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Geochlmlco et Cosmoch~mrca Acta Vol.SO.
PP.1249-1259
0 Pergamon Journals Ltd.1986.
Printedin
0016-7037/86/33.00
+ .oO
U.S.A.
Ra-Th disequilibria systematics: Timescale of carbonatite magma
formation at Oldoinyo Lengai volcano, Tanzania
Ross W. WILLIAMSand JAMESB. GILL
Earth Sciences Board, University of California, Santa Cruz, CA 95064, U.S.A.
and
KENNETH W. BRULAND
Institute of Marine Sciences, University of California, Santa Cruz, CA 95064, U.S.A.
(Received November 5, 1985; accepted in revisedform
March 17, 1986)
Abstract-Carbonatite magma can form and erupt within 7 to 18 years, and the event seems associated
with prior volcanic eruptions. This determination of magma age is possible because the carbonatite lava
and ash which were erupted in 1960-66 from Oldoinyo Lengai volcano, Tanzania, have the most extreme
disequilibria between U and Th series nuclides yet measured in volcanic rocks. At the time of eruption:
(228Ra)/(23*Th)= 27 and (226Ra)/(2qh) z 60; (238U)/(232Th)> 10, while (2?h)/(232Th) = 1.0; and (‘I%)/
(226Ra)= 0.3. Three end-member models are presented which enable interpretation of these disequilibria.
If the disequilibrium formed instantaneously, the event occur& about 7 years before initial eruption, and
just before the last preceding but small eruption of Oldoinyo Lengai. If, instead, the disequilibrium formed
continuously, the process must have begun 15 to 18 years before initial eruption, just after the last preceding
major eruption. The disequilibria data confirm tbat the carbonatites are not fused trona, but do not distinguish
between other genetic options (mantle fusion, selective assimilation, liquid immiscibility). However, the
shortness of magma-formation time together with mass-balance considerations suggest formation due to the
continuous exsolution of 2 to 20% of carbonatite from nephelinite which was itself Raenriched.
VOLCANOLOGICAL CONTEXT AND
COMPOSITION OF SAMPLES
INTRODUCTION
STUDY OF SHORT-LIVEDRa and Pb as well as U and
Th nuclides in recent volcanic rocks holds promise for
constraining both the timescale and processes of
magma genesis (CAPALDI et al., 1976; MCKENZIE,
1985). Previous contributions to this infant field of
research include those by OVERSBYand GAST (1968),
NISHIMURA(1970), CAPALDIet al. (1976, 1982, 1983),
BENNETT et al. (1982) and KRISHNASWAMIet al.
(1984). In general, these authors found (226Ra)2 (*qh)
- (238U) in alkali basalts to hawaiites and some calc>
alkaline andesites, (238U)> (23@Th)in nephelinite from
Vesuvius, and (*‘*Ra) > (232Th) in shoshonite (Stromboli) and hawaiite (Etna). (In the previous sentence
and throughout this paper, parentheses around isotopes
denote activities, i.e., concentration times decay constant.) As a contribution to this subject, and to illustrate
the power of the technique, we present here the most
extreme disequilibria between Ra and parent Th isotopes yet measured in volcanic rocks-those in 196066 carbonatites from Oldoinyo Lengai, Tanzania. We
also present interpretive models for the development
of Ra-Th disequilibria similar to those developed by
CAPALDI et al. (1976). The Ra-Th systematics are illustrated graphically using (228Ra)/(232Th) vs. (226Ra)/
(230Th) isochron plots. In addition, we propose that
(226Ra)/Ba vs. (23’?h)/Ba isochron plots, similar in theory to the Th-U isochron plot developed by ALL~ZGRE
(1968), may be used to date young (~8000 yrs) volcanics.
Oldoinyo Lengai volcano is a steep-sided cone 2 km high
and roughly 8 km in diameter, located within the Gregory
Rift Valley in northern Tanzania, near the western fault escarpment about 16 km south of Lake Natron (DAWSON,1966).
It is mainly composed of ijolitic pyroclastics with minor volume lava flows of nephelinite, phonolite and melanephelinite.
The summit has two craters: the southern one is inactive, and
the northern one formed during a major eruption in 1917
(DAWSON,1962a. 1966; DAWSONet al., 1968). The latter is
the eruptive center of the subsequent sodium carbonate lavas
and ashes, for which the volcano is famous. The next major
eruption of Oldoinyo Lengai occurred in 1940-4 1 and lasted
approximately six months. During this eruption ejecta were
distributed up to 95 km away (DAWSON,1962a). In 1954-55
small ash cones developed on the crater floor.
In early 1960 Oldoinyo Lengai began an eruptive cycle
characterized by quiet extrusion of sodium carbonatite lavas.
Both pahoehoe and blocky aa lava flows erupted onto the
northern crater floor. These eruptions were observed, and
samples collected, in early October, 1960, by J. B. Dawson.
who kindly provided sample BD 114, a pahoehoe lava, to us
for this study. Charles Milton observed the eruption in 1963
and, in early February, collected our second carbonatite lava
sample, which was hermetically sealed. We obtained this
sample (# 11354) from the U.S. National Museum of Natural
History. The type of activity changed in August 1966, when
ash was vented during Plinian and Vulcanian eruptions
(DAWSONef al., 1968). Our ash sample, BD 882, was erupted
on August 20, and collected by J. B. Dawson. All three samples
were collected within l-2 days of eruption.
The major element composition of both our lavas is quite
similar. Both are characterized as lengaiite by trace Si02, low
A1203 (. l%), high CO2 (30%), and high Na20 (30%) relative
to CaO and K20 (13%and 7W, respectively) (DAWSON.1962b;
1249
1250
R. W. Williams. .I. B. Gill and K. W. Bruland
and C. Milton, unpublished data). However. the trace element
data reported here (Table I) imply that the two eruptions are
chemically distinct, with higher concentrations of incompatible
elements (Th, U, Pb, Sr, Ba, Ra) in the earlier carbonatite.
The I966 ash (BD 882) is more siliceous than the earlier lavas
(Si02 = 25%) and has a nephehnitic mineral assemblage
(nepheline, melanite, clinopyroxene, apatite, sphene, wollastonite, magnetite * pyrite, calcite) in a matrix of sodium carbonate (DAWSONer al., 1968). Several authors have made
isotopic measurements of 1960 lengaiite. BELL ef n/. (1973)
found *‘Sr/%r = 0.7059: O’NEIL and HAY t 1973) found S’*O
= +7.l%‘and 6°C = -- 7.6%; and DEPA~LO and WASSERBURG(1976)found 6Nd= 0.1 -e0.9. DAWSONand GALE(1970)
and POOLE(1963) measured the Ll and Th concentrations in
1960 lava. Poole also concluded erroneously that the uranium
decay series was in radioactive equilibrium.
DATA
Activity, concentration, and Pb-isotope data for the lavas
and ash are given in Table 1 as measured in June 1984. U.
