and calculated intensities at every
2

Θ step in a powder diffraction pattern (Bish & Post 1993).

Quartz,  orthoclase,  plagioclase  (albite),  biotite  and  kaolinite
were detected in the P-XRD pattern. The Rietveld refinement
was performed using the FullProf program (Rodríguez-Car-
vajal 2006). The structure models used in the refinement were
as  follows:  quartz  (Le  Page  &  Donnay  1976),  orthoclase
(Prince  et  al.  1973),  albite  (Ferguson  et  al.  1958),  biotite
(Brigatti  &  Davoli  1990)  and  kaolinite  (Bish  &  Von  Dreele
1989). The structural model of oligoclase instead of albite was

also tested in Rietveld refinements, however the differences
in  the  profile  agreement  factors  between  both  Rietveld  fits
were  insignificant.  The  differences  in  the  estimated  modal
composition were below 0.1 wt. %. The background was de-
termined by linear interpolation between consecutive break-
points in the powder pattern. The pseudo-Voigt function was
employed to generate the line shape of the diffraction peaks.
The  refinement  involved  the  scale  factor  for  each  phase,
unit-cell parameters for each phase except albite, peak-width
parameters  for  each  phase,  two  asymmetry  parameters  for
biotite and 2

Θ zero error. Atomic coordinates, overall isotro-

pic  displacement  factors,  and  site  occupancy  parameters
were fixed during the refinement for all phases. The unit-cell
parameters  of  albite  were  also  fixed,  since  their  refinement
caused  divergence  of  the  fit.  The  March-Dollase  correction
for  preferred  orientation  was  applied.  The  [001]  direction
was used for biotite, kaolinite, feldspar and plagioclase. The
refinement converged to the values of the profile agreement
factors R

= 8.9 % and R

= 11.4 %.

Principles of the least-squares calculations

The least-squares method is employed to solve an overde-

termined  set  of  linear  algebraic  equations,  which  occur
where  there  are  more  independent  equations  than  variables
(Bryan  et  al.  1969).  Given  a  matrix  A  and  a  vector  y,  we
want to know the vector x that fulfils.

y = Ax

Our estimate of the vector x should also be chosen so that the
computed and real elements of the vector y differ as little as
possible.

y’= Ax’

The squares of these differences are commonly minimized

(so-called least-squares method: Bryan et al. 1969; Albarède
1995):

= y’—y

= min

and the sum of squared residuals is taken as the measure of

the goodness of fit. Albarède (1995) discussed in a detail all
the necessary mathematical apparatus that is behind the solu-
tion. Moreover, Janoušek & Moyen (in print) provide exam-
ples of various types of calculations (including normative
calculations using real mineral compositions by the least-
squares method) and their implementation into the freeware
R language.

In geochemistry we very often examine variables that sum

up, for instance, to a unity or 100 %. The least-squares method
generally does not produce normalized solutions, in the form
of vectors whose components would sum up to a given num-
ber. We can define the Lagrange multiplier

λ as (Albarède

(1995):

)

(

−

where x stands for an ordinary least-squares solution and J is
a vector, all elements of which are equal to 1. The con-
strained least-squares solution is than given by:
6

= x +

λ(A

—1

iii

GEOLOGICA CARPATHICA

GEOLOGICA CARPATHICA, 2014, 65, 4

Electronic supplement – Appendices 1—5

References

Albarède F. 1995: Introduction to geochemical modeling. Cam-

bridge University Press, Cambridge, 1—543.

Bish D.L. & Post J.E. 1993: Quantitative mineralogical analysis

using the Rietveld full-pattern fitting method. Amer. Mineralo-
gist 78, 932—940.

Bish D.L. & Von Dreele R.B. 1989: Rietveld refinement of non-

hydrogen atomic positions in kaolinite. Clays and Clay Miner.
37, 4, 289—296.

Brigatti M.F. & Davoli P. 1990: Crystal-structure refinements of

1 M plutonic biotites. Amer. Mineralogist 75, 305—313.

Bryan W.B., Finger L.W. & Chayes F. 1969: Estimating propor-

tions in petrographic mixing equations by least-squares approxi-
mation. Science 163, 926—927.

