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K/Pb FRACTIONATION TRENDS

Thesis for the Degree of M. S.
MICHIGAN STATE UNIVERSITY
JAMES EDWARD FLIS

1975 -

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ABSTRACT

K/Pb FRACTIONATION TRENDS
by

James Edward Flis

The examination of element pairs as petrogenic indicators has
been the prime interest of many geochemists in recent years. The
literature suggests that the element pair, K/Pb, also has the poten-
tial for being such an indicator, but has not been given full attention
due to its random chalcophile and lithophile characteristics.

This paper investigates the K/Pb ratio in various rock types.
The data from 338 igneous and 493 metamorphic rocks was researched
from the literature and statistically examined. Lead is the decay
product of three radioactive isotopes, U238, U235, Th232. In this
study of common lead concentrations it was necessary to mathematically
seperate the radioactively decayed lead from the reported lead values.
Through the use of a correction equation, it was found that the
addition of radiogenic lead, to the common lead concentrations, has
a minimal effect on the overall K/Pb correlations. The correlations
for nearly all the rock types examined varied widely and were
relatively poor.

A plot of the igneous averages showed a positive K/Pb trend.
The metamorphic averages were made obscure by large standard deviations.
Individual rock trends were examined by least squares regression
on those suites found significant at a 95% confidence level. The

overall K/Pb data suggests a depletion of lead in the upper crust

and mantle and an enrichment in the lower crust.

James Edward Flis

In conclusion, the poor correlations of the K/Pb data found in
this paper and elsewhere, demands a detailed examination of the
multiphases of lead. For example, very little research has been

done on the gaseous and liquid phases of lead in geological environ-

ments .

K/ Pb FRACTIONATION TRENDS

BY

James Edward Flis

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

1975

ACKNOWLEDGMENTS

I am totally grateful for all those who assisted me with this
thesis. Special recognition and appreciation is given to Dr. J.T.
Wilband, my thesis committee chairman, for his guidance and perser-
verance. For help with the manuscript, Drs. H.B. Stonehouse, W.F.
Cambray, H.F. Bennett, and with the correction equation, Drs. Ray
Warner of the Cyclotron Lab and Steve Ewald of the Engineering
Department.

A sincere thanks to Connie for typing of the manuscript and
moral support. Thanks for your concern and friendship, Dave, Pete,
Sue and Dewey from SUNY Fredonia and Rick and Carol from M.S.U. Also,

thanks a whole bunch Mom and Dad.

ii

TABLE OF CONTENTS

LIST OF TABLES O. O O o O O O O O O O O O O O O O O I O O 0

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . .

II.

III.

IV.

V.

VI.

VII.

VIII.

INTRODUCTION . . . . . . . . . . . . . . . . . . .
STATEMENT OF PROBLEM . . . . . . . . . . . . . . . .
CRYSTAL CHEMISTRY . . . . . . . . . . . . . . . .
RADIOGENIC LEAD CORRECTION . . . . . . . . . . . . .
K/Pb RELATIONSHIPS . . . . . . . . . . . . . . .
Pb AND K/Pb TRENDS . . . . . . . . . . . . . . . . .
DISCUSSION . . . . . . . . . . . . . . . . . . . .

CONCLUSION AND SUMMARY . . . . . . . . . . . .

APPENDIX 1 . . . . . . . . . . . . . . . . . . . . . . .

APPENDIX 2 . . . . . . . . . . . . . . . . . . . . . . .

REFERENCES . . . . . . . . . . . . . . . .

iii

Page

iv

11
16
34
37
38
40
58

61

10.

ll.

12.

LIST OF TABLES

Simple statistics of all raw data . . . . . . .
Ionic radii of associative elements . . . . . .
Lead concentrations in rock forming minerals .
Radioactivity of accessory minerals . . . . .

Radioactive decay constants for lead producing
isotopes O O 0 O O O O O O O O O C O O O O

Anomalous lead enrichment of various rock types
Anomalous lead enrichment of major rock types

Kurtosis and skewness of total data . . . . . .
Correlation table for variable modes . . . . .
Metamorphic ANOVA . . . . . . . . . . . . . .
Igneous ANOVA . . . . . . . . . . . . . . . .

Comparative literature values .

iv

Page

10

12
15
l6
18
18
21
22

35

LIST OF FIGURES

Figure Page
1. K/Pb plot by Sandell and Goldich (1943) . . . . . . . . 3
2. K/Pb igneous scattergram . . . . . . . . . . . . . . . 4
3. K/Pb metamorphic scattergram . . . . . . . . . . . . . 5

4. Regression lines for all K/Pb igneous rock types . . . 23

5. Regression lines for all K/Pb metamorphic rock

types . . . . . . . . . . . . . . . . . . . . . . 24
6. Plot of igneous averages . . . . . . . . . . . . . . . 25
7. Plot of metamorphic averages . . . . . . . . . . . . . 26

8. Average regression lines for the significant
igneous and metamorphic rocks . . . . . . . . . . . 33

INTRODUCTION

A literature search for investigations reporting lead analyses
for major rock types has revealed that lead isotope analyses,
rather than analyses for common lead,* are most often recorded.

This lack of common lead concentration data, especially for igneous
and metamorphic rocks, has been noted by Zartman and Wasserburg
(1969), Doe and Tilling (1967), Shaw (1972), Viswanathan (1972a)
and Rhodes (1969).