Th, and PO were purified from 1-2 gram ahquots of crushed
sample following the procedures given in Appendix I. Complete dissolution of lavas was obtained in dilute HCI-HNOs,
thereby assuring sample-spike equilibrium. (238U), (2uU).
(2%), (232Th)and (228Th)were measured by isotope-dilution
alpha-spectrometry using a 232U-22*Thspike. The (228Th)/
(232Th)ratio was measured on unspiked ahquots. (228Ra)was
calculated by assuming transient equilibrium with 228Th.The
232U-‘28Thspike was calibrated against the Hat-well uraninite
standard, and against well-known ‘“U, 23zTh and 23”Thsolutions. (210Pb)was measured by alpha-spectrometry of 2’oPo
usine a 2”Po soike. Radioactive eauilibrium between “‘Pb
and1210Po is certain, given the short half-life of ““PO ([r/z
= 138.4 d) and the relatively long time between eruption and
measurement (> 15 y).
The accuracy of (*‘*U). (“@fh), and (‘j2Th) is ~2% at the
I o level of confidence from replicate analyses of NBS standard
material RFS- I. The precision of these analyses is governed
by the countmg statistics (commonly _+1.5IO 5%). Because
this uncertainty is generally greater than the uncertamt~ in
the spike calibration, the errors reported in Table I are from
the counting statistics only. (226Ra)was measured by the Rn
emanation method and the error reported is the precisron o:
the calibration of the extraction and counting technique for
replicate analyses ofNBS standards (3%). The accuracy of the
(“‘Pb) can be estimated from measurements of samples rn
which *“Pb is in equilibrium with ‘*‘Ra (fresh rocks >2OO
years old). For these samples. the one-sigma error tram
counting statistics on (*“Pb) always overlaps with the 3c; error
on (226Ra).
Concentrations of Sr and Ba were measured by name atomrc
absorption. Pb concentrations were determined hy differential
pulse anodic stripping voltammetry. and conhrmed by mass
spectrometric isotope dilution. A total error of 5’: ISassigned
to these numbers which is a result of propagatmn of uncertaintiesarising from weighing. dilution. standard preparation.
and within-run variability.
Our uranium concentrations agree farrly well with those ol
DAWSONand GALE (1970). They found U -- 6.73 and 7.3 i
2 0.10 ppm by the delayed fission neutron method for two
1960 lavas, whereas we found 7.2 t 0.1 ppm. In contrast.
POOLE(1963)found significantly higher LJ in the I960 lava
by the total alpha emission method. He reports a value o!
34.5 ppm U which was calculated assuming secular equilihrium in the entire U decay chain. We attribute the discrepant!
to the extreme 226Raenrichment we have found. In fact. the
U ppm equivalent of (226Ra) is 39.1, verc close to Poole‘\
value.
Poole’s conclusion that the U chain was in secular equihhrium resulted from his comparison of the ratios of ““Th and
2’4Pbgammas between a uraninite sample in equilibrium and
the carbonatite. which he found to be “practically identical’.
However, pure uraninite emits no gammas from the nuclides
of the Th decay-series, whereas the natural carbonatite. hemp
enriched in 228Ra,will emit significant gammas from the decay
of 228A~.The analyzer Poole used had relatively poor resolution, so that the 228Acand 234Thpeaks probably were not
resolved. Poole had expected to hnd a radium enrichment in
Table 1. Oldomyo Lengal carbonawe activities (dpm/g) on June 1.1984
___--.--Sample
BD 882
L. Magadi Evap
BD 114
USNM #I I3544
*
Eruptton dare
Ocr 8.1960
Feb.3.1963
Au1.20,1966
WSWlCi
(X8,,)
.C..i7 f 0.08
?%)
J73iOO9
4.88iO
5 43 + 0.08
f3’Th)
047J~OO12
IO
0.316~0.016
7.90*0.13
0.457 i 0
1.97 + 0.13
0.684 i 0 01.
4.87 + 0.20
0.101 + 0 005
(226Ra!
29.2 i 0.6
24 7 i 0.5
10.07 * 0 25
(*“Pb)
io.7 f 0 4
I5 7 + 0.4
8.77+0
14
llii’
n a.
0.060 i O.OOJ
T‘h-srr,a
0469+0.01:
0 285 + 0.015
4.87 f 0.20
(l?ERA:
1 !diUO5
0.89 +_0.06
5.54 * 0.25
(=‘Th!
I s-i i 0.07
I.10 to.08
5.88 f. 0.27
(“‘Th,
!x00
i 1600
5400
Ba
i lJ%,O
x401)
4100
Pb
IX
110
90
Sr
(ppln!
0.169 + 0.00:
II rl
0.259 C 0
011,
I, 9
I: a
n a.
Th
I .(I.?+ 0.05
i17+0.06
19.96 k 0.82
0.69 i 0 03
u
7201to.10
6.341t0.12
10.59f0.17
0.61 + 0.01
“.I
“a
na
206Pb/20JPb
IY 19
‘07Pb/2(ilPb
Ii 55
2onPb/‘MPb
39.14
___..~..
‘?K
The (- Kd) wa) calculated by assuming it 10 be m transient equilibrium
“‘Th.
Evapontr
C2”‘Pb) wa, messwd
by alpha-spec(rometry
of *“PO.
wrh
*The Lake Magad!
was collected m Aug. 1985 and Ihe actlwtes are as measured on Sept !7
1985. ‘11a ” means not analyzed.
plven lri ihe appmd,x
Delailrd descnpttons of the analytical methods ;lic
1251
Carbonatite magma formation
the carbonatite, and it is ironic that the uranium enrichment
he reported was probably the result of the radium instead.
Table 2 presents the activities of the shorter-lived nuclides
decay-corrected to the time of eruption, plus certain activity
ratios. Decay corrections assumed closed system behavior,
because the samples all were collected and sealed very soon
after eruption. The ranges reported for (““Pb) and (**‘Ra) and
the ratios of these to their longer-lived ancestors, are the maximum and minimum values calculated by assuming the minimum and maximum, respectively, “parental” activities. Very
little error is introduced in these calculations due to the uncertainty in the time of ingrowth-decay, because the uncertainty in the date of eruption is very small with respect to the
half-lives of these nuclides.
PRINCIPLES
OF Ra/Th GEOCHRONOLOGY
Radioactive disequilibrium within a decay series occurs because of enrichment or depletion of any isotope of the chain
relative to its parent or daughter. The timescale over which
the perturbed system, once closed, returns to equilibrium depends on the half-life of the enriched/depleted isotopes. In
general, depending on the magnitude of the initial disequilibrium and on the precision of the analytical techniques, radioactive equilibrium is reestablished to within analytical error
(usually 3%) after approximately five half-lives of the perturbed
isotope.
