Irradiation of Samples for 

40Ar/39Ar Dating Using the 

Geological Survey TRIGA Reactor

GEOLOGICAL STRVEY PR O F E S Si I O N A L PAPER 1176
IRRADIATION OF SAMPLES FOR

40Ar /39Ar DATING USING THE

GEOLOGICAL SURVEY TRIGA REACTOR
Core of Geological SurveyTRIGA reactor in operation. Central thimble tube, which is about 4 cm in outside diameter and surrounded by control and transient rods, is in center of core. 

Blue glow is Cerenkov radiation, emitted by charged particles traveling faster than the speed of light in reactor cooling water.
Irradiation of Samples for 

40Ar/39Ar Dating Using the 

Geological SurveyTRIGA Reactor

By G. BRENT DALRYMPLE, E. CALVIN ALEXANDER, JR., 

MARVIN A. LANPHERE, and G. PATRICK KRAKER

GEOLOGICAL SURVEY PROFESSIONAL PAPER 1176

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1981
UNITED STATES DEPARTMENT OF THE INTERIOR 

JAMES G. WATT, Secretary

GEOLOGICAL SURVEY 

Doyle G. Frederick, Acting Director

40 39 Irradiation of samples for Ar/ Ar dating using the Geological Survey

TRIGA reactor.

(Geological Survey professional paper ; 1176) 

Bibliography: p. 26-29

Supt. of Docs, no.: I 19.16:1176

1. Argon Isotopes. 2. Radioactive dating. 3. Nuclear reactors.

I. Dalrymple, G. Brent. II. Series: United States. Geological

Survey. Professional Paper 1176. 

QE508.I77 551.7'01 80-607859

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, B.C. 20402
CONTENTS

Abstract ___ 

Introduction

Page

1

1

The 40Ar/39Artechnique __________________________ 3

The GSTR facility ___________________________________ 4

Sample encapsulation __________________________________ 4

Monitor minerals ______________________________________ 8

Flux characteristics of the GSTR _________________________ 10

Vertical gradients __________________________________ 12

Horizontal gradients ________________________________ 14

Self-shielding _____________________________________ 16

Activity predictions ____________________________________ 16

Corrections for interfering argon isotopes __________________ 18

Optimization of irradiation parameters ____________________ 25

Production of sufficient 39Ar _________________________ 25

Page 

Optimization of irradiation parameters Continued

Minimization of 40K(n, p)40Ar interference ______________ 26

Minimization of 40Ca(n, no) 36Ar interference ___________ 26

References cited ______________________________________ 26

Derivation of equations _________________________________ 32

_--__________---------_--- 32 40;'Ar/ Ar age equation

Error formulae ____________________________________ 33

37Ardecay correction _______________________________ 33

Effect of 40Ca(n, no) 36Ar interference ___________________ 35

Computer programs ___________________________________ 42

NEUT2 Activity prediction program for GSTR ________ 42

AR37 37Ar decay correction program _________________ 51

Selected bibliography __________________________________ 54

ILLUSTRATIONS

FRONTISPIECE. Core of the Geological Survey TRIGA reactor in operation.

Page

FIGURE 1. Schematic cross section through U. S. Geological Survey TRIGA reactor ________________________________________ 5

2. Diagram showing details of GSTR core __________________________________________________________________ 6

3. Photograph showing partly assembled aluminum sample holder and quartz sample vials ___________________________ 7

4-8. Diagrams showing:

4. Cross section of a sealed 8-mm quartz sample vial with 10-mm high sample ______________________________ 7

5. Clamp for cooling quartz vials while they are being sealed ___________________________________________ 7

6. Aluminum sample holder _____________________________________________________________________ 8

7. Aluminum sample holder plates showing four useful arrangements of quartz vials of various sizes within an irradiation level ___________________________________________________________________________ 9

8. Typical reactor tube for the central thimble ______________________________________________________ 9

9. Graph of approximate 39ArR productivity at centerline of central thimble as a function of K20 content and irradiation time 13

10. Graph of 40Arrad/39ArK ratio as a function of K-Ar age and irradiation time in central thimble of GSTR ________________ 14

11. Schematic diagram of change in true thermal power level as a function of fueling and calibration ____________________ 14

12. Graph showing vertical flux gradient in the central thimble of GSTR ___________________________________________ 14

13. Graph showing relative fluence in GSTR as measured with nickel wires and with the St. Severin monitor ______________ 15

14. Isometric drawing of sample locations in self-shielding experiment on diabase 8L691 ______________________________ 16

15-22. Graphs showing:

15. Results of self-shielding experiment on diabase 8L691 ______________________________________________ 16

16. Activity resulting from various neutron reactions in GSTR as a function of irradiation time atl MW ___________ 20

17. Effect of reaction 40Ca(n,na) 36Ar on calculated 40Ar/39Ar age ______________________________ 22

18. Approximate ranges of K/Ca atomic ratios for some common minerals and rocks ________________________ 22

19. Effectof 42Ca(n,a) 39Ar reaction on calculated 40Ar/39Ar age ______________________________ 23

20. Effect of 40K(n,p) 40Ar and 41 K(n,d) 40Ar reactions on calculated 40Ar/39Ar age _________________________ 24

21. 39ArK/37ArCa as a function of K/Ca atomic ratio in GSTR ____________________________________ 25

22. Irradiation time in GSTR required to maximize the 39Ar produced from 39K while minimizing interferences from

40ArK and 36ArCa ____________-____--_____________________--_-_--___---__-_-_-__-__________ 25

23-35. Graphs showing effect of the reaction 40 Ca(n, no) 36Ar on calculated 40Ar/39Ar ages:

23. K/Ca = 0.02 ____________________________________________________-----_____________ 35

24. K/Ca=0.05 ____________________________________________________--__-__-__-__----_--------- 36

25. K/Ca =0.1 _______________________________________________-_______----____-__-_____ 36

26. K/Ca=0.2 ________________________________________________________---_-___-_-------------- 37
VI CONTENTS

FIGURES 23-35. Graphs showing effect of the reaction 40Ca(n, no) 36Ar on calculated 40Ar/39Ar ages - Continued

Page

TABLE

27. K/Ca = 0.5 ________________________________________________________________________________ 37

28. K/Ca=l _______________________________________________________________________________ 38

29. K/Ca = 2 _________________________________________________________________________________ 38

30. K/Ca = 5 _______________________________________________________________________________ 39

31. K/Ca=10 _________________________________________________________________________________ 39

32. K/Ca=20 ________________________________________________________________________________ 40

33. K/Ca = 50 ______________________________________________________________________________ 40

34. K/Ca=100 ________________________________________________________________________________ 41

35. K/Ca = 200 _______________________________________________________________________________ 41

TABLES

Page

1. Natural abundance and decay constants for selected isotopes of chlorine, argon, potassium, and calcium _____________________ 2

2. Analytical data for monitor minerals _____________________________________________________________________________________________ 10

3. Results for mineral standards irradiated in GSTR ________________________________________________________________________________ 11

4. Neutron energy distribution on the centerline of the central thimble of the GSTR ______________________________________________ n

5. Comparison of nuclear reactors used for 40Ar/39Ar irradiations ________________________________________________________________ 12

6. Data for activity calculations, TRIGA reactor _____________________________________________________________________________________ 17

7. Principal neutron reactions leading to the production of argon isotopes _________________________________________________________ 18

8. Correction factors for Ca- and K-derived Ar isotopes for the U. S. Geological Survey TRIGA reactor __________________________ 19

9. Standard mineral and rock compositions used inBASIC programNEUT2 ______________________________________________________ 45

10. Selected bibliography of use of Ar/ 9Ar data in terrestrial, lunar, and cosmological studies _________________________________ 54
IRRADIATION OF SAMPLES FOR <°Ar /39Ar DATING USING THE 

GEOLOGICAL SURVEY TRIGA REACTOR

By G. BRENT DALRYMPLE, E. CALVIN ALEXANDER, JR.^MARVIN A. LANPHERE, and G. PATRICK KRAKER

ABSTRACT

The characteristics of the Geological Survey TRIGA Reactor 

(GSTR) as a source of fast neutrons for the 40Ar/3 Ar technique of 

K-Ar dating have been determined using data from more then 45 irradiations in the central thimble (core) facility. The GSTR has a flux 

over the entire energy spectrum of 1.1 x 1017 n/cm2 -MWH and a 

fast/thermal ratio on the centerline of the central thimble of 117 for 

fast neutron energies greater than 0.6 MeV. Production of 39Ar is 

about? x 10~13 mole/gram-percent KgO MWH, and the cross section 

for the reaction 39K(n, p) 39Ar is 65 ± 4 millibarns for epithermal (> 

0.6 MeV) neutrons. Most 4 Ar/ Ar dating applications require about 

10-40 hours of irradiation in the GSTR at the maximum continuous 

power level of 1 MW. The peak neutron flux in the central thimble is 

4 cm above the physical centerline, and the verticle flux gradient in 

the centermost 20 centimeters varies from a small fraction of a percent to a maximum of about 3.5 percent per centimeter. The effect of 

this gradient can be effectively cancelled by suitable sample encapsulation and the use of a sample holder designed for the purpose. The 

horizontal flux gradient is less than 0.5 percent over the width of the 

central thimble. Self-shielding in a solid core of diabase 2.40 cm in 

diameter and 2.54 cm high is approximately 3 percent from the outside to the center, but self-shielding is probably negligible for the 

smaller samples usually irradiated for K-Ar dating.

Corrections for interfering Ar isotopes produced by neutron reactions with Ca are relatively reproducible with values of 2.64 ± 0.017 

x 10~4 for ( 36Ar/37Ar) Ca and 6.73 ± 0.037 x 1Q~4 for ( 39Ar/37Ar) Ca. 

The measured values for ( 40Ar/39Ar)ic, however, vary by an order of 

magnitude. This variability, whose cause is unknown, has been reported from other reactors. The corrections for interfering Ar 

isotopes can be minimized by using optimization curves for the GSTR 

to choose the best sample size and irradiation time for a given material. Of more than 100 possible neutron reactions in common rocks 

and minerals, only 26 need be considered for purposes of radiological 

safety. The activity produced by these reactions upon irradiation of 

samples can be conveniently and accurately predicted either by a 

computer program or from graphs specifically devised for the GSTR.

INTRODUCTION

Since first proposed by Sigurgeirsson (1962) and 

Merrihue (1965), the 40Ar/39Ar technique of K-Ar dating has been investigated and utilized for geochronological studies by many laboratories throughout 

the world. Although most of the early studies involved 

meteorites and lunar rocks, it soon became apparent 

that the technique was a potentially powerful tool for 

the investigation of terrestrial chronology.

The U. S. Geological Survey's experiments on the 

4oAr/39Ar technique began in 1970 at Menlo Park, Calif. 

(Dalrymple and Lanphere, 1971), using the Geological 

Survey TRIGA2 reactor (GSTR), sited in Denver, Colo. 

Since then more than 700 samples have been irradiated 

for 40Ar/39Ar experiments in over 45 separate irradiations. In addition, the GSTR has been used extensively 

by several investigators pursuing 40Ar/39Ar research in 

academic institutions, principally the University of 

Minnesota and Ohio State University. During the 

course of the research at the Geological Survey in 

Menlo Park and at the University of Minnesota, we experienced many technical problems directly related to 

the reactor and its neutron flux. In pursuing solutions 

to these problems, we have collected much valuable 

technical information on the use of the GSTR for 

40Ar/39Ar dating. The degree to which satisfactory solutions have been found has a direct effect on the validity 

and accuracy of the scientific results from 40Ar/39Ar 

dating experiments. Thus it is important that this information on the GSTR be made readily available to 

other scientists in the field. Some of this information 

has been published in the scientific media but most,

1 Department of Geology and Geophysics, University of Minnesota. Supported by National 

Aeronautics and Space Administration under grant NGL 24-005-225. Publication No. 1029 

from School of Earth Sciences, University of Minnesota.

2 TRIGA (Training Research Isotope General Atomic) is a trademark of the General 

Dynamics Corp.
IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

because of the technical nature of the material and the 

inevitable editorial pressures for brevity, has not.

Some of the information in this paper, such as data 

on flux gradients and appropriate constants for interference corrections, is directly concerned with the particular characteristics of the GSTR and some, such as 

the derivation of equations and the methods of predicting activities, is more generally applicable. Most research reactors, however, are similar in many respects, 

and information concerning the problems, characteristics, and techniques for the GSTR can be applied quite 

easily to other reactors, at least in principle if not in 

detail. In particular, this report will be valuable to 

those who contemplate starting a program of 40Ar/39Ar 

research, whether using the GSTR or some other research reactor.

This paper is concerned with the technical aspects of 

sample irradiation and not with the interpretation of 

40Ar/39Ar age data. For the latter, we refer the interested reader to the section entitled "Selected Bibliography," a compilation of papers on the use and interpretation of the 40Ar/39Ar technique in terrestrial, 

lunar, and cosmologic problems.

Throughout this paper, we use the convention that 

the mass number of an isotope is indicated by a lefthand superscript, for example 40Ar for argon-40. 

Right-hand subscripts indicate the origin of the 

isotope:

atm = atmospheric 

rad = radiogenic 

Ca = calcium derived 

K = potassium derived

For example, 37ArCa denotes argon-37 formed by neutron reaction with calcium. For nuclear reactions we 

use the standard notation.

target (incoming particle, ejected particle) product

where n stands for neutron, p for proton, 7 for 

gamma-ray, a for alpha particle ( 4He nucleus), and d 

for np ( 2H nucleus). For radioactive decay, @~ indicates 

the emission of an electron and e indicates electron 

capture; X is the decay constant. Power in the reactor is 

indicated in either megawatts (MW) or kilowatts 

(kW). The abbreviation MWH is used for megawatthour and is a convenient way to indicate irradiation 

"time": 1 MWH is an irradiation time of 1 hour at a 

power level of 1 megawatt, 10 hours at a power level of 

100 kilowatts, and so on. We use the term neutron flux 

to represent the rate at which neutrons pass through 

the sample in units of neutrons per square centimeter 

per second (n/cm2 -s), and neutron fluence to represent the total time-integrated flux "experienced" by 

the samples in n/cm2 . Other symbols are defined, as 

necessary, in the text.

Finally, the natural abundances, half-lives, and decay 

constants for selected isotopes of chlorine, argon, 

potassium, and calcium are listed in table 1. These data 

are required for many of the calculations relevant for 

40Ar/ 39Ar experiments. The decay constants and 

isotopic abundances for potassium are those recently 

adopted by the International Union of Geological Sciences Subcommission on Geochronology at the 1976 International Geological Congress in Sydney, Australia

TABLE I.—Natural abundance and decay constants for selected isotopes of chlorine, argon, potassium, and calcium

[If no half life given, stable; y=years, d=days, and m=minutes. References: 1, Weast (1976); 2, Nier (1950); 3, Stoenner, Schaeffer, and Katcoff (1965); 4, Garner 

and others (1975); 5, Beckinsale and Gale (1969); and 6, Steiger and Ja'ger (1977)]

Element

Cl...... ......

Ar. ...........

K.... .........

Ca ...........

Atomic Isotope 

weight

..... 35.453 35 C1

36 d 

37C1 

38 Cl 

39C1

QQQ4Q 36Ar

37Ar 

38Ar 

39Ar 

40Ar

39 098 39K

40K 

41R

..... 40.08 40Ca

42 Ca 

43Ca 

44Ca 

46 Ca 

48 Ca

Relative 

natural 

abundance

0.7553

.2447 

.00337

.00063

.99600 

.932581

.0001167

.067302 

9fiQ47

.00646 

.00135 

.02083 

.00186 

.0018

Half-life

3.1 x I05 y

37.3m 

55.5 m

35.1 d 

259 y

1.250 x 109 y

Decay 

constant

2.236 X 10- 6 yi

1.858 x 10-2 m-i 

1.249 x lO-2 m- 1

1.975 x lO-2 d' 1 

2.58 x lO- 3 yi

X, = 0.581 x 10-io y-i 

\ f = 4.963 x 10-10 yi

References

1

1 

1 

1 

1

1,2

3 

2 

3 

2

4

4,5,6 

6

4

1

1 

1 

1 

1 

1
40 / /39 THE 4UAr/J9Ar TECHNIQUE

(Steiger and Jager, 1977). These values differ from 

those used in most of the earlier literature on 40Ar/39Ar 

dating, therefore, care should be taken when comparing K-Ar ages in this paper with those calculated using 

the earlier values. The effect of the new constants is 

nonlinear. For example, an age calculated with the new 

constants is 2.7 percent older than one calculated with 

the old constants at one million years but 1.7 percent 

younger at 4,500 m.y. Conversion tables and formulae 

are given by Dalrymple (1979).

THE 40Ar/39Ar TECHNIQUE

In the conventional K-Ar technique, the quantity of 

radiogenic 40Ar in a rock or mineral is measured by 

isotope-dilution mass spectrometry. In this procedure, 

an aliquant of the sample is fused in vacuum and the 

reactive gasses removed. During fusion, a tracer of 38Ar 

(which also contains some 40Ar and 36Ar) of known 

amount and composition is added to the gas released 

from the sample. The isotope ratios of this gas mixture 

are measured, and after correcting for atmospheric argon, which is present as a contaminant, the amount of 

40Arrad is determined by comparison with the 38Ar from 

the tracer. The potassium is measured, most often by 

flame photometry, in a separate experiment on another 

aliquant of the sample. Once the potassium is known, 

the amount of 40K can be calculated from the known 

abundance of the potassium isotopes (table l). The 

potassium and argon data are then combined and an 

age is calculated with the K-Ar age equation

t = - In 

X

(1)

A more thorough discussion of the conventional K-Ar 

technique is given in Dalrymple and Lanphere (1969).

