DETERMINATION OF SODIUM IN SILICATE MINERALS
BY NEUTRON ACTIVATION ANALYSIS
by
GERALD LAWRENCE 3CHROEDER
5.B., Massachusetts Institute of Technology
(1959)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF
SCIENCE
the
at
FROM
MASSACHUSETTS INSTITUTE OF
MIT
TECHNOLOGY
-ES
February, 1961
.
.
Signature of Author
.
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. .
.
.
, 1960
Department of Geology and Geophysics, December
Certified
by
.
.
.
7',~
-
-0
.
0
0
.
.
Thesis Supervisor
Accepted by .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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Chairman, Departmental Committee
on Graduate Studies
ABSTRACT
DETERMINATION OF SODIUM IN SILICATE MINERALS
BY NEUTRON ACTIVATION ANALYSIS
By Gerald Lawrence Schroeder
Submitted to the Department of Geology and
Geophysics on December
,
1960 in partial fulfillment
of the requirements for the degree of Master of Science.
A procedure for the neutron activation analysis
of sodium in silicate minerals is described.
Counting of
the 2.754 m.e.v. i'of Na24 with a NaI( TA ) crystal and an
integral discriminator provides a method in which the
precision is 2% and the interference by trace elements
less than 1%.
Na values obtained for the standard granite
G-1 are slightly lower than the mean of previous chemical
analyses, while values for the standard diabase W-1 are
slightly higher.
Thesis Supervisor:
Title:
John W. Winchester
Assistant Professor of Geology and Geophysics.
TABLE OF CONTENTS
Page No.
I. Introduction
5
II. Procedure for Analysis
9
III. Analytical Results
14
IV. Discussion of Errors
23
V.
Conclusions
33
VI. Acknowledgements
34
VII. Appendix
A.
Description of Apparatus
35
B.
Irradiation Fa cilities
36
0.
Statistics for Counting
37
D.
Interaction of Gammas With Matter
40
E.
Scintillation Counters
43
F.
Chi Squared Test
45
G.
Analytical Dat a for Sodium Standards
46
H.
References
47
TABLE Of FIGURES AND TABLE6
Page No.
Table 1
Counting Data for Run #1
15
Table 2
Counting Data for Run #2
16
Table 3
Counting Data for Run #3
17
Table 4
Counting Data for Run #4
20
Table 5
Summary of Sodium Analyses of G-1
and W-1
22
Prominent Elements and Their
Activities
24
Table 7
Theoretical Radioisotope Interference
26
Figure 1
Ratio of G-1 and W-l Gamma Spectra
to Na 2 003 Gamma 3pectrum
28
Figure 2
Winohester's Correction Curve for
Dif ferential Analyiseir
Figure 3
Ratio of G-1 and W-1 Decay Curves
to Na2 003 Decay Curve
Table 6
32
I
INTRODUCTION
The analysis for Na in silicate minerals presents
a problem to the investigator.
The chemistry of dissolving
the original mineral and ultimately separating it into its
constituent compounds is complicated (1).
Each step intro-
duces a new possibility of contamination, or loss during
precipitation.
In the conventional procedure of rock
analysis, the total alkalies are removed in a group filtrate
and Na and K are precipitated from this filtrate as chlorides.
The K is then determined and the Na value calculated from
the difference.
The value determined for sodium, as Na2 0,
will be in error if either the total alkalies value, or
the K2 0 value is invalid (2).
An independent method of
analysis i highly desirable.
A study of the precision of chemical analysis
of silicate rocks by Fairbairn (3) has revealed the poor
reproducibility achieved by conventional techniques.
In
the analysis of a standard granite, G-l, and of a standard
diabase, W-1, by 35 laboratories, the standard deviation
for sodium was 5.2% of the determined value in G--l and
9.3%in W-.
Chayes (4) stated well the seriousness of
this lack of reproducibility:
"Normative variation is so
6.
extreme that in the absence of direct evidence to that
effect there would be little
reason to suppose all these
abalyses were of the same two rocks."
Although the potas-
slum determination depends primarily on the complete extraotion of the alkalies, and is essentially independent of
other constituents, the standard deviation of determined
potassium in the G-1 analyses was 6.8% and in W-l 23%1
In
viewing this considerable range, one must remember the
dependence which the sodium value has on the determined
potassium.
winchester (5) successfully employed neutron
activation analysis as a highly precise method of determining the potassium composition of silicate and other minerals.
The analysis required no chemical treatment before irradiation.
In adopting this tool as a means of determining sddium
composition of silicate minerals, some difficulty was
encountered in adopting the correct electrical circuit to
handle the high flux of low energy Y 's, The final experiment, however, yielded encouraging results.
For neutron activation analysis to be useful for
the analysis of a particular element in a mineral, the
element under investigation must possess a radionuolide
producible by irradiation with thermal neutrons, which has
a form of activity unique among all other radionuclides
produced during the irradiation.
