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Technical Report

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Variations in the Isotopic Composition of Common Lead and the History of the Crust of the Earth

June, 1955

Digitized by the Internet Archive in 2020 with funding from Columbia University Libraries

https://archive.org/details/variationsinisotOObate

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Variations in the Isotopic Composition of Common Lead and the History of the Crust of the Earth

George L. Bate J Laurence Kulp

June 1955

Submitted by George L. Bate in partial fulfillment of the requirements for the degree of Doctor of Philosophy, in the Faculty of Pure Science, Columbia University.

The research reported in this document has been made possible through support and sponsorship extended by the Research Division of the Atomic Energy Commission under Contract AT (3C-1)-1114. It is published for technical information only and does not represent recommendations or conclusions of the sponsoring agency.

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Table of Contents

Page

Abstract . v. . i

Introduction . 1

Acknowledgements . 4

Mineral Selection . 6

Experimental Procedure

Chemical Preparation of Lead Tetramethyl . 7

Contamination Effects . 7

Possible Fractionation . 8

Instrumentation of Mass Spectrometer . 9

Operating Characteristics of Mass Spectrometer .

Re solving Power . 15

Background and Noise Effects . 17

Drift in Ion Beam Intensity . 19

Hydride Formation . 19

Operational Procedure for Isotopic Analyses . 21

Calculation of Abundances from the Pb+ Spectrum . 21

Mercury Correction . 22

Drift Correction . 22

Scale Correction . 23

Hydride Correction . 23

Calculation of Abundances from

the Pb(CH3)^+ Spectrum . 25

Page

Re suits

Inter calibration Experiments . . . 28

Tabulation of Isotopic Analyses . 33

Age Relations for Various Earth Models . 60

Derivation of Step-Differentiation Model . 60

Comparison of Common Lead Isotopic

Data with the Step -Differentiation Model . 67

Least Squares Fit of Dated Samples to

Step- Differentiation Model . 68

Age Considerations . 68

Mathematical Analysis . 73

Model Embodying Continuous Differentiation

of the Earth's Crust . 81

Comparison of Lead Isotope Constants and

Age Derivatives with Previous Results . 91

Regional Analysis of Common Leads . 96

Joplin-Type Anomaly - The Mississippi Valley Leads. . . . 101

Geologic Setting . 103

Ivigtut Type Anomaly . 115

Additional Possible Factors Affecting

Isotopic Composition . • . . 115

Conclusions . 118

Bibliography

121

ABSTRACT

Isotopic analyses have been completed on 161 samples in a reconnaissance of lead minerals from all the major continents, the majority coming from North America. The analyses were made with a 6-inch radius, 60° Nier-type, direction-focussing mass spectrometer utilizing lead tetramethyl vapor for sample introduction. Intercalibra¬ tion analyses show that relative abundances of the three heavier isotopes, Pb^6} Pb^^, Pb^8, obtained with the spectrometer agree to . 5%

with those reported by other investigators. Agreement on the lightest

Z 04

and least abundant isotope, Pb , is generally within 1%.

The majority of previous investigators have studied isotopic compo¬ sition of lead ores relative to their age and genesis on the basis of the simplest possible model, herein referred to as the step-differentiation model, which assumes broad uniformity of crustal conditions affecting lead mineralization and neglects secondary effects. On the basis of this model, isotopic compositions of the common leads reported in this work are generally in agreement with their geologic age. Data for a few dated samples have been fitted to the step -differentiation model by a least squares analysis. The constants required for best fit are in good agreement with those obtained by earlier workers, but incorporation of meteoritic lead composition as primeval lead composition leads to an age of the earth's crust which is considerably larger than those obtained

without meteoritic lead data.

This discrepancy has led to formulation of a model which permits continuous differentiation of the earth's crust throughout geologic time in an exponential manner. The constants introduced are evaluated independently of lead ore data and these calculations show that the maximum age of the earth is approximately 5. 3 billion years, this being the time when terrestrial lead had the composition of meteoritic lead.

In like manner it is shown that the major portion of the differentiating forces was expended in a time somewhat in excess of a billion years.

The isotopic composition of a number of leads is found to diverge markedly from that predicted on the basis of the step -differentiation model, and these anomalies are delineated together with their characteristics. Special consideration is given to the Joplin-type anomaly which is charac¬ terized by a moderate excess of the radiogenic isotopes, and is found to be prevalent throughout the several lead districts of the Mississippi Valley.

To account for this anomaly, a hypothesis is advanced which involves inhomogeneous extraction of lead from original or contaminating sources.

In this process it is pictured that on the basis of the known tendency of uranium and thorium to concentrate in interstitial rock material, their lead end-products are more easily removed in solution than lead inside mineral grains and thus give rise to leads with anomalously high radiogenic isotope content. Calculations based on the excess Pb^^ and Pb^^ in a number of the Mississippi Valley anomalous leads give an apparent age of about 2 billion years for the excess lead in these samples.

li

Average isotopic compositions for the anomalous Mississippi Valley leads and for other regions in the United States are tabulated. Consideration of other possible factors affecting isotopic composition leads to the conclusion that age, source, and mode of extraction are the main factors controlling isotopic constitution of lead in common lead minerals .

111

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Introduction

The isotopic analyses of lead from twenty-five lead minerals reported by

12.