Dempírová L. 2010: Evaluation of SiO

, Na

O, MgO, K

O determi-

nations in silicate samples by z-score obtained from nineteen
interlaboratory tests. [Zhodnocení stanovení SiO

, Na

O, MgO

a K

O v silikátových vzorcích pomocí z-skóre získaných z de-

vatenácti mezilaboratorních porovnávání.] Zpr. Geol. Výzk.
v roce 2009, 323—326 (in Czech with English summary).

Ferguson R.B., Traill R.J. & Taylor W.H. 1958: The crystal struc-

tures of low-temperature and high-temperature albites. Acta
Crystallogr. 11, 331—348.

Gabriel A. & Cox E.P. 1929: A staining method for the quantitative

determination of certain rock minerals. Amer. Mineralogist 14,
290—292.

Janoušek V. & Moyen J.F. (in print): Mass balance modelling of

magmatic processes in GCDkit. In: Kumar S. & Singh R.N.
(Eds.): Modelling of magmatic and allied processes. Soc.

Earth Sci., Ser. 83, Springer, Berlin, 225—238.

Doi: 10.1007/978-3-319-06471-0_11
Janoušek V., Farrow C.M. & Erban V. 2006: Interpretation of whole-

rock geochemical data in igneous geochemistry: introducing
Geochemical Data Toolkit (GCDkit). J. Petrology 47, 1255—1259.

Kretz R. 1983: Symbols for rock-forming minerals. Amer. Mineralo-

gist 68, 277—279.

Le Page Y. & Donnay G. 1976: Refinement of the crystal structure

of low-quartz. Acta Crystallogr., Sect. B 32, 2456—2459.

Merlet C. 1992: Accurate description of surface ionization in elec-

tron probe microanalysis: an improved formulation. X-RAY
Spectrom. 21, 229—238.

Pearce N.J.G., Perkins W.T., Westgate J.A., Gorton M.P., Jackson

S.E., Neal C.R. & Chenery S.P. 1997: A compilation of new
and published major and trace element data for NIST SRM 610
and NIST SRM 612 glass reference materials. Geostand.
Newsl. 21, 115—144.

Prince E., Donnay G. & Martin R.F. 1973: Neutron diffraction

refinement of an ordered orthoclase structure. Amer. Mineralo-
gist 58, 500—507.

Rodríguez-Carvajal J. 2006: Full Prof .2k Rietveld profile matching

& integrated intensities refinement of X-ray and/or neutron data
(powder and/or single-crystal). Laboratoire Léon Brillouin,
Centre d’Etudes de Saclay, Gif-sur-Yvette Cedex, France.

Strnad L., Mihaljevič M. & Šebek O. 2005: Laser ablation and solu-

tion ICP-MS determination of rare earth elements in USGS
BIR-1G, BHVO-2G and BCR-2G glass reference materials.
Geost. Geoanal. Res. 29, 303—314.

Young R.A. 2000: The Rietveld method. Oxford University Press,

Oxford, 1—312.

GEOLOGICA CARPATHICA

GEOLOGICA CARPATHICA, 2014, 65, 4

JANOUŠEK et al.: Distribution of elements among minerals of a single granite sample

Appendix 2

Electron microprobe analyses.

a – Average electron-microprobe data used in mass-balance calculations (wt. %).

SiO

TiO

FeOt MnO MgO CaO Na

O K

O P

70.34

0.36

14.64

1.5

0.024

1.14

1.36

3.71

5.55

0.15

Qtz

99.86

n.d.

0.02

n.d.

n.d. n.d. n.d. n.d. n.d. n.d.

64.16

n.d.

18.47

0.03

0.034

n.d.

0.01

0.96

15.61

0.01

62.97

n.d.

20.07

n.d.

0.01

3.95

9.2

0.44

0.02

37.5

3.33

14.8

17.26

0.24

13.35

0.04

0.14

9.47

n.d.

49.38 0.27

31.26 3.72 0.05 0.98 0.12 0.27 9.79 n.d.

Kln

45.59 0.91

39.84 0.02 0.01 n.d. n.d. n.d. n.d. 0.03

Ilm

0.01

50.32

n.d.