The primary constituents of W-1 and G-1 are 31,
Al, Te, Mg, Ca, Na, K, and 0 (6),
A study of the GE chart
of the nuclides (7) shows that a short irradiation period
(several minutes or less) followed by a "coOling off"
period of 30 hours will leave activity which is essentially
all 15 hour Na2 4 and 12.5 hour K42,
1,394 m.e.v.
P
,
Na24 decays by emitting
1.368 me,v. C' and 2,754 me,v,( for
100% of the decays (8).
K4 2 decays by emitting 3.55 mPe.v,
in 82% of the decays, and 1.99 m.e.v.
and 1.53 m.ev.
Y in 18% of the decays (8).
Using the proper electronic circuitry, it is
possible to count only gammas with energies greater than
2.75 m.e.v.
Na2 4.
This ensures recording solely the activity of
The apparatus employed consists of a thallitm
activated, Nal scintillation crystal monitored by a photomultiplier tube.
The output of the tube is amplified and
then sent through an electronic integral discriminator which
is biased so as to pass only those pulses corresponding to
Y 's with energies of 2.75 me.v. or higher.
From .the dis-
criminator the signal is fed to a scaler on which the decay
rate is recorded.
The experimental procedure is as follows:
10 mg
Na 2003 standards, and 50 mg., mineral samples (both finely
ground) are weighed and heat sealed in polyethylene packets.
8.
Standards and samples in their individual packets are irradiated as a unit for 10 seconds in the nuclear reactor
and "cooled" for 30 hours.
The activity of each is then
measured with the NaI crystal and the counting rate per
unit weight of standard is compared with that of the
mineral.
The per cent Na is computed. At the high bias
of the discriminator the background activity is low.
II
PROCEDURE FOR ANALYSIS
1) Grind the mineral sample and the
Na2 o3
standard (note 1) to a fine powder in an agate mortar.
Dry at 1100 0 (note 2).
2) Weigh 10 mg. portions of standard and 50 mg.
portions of sample.
Place each portion on a cleaned 0.001"
polyethylene sheet (note 3) and heat seal a second polyethyl-w
ene sheet over the sample (note 4).
Prepare several blank
polyethylene packets (note 5).
3) Number each packet (note 6).
4) Place samples and standards alternately in a
sealed polyethylene container (note 7). Irradiate as a
unit at a thermal nuetron flux (Mi)
5 x 10
n/cm - sec
for 10 seconds.
5) Allow specimens to cool for 30 hours (dote 8).
6) Mount the packets on aluminum planchets
(note 9).
7) Measure the 2.75 m.e.v. 2 activity (notes 10
and 11).
10.
8)
Compute the per cent Na in the sample (note
12).
1) Runs number 1, 2, and 4 utilized Na2 003 as a standard.
Because there was the possibility that the Na2 003
was ad-
sorbing significant water vapor, NaF was used as the standard for Run #3.
2)
Drying temperature should be no higher than 1100 0; at
elevated temperatures Na 200
of 002.
decomposes with the evolution
This will upset the stoichiometry of the compound.
3) The polyethylene sheet may be cleaned by wiping with
a dry cotton cloth to remove any solids which are contaminating the surface.
4)
To carry out the sealing operation place the specimen
in the center of a polyethylene square.
Lay a second square
over the sample and transfer the unit to the horizontal
face of a heat sealing iron.
With a bottle cap of 3/8"
diameter press the top sheet firmly down onto the undersheet so as to enclose the specimen.
Hold for several
11.
seconds and then remove the newly fomed plastic packet
from the iron.
Check the seal carefully for leaks.
It
is difficult to effect a satisfactory seal if the spoolmen powder has previously been scattered on to the part
of the plastic which is to be sealed.
The operator should
wear gloves and handle the packet with tongs in order to
avoid contamination.
The sodium content of the body is
high.
5) A blank packet consists of two clean polyethylene
sheets of a site similar to those used on the actual
specimens heat sealed together.
6) A convenient method for identifying the packets is
to write the packet number on a piece of paper and then
tape this paper to the edge of one of the polyethylene
sheets.
Before counting remove the tape and paper since
the tape, and ink, may have become radioactive during the
irradiation.
7) By placing the samples and standards alternately one
is ensured that both are subjected to the same neutron
flux.
8) This period allows the short-lived radionuclides to
12.
to dooay to very low levels of activity, while the 15 hour
Na
passes through only two half-lives and has 25% of its
activity remaining.
9) After cutting off the tape and number tag, attach the
packet to the flat side of a planchet using fresh tape,
Taping, and handling, the packet after irradiation does
not contaminate the specimen since neither the tape, nor
one*s body, contains any appreciable radioactivity.