Nier and co-workers ’ in 1938-1941 showed that the isotopic composition depends

upon geologic origin. Nier postulated that the variations are due to the addition of

radiogenic lead (i.e. Pb^^, Pb^^> Pb^^ formed from radioactive decay of 238 235 232

U , U and Th respectively) to "uncontaminated lead" during geologic time. He also suggested that this "uncontaminated lead" should be identified with primeval lead, (German "Urblei") which may be loosely defined as the lead

present at the time of formation of the earth's crust. The remaining stable lead 204

isotope, Pb , is not known to be produced by any radioactive decay and all 204

Pb existing today is therefore regarded as primeval. Accumulation of nuclear

data and advances in nuclear theory since the Nier analyses have not revealed any

206 207 208

process in nature whereby appreciable amounts of Pb , Pb and Pb may be formed (or destroyed), other than by the uranium and thorium decay schemes.

The current view on the geochemical occurrence of lead may briefly be described as follows. Lead in nature is found either dispersed as rock lead or concentrated as mineral lead. Since rocks also contain dispersed uranium and thorium in varying concentrations, it is seen that the isotopic composition of rock lead changes with geologic time due to the accretion of radiogenic lead from the decay of uranium and thorium. Rock lead may be extracted and separated from the host rock by various geochemical processes of differentiation and, depending on the efficiency of separation from the uranium and thorium, three types of minerals containing lead may be recognized: (1) common lead minerals, (2) uranium and

2

thorium minerals, and (3) mixed lead minerals.

If the separation of lead from a rock mass is essentially complete, common lead minerals are formed. In this case the lead isotopic composition does not change with time after the formation of the minerals and may reflect the isotopic com¬ position of the rock lead from which it was formed at the time of mineralization. Common lead is most frequently found as galena, PbS. Uranium and thorium minerals contain lead from radioactive decay of the parent elements. The isotopic composition of the lead in these minerals changes with time and together with chemical analyses for lead, uranium and/or thorium, may be used to determine the age of the minerals by the several procedures of the lead-uranium method of age determination. These minerals may contain some common lead incorporated at the time of formation. Finally, if common lead and significant radiogenic lead are both present it is designated a mixed lead mineral. In this case the isotopic composition is independent of time although the 207/206 ratio of the radiogenic component may give an indication of the time of formation.

Nier's common lead analyses formed the basis of a number of theoretical 3-11

papers , in which it was attempted to establish the following: (1) A satisfactory model to account for lead ore formation from the rocks of the earth's crust; (2) a value for the age of the earth's crust; (3) the isotopic composition of primeval lead; and (4) a relation between the isotopic composition of mineral lead and the

age of the mineral. The last three items follow from the type of model proposed

11

in (1). McCrady has reviewed the papers prior to his publication.

More recently a new fund of common lead isotopic data has begun to be

, 12-15 _ 16-17 J 18

published by laboratories in Canada , Germany and the U. S.S.R.

These data, together with Nier's original results have received further analytical

3

19, 20 21

treatment by Damon and have been summarized by Houtermans • The various

workers in the field have consistently cited the need for more lead isotopic abundance

data.

The present work was undertaken with the purpose of (1 y conducting a reconnais¬ sance of common lead minerals of world -wide distribution to add to the growing fund of lead isotopic abundance data, and (2) to catalog in more detail the variations in isotopic composition of common lead in the United States, The data obtained pro¬ vide the basis for a number of theoretical conclusions: (1) New limits on the possible variations in isotopic composition in various geologic settings can be defined. (2) This makes it possible to identify anomalous leads with greater certainty. (3) A revised model of crustal differentiation can be proposed. (4) The age of the earth's crust can be reassessed. (5) The relative abundances of uranium and thorium to lead in the earth's crust can be reevaluated. (6) It is possible to limit the speculation on the mechanism and origin of lead-ore formation. In summary, the acquisition of new common lead isotopic data permits further study of the history of the earth's crust, both in the broader aspects of crustal formation and composition, and in the local aspects of mineral formation throughout geologic

time at various differentiating foci,

The authors wish to express their appreciation for the helpfulness and interest of a number of geologists in making this research possible. Several members of the Geology Department of Columbia University have contributed materially to the success of the work. Professor C. H. Behre, Jr. encouraged the undertaking of the research program and made accessible the Economic Geology Collection for the selection of lead ore specimens, and provided valuable information on the origin of these samples. Through the courtesy of Professors P„ F. Kerr and R. J. Holmes, the Systematic Mineralogical Collection was made available for sample selection and information on pertinent mineralogy was generously provided. Professor G. M. Kay contributed helpful advice on stratigraphic problems connected with the dating of mineral specimens. Through the office of Professor A. Poldervaart a galena sample from South Africa was supplied, and we are also indebted to Dr . Poldervaart for assistance in communication with the various Geological Survey Offices in southern Africa. Through the kindness of Professor B. H. Mason and D. M. Seaman, several samples were obtained from the American Museum of Natural History. An additional note of appreciation is due Dr. Mason for calling our attention to the Vesuvius sample recently acquired by the Museum.

The authors are especially indebted to the Offices of the Geological Survey of South Africa and of Southern Rhodesia for their excellent cooperation in providing a suite of common lead minerals from various pre-Cambrian strata in southern Africa. Dr. L. T. Nel, Director and Dr. B. Wasserstein of the Geological Survey of South Africa provided eight samples together with a description of their geological environment, from the Union of South Africa. A similar set of samples from

5

Southern Rhodesia with descriptions was supplied by Dr. R. M. Tyndale -Biscoe, Acting Director, assisted by Dr. A. M. Macgregor, of the Geological Survey of Southern Rhodesia.