In the 40Ar/39Ar technique, the potassium and argon 

are measured on the same sample aliquant in a single 

experiment. First the sample is irradiated in a nuclear 

reactor, where fast neutrons convert some of the 39K to 

39Ar by the reaction 39K(n,p) 39Ar, which has a 

threshold of 0.22 MeV. After irradiation, the sample is 

fused and the argon ratios are measured by mass spectrometry in the usual way. If the fraction of 39K converted to 39Ar were known exactly, then the age could 

be calculated directly from the ratio 40Arrad/39ArK by

(2)

where C is a constant that includes factors for both the 

fraction of 39Ar produced from 39K and the fraction of 

potassium that is 40K. The conversion constant for the 

39K(n,p) 39Ar reaction, however, is not easy to measure 

accurately by direct methods, so a monitor mineral, 

whose age has been carefully determined by conventional techniques, is used. An aliquant of the monitor 

mineral is irradiated alongside the unknown mineral so 

that both receive the same neutron fluence. The age of 

the unknown is then calculated using

(3)

where the subscripts u and m refer to the unknown and 

the monitor minerals, respectively. To simplify, it is 

conventional to define the quantity

J =

(extm -l)

( 4 °Arrad /33ArK)m 

then rewrite equation (3)

tu = i In [ J ( 4 °Arrad /39ArK)u +1 ]

(4)

(5)

which is the 40Ar/39Ar age equation. The derivation of 

this equation is given at the end of this report after the 

"References Cited."

If the only contaminant present were atmospheric argon, then 40Arrad /39ArK could be calculated from the 

measured 40Ar/39Ar and 36Ar/39Ar ratios using

4 °Arrad

39Ar*

4 °Ar 

39Ar

40Ar \

/

where ( 40Ar/36Ar) atm is the composition of atmospheric 

argon. Several interfering argon isotopes, however, are 

produced by undesirable neutron reactions with other 

elements, principally 36Ar and 39Ar from calcium and 

40Ar from potassium. Fortunately, 37Ar is also produced 

from calcium, and accurate corrections can be made 

for the interfering argon isotopes using

4 °Arrad (4oAr/39Ar) - 295.5 [( 3 sAr/ 39Ar) - ( 3 <AT/ 37Ar)Ca ( 37Ar/ 39Ar)] - 

1 - ( 39Ar/ 37Ar)Ca ( 37Ar/ 39Ar) (7)
IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

where ( 36Ar/37Ar) Ca , ( 39Ar/37Ar) Ca , and ( 40Ar/39Ar) K 

are constants determined experimentally for a given 

reactor. (This equation is derived and the corrections 

discussed in detail in later sections.)

In spite of the necessity to correct for the interfering 

argon isotopes produced during irradiation, the 

40Ar/39Ar ^technique has several important advantages 

over the conventional technique. First, both the potassium and the argon are measured on the same aliquant, 

eliminating problems of sample inhomogeneity and reducing significantly the required sample amount. Second, no elemental abundance measurements are required, so the technique is both easier and potentially 

more precise than the conventional technique. Finally, 

instead of releasing the argon all at once in a single fusion (the total fusion technique), it is possible to release the gas fractionally by incremental heating (the 

incremental heating, stepwise heating, or age spectrum 

technique). The result is a series of apparent ages at 

successively higher temperatures, known as an age 

spectrum or release curve, from which useful information about the geologic history, the condition of the 

sample, and the age of the sample can be inferred. The 

selected bibliography at the end of this report lists 

sources for the use of the incremental heating and the 

total fusion 40Ar/39Ar techniques.

THE GSTR FACILITY

The GSTR, located in the Nuclear Science Building 

(Building 15) of the Denver Federal Center, Denver 

Colo., is administered by the Geological Survey's 

Geologic Division. It first reached criticality in February 1969, and since then has been in operation 8 

hours a day, 5 days a week. It has proved to be a very 

valuable tool for the Geological Survey's research programs in geology and hydrology. Among its many uses, 

in addition to 40Ar/39Ar experiments, are neutron activation analyses of a variety of geological materials, 

fission-track dating, uranium-thorium disequilibrium 

studies, delayed-neutron analyses for uranium and 

thorium concentrations, and hydrologic tracing with 

activatable materials. Since it first went into operation, 

the GSTR has generated over 8,000 MWH of thermal 

energy in the course of irradiating samples for scientific studies.

The GSTR (fig. l) is a light-water-cooled and -reflected reactor that uses uranium-zirconium hydride 

(U-ZrH) fuel moderator elements (fig. 2). The reactor 

is capable of continuous steady-state operation at 1,000 

kW (thermal) and may be pulsed repeatedly to yield a 

burst having a prompt energy release of about 15 MWseconds, a peak power of about 1,600 MW, and a pulse 

width at half maximum of about 11 milliseconds.

For 40Ar/39Ar dating, samples are irradiated in the 

central thimble, located in the center of the core at the 

point of maximum fast neutron flux (figs. 1 and 2). The 

central thimble is an aluminum tube 3.81 cm (l.50 in.) 

in outside diameter, with a wall thickness of 0.211 cm 

(0.083 in.). It extends from the reactor support bridge 

straight down through the central hole in the top grid 

plate. The central thimble is supported at its lower end 

by a safety plate about 40 cm beneath the bottom grid 

plate. Use of the central thimble has the advantages of 

maximizing the fast neutron flux and minimizing horizontal flux gradients.

The bulk water in the reactor has an operational 

temperature limit of 60° C but is normally kept within 

the range of 42°-45° C. The water is circulated within 

the reactor by convection. Although the central thimble 

space is enclosed by an aluminum tube, the tube is 

open to the water supply through several holes at its 

lower end (fig. l) and thus is also subjected to some 

convection cooling. In addition, the top of the central 

thimble tube is open to the atmosphere, and therefore 

the water in the central thimble can not exceed the 

boiling point. Because the water in the central thimble 

has never been observed to boil, the central thimble 

temperatures are probably actually less than about 95° 

C. Temperature-sensitive color tabs placed in the central thimble indicated an upper limit of 90° C, while direct thermocouple measurements indicated that the 

temperatures in the rabbit tube (fig. 2) are about 70° 

C. Thus, the data suggest that the temperature in the 

central thimble is probably between 70° C and 90° C.

Though the primary mission of the facility is the performance of experiments for the research groups 

within the Geological Survey, irradiations are done, as 

space is available, for other Government agencies, educational institutions, hospitals, and nonprofit research 

organizations. Persons interested in using the GSTR 

should contact the Reactor Supervisor, U. S. Department of the Interior, Geological Survey, Denver Federal Center, Denver, CO 80225.

SAMPLE ENCAPSULATION

Because the central thimble is water-filled, sample 

encapsulation must be leak tight. For adequate safety, 

two levels of containment are required. The rock or 

mineral samples are first encapsulated in heat-sealed 

quartz vials. These vials are then arranged in a multilevel aluminum sample holder (fig. 3) and placed in a 

cold-welded aluminum reactor tube that is lowered into 

the central thimble for irradiation.

The quartz sample vials are made from fused quartz 

tubing of various outside diameters (O.D.) and standard wall thicknesses. The most common are 6 and 8 

mm O.D., but vials as small as 3mm O.D. and as large
SAMPLE ENCAPSULATION

Control rod

Transient rod drive _/- 1LazX. SUSa " 

cr-^> loading tube

.'»»•;" °°;Aluniinuin tanker

';.°.^V.^'C!^°«°V.'o»°'»-/?>V0 5V%:BBi'''wced str"uc'tflral\≮re°tVVC"v»»V^

a ^oo °o A» O-<I Reinforced backfill concrete •<*,*. o » o«oo* O 0 d« e 'o

» °0 «", o » „ .0 a a a Ko40. o op o o . [y. o O ° ° qJ a a * »o »<» • ° [\» o • o « O • ,

FIGURE 1.—Schematic cross section through U. S. Geological Survey TRIGA reactor.
IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

as 12mm O.D. have been used. Other forms of glass, 

including vycor (96 percent silica), are not suitable 

either because of low strength or because other cations 

in the glass yield activation products of high activity 

and long half-life, making handling of the vials after irradiation a problem. Pure fused quartz (lOO percent 

silica) yields only 28Si and 30Si, both of which decay 

rapidly, allowing safe handling of the vials within a few 

days of irradiation. Because of vertical fluence gradients in the reactor, the vials are made with flat bottoms (fig. 4), and the sample amounts are adjusted so

that all the samples on a level, including the monitors, 

are the same height and thus intercept the same fast 

neutron flux.

Each vial must be numbered for positive identification. Conventional inks and marking pens will not survive irradiation. A diamond marking scribe will leave a 

permanent mark, but the numbers lack contrast and 

are difficult to read. The two most satisfactory methods 

are to use either a ceramic ink or small glass-marking 

decals, both of which are available from most glassblowing supply companies. After the vials have been

Central 

thimble

Removable 

hexagonal 

section

Irradiation 

space

Alternate 

source 

location

Irradiation 

space

Sou rce-V f r~\ \V_X.

Pneumatic transfer 

system (Rabbit) 

in-core terminus

EXPLANATION

Stainless steel 

end fixture

Graphite

Uraniumzirconium 

hydride 

(U-ZrH) fuel

Graphite

Stainless steel 

end fixture

Standard fuel element 

with ring (letter) and position (number) indicated

Graphite dummy element

Control rod

Transient rod

B

FIGURE 2.—Details of GSTR core. A. Plan view of core, showing location of central thimble facility. B. Configuration of typical fuel

moderator element.
SAMPLE ENCAPSULATION

marked, the numbers are heated to red heat with a 

hand torch, whereupon they fuse onto the quartz and 

become permanent.

The samples may be fine powders, mineral grains, 

rock chips, or rock cores. Mineral grains, rock chips,

FIGURE 3.—Partly assembled aluminum sample holder and 8- 

mm-diameter flat-bottomed quartz sample vials. Vials fit into holes 

in sample holder. Shown at right are spacers and knurled top nuts.

-8 mm

and cores are usually placed directly into the vials. Fine 

powders or fine mineral grains may tie wrapped in 

household-type aluminum foil before insertion into the 

vial for ease of handling after irradiation. Cores of 

rocks are preferable to chips, because they maximize 

the mass of sample within a given vertical space. Cores 

cut with standard diamond core bits of 5/16-inch and 

7/16-inch O.D. slip conveniently into 8-mm and!2-mm 

tubing, respectively. After the samples are placed in 

the vials, the tops of the vials are sealed with a 

hydro gen-oxygen torch and inspected for adequacy of 

seal. We have not found it necessary to evacuate the 

vials before sealing. During sealing, care should be 

taken to avoid overheating the sample. A method that 

we have found satisfactory is to hold the vial in a split 

aluminum cylinder, which is attached to a laboratory 

clamp (fig. 5). The lower part of the cylinder is immersed in a beaker of water. The heat from the vial is 

rapidly conducted by the aluminum to the water, preventing the sample from becoming hot.

The sample holder (fig. 6), made of 6061T6 

aluminum, keeps one level of samples in the same vertical position within the central thimble. This ensures 

that all the samples on a given level receive the same 

integrated fast neutron flux. To prevent galling and 

freezing during irradiation, the knurled nuts that hold 

the assembly together are coated with a permanently 

bonded, monomolecular layer of graphite or with a 

graphite lubricant. Sample holders of from one to four

FIGURE 4.—Cross section of a sealed 8-mm quartz sample vial with 

10-mm high sample (shaded). Tubing wall isl mm thick.

FIGURE 5.—Clamp for cooling quartz vials while they are being 

sealed. Vial (8 mm in diameter) is clamped in split aluminum cylinder, which is partly immersed in a beaker of water.
IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

Knurled and 

threaded nuts

Spacers—

Threadedplate

Bottom plate 

(1.130" diameter)

Rods

(Va" diameter)

levels may be assembled quickly from the various 

pieces by using rods of appropriate length. In addition, 

we have used top plates machined to hold a wide variety of quartz vials (fig. 7). The 7-sample plates shown 

in figure 1C are the most frequently used for terrestrial 

samples and hold as many as 28 samples (four levels) 

for a single irradiation. Filled to a height of 1 cm, each 

of the 8-mm vials will hold about 0.3-0.8 g of material. 

For smaller amounts of material, such as lunar and 

meteorite samples, the plates shown in figure 7'A, and 

B are used. The plate configuration shown in figure 1A 

permits up to 48 samples to be irradiated together. The 

plate configuration in figure ID is used for young 

basalt samples, usually rock cores of up to 5 g each; the 

3-mm holes in this plate hold the monitor minerals.

The sample holder (fig. 6) fits into the aluminum 

reactor tube, which has an outside diameter of 3.18 cm 

(l.25 in.), a maximum length of 30 cm (l2 in.) (fig. 8), 

and is supplied by the researcher. The reactor tube is 

sealed by the reactor staff by cold-welding and then 

leak tested in a column of ethylene glycol evacuated to 

less than 0.8 atm. As the interior of the reactor tube is 

at atmospheric pressure, even a minute leak in the 

seals is clearly and quickly detected by a stream of 

small bubbles.

The sealed, leak-tested aluminum reactor tube is 

suspended in the central thimble between aluminum 

leaders with 60-Ib test monofilament nylon line. Fishing weights are used to sink the tube, and they physically contact the bottom plug to ensure consistency in 

vertical positioning of the sample. After irradiation, the 

reactor tube is pulled out of the neutron flux and left 

suspended in the water column for several days to 

allow the radioactivity from products with short halflife to decrease. The tube is then removed from the 

reactor and opened. The aluminum tube is disposed of 

by the reactor staff, the sample holder is disassembled 

and saved at the reactor center for reuse, and the samples are shipped to the experimenter using packaging 

and shipping procedures specified by the Department 

of Transportation for radioactive materials.

MONITOR MINERALS

As explained above, the calculation of a K-Ar age 

using the 40Ar/39Ar technique depends on the use of a 

monitor mineral whose age is precisely known. The 

criteria for a suitable monitor mineral have been disFIGURE 6.—Diagram of aluminum sample holder. Only one 

sample level is shown, but as many as four levels may be 

assembled on longer rods. Top plates shown hold seven 

8-mm O. D. vials, but other configurations are also possible (see fig. 7).
MONITOR MINERALS

cussed by Alexander and Davis (1974). Briefly, they 

are:

1. The mineral should have a uniform ratio of 

radiogenic 40Ar to 40K.

2. Both potassium and radiogenic 40Ar should be 

homogeneously distributed.

3. The monitor should be similar in age and K/Ca 

ration to the samples being dated.

4. The monitor should be fairly coarse grained.

5. The monitor should be available in reasonable

quantity.

Because a 40Ar/39Ar age is calculated with reference 

to the 40Arrad/39ArK ratio of the monitor, criterion 1 is 

necessary to minimize errors due to monitor inhomogeneity. Criterion 2 is required because the 

monitor is calibrated by conventional K and Ar measurements, which are done on separate aliquants of the 

sample. Criterion 3 arises because the optimum 

parameters (primarily irradiation time and sample 

size ) for an irradiation are a function of both age and 

K/Ca ratio. If the monitor and the samples are greatly 

different in either age or K/Ca, then the irradiation 

may be less than optimum for one or both and interferFIGURE 7.—Schematic diagram of aluminum sample holder plates, 

showing four useful arrangements of quartz vials of various sizes 

within an irradiation level. Outside diameter of vials accommodated to each size hole is indicated. Shaded holes accept 1/8-or 

5/32-in. rods used to assemble plates into a complete sample 

holder. A, Smaller amounts of material, for lunar and meteorite samples. B, Smaller amounts of material, for lunar and 

meteorite samples. C, Most frequently used for terrestrial 

samples. D, For young basalt samples.

ing neutron reactions may lead to unacceptable errors. 

The satisfaction of criterion 4 eliminates radiological 

safety difficulties involved in handling a radioactive 

powder, which may easily become airborne. Criterion 5 

is desirable to provide continuity in measurements over 

a period of years.

We have used three different monitors (BS-1, SB-2, 

and St. Severin) in the GSTR, and a fourth (MMhb-l) 

(Alexander and others, 1978) has been recently prepared and calibrated (table 2). The first three are intralaboratory monitors and are not generally available. 

Hornblende MMhb-l is available to other laboratories 

for use as a 40Ar/39Ar monitor mineral. Interested investigators should write to E. Calvin Alexander, Jr., 

Department of Geology and Geophysics, University of 

Minnesota, 310 Pillsbury Drive, S. E., Minneapolis, MN 

55455.

BS-1, which is no longer in use, was biotite separated 

from 162-m.y.-old quartz diorite (sample 62A Lei) 

from the Aleutian Range, Alaska (Reed and Lanphere, 

1969). The size range of BS-1 was nominally 420 to 177 

micrometers, but the actual variation ranged from 420 

to 88 micrometers. K^O was measured by both flame 

photometry, using lithium metaborate fusion (ingamells, 1970), and by isotope dilution. The argon 

measurements were by isotope-dilution mass spectrometry using two independently calibrated 38Ar 

tracer systems. The separate was far from ideal for a 

standard because it contained about 4 percent impurities of hornblende, epidote, apatite, and chlorite. 