The duration and magnitude or rate of the enrichment/
depletion event is also important in conjunction with the halflife of the isotope. For example, an instantaneous enrichment
of a very short-lived isotope such as 224Rawill cause an enrichment of all the daughters of the Th-series following it within
a short time (hours), because of the very short half-lives of
these daughters. However, this enrichment will decay with
the half-life of 224Ra(3.64 days), and after about 20 days the
entire chain will return to equilibrium with 228Th,the parent
of 224Ra. A slow enrichment of 224Ra may not perturb its
equilibrium significantly, because the excess 224Racan decay
to undetectable levels as rapidly as it is enriched. However.
a Ra enrichment that is “slow” with respect to 224Ra may
be “rapid” with respect to *“Ra (f,,r = 5.76 y) or 226Ra(tllz
= 1600 y) and may result in a substantial enrichment for
these longer-lived isotopes.
If disequilibrium between 226Raand “Th occurs rapidly
with respect to the half-life of 226Ra(within tens of years),
then it may be possible to date the event causing the disequilibrium by normalizing the activities to a “stable” Ra
homoloaue such as Ba. A olot of fZZ6Ra)/Bavs. (23”Th)/Ba or
(228Ra)/Ba vs. (232Th)/Ba would be analogous to the (s”Th)/
(232Th) vs. (23*U)/(232Th)isochron plot developed by ALLI?GRE(1968). Both (226Ra)/Ba vs. (23@Th)/Baand (228Ra)/Ba
vs. (*‘*Th)/Ba systematics require physical separation of contemporaneous phases to provide an isochron. The weakest
assumption of this method is that Ra and Ba will fractionate
identically: that is. that the (226Ra)/Baor (228Ra)/Ba at timezero will be the same in all phases of the system. Our data
from Oldoinyo Lengai indicate that this may be true because
the (226Ra)/Ba ratios of the two lavas and the ash overlap at
the 20 confidence level. However. the precision of the analyses
only permits the age of fractionation to be constrained to be
recent with respect to the half-life of 226Ra,i.e.. less than 200
years. Our lava and ash samples are not contemporaneous
with respect to the half-life of 228Ra,and mineral separations
from an individual lava were not feasible. Thus. the (22*Ra)/
Ba W. (232Th)/Ba systematics could not be applied to these
samples.
However, the simultaneous consideration of (22sRa)/(232Th)
and (226Ra)/(23@Th)
disequilibria, each with their own unique
response time. for individual volcanic rock samples can allow
constraints to be placed on the age and duration of processes
which fractionate Ra from Th within the magmatic system.
Plots of (228Ra)l(232Th)
1’s.(226Ra)l(23@Th)
, enable visualization
of different Ra-Th fractionation processes, and evaluation of
their potential as geochronometers for volcanic processes occurring on timescales of less than half a century.
Theoreticallv. one also can utilize 210Pb/226Radiseauilibria
when observed; as here, to date processes which are short relative to the 22.4 y half-life of *“Pb. In the Oldoinyo Lengai
case, and perhaps in general, rigorous 2’oPb-2’6Rageochronometry is precluded by uncertainty concerning the chemical
and physical behavior of Pb in volcanic processes. For example,
Pbloss by volatilization on eruption could result in spuriously
young ages, Even so, (2’0Pb)/(226Ra)= 0.3 in both 1960 and
1963 lavas at the time of eruption (see Table 2) is consistent
with the young ages implied by the Ra-enrichment (discussed
below).
Pioneering work on the use of Ra-Th geochronology to
date volcanic processes was presented by CAPALDI etal. ( 1976).
Their samples were freshly erupted lavas from Etna and
Stromboli, in which (**‘Th) < (228Ra).Disequilibrium between
these short-lived isotopes of the Th-decay series can provide
strong constraints on geochemical models. Massimo Cortini
recently published (while our manuscript was in review) a
reinterpretation of these data in a paper entitled “An attempt
to model the timing of magma formation by means of radioactive disequilibria” (CORTINI, 1985). In this paper, Cortini
points out the need for a “reliable” model of magma formation, and develops single-stage and two-stage models for
Ra and Th growth in magmas. His single-stage linear model
is similar to our Model 2, developed below. Simple models
fail to explain the activities observed in the lavas from Etna
and Stromboli largely because of the 22*Th-228Rad&equilibria
which indicates recent Ra addition. Transient equilibrium
between 228Th(f,,r = 1.91 y) and 228Rain our samples from
Oldoinyo Lengai was established prior to analysis, and any
insight into the processes responsible for the original disequilibria which that pair might have given has been lost. Consequently, the following three models concentrate on 228Ra2’2Th and 226Ra-23qh disequilibria.
Table 2. Acliwtles decay-corrected to the time of eruption
Sample
BD 114
USNM #I 13544
BD a82
(226Ra)
29 5 + 0.6
24.9 + 0.5
10.1 + 0.3
(*“Pb)
9.3 (7.8-10.7)
7.3 (5.9-8.5)
7.8 (7.4-8.3)
(‘28Ra)
12.8 (12.0-13.5)
8.2 (7.5-8.8)
10.7 (10.1-11.1)
(238U)/(230Th)
11.3kO.3
15.0 f 0.8
1.6 i 0.07
(226Ra)/(230Th)
62.8 -t 2.9
a3 0 + 4.5
2.07+_0.11
(2’oPb)/(226Ra)
0.315 (0.26-0.37)
0.293 (0.23-0.35)
0.762 (0.712-0.847)
(228Ra)/(232Th,
27 4 (24.9-29.5)
27.2 (25.0-32.5)
2.19(1.99-2.38)
The activities
ax decay-corrected
to the time of eruption of each sample
(dates gwen in Table 1). The range in actiwties and activity ratios, (the numbers in
parentheses), it~e obtained by propagating
decay-correchon
and ratio calculations
the la errors of the analyses through the
R. W. Williams, J. B. Gill and K. W. Bruland
1252
FIG. 1. Model 1, Ra/Th activity ratios are plotted for the isotopes of the Th-series VS.the isotopes of the
U-series. Instantaneous enrichment of a magma with Ra that has (22sRa)/(226Ra)
= I.0 occurs at 1 .I- 0
followed by closed-system decay. The trajectory of an enriched system (point A’) is shown by the arrows as
it moves toward radioactive ~uiiib~um represented by the e&point. The isochrons represent the time
since en~chment. Point A is the 1960 lava from Oldoinyo Lengai.
GEOCHEMICAL MODELS
We have developed three geochemical modeis which
use (2*aRa)/(232Th) vs. (226Ra)/(23’?fh) systematics to
constrain the timescaie of the fmctionation process. In
them, we have chosen to speak of relative Ra enrichment, rather than Th depletion, because carbonatite
genesis seems more likely to concentrate Ra than to
remove Th from the carbonate liquid. However, the
two are identical mathematically. Note that the source
of the Ra will become relatively Th enriched and will
obey the same equations for growth toward secular
equilibrium. We have chosen parameters for the three
models to illustrate their application to our samples
from Oldoinyo Lengai. In Figs. 1. 2 and 3, the points
C
20
40
Cz26RoV
labeled “A” represent the 1960 lava at the time ol
eruption. The models are described here and in Appendix 2. A more detailed interpretation of their application to the data follows in the “Discussion”.