The original mass spectrometer tube was designed and constructed by H. R. Owen. W. R. Eckelmann worked out the initial chemistry of lead tetramethyl preparation. Technical assistance on routine operations was necessarily extensive. J. Gaetjen, R. Nuckolls, J. Miller and M. Trautman assisted with tetramethyl preparation; D. Miller, W. Knox and J. Hoover helped with routine spectrometer operation; M. Feely, L. Tryon, J. Averill and A. Toleno assisted with the abundance computations. The valued assistance of our instrument makers, W. Tamminga and F. Gwinner, is also acknowledged with appreciation. W. F. Kelly assisted with bibliographic research on the geologic origin of various lead deposits.

Financial support was provided by the Atomic Energy Commission under contract AT(30-1)1114. The senior author acknowledges with gratitude the grant of a pre- doctoral fellowship from the National Science Foundation, under tenure of which this

research was initiated.

6

Mineral Selection

The choice of comm n lead minerals was restricted largely to those available in the various mine r alogical collections so generously placed at the disposal of this laboratory. The samples were selected with as widespread distribution both in geographic location and geologic setting and age, as possible. Several suites of samples were chosen with a common geologic environment but with different mineral form, different mineral associations, etc. , in order to search for possible effects on isotopic composition. In one case, two samples were taken from opposite ends of a large galena crystal in order to check possible isotopic fractionation with crystal growth. In some cases more than one sample was taken from a given locality with the purpose of checking variations in random samples.

It will be noted (see Table II) that for some of the localities selected, common lead analyses have previously been reported in the literature. The Lamont data for these localities are included here however, not only to permit comparison with the earlier analyses, but also to present the whole body of data accumulated with the use of one mass spectrometer at this laboratory. By way of summary for the 161 samples shown, a total of 121 localities are represented, 100 of which are new localities, without previously published common lead anaylses.

Although the mineralogical collections were invaluable for the acquisition of samples, the value of some of the samples is diminished because of the lack of full description of the geographic and geologic source. A typical difficulty encountered is that some samples were originally collected from small mines whose operation ceased many years ago; consequently little or no further information can be obtained

at the present time. In any event, the table contains all the pertinent information as to geographic origin and mineral association obtainable with each specimen.

7

Experimental Procedure

Chemical Preparation of Lead Tetramethyl

In order to introduce the lead into the mass spectrometer in gaseous form it

was necessary to synthesize lead tetramethyl PbfCH^)^ from the mineral lead

22

samples. The general technique has been described in the literature and consists briefly of: preparation of pure lead chloride from the lead mineral; Grignard reaction with lead chloride; hydrolysis of excess Grignard agent; separation of ether solution of tetramethyl from water solution; separation of tetramethyl from ether by fractional distillation, completed by evaporation of excess ether under reduced pressure, until the vapor pressure corresponding to that for lead tetramethyl was observed on a mercury manometer. With an initial charge of about .3 gram lead chloride, the final yield of tetramethyl was of the order of a few hundredths milliliter by volume, sufficient for several runs of the spectrometer .

Contamination Effects

The possibility of appreciable lead contamination from the chemical reagents employed was ruled out on the basis of the following considerations. Only reagents of the highest purity commercially available were used and the possible lead content specified was very small compared to the amount of lead in the sample. Moreover, any lead present in the reagents would have been, most likely, common lead, and since the isotopic composition of common leads varies over small limits only, the effect on the isotopic composition of the sample would have been negligible. This conclusion was verified by two pieces of experimental evidence.

(1) An intercalibration sample was received in the form of metallic lead, and the

typical chemical procedure in its entirety was used to prepare the lead tetramethyl

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required for the analysis. The isotopic composition obtained was very close to that reported by other investigators for the identical sample (see Table I). (Z) An

even more conclusive proof was demonstrated in the following manner. A lead iodide salt was divided into two portions, one of which was converted into lead chloride for the Grignard reaction. Since the Grignard reaction will also take place with other halides, the remaining iodide portion was utilized directly for the Grignard reaction. The lead isotopic compositions of the two tetramethyls thus prepared were identical within limits of experimental error, and it was therefore concluded that contamination from inorganic reagents, the most likely source of contaminant, was negligible.

It was found that heavy organic residues were present in the tetramethyl

• I

sample, which could contribute to ion signals in both the Pb spectrum and in the trimethyl spectrum. These impurities exhibited low vapor pressures relative to Pb(CH^)^ and were a source of trouble only if the sample container was heated.

It was found that initially all of the Pb(CH^)^ could be transferred to the manifold by putting liquid air on a finger in the manifold while the sample container remained at room temperature. This process did not introduce any appreciable contaminants into the leak of the mass spectrometer.