This inhomogeneity is reflected in the errors of the K20

End fitting (top and bottom)

— diameter

Assembled total length=«12 inches

t

1.156 

+ .001 

-.000

1.125

FIGURE 8.—Typical reactor tube for central thimble. Tube is constructed from 6061T6 aluminum. All dimensions are in inches.
10 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

measurements (table 2) and no doubt contributed 

some error to the age calibration of this monitor. However, as all the impurities are the same age as the biotite, BS-1 had a relatively uniform 40Arrad/ 40K ratio and 

proved to be a useful 40Ar/39Ar monitor.

SB-2 was prepared by resizing and recleaning BS-1. 

Grains smaller than 177 micrometers were removed by 

sieving, and the remaining impurities were removed 

with heavy liquid and magnetic separation techniques. 

SB-2 contains less than 0.3 percent impurities, and the 

improvement in the homogeneity of this monitor is apparent from the small dispersion of the K^O measurements (table 2). The potassium measurements were 

done by both flame photometry and by isotope dilution, and the values obtained by both methods agree to 

within 0.004 percent K^O. The isotope dilution value, 

however, was used in the monitor age calculations. The 

radiogenic 40Ar value was measured using three independently calibrated ^Ar tracer systems. SB-2 is currently in routine use in the Menlo Park laboratories.

The St. Severin monitor consisted of about 400 g of 

the 250- to 149-micrometer silicate fraction from the 

St. Severin chondrite from which Lewis (1975) separated 0.242 g of whitlockite. The material was not initially prepared as a monitor and was polymineralic. It 

eventually became evident that the K and therefore 

40Arrad were concentrated in a minor phase. Since the 

St. Severin monitor violated criterion 2 above, Alexander and Davis (1974) were forced to calibrate the 

monitor via an indirect comparison with other 

monitors. In stepwise heating analyses it was shown 

that the sites in the monitor that degassed below 800° 

C had lost 40Arrad and so only those sites which degas at 

more than 800° C were calibrated. Finally, since the 

monitor was prepared from a meteorite that had been 

exposed to cosmic rays, a significant portion of the 36Ar 

in the monitor is of nonatmospheric, cosmogenic origin. These problems notwithstanding, Alexander and 

Kahl (1974) demonstrated that the St. Severin monitor 

contains an extremely reproducible 40Arrad/40K ratio 

and its age and K/Ca ratio are appropriate for the dating of most meteoritic samples. Therefore, the monitor

meets criteria 1 and 3-5 listed above. Alexander and 

others (1981) recalculated the age of the St. Severin 

monitor to be 4.425 ± 0.018 *109 yr, using the new 

constants recommended in Steiger and Ja'ger (1977).

The hornblende monitor MMhb-1 was separated from 

syenite from the Cambrian McClure Mountain Complex in Fremont County, Colorado. Alexander and 

others (1978) described the preparation of this 

monitor. Analytical data for the K and 40Arrad contents 

of MMhb-1 are listed in table 2, and the initial results 

of interlaboratory comparisons are given in Alexander 

and others (1978). The monitor is a 250- to 177- 

micrometer-sized hornblende separated with an age of 

about 520 x 106 yr.

Since 1970, several standards and monitors used by 

other laboratories have been run using our monitors 

and the GSTR. The results of 20 measurements on four 

of these standards are summarized in table 3. The 

pooled 40Ar/39Ar age of six measurements on SB-2 differ by only 0.1 percent from the reference age determined by conventional techniques.

The agreement onP-207 is not nearly as good. The 

pooled 40Ar/39Ar age of 80.8 ± 0.5 m.y. for eight measurements onP-207 is 2.2 percent younger than the mean 

age of 82.6 i 1.0 m.y. based on!46 measurements made 

in 33 laboratories (Lanphere and Dalrymple, 1976). The 

40Ar/39Ar age of P-207 is 2.8 percent younger than the 

mean of 15 conventional measurements made in the 

U.S.G.S. Menlo Park laboratory. The reason for this discrepancy is not known. However, SM-1, a finer size fraction of muscovite from the same rock as P-207, yielded 

40Ar/39Ar ages in excellent agreement with the results 

from P-207.

FLUX CHARACTERISTICS OF THE GSTR

Although the TRIGA is not a large reactor, its flux 

characteristics are quite suitable for 40Ar/39Ar dating. 

The neutron energy distribution in the central thimble 

of the GSTR is given in table 4. The fast/thermal ratio 

on the centerline of the central thimble is 1.17 for fast

TABLE 2.—Analytical data for monitor minerals

[Values given are for mean and standard error of the mean. FP = flame photometry and ID = isotope dilution. The K2O ID measurements were supplied by the National Bureau of 

Standards (E. L. Garner, L. A. Machlan, and W. P. Shields, written commun., 1973). The isotope dilution values and constants from table 1 were used in the age calculations ]

Monitor K20 

(weight percent) (mol/g)

Calculated age 

(106 years)

BS-1 .......................Biotite

SB-2.......................Biotite

8.841 ±0.027 (FP,13) 

8.907 (ID, 2)

9188 ±0.004 (FP,14) 

9192 (ID,2)

MMhb-1...................Hornblende 1.874 ± 0.001 (FP,12)

(2183 ±0.006) xlO-9 (14)

(2.245 ±0.008) xiO-9 (12)

(1.624 ± 0.005) x 10-9 (4)

162.7

1621

519.4
FLUX CHARACTERISTICS OF THE GSTR 11

TABLE 3.—Results for mineral standards irradiated in GSTR

[Mineral standards analyzed are P-207 muscovite (interlaboratory standard), NL-25 hornblende (State University of New York at Stony Brook monitor), and SB-2 

biotite and SM-1 muscovite (intralaboratory standards, U.S. Geological Survey, Menlo Park). The pooled ages were calculated by weighting each age according 

to the inverse of its estimated variance. The sources for reference ages were P-207 (Lanphere and Dalrymple, 1976); NL-25 (Ar data, Hanson and others, 1971; 

K20 data, E. L. Garner, L. A. Machlan, and W. P. Shields, written commun., 1973); SB-2 and SM-1 (G. B. Dalrymple and M. A. Lanphere, unpub. data)]

Date

of irradiation

8-73. .......... ..

11-73............

11-73............

11-73............

3-75.............

4-75 ............

6-75.............

6-75. .......... ..

6-72.............

6-72.............

11-72............

11-72............

3-73.............

3-73.............

3-73.............

5-73.............

5-73.............

5-73.............

3-75............

3-75 ............

Mineral

standard

...........P-207

...........P-207

........ ..P-207

...........P-207

...........P-207

...........P-207

...........P-207

...........P-207

............NL-25

........ ...JJL-25

............NL-25

............NL-25

............SB-2

............SB-2

............SB-2

............SB-2

............SB-2

............SB-2

............SM-1

............SM-1

Monitor

used

SB-2

SB-2

SB-2

SB-2

SB-2

SB-2

SB-2

SB-2

BS-1

BS-1

BS-1

BS-1

BS-1

BS-1

BS-1

BS-1

BS-1

BS-1

SB-2

SB-2

Irradiation time

(MWH)

10

5

5

5

40

20

10

5

40

40

40

40

80

80

80

30

30

30

25

25

Calculated age Pooled age Reference age

(10'

81.6

81.2

80.6

80.4

79.4

82.7

80.1

80.8

2389.

2631.

2598.

2621.

163.0

161.9

163.1

161.8

162.0

161.9

80.1

80.4

6 yr) (I06 yr) (106 yr)

± 1.4

± 1.9

± 1.7

± 1.5

± 1.0

± 1.1

± I- 1

+ 1.0 80.8 ± 0.5 82.6 ± 1.0

±26.

±21.

±21.

+ 21. 2576 ± 11 2674

± 1.9

± 2.2

± 2.0

± 1.9

± 1.8

+ 1.8 162.3 ± 0.8 1621 ± 21

± 1.0

± 1.0 80.2 ± 0.7

neutron energies greater than 0.6 MeV, and the cadmium ratio is 9.24; the fluence over the entire energy 

spectrum is about 3.2 x 1013 n/cm2 -s at 1 MW or 11 x 

1017 n/cm2 -MWH. Turner (l971a) used the relation between J and the integrated fast neutron flux (<f>) as a 

basis for comparing various irradiation facilities for 

4oAr/39Ar dating- For the GSTR, J=0.4 x 1Q-20 0 where

<p is for neutron energies greater than 0.6 MeV. The 

value given by Turner (l971a) for the core of the 

Herald reactor, Atomic Weapons Research Establishment, Aldermaston, U. K., is J = 0.6 x 10~20 <j> for 

neutron energies greater than 018 MeV; the comparable figure for the pool outside of the core of the GETR 

(General Electric Vallecitos Reactor), Pleasanton, 

Calif., is J=l xlQ-20 0.

For many reactors, the calculation of Turner's 

(l971a) relation using the available published data is 

ambiguous or impossible, because different authors deTABLE 4.—Neutron energy distribution on the centerline of the central 

thimble of the GSTR

[Data from W. M. Quam and T. M. Devore, U.S. Geological Survey TRIGA 

Mapping and Counter Calibration, unpublished report for the U.S. Geological Survey, May 19, 1969]

Energy

(MeV)

Thermal (< 0.4). ........

> .6 ...............

> .6 ...............

> 1.5 ...............

> 1.5 ...............

> 3.0 ...............

> 3.0 ...............

> 7.5 ...............

> 14..................

Foil

......... Au

.......... Rh

.......... Np

.......... U

.......... Th

.......... S

.......... Ni

.......... Al

.......... Zr

Fluence

(n/cm2 -s)

1.46 x 1Q13

1.54 X1013

1.88 xiO13

1. 14X1Q13

1.12 xiO13

2.98 xlQia

2.98 X1Q12

1.57 xiQii

5. 15 x 108

fine "fast" neutrons with different energy cutoffs or do 

not define them at all. We have therefore adopted 

another relation to compare the flux of neutrons capable of producing 39Ar from 39K in any given reactor. The 

relation is simply the irradiation parameter J (as defined in equation (4)) divided by the length of the irradiation in hours. The resulting quantity, J/hr, is a 

measure of the rate at which 39K is converted into 39Ar 

during any irradiation.

Table 5 lists J/hr and the thermal and "fast" fluxes 

of ten reactors that have been used for 40Ar/39Ar dating. The rate at which 39K is converted to 39Ar varies by 

two orders of magnitude between the reactors, with the 

GSTR in Denver being sixth on the list. The High Flux 

Beam Reactor at Brookhaven has the highest usable 

flux, and the HIFAR reactor in Australia has the lowest 

flux. All the fluxes are clearly adequate, and the only 

penalty for using a low flux reactor is the longer irradiation time required to reach any needed J value.

As the threshold for the 39K(n,p) 39Ar reaction is 0.22 

MeV (Everling and others, 1961), the exposure of the 

samples to energies of less than that value simply introduces unnecessary, unwanted, and potentially 

dangerous radioactivity into the samples and increases 

the probability that radiation damage will affect any 

results. The groups at Bern and Heidelberg routinely 

shield their samples from the thermal neutron fluence 

during the irradiation by wrapping the sample containers in cadmium foil (Stettler and others, 1974; Kirsten 

and others, 1972). We have not tried cadmium shielding because one of us (G.P.K.) thought it inadvisable to 

place a large neutron absorber into the core of the 

GSTR.
12 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

The fast neutron flux in the GSTR is such that sufficient 39Ar is produced in most samples in 10-40 hours 

of irradiation at 1 MW (fig. 9). Using data from 24 

analyses of biotite monitor BS-1, the average 39Ar production rate for 1 MWH on the centerline of the central 

thimble is

39Ar = (7.1 ± 0.4) x 10-13 mole/gram-%K20 (8)

This is equivalent to a cross section for the reaction 

39K(n,p) 39Ar of about 34 ± 2 millibarns for all neutrons or 65 + 4 millibarns for epithermal (>0.6 MeV) 

neutrons. For 40Ar/39Ar dating, it is desirable to choose 

the irradiation time so that the 40Arrad/39Arx ratio is between 300 and 1, and preferably less than 10 (Turner, 

1971b). Figure 10 shows 40Arrad /39ArK as a function of 

age and irradiation time in the GSTR.

Users of the GSTR should be aware that values taken 

from figures 9 and 10 are approximate as the true 

power level in the reactor fluctuates as much as 20 percent (but usually only 5-10 percent) within the fueling 

cycle. Typically, the addition of new fuel rods, done 

annually near the first of the year, causes a depression 

in the true (versus indicated) power level. This is probably a result of both the increase in core size and the 

geometric relation between the new fuel and the linear 

ionization chamber that is used to monitor the power 

level. This ionization chamber sits outside of the 

graphite reflector surrounding the core (fig. l) and 

thus does not measure the core power level directly. 

The power level is calibrated twice each year, after 

fueling in January and again in June. Between calibrations, the true thermal power level gradually increases 

relative to the indicated power level, thus the typical 

power level fluctuation over the year probably looks 

like figure 11.

VERTICAL GRADIENTS

A significant problem in irradiations for 40Ar/ 39Ar 

dating is the inhomogeneity of the neutron flux. The 

primary concern is that vertical or horizontal flux gradients will result in significant differences in fluence 

between the monitor minerals and the unknown samples. In some reactors, the gradients are severe. For 

example, McDougall (1974) reported a change in the 

fast neutron flux in Facility X33 of the HIFAR reactor 

of more than 30 percent over a vertical distance of less 

than 3.5 cm (>8 percent/cm). In contrast, the vertical 

fast neutron flux gradient in the core of the Karlsruhe 

FR-2 reactor (Stettler and others, 1974) is less than 2 

percent over 4.5 cm (<0.5 percent/cm).

The vertical flux gradients in the GSTR, while not 

extreme, are still large enough so that the resulting effects must be either corrected for or eliminated. There 

have been two experiments specifically designed to 

measure the vertical fluence gradient in the central 

thimble of the GSTR in detail. The first, using sulfur 

pills, was done by E. G. & G., Inc., shortly after the 

reactor achieved criticality. The results (fig. 12) indicated that the fast neutron flux was relatively symmetrical about the centerline. We did another experiment 

on November 16, 1976, using nickel washers placed at 

2.5-cm intervals within the central thimble and irradiated for 1 hour at 1 MW. After irradiation, the

TABLE 5.—Comparison of nuclear reactors used for 40Ar/39Ar irradiations

[J is defined in equation 4; it is a measure of the fraction of 3"K converted to **"Ar. The energy definition of "fast" neutrons varies from author to author if it is

defined at all. Consult the original references for details]

Reactor and location 

(irradiation position) J/hr Thermal flux

(n/cm2 -s)

Fast flux

(n/cm2 -s) References

GSTR-Denyer, U.S. 

(Centerline, core position) ............2.5 x 10'4

Herald-Aldermaston, U.K.

(Core) ...................................7.2 x 10'4

GETR-Pleasanton, U.S. 

(Shuttle tube in pool) ..................41 x 10' 4

HIFAR-Lucas Heights, Australia 

(Core-X33,face6,4H-3)..............3.3 x 10'5

HFBR-Brookhaven, U.S. 

(Core) ..............................41 x 1Q-3

FR-2 Karlsruhe, Germany 

(Core-Isotope Channel Facility) ......61 x 10' 5

BR-2 - Mol, Belgium 

(Core) ...................................7.5 x 10' 4

RRF-Columbia, Mo., U.S. 

(Flux trap) ............................. 2.9 xiO'3

(Pool)................................... 6.2 xlO-5

JMTR-Oarai, Japan...................... 1.3 x 10 4

McMaster UniversityHamilton, Canada ..................... 1.1 x 10 4

1.5 xlO"

...

1.3 xlO14

5 X1Q13

1.3 xlQi4

(1)

(1) .

5.8 xiQi4

4.0 X1Q13 

1 X1Q13

1.7 xlOis

3.7 xiois

1.7 X1Q13

3.5 x 1012

2 xlO14

3.4 x 1012

3.7 x lO13

3 xlO12 

1 xlO12

This work.

Turner (1970a, b; 1971a).

This work; Turner and others (1972); Podosek and

others (1973); Huneke, Podosek, and Wasserburg (1972). 

McDougall andRoksandic (1974); McDougall (1974).

Bogard, Husain, and Wright (1976).

Stettler and others (1974); Kirsten and others

(1972). 

Kirsten and others (1972)- Kirsten, Horn, and Heymann (1973);

Kirsten and Horn (1977). 

Bernatowicz and others (1978). 

Podosek (private communication, 1978). 

Ozima and others (1976).

-1.5 X1Q13 ~8 xlO11 Berger and York (1970).

'Samples were irradiated inside a cadmium-shielded container to eliminate the thermal fluence.
FLUX CHARACTERISTICS OF THE GSTR 13

washers were counted in the Nal gamma-counting system at the GSTR in Denver, using the 0.8 MeV gamma 

from the decay of 58Co. We placed each washer in the 

same position relative to the counting crystal; the more 

active washers near the centerline were counted for 4 

minutes, and the less active washers were counted for 

up to 20 minutes. The results (fig. 12) show that the 

flux for fast neutrons is relatively symmetrical but that 

the point of maximum flux is displaced downward from 

the physical centerline about 4 cm. We are unsure why 

our results do not agree with the earlier results of E. G. 

& G., Inc., Both sulfur and nickel respond only to neutron energies above 3.0 MeV, and both experiments resulted in nearly identical flux curves. We suspect that 

the sulfur pills used in the earlier experiment may not 

have been as precisely located with respect to the physical centerline as the nickel washers.

1000

The data in figure 12 show that the gradient over the 

central 20 cm, the part of the central thimble normally 

used in 40Ar/39Ar dating, ranges from a small fraction 

of a percent to as much as 3.5 percent per centimeter. 

We have used two methods to minimize the effects of 

this gradient.