Model i: Instantaneous Ra enrichmtmr
The simplest case to consider is a process in which
Ra is added instantaneously and the system then closed.
after which the excess Ra decays toward equilibrium
with the parent Th isotope. “instantaneous”
in thts
context means the enrichment process occurred in less
than a year. Fig. 1 is a plot of the activity ratio of the
daughter/parent Ra/Th isotopes of the Th-series (j’axis) VS.the same ratio for the isotopes of the Il-series.
60
100
(2X”Th)
FIG. 2. Model 2. Instantaneous and continuous Ra-emichment model curves and isochrons for the continuous process (dashed tines) are shown. Solid lines show representative ratesof Ra enrichment, as multiples
of the Th activity. per year. The added Ra has (‘%a)/(‘26Ra) = 1.0 and remains constant thrnu~out the
process, as if the Ra were derived from an infinite reservoir. The 1960 and 1963 lavas on eruption are plotted
as A and B. respectively.
1253
Carbonatite magma formation
lnstantonews
enrichment
wth
40
= 70
60
80
('26RaV(=oTh)
FIG.3. Model 3. The Ra enrichment in the magma evolves through time as a result of Rayleigh fractionation
of a finite reservoir. The partition coefficients (D’s) defined as (activity in the carbonatite)/(activity in the
source) are constant (Drt,/Dn = 70) for each incremental batch of carbonatite that forms. The (22SRa)/
(226Ra)of each successive increment increases because (228Ra)grows toward (232Th)in the residue. The
percentages denote the mass fraction of the source which has separated as carbonatite (i.e.. analogous to the
percent solidified during crystal fractionation). The isochrons refer to the time required for a given percent
of fractionation to occur. The 1960 lava is again plotted as “A”.
Model 2: Continuous Ra enrichment with constant
The line labeled “Instantaneous” has slope = 1, which
(zz8Ra)/(226Ra)
is the (*2sRa)/(226Ra) ratio of the added Ra in this
model. The isochrons are defined by the locus of points
In contrast to an instantaneous event, the disequirepresented by the “Instantaneous” line at t = 0, which
librium within the U and Th decay chains produced
have decayed for 1,5,10,20, and 30 years. They pivot
by a continuous Ra enrichment depends on the rate
through the point at (1,l) which we will call the “equiat which Ra is added. The trajectories of systems that
point”, representing radioactive equilibrium in both
have undergone continuous enrichment in Ra at difdecay series.
ferent rates are represented by the curves in Fig. 2. The
There is nothing sacred about the slope of the “Inadded Ra has a constant isotopic composition, specifstantaneous” line. It can be chosen on a case by case
ically (228Ra)/(226Ra)= 1.0, and the line labeled “inbasis to represent the assumed isotopic composition
stantaneous enrichment” has the same slope as the
of the added Ra. We chose the slope = 1 for the figure
“instantaneous” line in Fig. 1. The rates of enrichment
because (232Th)/(2Th) = 1.0 for our samples from
indicated on the individual curves are in units of decay
Oldoinyo Lengai. The added Ra isotopes will have the
per minute per gram per year, and are given as mulsame activity ratio as the Th isotopes if the Ra and the
tiples of the activity of Th (either 230 or 232) which
Th have a common source, and if the source is in rais constant. The great difference in the half-lives of
dioactive equilibrium.
226Ra and “‘Ra would allow a relatively slow enrichFor example, a system instantaneously enriched in
ment process (e.g., the curve representing 0.5 X (Th)/
Ra by a factor of 63 relative to the Th activity is shown
y on Fig. 2) to produce significant 226Ra excess while
in Fig. I as the point A’. If the system remains closed,
“‘Ra remained close to equilibrium with its parent,
this point will move along the trajectory shown by the
232Th. In contrast, a rapid enrichment rate (e.g., the
arrows. The rate of movement in the y-direction is
curve representing 10 X (Th)/y on Fig. 2) would procontrolled by the half-life of ‘*‘Ra (5.76 y), and is relduce Ra-enrichment approaching the instantaneous
atively rapid with respect to the rate of movement in
case for the range of (228Ra)/(232Th)plotted in Fig. 2
the x-direction, which is controlled by the half-life of
(i.e., less than 40). Isochrons are drawn on this figure
226Ra (1600 y).
through the locus of points made by systems that have
If the Ra in the source is not in radioactive equilibrium with the parent Th isotopes, then (228Ra)/(226Ra) undergone variable rates of radium enrichment
throughout the given interval since time zero. If the
will not necessarily equal (232Th)/(23@Th).
For example,
isotopic characteristics of a sample are produced by
if the source had been previously enriched in Ra, then
this continuous Ra-enrichment process, then its plot
it is probable that (228Ra)/(232Th) will be less than
on this diagram defines a unique duration and rate of
(226Ra)/(23@Th),because of the short half-life of ‘*‘Ra.
enrichment. Similar enrichment curves and isochrons
Instantaneous enrichment with Ra of this isotopic
can be constructed for any chosen Ra (or Th) isotopic
character will decrease the slope of the instantaneous
ratio. Continuous enrichment with Ra from a source
line and reduce the ages derived from Model 1.
I254
R. W.
Williams. J. B. Gill and K. W. Bruland
not in radioactive equilibrium, where (228Ra)/(226Ra)
c (‘“Th)/(*qh)
results in flattening of the enrichment
curves and isochrons, and yields younger Model 2 ages.
Model 3: Continuous Ra enrichment rvith increasing
f228Ra)/(z26Ra)
Models can be constructed to trace the isotopic evolution of a system in which the isotopic composition
of the added Ra changes with time. The temporal dependence of the added (228Ra)/(226Ra)must be known.
and assumptions must be made about the initial conditions. As an illustration, we have constructed a model
in which the (228Ra)/(226Ra)ratio of the added Ra increases with time as a result of growth toward secular
equilibrium with the parent Th isotopes in the source
of the Ra. The activities of the Ra and Th isotopes in
the system depend on the activities initially present,
the rate at which these activities change. and the time
span over which the change occurs. Fig. 3 shows a
model for Ra addition according to Rayleigh fractionation from a source which is homogeneous and initially
in radioactive equilibrium. A system enriched in Ra.
and its complementary residue enriched in Th, are
formed by this continuous fractionation process. We
define the partition coefficient. D, to be (the activity
of the nuclide in the system)/(the activity of the nuclide
in the source) for each increment of system that forms.