Successful studies by Shaw (1968), and Lewis and Spooner (1973),
of coherent element pairs, like K/Rb in igneous and metamorphic rocks,
has provoked interest in other elements that show close geochemical
coherence. Common lead has been recognized as a potential petrogenic
indicator. Within crystal chemical considerations lead is thought
to closely follow potassium in behavior and isomorphically replaces
potassium in K-rich minerals (Wedephol, 1956; Goldschmidt, 1937;
Stavrov, 1971; Zlobin, et al., 1965). Some investigations, especially
those on K-feldspar rich rocks, indicate a fractionation between
K and Pb while other investigators report contradictions between their
K-Pb data and crystal chemical theory. For example Heier (1962, p. 441)
could only call his K—Pb data "confusing", and others denote K-Pb as

a vexing problem (Heier, 1960; Taylor, et al., 1960; Howe, 1955).

*Common lead, PbZOA, is lead obtained from non—radioactive lead

minerals such as galena, cerussite, wulfenite, and from rock forming
minerals which accept lead into their structures, such as, potash
feldspars, muscovite, biotite, etc.

1

2

In natural systems, radiogenic leads, Pb206, Pb207 and pb208

are formed from parent U235, U232 and Th238 respectively. Common

lead, Pb204, can be distinguished from radiogenic leads only by mass
spectroscopy; other techniques yield total lead. Therefore,

data which report total lead must be corrected to common lead if
hypotheses concerning the distribution of lead in time and space

are to be meaningful. Since the concentration of radiogenic lead
increases as a function of time, the age of the rock as well as

the U, Th and total lead concentrations must be known before
corrections can be applied. The problem is further complicated

by the fact that lead has a complex geochemical behavior because

of its chalcophile and lithophile characteristics. These factors

partially explain why the distribution of lead has not been an

overly active area of geochemical research.
STATEMENT OF PROBLEM

A compilation of K-Pb concentrations in 338 igneous and 493
metamorphic rocks was researched from the literature. Only data
compared with certified standards or reporting a sufficient number
of replicate samples were utilized. Other trace elements, in
particular, Rb, Th, U and age of the rock, if reported, were also
compiled and incorporated into a correction equation for the
accumulation of radiogenic lead.

Correlation matrices of data from differing rock types were
arranged to examine the K—Pb fractionation problem. Least squares
analyses was used to determine the predictive equation for the K
versus Pb concentration in each rock type and other statistical tests

were used to evaluate K-Pb relationships.

3

CRYSTAL CHEMISTRY

The close geochemical association of K and Pb has been predicted
by many crystal chemists and geochemists, however, only a few
investigations have dealt with variations of lead and potassium
in rocks. A study by Sandell and Goldich (1943) reveals a large
amount of scatter of their K—Pb igneous rock data (Figure l). Sandell

and Goldich suggested that more research was necessary before valid

conclusions concerning K-Pb interactions could be made.

 

 

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MEAN 19.88
VARIANCE 237.99
RANGE 180.0
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RANGE 78.0

Table 1

STD ERROR
KURTOSIS

MINIMUM

Pb(Ppm)

STD ERROR

.073

-.69

.69

KURTOSIS 31.98

MINIMUM

STD ERROR
KURTOSIS

MINIMUM

Pb(Ppm)
STD ERROR
KURTOSIS

MINIMUM

.084

.004

.62

3.08

0

STD DEV

SKEWNESS

MAXIMUM

STD DEV

SKEWNESS

1.62

.70

7.45

15.43

4.22

MAXIMUM 180.0

STD DEV

SKEWNESS

MAXIMUM

STD DEV

SKEWNESS

MAXIMUM

1.54

.35

7.51

11.35

1.46

78.0

7
are compiled in Table 1. The range for lead in the igneous data is
78 ppm while that for the metamorphics is 180 ppm. Both plots have
correlation coefficients of .55 and .49 respectively and scatter
increases with increasing potassium.

It has been common practice among geochemists to arrange their
data in order of increasing ionic radii since Goldschmidt recognized
ionic size as a prime factor controlling the distribution of some
elements in mineral lattices (Table 2). With reference to Table 2,

some of the following diadochic substitutions have been reported.

Table 2
Cs+ 1.67 Ba2+ 1.35 Sr2+ 1.18
+
Rb 1.47 K+ 1.33 Ca2+ 1.02

Tl+ 1.47 Pb2+ 1.20 Na+ 0.97

Lead and strontium replace Ca2+ in calcium minerals and monoclinic
pyroxenes (Rankama and Sahama, 1950). Most often lead is present in
silicate minerals as a potassium-type trace cation. Potassium rich
minerals, particularly potassium feldspars accept lead into their
lattice. Several studies show that lead is enriched in late formed
potassium minerals such as pegmatitic potassium feldspars (Wedepohl,
1956; Heier and Taylor, 1959). Lead, therefore, violates Goldschmidt's
"capture" principle as there is a lack of Pb — enrichment in early
formed K-minerals. Siedner (1965) explains this reverse in enrichment
by Ringwood's (1955) rules: whenever diadochy in a crystal is possible
between two elements, the element with the smaller electronegativity

is preferentially incorporated (Pb2+ = 1.60, K1+ = .80).

In the orthoclase structure potassium cations are distributed

directly among the rings of the Si—Al tetrahedra that are united

8
into chains, and there exists a possibility of compensation of
a large bivalent cation (Pb2+) by a pair of Al—tetrahedra in the
[SiZA12081-2 framework (Byelov, 1953). The network of 8104 and
A104 tetrahedra is elastic to some degree and can adjust itself

to different sizes of cations. Natural potash feldspars can be

and PbAl Si O

isomorphic mixtures of KAlSi3O8 2 2 8'

Natural lead feldspars have never been found, however, research
has shown that they may be produced artificially (Sorrell, 1962).
Sorrell found high reactivities at low temperatures for artificially
produced Pb-feldspars and suggested that lead in potassium feld—
spars may be more common than realized. Potassium feldspars, pro-
gressively enriched with lead, are found in close proximity of lead
ore bodies (Cuturic, et al., 1968; Slawson and Nackowski, 1959;
Doe and Hart, 1963).