The first method is to carefully control the vertical 

position of the unknown samples relative to the 

monitors. The use of flat-bottomed quartz vials (fig. 4) 

and an aluminum sample holder (fig. 6) ensures that 

the bottom of each sample on a level is coincident with 

its corresponding monitors to within a fraction of a millimeter. In addition, the amounts of the samples and 

the monitors on each level are carefully adjusted so 

that all are the same height in the quartz vials. This ensures that all the samples on a level intercept the same 

fast neutron flux as the monitors.

100 -

cc

D 

O

I

39ArK , IN MOLES PER GRAM

FIGURE 9.—Approximate 39ArK productivity at centerline of central thimble as a function of KzO content and irradiation time (in MWH). 

Curves are based on equation (8) and were calculated using data obtained on BS-1 biotite. Each curve shows weight percent K20.
14 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

The second method is to monitor the fluence received by each sample and each monitor with a nickel 

wire. The wire is cut to the same length as the sample

10,000 F

1000 -

0.01

1 10 100 1000 

POTASSIUM-ARGON AGE, IN MILLIONS OF YEARS

10,000

FIGURE 10.—40Arrad/39ArK ratio as a function of K-Ar age and irradiation time (in MWH) in central thimble of GSTR. Ration is independent of K20 content of sample.

MONTH OF YEAR

FIGURE 11.—Schematic diagram of change in true thermal-power 

level for 50 kW indicated power level as a function of fueling 

and calibration. Fueling causes an instantaneous depression in 

true power level, whereas fuel consumption causes a gradual 

power increase over time. True and indicated power levels are 

made equal at time of calibration.

height, and the two are wrapped together in aluminum 

foil and placed in the quartz vial. Subsequent counting 

of the wires provides data to correct the monitor constant, J, to a value appropriate for each sample. This 

technique is especially useful when it is not possible to 

keep the vertical heights of all samples on a level identical. Data obtained in a single irradiation from both 

nickel wires and the St. Severin monitor (fig. 13) show 

that the use of nickel wires provides an accurate and 

effective method of monitoring the relative fast neutron 

fluence in the GSTR.

HORIZONTAL GRADIENTS

Horizontal flux gradients in the central thimble of

0.4 0.6 

RELATIVE FLUX

FIGURE 12.—Vertical flux gradient in central thimble of GSTR. 

Solid dots are data obtained using nickel washers, open circles 

with sulfur pills. Sulfur data are from W. M. Quam and T. M. Devore. (unpub. data, 1969). Point of maximum flux is approximately 4 cm below physical center of fuel rods.
FLUX CHARACTERISTICS OF THE GSTR 15

the GSTR are, for most purposes, negligible. They are 

so small (<0.5 percent) that they are barely detectable 

statistically and are not measurable with the 

techniques available to us.

Five different experiments were designed to determine the extent and effect of these gradients. The 

first three experiments were designed to test for flux 

gradients between the outside and the center of the 

central thimble facility.

Experiment 1. — On 47 levels in 19 irradiations done 

between December 1971 and October 1976, either BS-1 

(16 levels) or SB-2 (31 levels) biotite monitors were arranged in pairs so that one monitor was exactly in the 

center of the level and the other was in the outer ring. 

The arrangement of samples on each level was as in 

figure 7C, and the horizontal separation between the 

centers of the vials was 0.95 cm. The measured 

40Ar-rad/ 39ArK ratios for each biotite pair was normalized to eliminate difference in the fluence between 

levels and between irradiations by dividing the value of 

the center monitor by that of the outside monitor. The 

47 normalized values have a mean of 1.0042 and a 

standard error of the mean of 0.0016. A t-test indicates 

that the null hypothesis — this mean is equal to 1.0 — 

must be rejected at the 5 percent level of significance. 

This fact suggests that the fast neutron flux is slightly 

less in the center of the central thimble than on the 

outside.

Experiment 2. — One aliquant of BS-1 was placed in 

the center of a level and five in the outer ring (fig. 7C). 

These data were normalized in a similar way as the data

0.96

0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 

RELATIVE FLUENCE AS MEASURED BY NICKEL WIRES

FIGURE 13.—Comparison of relative fluence in GSTR, as measured 

with nickel wires and with St. Severin monitor. Error bars are 

one standard deviation.

in experiment 1. The resulting mean is 1.0039 with a 

standard error of the mean of 0.0020. For these data, 

the null hypothesis that this mean is equal to 1.0 (twotails test) cannot be rejected at the 5 percent level of 

significance, but the null hypothesis that the mean is 

equal to 1.0 against the alternative that it is greater 

than 1.0 (single-tails test) must be rejected. Though 

the results of this experiment are not so conclusive as 

those of experiment 1, they do suggest that there is a 

slight horizontal gradient in the central thimble with a 

lower flux in the center.

Experiment 3. — On six levels in two irradiations, 

nickel wires were so arranged that three were toward 

the center of the level and six to eight were in an outer 

ring (fig.7A, B). The horizontal separation between the 

inner and outer wires on a given level ranged from 

0.06-0.58 cm. The normalized data have a mean of 

1.0006 and a standard error of the mean of 0.0011. In 

this experiment, no horizontal flux gradient was detected, but this may be because the horizontal separation was only about two-thirds or less of that in experiments 1 and 2.

Experiments 4 and 5 were designed to detect differences between dispersion within vials and within layers 

of vials. Such differences would be expected if horizontal fluence gradients were a significant factor in limiting the precision obtainable with the GSTR.

Experiment 4. —On nine levels in three irradiations, 

nickel wires were included with the samples in 85 

quartz vials. Twenty-five of these sample vials contained two wires. After irradiation, the activity of each 

wire was measured. The pooled estimate of the standard deviation (Crow and others, I960), SP , of the 25 

pairs of wires from the same vial is 0.619 percent. The 

statistic sp for the groups of wires from the same layer 

was 0.672 percent. An F-test indicates that the null 

hypothesis—the dispersion of the two populations is 

equal—cannot be rejected at the 5 percent level of significance, that is, no difference was detected.

Experiment 5. — Thirteen samples of the St. Severin 

monitor were irradiated on seven levels in two irradiations. After irradiation, each sample was split into two 

aliquants, and each aliquant was analyzed separately. 

For the 13 pairs from the same vial, sp is 0.527 percent; 

for the 5 levels that contained more than 1 vial of St. 

Severin, sp is 0.598 percent. As in experiment 4, no 

significant difference in the dispersion of the two types 

of samples was detected.

Alexander and Kahl (1974), using the St. Severin 

monitor, performed an experiment similar to our experiment 4. Five pairs of the St. Severin monitor that 

were split after irradiation in the Vallecitos reactor 

have a pooled estimate of the standard deviation of 

precision of 0.077 percent; this reproducibility indi-
16 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

cates that the 40Arrad /39ArK ratio in St. Severin is very 

homogeneous. Because the reproducibility of the St. 

Severin analyses done in the GSTR does not approach 

that for the Vallecitos reactor, we suspect that the vertical fluence gradients in the GSTR are introducing inhomogeneities into the monitors and the nickel wires, 

and these effects are masking the effects of any horizontal gradients. It is quite likely that these inhomogeneities cannot be eliminated by mixing and 

splitting because the samples are small and are subject 

to significant sampling errors (Engels and Ingamells, 

1970).

The results from experiments 1 and 2 indicate that 

there may be a small horizontal flux gradient in the 

GSTR, with the flux in the center of the central thimble 

slightly less (0.5 percent maximum) than toward the 

side. The results from experiment 5, however, suggest 

that the vertical gradient and not the horizontal gradient is the primary factor limiting the precision in the 

GSTR. The data indicate that the precision of 40Ar/39Ar 

dating using the GSTR may be limited to a standard 

deviation of about 0.5-0.6 percent.

SELF-SHIELDING

Mitchell (1968) was the first to raise the possibility 

that neutron absorption within a sample might result in 

a significant error. He looked for this effect in the 

Herald reactor by irradiating a sphere of muscovite, 

then analyzing several parts of the sphere. The 

analyses of mica from the inside and outside of the 

sphere agreed to within 2 percent, from which Mitchell 

concluded that the effect was negligible.

We have looked for self-shielding in the central 

thimble of the GSTR. A cylinder of Jurassic diabase 

(sample No. 8L691; L21 of Dalrymple and others, 1975) 

2.40 cm in diameter and 2.54 cm high was irradiated 

for 5 MWH, receiving a neutron fluence of about 5 x 

1017 n/cm2 . The axis of the cylinder was parallel to the 

axis of the central thimble. After irradiation, a 6- 

mm-diameter core was taken with a diamond core drill 

across the axis of the larger core (fig. 14). This smaller 

core was sliced with a diamond saw into six cylinders, 

each of which was analysed. The 40Arrad/ 39ArK ratios 

show a progressive increase of about 3 percent from 

the outside inward (fig. 15). The effect appears to be 

larger than can be accounted for by horizontal fluence 

gradients, and we conclude that self-shielding has been 

detected. For most purposes, however, the effect will 

be very small over the width of a typical sample, and 

negligible from sample to sample. The effect will be 

even less in samples that consist of mineral grains or 

powders.

ACTIVITY PREDICTIONS

Rocks and minerals used in 40Ar/39Ar dating contain 

a variety of elements that generate radioactive products when bombarded with fast neutrons. For reasons 

of radiological safety, it is necessary to predict what 

the activity of each sample will be after irradiation. 

These predictions are also required by the conditions of 

the U. S. Nuclear Regulatory Commission licenses that 

govern both reactor operation and the use of activated 

samples by the 40Ar/39Ar investigator.

FIGURE 14.—Isometric drawing of sample locations in self-shielding 

experiment on diabase 8L691. Results for analyzed samples (A-F) 

are shown in figure 15.

84

83

82

^

<C 81

| 80

<C

' 79

78

77

0 4 8 12 8 4 0 

DISTANCE IN FROM SURFACE, IN MILLIMETERS

FIGURE 15.—Results of self-shielding experiment on diabase 

8L691. Error bars are one standard deviation. Analyzed samples 

(A-F) (see fig. 14) are shown at bottom of diagram.
ACTIVITY PREDICTIONS 17

The basis for these activity predictions is as follows. 

The rate of formation Rf of an activation product when 

a quantity of a target element is bombarded by fast 

neutrons is

R,= (9)

where 0 is the neutron flux (n/cm2 -s), m is the mass 

of the element (grams), L is Avogadro's number 

(6.0225 x 1023 atoms/mole), f is the fractional abundance of the target isotope, a is the nuclear reaction 

cross section (cm2 /atom), ma is the atomic mass of the 

element (g/mole), and n is the number of target 

atoms. The disintegration rate of the radioactive product nuclide is

Rd = XN (10)

where X is the decay constant (s"1 ) and N is the 

number of radioactive parent atoms. The rate of 

change of a radioactive product nuclide is, therefore,

dt

(11)

After an irradiation time t, the activity A of the product 

nuclide is

= 0no (1 — e~xt) (12)

where At is in disintegrations per second. If the sample 

sits for a time t1 after irradiation, then

(13)

It is customary to express activity in curies, where 1 

curie is 3.7 x 1010 disintegrations per second, so equation (13) becomes

. _ 0no (1 — e~xt) e~~xt> 

^ ~ 3.7 x 1010 ' (14)

In evaluating the radiological hazards from the irradiation of rock and mineral samples, we investigated 

more than 100 possible nuclear reactions involving 36 

isotopes of 13 elements. Only 26 of these reactions result in products of significant activity (table 6). The 

reactions involving Cu and Cr were included primarily 

because these elements are found in the aluminum

TABLE 6.— Data for activity calculations, TRIGA reactor

[Half-life given in y=years, h=hours, and m=minutes. Atomic mass and percent abundance and half-life after Weast (1976). Product is stable except 

noted. Q is based on data from Everling and others ( 1961). Fast-neutron cross sections based on data from activation analysis of Koch ( I960)]

Target 

element

Na ......

Mg......

Al ......

Si.......

P........

S. .......

K. ......

Ca .....

Cr......

Mn~. ..

Fe

Cu.....

Rb .....

Ti......

Ni......

Atomic 

mass

99 QQ

.............24.31

.............26.98

.............28.09

.............30.97

.............32.06

.............3910

.............40.08

.............52.00

.............54.94

.............55.85

.............63.54

.............85.47

.............47.90

.............58.71

Target 

isotope

23Na

24Mg

27A1

28Si

30Si 

31 P

32 S

33S 

34S

41 K

43Pa

44 Ca

48 Ca

55Mn

54Fe

63CU

S5Rb

46Ti

47Ti 

48Ti

58Ni

60Ni

62Ni 

64Ni

Percent 

abundance

100

78.7

100

Q9 91

3.09 

100

95.0

.76 

4.22

6.88

135

2 .08 

18 

4.31

100

5.82

91.66 

.33 

69.09

7215

7.93

7.28 

73.94 

68.27

2610 

3.59 

.90

Reaction

n,T

n,p

n,T

n,a 

n,p

n,T 

n,T

n,p 

n,a 

n,p

n,p 

n,T 

n,a 

n,T

n,p

n,T 

n,T 

n,T

n,T

n,p 

n,a 

n,p 

n,T 

n,T

n,7

n,p

n,p 

n,p 

n,p

n,p 

n,a 

n,T

Product

24Na

24Na

28A1

24Na

28A]

32p

28A1 

32p

33p 

35S _

42^

43K

45 CY 

49Ca2 

si Cr

56Mn

55Fe

54Mn 

5 iCr

56Mn 

59Fe 

64 Cu

86Rb

48Sc 

58Co

60Co

59Fe

65Ni

Q

(MeV)

4-fi qfi

A 70

+7 72

-3.14

3

QC

+6.59 

+7 94 -.69

-1.94 

qo

+.53 

+6.98 

-1.32

17 CLO

1 f>9

+7.42 

+5.14 

+9.25

4-1 97

+9.30

+.09 

+.84 

-2.93 

+6.58 

-J-7 99

Q CO

1

C Q

+.18 

-3.21 

+.40

-2.04 

-.43 

+6.13

Cross 

section 

( barns)

n ^

22

21

.1407

.11 

19

.14 

.15

qf>

.015 

.26 

.14 

1.1 11.

.67 

1.1

1 Q Q

9 ^

.023 

.00037 

.00044 

.98 

4.3

Oft

.0041

.00021 

.000077

099

.005 

.0057 

1.6

Product 

half-life

15.0 h

15.0 h

2.31 m

15.0 h 

2.31 m

2.62 h 

14.3 d

2.62 h 

2.31 m 

14.3 d

25 d 

88 d 

2.62 h 

12.4 h

99 4 h

165 d

8.8 m 

27.8 d

2.58 h

9 fi v

303 d 

27.8 d 

2.58 h 

45.1 d 

12.9 h

18.8 d

83.8 d

3.43 d 

1.83 d 

71.3 d

5.26 y 

45.1 d 

2.52 h

Flux 

(I0 13 n/cm2 -s) 

atl.OOOkW

1.7

.1

1.7

.3 

o

1.7 

1.7

1.6 

.7 

1.4

1.7 

1.7 

1.0 

1.7 1 ^

1.7 

1.7 

1.7

1.7

1.7

1.7 

1.7 

.3 

1.7 

1.7

1.7

q

1.7 

.3 

1.7

.7 

1.7 

1.7

'Value is an estimate.

-Decays to 49Sc, which decays by f' to "Ti with a half-life of 57.5d.
18 IRRADIATION OF SAMPLES FOR 4UAr/d9Ar DATING 40 / /39-

alloy (6061T6) used for the sample holder and reactor 

tube. Sulfur was included because potassium sulfate is 

used in determining reactor correction factors. The 

remaining elements are -commonly found in rocks and 

minerals.

The reaction energies, Q, were used as an estimate of 

the threshold energy for reactions with negative Q. The 

appropriate neutron flux was then estimated from the 

data of table 4. For reactions with positive Q, the average epithermal flux (>0.6 MeV) was used. Fast-neutron 

cross sections based on data from activation analysis 

(Koch, I960) were selected for the range of energies 

most appropriate for the particular reaction. Many of 

the cross sections are not well known or are known only 

for a range of energies different from those in the 

GSTR central thimble. Measurements of the activity of 

irradiated samples, however, have shown that the values in table 6 yield activity predictions that are accurate to within 20 percent.

The activity predictions are most conveniently done 

by computer. A BASIC computer program for predicting activities after irradiation in the GSTR is given in 

the section entitled "Computer Programs." If a 

computer is not available, activities may be estimated 

graphically using the curves in figure 16.

CORRECTIONS FOR INTERFERING 

ARGON ISOTOPES

Both Sigurgeirsson (1962) and Merrihue and Turner 

(1966) recognized that a principal difficulty with the

40Ar/39Ar dating method was that the fast neutrons may 

react with nu elides in the sample other than 39K to produce interfering isotopes of argon. These sources of interference were discussed in detail by Mitchell (1968) , 

Brereton (1970) , and Turner (l971b) . Of the principal 

reactions (table 7) , only four reactions occur with sufficient frequency to be of concern in most terrestrial 

samples (Turner, 1971b) . These are: 

40Ca(n, no) 36Ar 

42Ca(n,o) 39Ar

40K(n, p) 40Ar

41K(n, d) 40Ar

Fortunately, 37Ar is also produced by the (n, a) reaction with 40Ca, which permits corrections to be made 

for both the undesirable Ca- and K- derived argon 

(equation 7) . The corrections require that the following 

reactor constants be measured:

( 36Ar/37Ar) Ca

(39Ar/37Ar) Ca

In the interval from November 1970 through June 

1975, we irradiated 17 samples of optical grade CaF2 

crystals and 8 samples of reagent grade K^SCX in 8 

separate irradiations in the GSTR ranging from 5 to 80 

MWH. After irradiation, the salts were fused in an extraction line, and the argon released was purified and 

analyzed by mass spectrometry. The results are given 

in table 8. Unirradiated samples of the CaF2 and the 

K2S04 have also been analyzed and, within experimental error, yielded argon of atmospheric composition. 