42.71

3.091

n.d.

0.01

Ttn

30.49

35.77

2.79

1.11

0.092

n.d.

27.58

n.d.

0.01

0.04

0.01

n.d.

0.03

0.161

n.d.

55.98

n.d.

42.68

Mgt

n.d.

0.233

n.d. n.d. n.d. n.d. n.d.

Mnz

2.42

n.d.

0.04

n.d.

0.37

n.d.

25.61

Zrn

31.1

n.d.

0.29

0.44

0.006

n.d.

0.14

n.d.

0.28

97.35

n.d.

1.59

0.031

n.d.

0.08

n.d.

n.d. — not detected.

b – Typical analyses for the main and accessory minerals (wt. % and apfu).

Feldspars

Biotite

Magnetite

ID Plg15T

Plg19T

16T

Bt14

Mgt1

SiO

63.75

66.44

64.26

SiO

37.50

SiO

0.03

TiO

n.d.

0.01

n.d.

TiO

3.33

TiO

0.01

22.00

20.33

18.29

14.80

0.04

FeOt

n.d.

0.02

FeOt

16.95

FeOt

95.55

MnO

0.02

n.d.

MnO

0.24

MnO

1.17

MgO

0.009

n.d.

0.01

MgO

13.35

MgO

n.d.

CaO

3.59

1.72

0.03

CaO

0.04

CaO

0.01

9.72

10.84

1.30

0.14

O n.d.

0.38

0.21

15.48

9.47

O n.d.

0.013 0.009 0.008

O+

2.44

n.d.

Total

99.46

99.61

99.39

1.66

ThO

n.d.

Si apfu

2.834

2.930

2.987

Total

99.92

n.d.

0.000

0.000 Si

apfu

2.812 Y

n.d.

1.153

1.057

1.002 Al(IV)

1.188 TR

n.d.

0.000 0.000 0.001

4.000

Total

96.81

0.001

0.000

0.000 Al(VI)

0.121 Si

apfu

0.004

0.001

0.000

0.001 Ti

0.188 Ti

0.001

0.171

0.081

0.002 Fe

1.063 Al

0.005

0.838

0.927

0.117 Mn

0.015 Fe

0.964

0.021

0.012

0.918 Mg

1.492 Fe

1.995

0.000 0.000 0.000

Σ 2.879

0.037

8.000

8.000 Ca

0.003 Mg

0.000

An mol. % 16.6

8.0

0.1

0.020

0.000

81.3

90.9

8.5

0.906

0.000

2.1

1.2

91.4

Σ 0.930

K 0.000

F 0.394

P 0.000

OH* 1.606

Th 0.000

XMg

0.58

0.000

XFe

0.42

0.000

n.d. — not detected, n.a. — not analysed.

GEOLOGICA CARPATHICA

GEOLOGICA CARPATHICA, 2014, 65, 4

Electronic supplement – Appendices 1—5

Zircon

Monazite

Rutile

Titanite

ID Zrn5

Zrn7

Zrn10

Mnz8

Mnz9

Rt1

Ttn4

SiO

32.08

31.10

32.27

1.89

2.42

0.51

30.30

TiO

0.02

n.d.

0.01

0.00

98.82

36.32

0.06

0.29

n.d.

0.01

2.44

n.d.

26.61

25.61

0.00

0.02

FeO

0.14

0.44

0.05

0.00

0.04

0.46

n.a.

1.08

MnO

n.d.

0.01

n.d.

0.12

n.d.

0.11

CaO

0.02

0.14

n.d.

0.41

0.37

0.10

27.23

n.d.

0.39

0.11

0.55

0.40

0.06

0.36

ZrO

63.28

61.21

62.89

n.a.

HfO

1.87

1.89

1.30

n.a.

n.d.

0.04

32.74

32.78

0.14

0.50

0.13

0.07

n.d.

15.07

14.51

n.d.

0.07

n.d.

0.08

9.35

8.66

n.d.

0.60

0.12

0.10

n.d.

2.87

2.86

0.04

0.23

0.00

0.09

0.04

1.07

1.18

0.00

0.02

0.01

0.02

0.01

n.d.