In the model shown, D~DT,, = 70. “Source” here can
denote solids being fused, residue from leaching. or
silicate liquid which separates to yield carbonatite (see
“Geological Processes” section below). and “system”
denotes carbonatite magma in each case. Note that D
here retains the form carbonate liquid/silicate liquid,
as used by FREESTONEand HAMILTON ( 1980), but inverts the usual solid/liquid convention in order to retain
carbonate liquid in the numerator consistently.
The source in Fig. 3 has (“‘Th)/(*“Th) = I, and is
initially in radioactive equilibrium. The first infinitesimal bit of system that forms has an isotopic composition represented by the point A’. With time the system
moves from A’ into the field where (22bRa) > (“‘Ra)
because of the relatively rapid decay of unsupported
**‘Ra. The source is strongly depleted in Ra relative
to Th very early in the fractionation process because
of the large D chosen for Ra. However. 228Ra builds
into its parent in the source much more quickly than
does 226Ra, and the available Ra in the source for the
next incremental
fractionation
step has (**‘Ra)
> (226Ra). Thus, the difference between Models 2 and
3 is that the former assumes an infinite pristine source,
whereas the latter assumes a finite source which constantly rehomogenizes its increasingly residual character at a timescale short with respect to the half-life
of 228Ra.
The isochrons in Fig. 3 are drawn through the locus
of points defined by variable final percentages of system
formed in that length of time. The trajectory from point
A’ to point A is one in which 4% of the total system
becomes Ra-enriched throughout I8 vears. As we dis-
cussed above. previous Ra-enrichment of the source
will tend to reduce the (zz8Ra)/(2’6Ra) I relative to
(232Th)/(23@Th))
of the added Ra, and decrease the ages
obtained from both Models I and 2. The same IS true
for Model 3. Prior Ra-enrichment of the source dis..
places it into the field where (‘-?bRa) b IZZXRa).From
this starting point. less time is needed to produce the
observed Ra-enrichment. and a lower \aiue of I),,,
DTh is allowed.
GEOLOGICAL
PROCESSEls
The three models presented above are end-member
possibilities of Ra-enrichment processes. Each may be
applicable to the geological processes h\ which carbonatite magma forms: partial melting in the mantle
(KOSTER VAN GROOS. 1975): assimilaCon or fusion
of carbonate sediment (EUGSTER. 1970: VII IX?>.
1968); or exsolution from a phonolitic or nephelemtii
magma (DONALDSON and DAWSON. 1978: FREI-STON~
and HAMILTON, 1980).
Partial melting can be described by Model I it’ the
magma is formed and leaves the source region rapidI!
(within a year). Models 2 and 3 allow the magma to
be generated more gradually. Model 2 requires a large
homogeneous source region, portions of which, once
fused, become isolated or refractory and play no further
role in the generation or evolution of the magma. On
the other hand, Model 3 allows gradual extraction 01
magma from a progressively depleted and continuousI>
re-homogenized source, and is most consistent with
current ideas of melt extraction (e.S.. MCKENZIE.
1985).
Both bulk assimilation and selective leaching also
can be described by all three models. Models I and 2
describe rapid and gradual bulk assimilation of Raenriched material, or rapid and gradual selective addition of Ra, respectively. Model 3 implies continuous
leaching of Ra from a finite volume of country rock.
As regards liquid immiscibility, Model i applies to
rapid exsolution when a body of magma reaches the
2-liquid field and all the carbonatite exsolves simultaneously from the source magma. Model 2 describes
exsolution in which the exsolving carbonatite volume
increases gradually, but requires that a given increment
of source magma exsolves carbonatite only once.
Model 3 applies when exsolution accompames differentiation of a source magma which is constantly rehomogenized and continuously exsolvmg
DISClJSSlON
The enrichments of 238Uand 226Raover .““Th, and
of **‘Ra over 232Th in the 1960 and 1963 lavas are the
most extreme ever measured in lavas. The deficiency
of*“Pb with respect to 226Rais also the most extreme.
These extremities result from the strong partitioning
of U and Ra into carbonatite. and make possible the
detailed interpretations which follow.
The greatest disequilibrium between ““Ra and ‘q-h
previously reported was in a 1944 nephelinite from
Vesuvius (CAPALDI et al.. 1982) in whkh tL2’Ral~
Carbonatite magma formation
(230Th)was 7.5-10, compared with values of 63-83 for
the Lengai lavas (Table 2). However, (226Ra) in some
cumulate rocks from Vesuvius is extremely high, with
(2z6Ra)/(2qh) = 170 (CAPALDIet al., 1982). CAPALDI
et al. (1976) also found (228Ra)/(232Th) of 1.1-1.5 in
197 l-1974 lavas from Etna and Stromboli, which is
an order of magnitude less than the values at Oldoinyo
Lengai. Although 228Ra-232Thdisequilibrium has been
looked for in several other recent eruptions (BENNETT
et al., 1982; R. WILLIAMS, unpublished data), it has
been found only at Etna, Stromboli and Oldoinyo
Lengai.
The (230Th)/(232Th)ratio of all three samples is 1.OO
f .05, which represents equilibrium with material that
has a Th/U ratio of 3.04. These values, together with
the Sr-Nd-0 isotopic compositions cited above and
the Pb isotope ratios of Table 1, are consistent with an
upper mantle source for this carbonatite, as has been
argued for carbonatites in general by LANCELOTand
ALLBGRE(1974) and others. In particular the low 207Pb/
204Pb and 20*Pb/Z04Pb,lie near the Northern Hemisphere reference line of HART ( 1984), and well below
crustal values expected for the Tanzanian Shield.
The Th activity ratio, like the 6”O values of O’NEIL
and HAY (1973), preclude the possibility that the carbonatite is remobilized trona-rich evaporite lake deposits. We analyzed a sample of such deposits from
Lake Magadi in Kenya (see Table 1). The (234U)/(238U)
of the evaporite is 1.50 and the (*38U)/(232Th)is 2.70.
In contrast, the U-isotopes of the carbonatites are in
radioactive equilibrium: (234U) = (238U). If the Oldoinyo Lengai carbonatites represent remobilized
evaporite similar to the Lake Magadi deposits, then
the process must have taken at least 0.75 million years,
which is the minimum time required to reestablish
equilibrium in the U-series. In this much time, the
(2?h)/(232Th) would become 2.70, a value much
greater than observed in the carbonatite.
Also, the extreme 228Ra enrichments preclude the
alternative hypothesis of EUGSTER( 1970) that the lavas
are the result of interaction of alkaline magma with
the groundwater reservoir. That is, a convecting hydrothermal system within low Th sediments could not
maintain a sufficiently great standing crop of 228Ra.
For these reasons, partial melting of the upper mantle,
and exsolution from mantle-derived silicate magma
are evaluated further using the three models developed
in this paper, whereas fusion or assimilation of nearsurface sediment are not.