The values given in the table were calculated assuming

TABLE 1.—Principal neutron reactions leading to the production of argon isotopes

[AfterBrereton, (1970), The Q values, in MeV, are shown in brackets below each reaction (Everling and others, 1961]

Target 

element

Calcium

Potassium

Argon

Chlorine

36Ar "Ar

40Ca(n,na) 40Ca(n,a) 

[-7.04] [+1.75]

39K(n,nd) 

[-9.73]

36Ar(n,T) 

[+8.79]

F4.57] ^

Argon isotopes produced

38Ar

42Ca(n,na) 

[-6.24]

40K(n,d) 

[-4.14] f

RUG] "*

40Ar( n,nd) 38Cl I 

[-12.11]

37Cl(n,T) 38Cli 

[+6.11]

39Ar

42Ca(n,a) 

[+0.34] 

43Ca(n,na) 

[-7.59]

39K( n,p) 

[+0.221 

4°K(n,d) 

[-5.36]

38Ar(n,T) 

[+6.58]

[-10.30]

40Ar

43Ca(n,a) 

[+2.29] 

44Ca(n,na) 

[-8.85]

4°K(n,p) 

[+2.30] 

41K(n,d) 

[-5.58]
CORRECTIONS FOR INTERFERING ARGON ISOTOPES 19

that all of the 40Ar in the irradiated CaF2 and all of the 

36Ar in the K2S04 were atmospheric. These assumptions 

may not be correct, but their effects cancel out in 

equation (?) and do not introduce any error into a

Two of the three principal reactor constants 

(( 36Ar/37Ar) Ca and ( 39Ar/37Ar)Ca ) are relatively reproducible and their values known for the GSTR to within 

less than 1 percent. We have been unable, however, to 

satisfactorily reproduce the value for ( 40Ar/39Ar)K from 

one irradiation to the next (table 8). We are convinced 

that the variability is real and that it is not a property 

of the GSTR alone, for similar results have been reported for other reactors. For example, values of 

(6.252 ± 0.087) x 10~2 and (3.72 ± 0.30) x 10~2 have 

been found for the GETR at Vallecitos by Alexander 

and Davis (1974) and Davis (1977), respectively. Saito 

and Ozima (1977) have found that values for 

( 40Ar/39Ar)K vary by nearly a factor of ten within the 

JMTR. As noted by Alexander and Davis (1974 ), the 

variation in this correction factor between reactors also 

is much larger than the variation in the corrections for 

the Ca- derived isotopes. Saito and Ozima (1977) tabulated correction factors found for various reactors and 

noted that the values reported for ( 40Ar/39Ar)K vary by 

nearly a factor of 50 whereas the values for 

( 36Ar/ 37Ar) Ca and ( 39Ar/37Ar) Ca tend to be relatively 

uniform even from one reactor to another. Saito and 

Ozima (1977) and Davis (1977) suggested that 

( 40Ar/39Ar)K may be strongly dependent on the neutron 

energy distribution and can be expected to vary from 

reactor to reactor and even between locations within a 

single reactor. All of our measurements, however, were 

made in the same location in the GSTR and we cannot 

satisfactorily explain the wide variation in results in 

this way unless the neutron spectrum in the central 

thimble varies considerably over distances of only a few 

centimeters. One possibility that we have not explored 

is that ( 40Ar/39Ar)K varies with the fueling cycle. Whatever the cause, it is clear that where this correction is 

potentially an important source of error, it must be 

measured separately for each irradiation, preferably by 

placing the potassium salt as close as possible to the 

unknown sample.

The most serious interference is caused by the 36Ar 

produced by the (n,na) reaction with 40Ca. This 36Ar interferes with the atmospheric argon correction, which 

is made using 36Ar as a reference isotope (equation 6). 

The extent of the interference is a function of integrated fast neutron flux, age, and the K/Ca ratio of the 

sample (figs. 17,18). The effect becomes larger as the 

integrated fast neutron flux increases and as the age 

and K/Ca ratio of the sample decrease. Errors in this 

correction factor become increasingly important as the 

amount of 36Arca increases. This interference has the 

same type of effect as the atmospheric argon correction, and in young, high-calcium samples these two 

corrections combine to seriously degrade the usefulness of the 40Ar/ 39Ar dating technique. Additional 

curves showing the effect of this correction as a function of age, irradiation time in the GSTR, and K/Ca, 

are given in the section entitled "Effect of 

40Ca(n,na)36Ar Interference."

36Ar and 38Ar are produced by neutron capture followed by @~ decay from the two naturally occurring 

isotopes of chlorine, 35C1 and 37 C1. Since 35C1 is three 

times as abundant as 37 C1 (tablel) and has much larger 

thermal and resonance integral capture cross sections, 

45 and 15 barns, respectively versus 0.43 and 0.32 

barns (Walker and others, 1977), neutron capture produces about 300 times more 36C1 than 38 C1. 36C1, however, has a half-life of 3 x 105 yr while 38C1 has a halflife of 37.2 minutes (table l). In most experimental 

situations, the 36 C1 does not decay appreciably to 36Ar. 

Bernatowicz and others (1978) documented a case 

where the combination of a relatively high chlorine 

content of a monitor, a very high thermal fluence, and 

a long delay between irradiation and the analysis of the

TABLES.—Correction factors for Ca- and K-derived Ar isotopes for theU:S. Geological Survey TRIGA reactor

Irradiation 

date

Nov.

Mar.

Oct.

Mar.

Apr.

Apr.

June

June

1970

1973

1973

1974

1975

1975

1975

1975

MWH

80

80

80

60

40

20

10

5

Material Number of 

measurements

CaF2

K2S04 

CaF2

K2 SO,

CaF2

K2SO,

CaF2

CaF2

CaF2

CaF2

4

3 

4

3

2

2

2

2

2

1

Weighted means 1

( S6Ar/ 

x

2.72

2.66

2.72

2.66

2.68

2.54

2

2.64

3 'Ar>Ca 

1(T 4

± 0.029

± 0.054

+ 0.018

+ 0.014

+ 0.057

±0.014

.63

±0.017

x 10' 5 x 10"" x 10" 3

6.33

6.57

3.174 + 0.024 6.78

6.76

6.74

6.58

6,

6.73

+ 0.043

±0.115

± 0.026

2.20 + 0.066

+ 0.035

+ 0.007

±0.106

.70

7TO37

( 38Ar/39Ar)K ( ">Ar/ 39Ar)K 

x 10' 2 x 10' 2

0.594 ± 0.072

1.01 +0.046

1.34+0.024 0.1 +0.1

'Weighting is by the inverse of the variance. Errors are estimates of the standard error of the mean.
20 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

10

10 100 

IRRADIATION TIME AT ONE MEGAWATT, IN HOURS

1000

FIGURE 16.—Activity resulting from various neutron reactions in GSTR as a function of irradiation time at 1 MW. Curves are for 1 g of target

from dashed curves must be
CORRECTIONS FOR INTERFERING ARGON ISOTOPES 21

C/5 

UJ

O

i———i——i——i—i—i—n

55 Mn(n,y)56Mn[10]

10 100 

IRRADIATION TIME AT ONE MEGAWATT, IN HOURS

1000

element; natural abundance of target nuclides has been taken into account. Solid curves yield activities directly, whereas activities read 

multiplied by factor in brackets.
22 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

-100

10 100 

TRUE AGE, IN MILLIONS OF YEARS

1000 10,000

FIGURE 17.-Effect of reaction 40CaU, na) 36Ar on calculated 40Ar/39Ar age as a function of age and K/Ca ratio for irradiation time of 40 

MWH. Graph gives approximate errors that would result if no corrections were made. Effect depends on age, K/Ca, and irradiation time. 

See also section entitled "Effect of 40CaU, na) 36Ar Interference" (figs. 24-36).

monitor resulted in a significant but indeterminable 

contribution to the measured 36Ar in their monitor from 

neutron capture on 35C1. This indeterminable component introduced a major uncertainty into Bernatowicz 

and others' (1978) calibration of their irradiation.

38Ar is produced by neutron-induced reactions on 

both K and Ca as well as the neutron capture reaction 

on 37 C1 via 38C1. In samples exposed to cosmic rays 

there is commonly a significant cosmogenic 38Ar component, which can be used to calculate cosmic-ray exposure ages. The components of the measured 38Ar due 

to reactor-induced reactions on K and Ca can be determined if the ( 38Ar/37Ar) Ca and ( 38Ar/39Ar)K values 

are measured on potassium and calcium salts. One 

measurement of each of these correction factors for the 

GSTR is listed in table 8.

In the analysis of terrestrial samples, the measured 

36Ar can usually be corrected to yield the atmospheric 

36Ar component. Any 38Ar in excess of the atmospheric 

38Ar/36Ar value, after the components from neutroninduced reactions on K and Ca are subtracted, can then 

be attributed to neutron capture on 37 C1 and can be 

used to measure the Cl contents of the samples (Stettler and Bochsler, 1979). In the analysis of extraterrestrial samples, however, the subtraction of the 

reactor-produced 36Ar and 38Ar leaves a threecomponent mixture, cosmogenic 36Ar and 38Ar, atmospheric (or trapped) 36Ar and 38Ar, and Cl-derived 38Ar. 

The measurement of 36Ar and 38Ar does not supply 

enough information to allow these components to be 

resolved.

BIOTITE

MUSCOVITE

HORNBLENDE

AUGITE

SANIDINE

OLIGOCLASE

LABRADOR ITE

BASALT

LUNAR BASALT 

RHYOLITE OBSIDIAN

1Q-32 Q-Z 2 51Q-12 5 -\ 2 5^Q2 5-\Q22

RATIO OF POTASSIUM TO CALCIUM

5 10 3

FIGURE 18.—Approximate ranges of K/Ca atomic ratios for some 

common minerals and rocks. K/Ca for an analyzed sample can 

be found by multiplying K20/CaO (weight-percent ratio) by 

1190.
CORRECTIONS FOR INTERFERING ARGON ISOTOPES 23

Only in those cases where one of the three components 

is negligible relative to the other two can the 36Ar and 

38Ar data be resolved into individual components. Many 

lunar and meteoric samples are relatively depleted in 

Cl, and 38ArCi is negligible. In such cases, a cosmogenic 

component can be resolved and used to calculate 

cosmic-ray exposure ages. The same data set can therefore simultaneously yield 40Ar/39Ar formation ages and 

38Ar cosmic-ray exposure ages. The details of such calculations are given in several of the papers listed in the 

selected bibliography (table 10).

The effect of 39Ar derived from neutron reactions 

with 42Ca is an inverse function of the K/Ca ratio of the 

sample, is independent of the integrated fast neutron 

flux, and is essentially independent of age, except for 

old samples (fig. 19). For all but very low potassium 

samples, the effect of this interference is negligible and 

even large errors in the applicable correction factor 

would result in a negligible error in the age. In samples 

with very low K/Ca ratios such as lunar anorthosite, it 

is not uncommon for half of the measured 39Ar to be 

39ArCa .

The magnitude of the K-derived 40Ar correction is a 

direct function of the integrated fast neutron flux, an

inverse function of the age of the sample, and independent of the K/Ca ratio (fig. 20). For a 30-MWH irradiation in the GSTR, this interference produces an effect 

of about 0.1 m.y. for samples of any age. As noted 

above, however, this correcton may vary from one irradiation to another for reasons that are as yet unknown. For most dating studies even a 100 percent 

error in the reactor constant ( 40Ar/39Ar)ic would produce a negligible error in the calculated age. For 

studies involving very young samples, however, the uncertainty and variability in this correction factor could 

be a serious source of error.

Occasionally, it is useful to know the relation between the atomic ratio K/Ca and the measured ratio 

39ArK/37ArCa . For the GSTR the relation is

K/Ca = (0.49 ± 0.09) 39ArK /3?ArCa. (15)

The constant of proportionality was calculated using 

data from 19 samples for which K/Ca was measured 

independently (Dalrymple and Lanphere, 1971). Equation (15) is graphed in figure 21. Three of the samples 

give individually calculated constants that are unusu-

-100 i—i—i i i i u

-10

DC

o

BE -1

-0.1

~i—i i i i I————r 

K/Ca=0.001

i—i i i i i i—i i i i i

K/Ca=0.002

K/Ca=0.005

K/Ca=0.01

K/Ca=0.02

K/Ca=0.05

K/Ca=0.1

K/Ca=0.2

0.1 10 100 

TRUE AGE, IN MILLIONS OF YEARS

1000 10,000

FIGURE 19.-Effect of 42Ca(n, na ) 39Ar reaction on calculated 40Ar/39Ar age as a function of age and K/Ca ratio. Graph gives approximate 

errors that would result if no corrections were made. Effect is independent of irradiation time and is negligible for K/Ca greater than 

about 0.2.
24 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

ally high, but the remaining 16 values fall between 0.36 

and 0.64 with mean and standard deviation as given in 

the equation above. Probably most of the variability, 

including the anomalous values, is due to inhomogeneities in the samples that makes it difficult to 

obtain representative splits for separate analyses. 

Another contributing factor is that either K or Ca is 

present in only trace amounts in nearly all these samples, and that fact adds to the difficulty in obtaining 

accurate analyses.

The ratios involving 37Ar must be corrected for the 

decay (table l) that occurs both during and after irradiation. For uninterrupted irradiation, this calculation an be done quickly with a desk calculator (equation 38, below). Because the GSTR is used for a variety 

of purposes, some of which require pulsing or very low 

power levels, samples for 40Ar/ 39Ar dating are frequently pulled up out of the core while other experiments are being accommodated. The aluminum capsule 

is not removed completely from the central thimble

tube; instead it is positioned out of the neutron flux but 

left deep enough for adequate radiological shielding by 

the column of water above. We are not sure that this 

procedure is necessary, but it seems worthwhile to try 

to ensure that the samples are irradiated at more or 

less constant power level. In addition, the reactor is 

normally operated 8 hours a day for 5 days a week. 

This means that samples for 40Ar/39Ar dating are irradiated in increments rather than continuously, a factor which complicates the 37Ar correction procedure 

somewhat but does not degrade the accuracy of the 

calculations.

Formula 39 is used to calculate the 37Ar decay correction for samples that have been irradiated in increments and at different power levels. This calculation 

can also be done with a desk calculator, but for more 

than a few increments the calculations become very 

cumbersome and a computer is much more convenient. 

A BASIC computer program for this calculation is 

given in the section entitled "Computer Programs."

+ 100

+0.1 100 1000

TRUE AGE, IN MILLIONS OF YEARS

FIGURE 20.-Effect of 40K(n, p) 40Ar and 41K(n, d ) 40Ar reactions on calculated 40Ar/39Ar age. Graph gives approximate errors that would

result if no corrections were made. Effect is independent of K/Ca ratio.
PRODUCTION OF SUFFICIENT 39 Ar 25

1000

100

10

0.1

0.01

Muscovite

Basalt 

Plagioclase 

Hornblende

0.01 0.1 1 10 100 

ATOMIC RATIO OF POTASSIUM TO CALCIUM

1000

FIGURE 21.— ArK/37Arca as a function of K/Ca atomic ratio in

200

100

GSTR(eq.l5).

OPTIMIZATION OF IRRADIATION PARAMETERS

Turner (I971b) showed that for any reactor the various interferences can be minimized by choosing an optimum irradiation time and an appropriate sample size. 

Following Turner (I971b) we analyzed our results from 

the GSTR, and we provide an irradiation optimization 

diagram as figure 22. The optimum irradiation is based 

on the satisfaction of three conditions: production of 

sufficient 39Ar and minimization of interference from 

the reactions 40K (n, p)40Ar and 40Ca(n, na) 36Ar.

PRODUCTION OF SUFFICIENT 39Ar

Theoretically, production of 39Ar is controlled by 

sample size, K20 content, and irradiation time. There 

are also several limiting practical considerations, including mass spectrometer sensitivity, the amount of 

reactor time available, and the maximum sample size 

that can be physically accommodated in the irradiation 

facility.

^For the GSTR we have chosen 01 MWH as a lower 

practical limit for the irradiation time. The largest

Excessive interference "° 

from 40ArK and 36Arc

/

Insufficient 39Ar production

10 100 

POTASSIUM-ARGON AGE, IN MILLIONS OF YEARS

1000 10,000

,36. FIGURE 22.—Irradiation time in GSTR required to maximize 39Ar produced from 39K while minimizing interferences from 40 ArK, anddbArca- For 

irradiations in unshaded parts of graph, either 39Ar production will be too low (lower right), or interference from 40ArR 

(upper left). Dashed lines give maximum irradiation for minimization of 36Arca interference.
26 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

sample that can fit easily in the larger quartz vials 

weighs about 5 grams. In 01 MWH, a 5-g sample that 

contained 10 percent K2 0 would yield about 3.6 x 10~12 

moles or 0.8 x KT8 cm3 (SIP) of 39Ar (fig. 9), which is 

about as small a quantity as can be measured on most 

mass spectrometers and still maintain an accuracy of 1 

percent or better. Two hundred hours is probably the 

upper limit, considering that the reactor is only available for a limited period of time (< 40 hours) each week, 

except under special circumstances.