Record the sample number on the reverse side of the planchet.
10)
The thallium activated Nal crystal used as the scin-
tillating material provides a high light pulse per unit
energy of impinging particle, and has a low (2 x 10"
seconds) resolving time (9).
11)
It is possible to count the specimens manually or
automatically.
To count manually, each specimen is
individually placed on a rack at a fixed distance from
the Nal crystal.
The radiation is counted for a suffi-
ciently long time so that the statistical variation of
the count is less than 2%.
To count automatically, the
samples and standards are placed alternately in the magasine of a Baird-Atomic automatic sample changer which feeds
13.
and removes the specimens after a predetermined number of
counts is reached.
The time taken to reach this number is
printed on a tape next to the specimen number.
In both
manual and automatic counting, the activity of background
and blank polyethylene packets is measured and this activity is subtracted from the gross number of counts to give
the net Y activity.
12)
After determining the net counts per mg. for the
sample and standard, and knowing that Na20
Na, it
3
is 43*4%
is possible to compute the per cent Na in the
sample by the following:
net countts/m; sample
x 43.4%
net counts/mg standard
14.
III
ANALYTICAL RESULTS
Four separate groups of analyses were made during
the course of this investigation.
Runs 1 through 3 were
carried out using a differential discriminator as the
means of counting only 2.75 m.e.v.
''s.
This apparatus
allows the selection of a maximum and minimum
height.
All
2' is with energies which lie within these
limits will be counted.
ator was used.
' pulse
For run #4 an integral discrimin-
With this, a minimum base line setting
is chosen and all
'a with energies greater than this
base line are counted.
Tables 1-3 give a summary of the data obtained
for the first three runs.
Specimens for run #1 were ir-
radiated by thermal neutrons for one minute
(neutron
flux 5 x 1012 n/om2 .seo.) and were "oooled" for 24 hours
before counting, while specimens for runs #2 and 3 were
irradiated for 6 minutes and had cooling periods of 35 and
32 hours, respectively.
In column 4 of tables 1-3 is tabulated the
corrected net counting rate of all observed Z( 's having
energies between 2.675 m.e.v. and 2.925 m.e.v., the mini-
Coumtlne Data for Run #1
.s
Na 2 003'
"
"
Avnrage
4
G-l
SA Wt.
Corrected
Net
/O
Corrected
Not e/j-eg
12.9
11.0
11.1
265
244
259
20.6
22.2
23.4
22.1 ±
106.4
103.1
105.2
142
138
140
1*33
Average
Trace element correction
Net
W.1l
101.6
*
103.2
*
108.0
Average
Trace element oorrection
Not
88
90.5
88.5
TABLE I
1.34
1.33
0.866
0.876
04819
i
2,62
2.63
2.62
2.62
.02
2,60
1.45
1.46
1.37
1.43
0.01
1.42
Na
±.01
±.01
± *03
±.03
16.
Counting Data for Run #2
wt.
Correoted Correoted
1//s1 n1 I/I
n
U Ag.
1
2
3
4
Na CO
ft
"
10.07
8.90
10.32
10.51
1060
918
1150
1170
105 .2
103.2
111.3
111.2
107.8 ± 2.6
Aere*
G~*l
"
*
"t
29.23
30.71
31.03
29.50
29.59
172
193
182
180
184
5.88
6.28
5.87
6.11
6*22
2 * 37
2.51
2.,51
2.45 ± .03
Avrage
.02
Tr, E1. Cor,
2.43 ± .03
Net
10
11
12
13
2.37
2.53
w-1'
"
*'
"t
29.85
29.81
29.52
30.03
117
122
123
128
4.26
4.08
4.17
4.26
1.72
1.65
1.68
1.72
,1.69 ± .02
Average
.01
Tr. E1. Cor.
1.68 ± .02
Net
TABLE 2
17.
Counting Data for Run #3
lyge
1
2
NaF
Sa Wt
10.70
10.15
10-10
11.40
3
4
Corrected
2270
2160
2150
2530
Corrected
212
213
213
222
215 ± 2.3
Average
G-l
244
7.78
1.98
7*66
1095
31.17
236
231
7.40
1.88
29.82
222
7.42
1.88
31.31
30.70
1.92 ±.02
Average
'02
Tr. El. Cor.
1*90 ± '02
Net
10
_LaI
W-a1
138
146
149
31.15
11
31.42
12
32.16
13
31.64
143
4.41
4.62
4.61
4.50
1.12
1.17
1017
1014
1.15 ± .01
Average
.01
Tr. El. Cor.
1.14 ± *01
Net
TABLE 3
18.
mum and maximum pulse height settings of the differential
discriminator.
The correction refers to the failure of the
differential analyser to show a linear response in the
observed counting rates when linear changes in the activity
level of the specimen were made.