The parameters governing the partitioning of lead between

coexisting potash feldspars and plagioclase is unknown (Doe and

- - Pb
Tilling, 1967). The average partitioning factor (C K-Feldspar
Pb n n . , .
Plagioclase) where C is the concentration of lead in parts

per million, is reported as less than one by some (Heier, 1960;
Howie, 1955; Barth, 1967), while Doe and Tilling (1967), report a
partitioning factor with a range of 2 to 4.5. Table 3 lists the
major minerals allowing lead substitution, and their concentrations.
A partitioning factor of 2.4 was determined between the K—feldspar
and plagioclase. This factor is only a approximation since some of
the analyses in Table 3 are not from coexisting minerals. A factor
of 2.4 suggests that lead is more receptive in the K-feldspar

structure.

Table 3
Potassium Feldspar Plagioclase Biotite Horneblende
Pb(ppm) (Author,#) Pb(ppm)(Author,#) Pb(ppm) (Author,#) Pb(ppm) Author,#)
GRANITBS 56.0 (3,3) 25.0 (3.3) 10.0 (3.3) 34.0 (3.3)
" 37.0 (4,6) 11.0 (4,6) 48.0 (8,2)
" 29.0 (1,31) 36.0 (7,1)
" 67.0 (2.56)
DIORITE 15.0 (7,1) 9. (783.2) 16.0 (7&3,2)
SYENITE 50.0 (6,1) 22.0 (6,1)
GRANODIORITE 28.0 (5,2) 15.0 (7,1)
ALASKITE 45.0 (4,1) 19.0 (4,1)
GNEISS 33.0 (154.4) 15.0 (4,1)
PEGMATITE 37.0 (1,4) 46.0 (4.1)
" 114.0 (4,1)
AVERAGE 49.6ppm 20.9ppm 25.0ppm
Cpb 4
K-Feldspar Plagioclase = 9.6ppm/20.9ppm = 2.4 part. factor

Zartman, Wasserburg (1969)
Rhodes (1969)
Fershater, et al., (1969)
Doe, Tilling (1967)

5
6.
7.
8

Cuturic, et al., (1968)
Zhirov, Chernyshev (1959)
Rabinovich, et al., (1959)

Viswanathan (1972)

Diadochic substitution of lead for potassium can occur in the

potassium interlayer position of biotite.

For each lead captured,

an additional aluminum must be admitted to the biotite tetrahedral

layer to compensate for the charge difference.

Zlobin and Gorshkova

(1961) noted this aluminum replacement and concluded that lead is

admitted into the biotite structure only with some difficulty.

Parry and Nackowski (1963) studied biotites in monzonites and found

increased concentrations of lead in biotite samples taken progressively

away from lead ore bodies.

They suggest solutions and leaching could be

10

responsible for the negative correlation in their data. Viswanathan
(1972) found a positive correlation of lead with potassium in
biotites from the Canadian Shield. Stavrov (1971) did not consider
biotites as major lead carriers in his analyses of granites.
Table 3 shows a wide range of lead concentrations in biotites
and hornblende. Moorbath, Welke and Gale (1969) noted minimal lead
concentrations in hornblendes and pyroxenes of metamorphosed suites.
Radioactive minerals are also important, as they contain sites
for lead produced through radioactive decay. These minerals can
contain anomalous lead. Zircon, allanite, and sphene commonly
contain radiogenic lead, derived from U and Th disintegration. It
can be expected therefore, that diorites and granodiorites, those
rocks containing a high proportion of accessory minerals will contain
anomalous leads whereas, gabbros, basalts and granites should contain
higher amounts of common lead. The mode of bonding of radio—
genic lead in these accessory minerals is unknown, but Boyle (1959)
reports that lattice vacancies can be produced through radiation
and may provide lead sites. Doe (1967) suggested that radiogenic
lead is probably not found in the same lattice positions as common lead.

Table 4 shows the high radioactivity of accessory minerals, zircons,

Table 4
Pb0(ppm) (x/mg/sac Total Pb(ppm) Pb206

lGRANITE 18.0 .9 2ZIRCON 461.0 34.2
PLAGIOCLASE 15.0 3 SPHENE 1 113.0 39.9
QUARTZ 5.0 .2 ACID WASH SPHENE 1 222.0 44.5
BIOTITE 32.0 .4 SPHENE 240.0 68.4
HORNEBLENDE 12.0 .8 MAGNETITE 1.4 .33
APATITE 5.0 56 0 APATITE 136.0 34.5
ZIRCON 40.0 400.0 QUARTZ 5.5 1.36
SPHENB 36.0 260.0 PLAGIOCLASE 3.8 .94

PERTHITE 9.5 2.35

1
Larsen et a1.(l952) 2Tilton,Patterson(1955)

11

sphene and apatite as found in some granites. There is a large

. 2
concentration of Pb 06 in the acid wash from sphene l, which suggests
this isotope is loosely bound in the lattice. Picciotto (1950)

found radioactive elements present in mineral interstices and intra—

crystalline fractures of some granites.
RADIOGENIC LEAD CORRECTION

Examination of common lead concentrations demands a knowledge
of the initial amount of common lead introduced into the rock at
its time of crystallization. A sample of ordinary lead can be
considered a mixture of common and radiogenic lead. The radio-
genically derived lead is composed of equal amounts of thorium
lead and U238, U235 derived lead. Any additional amount of lead
accumulated through radioactive decay in a sample must be corrected
by subtraction from the ordinary lead content. In general, radio-
genic lead enrichment is a function of time, however, the growth
curve is not well known. U—Pb and Th-Pb isotOpe determination
requires a primary lead correction through the use of mass spectro-
metry. The nature of the data in this paper does not make it possible
to make common lead corrections through isotopic determinations.
Rather corrections can be made if a series of critical factors are
known; concentrations of Pb, Th and U and age of the rock.