The size of the sample should be chosen (fig. 9) to 

provide as much 39Ar as can be conveniently measured, 

but the 40Arrad /39ArK ratio also must be limited to some 

reasonable value for accurate measurement. Turner 

(I971b) selected a ratio of 300 as probably the largest 

that could be measured without intolerable interference between the 40Ar and 39Ar mass beams. Thus, condition 1 requires that both the sample size and the irradiation time be adjusted to provide optimum 

amounts of both 40Arrad and 39ArR, and to keep the 40Arrad/ 39ArK ratio less than 300.

MINIMIZATION OF 40K(n, p)40Ar INTERFERENCE

As discussed above, the production ratio ( 40Ar/39Ar)K 

varies considerably and may only be known for the 

GSTR to within a factor of two or so. If we select the 

maximum tolerable error from this interference as 0.5 

percent, then the quantity of 40ArK should be kept to 

less thanl percent of the 40Arrad. In terms of ratios, this 

requires that

40Arrad /39ArK> 100( 40Ar/39Ar)K

the largest value for ( 40Ar/39Ar)K that we have measured for the GSTR is 1 x 10~2 (table 8), so conservatively, the desired ratio becomes

40Arrad /39ArK^l.

All points that satisfy both the above conditions are 

included within the shaded area of figure 22. The line 

representing 40Arrad/ 39ArK = 10 is also shown for reference. Generally, it is easier and more accurate to 

measure ratios if the two isotopes are within a factor of 

10 or so in size, that is,

1< 40Arrad /39ArK<10,

but for very old samples this is not possible because 

impractically long irradiation times are required.

MINIMIZATION OF 40Ca,(n, na) 36Ar INTERFERENCE

The rate of production of 36Arca relative to 37Arca is 

known for the GSTR to within a few percent (table 8) 

so accurate corrections can be applied. It is desirable,

however, to limit the amount of 36Arca produced to 

avoid magnifying the error. If we limit 36ArCa to 10 percent of the 36Ar mass beam, then this condition becomes

36ArCa < 0.1 36Aratm 

or

40Arrad /36ArCa >2955.

This condition depends not only on irradiation time and 

the age of the sample, but also on the K/Ca content. 

The dashed lines on figure 22 show the maximum 

irradiation times that will allow this condition to be met 

for various values of K/Ca.

As can be seen from figure 22, it is not difficult to 

satisfy all three of the conditions discussed above provided that K/Ca is greater than about 0.002. Theoretically, these conditions can always be satisfied for samples with K/Ca greater than 0.002, but there are also 

practical limitations imposed on the sample size and on 

the amount of gas that can be accurately measured by 

the mass spectrometer. All these factors need to be 

considered when choosing the irradiation parameters, 

and for many samples, it will be necessary to compromise.

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Laboratory.

Weast, R. C., ed., 1976, Handbook of chemistry and physics (57th 

ed.): Cleveland, The Chemical Rubber Company.

York, Derek, and Berger, G. W., 1970, 40Ar/ 39Ar age determinations 

on nepheline and basic whole rocks: Earth and Planetary Science Letters, v. 7, no. 4, p. 333-336.

SUPPLEMENTAL DATA
32 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

DERIVATION OF EQUATIONS

30Ar /39Ar AGE EQUATION

Beginning with the basic equation for the production 

of radiogenic 40Ar from the decay of 40K,

X,

40A Arv TM — 40T£ ——————-———— ( pXt — 1 ) (-\ \ d ~ \« + x/e (1)

where X* is the decay constant for electron capture, X/j 

is the decay constant for @~ emission, X = X* 4- X/j , 

and t is time, and using the subscripts u and m for the 

unknown and monitor minerals, respectively, then

-40K _^PXtUand

Dividing equation (2) by (3),

40Ar rvi

4 °Arrad,m

4 QR

^OK

u / extu_i \

-( m \ e k m — - i > * <4>

If the unknown and the monitor minerals are irradiated 

together and receive the same neutron dose, and a 

fraction F of the 39K in each is converted to 39ArR, then

(5)

39ArK>m =F39Km.

and

Dividing equation (5) by (6),

Substituting equation (7) into (4),

4 oArrad>u

40Ar j

rilrad,m

Solving for tu,

t = - In I

X L (4 oArrad /39ArK)I

To simplify, we define the quantity

^->

(4 oArrad/39ArK)u 

1 4.—————————( extm -1) >] • (9)

J =

(4 oArrad /39ArK)m 

and substitute equation (10) into (9), which becomes

tu = i-ln [l + J( 4 °Arrad /39ArK)u J. (ll)

To determine the quantity 40Arrad/ 39ArK for use in 

equation (11), it is necessary to correct the isotope 

ratio 40Ar/39Ar, measured in the mass spectrometer, for 

atmospheric Ar as well as for Ca- and K-derived Ar 

isotopes. If there were no Ca-derived 36Ar, then the atmospheric component would be(40Ar/36Ar)atm( 36Ar/39Ar) 

or 295.5 ( 36Ar/39Ar), which would be subtracted from 

the measured 40Ar/39Ar ratio. However, part of the 36Ar 

is derived from neutron reactions with 40Ca, and the 

appropriate atmospheric correction is

295.5 (12)

where ( 36Ar/37Ar)Ca is a constant for a particular reactor. 

In addition, there is 40Ar generated by neutron reactions with potassium, and this component, ( 40Ar/39Ar)K 

also a reactor constant, must be subtracted from the 

measured 40Ar/ 39Ar ratio. Finally, the measured 

40Ar/39Ar ratio must be corrected for the 39Ar generated bv neutron reactions with Ca, which is ( 39Ar/ 

37Ar)Ca (3?Ar/39Ar), where ( 39Ar/37Ar)Ca is a constant.

After incorporating these corrections, the complete 

expression becomes

40Arrad ( 4 °Ar/39Ar) - 295.5
ERROR FORMULAE

DERIVATION OF EQUATIONS

Equation (19) then becomes

The basis for the derivation of the error formulae is 

as follows:

If y = F(x p x2 , ....,xk) 

and the changes Ax; are small, then

9F 

3xt

Axt.

(14)

(15)

Further, if the quantities Ax; are independent, then the 

variance in Ay is approximately

(16)

To simplify notation, let

F = 40Arrad / 39ArK

A = 40Ar/39Ar

B - 36Ar/ 39Ar

D = 37Ar/ 39Ar (corrected for 37Ar decay) 

Ci = ( 40Ar/36Ar) atm = 295.5 

C2 = ( 36Ar/ 37Ar) Ca = reactor constant 

C3 = ( 40Ar/39Ar)K = reactor constant 

C4 = ( 39Ar/37Ar)ca = reactor constant

Then equation (13) becomes

A-CLB -fCAp-Cj F =

1-C4D

From equation (15),

^T?

AF = dF = + AB +

3A oB 

Differentiating equation (17) and rearranging it,

dF =

(17

(18)

(19)

(1-C4D)AA -C1 (1-C4D)AB + [C4 (A-C 1B-C3 )+C 1 C 2 ]AD

Equation (19) can be simplified because for the GSTR 

( and probably for all reactors) ,

and

and is negligible.

1 - C4D = 1

C4 C3 = 4 x lO-e,

and

aF 2 ~ aA [C4A -

-f33

( 2o)

(21)

where the errors a are absolute errors.

It is usually more convenient to use percentage or 

fractional errors, a 1 , whereupon equation (21) becomes

(22)

JT2

which can be used to estimate the error in 40Arrad/39Ar.

Using the same approach and terminology, an expression for estimating the error in a 40Ar/39Ar age can 

be derived.

Starting with equation (11),

= Mn[l +FJ],

A

then

Differentiating (23) and rearranging,

At =

I

+FJ) (JAF + FAJ)

and

X 2 (l

(23)

(24)

(25)

(26)

Expressed in percentage or fractional errors, (26) becomes

J2F2

t2 X 2 (l + FJ) 2

(27)

Let

7Ar DECAY CORRECTION

n = neutron density, 

v = neutron velocity, 

nv = flux,

a = nuclear cross section, 

t = irradiation time, 

T = number of 40Ca target atoms, 

N = number of 37Ar atoms at time t, and 

X = decay constant of 37Ar.
34 IRRADIATION OF SAMPLES FOR 4UAr/d9Ar DATING 40A../39/

The rate of change of 37Ar is 

dN

dt = nvoT - AN. (28)

Equation (28) can be rewritten 

dN , ext

dt

or

dt x *'~ ' 

Integrating (30) and rearranging,

X

NowN =0 at t = 0,so

or

C =

X

-nvoT

X

Substituting (33) into (31),

X

(29)

(30)

(31)

32

(33)

34

If a finite time tr elapses between irradiation and measurement, then at time t +1',

(35)

Now the total number of 37Ar atoms produced, including those that have decayed, is

Nn = nvoTt,

so

t '

Substituting (36) into (35) and rearranging,

(36)

37

Expressing (37) in terms of Ar isotope ratios,

(1 - e- (38)

The above presumes that the irradiation is continuous for a time t and at the same reactor power level. If 

the irradiation I is done in n increments at various 

power levels, then equation (38) becomes

seAr

axt'i

(39)

i=0

where P; = reactor power level, in megawatts,

for the increment, 

ti = increment length, 

t1 = corresponding decay time for 

the increment (that is, 

the time from increment end 

to analysis), and

I = Pjti in MWH. 

Z—/

i=0
EFFECf OF 40Ca(ii,na) H>Ar INTKRFERENCE 35

EFFECT OF 40Ca(n, na) 36Ar INTERFERENCE

The following 13 graphs (figs. 23-35) supplement 

figure 17 and show the effect of the 40 Ca(n, na) 36Ar 

reaction on the calculated 40Ar/ 39Ar age as a function

of age and irradiation time in (MWH) for various 

K/Ca atomic ratios. The graphs give the approximate 

errors that would result if no corrections were made. 

On the centerline of the central thimble, 1 MWH results in a fluence of approximately 1 x 1017 n/cm2 .

-100

-0.1 

0.1 10 100 

TRUE AGE, IN MILLIONS OF YEARS

1000 10,000

FIGURE 23.-Effects of reaction 40 Ca(n, no) 36Ar on calculated 40Ar/39Ar ages.
36 IRRADIATION OF SAMPLES FOR 4UAr/ a9Ar DATING 40* /39 1

-100

10 100 

TRUE AGE, IN MILLIONS OF YEARS

1000 10,000

FIGURES 24 (top) and 25 (bottom).- Effects of the reaction 40Ca(n, no ) 36Ar on calculated 40Ar/39Ar ages.
EFFECT OF 40Ca(n,na)HfiAr INTERFERENCE 37

-100

10 100 

TRUE AGE, IN MILLIONS OF YEARS

1000 10,000

FIGURES 26 (top) and 27 (bottom).- Effects of reaction 40Ca(n, na) 36Ar on calculated 40Ar/39Ar ages.
38 IRRADIATION OF SAMPLES FOR 40Ar/ 39Ar DATING

-100

-10 -

UJ

O 

cc

UJ

Q.

- -0.1

-100

cc 

O

cc 

cc

-10

-0.1

0.1 10 100 

TRUE AGE, IN MILLIONS OF YEARS

1000 10,000

FIGURES 28 (top) and 29 (bottom).-Effects of reaction 40 Ca(n, no) 36Ar calculated 40Ar/39Ar ages.
EFFECT OF 4 "Ca(n,nar'Ar INTERFERENCE 39

-100

0.1 10 100 

TRUE AGE, IN MILLIONS OF YEARS

1000 10,000

FIGURES 30 (top) and 31 (bottom).- Effects of reaction 40Ca(n, na) 36Ar on calculated 40Ar/39Ar ages.
40 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

-100

-10 -

CJ

en

Hi

o_

^ -0.1

10 100 

TRUE AGE, IN MILLIONS OF YEARS

1000 10,000

FIGURES 32 (top) and 33 (bottom).- Effects of reaction 40 Ca(n, no) 36Ar on calculated 40Ar/39Ar ages.
EFFECT OF 4 "Ca(n,nar'Ar INTERFERENCE 41

-100

10 100 

TRUE AGE, IN MILLIONS OF YEARS

1000 10,000

FIGURES 34 (top) and 35 (bottom).- Effects of reaction 40Ca(n, no) 36Ar on calculated 40Ar/39Ar ages.
42 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

COMPUTER PROGRAMS

The following two computer programs are written in 

DEC (Digital Equipment Corporation) OS/8 Basic 

(version 5A) for a PDP8/e or PDP8/a computer. This 

version of BASIC runs as a true compiler under the 

DEC OS/8 operating system and contains certain file 

and string handling capabilities that may not be available in some versions of BASIC. Each program is sufficiently documented, however, so that the programs 

can be converted easily to other versions of BASIC or 

to other computer languages.

NEUT2 - ACTIVITY PREDICTION PROGRAM FOR THE GSTR

INTRODUCTION

This BASIC program predicts the activity of 18 

radioisotopes upon irradiation of rock and mineral 

samples in the central thimble (core) of the U. S.

READY

RUN

Geological Survey TRIGA reactor (GSTR) at a 1 MW 

power level. Predictions are made for 0 day, 2 days, 7 

days, and 20 days after irradiation so that an appropriate cooling time can be estimated. The program also 

sums the activity of the 18 isotopes at t = 0 for all the 

samples in an irradiation. Activity is in millicuries and 

is accurate to no more than two significant digits because the neutron cross sections of most of the nuclear 

reactions are poorly known. Data used by the program 

for the activity predictions are given in table 6 and discussed in the section entitled "Activity Predictions".

DESCRIPTION

Paging is done by the program, so it is advisable to 

begin at the top of a page if fanfold paper is used. The 

program begins by printing a heading, the current 

date, and a list of material choices as shown below:

NEUT2D BA 30-JUL-BO

NEUTRON 2 CVER* 1/6/78) 

ACTIVITY PREDICTION FOR U 

07/30/80

TRIGA REACTOR

MATERIAL CHOICE!

1--BIOTITE

2--MUBCOUITE

3-BASALT

5-ACTINOLITE

6--HORNBLENDE

7--PLAOIOCLA8E

9-AUGITE

10-CAF2

11-K2804

4 - H G R A Y W A C K E 8 - K - F E I... D S P A R 1 2 - A N D E SIT E

13--RHYOLITE

14--AL TUBE

15-QTZ VIALS 

99-YOUR CHOICE

Typical compositions for these 15 materials are contained in the DATA statements 9000-9300. There is also 

an option (99—your choice) to allow entry of any composition desired.

After the material list, the program requests an irradiation number and a sample number. Any combination of alphanumeric characters (up to 20) may be 

used as the information is for identification only. The 

weight is entered in grams. The irradiation time should 

be in hours at al MW power level. The material is chosen by entering the appropriate material number, after 

which the program will print the material selected and 

the activity table.
IR R A DI A T10 N N 0 ,'!J X X X11 

SAMPLE NO,?P-~207 

WGT (GMB)?0,0706 

IRRAD, IIHE (MRS)?25 

MATERIAL N0?2 

MUSCOVITE

COMPUTER PROGRAMS 

•C--7

43

PKauuu i

AL.-28

8 1 -31

MA -2 4

FE--55

MN--54

CR--51

MN--56

FE--59

K--43

CA--45

CA--49-fSC--49

K--42

P-32

P-33

S-35

S-31

RB--86

CLI-64

0 DAYS

31 ,7284

,.505674

3,34828

,00136735

0

0

4,26675

,000588632

0

0

,000481701

2,3535

,0011733

0

0

0

,00401179

0

ACTIVITY CMC.1

2 DAYS

0

0

,364327

,00136535

0

0

0

,000570828

0

0

0

,160454

,00106527

0

0

0

,00372586

0

:> AFTER COOLING

7 DAYS

0

0

,00140912

,00136037

0

0

0

,000528639

0

0

0

,000194736

,000836719

0

0

0

,00309706

0

20 DAYS

0

0

0

,00134752

0

0

0

,000432972

0

0

0

0

,000446576

0

0

0

,00191526

0

TOTALS 42,2102 531509 * 00742665 ,00414233

DATA OK?YES 

MORE SAMPLES?YES

If the optional material is chosen (99), the program 

will request a material name, then the elemental composition (weight percent) of the material.

IR RA DIA T10N NO.?XXIU-B-4 

SAMPLE NO..TT-S235Z 

WGT (GMS)?0,3042 

IRRAJiU TIME <HR8)?25 

MATERIAL NOT99 

MATERTALTSERICITE

S3.

A I...

FE

HG

CA

NA

K

MN

CR

P

RB

CU

'3*40 

"0*57 

?0,06 

TO* 42 

?8*66 

TO* 09 

TO

TO*017 

TO*078 

?() 

TO
44 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

After the activity table is printed, the program will 

ask DATA OK? A "YES" will accumulate the nuclide activities at 0 days for the summary table. A "NO" will 

exclude that sample from the irradiation totals. The 

next question MORE SAMPLES? tells the program 

whether to request data for another sample (YES) or to 

print the summary table (NO).