A chart comparing the
actual disintegration rate with the observed oounting rate
was made by Winchester (see fig. 2, Discussion of Errors).
From this figure it is seen that for all activities yielding an observed counting rate of greater than 40 c/s some
correction in the observed counts must be made; the
higher the level of observed activity, the greater the
correction.
Because the level of activity of the Na
standard was consistently higher than either the G-1
or W-1 samples, the correction required for it was greater,
The chart apparently did not compensate for the entire
error, since even with the use of it,
the values of per
cent Na in G-1 and W-1 determined in the first three
runs are consistent neither among themselves nor with
the literature values.
To obtain the not counting rate, the activity
of the blank polyethylene packets was measured and subtracted from the gross counting rate of the specimens.
In all cases this correction was less than 0.5% of the
lowest sample counting rate for the particular run.
The
19.
statistical counting errors were never greater than 1%.
The errors indicated for the average activity of the standards and for the average per cent Na are the standard
deviations of the mean.
Trace element correction was determined by
theoretically predicting the activity induced in elements
present in G-1 and W-l which have
radiations similar
to Na and comparing this activity level to the measured
counting rate of the Na (see Discussion of Errors).
The
correction is well under 1% of the determined Na value.
Table 4 summarises the data obtained from
Run #4. Counting was carried out using an integral discriminator, and all Y's with energies greater than 2.70
m.e.v. were counted.
Preliminary trials on this apparatus
indicated that a considerably higher counting rate than
the permissible 40 c/s of the differential discriminator
could be handled without introducing a dead time error.
The irradiation time of the specimens was reduced to 10
seconds.
The fifth column lists the decay corrected, not
c/M - mg.
This decay correction was necessary because the
use of the automatic sample changer in this run increased
the time taken to complete one counting cycle of the samples
20.
Counting Data for Run #4
SA No. Type
1
Na2 003
Decay
corrected
Sa Wt Net O/M Net O/M-mg not
(. t).
/M-mMal
140.8
146.3
1392
9.53
11.25
9.31
1486
1226
132.0
131.7
135.2
139,2
138*8 ± 1*8
Average
44.97
49.70
52.21
50.31
366
392
396
347
8.14
7.86
7.58
6.89
7.86
7.86
7.76
7.31
2.46
2.46
2943
2.29
2.41 ± .04
Average
.02
Tr. El. Gor.
2.39 ± .04%
Net
9
10
11
% Na
W-1
12
47.74
49.94
48.97
50.37
268
254
239
231
5.59
5.43
4.88
4.59
5.04
5.12
5*12
4.90
1.71
1*61
1.58
1*54
1.61 ± .04
Average
-01
Trace E. Cor.
1*60 ± .04%
Net
Two additional runs of the above eyele yielded the following
resultst
2.38 ± .04%
Net % Na in G--A
1.60 ± .03%
2.41 ± .o4%
Net % Na In GAr
in w-1
1.62 ± .03%
TABLE 4
21.
and standards.
In decay correcting, the sero time point
was chosen at a time approximating the half-way mark of
the cycle.
possible.
This kept the average correction as low as
The results of three cycles run over a period
of two days are listed.
All of the determined per cent
Na values lie within the standard deviation of the mean
of the most extreme value.
Table 5 is a summary of Na analyses including
literature values for the per cent Na in G-l and W-1 as
well as the results of Run #4. New chemical analyses of
the G-1 indicate a decrease in the Na found as compared
with past work, while in W--l the new chemical analyses
indicate an increase in the observed Na composition.
The results of the determinations by neutron activation
analysis follow this trend of increasing Na in W-* and
decreasing Na in G-1.
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IV
DISCUSSION OF ERRORS
For the Na analysis of a mineral to be adaptable
to neutron activation analysis there must be no appreciable
amount of elements present in the mineral under investigation which will contribute conflicting radiations.
One
must be certain that the 3"s counted are those which
originate from the decay of Na 24
The first section of table 6 lists the prominent
constituents of G-1 and W-1 and their radionuclides produced during irradiation by thermal neutrons.
The
second half of the table lists other elements which, upon
irradiation, give rise to radionuclides which have similar
decay characteristics to Na
.
The second column lists
the radionuclide and its half-life; the third column,
the energy, or energy range of the
's given off; and
the fourth column, the activity in disintegrations per
second obtained when 1 gm of the pure parent element is
irradiated for 10 see. under a thermal neutron flux of
1013 n/cm 2see. and then allowed to oool for 30 hours.
the prominent elements
Of
present in G-1 and W-l it is seen
that only Mn has a ('sufficiently energetic to interfere
with the Na determination.
Of the other elements listed,
24.