1255
requires the event to have occurred in late 1953. Thus,
the instantaneous model is self-consistent, but the
roughly synchronous occurrence of an event which
produces a chemically zoned magma, with higher concentrations of incompatible elements including Ra at
the top, seems fortuitous. It is more likely that the
1963 and 1960 lavas, though consanguineous, differ
in activities as the result of magmatic differentiation
in the 2.4 years that separate the eruptions, for reasons
given later under the heading “Carbonatite Differentiation”.
Model 2: Continuous processes adding isoropicallJ*
constant radium
The activity ratios of the 1960 and 1963 lavas decaycorrected to the time of eruption are shown on Fig. 2,
as “A” and “B”, respectively. The 1966 ash plots close
to the equipoint and is not shown.
The Model 2 age of these disequilibria can be evaluated according to the principles discussed earlier. First,
consider the 1960 lava (point A). If its isotopic characteristics were produced by continuous enrichment
of Ra with a constant 2261228 activity ratio of 1.0,
then the process must have operated for approximately
17 years prior to eruption, at a rate of 3.8 times the
activity of Th in the lava per year (1.8 dpm/g-y). Because both lavas and ash have (23’?h)/(232Th) = 1.O at
the 1u confidence level, we assume initially that (226Ra)/
(*“Ra) = 1.O also, which is an underlying assumption
in the construction of all three figures.
Figure 2 also shows that if the 1963 lava (point B)
was produced by this model, the Ra-enrichment process operated at a slower rate for a longer time, i.e.,
for roughly 24 years prior to eruption at a rate of 3.4
times the activity of Th. Considering the higher activities of Th (both 232Th and 23@I’h)in the 1960 lava,
and the analytical errors, the minimum Ra-enrichment
rate that could produce this lava is 1.5 dpm/g-y. Similarly, the lower Th-activities in the 1963 lava, fixes
the maximum Ra-enrichment rate that could produce
this lava at 1.3 dpm/g-y. It is possible that the Raenrichment process stopped prior to the eruption of
the 1963 lava, and closed system decay of “‘Ra (a
vertical vector in Fig. 2) accounts for the lower enrichment rate given by Model 2. As for Model 1, this
is possible, but, because of the different incompatible
element concentrations in the two lavas, fortuitous,
and therefore, deemed unlikely.
Model 1: Instantaneous processes
Model 3: Continuous processes with
changing radium
If the Ra enrichment was produced instantaneously,
then the 1960 lava formed in late 1953 when it would
have been at the point (63,63) (point A’, Fig. I). This
date is within a year of the last previous eruption of
Oldoinyo Lengai when small ash cones developed on
the crater floor. Subsequently, 7 years of decay would
have reduced the (228Ra)/(232Th) to the value at the
time of eruption (point A). Analogously, instantaneous
production of the Ra enrichment in the 1963 lava also
This model was described in detail earlier and is
presented in Fig. 3. As often is the case geochemically,
the more complicated and less constrained explanations seem most applicable. However, the timescales
of magma formation, and the caveat that the same rate
cannot explain formation of both lavas, are the same
as for Model 2.
For both lavas to have been produced by the same
continuous fractionation process, the D&DT,, ratio
1256
R. W. Williams, J. B. Gill and K. W. Bruland
must have been at least 85. This value is required if as
little as 0.5% fractionation is necessary to produce the
1963 lava which has a (226Ra)/(23?h) of 83. Some 25
years of such fractionation would be necessary. The
1960 lava, with its higher concentrations, would require
approximately 10% of similar fractionation over 22
years. So the later erupted lava would represent an
older, yet less fractionated magma. Again. this is possible, but fortuitous. Therefore, we chose to apply
Model 3 only to the 1960 lava (point A on Fig. 3). The
1963 lava was not plotted because the grid of intersecting percentages and isochrons would be different
for the higher value of DdDTh (i.c., greater than 85)
that is needed to model this lava.
Convection in carbonatite magma chambers will be
turbulent (TREIMANand SCHEDL,1983), which makes
it unlikely that the differences between the 1960 and
the 1963 lavas are the result of a stratified magma
chamber with higher incompatible element concentrations at the top. Instead, we believe the 1960 lava,
being the first-erupted carbonatite from the volcano,
represents a less differentiated magma than the 1963
lava. Also, we believe DdalD~~ = 70 is a more reasonable estimate of the Ra-Th partitioning because it results in a lower percentage of carbonatite formed from
the initial system. Although model-dependent. it can
be shown that the percentage of carbonatite formed is
probably less than 20% (see next section). Thus, if the
magma formed in this manner, then it began the fractionation process in 1942, just after the last preceding
major eruption. This conclusion is robust whether one
assumes the isotopic composition of the Ra from the
source remained constant (Model 2). or varied systematically (Model 3).
Carbonatite formation
The preceding analysis demonstrates that the carbonatite magma erupted in 1960 and 1963 formed either about 7 years before initial eruption, just before
the immediately preceding small eruption (if it formed
instantaneously), or about I8 years before initial eruption, just after the last major eruption (if it formed
gradually). The disequilibria rule out magma derivation
from near-surface trona, but by themselves do not further constrain whether formation reflects mantle fusion, selective assimilation of carbonate, or crustal-level
immiscibility from phonolite or nephelinite.
If the Oldoinyo Lengai carbonatites came directly
from the subcontinental mantle, our conclusion, that
at most 20 years separate melt formation and eruption,
would be stunning. Following MCKENZIE’S (1985)
reasoning, for example, would require that KRa <<k;,,
(K = CmI./Cliq.)
during initial mantle fusion. Mantle porosity is required to be less than 1%. even if k;,, is as
large as .O1, and will be even less if Th is more incompatible. Chemical equilibrium
is required to be
achieved within centuries, perhaps decades. If carbonatite magma convects turbulently and flows rapidly
(TREIMANand SCHEDL, 1983: SPERA. I98 1). heat and
mass transfer could be rapid enough during ascent for
the melt to erode conduit walls “instantaneously” with
respect to the half-life of “*Ra. However, mantle fusion
and bulk assimilation seem least consistent with the
short timescales deduced from the &equilibria. insofar
as both must melt rock. The soundness of this temporal
argument hinges on the volume of magma produced.
which we do not know. Similarly, if carbonatite could
form in the mantle and be erupted within decades, it
is surprising it is so uncommon.
The experimental work of ROSTERVANC&OOSand
WYLLIE (1966, 1968) WENDLANDTand HARRISON
( I979), and FREESTONEand HAMILTON( 1980) demonstrates unambiguously that immiscibility occurs brtween silica-rich and carbonate-rich liquids of a variety
of compositions at common magmatic temperatures
and pressures. In particular. the natrocarbonatite ot
Oldoinyo Lengai is thought to have separated from a
parental silicate magma which was more likely a
phonolite than a nephelinite (DONALDSONand DAN’SON, 1978; FREESTONEand HAMILTON, 1980).