ACTIVITY SUMMARY AT T-0 

(3 E 0 C I"! R 0 N 0!... 0 G Y P R 0 J E C T ? M E N i... 0 P A R t 

A C; C 0 M P A NIE S R A JO 101 B 0 T 0 P E: R E Q U E 3 T 

07/30/80

IRRADIATION NO, XL.IV 

3 SAMPLES

: ORM NO

PRODUCr

AL-28

SI-31

NA-24

FE--55

MN--54

CR-51

MN--56

FE-59

K-43

CA--45

CA--49 + SC-49

K--42

P-32

P--33

S-35

S--31

RB-86

CU-64

MCI

227,33 

4*07664 

25,99:1.4 

,0336044 

,0009272 

<. 000131501 

34,4166 

..0144665 

,000572499 

,000610968 

,0207518 

19,1344 

,00547047 

0 

0

0

.0208656

0

311,046

For options 1-9 and 12-13, standard mineral and rock 

compositions have been used. Because of the poorly 

known neutron cross sections of most of the reactions 

involved, the use of an exact composition for any given 

sample generally would result in insignificant differences in the predicted activities. If an exact composition 

is required, option 99 can be used. The standard compositions and their sources are given in table 9.

VARIABLE LIST

W

I

X

E(l ) 

E(2) 

E(3) 

E(4) 

E(5) 

E(6) 

E(7) 

E(8) 

E(9) 

E(10)

E(12)

E(13)

T

H

B

D

N

M

M$ 

AO

A2 

A3 

A4 

SO, S2, S3, S4,

ZO , Z2 , Z3 , Z4 ,

L( J )

Sample weight, grams.

Irradiation time, hours.

Irradiation time, seconds.

Si, weight percent.

Al

Fe

Mg

Ca

Na

K

Mn

Cr

P

Rb

Cu

S

Amount of target isotope.

Product isotope half-life, seconds.

Neutron cross section, barns.

Neutron flux, n/cm2 -s.

Number of atoms in 1 gram of target isotope.

Irradiation number.

Sample number.

Material ( option) number.

Material name.

Activity in millicuries at 0 days for a

particular reaction 

Activity in millicuries at 2 days for a

particular reaction 

Activity in millicuries at 7 days for a

particular reaction 

Activity in millicuries at 20 days for a

particular reaction 

Sums of AO,A2, A3, A4 when several reactions have the same product nuclide. 

Sums of activities at 0 , 2 , 7 , and 20 days. 

Sums of product activities for summary total.
TABLE 9.— Standard mineral and rock compositions ( weight percent) used in BASIC program NEUT 2

[Numbers are material choices in computer program]

Elements 

and 

oxides

Si

Al— — —

Fe— — —

Mg— — ..

Ca— — —

Na— — —

K— — — .

Mn— -—

rv

P

Rb— — ...

Cu — — -

S— —— .

Si02 —— -

A12 03— —

Fe2 03 ——

FeO

MgO— — -

Na2 0— ...

K2 0— — -

P O

MnO— —

Cr2 03 — .

Rb2 0—— -

i

Biotite

... -17.9

... .. 7.4

..... 18.5

..... 4.8

.... . .64

...... .37

...... 6.9

07

...... 0

.... .. 0

.... - 0

.... .. 0

..... . 0

.—.38.30

1 1 QQ

— - 3.98

20 24

.... - 7.96

...... .90

—— .50

— — 8.31

OQ

..

2 

Muscovite

22.1

16.5

3.4

.57

.06

.42

8.66

.09

0

.02

.08

0

0

47.14

31.28

3.98

79

.94

.09

.57

10.43

.04

.11

3 

Basalt

23.6

7.65

7.65

5.46

6.25

1.94

.12

.12

.06

.09

0

0

0

50.50

14.47

3.43

6.76

9.06

8.74

2.62

.14

91

.15

.09

4 

Metagraywacke

34.8

6.0

3.0

1.5

.9

1.6

.6

.05

0

.05

0

0

0

74.3

11.4

0

3.8

2.5

1.3

2.1

.72

19

.06

5 

Actinolite

26.3

1.13

8.52

9.71

7.36

1.01

.25

.05

0

0

0

0

0

56.06

2.14

2.22

8.97

16.11

10.28

1.36

0

.23

..

6 

Hornblende

22.8

5.0

8.7

8.7

8.5

.86

.1

.2

0

0

0

0

0

48.71

9.48

2.33

9.12

14.43

11.93

1.16

.15

.23

7 

Plagioclase

25.3

15.5

.1

.01

7.9

3.5

.35

0

0

0

0

0

0

54.01

29.28

.05

.10

.02

11.09

4.77

.42

..

..

..

8 

K-feldspar

30.1

10.3

.3

.04

.8

3.1

7.8

0

0

0

.06

0

0

64.40

19.50

.35

.05

.07

1.19

4.19

9.40

..

..

..

9 

Augite

23.6

1.3

11.5

7.9

12.4

.2

.02

.3

0

0

0

0

0

50.53

2.49

.59

14.25

13.08

17.38

.23

.03

..

.38

..

10 

CaF2

0

0

0

0

51.3

0

0

0

0

0

0

0

0

11

K2SO4

0

0

0

0

0

0

44.9

0

0

0

0

0

18.4

12 

Andesite

28.1

9.4

4.2

2.1

4.5

3.1

1.1

0

0

.1

0

0

0

60.09

17.85

2.03

3.45

3.5

6.28

4.17

1.31

.23

Trace

..

R

. ource o ata

1. Biotite: from southern California batholith. Deer, Howie, and Zussman (1962,

2. Muscovite: P-207 standard. Lanphere andDalrymple (1965). . - . 

3. Basalt: tholeiite from Koolau Volcani

9. Augite: from diabase pegmatite, Virginia. Deer, Howie, and Zussman (1962, v. 2, p. 117).

12. Andesite: hypersthene andesite from Crater Lake, Oregon. Turner and Verhoogen (1960, p. '.

13. Rhyolite: obsidian from Medicine Lake highland, California. Turner and Verhoogen (1960, 

, 

p

p. 116). 

n (1962, v. 4, p. 40).
46 ffiRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

600 

6.[ 0 

620 

630 

640 

650 

660 

700 

710 

720 

730 

740

PRINT "NEUTRON 2 (VER * 1/6/7S)"

PRINT 'ACTIVITY PREDICTION FOR U*S*G.S* TRIGA REACTOR"

REM - BY G* BRENT DALRYMPLEy U.S*G»S»» MENLO PARK? CA

PRINT DAT*<X)

PRINTAPRINT

P RIN T " M A T E RIA L C H 01C E S J " \ P RIN T

PRINT -1-BIOTITE' r" 5--ACTINOLITE' , "9--AUGITE','13-RHYOLITE'

PRINT "2--MUSCOVITE" > "6--HORNBLENDE" , '10-CAF2' r '14-AL TUBE'

P RIN T " 3 - B A S A L. T' , " 7 - P L A G10 C L A S E '»"!!- K 2 S 0 4" r " 15 - Q T Z VIALS'

PRINT "4-MGRAYWACKE" T " 8-K-FELDSPAR' r" 12-ANDESITE' r '99-YOUR CHOICE'

PRINT\PRINT\PRINT

GOSUI 7600XGGSUB 7600

DIM fi C13 ) r M * < :l. 6 9 2 0 ) > K < 19 )»I... C19) » R * < 2 0 )

DIM ]*C20>

FOR J=l TO 19

NEXT J

F-l

PRINT'

INPUT :

PRINT

INPUT

PRINT

INPUT

PRINT

INPUT

IRRADIATION NO*

"SAMPLE NO

R*

"WGT (GMS)'f

Ul

 IRRAD* TIME (HRS)"i!

I

X=1*3600

PRINT "MATERIAL NO"? 

INPUT M

IF M<0 THEN 350 

IF M>15 THEN 310 

GOTO 400

IF MX99 THEN 350 

GOTO 400

P RIN T " IN V A LID M A T E RIA I...' 

GOTO 260

IF M=99 THEN 500 

FOR J=l TO M 

FOR K=l TO 13 

READ E(K) 

NEXT K 

NEXT J 

GOTO 700

PRINT "MATERIAL"? 

INPUT M*<1> PRINTPRINT PRINTPRINT PRINTPR I NTPR I NT 

PR I NTPR I NTPR I NT 

PR I NTPR I NTPR I NT PR I NT-- 

GOT 0

'SI

'AL 1

'FE

'MG'

'CA

'NA 1

1 K" »'

' MN"

[ CR"

E (1) 

E(2) 

E(3) 

E(4) 

E(5) 

E(6) 

E(7)

»\INPUT 

»\INPUT 

y\ INPUT 

»\INPUT 

r \.INPUTS' \INPUT 

\INPUT 

AINPUT E(8) 

AINPUT E(9> 

"P" r \INPUT EC 10) 

"RB% \INPUT ECU.) 

"CU" , \INPUT E(12) 

"S" r \INPUT EC 13) 

.000

="BIOTITE"\M*C2) = "MUSCOVITE'\M* C3) = 'BASALT" 

M$(4) := 'METAGRAYWACKE'\M$(5) = "ACTINOLITE'\M*(6) = 'HORNBLENDE 

M$ ( 7 ) :; =" PL AGIOCL ASE " \M$ ( 8 ) = ' K-FEL DSP AR " \M* C 9 ) ~ ' AUGI TE " 

M * (10 ) ::;: " C A F 2 " \ M * (11) = " K 2 B 0 4 '\M*C12) = 'AN D E SIT E ' \ M * < 13 ) = 

M*(14)="AL TUBE"\M*C15)="QTZ VIALS"

RHYOLITE 1
COMPUTER PROGRAMS

750 PRINT M$CM)

1000 ZO-Q\Z2=0\Z3=0\Z4=0

1010 P RIN T \ P RIN T \ P RIN T

1020 PRINT "PRODUCT"yTAB(28)5"ACTIVITY (MCI) AFTER COOLING 1

1030 PRINT , " 0 DAYS"?" 2 DAYS'>' 7 DAYS'*" 20 DAYS"

1040 PRINT

1100 REM - SI-28<NrP>AL--28

:l:l. 10 T=W*E<l>**9921E-2

1120 H=l»38E2\B=*37\B=2E12\N=2*15E22

1130 OGSUB 7070

1200 REM - AL-27(N»G)AL-28

1210 T=W*E(2)*1E~2

1220 B-- , 21 \D= 1, 7E13\N=2 » 23E22

:L230 GOSUB 7:1.00

1.240 00SUB 7400

1300 R E M - P - 31( N r A ) A I... - 2 8

1310 T=W*E(10)*lE-2

1320 B=*15\D=7E12\N=1«94E22

1330 GOSUB 7:1.00

.1.340 GOSUB 7400

1400 GOSUB 7500

1410 PRINT "AL-2B"»SO»S2»S3»S4

1420 K<1 ) = SO

1500 REM - SI-3QCN»G>SI-31

1510 T--W*E(l)*»0309E-2

11520 H=9»43E3\B=.11\D=1*7E13\N»2.01E2:

1530 GOSUB 7070

1600 REM - P -31(NrP)SI-31

1610 T=W*E(10)*lE-2

1620 B= * 14\N==1 * 94E22\D = 1 *6E13

1630 GOSUB 7100

1640 GOSUB 7400

1700 GOSUB 7500

1710 PRINT "SI-31',SO r S2 , S3 rS4

1720 K(2)=SO

1800 REM - AL-27(N>G>NA-24

1810 T=W*E(2)*lE-2

1(320 H=5.4E4\B*.14\D = 3E12\N=2»23E22

1830 GOSUB 7070

1900 REM - MG-24<N*P)NA-24

1910 T=W#E(4)*»787E-2

1920 B = " * 2 2 \ D ~ 1E12 \ N -~ 2 . 51E 2 2

1930 GOSUB 7100

1940 GOSUB 7400

2000 REM - NA-23<N»G)NA-24

2010 T=W*E(6)*lE-2

2020 B=453\D=1»7E13\N=2.62E22

2030 GOSUB 7100

2040 GOSUB 7400

2100 GOSUB 7SOO

2 J. 10 P RIN T " N A - 2 4VSO>S2»S3»S4

2120 K<3)=SO

2200 REM - FE~54<N»G)FE-55

2210 T=W*E<3)*.0582E-2

2220 H-8 t 2E7\B=2i.5\N=l *12E22

2230 GOSUB 7010

2240 PRINT "FE-55" r AO r A2>A3 f M

2250 K<4)=AO

2300 REM - FE-54(NrP)MN-54

2310 H=2»62E7\B = 0* 023

2320 GOSUB 7010

2330 PRINT "MN-54% AO c A2>A3 , A4

2340 K<5)=AO

2400 REM -- FE-54(N»A)CR-51

47
48 ffiRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

2410 H=2,4E6\B=* 00037

2420 GOSUB 7070

2500 REM - CR-50(NfG>CR-51

2510 T==U*E(9MU«0431E~2

2520 B=13*5\N=1»2E22

2530 GOSUB 7100

2540 GOSUB 7400

2600 GOSUB 7500

2610 PRINT CR-51"»SO»S2»S3»S4

2620 K(6)=SO

2700 REM - FE-56(N»P)MN-56

2710 T=W*E(3)*»9:L66E-2

2720 H=9*29E3\B=*00044\D=3E12\N=1*08E22

2730 GOSUB 7070

2800 REM - MN-55(N»G)MN-56

2810 T=W*E(8)#lE-2

2820 B = 13.3\B~1 * 7E13\N = 1 * 1E22

2830 GOSUB 7100

2840 GOSUB 7400

2900 GOSUB 7500

2910 PRINT "MN~56'fSO»S2»S3»S4

2V20 K(7)~SQ

3000 REM FE-58<N»G)FE-59

3010 T=UI*E<3)*33E-6

3020 H=3.9E6\B=*98\N=1.04E22

3030 GOSUB 7010

3040 PRINT "FE-59 1 »AOjA2»A3»A4

3050 K<8)=AO

3100 REM - CA--43<N»P>K-43

3110 T--W#E<5)#135E-7

3120 H = 8 * 0AE4\B= * 1 \N = 1 * 4E22\D= 1 ,- 3E13

3130 GOSUB 7010

3140 PRINT " K-43 " r AO > A2 » A3 r A4

3150 K<9)-~AO

3200 REM - CA-44(N»G)CA-45

3210 T = W#E< 5)#208E-6

3220 H--1»43E7\B=.67\N=1»37E22\D = 1.7E13

3230 GOSUB 7010

3 2 4 0 P RIN T " C A - 4 5 " r A 0 r A 2 r A 3 ? A 4

3250 K(10) AO

3300 REM - CA-48(N>G)CA-49+SC-49

3310 T=W*E(S)*18E--6

3320 H = 3« 6E3\B = 1.1\N=1.25E22

3330 GOSUB 7010

3340 PRINT "CA-49 + SC-49"»AO r A2 r A3 P A4

3350 K(11)=AO

3400 REM - K-41(N»G)K-42

3410 T=W*E<7)*688E-6

3420 H=4.46E4\B=1*1\N=1*47E22

3430 GOSUB 70.1.0

3440 PRINT "K-42"»AO , A2 , A3 , A4

3450 K<12)=AO

3500 REM - P~31(N»G)P-32

3510 T=W*E<10)*lE-2

3520 H~l»24E6\B=»19\N=1*94E22

3530 GOSUB 7070

3600 REM - S-32<NrP)P-32

3610 T = W*E<13)* »95E-2

3620 B=.3\D~1*4E13\N=1.88E22

3630 GOSUB 7100

3700 GOSUB 7500

3710 PRINT 'P-32'fSO»S2»S3»S4

3720 K<13)=SO

3800 REM - S-33(N?P)P-33

3810 r=W*E<13)*76E-6
COMPUTER PROGRAMS 49

3820 

3830 

3840 

3850 

3900 

3910 

3920 

3930 

3940 

3950 

4000 

4010 

4020 

4030 

4040 

41.00 

4 :l 10 

4:1.20 

4:130 

4140 

4150 

4200 

4210 

4220 

4230 

4240 

4250 

5000 

50:1.0 

!5020 

5030 

5035 

5040 

5050 

5060 

5065 

5070 

5080 

5090 

5100 

5200 

5210 

5220 

5230 

5240 

5250 

5300 

5305 

53:10 

5320 

5330 

5340 

5350 

5360 

5370 

5380 

5390 

5400 

5410 

5420 

5430 

5440 

5450 

5460 

5470

H--=2»16E6\B=»015\D=1«7E13\N=1»82E22

GO8UB 7010

P RI N T " P - 3 3 " .v A 0 r A 2 , A 3 , A 4

K(14>=AO

REM - S-34(N>G>S-35

T=W*E(13)*422E-6

H=7»6E6\B=*26\N=1.77E22

GOSUB 7010

PRINT "S-35"»AO»A2>A3rA4

K(15)=AO

REM - S-34<NrA)S-31

H=P» A E3\B=»14 \D=1E13

GOSUB 7010

P RIN T ' S - 3 1 " >- A 0 ? A 2 ? A 3 y A 4

K<16)=AO

REM - RB-85<NrG)RB-86

T=U*E(11)**7215E-2

H=l .. A2E6\B= - 8\N= * 709E22\D=1 * 7E13

GOSUB 7010

P RI NT' " R B - 86"fAO»A2»A3»A4

K<17)=AO

REM - CU-63<N*G)CU-64

T=W*E<12)**691E-2

H=4 <- 64E4\B«4 * 3\N= » 96E22

GOSUB 7010

AOrA2 r A3 rA4

"TOTALS"»ZO»Z2»Z3»Z4

OK"

PRINT "CU-A4" 

K(18) AO 

PRINT 

PRINT 

K<19)=ZO 

PRINTXPRINT 

RESTORE 

PRINT "DATA 

INPUT E*

IF E*='YES" THEN 5080 

GOSUB 7600\PRINT 

GOTO 1.60 

FOR J=l TO 19 

L(J)=L(J)+K(J) 