Parent
element
Na
Prominent elements and their aetivities
Prominent elements of 0- and W-I
Aet Lvity of 1 gm
s ir
of arent after
15h
(Mov) (7), (8)
3a24
2.75
1.26
1,78
si
2 .62h
31
Al
2.30s
A128
Fe
4.58
0.19-1.29
Ms
L
9.53
4.78
0.18-1.02
a
K
TI
P
Mn
a 10 0e
td S30 hr
te
Radionuelide
12.5h
5.800
Ca47
t42
Ti51
p32
14.58
2.58h Mn56
0.5-1.30
0.32-1.5
0.32-0.93
no
0.85-3
(50 with Er 2.65)
4.46 x 106
1.95 x 102
5.60 x 102
-a
2.06 x 101
3.36 x 105
a-
2.05
3.48
105
105
other element
Ni
Cu
Zn
Ga
2. 56h
12. 8h
3, Oh
lb
N165
CU64
0.37-1.5
1.34
Znrl
0.4-0,6
Ga7 2
o.6-3.35
4.63 S102
106
8.76
3.26 2 101
4.11 x 106
(83% with Ey 2.508)
sn
26.Th
104
As7 6
s1125
La
40.2h
La140
Ir
19h
Ge
0.55-2.1
0.33-2.0
0.11-2.*9
(48% with F r 2.6)
0.29-2.0
TABLE 6
1.14
9.18
1*10
10T
101
107
7.86 x 107
25.
Ga, La, Mn, and possibly Ge may interfere.
For equal weights
of parent element, La will yield approximately 2,5 times
the activity of Na after 30 hours of decay.
Ahrens and
Fleischer (10) have compiled the known trace element composition of W-1l and G-1.
In table 7, the second and fourth
columns, this data is listed for Ga, Ge, La, and Mn.
The
third and fifth columns list the apparent per cent Na
which these elements will account for when counting the
2.75 m.e.v. Na24
.'
This apparent per cent Na is arrived
at by determining what fraction of the counting rate which
is observed as Na24 decay is, in reality, originating
from these four elements.
The correction is found to be
small in both G-1 and W-1.
The foregoing gives a theoretical verification of
the adaptability of the determination of Na in Gel and W-1
by neutron activation analysis.
is the comparison of the
2
A delicate practical test
spectra of G-1, and W-1, with
the
Z spectrum of pure Na as obtained from a Na 00
2 3
standard. A rigorous check on the similarity of the
spectra is to take point-by-point ratios of the counting
rates over a wide range of energy levels and to plot these
ratios as a function of the energy level.
should be a horizontal straight line.
a plot.
The result
Figure 1 is such
The upper line is the ratio of G-1 to Na2 003 and
AL flU VI
1"M,*Puv T-0 tfl ,e*ouazJ#wvz
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T
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(Oc) (Kati)
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27.
the lower is W-1 to Na2003 . The specimens used to obtain
the data for this figure were prepared in the same manner
as ones which were later used in the experiments.
Thus a
test of possible contaminants in the polyethylene container,
as well as the samples, is made.
While there is consider-.
able scatter there! roes not appear to be any trend other
than horizontal.
An upward slope, if it did occur, would
occur most likely at the low energy range, since it is in
this region that most of the residual contaminating activity would be.
This activity would augment the Na activ-
ity of the specimen andi inorease the value of the ratio.
In light of this apparent lack of conflicting
activity, and the very low background and polyethylene
packet activity, there was some question as to the cause
of the erratic data obtained in the first three runs.
Plotting the decay curves of the samples over several
days revealed half-lives of the standards in the order of
20 hours, half-lives of the G-1 samples in the order of
16 hours, and half-lives of the W- samples close to the
normal 15 hours.
From tables 1-3, column four, it is seen
that this increasing of the half-life, from W-1 to the
standard follows the same trend of the increasing level of
activity from W-1 to the standard.
This gives the possible
implication that the erratic data may be connected with
i 11.i,.-I :
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.
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electronic counting equipment and not with the feasibility
of the experiment.
Because the observed counting rate is
relatively low as compared with the theoretical capacity
of the apparatus, the difficulty may lie with the high
flux of not recorded low energy gammas and thbir effect
on the dead time of the apparatus.
The higher the level
of observed activity the proportionately higher the level
of low energy activity and hence the greater the effect on
observei counting rate, and measured half-life,
Figure
2, prepared by Winchester, is the counting correction
chart for the first 3 runs,
It was obtained as follows:
A group of Na standards with a wide range of activity
levels known by theoretical predictions was prepared.
The
activity of these standards was counted using the differen-*
tial discriminator (which was employed during the first
3 runs) as the pulse height analyser and the observed
counting rate versus the relative disintegration rates
of the standards was plotted on logarithmic paper.
The
line should be a straight line following a 450 angle;
that is, increasing the relative disintegration rate
(or specimen strength) by a factor of ten should also
increase the observed counting rate by a factor of ten.