The LREE are partitioned more strongly into the
carbonate phase than the HREE, and all the REE partition more strongly into the carbonate liqutd with increasing pressure and decreasing temperature (BEDSON.
1984). Hence, immiscibility in which Ra. like the
LREE, partitions strongly into the carbonate hquid.
and U partitions more strongly than Th. seems most
consistent with our data. To test this hypothesis further,
the disequilibria between the nuclides of the U and Th
decay-series are used to constrain the relative proportions of the immiscible carbonate and silicate fractions.
The composition of the pure carbonate phase 1s
taken to be that of BD I 14. Although the composition
of the pure silicate phase is unknown, it can be inferred
from the composition of the 1966 ash. If the ash is ;i
physical mixture of the two components, then massbalance calculations show that the maximum carbonate component permissible in the ash is about 30%.
because negative concentrations of Sr. Ba and Ra III
the silicate phase are required for greater mass fractions
of carbonate. The composition of the silicate component is roughly fixed by this constraint and is very similar to the nephelinites or melanephelinites, but not
the phonolites, previously erupted from Oldoinyo
Lengai (DAWSON, 1966).
Taking these compositions to represent those of the
carbonate and silicate phases. theoretically one can find
the proportion of these phases that can be mixed together to produce a system originally in radioactivr
equilibrium. This is a unique application of the radioactive decay series, possible because in secular equilibrium the different elements of the series all have the
same initial activity. Similar mass-balance calculations
using elemental concentrations are generally under..
determined, whereas the equations for the activities of
the decay series nuclides define an overdetermined
system. However, as can happen for an overdetermined
system of equations, no unique solution exists. Therefore, the system prior to fractionation apparently was
1257
Carbonatite magma formation
not in radioactive equilibrium. It was slightly enriched
initially in U and Ra, as might be expected from the
affinity of U and Ra for COz-rich fluids. Using a leastsquares approach, one can find “solutions” to the massbalance equations in which the parent magma is closest
to radioactive equilibrium. The residuals are least when
between 2 to 20% carbonatite exsolves from the parent
magma.
Ra, the 1960 lava was enriched.in Ra less than 20 years
prior to eruption. The association of these ages with
prior eruptions is consistent with movement of a new
batch of magma to crustal levels beneath the volcanic
edifice. Exsolution of immiscible carbonatite from a
nephelinitic parent magma is compatible with the radioisotope data, as is differentiation of the 1960 magma
to form the lava erupted in 1963.
Carbonatite
Acknowledgements-We
differentiation
As noted earlier, whatever model explains the disequilibrium in one of the lavas cannot explain it in the
other. We believe, instead, that the differences between
the two lavas reflects differentiation during the intervening 2.4 years. The activities of all the nuclides and
the concentrations of Sr, Ba and Pb decreased between
1960 and 1963. The Th activities decreased by about
36%, while (226Ra) only decreased by about 16%, resulting in higher (226Ra)/(23?h). However, (22”Ra)/
(232Th) remained approximately constant, because of
the more rapid decay of 228Ra. Assuming that “‘Ra
would be depleted by the same percentage as 226Ra,
the Ra-Th systematics of the 1963 lava can be explained
by 36% decrease in Th and 16% decrease in Ra of the
1960 lava over the 2.4 y time interval observed between
eruptions. Regardless of whether the differentiation
process occurred instantaneously
(e.g., volatile loss
during the 1960 eruption) or continuously (e.g., crystal
fractionation or volatile streaming-fenitization), the RaTh systematics indicate an age of 2.4 + 1.2 years, which
is consistent with the time between eruption of the two
lavas. If differentiation occurred instantaneously
in
1960, then immediately thereafter the magma would
have lain at the point (83,36) on the (228Ra)/(232Th)vs.
(226Ra)/(2qh) plot, and 2.4 years of closed system decay would have reduced (228Ra)/(232Th)from 36 to 27.
A continuous differentiation process, in which Th and
Ra are reduced by 36% and 16%, respectively, produces
the same results if it operates over the same length of
time.
CONCLUSIONS
(228Ra)/(232Th) vs. (226Ra)/(230Th) plots can aid interpretation of the chronology of recent Ra-emichment
events and evaluation of the processes responsible for
the disequilibria. Meaningful, albeit model-dependent,
ages can be found for single samples. In contrast to
(226Ra)/Ba vs. (23?h)/Ba isochron plots, neither separation of phases to give leverage on an isochron, nor
identical fractionation of Ra and Ba between phases
is required. However, coupled 228*226Ra
disequilibria
have been found only in some highly alkaline magmas.
We believe that the Ra enrichment in the Oldoinyo
Lengai carbonatites is a primary characteristic produced during magma genesis. The Ra enrichment in
the 1960 lava either occurred instantaneously between
1952-54 (Model I), or began developing by a continuous process (Model 2 or 3) between 1942-45. Despite
uncertainty in the isotopic composition of the added
thank J. B. Dawson. and the U.S.
National Museum of Natural History for the samples from
Oldoinyo Lengai, and Ellery Ingall for collecting the Lake
Magadi evaporite for us. John Donat measured the Pb concentrations. We also thank George Tilton, and Sam Mukase
for assistance with the Pb-isotopic measurements. and Michel
Condomines for a helpful review of this manuscript. This research was supported by NSF Grants EAR8218467 and
EAR84 17459.
Editorial handling: J. D. Macdougall
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APPENDIX 1
column separation must be done. or if only a small amount
of contaminant remains a TTA-benzene extraction of Th wtll
Reagents
suffice. For the TTA-benzene extraction. the Th-fraction IF
taken in I5 ml of pH = 2 HNO, and shaken in a sep-funnel
AG-IX8 (Bio-Rad Laboratories), 100-200 mesh, chloride
with I5 ml of TTA-benzene. (The TTA-benzene is prepared
form, anion exchange resin is used for all the exchange sepby dissolving 5.5 g thenoyl-trifuoroacetone in IO0 ml of benaration steps. Fisher certified thenoyl-trifluoroacetone and
zene.) The aqueous phase is discarded, the TTA-benzene is
Mallinckrodt spectrophotometric-grahe benzene are used for
rinsed once with - I5 ml of clean pH = 3 HNO,. and the
the TTA-benzene Th purifications. Glass distilled. deionized
Th is back-extracted from the organic phase mtn I5 ml of I?
Hz0 and analytical &ade (Mallinckrodt) acids are used
N HNO,. The 2 N HN03 phase is taken to dryness and the
throughout. 232U, 22*Th, and ““PO tracers are used for the
Th is ready for plating. The purified U and Th fractions arc
isotope dilution a-spectrometr).
electroplated (-2 amps at 7 volts, for 30 minutes) on Pt planchets from a 2 M NH$ZI solution adjusted to pH 2.2.