NEXT J

PRINT "M0 RE SAMP LE S" r 

INPUT E*

IF E*='NO" THEN 5300 

GOSUB 7600

GOTO

REM --

GOSUB

PRINT

P R I N T

PRINT

PRINT

PRINT

PRINT

PRINT

P R I N T

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

SUMMARY TABLE

160 

PRINT 

7600

"ACTIVITY SUMMARY AT T=0" 

" G E 0 C H R 0 N 0 L 0 G Y P R 0 J E C T , M E N L 0 P A R K " 

"ACCOMPANIES RADIOISOTOPE REQUEST FORM 

DAT*<X)

"IRRADIATION NO. " ?I$ 

Ff " SAMPLES" 

\PRINT\PRINT 

" P R 0 D U C T " ?T A B ( 1 9 ) r " M C I " 

"AL-28" rL<l> 

" SI-31 " ? L(2) 

"NA-24" »L(3>

Fl_<4>

,L ( 5 )

yl...(6)

»L<7)

»L(8>

NO*

"PE-55 

"MN-54 

"CR--51 

"MN--56 

"FE-59

K-43" ? l...(9)
50 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

54 BO

5490

5500

5510

5520

5 5 3 0

5540

5550

5560

5570

5580

6000

6010

7000

7010

7020

7030

7040

7050

7060

7070

7075

7080

7035

7090

7100

71.1.0

7120

7130

7140

7:150

7160

7162

7164

7166

7170

7172

7174

7176

7180

7.182

7184

7.1.90

7300

7310

7320

7400

7410

7420

7430

7440

7450

7500

7510

7520

7530

7540

7550

7600

7610

7620

7630

9000

9010

9020

PRINT "CA-45" »L<10)

PR I NT " C A-49+SC-49 " t L ( 1 1 >

PRINT "K~42"»L<12>

PRINT "P-32" yl...<13)

PRINT "P~33" y |_<14)

PRINT "S-35"»L<15>

PRINT n S-31" ?L<16)

PRINT "RB-86" H_<17>

PRINT ' CU-64' »L<18)

PRINT

PRINT "TOTAL" ,L<19>

PR I NTXPR I NTXPR I NTXPR INTXPR I NT

STOP

REM - SUBROUTINES

REM - SUBR CALL 1

GOSUB 7100

GOSUB 7300

GOSUB 7400

GOSUB 7500

RETURN

REM - SUBR CALL 2

GOSUB 7100

GOSUB 7300

GOSUB 7400

RETURN

REM - CALCULATE ACTIVITY

AO=T*D*N#B*1E-21*<1-EXP(-*69315#X/H) )/3»7E10

G=-5»9B9E4/H

IF AOME-4 THEN 7160

AO=0\A2=0\A3=0\A4=0

GOTO 7190

A2=AO*EXP(2#G)

IF A2ME-4 THEN 7170

A2=0\A3=0\A4=0

GOTO 7190

A3=AO*EXP<7*G)

IF A3>lE--4 THEN 7180

A3=0\A4=0

GOTO 7190

A4=AO*EXP(20*G)

IF A4ME-4 THEN 7.190

A4«0

RETURN

REM - INITIALIZE SUM VARIABLES

SO=0\S2=0\S3=0\S4=0

RETURN

REM SUM INDIVIDUAL PRODUCT ACTIVITIES

SO=SO+AO

S2=S2+A2

S3=S3+A3

S4-S4+A4

RETURN

REM - SUM SAMPLE TOTAL ACTIVITIES

ZO=ZO+SO

Z2=Z2+S2

Z3"Z3-fS3

Z4=Z4+S4

RETURN

PR I NTXPR I NTXPR I NTXPR INTXPR INTXPR INTXPR I NTXPR I NTXPR INTXPR I NT

PRINTXPRINTXPRINTXPRINTXPRINTXPR INTXPR INTXPR INTXPR INTXPR INT

P R I N T X P R I N T X P R I N T X P R I N T X P R I N T X P R I N T X P R I NTXPR I N T X P R I N T X P R I N T

RETURN

REM - COMPOSITION DATA

REM - BIOTITE (1)

DATA 17*9*7.4»18,5»4.8**64»*37»6*9»*07»0»0»0»0 yO
COMPUTER PROGRAMS 51

9030

9040

9050

9060

9070

9080

9090

9100

9110

9:120

9130

9140

9150

9160

9170

91 SO

9190

9200

92.10

9220

9230

9240

9250

9260

9270

9280

9290

9300

9999

REM -

DATA

REM -

DATA

REM -

HAT A

REM -

DATA

REM -

DATA

REM -

DATA

REM - 

DATA :

REM -

DATA :

REM -

DATA

REM - 

DATA 

REM -

DATA :

REM -

DATA ;

REM -

DATA

REM -

DATA 

END

- MUSCOVITE (2) 

22»1F16.5 > 3 * 4 F , 57 r *06 r , A2 F 8.66 F.09 F 0 F.02 ».08 , 0 »0

"f H 0 L E11TIC B A S A L T < 3) 

23f 6 F 7 * 65 F 7« 65 F 5« 46 F 6 * 25 F1 * 94 F »12 F »12 F.06 F.09 F 0 F 0 F 0

- METAGRAYWACKE (4) 

34»8»6»0»3*0»l*5f,9»l«6».6»,05»OF*05F0 r 0 , 0

ACTINOLITE (5) 

26 * 3 f 1»13 F 8.52F 9.71F 7 * 36 F1 * 01r * 25F.05F0 F0»0 F0 F0

HORNBLENDE (6) 

22 * 8 F 5 F 8 ,. 7 F 8 * 7, 3 * 5 F * 86 F * 1F « 2 ;> 0 F 0 F 0 , 0 r 0

- PLAGIOCLASE <7) 

25*3Fl5*5F*lF*01F 7 9 F 3 * 5 F ,.35?OyO ? 0?0?0?0

K-FELDSPAR (8) 

30.lFlO*3F*3Ff04F*8F3*lF7.8FOFOFOF*06FOFO

AU6ITE <9> 

2 3 * 6»1»3Fll*5F7*9Fl2*4F*2F,02»*3FOFOFOFOF0

CAP2 (10)

0 n0 y0 F0 F 51 o 3 F 0 F 0 r 0 F 0 f 0 F 0 ? 0 t 0

K2S04 (11) 

0 ? 0 ? 0 ? 0 ? 0 ? 0 ? 44 * 9 ? 0 y 0 ? 0 ? 0 ? 0 ? 18 » 4

ANDES.TTE <12) 

28«lF9,4F4*2F2*lF4*5F3*lF1 * 1F0 F0 F.1F0 F0 F0

RHYOLITE (13) 

34.4F7*4fl.4F.2F1F3F 3«6 F* 2 F0 F* 04 F0F0 F0

AL TUBE (14)

*6F97*2F.7Fl»OFO»OFOF.2FOFOF,27FO

GTZ VIALS (15)

46 » 8 !> 0 ? 0 ? 0 ? 0 ? 0 ? 0 ? 0 F Q ? 0 ,. 0 ? 0 ? 0

AR 37 — Ar DECAY CORRECTION PROGRAM 

INTRODUCTION

This program calculates the 37Ar decay correction 

factor used in 40Ar/39Ar dating. The calculation allows 

for episodic irradiation at various reactor power levels 

and is equal to

n

£[ ti\e'

I

where Pi = power (megawatts) for the increment, 

ti = length (hours) of increment, 

t'i = time (hours) between irradiation

increment and 37Ar measurement, 

A = decay constant of 37Ar = 8.25 x lO^hr

(half-life = 351 days),

I =

n =

n

E

i=0

and

number of increments in the irradiation.

The derivation of the formula is given above.

DESCRIPTION

The irradiation history of each irradiation is stored in 

a file (IRHIST.DA) called by the program upon entry of

the irradiation number. This file is maintained using a 

symbolic editor, available on most computer systems. 

If the data fo/ that irradiation are not in the file, an 

error message results.

Upon execution, a limited amount of information 

about the irradiation (number of increments, date and 

time the last increment ended, and total MWH) is 

printed so the operator can verify that the irradiation 

history is correct. The operator also has the option of 

printing the entire irradiation history.

Data for each sample are entered (sample number, 

day, and time measured) and the program prints the 

37Ar correction factor, which is applied as a multiplier 

directly to the measured 37Ar/ 39Ar ratio. The day 

measured should be the Julian day, that is, Jan. 1 = 

1, Dec. 31 = 365. As the day numbers are subtracted 

to determine the decay times, it may be necessary to 

add 365 to the day number if the measurement was 

made in the year following the irradiation. (If a sample was irradiated in December and measured on the 

mass spectrometer the following January 15, for instance, then the day number would be entered as 

380.) The hour is entered as a decimal in 24-hour notation, so 3i2 in the afternoon is entered as 15.2.

The program continues to request sample data and 

calculates correction factors until execution is halted 

by the operator.

A sample program execution is given below.
52 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING 

VARIABLE LIST

E$ Sample No. [DIM (20)]

El$ Irradiation number

E2$ Date last increment ended

E3$ Last person to modify file

E4$ Date modified

N Number of increments in the irradiation

Y Total MWH = E W( J) = E P{ • ti

T( J) Length of increment (hrs)

E( J) Day increment ended

H(J) Hour

W( J) Power level of increment

Ml Day measured

M2 Hour

X Number of sets in data file

Z Set counter

Q(J) =W(J)*T(J)=Pi .ti

D(J) =t'i

P(J) =Pi.ti/I=Q(J)/Y

A(J) =\ti/(l-e~xti)

C(J) = A(J)*P(J)*eX 'i

C = E C( J) = correction factor

16,.4 ON 15APR1980

i 1 R A .0IA J1 0 N !••! IS T 0 R Y ? Y E S

DAY HOUR
COMPUTER PROGRAMS 

FILE FORMAT

53

Data used by the program are stored in an ASCII file 

called IRHIST.DA. These data consist of irradiation histories, which occur in the file in the format shown below. The file can be maintained or updated using any 

symbolic editor. Variables are explained in the variable 

list.

X

E3$ 

E4$ 

El$

E2$

N

T(N)E(N)H(N)W(N)

File information

Irradiation El $ history

El$

E2$

N

T(N)E(N)H(N)W(N)

Irradiation El $ history

U.S.G.S* ? MENI...O PARK"

PRINT "AR37.BA (VER*12/30/77)'

PRINT "AR-37 DECAY CORRECTIONS

PRIN T "IS 0T0 PE GE0L0 GY BRAN C H r

PRINT DAT$<X>

PRINT\PRINT\PRINT

DIM E*(20) »E3$<20) i-E4*<.1.2) j-E2*<12)

DIM T (50 ) :' E (50 ) , H (50) , (J < 50 ) t Q (50) t D < 50 ) r P < 50 ) , A < 50 ) , C < 50)

PRINT "IRRADIATION NO,"?

INPUT E$

Z = 0

FILE*1 I"IRHIST.DA"

INPUT*!JXfC

INPUTtl:E3*»E4*

INPUT*!5Et*?E2$

INPUT*!

FOR J=l

INPUT*!

NEXT J

IF E!*=E* THEN 600

N t C 

TO N 

T ( J ) i E ( J ) r H ( J ) , (A! C J ) r C

IF Z=X-H THEN 535

GOTO 400

CLOSE*!

PRINT "INPUT ERROR"

GOTO 200

CLOSE*!

Y=0

FOR J=l TO N

Q<J)=W<J)*T(J)

Y-Y-ffK J)

NEXT J

P RIN T N r " 1 N C R E M E N 'I'S "

PRINT "LAST INCREMENT ENDED AT i|-i(N)5» ON "?E2*
54 IRRADIATION OF SAMPLES FOR 40Ar/39Ar DATING

820

8 3 0

040

845

850

855

860

865

870

Q B 0

88 f 5

890

900

910

920

930

940

950

960

.1000

10:1.0

1020

.1030

:l 040

1 050

1060

1070

1 1 0 0

1110

•I -I •") A 

J. 1 ju. s/

1 1 3 0

1140

9999

PRINT " TOTAL MWH= " 9 Y

P R I N T \ P R I N T \ P R I N T

PRINT "PRINT IRRADIATION HISTORY"!!

INPUT E*

IF E*='YES' THEN 860

GOTO 900

PRINT "TIME" ? TAB (16) 9 "DAY" 9 TAB (29) 9 "HOUR 8 J TAB (44) 9 "PWR 1

PRINT

FOR J=l TO N

P R I N T T ( J ) i E < J > y H ( J ) » U ( J )

NEXT J

P R I NTN P R I N T \ F' R I N T \ P R I N T

PRINT "SAMPLE NO, " 9

INPUT E$

PRINT "MEASURED ON DAY NO . " 9

INPUT Ml

PRINT TAB (16) 9 "TIME'S

INPUT M2

PRINT

(3 = 0

FOR J=l TO N

D < J j =24* < M 1 --E ( J ) ) -H < J ) -f M2

P<J)=R(J)/Y

A ( J ) = ( 8 » 23E-4 ) *T ( J ) / ( 1 -EXP < ( -8 * 23E--4 ) *T < J ) ) )

C ( J ) =A ( J ) *P < J ) *EXP « 8 . 23E-4 ) *D ( J ) )

G-G-fC(J)

NEXT J

P R I N T " A R •- 3 7 0 0 R R E C T 1 0 N F A C T 0 R = " 9 G

PRINT

P R I N T \ P R I N T \ P R I N T

GOTO 900

END

SELECTED 

BIBLIOGRAPHY

The following bibliography (table 10) was selected to 

illustrate the use of 40Ar/39Ar data in terrestrial, lunar, 

and cosmological studies. Ten subject categories have

been set up in the table. An "x" indicates that a particular subject category is covered in varying degree in 

the reference. The bibliography is not a complete list of 

40Ar/39Ar dating references, but it should give the interested reader an introduction to the 40Ar/39Ar literature.

TABLE 10.— Selected bibliography of use of 40Ar/39Ar data in terrestrial, lunar, and cosmological studies

References Theory Technique Irradiation Lunar Meteorites Terrestrial Age Excess Argon Isochrons/

development parameters/ samples samples spectra 40Ar loss correlation

reactors diagrams

Alexander (1975)

Alexander and Davis ( 1974) .

Alexander and Kahl ( 1974) ...

Berger(l975) ........... . ....

Berger and York ( 1970) .......

Bogard, Husain, and Wright ( 1976)

Brereton( 1970) ................

Brereton( 1972). .......... ...

Dallmeyer ( 197 5a).....

Dallmeyer (1975b).... .........

Dallmeyer(1975c) .............

Dallmeyer, Maybin, and Durocher( 1975)..........

Dallmeyer and Sutter( 1976) ......... ......

Dalrymple and Clague ( 1976) ........

Dalrymple and Lanphere( 1971)......

Dalrymple and Lanphere ( 1974) ......

Davis( 1977). ...........

Dunham and others (1968) ........... . . ..

Fitch, Miller, and MitchelK 1969). ..................

Fitch, Hooker, and Miller( 1976) ....................

Fleck, Sutter, and Elliot (1977) .....................

Hanson, Simmons, and Bence( 1975) ......

Horn and others( 1975) ..............

........... X

........... X

........... X

........... X

........... X

..

. .

........... X

........... X

........... X

........... X

........... X

........... X

. .

........... X

X

X

X

X

X X

x

X

X

X

x

X

X

X

X

X X

X

X X

X

X

x

X

x

X

X

X

X

X

X

..

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

..

..

X

..

..

X X

X

..

X

..

..

..

X

X

..

X

--

X

.-

X

..

X

--

--

-.

X

--

X

--

X

X

.-

--
SELECTED BIBLIOGRAPHY

TABLE 10. — Selected bibiography of use of 40Ar/39Ar data in terrestrial, lunar, and cosmological studies — Continued

55

References Theory Technique Irradiation Lunar Meteorites Terrestrial Age Excess Argon Isochrons/

development parameters/ samples samples spectra "Ar loss correlation

reactors diagrams

Huneke(l976) ...................................................... X

Huneke and others(1973) ......................................... -- - X

Huneke and Smith(1976) ......................................... X X

Jessberger and others( 1974) ..................................... .... - X

Kaneoka(l974) ..................................................... --

Kirsten, Horn, andKiko( 1973) ................................... - - - X

Kirsten, Horn, and Heymann( 1973) ............................. -- X

Lanphere and Albee( 1974)........................................ --

Lanphere and Dalrymple( 1971)................................... -- X

Lanphere and Dalrymple( 1976)................................... -- X

McDougall(l974)................................................... -- -- X

McDougall and Roksandic( 1974)................................. -- -- X

Mateen and Green(1974).......................................... -- -- X

Merrihue and Turner (1966)....................................... X X

Miller, Mitchell, and Evans (1970).._——.———————.-- -- X

Mitchell(l968)...................................................... XX X --

Ozima and Saito (1973) ............................................ --

Pankhurst and others( 1973) ...................................... --

Podosek(l97l)...................................................... --

Podosek and Huneke (1973)....................................... --

Schaeffer and Husain (1974)...................................... -- -- -- X

Sigurgeirsson(l962) ............................................... X -- X

Stettler and others(!973) ......................................... -- -- -- X

Turner 1969) ....................................................... X

Turner 1970a)...................................................... -- -- -- X

Turner 1971a)...................................................... X -- -- X

Turner 1971b).................................. ................... -- -- X

Turner 1972) ....................................................... -- -- -- X

Turner and Cadogan(l974) ....................................... X -- -- X

Turner and Cadogan( 1975) ....................................... -- -- -- X

Turner, Miller, and Grasty( 1966) ................................ --

Turner and others(1971) .......................................... -- -- -- X

York and Berger( 1970)............................................ -- X

X

X

GPO 791-267