Up to 40 c/s the observed counting rate followed the 450
line; however, above this the variation continually became
more pronounced until at an observed counting rate of 1400
Q'
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c/s one is actually counting 65% below the theoretical
counting rate.
A similar test was performed using the integral
pulse height analyser which was used for Run #4.
The
observed counting rate was found to follow the 450 line to
above 100 c/s.
This was satisfactory for the experiment,
and as a safety factor, the irradiation time was reduced
to 10 see. so that the maximum counting rate was below
60 c/s at all times.
Above 100 c/s the trend of the meas-
ured counting rate was to be greater than the 450 theoreti-u
cal Ine.
This may result from coincidence adding of sev-
eral low energy 2'(t to appear as a single high energy
As a sensitive check on the reproducibility of
the counting data obtained in Run #4 the decay of the
specimens was measured over a 3-1/2 day period and the
ratios of the G-1 and W-1 counting rates to the Na2 0 3
counting rate was plotted (fig. 3) While there is considerable scatter, all the points for G-1.,
and most for W-1.,
lie within their statistical counting error of the lines
drawn.
The horizontal lines found for G-1 and W-1 indi-
cate that there is no trend for either of the samples to
have half-lives other than 15 hours, and therefore the
observed counting is assumed to be correct, and resulting all from the 15 hour Na
.
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33.
V
CONCLUSIONS
Barring difficulties encountered in the eleotrioal phase of the counting, determining the Na composition of G-1 and W-1 by neutron activation analysis appears
practical.
The calculated trace element interference in
both Gel and W-1 is less than the standard deviation of
the mean.
The purity of the Na24
Y'is verified by the
15 hour half-life measure4 in the decay of the minerals.
Care must be taken to keep the observed level of activity
low enough so that the low energy ?"s do not cause dead
time complications with the counting apparatus.
In any
ease, the characteristics of the counting apparatus
should be studied before attempting an experiment.
It is possible to determine theoretically'
whether the minerals are adaptable to this form of analysis, provided previous chemical analyses are available.
Using the data of table 6, an estimation of the interference other elements present in a mineral can be made.
The method of heat-sealing the specimens in
polyethylene provides an efficient and contaminationfree means of handling.
)4.
VI
ACKNOWLEDGEMENTS
The author wishes to thank Professor John W.
Winchester for his invaluable advice and cooperation.
Mr. James Grooket's instruction in the operation of the
counting equipment used is sincerely appreciated.
350.
VII
APPENDIX
A.
Description of Apparatus
Primary deteetion of the radiation was effected
by a 2" x 2" cylindrical, thallium activated Nal crystal.
At a height of 2 cm. above the face of the crystal a
fixed aluminum rack was located.
This held the specimens
during their counting and ensured identical counting
geometry in all instances.
The NaI(7~/ ) crystal was
monitored by a 10 stage photomultiplier tube which relayed
the scintillation information to a Baird-Atomic amplixier
and pulse height analyser, and ultimately to a scaler.
Daring the first three runs of the experiment a differ%
ential analyser was used.
analyser was chosen.
For the last run an integral
Coupled to the integral pulse
height analyser and its scaler was an automatic sample
changer. This enabled the investigator to preselect
the total number of counts desired for each sample and
to
have a register print out next to the sample number,
the time taken for the scaler to record this number of
counts.
Weighing of the specimens was performed on a
36.
Mettler balance, with a maximum sensitivity of 0,001 mgs.
For fine determinations in weighing an excess of specimen
should be 'placed on the balance pan and weighed.
From
this the desired amount of specimen is removed and a
second reading Is taken.
The weight of the specimen
taken is simply the difference of the two readings.
B. Irradiation Facilities
All irradiations were carried out in the M.I.T.
Reactor.
Sealed samples are placed in a cylindrical
"rabbit" 2.5 cm, in diameter and 7 om. long.
This rabbit
is taken into and removed from the pile by a pneumatic
tube.
As a test for uniformity of the neutron flux over
the length of the rabbit,acourately weighed Na standards
were placed at intervals along the rabbit and the rabbit
was fed into the pile and irradiated. The absolute
activity of each sample was then determined and found to
be the same within statistical limits.
Thus it is assumed
that the neutron flux is the same over the entire rabbit.
It is good practice, even so, to alternate samples and
standards when packing the rabbit with several small
37.
specimens.
Thermal neutron flux (n 9) equals
5 x 101 2 n/Om2 -seo.
C. Statistics of Counting*
Starting with the binomial disttAbution law
and applying the general characteristics found in most
counting circumstances it is possible to arrive at a
convenient equation describing the probability of obtaining a particular number of counts in a given time.
The binomial distribution law is
W(r)
=
r(1 p n-r
.L..!.M...Mfi
(n-r)Irt
where, in a very large set of objects,
(1)
P is the proba-
bility of the occurance of a particular object W. n
objects are removed.
y(r) is the probability that r
of the objects are of the kind W.