Uranium235, Uranium238 and Thorium232 will, through complex

206 207

20 .
transformations, decay to Pb , Pb and Pb 8 respectively

(Table 5).

12

 

 

 

 

TABLE 5
-10 -1
2 = .
Th 32 A 499x10 yr Pb208 + 6He + E
_ -10 -1
U235 A — .972x10 yr Pb207 + 7He + E
_ —10 —1
U238 A - 1.54x10 yr Pb206 + 8He + E
Pb204 unchanged pb204

Each parent nuclei produces an unstable nucleus that decays to

a final stable isotope. Lambda (A ) is the probability of decay

governed by each nucleus. Common lead (Pb204) is known to exist

as a stable isotope and is not a product of radioactive decay and
therefore, unchanged through time.

The relationship between the number of parent atoms and their

decay rate is:
d/dt (N)=- AN (1)

where N is the number of the parent atoms at time t and A.is again
the decay constant for that particular isotope. Integration of

Equation 1 gives:
N=Ne (2)

where N is now the number of parent atoms which were remaining

after time t, and No is the initial number of parent atoms at time

zero. The decay of U238 to Pb206 can be expressed as follows:

dU238 = _ A (U238) = _ d Pb206 (3)
dt 238 i dt
or

206

d Pb _ 238

7752—77' ‘ + A238 (U )1 (4)

206 _ . .

The amount of Pb atoms produced after a time t is:
Pb206 = ft d Pb206 dt = A It 0.238 dt (5)

O T 238 0 1

It is seen from equation 2 that:

238 = 0 238e—At

UP 1 (6)
and 11.238 = u 238.“ <7)
1 P
Substitution of equation 7 into equation 5 gives:
206 _ t 238 At
Pb — A238 6 Up e (8)
_ 238 A238t
A238 Up [3—14- (8 ’l)] (9)
238
= U 238 (eA238t-l)* (10)
P
The decay equation of Pb207 and Pb208 is constructed in a similar
manner giving,
Pb207 = U235 (CA235t_l) (ll)
Pb208 = Th232 (eA232t_l) (12)

*(eAt-l) values are reported in Tables 1.6; 1.7; 1.8; by Russell

and Farqhaur (1960).

l4

Summing equations 10, 11 and 12 gives the amount of radiogenic lead

 

added in a rock sample formed at time t. (13)
232 A232t
_ 238 A238t_ 235 A235t_ (e -l)
ZPbRADIO Up (e l) + Up (e l) + Th
Dividing equation 13 by total lead (Pbtot) and multiplying by 100
yields the percent of radiogenically derived lead.
235 (14)
238
ZPbRAD I Pb204 Up (8A238t_1) + Up (eA235t_1) + Th232 (eA232t_1)
Pbtot Pbtot Pb204 Pb204 Pb204
where
238 + 238*
U U__x Pb x U = U x 67.5675 x .9927 (15)
Pb204 Pb Pb204 U Pb
235 235+
U U x Pb x U = U x 67.5675 x .0072 (16)
Pb204 Pb Pb204 U Pb
Th U__x Th_x Pb_ = U__ x Th.x 67.5675 (17)
Pb204 Pb U Pb204 Pb U
Uranium, thorium and lead concentrations are in parts per million.
Finally, simple manipulation yields the radiogenic lead correction
equation.
Pb (18)
_ Z RAD x (Reported Lead )) = P
Reported Leadppm) (—§B;;:- (ppm) boriginal(ppm)

Equation 18 has an error of approximately 4 percent with the premise

238

that the bulk of the radiogenic lead produced is thru the decay of U .

This is a good assumption since U238

99.12775r

1'U.S.A.E.C. Chart of Nuclides (1968).

has a crustal abundance of

15

A Fortran IV computer program was written to facilitate in
correcting the available lead data. Only data reporting concentrations
(ppm) of Pb, U and Th and age could be used in the correction
equation (E0. 14 and 18). A listing of the individual corrected
and uncorrected lead values is found in Appendix 1. As expected,
the older, more uranium rich rocks give larger lead corrections
(Table 6). The standard deviations (0) show a general decrease,

which suggests that the corrected values reduces scatter. One value,

 

TABLE 6

Rock Type(#) _flUncorrected ___ Corrected Radiogenic

Pb(PPm) o Pb(ppm) o Pb(me)
ANDESITES(17) 4.77 2.91 4.75 2.89 .02
ANORTHOSITES(7) 9.77 9.24 9.60 8.86 .17
GRANITES(13) 28.71 8.50 28.10 7.74 .61
BASALTS(22) 4.78 3.68 3.89 5.00 1.09
GRANULITES(77) 26.26 12.10 25.17 12.25 1.09
AMPHIBOLITES(56) 28.15 14.85 26.88 14.39 1.27

from a granulite (Heier and Thorensen, 1971), had an overcorrected
negative value (-22 ppm) and was discarded.