0.05

n.d.

0.02

0.04

0.01

0.48

0.37

n.d.

0.15

n.d.

0.08

0.03

n.d.

0.08

0.01

0.04

n.d.

0.01

0.08

n.d.

0.01

0.03

0.01

0.04

0.02

0.00

0.02

0.00

0.05

0.02

0.00

0.03

n.d.

0.08

0.09

0.02

n.d.

0.04

n.d.

0.03

0.02

0.01

n.d.

0.00

n.d.

ThO

0.13

0.17

0.03

8.18

10.42

0.02

0.18

0.20

0.60

0.50

0.37

0.03

0.01

Total

98.05

96.19

97.54

100.110 100.144 100.322 99.66

Si apfu

1.007 0.998 1.015 0.077 0.099 0.007 1.001

0.000 0.000 0.000 0.000 0.000 0.988 0.903

0.002 0.011 0.000 0.000 0.000 0.000 0.095

0.000 0.000 0.000 0.912 0.887 0.000 0.001

0.004 0.012 0.001 0.000 0.001 0.005 n.a.

n.a.

0.027

0.000 0.000 0.000 0.004 0.000 0.000 0.003

0.001 0.005 0.000 0.018 0.016 0.001 0.964

0.000 0.007 0.002 0.012 0.009 0.000 0.006

0.968 0.958 0.965 n.a. n.a. n.a. n.a.

0.017 0.017 0.012 n.a. n.a. n.a. n.a.

0.000 0.000 0.000 0.485 0.491 0.001 0.006

0.001 0.001 0.000 0.225 0.219 0.000 0.001

0.000 0.000 0.001 0.135 0.127 0.000 0.007

0.001 0.001 0.000 0.042 0.043 0.000 0.003

0.000 0.001 0.000 0.015 0.017 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.006 0.005 0.000 0.002

0.000 0.000 0.000 0.001 0.000 0.000 0.001

0.000 0.000 0.000 0.000 0.000 0.000 0.001

0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.001 0.000 0.000 0.000

0.000 0.000 0.000 0.001 0.001 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.001 0.001 0.000 0.075 0.097 0.000 0.000

0.001 0.001 0.004 0.005 0.003 0.000 0.000

0.995 1.005 0.988 1.020 1.024

1.009 1.009 1.015 0.988 0.986

Sum cat.

2.004 2.014 2.003 2.015 2.016 1.004 3.021

GEOLOGICA CARPATHICA

GEOLOGICA CARPATHICA, 2014, 65, 4

JANOUŠEK et al.: Distribution of elements among minerals of a single granite sample

Appendix 3: Laser-ablation ICP-MS data for the main rock forming minerals (ppm).

LA ICP-MS

Quartz

DL (LA)