To find the probability, W(m), that m disintegrations will occur in time t from N0 original active
*1
Friedlander & Kennedy, Nuclear A
John Wiley & Sons, Inc., N. Y.,
Rao,
.
p.
3.
38.
nuolides, let No equal n, and m equal r.
After time t,
the number of atoms left N from the original N, in just
N
.
*
*4
Thus the probability of an atom surviving t
seconds is N
r
- e
P
.
e
NO
This equals I- P .
Therefore
)It.
Substituting in the original equation yields
W(m)c
N!
A t)I,-?tNM
.
(NO-M) IMI
(2)
Now if the number of active atoms is large, the observation time t short compared with half life, then A t 4.
N07P 1 and me4< N .
Approximating as follows:
1 + 'At
e k
XI =
1,
Xx e"X
/2-f 7F
(1 0)No
N
0
.
N
N -+*0(l-e)
0
e
0
NO
and applying this to equation (2) we have
m -M
W(m) =
I IeW
where M is the average to
ml
be expected. This is Poisson's Law. It is aocurate for
N0 as low as 100 and At as large as .01.
Studying this equation shows that
W(M)
s
W(N-l).
For large numbers of ooints (M) the dis-
tribution is nearly symmetrical about M.
From this the
39.
fact that 6 = /'
may be obtained.
That is, the standard
deviation in counting is just equal to the square root of
the total number of counts.
It is extremely useful to be able to carry out
simple arithmetic functions on numbers containing standard
deviations.
The sum of two Poisson distributions is also
a Poisson distribution.
The variance 6
summing the individual variances.
Thus
Is
i2 found by
s ~- '
a
The difference of two Poisson distributions, however, is
not a Poisson distribution.
The variance 6d 2 is found
by summing the individual variances.
Again
4
67
6%-
To find the standard deviation of the quotient of two
counting rates,
,
Q
(
t
+
where Q is the
qU-
tient.
The standard deviation of a product is found
in a similar mannerrf
+
40.
D.
Interaction of (ammas Yith matter
Unlike
0< and ( rays, the
and zero rest mass.
le has zero charge
Its velocity in a given medium is
constant and equal to velocity of light (3.0 x 1010 a
in vacuum) in that medins.
Since it adheres to the wave-
particle theories concerning matter, the energy of the
ray is determined by its frequency.
The range of a
beam of 15 is truly infinite and falls off exponentially
acoording to the equation
I WI,
where
e-A
I a intensity of the beam
Ia original intensity
X distance traversed
p = absorption coefficient
=
6 abs - n atoms/oo.
Thus a plot of the log c/s versus gm/cm2 of absorber will
yield a straight line with a negative slope proportional
tot.
The ' interacts with matter in the three follow-
of
ing ways, considered here in the orderjinreasing energy
requirements,
In Compton scattering the 4 transfers a
small fraction of its energy to an atomic electron in
a nearly elastic collision.
the /
The electron flies off and
changes direction accordingly, to conserve momentum.
41.
If the direction and velocity of one of the participating
particles is known, the direction and velocity of the
other may be calculated by classical methods.
transfers
In the photoelectric effect the
all of its energy to a single atomic electron which is
ejected with a kinetic energy equal to the energy of incoming Y minus the ionization potential of the electron.
After this photoelectric emission of the electron, characteristio X-rays are given off as the energy levels which
the electron has vacated are refilled.
The reaction orosse
section for the photoelectric effect is proportional to
Z4 and inversely proportional to (KE e)
.
For a true understanding of pair production, one
must first have a knowledge of the theory of what positrons are.
In the normal state of nature, eleotrons at
rest have an energy of M0C2 relative to a state of zero
energy.
When given motion the energy of the electron
increases by the value of the kinetic energy.
Electrons
may also have a negative rest energy equal to -M002 and
negative kinetic energies.
levels are all filled.
Normally these
negative
To create an electron pair one
must impart sufficient energy to an electron in the neg-
42.
ative state to move it into the positive state.
The
minimum energy requirement would be to move a stationary
electron in the negative state (at -X0
2
) to a stationary
position in the positive state (at +M 0 2).
total of 2 !02 is needed.
Thus a
This is equal to 1.02 Rev for
an N0of an electron. what one sees as a positron is merely
a space or a hole in the otherwise completely filled negaThe destruction of a oositron is always accom-
tive state.
panied by the
destruction of an electron.
This is
because what actually actually happens is that the electron
falls back into the space in the negative state.
Thus the
electron i gone, and so is the space.
In pair production, a i, having an energy
equal to, or greater than 1.02 Xev strikes an electron
which is in the negative state, and moves it into the
nositive.