Ninety—one igneous and one hundred seventy two metamorphic
corrected values were incorporated into the total data available
in an attempt to reduce the amount of scatter in the raw data.

The Ksz correlation matrix (Table 7) shows a relative consistency
of correlations in the igneous data, even with the addition of
the corrected values. The corrected metamorphic rocks decrease

in correlation (r).

16

Table 7
(r) (r)
Rock Type(#) Uncorrected Corrected
LogK/Long LogK/Long
IGNEOUS(91) .76 .77
TOTAL IGNEOUS(338) .47 .48
METAMORPHICS(172) .81 .76
TOTAL METAMORPHICS(493) .52 .47
ALL DATA(831) .44 .43

Table 7 suggests that the addition of anomalous lead caused by
radioactive decay, is so minimal that this addition has only a
small or insignificant effect on the overall K/Pb correlation.

The corrected rock types in Table 7 give very high correlations.
The data was collected from authors that analyzed their rock samples
from specific geographic locations, for example, Heier and Thoresen,

(1970), and not geographically dispersed.
K/Pb RELATIONSHIPS

The co-existing potassium — lead values were first examined
assuming a linear relationship. The coefficients, b0 (intercept)

and b1 (slope), of the linear predictive equation:

A

YPb = b0 + bl xK (l)

were found by regression analysis. The nineteen rock suites presented
represent data from 338 igneous rocks and 481 metamorphic rocks.
Only chemical data which satisfied the following prerequisites were

used: (1) the analyses were compared to certified standards, and

l7

(2) the authors performed a sufficient number of replicate deter-
minations to report the precision of their analytical method. If

the mean and frequency do not coincide, the data is skewed. Table

8 lists kurtosis and skewness for the arithmetic and lognormal

Ksz data. Metamorphic K and Pb values show a high tendency for
lognormality with a negative skewness. In the igneous data, potassium
shows arithmetic normality while that for lead suggests a lognormal
distribution. Miller and Goldberg (1955) also noted that potassium
was arithmetically normal. Their lead data was lognormal. Ahrens
(1954) found both potassium and lead had lognormal distributions.

It is interesting to note that all the lognormal data is
negatively skewed, the igneous more negatively skewed than the
metamorphics. Zhirov and Chernyshev (1959) suggested that the
igneous lognormal distribution of the elements characterizes the
primary content of the magma. Any addition to that content would
skew a lognormal distribution. If this is the case, the igneous
and metamorphic data suggests contamination of Pb and possibly K
from other sources.

Many investigators have reported that elements (in particular
trace elements) have a lognormal distribution. In effect the log of
the variables should give a higher correlation coefficient than
arithmetic values of the same variables. Mixed mode (arithmetic—log)
and common mode (log-log or arithmetic—arithmetic) correlations are
reported in Table 9. These variables are also compared to the ratio
value R, where R = 10,000 E / PB. The correlation coefficients
in Table 9 indicate considerable variations between mixed and common

mode correlations. For example, diorites and anorthosites consistently

Igneous

GRANITE
ULTRABASIC
ANDESITE
DIORITE
DACITE
MIGMATITE
BASALT
ANORTHOSITE

Metamorphics

SCHIST
AHPHIBOLITE
GRANULITE
SLATE
GNEISS

Metamorphics

KZ

LogK

Pb(PPm)

Long

Igneous

KZ

LogK

Pb(ppm)

Long

(r) (r)
K/Pb K/Long
.10 .19
-.33 -.22
.38 .31
.43 .44
.37 .16
.04 .15
.33 .43
.97 .88
.58 .56
.77 .83
.58 .65

-.OS -.21
.50 .41

fl _—
R - 10,000(K/Pb)

18

Table 8
KURTOSIS SKEWNESS
-.70 .71
1.46 —.88
31.98 4.22
3.13 —.69
—.71 .35
6.09 -1.96
3.08 1.46
2.49 -1.04
Table 9
(r) (r) (r)
LogK/Pb LogK/Long Pb/R*
.17 .29 -.60
-.02 .15 -.44
.32 .28 -.55
.41 .42 -.05
.38 .17 -.34
—.O4 .03 -.47
.34 .42 -.38
.96 .89 .40
.55 .46 .14
.69 .88 .06
.59 .68 _-.35
-.O6 -.20 -.58
.45 .41 -.20

(r)
K/R*

.34
.90

-.89
.44
.54
.30

.61

.82
.66
.31
.37
.46

19
gave similar correlation coefficients for all modes presented,
whereas granites gave a wide range of values. The log values log
K/long gave the most consistent positive correlations. Since the
ratio of the log values is most generally reported in the literature,
this precedent will be followed.

The statistical F test was used on the data to compare the
variance of the two populations. For the F test to be valid, the
data must represent random samples from a normally distributed
population. The data used in this study satisfies normality (it is
nearly lognormal) and randomly sampled from the literature. The
null hypothesis was proposed that no differences exist between the
two variances to be compared, i.e., HO:Oi = 0:. The test ratio of
the two variances was computed according to the relationship
F = of / a; where O is the standard deviation and 02 is the variance.
The calculated F value was then compared with the corresponding
value in F distribution tables (Table — S, Rohlf and Sokal, 1969) at
the 95% confidence limit and appropriate degrees of freedom. The
choice of a 95% confidence level is satisfactory for most geological
problems (Kauffman, 1969) and will be used in this study.

If the calculated F was less than the F distribution value
found in the tables, there was no significant difference between
the variances at a 95% confidence level. One could not therefore,
reject the null hypothesis. If the calculated F was greater than
the F distribution value found in the tables at 95% confidence level,
then the ratio of the variances is larger than would be due to chance,

and variations are considered to be caused by some outside influence

and not chance alone.