ppm

q1 q2 q3 q4 q1 q2 q3 q4 q1 Avg

0.01

0.08 0.11

0.17 0.03 0.00 0.05 0.00 0.00

0.06

0.35

0.12 0.12 0.16 0.10 0.09 0.21 0.22 0.20 0.20

0.16

0.05

0.095

0.01 0.01 0.00 0.01 0.01 0.01 0.03 0.00 0.01

0.01

1.15

1.97 1.77 0.94 1.27 2.29 2.17 3.02 2.93 3.12

2.16

0.77

0.48

0.10 0.22 0.26 0.19 0.11 0.64 0.69 0.69 0.65

0.39

0.26

0.03 0.05 0.05 0.05 0.35 0.08 0.07 0.05 0.09

0.09

0.10

0.085

0.10 0.16 0.09 0.06 0.12 0.13 0.07 0.13 0.12

0.11

0.03

0.045

0.00 0.00 0.01 0.05 0.00 0.00 0.00 0.00 0.00

0.01

0.02

0.25

0.05 0.03 1.31

0.09 0.14 0.06 0.04 0.03

0.22

0.44

0.05

Nb 0.01

0.00

0.04

0.01

0.23

0.16 0.08 0.02 0.01 0.11 0.05 0.01 0.01 0.03

0.05

0.085

0.19 0.28 0.12 0.13 0.80 0.39 0.36 0.38 0.38

0.34

0.20

0.020

La 0.001 0.009 0.003 0.007 0.001 0.01 0.00 0.00 0.00

0.004

0.00

0.028

Ce 0.008 0.013 0.007 0.021 0.011 0.03 0.00 0.01 0.00

0.012

0.01

0.008

Pr 0.000 0.000 0.000 0.003 0.000 0.00 0.00 0.00 0.00

0.001

0.00

0.083

0.000 0.000 0.007 0.004 0.003 0.01 0.00 0.00 0.00

0.003

0.00

0.097

0.000 0.000 0.000 0.000 0.000 0.00 0.00 0.00 0.00

0.000

0.00

0.008

Eu 0.000 0.000 0.000 0.000 0.000 0.00 0.00 0.00 0.00

0.000

0.00

0.032

0.000 0.000 0.000 0.000 0.000 0.00 0.00 0.00 0.00

0.000

0.00

0.009

Tb 0.000 0.000 0.000 0.000 0.000 0.00 0.00 0.00 0.00

0.000

0.00

0.030

0.000 0.000 0.000 0.001 0.000 0.00 0.00 0.00 0.00

0.000

0.00

0.004

0.000 0.000 0.001 0.001 0.000 0.00 0.00 0.00 0.00

0.000

0.00

0.012

Er 0.000 0.000 0.003 0.005 0.000 0.00 0.00 0.00 0.00

0.001

0.00

0.002

0.000 0.000 0.000 0.001 0.000 0.00 0.00 0.00 0.00

0.000

0.00

0.022

0.000 0.000 0.000 0.002 0.000 0.00 0.00 0.00 0.00

0.000

0.00

0.003

Lu 0.000 0.000 0.000 0.000 0.000 0.00 0.00 0.00 0.00

0.000

0.00

0.03

0.00 0.00 0.08

0.00 0.01 0.00 0.00 0.00

0.01

0.03

0.05

Ta 0.01

0.01 0.01

0.01

0.02 0.02 0.02

0.01

0.21

0.08 0.07 0.07 0.08 0.11 0.15 0.13 0.12 0.11

0.10

0.03

0.02

0.66 1.01 0.11 0.04 0.35 0.97 0.31

1.13

0.57

0.43

0.011

0.01 0.01 0.04 0.11 0.01 0.02 0.02 0.02 0.02

0.03

DL = detection limit.