Thus a new electron is seen in the positive
state, and a positron (actually a hole in a negative
field, thus appearing as a positive charge) is found to
accompany it. The two quanta conserve the momentu4 of the
original
Y .
When
the positron encounters an electron,
the two disappear and a Y , which conserves the momentum
of the two disintegrated quanta, is formed.
43.
E.
3intillation Counters
The basic mechanism in the operation of the
scintillation counter is the internation of a quantum,
usually an alpha or a gamma, with a phosphor.
The resul t-
ing pulse of light is observed by a photomultiplier,
amplified and recorded.
By selecting a large enough
crystal, usually thallium-activated sodium iodide, gamma
counting efficiencies, which are very low in proportional counters, approach l005.
The pulse height of the
interaction Is found to be proportional to the energy
of the incident particle.
This enables the construction
of multi--ehannel counters which when coupled with continuous recorders are able to plot pulse height, and hence
incident particle energy, versus the number o
that
Particular pulse height.
pulaseas at
A sample placed in .the counts
ing chamber can have its entire spectrum of gammas analysed in a single operation.
The construction of the oounter may be accom--
44&
plished by placing a thin phosphor directly on the surface
of a photomultiplier tube, or, more generally, by coating
a transparent light pipe such as lucite with the phosphor
and have this lucite conduct the light to the photomultiplier.
Recent developments have brought forth fluorescent
plastics which combine the action of the phosphor and the
lightoonductor.
In coating a lightoonductor one must
arrive at an optimum thickness for the phosphor which
will maximize the interaction with the incident quanta
and minimize the self-absorption of the light pulse produced.
Since the fluorescent material must be
shielded from all external light certain difficulties
arise if the sample is located outside of the counter
housing.
A thin aluminum cover may be placed over the
phosphor; however, if alphas are to be counted their short
range dictztes that this cover be of absolute minimun
thickness.
Ideally an alpha source should be placed
directly in the housing.
This is most convenient when
dealing with gases.
A marked advantage of the scintillation counter
is its extremely low dead, or resolving, time.
The
thallium-activated sodium iodide crystal has a resolving
time in the order of 2 x 107 second, thus enabling the
45.
metering of an extremely high alpha or garma flux.
F. Chi Squared Test
It is often useful to be able to perform a rapid
test on a counter and scaler to determine whether or not
the unit is functioning properly.
The chi squared test
If a oounter is register-
performs just such a service.
ing incorrectly, the scattering of the data obtained will
follow a pattern such that when the probability of the
next set of data falling within the standard deviation
of the previous data is calculated the probability will
either be too high (>0.98) or too low (<0.02).
To
determine the probability take a set of data, find the
average value (i), and then
he
average valex
2
1
X)d
x
on page
Zba Aa ata
in Evans Malana
(11)
a chart relates X2 to the number of degrees of freedom
F which is equal to the number of sets of data taken minus
one. An example of the test allows using background
46.
noise as a source.
This is a convenient source to use,
since its rate is low and the low numbers allow for rapid
cal culations.
G.
Analytical Data for Sodium Standards
Na200
3
Produced by:
Grade:
J. T. Baker Chemical Co., N.J.
Reagent
Per cent Na2 0 3: 9908
HaF
Produced by:
Grade:
Merok Chemical Co., N. J.
Reagent
Per cent NaF:
99.4
47.
H.* References
1.
Stevens, Rollin E. et al, U.S. Geol. Surv. Bull.,
1113 (1960), 4Second Report on a Cooperative
Investigation of the Composition of Two Silicate
Rooks," p. 7.
2.
Stevens, R. E., ibid.
3.
Fairbairn, H. W., Geochim. et Cosmochim. Acts ',
143-156 (1953) "Precision and Accuracy of
Chemical Analysis of Silioate Rocks."
4.
Fairbairn H. W., et al, U.S. Geol. surv. Bull.,
980 (1951), "A Cooperative Investigation of
Precision and Accuracy in Chemical, Spectrochemical and Model Analysis of Silicate Rooks."
5.
Winchester, J. 1*., (manuscript submitted for publication in Anal. Chem.) "Determination of Potassium
in Silicate Minerals and Rocks by Neutron Activation Analysis."
6.
Stevens, R. E., op. cit., p. 31,
7.
G. E. Chart of the Nuclides, 5th ed., Knolls Atomic
Power Laboratory, April, 1956,
8.
Strominger, D.; Hollander J. M.; Seaborg, G.T.;
Rev. Mod. Phys. ;0 5 8 5 (1958), "Table of
Isotopes."
9.
Friedlander, G.; Kennedy, J.; Nuclear gd Ra
. .,1960.
Chemistry, John Wiley and Sons, Inc.,
32.
10. Stevens, R. E., op. cit., p. 91-93.
11. Evans, Robley D.,
N. Y., 1955.
g Atomig jagls,
McGraw-Hill,