Possible Fractionation

Further tests were conducted to detect any fractionation effects in the chemical procedure. It may be noted that in the last two steps of ether removal by fractional distillation and by evaporation, the effect of isotopic fractionation would be such as to favor removal of the lighter isotopes and thereby increase the percentage com¬ position of the heavier isotopes in the residual sample. For the typical sample,

9

the fractional distillation reduced the volume of the ether solution by a factor of about 4 and the final evaporation involved a volume reduction by a factor of about

100. Although the predicted fractionation at the boiling temperature of the mixture

204 206 207 208

based on the mass difference of the Pb (CH3)4, Pb (CH3)4> Pb <CH3)4,pb (Ch3)4

molecules, is negligibly small, two experimental tests were resorted to for the

final proof. These tests simply consisted of repeating the fractionation and

evaporation process two times, one process at a time, after adding a volume of

ether equal to that just removed. Any effect originally present would have been

multiplied by about a factor of 3, but although the tests were repeated several

times on two different samples, no change from the original isotopic composition could be detected.

It is believed therefore, that errors in the data due to contamination or isotopic fractionation in the chemical preparation process are well within the experimental error reported.

Instrumentation of Mass Spectrometer

The mass spectrometer employed for the isotopic analyses was a direction¬ focussing 60° sector type instrument of glass-metal construction with 6" radius,

23

previously made at this laboratory after a design originally reported by Nier Following several modifications a mass resolution of better than 1 part in 220 was obtained, together with other characteristics suitable for work with the Pb+ spectrum. A later re-alignment of the entrance and e:>y.t slits gave a mass resolution of nearly 1 part in 300, which permitted satisfactory operation in the range of the trimethyl spectrum.

10

The most important modification consisted of the utilization of a new source,

24

designed essentially after that described by Palmer and Aitken (Figure 1). The exit slit of the source was made .075 mm wide, and the entrance slit at the collector was made .3 mm wide in order to give maximum signal with optimum resolution.

With these slit configurations the typical ion current at mass 208 was of the order

of 10 ampere.

204

In order to avoid Hg at mass number 204, an oil diffusion pump was

initially used to provide high vacuum in the tube. However, on prolonged use,

increasingly large backgrounds of organic origin were encountered in the mass

range of the lead spectrum, particularly at mass number 207. This background

was essentially eliminated on replacement of the oil diffusion pump with a

mercury diffusion pump. The 3 -stage mercury pump also lowered the ultimate

vacuum of the system to an indicated pressure (Research Corp. ionization gauge)

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of 5 x 10 mm Hg., as well as providing a considerable improvement in the pumping speed of the system. The fore vacuum was maintained by a mechanical pump of 58 1pm free air capacity and rated with an ultimate vacuum of .1 micron.

A commercial high voltage supply (Beva Model 301) proved very satisfactory for the high voltage required for ion acceleration. The accompanying voltage divider loop was designed for our particular source requirements and is shown schematically in Figure 2. The electromagnet and magnet supply were also commercial items.

The emission regulator was slightly modified from a design reported in 25

the literature . The schematic circuit is shown in Figure 3. The time constant

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Filament

Stainless steel source plates.

Quartz glass spacers and insulators.

Source slit .65 mm.

Draw out,

plate separation .35 mm.

Focus, plate separation .35mm.

Aligning Slit .15 mm.

Centering, plate separation .35 mm.

Exit slit . 075 mm.

SOURCE FOR MASS

ASSEMBLY

SPECTROMETER

Figure 1. Source Assembly for Mass Spectrometer

Figure 2. Schematic of High Voltage Divider Circuit for

Mass Spectrometer Source

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of the control circuit was highly sensitive to the value of condenser Cj and values larger than .01 jxf were found to give rise to regenerative conditions.

A commercial vibrating reed electrometer (Applied Physics Corp. Model 30) gave satisfactory amplification of the ion currents received at the collector.

A voltage signal was developed in the usual manner by passing the ion current through a grid resistor of large resistance. The optimum value of 10^ ohms for the grid resistor was obtained by compromising the requirement of maximum signal with that of minimum noise for the greatest amplification used. The resultant time constant was larger than desired and necessitated a relatively slow scanning rate in order to allow the full signal to be developed at the peak heights .

With later improvement of the resolution and sensitivity which permitted use of the trimethyl spectrum, a grid resistor of 10 ^ ohms was found to be very satisfactory. This change substantially reduced the input time constant of the detecting system and permitted more rapid scanning.

The output of the vibrating reed electrometer was fed to a pen and ink recorder through a decade resistance box which served as a voltage multiplier. The gain control on the electrometer, together with the following voltage multiplier bridge permitted a complete range of amplification of ion current signals. The linearity of amplification of the combined system was checked by applying known signals from a standard potentiometer to the reed input.

The sample introduction system was made as simple as possible. In order to avoid contamination (from mercury or organic vapors) from diffusion pump vapors, the vacuum in the sample manifold was supplied solely by a mechanical pump followed by a liquid air trap. With an ultimate vacuum rating of . 1 micron

15

Hg, the mechanical pump gave good pumping characteristics. It was found that tetramethyl vapor was readily absorbed on all types of stopcock grease, and it was therefore necessary to use a metal manifold with all-metal needle valve s .

The sample pressure was reduced by admitting the gas into the spectro¬ meter through a viscous leak. The leak was made by drawing out glass capillary tubing, giving a final capillary of some 30" in length with an average diameter of about 4 mils. A specially constructed gas inlet system for transfer of the gas from the low pressure side of the leak into the ion source proper is shown in Figure 4. This system provided for a highly efficient transfer of the gas,

with the result that typical analyses were made at indicated tube pressure of -7

1 - 4 x 10 mm Hg.