20

Regression analysis was used to examine data and draw meaningful
conclusions about dependency relationships of potassium and lead.
Nineteen rock suites were analyzed.

All regression studies require that one variable takes fixed
values subject to minimal error. It is a problem fitting regressions
when errors of measurement are present in one or both of the variables.
Geochemical data commonly has errors in one or more variables.

Shaw (1968) partially avoided this problem by calculating both
regressions, y on x and x on y and averaged the final slopes.

In itself, the question of which regression line is more appropriate
is meaningless as it stands. Before it can be answered, we must
determine; (1) how the (x,y) values were obtained and (2) the
purpose of the regression (Winsor, 1946). In this study the pairs
of K and Pb values (y,x) were obtained (1) as a random sample
from the general population. It is then possible to estimate the
constants of the (y,x) distribution; (2) it is desirable to present
a relation to estimate in the future, the value of lead (x), given
a future measurement of potassium (y). Consideration of l and 2
statistically allows the validity of the regression of x on y (xly)
and is uneffected by the fact that positive errors of measure-
ment are involved. Tables 10 and 11 are the ANOVA statistics for
the logarithmic and arithmetic data.

Regression lines (xly) were drawn on log scale for twelve
igneous and seven metamorphic rock suites (Figures 4 and 5). All
suites, excluding diorites, exhibit subparallel behavior and steep
to vertical slopes. The means and standard deviations for these

regression lines are plotted in Figures 6 and 7. The igneous rocks

21.

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24

 

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26

 

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27

contain large standard deviations but Show a definite K/Pb trend.

The potassium deficient ultrabasics have the lowest lead concentrations,
while the potassium rich migmatites and granites contain the largest
concentrations of lead.

The plot of the metamorphic averages and standard deviations
does not present a clear picture (Figure 7). The high temperature
and pressure suites have the highest lead and potassium concentrations
but the large standard deviations make conclusions difficult. It
is interesting to note however, that the standard deviations for
the metamorphics is largest in the potassium range while the larger
standard deviations for the igneous rocks is found in the lead
range. This suggests that lead is much more variable in the igneous
rock suites.

The F statistic was calculated to select the suites most
significant at the 95% level. Nine suites were obtained, four
metamorphic and five igneous rocks. The appropriate summary statistics
are found in the ANOVA Tables 10 and 11.

The regression lines for these significant rocks were replotted
on scattergrams on log scale, and examined (Pages 28-31). The
t statistic was used to determine whether the lead and potassium
vary significantly between suites. The ratio of the difference
between the two slopes to its standard error was compared against a
t statistic. The hypothesis, that the slope of one regression line
b1 is significantly different from the slope of another regression
line b2, was examined. Rock types that visually appeared parallel
(Figures 4 and 5) were statistically compared, i.e., granite vs.

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28

 

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found in Appendix 2. Of the six groups examined, the slopes of two
groups were not significantly different at a 95% confidence level,
i.e., the andesites-gneisses and andesites-basalts. It is doubtful
though, that the K/Pb environment of the andesites could be related
to two distinctly different rock types (gneiss-basalt). The other
groups examined had significantly different slopes.

Finally, a single regression line was drawn for an average of
all the significant igneous as well as for the significant metamorphic
rocks. The significant igneous and metamorphic regression lines
are drawn in Figure 8. The igneous trend (R=1529.4) contains a larger
range of lead values, but a smaller Pb average than the metamorphic
trend (R=1027.6).

Statistical analysis of the K/Pb data has led to the following

conclusions:

(a) most K/Pb correlations for the 19 igneous and metamorphic
suites were poor;

(b) lead was found lognormal while potassium appears to be
more arithmetically than lognormally distributed;

(c) of all the possible variables the log K/ log Pb correlation
was chosen to best represent the data;

(d) of the 19 suites, 5 igneous and 4 metamorphic rocks were
found significant at the 95% confidence level;

(e) of those accepted as significant, the andesite—basalt
regression lines were parallel as were the andesite-gneiss

regression lines;

33

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(f) the regression line best fitting the metamorphic data can

be expressed as:

Pb

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PPm

log pmeb .35 log (KZ) = 1.15

(g) the regression line best fitting the igneous data can be

expressed as:

Pb

4.62 (KZ) + 4.05
PPm

log pmeb .73 log (K4) + .841

Pb AND K/Pb TRENDS

The lead concentrations and R values are inconsistent with
published values. R values in the andesites have a wide range,
1530 - 1720; the basalts (including tholietes) range from 1000 to
8333; granites, with an average lead concentration of 20 ppm has
an R range of 1670 to 1995 (Table 12).
Wedepohl (1956) reported average Pb contents of basic, granodiorite
and granitic rocks as 6, 15 and 20 ppm respectively. He used
standards G-1 and W—l and reported lead values at 26 and 6 ppm.
Recent results on G-1 and W—l reported in Stevens, et al., (1960)
and Fleischer and Stevens (1962) indicate 49 ppm and 8 ppm, respectively
for those standards (Flanagan, (1973) reports 48 and 7.8 ppm Pb).
Any report using Wedepohl's (1956) data would therefore, have
lead concentrations reported too low. Using Steven's analyses,
Kolbe and Taylor (1966) reported 30 ppm Pb for seventeen samples
of porphyritic Cape granites. This paper reports an average of

22 ppm lead for 75 granite samples. The wide ranges (Table 12)

Rock Type(Author)

GRANITE(1)

H (3)

ll (2)

II (6)

H (10)

M (11)
BASALT(1)

H (3)

H (3)

H (2)

H (6)

H (10)

ll (11)
ANDESITE(1)

ll (6)

ll (10)
DACITE(6)

(10)
ULTRABASIC(6)
(10)
(11)

DUNITE(3)
GRANODIORITE(11)

SIAL CRUST(B)
CRUST(7)
UPPER CONTINENTAL CRUST(9)
LOWER CONTINENTAL CRUST(9)
MANTLE(9)
MANTLE(8)
UPPER MANTLE(7)
CORE(9)
CHRONDRITE(9)
H (4)
IRON METEORITE(5)
I!