K-feldspar

k1 k2 k3 k4 Avg

0.58 0.85 2.15 1.77 1.34

0.74

2.15 2.44 1.33 1.72 1.91

0.49

0.04 0.07 0.03 0.01 0.04

0.02

0.60 0.65 0.54 0.19 0.49

0.21

1.28 1.18 0.97 0.29 0.93

0.45

323.07 328.94 342.18 337.47 332.91

8.55

529.10 458.50 390.70 325.38 425.92

87.67

0.07 0.56 0.14 0.10 0.21

0.23

2.05 5.52 5.23 1.16 3.49

2.21

0.10 0.13 0.04 0.05 0.08

0.04

0.06 0.04 0.02 0.04 0.04

0.02

4104.54 3186.51 1552.54 1134.56 2494.54 1391.38

1.76 1.77 1.58 1.49 1.65

0.14

1.41 2.07 2.61 1.26 1.84

0.62

0.07 0.17 0.12 0.12 0.12

0.04

0.14 0.72 0.46 0.44 0.44

0.24

0.02 0.17 0.08 0.06 0.08

0.06

1.21 1.07 0.93 0.75 0.99

0.19

0.02 0.14 0.05 0.04 0.06

0.05

0.00 0.02 0.00 0.00 0.01

0.01

0.01 0.09 0.02 0.02 0.03

0.04

0.00 0.01 0.00 0.00 0.00

0.01

0.00 0.04 0.02 0.00 0.02

0.02

0.00 0.01 0.00 0.00 0.00

0.00

0.00 0.03 0.02 0.01 0.01

0.01

0.00 0.01 0.00 0.00 0.00

0.00

0.09 0.13 0.14 0.03 0.10

0.05

0.04 0.04 0.03 0.03 0.04

0.01

121.45 107.57 121.25 115.96 116.56

6.51

0.14 0.16 0.23 0.07 0.15

0.07

0.10 0.28 0.25 0.83

0.36

0.32

vii

GEOLOGICA CARPATHICA

GEOLOGICA CARPATHICA, 2014, 65, 4

Electronic supplement – Appendices 1—5

Plagioclase

Excluded from calculation

p1 p2 Avg

SD p3 p4 p5

19.66 23.66 21.66

2.83 17.25 18.36 22.67

77.23 33.80 55.52

30.71 47.62 40.88 56.09

2.29 0.92 1.61

0.97 1.28 0.77 1.54

2.90 1.35 2.12

1.10 3.29 2.22 2.33

18.12 7.98 13.05

7.17 10.68 6.73 12.87

268.20 46.29 157.25

156.91 154.30 101.40 90.50

499.30 500.80 500.05

1.06 524.90 606.90 512.70

0.13 0.16 0.15

0.02 0.66 0.57 5.25

16.53 3.90 10.21

8.93 14.43 6.36

293.40

9.51 1.60 5.55

5.59 0.24 1.77 1.47

0.07 0.04 0.06

0.02 0.10 0.03 0.11

213.10 57.97 135.54

109.69 104.40 111.10 72.53

20.43 27.00 23.72

4.65

213.50

326.80

54.60 inclusions of Mnz, Ap?

36.29 40.69 38.49

3.11

283.30

356.50

129.40

3.94 5.47 4.71

1.09

40.92

51.38

10.52

11.22 13.24 12.23

1.43

125.50

159.00

34.09

0.57 0.88 0.73

0.22

6.80

8.76

3.22

0.60 0.84 0.72

0.17

1.12

1.32

1.05

0.59 0.57 0.58

0.01

4.45

5.88

2.33

0.02 0.03 0.024

0.01 0.18 0.25 0.22

0.03 0.05 0.037

0.01 0.27 0.28 1.05

0.00 0.00 0.004

0.00 0.03 0.03 0.21

0.03 0.03 0.027

0.00 0.17 0.25 0.61

0.00 0.00 0.001

0.00 0.01 0.01 0.10

0.01 0.00 0.007

0.01 0.03 0.03 0.80

0.00 0.00 0.001

0.00 0.00 0.00 0.12

0.95 0.20 0.58

0.53 0.63 0.19 7.68

0.09 0.02 0.05

0.05 0.02 0.18 0.03

62.66 58.04 60.35

3.27 78.75 78.32 76.86

4.90 1.34 3.12

2.52 14.98 8.14 21.04

1.97 1.35

1.66

0.44

10.26 10.11 8.87

Biotite

B1 B2 B3 Avg

4.481 5.162 4.468 4.70

0.40

1357.579 1380.579 1358.579 1365.58

13.00

24.955 24.765 23.835 24.52

0.60

109.12 119.72 117.52 115.45

5.59

259.247 263.847 256.847 259.98

3.56

828.107 756.107 633.507 739.24

98.39

1.395 1.844 1.951 1.73

0.30

0.053 4.416 4.036 2.84

2.42

0.915 2.243 0.567 1.24

0.88

91.419 95.239

124.999 103.89

18.38

0.079 0.096 0.005 0.06

0.05

1114.197 1186.197 1458.197 1252.86

181.43

0.031 0.801 0.901 0.58

0.48

0.03 2.372 2.756 1.72

1.48

0.001 0.623 0.568 0.40

0.34

0.003 3.189 3.232 2.14

1.85

0.001 1.139 1.017 0.72

0.62

0.054 0.103 0.132 0.10

0.04

0 0.915 0.918 0.61

0.53

0 0.139 0.124 0.09

0.08

0.002 0.733 0.695 0.48

0.41

0.001 0.134 0.141 0.09

0.08

0.004 0.281 0.282 0.19

0.16

0 0.037 0.034 0.02

0.02

0.001 0.243 0.186 0.14

0.13

0.001 0.028 0.025 0.02

0.01

0.115 0.141 0.028 0.09

0.06

6.912 9.562

14.066 10.18

3.62

2.832 3.554 3.959 3.45

0.57

0.076 0.709 0.534 0.44

0.33

0.027 0.133 0.086

0.08

0.05

GEOLOGICA CARPATHICA

GEOLOGICA CARPATHICA, 2014, 65, 4

Electronic supplement – Appendices 1—5

Appendix 5

Typical electron-microprobe analyses of the zircon-like
ABO

-type phase (wt. % and apfu).