Operating Characteristics of Mass Spectrometer

Resolving Power

A useful and perhaps more definitive index of resolving power than the

, , 17

customary mass resolution, is the quantity Q defined by Geiss , e.g., as

the ratio of the ion current minimum between the peaks at mass numbers 207

and 208, to the maximum ion current at mass number 208. The optimum value

obtained for our spectrometer was Q 05%, while for the average analysis

the value of Q might be as high as . 3%. However, it was shown that for even

higher values of Q the effect on the peak heights and therefore on the apparent

isotipic composition varied only in a secondary manner with Q.

Extensive tests were made to determine the factors affecting Q, inasmuch as

the resolving power occasionally became very poor, with no known change of

Figure 4. System for Transfer of Sample Gas to Ionization Chamber

16

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17

the control parameters. No dispersion due to pressure effect alone could be

established and none would be expected since the indicated tube pressure , -7

during analyses never exceeded 5 x 10 mm Hg. Variation of the position

of the aligning magnet, of the source plate potentials, and of the electron

accelerating potential affected primarily the intensity of the ion beam, and

had little if any effect on the resolving power. It was observed however, that

the resolution invariably decreased when considerable impurity (primarily

ether) was present in the sample and moreover the apparent dispersion increased

during an analysis. It was finally concluded that the primary cause of loss of

resolution was the accumulation of surface charge on the walls of the tube. The

-11

fact that small ion currents (about 10 ampere maximum) were employed, made the instrument especially sensitive to surface charge accumulation. Preventive measures to avoid surface charge effects consisted of maintenance of clean metallic surface conditions within the tube, and of regular heating of the tube between runs.

In general, the resolving power of the instrument is considered more than adequate for the lead isotopic abundance reconnaissance undertaken in this work. Even for work on a regional basis the inherent resolution is sufficient, unless differentiation of isotopic compositions to better than .3% is required.

Background and Noise Effects

With the introduction of a mercury pump the background mass spectrum was reduced to a negligible level. After extended use a background common lead spectrum was consistently present, but since the 208 peak height was of the order of 1 mv, the background effect was disregarded in comparison to actual

18

sample signal, for which in a typical analysis the 208 peak height lay in the

range of . 5 - 1 volt. A substantial background signal was rarely observed

in the trimethyl spectrum. The tube was baked for about 15 minutes between

runs primarily to dissipate surface charge accumulated within the tube, and

this procedure also had the beneficial effect of essentially eliminating memory

effect from the preceding sample. The pumping speed of the vacuum system

was such that on sample removal, peak heights were decreased by a factor

of several hundred within a few minutes' time.

The use of a mercury diffusion pump necessarily introduced a background

mercury spectrum which, under conditions of sustained baking, could not be

204

entirely eliminated. However, since Hg constituted about only 1% of the

204

signal at mass number 204, it is evident that errors in the Hg correction

204

can contribute only errors of the second order to the Pb abundance.

The maintenance of a low noise level in the amplifying system depended in a critical manner upon proper shielding of the ion collector. With optimum

shielding the noise level was of the order of .05 mv, which is quite negligible for

i 204

the heavier isotopes and is not serious for the smaller Pb isotope, the

signal for which rarely was less than 10 mv. The usual stability problem in a high-gain d.c. amplifier was not encountered with the vibrating reed electrometer, due to the reed method of changing the d.c. signal into an a.c. signal. The short term drift of the particular vibrating reed electro¬ meter used was stipulated not to exceed .004 mv/sec, well within the required

accuracy of analysis.

19

Drift in Ion Beam Intensity

With the higher value of input grid resistor previously noted, the time constant of the amplifying system was about 1 sec. With the relatively slow scanning rate required to permit full development of signals, the time required to scan through the lead spectrum from mass number 202 was about six minutes. Coupled with a drift rate in ion current of about . 2% per minute, this factor was probably the major source of experimental uncertainty. The magnitude of the effect was substantially reduced, however, ny applying a drift correction based on the assumption of a linear variation, to the recorded peak heights. This assumption was justified on the basis of the following two considerations. First, direct observation of drift by "sitting" on a peak showed that the drift rate was essentially linear. In the second place, the isotopic composition calculated with drift correction was identical to within .1% to that obtained without drift correction, the major difference being that the deviations were substantially reduced. Since the spectra were scanned alternately up-mass and down-mass, a composition calculated without drift correction would be expected to cancel the drift effect if the drift rate were linearly uniform. The fact that identical composition was obtained with both methods of calculation was taken as an indirect verification of linearly uniform drift rate.

Hydride Formation

A variable of particular importance in using the Pb spectrum from Pb(CH^)^ vapor is the formation of PbH^ . The efficiency of hydride formation is pressure and temperature dependent. However these variables are not known to change appreciably during the course of an analysis, and the hydride efficiency was in

20

fact never observed to change significantly during a run and was remarkably

constant from day to day for long periods of time. The hydride efficiency is

calculated from the ratio of the peak height at mass number 209, due to the 208 +

hydride Pb H , to the peak height at mass number 208.

The hydride factor was found to be very sensitive to the electron accelerating voltage, which was variable over a range of about 90 volts. The isotopic com¬ position of a sample was shown to be independent of the electron accelerating voltage, E , and hence independent of the hydride efficiency. It was found that the ion current increased with electron accelerating voltage to a maximum at about 40 volts, and then decreased on further increase of electron accelerating voltage. Higher values of the electron accelerating voltage were found to give rise to unstable source conditions and most of the analyses were therefore made with Eg = 40 volts. For this value of Ee, the efficiency of hydride formation was approximately 10%.