Digesf ion
r
Aliquots of carbonatite were weighed inio teflon beakers.
dampened with H20. and digested with 6 N HCI added in
small increments to prevent vigorous effervescence. After the
.4lpha spectrometr)
Separate detectors are maintained for countmg L. I h and
PO. The spectrum from each detector is collected on q ! 1
Carbonatite
magma
channels of a 2048 channel multichannel
analyzer. The alpha
resolution (FWHM) at 5.11 MeV is between 30-40 KeV. Reagent and processing blanks are spiked. This allows the extent
of tracer cy tailing into the 234U, “‘U, *qh and 23’Th regions
of interest to be determined. Unspiked reagent and processing
blanks have detector blank count rates in the 238U, *%J. 232Th.
and *qh regions of interest (0.7 to 3 cts/day). The 232U-2’8Th
tracer is very pure. No peaks in the lower energy U or Th
regions are detectable. However. blanks spiked with 23*U-228Th
have elevated count rates in these regions of interest due to
tailing. Commonls.
O.l-0.3% of the mikes alohas will tail
into the lower energy regions of interest. The counts in these
regions arc corrected for the detector blank and for tracer
tailing.
Polonium. The counts from 20sPo and 2’oPo are corrected
for the detector blanks of 5 and 12 counts per day, respectively.
Since the odecay emissions of *“PO and *“PO are close in
energy. correction must be made for tailing of *“PO into the
208Po region. Despite these peaks being well resolved. 1.6% of
the *“PO alphas tail into the 208Po region. This percentage
was determined by counting a Ag-disk plated with only 210Po.
Reagent and processing blanks for PO show no detectable *“PO
contamination.
The counts from each nuclide are then decay
corrected from the midpoint of the count to the time of PO
separation (the first 8 N HCI column). The value for the *08Po
spike at this time is used to calculate the activity of ““Po.
Uranium. U and Th cross contamination
is resolvable, but
has never been observed. The 5.423 MeV-cu (73%) peak of
***Th is easily distinguishable
from the 5.321 MeV-a peak of
232U. Only the 5.34, 5.2 1 and 5.18 MeV-(Y peaks (total 27%)
of ***Th fall within the 232U region of interest. Decay of 13*U
results in some recoil contamination
of 228Th on the U detector. This contaminant
builds in so slowly that the detector
blank in the 232U region does not change during sample
counting.
Detector blanks are monitored
before and after
samples are counted. (2”U)/(238U) ratios are calculated directly
from the detector blank and tailing corrected counts in these
regions. The value for the *“U spike at the mid-point of the
U count is used to calculate the 238U activity.
Thorium. To calculate the counts solely due to the 2z8Th
tracer. several corrections need to be made to the total counts
in this region. First, the detector blank (-5
cts./day) and
0.0638 times the 224Ra counts are subtracted.
The value of
0.0638 represents 6% of the total ‘24Ra alphas. Onlv 94% of
the 224Ra decays with the 5.686 MeV-cu energy, which is resolvable from the ***Th region of interest. The other 6% of
the 224Ra decays with alpha energy almost identical to “‘Th.
Second. tailing of the recoil contaminant.
224Ra. into the 228Th
region is taken into account. In addition to the 6% of the total
224Ra alphas that fall in the “‘Th region of interest. another
2-3s ofthe 5.686 MeV 224Ra alphas tail into the 228Th region.
This percentage is determined
by counting backgrounds
on
the contaminated
detector. Third. the decays due to 228Th
from the sample must be subtracted. In the Oldoinyo Lengai
case, where direct measurement
of (228Th)/(232Th) was made
on unspiked aliquots, the correction for *‘“Th from the sample
came directly from the counts in the “‘Th region. Before
subtraction,
the ***Th counts from the sample are decay corrected for the length of time between Th-Ra separation (the
7.5 N HNO, column) and the mid-point of the count. Lastly,
the 228Th spike counts are decav corrected back to the time
of U-Th separation (the 8 N HCI column) and the value of
the spike at this time is used to calculate the “‘Th and “@fh
activities.
Our methods of reducing the data from a-spectrometry
differ from those reported by KRISHNASWAMI et nl. (1984).
We consider the tailing of the higher energy alphas from the
tracers into the lower energy regions of interest. Also. the correction for 224Ra tailing into the 228Th region can be substantial
when long counting time results in substantial build-in of 224Ra.
We also consider the unsupported
decay of 228Th from the
sample. Ten days of unsupported
decay of *“Th reduce the
number of counts expected from the sample by I %.
1259
formation
APPENDIX
2
The activities of the parent and daughter isotopes of a simple
two-membered
radioactive decay series are given by
(P), = (P),e@
and
(1)
(2)
(0, =
where(P),, (D),. and (P)O. (D)O are the activities ofthe parent
and daughter at time = I and time = 0. respectively: and Xp
and XDare their decay constants. The daughter/parent
activity
ratio can be simplified by assuming Xp = 0. which is justified
if the parent has a very long half-life compared to the daughter
and compared to the timescale of interest. Making this assumption for the Ra-Th systematics. the daughter/parent
activity ratio is given by
(E),
= I + ($$
- +*u’.
(3)
where Ra and Th can refer to the isotopes of either the Th or
U decay series.
Model 1
Fig. I was constructed
from Eqn. 3 using the same value
of (Ra)*/(Th)o for both axes, resulting in an “instantaneous”
slope = 1. The slope of this line reflects the isotopic character
of the added Ra.
Model 2.
The Ra activity in a system that is continuously
in Ra can be expressed by
(Ra), = (Th),( 1 - e-@‘) + (Ra)oe-“b’
+
s
enriched
0’ RemAb”dl’.
(4)
where R is the rate at which Ra is added, and it is assumed
that Xn’ iz 0. If R is a constant and is expressed in terms of
(Th), then
R
= ’ +
(Th)JRa
which is the equation used to produce the continuous enrichment curves in Fig. 2. The isoshrons can be produced
by
holding I constant while varying R.
Model 3.
In Model 3. the isotopic composition
of the Ra added to
the system changes with time. This is because the source is
finite, and is modified by the extraction of the system. The
R-term inside the integral in Eqn. 4 is not a constant: rather.
it is a function of the rate of fractionation
and &J&,,
We
did not attempt to find an explicit solution to this problem.
Instead. we used numerical integration to obtain the isochrons
and percentages of system formed shown in Fig. 3. For each
small incremental fractionation
step (approximating
Rayleigh
fractionation)
the (Ra)/(Th) of the system and of its complement. the source, are calculated for the given DRJDTh. Both
system and source activities are decay-corrected
for the small
span of time between fractionation
steps, and updated activity
ratios are calculated for the next increment of system to fractionate from the source. As well as the time factor. the relative
weight fractions of system already formed, and of the new
increment added are taken into consideration when calculating
the cumulative activities and activity ratios. A listing of a BASIC computer
program which performs these calculations
is
available on request from R. W. Williams, or interested persons
can send a formatted IBM-PC compatible diskette.