TROILITE(4)
N

1.Vinogradov(1956)

2.Taylor(l969)

35

TABLE 12
Pb(ppm) K%
20.0 3.34
19.0 3.79
20.0
20.0
22.0 3.98
19.0
8.0 .83
6.0 5.00
1.0 .10
5.0
6.0
7.08 1.04
6.0
15.0 2.30
10.0
7.74 1.34
10.0
10.7
3.0
9.1
6.0
.03 .01
15.0
11.5 1.65
10.2
15.0 2.60
20.0 2.00
.05 .005
.27 .04
24 _5
10 2.5x10
.18 .084
.15 .08
.224
.099
.098
3.88
5.68

3.Turekian,Wedephol(1961)

4.Mason(l962)

5.Marshall,Feitknecht(1964)

6.Wedephol(l956)

1670
1995
1796
1040
8333
1000
1469

1530

1731

3333

1434

1730
1000
1000
1482

25
4600
5333

7.Armstrong,Hein(1973)

8.Armstrong(l968)
9.Shaw(l972)
10.This paper

11.Hur1ey,et al”(1962)

36
and low correlations (Tables 10 and 11) of the igneous data questions
the significance of K/Pb fractionation in igneous rocks.

Comparative literature for the K-Pb metamorphic data is lacking.
Similar to the igneous data, the increase in lead is generally correlative
with an increase in potassium. It is of interest to note that the
high grade metamorphics contain high concentrations of potassium
and lead. Doe and Hart (1963) and Doe, Tilton and Hopson (1965),
reported that lead may enter K feldspars that are subject to meta-
morphism. The R values for the granulites and amphibolites are
1388 and 1238 respectively. The large standard deviations found in
these two suites makes any conclusions on their possible K/Pb
fractionations obscure. Lambert and Heier (1968) found a lead
depletion in granulites as Opposed to amphibolites, as was found
in this paper, but the variability of their K/Pb ratios placed
doubt on the significance of the lead loss.

Shaw (1972) reports an R ratio of 1730 for rocks of the upper
crust. An average of granites, granodiorites and diorites from this
study gives a much lower value of 1482. Representative rocks from
the lower crust (basalts, granulites, amphibolites) average 1365.
Shaw (1972) reported a value of 1000 for lower crustal rocks. The
ratios reported here and in Shaw (1972) suggests a depletion of Pb
in the upper crust. Wedepohl (1974, written commun.) suggests a
depletion of Pb in the lower crust. Armstrong (1968) and Shaw (1972)
show a depletion of Pb in the mantle and core. This is supported by
Jamieson and Clarke (1970) who report that lead is probably rejected
from the zone of magma generation of the upper mantle. Primitive

iron and chrondritic meteorites have concentrations of .098 - .18 ppm

37
lead. Fish, et al., (1960) surmise that depletion in chrondrites

could result from the fractionation of Pb S in the parent asteroid.
DISCUSSION

Analysis of the lead—potassium data reported here reveals that
an increase of potassium is not a linear concomitant increase of
lead in either metamorphic or igneous rocks.

Since the work of Goldschmidt (1954) the prevailing explanation
in minerals has been that the size and charge of the ions and the
nature and strength of the bonds govern the behavior of trace
elements during magmatic and metamorphic fractionation (Taylor
and Heier, 1960). Lead should therefore be concentrated in the
early formed K-feldspars of granodiorite — dioritic melts and their
concentration decrease as fractionation proceeds. This phenomenon
is not observed in this paper. Granitic melts, such as migmatites,
contain a high concentration of lead (42 ppm average). Cuturic et al.,
(1968) found that later formed K—feldspars in the Dinarids area were
enriched in lead. Gavrilin, et al., (1972), Cuturic et al., (1968),
Parry and Nackowski (1963), Kolbe and Taylor (1966) concluded that
their lead data was affected by the loss or gain of lead through
hydrothermal fluids, either by the formation of a fluid phase or
by the formation of a gaseous phase. Jagitsch and Perlstrom (1946)
claim to have evidence for diffusion of less highly charged ionic

groups such as P PbO or ZnO. Doe and Hart (1963) report that lead

205’
can be exchanged between mineral fractions at temperatures estimated
by Bart, et al., (1968) to be 4000 - 450° c. Richards (1971)

suggested that leached aqueous solutions could be the immediate

source of some lead ore bodies. Drury (1971) found high lead

38
concentrations in granitic veins of C011 and Tire. Galena was
not found in polished sections even though galena was mined in
the C011 area. Doe and Hart (1963) noted that lead in their
mineral fractions was located on intergranular surfaces. DeVore
(1955) observed that important amounts of trace elements do not
occupy regular lattice sites but, through adsorption, occur on
growth surfaces, imperfections, dislocations and various interfaces

within the crystal.
CONCLUSION AND SUMMARY

The concensus that the K/Pb problem, reported by several authors,
as "vexing" seems justifiable. The generally accepted empirical
rules of Goldschmidt (1937), and modified by Ringwood (1955) and
Ahrens (1964) governing element distribution in geological processes
does not fully encompass the geochemical properties of lead. The
existing rules do not describe the possible coexisting lead phases
and probable competition between elements during fractionation.