The operating performance of the spectrometer may finally be evaluated on

the basis of the reproducibility of isotopic composition of a given sample. A

reference standard sample of tetramethyl was analyzed nearly 40 times during

the course of sample analyses, involving a time span of approximately one year.

The average deviation of an analysis from the mean was about . 2% for the

204

heaviest isotopes and nearly . 5% for Pb . These variations were usually within the deviation of each individual analysis. The greatest deviation observed was about .4% for the heaviest isotopes and 2% for Pb^^.

21

Operational Procedure for Isotopic Analyses

The sample schedule was arranged so that no sample was analyzed twice in the same day, at the same time providing for a change in sample order on repeat analyses. With but few exceptions, all samples were analyzed at least twice. Two analyses usually gave results within the average deviations of each other and a third analysis was made if this condition was not met. Most of the analyses consisted of 10 single-peaked spectra or the equivalent.

The purity and amount of sample were initially checked by the nature of the spectrum obtained with a given sample manifold pressure and resulting tube pressure. Any sample purification further required was accomplished by pumping off repeated portions of the ether-rich vapor. For the typical analysis a sample pressure of about . 5 mm Hg was required.

Allowing for tube bake -out between runs, the usual routine permitted 5 analyses during a 10 hour period. The reference tetremethyl standard was analyzed at various intervals to detect possible changes in performance of the instrument. For several of the Nier samples the reference tetramethyl was run before and after each analysis.

In general, the large number of analyses per unit time is the main advantage of the tetramethyl method. Without such a facility the number of samples herein reported would not have been possible.

Calculation of Abundances from the Pb^ Spectrum

The sequence of computation for calculating the isotopic abundance from an

+ 204

analysis of the Pb spectrum consists of: (1) correction of 204 peak for Hg ;

(2) correction for drift in ion current intensity; (3) correction for resistance of

secondary multiplier bridge coupled with (4) reduction to common scale on the

22

basis of amplification factors used; (5) reduction to percentage composition; and finally (6) hydride correction.

Mercury Correction

The mercury correction was made in the usual manner by computing the

^ Q ^ ^ Q ^

amount of Hg from the amount of Hg at mass number 202, using the

204 202 . 204 202

known ratio of Hg / Hg . The measured ratio of Hg /Hg from back¬ ground spectra agreed with the value cited in the literature within the experi¬ mental error; however, the accepted value was used in the calculations due to

the large uncertainty in the measured ratio, resulting from the small signals

204

invloved. As noted previously, the amount of Hg in the typical analysis was

about 1% of the total 204 peak; hence any reasonable uncertainty in the

204 202 204

Hg /Hg ratio would have a very small effect on the Pb abundance.

It was observed, however, that for some extreme cases in initial test analyses

204 204

for which Hg comprised about half the signal at mass 204, the Pb abundance

204

was experimentally identical to that later obtained with Hg down to the one per cent level. This was taken as evidence that the ratio used for Hg^^/Hg^^

was correct.

Drift Correction

Occasionally the change in ion current intensity during an analysis was so small that the drift correction was not necessary; but for most analyses it was necessary to apply the drift correction in order to obtain a true picture of the deviations. Since the 208 peak was the largest, the drift correction was applied so that all other peak heights were computed to give their true values at the time the 208 peak was recorded. The correction was computed by pairing spectra scanned

23

up-mass and down-piass and obtaining for each set an average drift rate from the percentage changes in peak height of the three heavier isotopes. The remainder of the calculation follows in a straightforward manner and, as noted before, is perfectly valid providing the drift rate is uniformly linear.

Scale Correction

When adjusting for the scale of amplification used, an additional small correction was made for the resistance of the voltage multiplier bridge follow¬ ing the vibrating reed electrometer. The resistance employed on the voltage multiplier varied from 10 to 90 ohms (to supply signal to a 10 mv recorder from maximum 1 ma reed current), which was not negligible compared to the electro¬ meter output loop resistance of 2000 ohms. The correction follows directly from an elementary application of Ohm's law.

Hydride Correction

The true abundance of the isotopes is calculated from the peak heights observed

on the recorder chart in the following manner. Let 204', 206', 207', 208' and

204

209' represent the observed peak heights of these isotopes (2041 excludes Hg ) and let 204, 206, 207, and 208 represent the corresponding true abundances.

Both sets of numbers express percentage composition. The true hydride factor may then be written as:

C = 2097208 = PbZ08H+/Pb208+.

From the nature of the hydride formation, the following equations can be written:

204' = 204 - C(204) = (1-C) 204 206' = 206 - C(206) = (1-C) 206

(1)

(2)

24

207' a 207 - C(207) + C(206) = (1-C) 207 + C(206)

208' a 208 - C(208) + C(207) a (1-C) 208 + C(207) C

Now writing k a ^ji q} » foregoing equations become:

204 = ( 1 + k) 204'

206 a (1 + k) 206'

207 = (1 + k) 207' - k (206)

208 a (1 + k) 208' - k (207)

(3)

(4)

(5)

(6)

(7)

(8)

Equations (6), (7), and (8) are actually three non-linear equations in the unknowns 206, 207, and 208, for which the exact analytical solution becomes somewhat cumbersome. This difficulty may be avoided and the roots may be obtained with the desired accuracy by using repeated approximations. For the first approximation k' =s 209'/208', and corresponding values of 206', 207', and 208' are calculated. The next approximation of k is k" = 209'/(208'-209') and corresponding values of 206" and 207" and 208" are computed. This is then followed with k"' = 209' /(208" -209'), etc., until the required precision is obtained. Usually the closure is so rapid that two approximations suffice.