1 2 3 4 5 6

SiO

16.055 14.810 14.704 15.398 14.739 16.300

TiO

0.090 n.d. 0.087 n.d. 0.058 0.034

0.667 0.733 0.650 0.642 0.878 0.704

FeO

1.220 2.241 4.426 0.732 6.781 1.002

MnO

0.026 0.132 0.186 0.057 0.439 0.058

MgO

0.101 0.202 0.174 0.186 0.236 0.128

CaO

4.765 4.875 4.612 4.795 4.574 4.641

0.137 0.091 0.098 0.086 0.095 0.218

6.582 6.699 6.684 6.888 6.353 6.407

0.149 0.241 0.202 0.188 0.198 0.172

0.021 0.014 0.030 0.003 0.012 0.009

0.479 0.332 0.285 0.264 0.362 0.483

ZrO

27.758 24.869 23.731 26.561 25.640 27.874

HfO

0.570 0.569 0.596 0.617 0.571 0.692

n.d. 0.014

0.003

0.017

n.d. n.d.

SnO

0.010 n.d. 0.029 n.d. 0.036 0.005

PbO

0.214 0.265 0.278 0.296 0.192 0.208

1.278 1.106 1.179 1.208 1.240 1.033

ThO

31.947 32.353 31.751 35.250 29.028 31.265

3.236 2.377 2.104 2.238 2.058 3.378

SmO

0.122 0.172 0.011 0.061 0.213 0.206

n.d. n.d. 0.169

0.210

n.d. 0.041

0.170 0.119 0.042 0.067 0.371 0.181

n.d. n.d. n.d. n.d. n.d. n.d.

0.077 0.099 n.d. n.d. n.d. n.d.

0.298 0.215 0.207 0.137 0.219 0.287

0.606 0.358 0.345 0.651 0.163 0.681

Total

96.578 92.886 92.583 96.552 94.456 96.007

0.647 0.624 0.622 0.631 0.606 0.658

0.003 0.000 0.003 0.000 0.002 0.001

0.032 0.036 0.032 0.031 0.043 0.034

0.041 0.079 0.156 0.025 0.233 0.034

0.001 0.005 0.007 0.002 0.015 0.002

0.006 0.013 0.011 0.011 0.014 0.008

0.206 0.220 0.209 0.210 0.201 0.201

0.007 0.005 0.005 0.004 0.005 0.011

0.225 0.239 0.239 0.239 0.221 0.219

0.006 0.010 0.008 0.007 0.008 0.007

0.001 0.001 0.001 0.000 0.000 0.000

0.012 0.008 0.007 0.007 0.009 0.012

0.546 0.511 0.489 0.530 0.514 0.549

0.007 0.007 0.007 0.007 0.007 0.008

0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.001 0.000 0.001 0.000

0.002 0.003 0.003 0.003 0.002 0.002

0.011 0.010 0.011 0.011 0.011 0.009

0.293 0.310 0.305 0.329 0.271 0.287

0.048 0.037 0.033 0.034 0.031 0.050

0.002 0.003 0.000 0.001 0.003 0.003

0.000 0.000 0.002 0.003 0.000 0.001

0.002 0.002 0.001 0.001 0.005 0.002

0.000 0.000 0.000 0.000 0.000 0.000

0.001 0.001 0.000 0.000 0.000 0.000

0.006 0.005 0.005 0.003 0.005 0.006

0.077 0.048 0.046 0.084 0.021 0.087

site A

0.921 0.917 0.909 0.914 0.886 0.929

site B

1.183 1.210 1.249 1.175 1.321 1.175

The EPMA results are recalculated on the basis of 4O apfu.
n.d. – not detected.
Site B includes Si, Al, P, As and S, the site A comprises all other
elemets (except F).