These conditions may cause the magnitude and direction of fractionation
of potassium and lead to reverse in different chemical systems.

For example, Shrivastava and Proctor (1962) and Putman and Burnham
(1963) found high concentrations of lead (155 ppm) in the mafic
minerals of some plutonic rocks. Putnam and Burnham (1963) discussed
the difficulties of empirically determining whether K-feldspar in
equilibrium with granitic magma will have a higher lead content than
that in equilibrium with a granodioritic magma. Viswanathan (1972)

in his studies of lead in granitic rocks suggested that lead in
granitic rocks and minerals was useful in interpreting problems

of granite petrogenesis. His examination of Ca/Pb, Sr/Pb, K/Pb and

39
Ba/Pb ratios in biotites proved to be instrumental as petrogenetic
tracers. His conclusions should be tested elsewhere.

The K/Pb whole rock data analyzed here was an attempt to under-
stand the geochemical behavior of lead in various igneous and
metamorphic rocks. The correlation coefficients for those two
major groups were .53 and .49 respectively, scatter was evident
with an increase in potassium and lead. The appropriate data was
corrected for anomalous radiogenic lead in an attempt to improve
the correlation coefficients. It was found that the addition of
radiogenic lead produces a minimal effect on K/Pb geochemical
coherence. Statistical analysis of individual rock types reveals
a general increase of lead with potassium but not in a normal gabbro
through granite magmatic trend. Large standard deviations within
the igneous and metamorphic trends render conclusions awkward.

The general trend found was for an enrichment of lead in the lower

crust (R=l365) while the upper crust (R=l482) was depleted in lead.

APPENDIX 1

Corrected and uncorrected K/Pb ratios

APPENDIX 1

Abbreviations and Definitions

ADAMELLITE - quartz monzonite

GRANOFELS - medium - to coarse - grained granoblastic metamorphic rock
MANGERITE - monzonite

PYRIBOLITE - mnemonic term igneous rock pyroxene + amphibole
ABIOTIGNEISS - acid biotite gneiss '

BBIOTIGNEISS - basic biotite gneiss

AHORNGNEISS - acid hornblende gneiss

BHORNGNEISS - basic hornblende gneiss

PYROXGNEISS - pyroxene gneiss

AHORBIOGNEISS - acid hornblende gneiss

BHORBIOGNEISS - basic hornblende gneiss

QGARGNEISS - quartz garnet gneiss

GRAN (A) — granulite acid

GRAN (SA) - granulite sub-acid

GRAN (INT) - granulite intermediate

AMPFGNEISS - amphibolite gneiss

AMPHIB (A) - acid amphbolite

AMPHIB (B) - basic amphbolite

AMPHIB (SA) - sub-acid

AMPHIB (INT) - intermediate

ERRATA - change Heier Thor (1970) to Heier Thor (1971)

40

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APPENDIX 2

t test for parallelism

Appendix 2

Comparison of Two Slopes

Basically the method is to compare the ratio, of the difference
between the two slopes to its standard error, against a t variable

with (n1 + n2

n= 75

bl= 1

C 2:

Granite:

S

Faun:

Andesite: n 69
b = 3
C =

y
= l

hanr< h‘

S

Basalt: n
b:
C =

y
= 1

hanr< h‘

S

Anorthosite:

41
2.

- 4) degrees of freedom.

n

b

C
2

s =

1

.17
13546.51

13,392.95

.63
1349.79

154.34

26
1389.43

240.19

58

= number of samples
= slope
y: sum of squares of y

residual sum of squares

n= 76

b1= 5.18

C = 11319.56
YY
2

S1 = 7457.01

Granulite:

n= 27

bl= 4.75

C = 3235.99

Schist:

hlnfij

s ; 2133.22

Amphibolites: n= 56

b1: 6.73

C = 11686.55
YY

Si: 4613.79

59

Sample Calculation

Anorthosites-Andesites

y1Y2

s _

B .234

calc.

ttab1e= t.os, 60 = 1.98

 

13

 

ylyz

3.78 - 4.7

= 81.72

72.0 = 19.19

.014 + .041 = .055

5

 

.145

-7.26

slopes are signf.

 

 

different.
Schist-Gneiss sz= 57.32
2
B— .021
SB= .145
_ 3.78 d 4.75 _
calc._ .145 - 6'69
ttable= t.05,120 = 1.98 slopes are signf.
different.
Amphibolite-Granulite 32: 94.30
2_
SB— .016
SB: 127
_ 6.73 - 5.18 _
calc._ .127 - 12°20
ttable= t 05,120 = 1.98 slopes are Signf.

different.

Granite-Basalt

Gneiss-Andesite

Andesite—Basalt

60

 

 

 

sZ= 133.36
2-
sB- .105
sB= .325
tcalc = 1.17 - 2.26 = _.3
' .32
ttable= t.05,120= 1'98
82: 42.84
2
sB— .035
sB= .19
tealc = 3.63 - 3.78 = _
' .19 '
= :3 °
ttable t.05,120 1'9”
sz= 22.59
2
sB— .97
SB= .95
Gale = 3.63 - 2.26 = .14
' .95
= 1.98

ttab1e= t.05,120

.35

Slopes are signf.
different.

79

slopes are not
signf. different.

slopes are not
signf. different.

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