For a given analysis, 204', 206', .207', 208', and 209' are actually the averages of percentage compositions of the individual scans comprising the analysis. For each average ion abundance an average deviation is computed.

The average deviations of the true composition will have added uncertainty due to the error in the 209' peak. The effect of the hydride error was calculated for each analysis, but invariably the contribution to the error in the true composition was found to be small, usually negligible. The relative error in 209' never exceeded 1% and the resulting uncertainty contributed to the true abundances of the lead isotopes rarely approached .1%.

25

It is to be noted that the foregoing hydride correction assumes that the

208

hydride efficiency obtained for Pb applies to the remaining lead isotopes.

A possible systematic effect violating this assumption would consist of a mass discrimination in hydride formation. If such an effect did exist, the hydride

r . r t-,,204 ?08

factor for Pb would differ to the greatest extent from that obtained by Pb

204

However, even for Pb , the greatest possible effect on k, assuming a functional dependence as the square root of the ratio of the masses, would not exceed 1%.

A systematic error in the hydride factor of this order of magnitude would introduce an uncertainty in the true abundances well within the experimental error reported.

Calculation of Abundances from the Pb(CH^)^+ Spectrum

In the trimethyl mass region (mass numbers 248 through 254) there is no interference from mercury. The drift and scale corrections are made in an identical manner to that described under the calculation of abundances from the Pb^ spectrum. The hydride effect is present but to a lesser extent than in the case

I -j-

of the PbT spectrum. Additional corrections must be made in the PbfCH^)^

13 12

spectrum for the C /C effect and for the loss of a hydrogen atom.

The analytical expressions for the Pb(CH^)^+ spectrum may be developed

as follows. Let 249', 251’, 252', 253', and 254' represent the observed signals

at these mass numbers. Also, designate by 249, 251, 2 52, and 253 the true

204 206 207 " 208

abundances of Pb , Pb , Pb , and Pb , respectively, appearing at the

13 12

indicated mass numbers in the trimethyl spectrum. The C /C ratio and hydride formation have the same effect of increasing the observed signal at mass number

(m + 1), at the expense of the signal at mass number m. Let p therefore represent

26

the fraction of the true signal at mass number m appearing at mass number

13

(m + 1) due to the combined effects of hydride formation and C appearance.

Similarly, let q represent the fraction of the true signal at mass number m lost to mass number (m - 1) due to the loss of one hydrogen atom. Neglect¬ ing second order effects, the observed spectrum may be analytically expressed as follows:

249' = 249 - p(249) - q(249 = 249(1 - p - q) (9)

251' = 251 - p(251) - q(251) + q(252) = 251(1 - p - q) + q(252) (10)

252' = 252 - p(2 52) - q(252) + p(251) + q(253) = 252(1 - p - q) + p(251) + q(253) (11)

253' = 253 - p(2 53) - q(253) + p(252) = 253(1 - p - q) + p(252) (12)

254' = p(2 53)

r

Writing r = p + q and s = ^ - — , equations (9) through (12) may be implicitly

solved for 249, 251, 252, 253:

249 = (1 + s)249' (13)

251 = (1 + s)251' - q(l + s)252 (14)

252 = (1 + s)252' - p(l + s)251 - q(l + s)253 (15)

253 =e (1 + s)253 - p(l + s)252 (16)

As with the Pb+ spectrum, equations (13) through (16) may be solved by repeated approximations, q was found to have a value consistently in the neighborhood of 1%. Small variations in this value would have a negligible effect on the final abundances. The value of p was fairly constant at 3.2%. If the C /C ratio is taken as .011, then the trimethyl hydride effect amounted to about 2.1%. This value is considerably larger than that of 0. 33% reported by Dibeler and Mohler2^ and that of .08% reported by Collins, Russell and Farquhar . The different values 0. 33%, .08% and 2.1% are due presumably to differences in temperatures

27

of the sources, in geometric configurations of the electron beam, and in conditions of secondary emission.

The corrections in the trimethyl spectrum are therefore about one -third that in the Pb+ spectrum. This is particularly important for the analysis of radio¬ genic lead where the correction factors from preceding and following common lead analyses must be assumed to be constant.

28

Re suits

Intercalibration Experiments

In the absence of a lead standard of known absolute isotopic composition, the only possible recourse to check possible systematic discrimination by a given mass spectrometer is to make comparison analyses of samples analyzed on other spectrometers. Unfortunately, at the time of research herein reported, no systematic program of comparison of lead samples at different laboratories was yet in effect, with the exception of the circulation of a reference lead sample by the United States Geological Survey. However, through the excellent cooperation of interested investigators, a number of samples were obtained which provide the basis for a correlation of the performance of our instrument with that of instruments at other laboratories.

The largest suite of samples for comparison purposes was provided by

Dr. J. P. Marble jn the form of a number of the identical lead salts used by

1 2

Nier in his work ’ previously referred to. The United States Geological Survey has recently circulated a "standard" lead sample for intercalibration purposes, and through the courtesy of Dr. L. R..Stieff, a portion of the U. S. G. S. "standard" was provided for this work. This identical sample has also been analyzed at Toronto, Canada, and at Harwell, England. Finally, two more samples were obtained which had been analyzed at Toronto and Oak Ridge.

The comparison of analyses of identical samples is displayed in Table I. All of the Lamont analyses shown are based on the Pb+ spectrum, but later analyses of our reference standard in the trimethyl region gave results identical to those obtained on the basis of the Pb^ spectrum. The comparison is even more significant in view of the different methods used for sample introduction. The lead was

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31

volatized from solid lead salts in the instruments used by Nier, Oak Ridge,

and Harwell, while lead tetramethyl vapor was employed at Toronto and Lamont.

The Toronto results also include analyses based on the lead trimethyl spectrum, in

addition to the Pb"^ spectrum. It is significant that in spite of the considerable

differences in chemistry, in method of ion formation, etc. , the results are

comparable to within a fraction of a per cent for the heavier isotopes, and to

the order of a per cent for Pb^^. The greater divergence of values for Pb^^

is to be expected from the relatively small signals obtained at mass number 204.

The results from the various laboratories are of further interest in that

different geometry was used for beam collimation and focussing. The Nier

spectrometer and the Toronto spectrometer were both 180° instruments while

the Lamont, Harwell and Oak Ridge spectrometers are 60° instruments. In

all cases magnetic scanning was used.

The Lamont analyses are averages of at least three runs in most cases.

The Wallace, Idaho, cerussite was analyzed about a dozen times, for reasons

enumerated below. The Pb^^ composition is shown with parentheses about

204

the fourth significant figure in order to emphasize that Pb does not have associated with it the same relative precision as in the case of the heavier isotopes .

A very close comparison of the Lamont analyses with the Nier analyses is

not possible since Nier's numbers are stated to have a probable error of about

. 5%. It is observed that with the exception of Nier's sample No. 10 (Lamont

No. 23), the compositions for the heavier isotopes generally agree within . 5%,

204

while the divergence for Pb may approach 2%, but more usually about 1%.

204

A greater spread is to be expected for the Pb values, but it nevertheless

32

seems evident (see especially the seventh column in Table I) that relative to

204

Nier's values, Pb is suppressed in the Lamont analyses. Such an argument

204

based on comparison of Pb compositions alone would not be conclusive; however, the same trend is definitely reflected in the heavier isotopes (note especially the last column in Table I). Although the differences invloved lie within the experimental uncertainty, the statistical weight of the numbers shows a trend toward a lower abundance of the lighter isotopes in the Lamont analyses as compared with those of Nier.

The distinct discrepancy between the analyses on the cerussite from Wallace, Id. (Nier No. 10) has no explanation. The sample was repeatedly analyzed under varying conditions, but the isotopic composition consistently differed as shown from that reported by Nier. It is suggested that the sample had in some manner become contaminated.

A comparison with more recent instrumentation is provided by the remaining analyses shown in Table I. For the U . S . G. S ." standard" the Toronto anaylsis is an average of five runs, four of which utilized the trimethyl spectrum and the fifth the Pb spectrum . The Harwell analysis is an average of seven runs - three based on the PbCl+ spectrum, two on the Pbl+ spectrum and two on the Pb+spectrum. Two analyses are shown for the Lamont measurements, and although the operating conditions were not highly satisfactory, circumstances prohibited further analyses prior to this publication.

In general, the analyses on the U.S.G.S. standard agree to about .3% for the heavier isotopes and the probable error in values for Pb^4 is less than 1%.

For the remaining two samples the Lamont analyses are roughly intermediate between those reported by Oak Ridge and Toronto. The Goldfields No. 1 sample

33

has an anomalous composition and the discrepancies between the analyses are considerable. However, this sample was known to contain a small amount of uranium and the spread in composition reported may merely reflect inhomo¬ geneity of samples. The Goldfields No. 2 is a more typical common lead and for this case the Lamont and Toronto values are in good agreement.

More data and greater precision are necessary for conclusive comparisons, but at this point there is just a suggestion that instruments utilizing volatilization of lead from the solid state give analyses tending to suppress the heavier isotopes, compared with analyses obtained with tetramethyl vapor. The internal precision claimed for the Lamont data is of the order of .2% for the heavier isotopes and . 5% for Pb . On the basis of the foregoing comparisons, the Lamont analyses are comparable to those of the laboratories cited within . 5% for Pb^^, Pb^^, and Pb^^ and to within 1% for Pb^^.

Tabulation of Isotopic Analyses

The isotopic abundance data for the samples analyzed are tabulated in Table II according to geographic distribution. Of the 161 analyses shown, the majority are for samples from the North American continent. Unless otherwise noted, the mineral samples were obtained from the Economic Geology Collection and from the Systematic Mineralogical Collection, both of the Department of Geology of Columbia University. Most of the analyses were made with the Pb+ spectrum. Those based on the trimethyl spectrum are denoted with an asterisk (*).

Although the experimental uncertainties for the various analyses do not vary greatly, they are shown as average deviations for each analysis in order to show to some extent the analyses with which greater precision can be associated. In

Isotopic Abundances of Common Lead

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Table II, Continued

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